Laser-induced
Laser -induceddamage
damageand
andthe
the role
role of
of self-focusing
self- focusing
M. J. Soileau, FELLOW
FELLOW SPIE
SPIE
M.
influence of
of selfself-focusing
Abstract. We review the influence
focusing on the measurement of bulk
bulk
Florida
University of Central Florida
in ElectroElectro-Optics
Center for Research in
Optics
and Lasers
Orlando, Florida
Orlando,
Florida 32816
32816
laser-induced-damage
optical matematelaserinduced -damage(LID)
(LID)thresholds
thresholdsinin normally
normally transparent optical
rials.
is experimentally
experimentally determined
determined by
by measuring
measuring the
the spot
spot size
size and
rials. This role is
and
polarization dependence of LID
LID and
and by
byobserving
observing beam
beam distortion
distortion in the far field.
field.
Utilizing these
geometry in
these techniques,
techniques, we
we find that by using a tight focusing geometry
in
which the breakdown
breakdown power
power is
is below
below P2, the effects
effects of
of selfself-focusing
focusing can be
practically eliminated
eliminated ininan
anLID
LID experiment.
experiment.P2
P2isisthe
thesoso-called
second critical
critical
called second
power for
for selfself-focusing,
and P2
P2 = 3.77P1,
3.77?^, where
P., = cÀ2
cX2 /327T2
n2 , where
where cc is
is
focusing, and
where P1
/3272n2,
the speed
speed of
A is the
and n2
n2 is the nonlinear
of light in vacuum, X
the laser wavelength
wavelength and
accordance with
numerical calculations
calculations by
by J.
J. H.
H.
index of refraction. This is in accordance
with numerical
Marburger [in Progress
Progress in Quantum
Quantum Electronics,
Electronics, J.
J. H.
H. Sanders
Sanders and
and S.
S. StenSteneds., Vol.
Vol. 4, Part
1, pp.
pp. 35-110,
Pergamon, Oxford
holm, eds.,
Part 1,
35 -110, Pergamon,
Oxford (1975)].
(1975)]. With
With this
knowledge we determine
determine that
that damage
damage is
is only
only partially
partiallyexplained
explainedby
by avalanche
avalanche
and that the initiation
initiation of
of damage
damage is
is strongly
strongly influenced
influencedby
by extrinsic
extrinsic
ionization and
processes.
LID.
processes.We
Wetherefore
therefore conclude
conclude that
that we
we are measuring extrinsic LID.
William E.
SPIE
William
E. Williams, MEMBER SPIE
Laser Systems
Litton Laser
2787 S.
S. Orange Blossom Trail
Apopka,
Apopka, Florida
Florida 32703
32703
Nastaran Mansour
Eric
MEMBER SPIE
SPIE
Eric W.
W. Van
Van Stryland,
Stryland, MEMBER
University of Central
Central Florida
Florida
Research in
in ElectroElectro-Optics
Center for Research
Optics
and Lasers
Orlando, Florida
Orlando,
Florida 32816
Subject terms:
terms: laserlaser-induced
modification;laserlaser-induced
damage; laserSubject
induced material
material modification;
induced damage;
induced
laser-induced
breakdown; avalanche
avalanche ionization;
breakdown; multiphoton
multiphoton absorption;
absorption;
breakdown;
ionization; dielectric breakdown;
self-focusing.
selffocusing.
Optical Engineering 28(10),
28(10), 1133
1133-1144
1989).
-1144 (October 1989).
CONTENTS
1. Introduction
1.
2.
Historical review
review
2. Historical
3.
3. Theory
3.1.
Self-focusing
3.1. Self
-focusing
3.2.
Polarization dependence
dependence of
ofselfself-focusing
3.2. Polarization
focusing
4. Experiment
Experiment
4.
4.1. Experimental verification
verification of Marburger's theory
4.2. Polarization
Polarization dependence
dependence
4.2.
5.
Conclusions from
fromthe
therole
roleofofselfself-focusing
inlaserlaser-induced
5. Conclusions
focusing in
induced
damage
5.1.
Re-evaluation
5.1. Reevaluation of extrinsic laserinduced damage data
laser-induced
5.2.
Wavelength, temporal, and spot
spot size
size dependence
dependence
5.2. Wavelength,
6.
Controlled defect studies
6. Controlled
7.
Conclusion
7. Conclusion
8.
Acknowledgments
8. Acknowledgments
9.
References
9. References
Paper LI
LI-112
Invited Paper
-112 received
received March
March 24, 1989;
revised manuscript received
1989; revised
1989; accepted
June 26,
May 5, 1989;
accepted for
for publication June
26, 1989.
1989.
©
© 1989
1989Society
Societyof
ofPhoto-Optical
Photo -OpticalInstrumentation
Instrumentation Engineers.
1. INTRODUCTION
INTRODUCTION
1.
In this paper we discuss bulk (as opposed
opposed to
to surface)
surface) laser
-inlaser-induced-damage
duced- damage (LID) in transparent
transparent optical
i.e.,i.e.,
opticalmaterials,
materials,
materials
the input
input laser
laser wavewavematerials whose
whose linear
linear absorption
absorption at the
length
is the order of
of l0
10~3
or less.1
less. 1 "-3
3 In
length is
-3 or
In anticipation
anticipation of our
conclusion
with few
few possible
possible exceptions, LID is
is influinfluconclusion that, with
enced by extrinsic processes, we refer to the damage
damage as extrinextrinsic
However,
sic laser-induced-damage
laser- induced -damage(ELID)
(ELID) in what follows. However,
it is
to realize
realize that
that how
how self
self-focusing
is important
important to
-focusing affects
affects damage
damage
threshold data
data is
is independent
independent of
of the
the damage
damage mechanism
mechanism (i.e.,
(i.e.,
intrinsic or extrinsic). By
By intrinsic we mean that the threshold
is
is not
not increased by reducing the defect or impurity density. We
investigate the
the role
role of
of selfself-focusing
focusing in LID
LID and how the experimental geometry can alter this role. Misunderstandings
Misunderstandings conconcerning self
self-focusing
-focusing effects
effects have
have led
led researchers
researchers to incorrect
conclusions concerning the observed parametric
parametric dependences
of ELID, which in turn affect conclusions of the importance
of extrinsic effects
of the role of
effects in
in LID.
LID. A clear understanding
understanding of
self-focusing
geomeself -focusingininLID
LID allows
allows us
us to design experimental
experimental geometries
which such
such effects
effects can
can be
be practically
practically eliminated.
eliminated.
tries in which
OPTICAL
/ October
1989
/ Vol.
1010
/ / 1133
OPTICALENGINEERING
ENGINEERING
/ October
1989
/ Vol.2828No.
No.
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SOILEAU,
MANSOUR, VAN
VAN STRYLAND
STRYLAND
SOILEAU, WILLIAMS, MANSOUR,
DAMAGE
IR
NO DAMAGE z
.x
Si02
1.06pm
ñX ==1.06ym
t p =40ps
tp=4Ops
x
2234
4
3
IRRADIANCE
IRRADIANCE (x1O12
(x1012 W/cm2
W /cm2))
Fig. 1.
Method of
of LID
LID threshold
threshold determination.
determination.Damage
Damage(X
(X on
on upper
Fig.
1. Method
line) or no
2.
line)
no damage
damage (X
(Xon
onlower
lower line)
line) for
for SiO
Si02.
Parametric
Parametric dependencies
dependenciesofof ELID
ELID thresholds
thresholds can
can then
then be
unambiguously
unambiguouslycompared
comparedwith
with predictions
predictions of
of theory.
theory. The
The
overwhelming
overwhelmingevidence
evidencefrom
fromsuch
suchstudies
studiespoints
points to
to the
the conconclusion
materials isis not
clusion that
that damage
damage in
in these
these transparent
transparent materials
not
completely explained by avalanche
ionizationtheory4,5
theory 4' 5 but
avalanche ionization
but is
is
heavily
heavily influenced
influenced by extrinsic effects. We give evidence supconclusion by
porting this
this conclusion
by presenting
presenting ELID
ELID data for doped
glasses and
SiO2 .
glasses
and gamma-irradiated
gamma- irradiated Si02.
ELID is
is aa threshold
threshold-like
phenomenon. The
The threshold
threshold
ELID
-like phenomenon.
1, which shows
behavior is
is illustrated
illustrated in Fig. 1,
shows aa set
set of ELID
data
on aa fused
fused silica
silica sample
sample using
using 40
40 ps,
data taken on
ps, linearly
linearly
1.06 /zm
size of
polarized, 1.06
µm pulses
pulses focused
focused to a Gaussian spot size
approximately 6.8
this paper
paper pulsewidths
pulsewidths
approximately
6.8 ^m.
µm. Throughout this
and spot
spot sizes
sizes are
are the
the HW
HW 1l/e2
M in
are quoted as FWHM, and
/e2M
irradiance. The
function of
of internal
internal
irradiance.
The data
data are
are plotted
plotted as
as a function
lower line if no damage occurred
irradiance with an X on the lower
and on the upper line if damage did occur. The threshold is
is
defined
the peak
peak-on-axis
fluence (J/
(J/cm2
), irradiance
irradiance
defined as the
-on -axis fluence
cm2),
(W/cm2),
(W /cm2),oror rms
rms electric
electric field
field (V/cm),
(V /cm), which
which results
results in
in an
irreversible change
irreversible
change in
in the
the specimen
specimen as
as determined
determined by one or
more of the following:
following: an
increase in scattering of
of aa HeNe
HeNe
more
an increase
probe
beam (either
(either by visual
visual observation
observation or
or photometric
photometric
probe beam
detection),
as seen
seen in
in aa microscope,
microscope,
detection), a change in morphology as
of the sample.
sample. In
or a permanent change in the transmittance
transmittance of
most
most cases
cases this
this type
type of
of damage
damage isis obvious
obvious and
and all
all of
of the
symptoms are
are observed.
observed. In
In addition,
addition, ELID in these materials
materials
symptoms
is
is usually
usually accompanied
accompanied by
by a visual flash associated with the
onset
dielectric breakdown (i.e.,
(i.e., avalanche
avalanche ionization).
ionization).
onset of dielectric
These
discussed in
These data
data as
as well
well as
as other
other data discussed
in this
this paper are
one-on-one
one -on -onemeasurements
measurements in
inwhich
which each
each site
site isisirradiated
irradiated only
once
once even
even ififthe
the site
site did
did not
not incur damage.
damage. It is observed
observed in
some
preirradiation with
with pulses
pulses below
below the
some materials
materials that
that preirradiation
damage threshold
threshold as
as defined
defined can
canalter
alter the
theELID
ELID threshold,
threshold, the
so-called
threshold
so- calledN-on-one
N -on -oneeffect.
effect.Note
Notethe
the very
very sharp
sharp threshold
shown
shown in
in Fig.
Fig. 1,
1, which
which isisindicative
indicative of
ofdamage
damage in
in transparent
transparent
thresholdshown
shownofofapproximately
approximately
dielectrics. The threshold
3.33.3XX10
101212
W/cm2
W/ cm2isisabout
abouttwo
twoorders
orders of
ofmagnitude
magnitude larger than could be
expected from the same
same sample
sample used
used as
as an
an optical
optical component
component
in a system.
This isis the
the case
case since
since the failure mode for large
in
system. This
large
illuminated areas used in practice is
is more likely
likely surface damage
age where
where other
other extrinsic
extrinsic effects
effects cause
cause damage.
damage. In the experiments
ments relevant
relevant to
to this
this paper, surface damage is avoided by
Reusing
'ocusing into
into the
the bulk
bulk of
of the
the material,
material, keeping
keeping the irradiance
itd the damage
damage-prone
-prone surfaces low.
threshold-like
The threshold
-like behavior
behavior illustrated
illustrated in Fig. 11 is
is indicative
extremely nonlinear process.
process. Considerable effort
tive of an extremely
has been spent
spent to
to monitor
monitor subthreshold
subthreshold changes in the optical
properties of these materials with
with little
little success.
success. A
A notable
notable
properties
exception is
is the
the recent
recent work
work of Braunlich
Bräunlich and coworkers at
State University.6
University. 6"-8
8 They
Washington State
They report
report the observation
multiphoton absorption
absorption of 532
532 nm
nm light
light inincarefully
carefully
of multiphoton
selected alkali halide samples of as
as high
high an
an order
order as
as four
four prior
prior
luminescence and
to damage using luminescence
and the
the photoacoustic tech-
nique.
We comment
comment on the
the possible
possible implications
implications of their
their
nique. We
results
Sec. 5.
5. No connection
connection between
between the linear optical
optical
results in
in Sec.
properties and the ELID thresholds has
has been
been found. ExperiExperiments have
have also
also shown that the transmittance
transmittanceof
ofaalaser
laser pulse
pulse
is
is cut
cut off within
within aa few
few picoseconds
picoseconds of
of the
the initiation of damage
damage
distortion prior
priortotodamage.9
damage. 9This
Thishighly
highly nonnonwith no pulse distortion
linear
linear behavior of ELID makes precise determination of the
damage mechanism(s)
mechanism(s) difficult.
fact, we must
must infer
infer the
the
damage
difficult. In
In fact,
mechanism(s)
mechanism(s) of failure
failure from parametric dependences
dependences (e.g.,
(e.g.,
pulsewidth and wavelength dependence). This has resulted in
slow
slow progress
progress in
in developing
developing aa complete
complete understanding
understanding of the
physical processes involved in ELID. On
On the
the other
other hand,
hand,as
as we
we
shall see
see later
later in
in this
this paper,
paper, the
the first
first qualitative
qualitative description
description of
of
ELID was
was essentially
essentially correct)
correct. °,)
10 ' 11)
2.
HISTORICAL REVIEW
2. HISTORICAL
The first
first reports
reports of
of bulk
bulk ELID
ELIDwere
were by
The
byBruma1°
Bruma 10 and
and
Hercher 11 ininpapers
papersatatthe
the1964
1964 spring
springmeeting
meeting of
of the
the Optical
Optical
Hercher"
Society of America.
America. The principal conclusions of these initial
reports are as follows:
follows: (1)
plays no major
(1) Linear absorption plays
role in this type of
of failure.
failure. (2)
(2) The
The damage
damage process
process isis highly
highly
nonlinear. (3) Electron avalanche
avalanche breakdown
breakdown may
may be initiated
by
defects and/or
by defects
and / or impurities.
impurities. (4)
(4) The
The ELID
ELID threshold and
morphology depend on
on spot
spot size.
size. While
While there
there has
has been
been some
some
controversy regarding the third statement, data
data now
now tends to
confirm
statements made
made 25
25 years
years ago.
ago. Excellent
Excellent
confirm all
all of the statements
sources
in many
many materials
materials are
are the
sources for data on ELID in
the proceedproceedings
Boulder Damage
Damage Conference
Conference starting
ings of the annual Boulder
starting in
in
1970 and the references
references therein.12
therein. 12
1970
One
One can
can divide
divide much
much of the
the past results in ELID experiexperiments into two distinct categories. Category
Category A
A consists
consists largely
of work conducted at
at Harvard
HarvardUniversity
UniversitybybyBloembergen
Bloembergen11
and his
his students
studentsYablonovitch,13
Yablonovitch, 13-15
" 15 Fradin,16
Fradin, 16 ~-20
20 and
and
Smith
2' 21 " 23
Smith2,21
-23and
andbybytheir
theircoworkers.
coworkers. The
The Category A experiments
ments represent a systematic investigation of the breakdown
thresholds
several alkali
halides and fused
fused quartz
thresholds of several
alkali halides
quartz over
over
wavelengths
10.6 jum
wavelengths ranging from 10.6
µm to 0.355 ;um
µm and for pulse
durations ranging
ranging from
from nanoseconds
nanoseconds to
totens
tensofofpicoseconds.
picoseconds.
The results were interpreted in
in terms
terms of
of an
an intrinsic
intrinsic model
model of
of
electron
breakdown. 2 The breakdown thresholds
thresholds
electron avalanche breakdown.2
were
sample to
to sample
sample for
for aa given
were found
found to vary little from sample
given
material
material even if the samples were supplied by different crystal
growers.
thresholds were
were found
found to agree
agree
growers. The
The breakdown
breakdown thresholds
within
wavelengths ranging
10.6 µm
within ±15%
±15% over wavelengths
ranging from
from 10.6
jum to
to
1.06 jum.
that this
this agreement
agreement in
in damage
1.06
µm. It isis important
important to note that
threshold
alkali halides
halides was
was obtained
obtained by
by comparing
comparing
threshold for the alkali
damage
different focusing
focusing conditions
damage thresholds
thresholds for
for different
conditions at
at the
the
different
pulse durations
different wavelengths
wavelengths over
over aa wide
wide range
range of pulse
durations
and focusing conditions. In addition,
the Category
Category A
A workers
addition, the
found that the frequency dependence of the
the breakdown
breakdown thresholds
of intrinsic
intrinsic avalanche
olds agreed
agreed with
with the theory of
avalanche ionization
ionization
over
full wavelength
wavelength range, although
although some
some evidence
evidence of
over the full
22
multiphoton ionization
ionization was
was observed
observed at
at 0.355
0.355 µm
/xm.22
In part,
part, the
the agreement
agreement of
of the
the results
results of
of the
the Category
Category A
A
workers with the predicted frequency dependence of
of intrinsic
electron avalanche breakdown arose from attempts to correct
correct
the data at 1.064
1.064 µm,
Mm, 0.694 µm,
jum, 0.532 µm,
µm for
jum, and 0.355 ^m
the presumed effects
effects of
of self
self-focusing.
-focusing. For
For example,
example, Smith
Smith
et aí.21,22
al. 21 ' 22 scaled
scaledthe
theresults
resultsof
of their
their picosecond
picosecond breakdown
work
assumption that PI
Pj (discussed
(discussed in
in the next
work under
under the assumption
section)
critical power
section) was
was the
the critical
power of importance
importance for
for focused
focused
Gaussian beams. They observed
observed aa slow
slow increase
increase in
in the scaled
scaled
1134 / /OPTICAL
OPTICALENGINEERING
ENGINEERING // October
Vol. 28
28 No.
No. 10
10
1134
October 1989
1989 // Vol.
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SELF-FOCUSING
OFSELF
ROLEOF
THEROLE
ANDTHE
LASER-INDUCED
LASER- INDUCED DAMAGE
DAMAGE AND
-FOCUSING
thresholds with increasing frequency, consistent with the prePj is not
now know PI
We now
theory. We
dictions of intrinsic avalanche
avalanche theory.
the critical power of importance
importance in those experiments and the
conthe coninvalidating the
scaled, thus invalidating
been scaled,
have been
should not have
data should
increasing
with increasing
decrease with
clusions.
clusions. The
The unsealed
unscaled thresholds decrease
avaintrinsic avathe intrinsic
of the
prediction of
frequency, opposite
frequency,
opposite to
to the
the prediction
lanche
lanche ionization theory.
Category BB workers were
of Category
results of
On the other hand, the results
Harvard
inconsistent with
often found
found to
to be inconsistent
with those
those of the Harvard
often
Olness,24* 25 Yasojima and
includeOlness,24,25
workersinclude
CategoryBB workers
group. Category
28 and
Bassand
and Barrett
Barrett28
and coworkers
coworkers at
Japan,26' 27 Bass
coworkers in Japan,26,27
Manenkov 29 and
California, Manenkov29
Southern California,
University of Southern
the
the University
Stryland, 32
Van Stryland,32
Soileau, 30' 31 Van
Union,Soileau,30,3'
Soviet Union,
coworkers in the Soviet
One of
of the
the main conclusions
conclusions to be drawn from
Sparks.4 One
and Sparks.4
laser-induced
induced breakdown
B experiments is that laserthe Category B
study
is
is caused
caused by
by extrinsic
extrinsic properties
properties of
of the
the material.
material. In a study
Manenkov 29 in
reported by Manenkov29
in 1977,
1977,the
thebreakdown
breakdown irradiance
irradiance at
NaCl samples varied from sample
100 NaC1
for 100
jum measured for
1.06
1.06 µm
in
to sample by aa factor
factor of 50.
50.The
The highest
highest thresholds
thresholds reported
reported in
reported
previously reported
than previously
higher than
were higher
Manenkov's
work were
Manenkov's work
(e.g., three times
times those
those reported in Ref.
Ref.
"intrinsic" thresholds (e.g.,
Soileau 30' 31 and
by Soileau3°,31
seen by
13). Similar
Similar results
results have
and in
been seen
have been
13).
no
Yasojima. 27 In
Olness 25 and
earlier studies by Olness25
and Yasojima.27
In addition, no
funcas aa functhresholds as
systematic
variation in the breakdown thresholds
systematic variation
results of
the results
observed in
was observed
bandgap was
material bandgap
tion of material
tion
in the
A
26' 27 inincontrast
Olness24,25
andYasojima
Yasojima26,27
contrasttoto the
the Category A
Olness 24' 25 and
measurements.
A decrease
decrease in
in the
the breakdown threshold with
measurements. A
al. 30' 31 in
Soileauetetal.3o,31
bySoileau
seenby
was seen
wavelength was
decreasing laser wavelength
10.6 /xm
halides over wavelengths
the alkali halides
wavelengths ranging
ranging from 10.6
µm to
Smith
of Smith
1.06
µm, as
as was
wasobserved
observed for
for the
the unsealed
unscaled thresholds of
1.06 /zm,
et aí.21,22
Again,this
thisisisopposite
oppositetoto the
the trend
trend predicted by
al. 21 ' 22 Again,
in Cateresults in
Finally, results
intrinsic avalanche ionization theory. Finally,
size
spot size
gory B
B experiments indicate the presence of a strong spot
dependence for the
the breakdown field in the alkali halides
halides and
be
could not be
materials that
fused
quartz as
as well
well as
as other
other materials
that could
fused quartz
self-focusing
explained by selffocusingand
and isis inconsistent
inconsistent with intrinsic
damage
measured damage
Also, the measured
avalanche
breakdown theory.
theory. Also,
avalanche breakdown
materials
in materials
even in
sample even
to sample
thresholds differed from sample to
from the same manufacturer.
Much of the
the controversy
controversy found
found in the literature is due to
Much
account
differences in
the differences
in the ways
ways in
in which
which various authors account
the
in the
Early in
self-focusing.
for,self
accountfor,
attempt totoaccount
or attempt
for, or
-focusing. Early
self-focusing
ELID, selfof ELID,
focusing was recognized as
history of studies of
irreversible
catastrophic, irreversible
to catastrophic,
contributors to
major contributors
one
one of the major
properties. 12 Over the years many studies,
changes in material
material properties.12
in
conducted in
been conducted
have been
experimental, have
both theoretical
theoretical and experimental,
damage
self-focusing
forself
attempts to
-focusing effects in bulk damage
accountfor
to account
problem,
of the problem,
complexity of
experiments. However, due to the complexity
mixed.
been mixed.
has been
experiment has
agreement
between theory and experiment
agreement between
While accurate,
accurate, direct measurements of the nonlinear
nonlinear index of
n2 , have
refraction, n2,
have been
been made
made using various techniques (e.g.,
interferometry33,34),
thepower
power for
for which significant changes
33' 34), the
interferometry
beams
Gaussian beams
focused Gaussian
offocused
propagation of
occur
occur in the linear propagation
estabbeen estabrecently been
only recently
through nonlinear
materials has only
nonlinear materials
through
lished
Wepresent
presentsome
someof
of that
that work in
experimentally. 35' 36 We
lished experimentally.35,36
follows.
what follows.
THEORY
3. THEORY
Self-focusing
3.1. Self
-focusing
results
dielectric results
transparent dielectric
in a highly transparent
Nonlinear refraction in
by
given by
refraction given
of refraction
from a change in the index of
(1)
(1)
n2 <E2>
An
On = n2
<E2> ,
field
electric field
theelectric
squareofofthe
time-averaged
thetime
where <E2>
-averaged square
<E2 >isisthe
where
assume
we assume
Here, we
n2 isis the
and n2
the nonlinear
nonlinear index of refraction. Here,
less than the
much less
time much
response time
has aa response
nonlinearity has
that the nonlinearity
index
expressing the index
of expressing
way of
alternative way
pulse
pulse duration. An alternative
7!,
recently isis An
come into common use recently
change that
that has come
On == yI,
change
theirradiance
irradiance and
and 7
y is aa nonlinear
nonlinear index coefficient.
coefficient.
where II isisthe
n2 (esu)
with 33 n2
constantwith33
by aa constant
related by
These coefficients are related
(esu) =_
light in vacuum
cn /407r7(m2
y(m2/
W),where
whereccisisthe
the speed
speed of light
/W),
cn/40?r
mechaMany mecharefraction. Many
of refraction.
index of
linear index
(m/ s)
s) and
and n is the linear
self-focusing
focusing effects
effects in
in solids.
solids. For tight
nisms can give rise to selffocusing geometries using
using nanosecond
nanosecond and longer pulse duraelecthe elecself-focusing,
thermal self
tions, electrostriction,
-focusing, and the
electrostriction, thermal
tions,
self-focus.
catastrophicselfto aa catastrophic
Kerr effect can all contribute
contribute to
focus.
tronic Kerr
mechanism in
dominant mechanism
pulse durations the dominant
For picosecond pulse
effect.
Kerreffect.
electronic Kerr
the electronic
be the
to be
believed to
solids isis believed
transparent
transparent solids
volume of work
work has been devoted
devoted to the study of
large volume
A large
12 The
self
-focusingeffects
effectsinin solids.
solids.12
The theories
theories developed
developed to
to
self-focusing
self-focusing
thatself
indicate that
describe
describe the process indicate
-focusing is dependent
critical
Two critical
material. Two
the material.
in the
laser beam in
on the power of the laser
for
literature for
the literature
cited in the
often cited
powers of
of importance
importance are
are often
powers
by 37
given by37
Pj,isisgiven
these,P1,
ofthese,
first of
The first
Gaussian beams. The
Pl =
cA2
cx2
(2)
(2)
327r2n2
where X
the laser
laser wavelength.
wavelength. Many theories based on the
X isis the
cataassumed that
have assumed
approximation have
shape approximation
constant
that a cataconstant shape
strophic collapse of the beam will occur in the material when
introduced
was first introduced
idea was
This idea
P,. This
approachesP1.
the beam power approaches
by Zverev and Pashkov,38
Pashkov,38 who suggested the following equaself-focusing:
duetotoself
enhancementdue
irradianceenhancement
the irradiance
for the
tion for
-focusing:
In
I0
ISF
1SF
(3)
~ I-P/P,
I - P/PI
self-focuspresenceofofselfthepresence
inthe
where ISF
the peak
peak irradiance
irradiance in
focusISF isis the
self-focusing.
absenceofofself
theabsence
in the
the peak
peak irradiance
irradiance in
-focusing.
I0 isisthe
ing and I0
to "scale"
researchers to
by researchers
used by
subsequentlyused
was subsequently
equation was
This equation
self-focuseffectsofofselftheeffects
forthe
"correct" for
and "correct"
damage
focusdamage data and
give the following 16,21,22 Equation
ing.'6.21,22
Equation(3)
(3)can
canbe
be rearranged
rearranged to give
ing equation:
1
P
1
(1
1
ID \A + PI
(4)
self-focusing.
absenceofofselftheabsence
in the
area in
where A is
is the
the focal beam area
focusing.
inverse area,
versus inverse
damage, versus
for damage,
power for
inverse power
of inverse
plot of
Thus, aa plot
Thus,
critical
the critical
yield both the
expected to yield
size squared, was expected
or spot size
self-focusing
power for self
-focusingPj
P1asasthe
the intercept
intercept and
and the damage
slope. A critical assumption made in
ID from
irradiance ID
from the slope.
indepenirradiance isis independamage irradiance
the damage
using this
this equation is that the
using
self-focusing.
absenceofofself
theabsence
in the
-focusing. We find this
area in
of focal area
dent of
5.2.
Sec. 5.2.
in Sec.
discussed in
as discussed
assumption invalid as
soluexact solustudies, exact
self-focusing
earlierself
theearlier
to the
contrast to
In contrast
-focusing studies,
Marburger 37
byMarburger37
made by
equation made
wave equation
nonlinear wave
tions of the nonlinear
devisignificant devigeometries, significant
have shown that even for focused geometries,
occur until the
ations from normal linear propagation do not occur
the
of the
collapse of
catastrophic collapse
power exceeds
beam
beam power
exceeds P,
PI and aa catastrophic
beam within the depth of focus does not occur until the beam
/ Vol.
1989
/ October
OPTICAL
ENGINEERING
/ October
1989
/ Vol.2828No.
No.1010/ / 1135
OPTICAL ENGINEERING
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SOILEAU, WILLIAMS, MANSOUR,
MANSOUR, VAN
VAN STRYLAND
STRYLAND
SOILEAU,
TABLE I.I. Comparison
Comparison of
of the
the constant
constant shape
shape approximation
approximation (CSA)
(CSA) to
to
numerical solutions37
solutions 37 (NS)
focused Gaussian
Gaussian beams.
beams.
numerical
(NS) for focused
P/P2
P/P2
l/lo
In,
CSA
l/lo
Ino
0.27
0.27
0.60
0.60
0.80
0.80
0.90
0.90
0.95
0.95
0.96
0.96
0.97
0.97
0.98
0.98
0.99
1.37
2.50
5.00
5.00
10.00
20.00
20.00
25.00
33.30
33.30
50.00
100.00
1.30
2.08
2.08
3.94
3.94
7.15
16.45
28.60
63.40
100.00
192.00
NS
NS
power
P2 . P2
P2 is defined as
power exceeds
exceeds the
the second
second critical power P2.
(for Gaussian beams)
P2
3.77P,
P2 == 3.77P1
.
(5)
The factor of 3.77
3.77 in Eq. (5) comes from numerical
numerical solusolutions of the
input beam
beam with a
the nonlinear
nonlinear wave equation
equation for an input
spatial profile.
profile. The
The power
powerP2
P2 is the least power for a
Gaussian spatial
singular self
self-focus
-focusto
tooccur
occurwithin
within the
the Rayleigh
Rayleigh range, i.e.,
i.e., the
beam confocal parameter,
parameter, for both prefocused and unfocused
geometries.
samples thicker
geometries.This
Thismeans
meansthat
that for
for samples
thicker than
than the
Rayleigh range
is the case
case for
for most
most bulk
bulklaserlaser-induced
Rayleigh
range (as
(as is
induced
damage experiments) a singular
singular self
self-focus
-focus will
will occur
occur within
the sample, and LID
LID will occur for an input
input power
power equal
equal to
to P2.
P2 .
Note that for
for tightly
tightly focused
focused beams,
beams, i.e.,
i.e., very
very small spot sizes,
the breakdown
field will
will be reached before PP approaches
approachesP2.
P2 . 1f
If
breakdown field
that is the case,
case, then
then LID
LID results can be
be nearly
nearly independent of
self-focusing
size needed
needed will
will
self -focusingeffects.
effects.The
Thesmall
smallfocal
focal spot
spot size
depend
material, P2,
P2 , and the
the material
material breakdown
breakdown
depend on
on the
the material,
threshold.
Marburger
37 found
Marburger37
found that
that the
the irradiance
irradiance enhancement within
the nonlinear material was given approximately by
by
Indeed, Eq. (5) can be
be "verified" (i.e., we
we show that P2
P2 is
is the
critical power of importance) as
as shown
shown in
in Sec.
Sec. 4. Additional
evidence for high P2
P2 materials
materials is given by
by measurements
measurements of the
polarization dependence of the breakdown powers
powers and meameasurements
distortions in
in the
the transmitted,
transmitted,time
time-intesurements of beam distortions
-intespatial beam
beam profile
profile discussed
discussed in
in Sec.
Sec. 4.
4.
grated spatial
Polarizationdependence
dependenceofofself
self-focusing
3.2. Polarization
-focusing
The use of short pulses presents
presents us
us with the advantage
advantage that
that we
we
need only consider the fast
fast electronic
electronic Kerr
Kerr nonlinearity
nonlinearity in
need
in
analysis. This
This nonlinearity
nonlinearity isis polarization
polarization dependent,
data analysis.
dependent,
polarization dependence
dependence presents
presents us
us with
with aa simple
simple
and this polarization
way of determining whether
whether or
ornot
notself
self-focusing
effects are
-focusing effects
measurements.
present in LID measurements.
Early papers in the
the literature
literature have shown
shown that
that the
the nonlinear
nonlinear
isotropic materials
materials (such
(such as
as fused
refractive index for isotropic
fused quartz)
quartz)
is given
givenbyby39-41
39~41
is
n2
n2 (L.P.)
(L.P.) =
n2 (C.P.)
n2
(C.P.) =
II~P/P2
- P0P2
(6)
which
P2 /4.
which isis only
only valid
valid for
for PP <
< P2/
4. Note
Note that this is identical to
Eq.
(3) with
with P1
Pj replaced
replaced by
P2 . When
power is
is
Eq. (3)
by P2.
When the
the input power
significantly
/4 one
significantlygreater
greaterthan
than P2
P2/4
one must
must use
use the
the more
more comcomplete
plete numerical
numerical solution
solution to compute the enhanced irradiance
due
self-focusing.
due to self
-focusing.Table
TableI Iisisaacomparison
comparison of
of the
the approxiapproximation
exact numerical
numerical solution
solution
mation given
given by
by Eq.
Eq. (6)
(6) and
and the exact
given
while the
given by
by Marburger
Marburger (see
(see Ref.
Ref. 37,
37, p.
p. 66).
66). Note
Note that while
enhancement cannot
cannot be
be calculated
calculated accurately
accuratelyby
by Eq.
Eq. (6)
(6) for P
> P2/4,
P2 /4, itit still
still correctly predicts breakdown
breakdown at
at aa power
power of
of P2.
P2 .
In 1977
1977 Smith et aí.22
al. 22 also
in using
using P1
Pj
alsofound
found some problem
problem in
for correcting their 532 nm and 355 nm picosecond damage
thresholds for selfself-focusing.
focusing.In
Inmost
mostcases,
cases,their
their 355
355nm
nmthreshthresholds were
were higher
higher than
than Pj.
P1. A
A scaling
scaling factor
factor was
was proposed
proposed such
that the critical power varied between
between P1
P l and P2 depending on
the value
value of
of PP at
at damage.
damage. However,
However, since
sincethe
theexact
exactfunctional
functional
dependence
time,
dependence for
for the
the intensification
intensification was
was unknown at the time,
the thresholds
thresholds reported in Ref. 22
22 included
included the breakdown
breakdown
power
power and
and the
the uncorrected
uncorrected focal
focal area
area so
so that
that future workers
workers
could
could re-examine
re- examinethe
thedata
data in
in the
the light
light of new
new measurements.
measurements.
We
We re-examine
re- examinethat
that data
data in Sec. 5.1.
We
evidence showing
We previously
previously presented
presented experimental evidence
that,
as predicted
predicted by
Marburger, the important
important power
power for
for
that, as
by Marburger,
focused geometries
geometries is
is the
thesecond
secondcritical
criticalpower,
power,
P2 . 35' 37
focused
/32.35,37
n
,(3)
Xiiii
Xi31 i1
(7)
(7)
247T
247
3
v (3)
X1122
122
X1)
for linearly polarized and circularly
circularly polarized
polarized light,
light, respecrespectively, where the
the X(32¡
x^Vi are
arethird-order
third -ordernonlinear
nonlinear susceptibility
tensor
elements. A symmetry
symmetry relation
relation exists
exists for
for isotropic
isotropic
tensor elements.
materials such that
(3) _ > ) (3)
Xllll
~= Z
XH22 + X1221
X1(311)1
2X1(3122
(8)
Measured values
values for these tensor elements
elements indicate that for
for
Measured
fused quartz
quartzX1(3122
Xm2 ls isapproximately
equaltotoX1221.41
Xi22i-41 Thus,
fused
approximately equal
Thus, we
we
can express n2
n2 (C.P.) in
in terms
terms of
ofthe
thesame
samex(3)
x^ tensor
tensor element
element
as n2
n2 (L.P.), giving
giving
Io
ISF
127T
12 7r
n2 (C.P.)
=
87T
X1
(9)
We see
of n2
n2 for circular polarization to
to n2
n2 for
We
see that
that the ratio of
linear polarization is 2/3. This
This implies
implies that the
the 9ratio
9ratio of the
critical powers for
for self
self-focusing
two cases
cases isis 1.5.
1.5.
-focusing for the two
slightly more
more complicated
complicatedanalysis
analysisfor
forNaC1
NaCl
A similar but slightly
gives
the critical
critical powers
powers that
thatvaries
variesbetween
between 1.37
1.37
gives aa ratio for the
1.46 depending
and 1.46
depending on
on the propagation direction in the cubic
orientationof
ofthe
the large
large grain size
crystal. We do not know the orientation
crystalline samples and, therefore, expect
expect aa ratio
ratio between
between the
the
above values near 1.4.
1.4.
If we
we extend
extend this
this concept to measurements of bulk optical
breakdown and ifif self
self-focusing
breakdown
breakdown
-focusing dominates
dominates the breakdown
process, then, in both the isotropic
isotropic and
and cubic
cubic cases,
cases, the ratios
the breakdown
breakdown powers
powers for the
the two
two polarization
polarization states
states
of the
should be equal to the ratio
ratio of
of the
the critical
critical powers
powers (i.e.,
(i.e., 1.5
1.5 for
SiO2
and-1.4
forNaC1).
NaCl).
Si02 and
=1.4 for
The polarization
polarization dependence
dependenceof
ofself
self-focusing
-focusing has already
been well
well established
established experimentally.
experimentally. For example, Moran et
al.
34 measured
aí.34
measured n2
n2for
forvarious
variouslaser
laserglasses
glasses(isotropic
(isotropic materials)
materials)
using time-resolved
and found
foundthat
thatn2
n2 (L.P.)
(L.P.) --time -resolved interferometry
interferometry and
1.5n2
al. 42 measured
1.5n2(C.P.).
(C.P.). Feldman
Feldman et aí.42
measured the
the breakdown
breakdown powers
function of polarization for fused
fused quartz and other
ers as
as a function
glasses
at 1.06
1.06 µm.
jum. He used
glasses using
using nanosecond
nanosecond pulse durations
durations at
used
the observed
observed polarization dependence in an attempt
attempt to
to sepasepa-
1136
OPTICALENGINEERING
ENGINEERING // October
Vol. 28 No.
No. 10
1136 / /OPTICAL
October 1989
1989 // Vol.
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SELF-FOCUSING
OFSELF
ROLEOF
THEROLE
ANDTHE
LASER-INDUCED
LASERINDUCED DAMAGE
DAMAGE AND
-FOCUSING
beam
using beam
measured using
as measured
n2 as
indexn2
refractiveindex
TABLE II. The nonlinear refractive
43 compared
distortion
distortion43
comparedwith
with other methods.
MATERIAL
MATERIAL
10" esu)
(x 1013
n2 (Others)
10" esu)
(x 1013
1.06
0.53
0.53
128130
128
±30
+ 30*5
125
125 ±
3045
NaCI
1.06
0.53
0.30
1.37 +±0.30
1.37
+ 0.30
1.38
1.38±0.30
33
1.22
1.22 ±0.21
±0.2133
1.5957
1.5957
Si02
Si02
1.06
0.53
0.62
0.62±+ 0.15
+ 0.15
0.60
0.60±0.15
0.95 + 0.10 33
0.95±0.1033
BK-7
BK-7
1.06
0.53
0.53
1.45 + 0.30
1.45±
1.01+0.25
1.01
±0.25
1.46
1.46 +
± 0.10«
0.1046
1.3047
1.3047
CS2
CS2
N a CI
WAVELENGTH
^m
µm
n2
other
P2 with
using P2
method using
LID method
Comparison of
TABLE
TABLE III.
Ill. Comparison
of the
the LID
with other
CS2 .
in CS2.
n2 in
measuring n2
methods of measuring
METHOD
METHOD
Equation 55
Equation
Equation 5
Equation
Beam
Beam Distortion
Distortion
Beam
Beam Distortion
Interferometry
123 + 30
123±30
\0irn)
x(um)
10" esu)
n2
n2 (x
(x 1011
1.06
1.06
0.53
0.53
1.06
1.06
0.53
1.32
0.3 48
1.3 +±0.34a
1.3
48
1.210.3
1.2
±0.346
0.3 43
1.5 +±0.343
1.5
0.343
1.5
1.5±+ 0.343
1.3 + 0.345
1.3±0.345
-H-
0.8547
0.8547
1.5
T
X =0.53µm
1.4r
r -30 ps
'BC
n2 and was the first to point
to n2
rate the various
various contributions to
self-focusing
-focusingininbreakdown
breakdown
out that the presence or absence of self
measurements
measurements could
could be
be determined
determined by
by measuring
measuring the
the breakbreakWe use
down threshold
threshold power
power as
as aa function of polarization. We
conthe condetermine the
to determine
this concept in our own measurements to
self-focusing.
of selftribution of
focusing. The
The data
data presented in Sec. 4.2 on
NaCI clearly
fused quartz and NaC1
fused
clearly show
show the
the transition
transition from
from an
self-focusing
which self
in which
experimental geometry in
-focusing dominates
dominates the
be
can be
self-focusing
whichselfgeometryininwhich
damage process to aa geometry
focusing can
neglected.
neglected. In
In the
the next
next section
section we
wefirst
firstverify
verifyMarburger's
Marburger's theory
theory
by
by monitoring
monitoring breakdown
breakdown in CS2
CS2 at
at 1.06
1.06 p,m
um and 0.53
0.53 /zm.
µm.
EXPERIMENT
4. EXPERIMENT
Experimental verification of Marburger's theory
4.1. Experimental
4.1.
37 that
Marburger's
Marburger's prediction
prediction37
that breakdown
breakdown will
will occur
occur at
at an
P2 given
input power P2
given by
by Eq.
Eq. (5)
(5) in a tight focusing geometry
which the
experiment in
verified by
can
can be
be verified
by arranging
arranging an
an experiment
in which
the
P2 is very low. A classic
threshold isis very high and P2
breakdown threshold
CS2 . This material is
example
example of such
such aa material
material is the liquid CS2.
nonsince its nonstudies since
system studies
excellent choice
an
an excellent
choice for
for model system
is relatively well
for years and is
well
linear behavior has been studied for
understood. The nonlinearity isis due
dueto
tononresonant
nonresonant reorientareorientaCS2 molecules,
tion of the CS2
molecules, which
which relaxes
relaxes with
with aa time
time constant
constant
n2 in
measure n2
of
of approximately
approximately 22 ps.
ps. The
The first
first step
step is
is to measure
in aa
meamanner independent
induced breakdown mealaser-induced
the laserindependent of the
manner
surements.
surements. Table
Table IIII isis aa summary
summary of such
such measurements
measurements for
for
CS2and
andother
othermaterials
materials of
of interest
interest using
usingthe
the beam
beamdistortion
distortion
CS2
other
obtained by other
Values obtained
technique described
technique
described in
in Ref.
Ref. 43.
43. Values
comparifor comparilisted for
workers using
workers
using various
various techniques
techniques are
are listed
\yith
son.33,44-47
son.33,44-47
Withthe
thepossible
possibleexception
exceptionof
of SiO2
Si02 (a
(a 30%
30% differdifferIt isis
excellent. It
is excellent.
methods is
agreement with
ence) the
ence)
the agreement
with other methods
important to note
note that the observation of beam
beam distortion in
in
the far
far field
field as
asreported
reported in
in Ref.
Ref. 43
43 isisperformed
performedatat irradiance
irradiance
levels
levelsnot
not far
far below
below damage,
damage, and
and the
the agreement
agreement with
with other
other
powers.
input powers.
high input
for high
analysis for
data confirms the propagation
propagation analysis
CS2 , i.e.,
in CS2,
experiment in
We
We next
next set
set up
up aa bulk
bulk breakdown
breakdown experiment
arranged the sample length to be much longer than the confopower.48
breakdownpower.48
the breakdown
measured the
cal
cal beam
beam parameter, and measured
0.53
and 0.53
^m and
1.06 pm
n2 at both 1.06
We
We then
then used
used Eq.
Eq. (5)
(5) to
to calculate n2
/zm
pm and compared this with values obtained by beam distorinterferometry.45
time-integrated
measurements 44 and time
tion measurements44
-integrated interferometry.45
The results of this
this comparison
comparison are shown in Table III. In this
experiment laser-induced
laser- inducedbreakdown
breakdown isistotally
totally dominated
dominated by
by
self-focusing
self -focusingand
andthe
thebreakdown
breakdown power
power was experimentally
conditions.
focusing conditions.
the focusing
of the
independent of
determined to
determined
to be independent
n2 determined
between the n2
Note the excellent agreement between
determined from
assumes
measurements using Eq. (5), which assumes
the
the breakdown measurements
pB 1.3
11
1.1 1.1
1.0 _
10
i
15
20
2s
30
W6I/ rol
PB for
to PB
light to
polarized light
circularlypolarized
for circularly
PB for
ofPB
ratioof
theratio
ofthe
plotof
Fig. 2.
Fig.
2. AA plot
for
(sample
SiO 2(sample
size inin Si02
spotsize
of spot
as a function of
polarized light as
linearly polarized
self-FQ-7940-1).
7979 -F0.7940 -1). The
Thedashed
dashed line
linerepresents
represents the
the expected
expected ratio when
when self
focusing dominates.
beam
by beam
determined by
those determined
that P2 is
is the critical power, and those
3.77
of 3.77
factor of
the factor
verifies that the
This verifies
measurements. This
distortion measurements.
predicted by the theory in Ref. 37 is
is correct
correct to within the error
error
bars shown.
self-focuswhenselfdeterminedwhen
experimentally determined
We
We have also experimentally
focusobserving
by observing
experiments by
ing isis present
present in bulk breakdown experiments
ing
discussed in the
as discussed
dependence of damage as
the
the polarization dependence
following section.
4.2. Polarization dependence
4.2.
for
power for
breakdown power
the breakdown
of the
ratio of
Figure
Figure 22 isis aa plot of the ratio
linear polarfor linear
power for
breakdownpower
the breakdown
to the
circular polarization
polarization to
in
measured in
radius measured
spot radius
focal spot
the focal
of the
function of
ization
ization as
as a function
is
wavelength is
laser wavelength
35 ' 36 The
air.
air.35,36
Thematerial
materialisisfused
fusedquartz,
quartz, the laser
regions of
ps. Three regions
30 ps.
0.53
0.53 jum,
µm, and
and the pulse duration isis 30
small
and small
small focal radii and
evident. For small
clearly evident.
interest are clearly
interest
is approxiPBcirCuiar/ pBiinear
ratio PBcircular/
breakdown
breakdown powers
powers the
the ratio
PBlinear iS
self-focusing
electronicself
lackofofelectronic
thelack
indicatingthe
mately unity, indicating
-focusing as
as
23 jum
discussed
discussed in
in Sec.
Sec. 3.2.
3.2. For
For focal
focal radii
radii greater
greater than 23
µm and
levels off to near the theoratio levels
large breakdown powers the ratio
self-focusing.
dominanceofofself
the dominance
indicating the
1.5 indicating
retical value of 1.5
-focusing.
increasing from unity to
data increasing
The transition regime
regime shows the data
Thejransition
elecof eleconset of
the onset
showing the
clearly showing
maximum, clearly
the theoretical maximum,
self-focusing
tronic self
-focusing in
in fused
fused quartz.
quartz.
critical powers
the critical
of the
ratioof
the ratio
at the
looking at
than looking
Now, rather than
we
we examine
examine the
the behavior
behavior of the breakdown
breakdown powers directly in
power in megawatts is plotted as
Fig. 3.
3. Here, the breakdown power
as
repretriangles repreThe triangles
air. The
in air.
radius in
a function of the focal spot radius
the
sent the breakdown powers for linear polarization, and the
sent
polarization.
powers for circular polarization.
circles
circles are
are the
the breakdown powers
P2 for
the critical power P2
represents the
line represents
dashed line
The horizontal
horizontal dashed
n2 values for
measuredn2
ourmeasured
fromour
calculatedfrom
linear polarization
polarization calculated
sample. 43 As
this sample.43
Ascan
canbe
beseen,
seen,the
thebreakdown
breakdown power for linear
then
focal radius and then
increases with increasing focal
polarization increases
the
where the
region where
the region
In the
radii. In
focal radii.
larger focal
P2 for
reaches P2
for larger
OPTICAL ENGINEERING
OPTICAL
ENGINEERING/ /October
October1989
1989// Vol.
Vol. 28
28 No.
No. 10
10 // 1137
1 137
Downloaded From: http://proceedings.spiedigitallibrary.org/ on 01/30/2015 Terms of Use: http://spiedl.org/terms
STRYLAND
SOILEAU, WILLIAMS,
WILLIAMS, MANSOUR, VAN
VAN STRYLAND
SOILEAU,
3.0
3
'-PBc
2.5
2.5
PB
r
T
I
i
1
T
*
' PBL
L P.
--P2 for
for L.P.
-P2
i
/urn
A- 0.53
0.53pm
2.0
20
IMWI
|MW|
I
rri_______
I
t
P~
1.5
1.5 -P2
_____ ________I
P
*•
|s
PB
PB
IMWI
NW!
1.5
P2 - 1.5
1.00
l
r
LhWM Polarization
Polarization
Linear
66
I-- L 2"
I——
PB
Pg
1MW]
IMW)
44
P2
P2
I
22
J
I
05
05
00
I
*
À = 1.06µm
r =42ps
68
I
10
1.0
I-"
I-
IU
10
2.5
2.5
2.0
20
r- 30 ps
PS
r-30
PB
30
3.0
I
05
0.5
00
I
11
_r
1
1
I
1I
I1
5
10
15
20
25
Wolµml
1
T
00
*A
*
0
1
50
|
1
100
150
ioof
200
200
Zp=L
30
OJol/im)
Wolµml
ZR t
71: t
versus spot
breakdown power versus
the breakdown
plot of the
spot size
size for
for the
the
Fig. 3. A plot
circular
polarization, circles -circular
sampleof
of Fig.
Fig. 22 (triangleslinear polarization,
(triangles linear
sample
meapolarization). The
The dashed
dashed line
line gives
gives P2
P2 as
ascalculated
calculated from
from the meapolarization).
ru
ofn2.43
"2- ~
value of
sured value
in.
foraa22 in.
NaCIfor
sizeininNaCI
spotsize
functionofofspot
as aa function
Fig. 4. Breakdown
poweras
Breakdown power
(X). The horizontal
sample (X).
thick sample
and aa 11 in. thick
(triangles) and
thick
sample (triangles)
thick sample
dotted
n2 , 43 and
fromn2,43
P2 as
dashed line gives P2
as calculated from
and the
the vertical
vertical dotted
focused
the focused
of the
range of
Rayleigh range
the Rayleigh
size at which the
line gives the spot size
sample.
in. sample.
beam
equals the
the sample
sample thickness
thickness for
for the 2 in.
beam equals
breakdown power becomes
becomes constant,
constant, the polarization ratio is
seen for fused quartz at
are seen
results are
Similar results
approximately
1.5. Similar
approximately 1.5.
self-focusing
thatself
indicate that
1.06 nm.
pm. Both
Both of the these trends indicate
-focusing
1.06
breakdown
the breakdown
when the
process when
breakdown process
dominates
the breakdown
dominates the
P2 .
approaches P2.
power approaches
for
observed for
are observed
SiO2 are
seen for Si02
those seen
Results
similar to
to those
Results similar
NaCl.
0.53 i^m
pm for 30
30 ps
ps pulses
pulses and
and small
small focal
focal radii and
NaCI. At 0.53
approxitherefore,
small breakdown
breakdown powers,
powers, the
the ratio isis approxitherefore, small
self-focuselectronicselfofelectronic
lack of
the lack
mately unity. This indicates the
focuspowers
ing, whereas
whereas for
for large
large focal
focal radii
radii and
and large breakdown
breakdown powers
levels off
the ratio levels
off near
near the
the mean
mean theoretical
theoretical value of approxapproxself-focusing
imately 1.4.
focusing dominates
dominates the break1.4. In this region selfbreakdown
the breakdown
where the
region where
down process.
process. Again,
Again, in
in the region
down
powers
remain constant with increasing spot size, the ratio of
powers remain
Similar
1.4. Similar
reaches approximately 1.4.
powers reaches
the breakdown powers
discuss
We discuss
pm. We
1.06 pm.
sample at 1.06
seen for this sample
results
are also
also seen
results are
below.
significance below.
their significance
some
those measurements and their
some of those
this point we
we remind
remind the
the reader
reader of the definition of the
At this
Mar-of Mar
more of
self-focusing
critical power
power for selffocusing and
and discuss
discuss more
critical
37 P2P2isisthe
burger's results.
results.37
theleast
leastpower
power for
for which
which aa cataburger's
unfocused
strophic collapse
collapse will
will occur
occur for
for both focused and unfocused
does
on-axis
maximum on
geometries. The
The point of maximum
-axis irradiance does
geometries.
waist; it occurs "downstream"
"downstream" of the
occur at the beam waist;
not occur
waist at
at aa distance
distance comparable
comparable to the Rayleigh range in
beam waist
P2.. If
If the
the sample
sample thickness
thickness isisthinner
thinner than
than
the material for P = P2
range, insufficient
insufficient nonlinear
nonlinear material
material exists
exists for
for
Rayleigh range,
the Rayleigh
selffocusingtotocause
causeaacatastrophic
catastrophic collapse
collapse of
of the
the beam
beam to
self-focusing
self-byself
dominatedby
damage dominated
For damage
P2 . For
occur
in the material at P2.
occur in
focusing, this
this means
meansthat
that the
the material
material will
will not
not fail
fail until
until the
focusing,
seen in
be seen
can be
P2.. This
This type of behavior
behavior can
beam power exceeds P2
the data presented in Fig. 4. Here we have plotted the breakspot
focal spot
down power
power in
in megawatts
megawattsasas aa function
function of
of the
the focal
down
1.06
wavelengthisis 1.06
laser wavelength
NaCI sample. The laser
radius in air for the NaC1
is 42
pm,
42 ps.
ps. The
The horizontal dashed line
jum, and the pulsewidth is
n2
measured n2
P2 calculated from measured
represents the critical power P2
represents
line
II). 43 The
this sample (see Table
Table II).43
The vertical
vertical dotted line
values of this
divides the
the data
data for which
which the
the sample
sample thickness is
is less
less than
than the
the
divides
which the
Rayleigh
range (region
(regiontoto the
the right)
right) from
from that in which
Rayleigh range
left).
the left).
to the
sample isis thicker
thicker than
than the Rayleigh range (region to
Let us first
first examine
examineonly
onlythe
thetriangular
triangular data
data points that are for
sample thickness
thickness of 22 in.
in. If
Ifwe
weexamine
examinethe
thedata
data for
for the
the
a NaCI sample
left, we
we see
seethat
that the
the breakdown
breakdown power increases
region to the left,
However,
P2 . However,
with increasing
increasing focal
focal radius
radius to
to approximately P2.
with
focus
of focus
depth of
when
the sample
becomes shorter
shorter than
than the depth
sample becomes
when the
to
continues to
power continues
breakdown power
the breakdown
(region
to the right),
right), the
(region to
increase. If we
we now
now rotate
rotate the sample so
so that
that the beam propapropadramatic
in., aa dramatic
gates through
through 11 in.
in. of material instead of 2 in.,
gates
by
seen by
This isis seen
observed. This
powerisis observed.
breakdown power
increase in the breakdown
The
size. The
spot size.
^tm spot
150 pm
examiningthe
the data
data points
points for
for the 150
examining
for a sample thickness of 22 in.,
point isis for
triangular point
in., and
and the
the point
point
triangular
other
No other
material. No
of material.
in. of
for 11 in.
is for
representedby
by the
the XX is
represented
the change in the
that the
show that
To show
have been changed. To
parameters have
parameters
effect a
orientation effect
breakdown power
power was
was not
not due
due to
to an orientation
breakdown
in which the sample was
case in
for aa case
was performed for
similar test was
for 11 in. of material.
range for
Rayleigh range
the Rayleigh
with the
thick compared with
when the
observed when
was observed
power was
No change
change in
in the breakdown power
No
effects
was rotated.
rotated. This simple test clearly shows the effects
sample was
self -focusingininbreakdown
breakdown measurements.
of self-focusing
SELF-OFSELF
ROLEOF
THEROLE
FROM THE
5. CONCLUSIONS
CONCLUSIONS FROM
5.
FOCUSING IN LID
Re-evaluation
5.1.
evaluation of
of ELID
ELID data
5.1. Resignificance of
of this
this work
work should
should be
be emphasized.
emphasized. Much
Much of
of
The significance
scaling
self-focusing
onself
work on
-focusing used the scaling
experimental work
the early experimental
self-forself
datafor
the data
correct the
al. 38 to correct
et al.38
Zverev et
by Zverev
law proposed by
law
was
critical power of importance was
focusing. In
In that work the critical
focusing.
laser-induced
of the laserP,.. Spot
be PI
Spot size dependencies of
induced
assumed to be
reflection of
of
damage thresholds were assumed to be merely a reflection
in
were in
powers were
self -focusing since
since the
the breakdown
breakdown powers
the effect of self-focusing
self-focustheselfsincethe
However,since
of P l. . However,
focusmost cases a fair fraction UPI
critical
the critical
confirms that the
ing theory
theory predicts
predicts and
and this work confirms
ing
size dependencies are in
spot size
fact P2
P2and
and not
not Pj,
PI, the spot
power is in fact
possibly
material, possibly
the material,
in the
mechanisms in
cases due to other mechanisms
most cases
defects to the LID thresholds. Work that
the contribution of defects
re-examined.
beretobe
needs to
al. needs
et al.
Zverev et
used the method of
examined.
of Zverev
used
and
Zverev and
the Zverev
using the
work using
Unfortunately, much
much of the work
Unfortunately,
since
literature since
Pashkov38
scaling isis not
not recoverable
recoverable from the literature
38 scaling
Pashkov
be
cannot be
and cannot
the uncorrected
thresholds are
are not reported and
uncorrected thresholds
the
et
Fradin et
However, Fradin
extracted due to insufficient information. However,
Zverev and
a1.19
anticipationofofsome
some problem
problem with
with the
the Zverev
and
19 ininanticipation
al.
1973 for
in 1973
reported in
data reported
scale the data
Pashkov method did not scale
self -focusing,and
and in
inretrospect
retrospect they were correct in not scaling
self-focusing,
NaCI
powerininNaC1
damagingpower
thedamaging
that the
observed that
They observed
the data. They
used for
lenses used
the lenses
of the
length of
focal length
scaled as
as the square of the focal
scaled
1977 Smith et
in 1977
earlier, in
noted earlier,
As noted
the picosecond pulsewidths. As
532
their 532
Pj to correct their
aí.22
alsofound
found some
some problem
problem in using P1
al. 22 also
self-focusforselfthresholdsfor
damagethresholds
focuspicosecond damage
nm and 355 nm picosecond
ing. They
They included
included the
thebreakdown
breakdown power and
and the
the uncorrected
uncorrected
ing.
recould reworkers could
future workers
that future
so that
report so
focal
area in their report
focal area
10
No. 10
28 No.
Vol. 28
ENGINEERING // October
OPTICALENGINEERING
1138
October 1989
1989 // Vol.
1138 / /OPTICAL
Downloaded From: http://proceedings.spiedigitallibrary.org/ on 01/30/2015 Terms of Use: http://spiedl.org/terms
LASER-INDUCED
ANDTHE
THEROLE
ROLEOF
OFSELF
SELF-FOCUSING
LASER- INDUCED DAMAGE
DAMAGE AND
-FOCUSING
TABLE IV.
scaled for
TABLE
IV. Breakdown
Breakdown thresholds
thresholdsat
at0.53
0.53 urn
µm of
of Ref.
Ref. 22 scaled
for
self-focusing
self- focusing using
using P1
Pt (column 7) and P2
P2(column
(column 8).
8). PPstands
standsfor
forthe
the
breakdown
PB , E0
breakdown power PB,
E0isisthe
the breakdown
breakdown field,
field, and A is the focal
area
area calculated
calculated using
using linear
linear optics.
Material
Material
PB
PB
(KW)
(Kw)
AA
G»m)»
(µm)=
P/Pi
P/P,
P/P2
P/P=
(unsealed)
)unsealed)
E.
Eo
(MV/cm)
(MVrcm)
(unsealed)
(unsealed)
EPi
Ep,
EP2
(scaled)
(scaled)
(scaled)
(scaled)
EP2
KH2P04
KH2PO4
151.0
151.0
16.0
16.0
0.57
0.57
0.15
0.15
15.3
15.3
23.4
23.4 (53o/a)
(53%)
16.6 (8%)
(8%)
16.6
Si02
Si02
129.0
129.0
15.9
15.9
0.46
0.46
0.12
0.12
14.5
14.5
19.0(31%)
19.0
(31o/a)
15.4(6%)
15.4
(6%)
NaCI
NaCI
38.4
38.4
15.1
15.1
0.60
0.60
0.05
0.05
7.9
7.9
12.4(57%)
12.4
(57%)
8.1
(3%)
8.1 (3%)
CaF2
CaF2
146.0
146.0
15.9
15.9
0.62
0.62
0.09
0.09
15.5
15.5
25.2 (63%)
(63%)
25.2
16.3 (5%)
(5%)
16.3
NaF
NaF
126.0
126.0
15.8
15.8
0.45
0.45
0.05
0.05
15.0
15.0
19.4 (30%)
19.4(30%)
15.4 (3%)
(3%)
15.4
LiF
LiF
171.0
171.0
16.1
16.1
0.59
0.59
0.06
0.06
16.9
16.9
26.5 (57%)
(57%)
26.5
17.5(4%)
17.5
(4%)
examine
light of
of new
new measurements.
measurements.
examine the
the data in the light
We
We can
can now
now use
use Eq. (5) to reexamine the
the 532
532 nm
nm breakbreakre-examine
down
al. 22 In
work, the breakdown
breakdown
down data
data of Smith et al.22
In that
that work,
powers
powers are
are all
all below
below P,,
P1, so
so the
the irradiance increase predicted
by Eq.
Eq. (5)
(5)should
should be
bevalid.
valid.Six
Sixmaterials
materials were
were studied,
studied, includincluding fused
NaCI, as
fused quartz
quartz and NaC1,
as shown in Table IV.
IV. In examining
we find that
that the
the breakdown
breakdown threshold
threshold fields
ing the
the data we
fields
increased
These increased
increased
increased as
as much
much as
as 50%
50% to
to 60%
60% using
usingP,.
P. These
thresholds
However, when the thresholds are
thresholds were
were reported.
reported. However,
properly corrected using
using the
the second
second critical
critical power
powerP2
P2 we
we find
on
average only
only a 5%
5% increase.
increase. This is
on the average
is well
well within the
±15% absolute uncertainty in the measurements.
Smith et al.
22 also
at 355
355
al.22
alsoreported
reported breakdown
breakdown thresholds at
nm for three
three of the
the materials
materials listed in Table
Table IV.
IV. The
The results
results for
for
near-UV
this near
-UVstudy
studyindicate
indicatethat,
that, in
in most cases,
cases, the breakwere substantially
down threshold powers for these materials were
than the
the P1
Pj critical powers at this wavelength.
higher than
wavelength. The
The only
only
exception was CaF2
CaF2 where PB
PB was
be 0.7P1.
0.7Pj. In an
was found
found to be
to correct
correct their
theirdata
datafor
forthe
thepresence
presenceofofself
attempt to
-focusing
self-focusing
they scaled
scaled their breakdown
breakdown threshold
threshold irradiance
they
irradiance levels
levels in
in
KH2 PO4 , LiF,
KH2PO4,
LiF, and SiO2
Si02 using Eq. (5) but with a critical power
Pj and
and P2.
P2 .
somewhere between P1
While
While they
theywere
wereon
onthe
theright
righttrack,
track, meaningful
meaningful comparison
comparison
of the
the 355
355nm
nmdata
data with
with results
results at other wavelengths
wavelengths is
is difficult
poor spatial
spatial quality
quality of
due to the reported poor
ofthe
the 355
355 nm
nm beam
beam
used in the
the measurements.
measurements. The
The uncertainty
uncertainty in the
used
the energy
energy
distributionwithin
withinthe
thefocal
focalarea
arealead
leadSmith
Smithetetal.22
al. 22 to assign a
distribution
factor of two range for the scaled breakdown threshold
threshold fields
fields
at this wavelength.
wavelength. The
The actual
actual breakdown thresholds may or
may not be within
may
within this
this range.
range. A
A further complicating factor
355 nm work is the recent result that the
the
for interpreting the 355
effective n2
effective
n2for
foraamaterial
materialmay
maynot
notbe
beconstant
constant as
as aafunction
function of
of
wavelength
energies approaching
wavelengthfor
for photon
photon energies
approaching aa substantial
substantial
fraction of the band
band-gap
-gap energy.
energy. Based
Based on our measurements
measurements
using the technique
of Ref.
Ref. 43
43 in
in BK
BK-7
technique of
-7(see
(seeTable
Table II
II comparing
comparing
n2 at
jum) and
and those
thoseofofWhite
Whiteetetal.
BK-10
n2
at 11 jumandO.5
µm and 0.5 µm)
al.4949ininBK
-10 at
at
355
355 nm,
nm, the
the n2
n2 values
valuesfor
for the
the three
three materials
materials studied
studied at
at the
third harmonic wavelength
wavelength may well
well be substantially
substantially lower
lower
than
the values
values at
1064 nm.
the need
need for
for
than the
at 1064
nm. This
This points
points to
to the
accurate measurements of
of n2
n2 in these materials in
in the
the regime
regime
where
effects may
play. It may
where multiphoton effects
may be
be coming into play.
also
necessary to
measure nonlinear refraction
refraction at
at near
near-also be necessary
to measure
damaging
levels as
damaging irradiance levels
as isis done
done in
in the beam distortion
method.43 This
method.43
This being
beingthe
the case,
case, we
wewill
willnot
notattempt
attempt at this time
to reexamine the 355
355 nm
nm thresholds.
In our
our rere-evaluation
breakdown results
results of other
other
evaluation of
of the breakdown
workers, we have concentrated
onthe
thework
workof
ofRef.
Ref. 22
22 for
for two
concentrated on
reasons. The first reason is that the breakdown
measurements
breakdown measurements
in that work were
were conducted
conducted for pulse
pulse durations comparable
to our
our own.
own. Therefore,
Therefore,the
theselfself-focusing
mechanisms in the
focusing mechanisms
the
test materials will
will be
second reason is
be the same.
same. The second
is that, of
the experimenters who scaled
scaled their breakdown thresholds for
the presumed
presumedpresence
presenceofofselfself-focusing,
Smithetetal.22
al. 22 compose
compose
focusing, Smith
one of few
fewgroups
groups whose
whosework
workcontains
contains sufficient
sufficient information
information
and
experimental parameters
determine the true
true breakbreakand experimental
parameters to determine
down
workers merely
merely reported
reported the
the scaled
scaled
down thresholds. Other workers
breakdown threshold irradiance
irradiance levels
levels without including
including the
focal
used in
in the
the measurements.
measurements. This
This makes
makes itit
focal spot
spot radii used
impossible
thresholds. In
In addiimpossible to
to recalculate the breakdown thresholds.
addition, the incorrectly
incorrectly scaled
scaled data
dataofofSmith
Smithetetal.22
al. 22 was
was used
used in
in
support of the intrinsic
intrinsic avalanche ionization
ionization model.
model.
studies have
Several other breakdown studies
have been
been conducted in
these materials in
in which
which no
noselfself-focusing
corrections were
were
these
focusing corrections
For example,
example, Manenkov29
made. For
Manenkov 29 reported breakdown
breakdown meameasurements in the alkali
alkali halides
halides (including
(including NaC1)
NaCI) for nanonanosurements
at 10.6,
10.6, 1.06,
1.06, 0.69,
0.69, and 0.53
0.53 µm
pm laser
laser
second pulse
pulse durations at
wavelengths.
wavelengths.There
There isis some
some uncertainty
uncertainty in
in the focal
focal spot
spot
radius used in the measurements
measurements since
since two values are reported
without specifying
specifying which
which correspond
correspond to the breakdown irradiance levels
levels listed in Manenkov's
Manenkov'swork.29
work. 29 Feldman
Feldmanetetal.42
al.42
electrostriction isis of relatively minor importance
estimate that electrostriction
for the nanosecond
nanosecond pulses
pulses used
used in
in these
these experiments.
experiments. HowHowever, we will use the
the larger
largervalue
valueofofn2n2==4 4X
10~13
X 10
-13 esu calculated
from nanosecond
nanosecondthree
three-wave
lated from
-wave mixing
mixingexperiments.50
experiments. 50
With this in
in mind
mind we
we find
findthat
thatPB
PBininNaC1
NaCI isis 0.5P2
0.5P2 at 532
532 nm
and PB isis 0.14P2
0. I4P2at
at 1064
1064nm
nm ififwe
weuse
usethe
the larger
larger of the
the two focal
radii cited in Ref. 29. If we use
use the small focal radius we find
find
that PB
PB for NaCI is 0.07P2
0.07P2 at 532 nm and 0.02P2 for 1064
nm.
1064 nm.
Thus, self
self-focusing
-focusing effects
effects in
in Manenkov's
Manenkov's29
are
29 work for NaC1
NaCI are
negligible
negligible except
except perhaps
perhaps for
for the
the combination of the largest
spot size
size and
and shortest wavelength and, therefore, should
should not
not
be scaled.
scaled. The
The wavelength
wavelength dependence
dependence reported
reported by
by Manenkov
Manenkov
from 10.6
10.6 /xm
0.69 µm
µm to 0.69
/zm was an increase in threshold much
stronger
stronger than
than that
that reported
reported by
by Fradin 1717 (a factor of
of three).
three).
However,
0.53 )um
net drop
However, the
the threshold
threshold dropped
dropped at 0.53
µm for a net
going from
from 11 /im to 0.5
0.5 pm
µm consistent with our measurements.
In a similar
similar nanosecond
nanosecondstudy,
study,Merkle
Merkleetetaí.51
al. 5I-53
~ 53 reported
single
for Corning
Corning 7940
7940 fused quartz
single shot
shot damage thresholds for
for laser wavelengths
wavelengths ranging from 1064
1064 nm to 355
355 nm. In
In
fused quartz as well as in NaCl,
NaCI, for
for the
the tight
tight focusing
focusing geomegeometry used, electrostriction
has been
been shown
shown to
to play
play aa small role in
electrostriction has
self-focusing
around30
30ns.42
ns.42 We
We
self- focusingeffects
effectsfor
for pulse
pulse durations
durations around
use
n2 value of
of 0.95
0.95X10"
13 esu
use the n2
X 10 -13
esureported
reportedby
by Feldman
Feldman et
et
al.
42 for
al.42
fornanosecond
nanosecondpulse
pulsedurations
durations in SiO2
Si02.. We
We find
find that
that the
the
breakdown powers
powers reported by
by Merkle
Merkle et
et al.51
al. 51 for
for Corning
Corning
7940
1064 nm and equal to 0.07P2
7940 were
were less
less than
than 0.08P2
0.08P2 at
at 1064
0.07P2 at
532
self-focusing
532 nm.
nm. Therefore,
Therefore, self
-focusing effects in the work of Merkle
et al.
51 are
of two
al.51
arenegligible.
negligible.They
Theyreport
report a decrease by a factor of
in threshold in
in going
going from
from 1.06
1.06 pm
/im to
to0.53
0.53 µm.51
/xm. 51
We
re-examined
We have
have also reexamined our
our own
own results published
published in
Refs.
Refs. 33 and
and 32.
32. In Ref.
Ref. 33 we
we used
used beam
beam distortion
distortion and polarization
dependence to verify
verify that
that self
self-focusing
zation dependence
-focusing was
was not
not the
dominant breakdown
breakdowneffect.
effect. However,
However, these
these tests
tests (i.e.,
(i.e., polardominant
ization dependence
dependence and beam distortion) were not conducted
conducted
condition used.
used. For
for each experimental condition
For the
the most part, little
few percent)
of the
(a few
percent) or no adjustment of
the originally
originally published
published
numbers is
is needed.
needed. For
For the ultra-short
ultra -short pulse data (pulsewidth
(pulsewidth
OPTICAL ENGINEERING
/ October
1989
/ Vol.
1139
OPTICAL
ENGINEERING
/ October
1989
/ Vol.2828No.
No.1010/ / 1139
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STRYLAND
VAN STRYLAND
MANSOUR, VAN
SOILEAU, WILLIAMS, MANSOUR,
1054
at 1454
SiO2 at
jum for Si02
14 µm
size of 14
less
ps) and largest spot size
less than 55 ps)
nm, adjustments
as high as a factor of two were needed. These
adjustments as
observed or
trends observed
corrections
do not
not change
change any
any of the trends
corrections do
discussed in
conclusions
drawnfrom
from that
that data as discussed
in the next
conclusions drawn
section.3,32
addition,we
weshould
should note
note that
that we have studied
section. 3' 32 InInaddition,
techniques
many samples of these materials grown by various techniques
over the past
past 15
15years.
years.While
Whilethe
thethresholds
thresholds vary from sample
different
from different
even from
and even
boule, and
boule to boule,
from boule
sample, from
to sample,
is
here is
presented here
samples taken from the same boule, the data presented
optical
"good" optical
similar "good"
consistent with
consistent
with data
data obtained from similar
sample
exceptional sample
quality
material. We
We have
have not found an exceptional
quality material.
samples
the samples
of the
behavior of
that behaved
from the behavior
differently from
behaved differently
here.
reported here.
dependence
size dependence
spot size
5.2. Wavelength,
Wavelength, temporal, and spot
5.2.
self-focusing
ofselfeffects of
theeffects
for the
account for
focusing
Given that we now can account
we can
can unambiguously
unambiguously determine
determine the
in an LID experiment, we
as
such as
dependence of
of the
the threshold
threshold on various parameters such
dependence
pulsewidth, spot size,
size, and
and wavelength.
wavelength. The
The conclusion
conclusion reported
reported
dependence
wavelength dependence
observed wavelength
al. 22 that
by
by Smith et aí.22
that the observed
theory
ionization theory
avalanche ionization
predictions of avalanche
agreed with
with the predictions
agreed
P l as the critical
depended on the scaling using Eq. (3) with P1
depended
decrease in
shows a decrease
Ref. 22 shows
, the
power. Using
Using P2
P2,
the data
data of Ref.
power.
threshold with decreasing wavelength, which isis not
not consistent
consistent
We find
with intrinsic
intrinsic avalanche
avalanche breakdown.
breakdown. We
find similar
similar results
results
with
wavelength
this wavelength
While this
dependence. While
wavelength dependence.
the wavelength
for
for the
multi-intrinsic multi
by intrinsic
predicted by
dependence isis in
in the direction predicted
dependence
damage,54 the
photon- induced damage,54
the dependence
dependence is
is much
much too weak.
photon-induced
process is
As the
the order
order m
m of the
the multiphoton absorption process
As
increased, the
the irradiance
irradiance needed
needed to
to obtain
obtain the same
same absorpabsorpincreased,
inverse ratio of the nonincreases approximately
approximately as the inverse
tance increases
by
linear absorption coefficients.55
This ratio
ratio is
is estimated by
coefficients. 55 This
linear
ExperiI, where
55 to
Wherrett
Wherrett55
to be
be = 10~4
10 -4I,
whereII isis the
the irradiance. Experi10~3
ments indicate
indicate that
that this ratio is =10
-3II (Refs.
(Refs. 56
56 and
and 58).
58). For
For
ments
CdS at
coefficient of CdS
two-photon
example, the
the two
-photon absorption
absorption coefficient
example,
three-photon
its three
cm/GW,
5.5 cm
reported 56 as
is reported56
nm is
0.53 µm
0.53
as 5.5
/GW, and its
-photon
0.01
as 0.01
reported 58 as
coefficient at 1.06
absorption
1.06 pm
µm isis reported58
absorption coefficient
. Thus,
cm3
cm3/GW2
/GW2.
Thus,totoobtain
obtainthe
the same
same absorptance
absorptance at the two
550
different
wavelengthswould
wouldrequire
requirean
an irradiance
irradiance of =550
different wavelengths
GW/cm2
GW /cm2(or
(ormore,
more, theoretically).
theoretically). Four-photon
Four -photon absorption
10
would require
would
require a correspondingly higher irradiance. From 10
µm to 0.5
0.5 jum
µmthe
theexperimentally
experimentally measured
measured irradiance
irradiance threshjum
olds
olds change
change but
but only
only by
by factors
factors of
of two
two to
to four.
four. The
The reported
observation of
of four-photon
four -photonabsorption
absorptionatat 532
532 nm
nm prior
prior to
to
observation
damage by the
the group
group at
at Washington
Washington State University is interesting and
and may
mayindicate
indicatethat
that intrinsic
intrinsic multiphoton
multiphoton absorption
the
damage in the
responsible or
or partially
partially responsible
responsible for
for damage
isis responsible
note,
We note,
selected samples
samplesof
of NaCl
NaC1studied
studiedby
by that
that group.
group. We
selected
however,
that the high
high irradiance used by
by the WSU
WSU group
group of
however, that
550
GW /cm2for
forpicosecond
picosecondpulses
pulsesisis 5.5
=5.5 times
times the
the damage
damage
550 GW/cm2
by
reported by
samples reported
"best" samples
threshold
observedfor
for the
the "best"
threshold observed
pulses. 29 The
Manenkov using nanosecond
The absorptance due
nanosecond pulses.29
be of the order of
then be
to direct four-photon
four -photon absorption
absorption would then
It
, lower
5.5
-3,, which
which isis = 66XX10~3
10 -3,
lowerfor
forthe
thenanosecond
nanosecond pulses. It
5.5~3
is caused
pulses is
seems unlikely
unlikelythat
that if
if damage
damage for picosecond pulses
seems
same mechanism
the same
that the
by intrinsic
intrinsic multiphoton
multiphoton absorption
absorption that
Manenkov. 29
dataofofManenkov.29
nanosecond data
is
for the
the nanosecond
responsible for
is responsible
inconsistencies with
Gorshkov
also found
found inconsistencies
with the avaal. 59 also
Gorshkov et aí.59
of the
damage of
of damage
dependence of
lanche model in the
the temperature
temperature dependence
Ref. 88
of Ref.
authors of
0.53 jum.
µm. We agree with the authors
alkali halides at 0.53
in
and contradictory
contradictory data
data exist
exist for
for m
m = 4 in
"insufficient and
that "insufficient
assign
unequivocally assign
eV) to unequivocally
2.33 eV)
NaCI (E
(Eg== 8.6
8.6 eV,
eV, hv
by = 2.33
NaCl
NsCI
150 + 15
150515
105±15
105315
m=7.2Nm
36 + 4
3634
5
EO(MVIcm)
EB(MV/cm)
0.5
1.06
150315
105315
3634
5
10
15
20
EB(MV/cm)
EgOMVkm)
several
forseveral
SiO2 for
and Si02
NaCl and
forNaCI
E B for
ofEB
dependenceof
Fig. 5. Wavelength
Wavelengthdependence
Fig.
scaled
beenscaled
havebeen
thresholdshave
Thesethresholds
/urn.These
0.53µm.
and0.53
1.06and
at1.06
pulsewidths
pulsewidths at
values
measured values
and measured
P2 and
usingP2
self-focusing
forselfpercent for
by
by a few percent
focusing using
n2 . 43
of
of n2.43
since the
However, since
mechanism." However,
avalanche mechanism."
damage
damage to the avalanche
the
sample to sample,
from sample
considerably from
damage threshold varies considerably
present and
effects are
we
we must
must still
still conclude
conclude that extrinsic effects
are present
and
Additionally,
samples. Additionally,
thresholdsamples.
lower threshold
dominant for the
the lower
dominant
may contribute carriers for
intrinsic multiphoton absorption may
intrinsic
was
evidence for
an eventual
although no evidence
for this was
avalanche, although
eventual avalanche,
an
jum in
0.5 µm
8. At 0.5
Ref. 8.
observed
observed in
in the
the photoacoustic
photoacoustic data
data of Ref.
these wide-gap
wide -gapmaterials
materialsthe
the question
question of the role of intrinsic
these
However, it is
remains. However,
LID remains.
multiphoton
multiphoton absorption
absorption in
in LID
jum and longer intrinsic
unlikely
unlikely that
that for the wavelengths
wavelengths of
of 11µm
is playing a role.
multiphoton absorption is
NaCl at
of NaC1
samples of
13 samples
on 13
We reported damage on
at 11 /zm
µm and
We
from
varied from
thresholds varied
field thresholds
thefield
While the
Ref. 3.3. While
in Ref.
nm in
0.5 µm
0.5
we saw no
of four, we
sample to
to sample
sample by
by as
as much
much as a factor of
sample
dependencies of the
systematic differences
differences in
in the
the parametric
parametric dependencies
the
systematic
were perexperiments were
all experiments
thresholds, although
ELID
ELID thresholds,
although not all
formed for all samples.
samples. Figure 55 shows aa bar
bar graph
graph of damage
damage
size in air of
spot size
focal spot
for aa focal
SiO2 (lower) for
NaCl (upper)
(upper) and Si02
in NaCl
1.06 /zm
7.2 )um
µm for various pulsewidths as indicated, for both 1.06
µm
small corrections
(unshaded) and 0.53
(shaded). The small
corrections for
^m (shaded).
0.53 ,um
self- focusinghave
havebeen
beenincluded
included in
in this
this figure.
figure. Except for the
self-focusing
ELID
the ELID
samples, the
SiO2 samples,
NaCl and Si02
shortest
shortest pulses
pulses in
in both NaCI
to 0.5
1 ^m to
in going from a wavelength of 1µm
threshold isis reduced in
threshold
µm, which
is inconsistent
inconsistent with an intrinsic avalanche model.
which is
/im,
Refs. 44 and
In the avalanche
breakdown model
model of Refs.
and 55 the
avalanche breakdown
In
(i.e.,
limit (i.e.,
field limit
highfield
thehigh
E2ininthe
proportionaltotoE2
ionization
rateisis proportional
ionization rate
by
given by
carriers isis given
ofcarriers
buildup of
short pulse limit). Then, the buildup
N0 exp(aE2t) ,
N
N == Noexp(aE2t)
(10)
(10)
N0 is
where N is
is the carrier density, No
is the
the initial carrier density,
and a is
is aa material
material dependent
dependent constant. This limit corresponds
electrons
the electrons
of the
energy of
in energy
increasein
theincrease
which the
in which
situationin
to the situation
simply proportional
in the conduction
proportional to
to the input
conduction band is simply
says that the
negligible. This says
are negligible.
losses are
all losses
that all
irradiance and that
light
input light
the input
which the
at which
rate at
ionization rate is
is limited by the rate
electrons. It is
band electrons.
beam can supply energy to the conduction
conduction band
carrier
the carrier
when the
occurs when
damage occurs
commonly assumed
commonly
assumed that
that damage
can be solved
(10) can
Eq. (10)
Thus, Eq.
Nc . Thus,
value Nc.
critical value
reaches aa critical
density reaches
dependence:
t^°-5
showing aa tp
field showing
.5 dependence:
breakdown field
for the breakdown
EB =
1
1
/at!
atp
Nr
N
ln' /2
(11)
(11)
No
pulsewidth
this pulsewidth
NaCl this
forNaC1
pulses for
shortpulses
very short
for very
We find that for
We
constant,
is constant,
fluence is
breakdown fluence
dependence
dependence is
is valid
valid and the breakdown
t^° 3 dependence.
weakert-13-3
somewhatweaker
while for Si02
see aasomewhat
we see
SiO2 we
while
No. 10
Vol. 28 No.
ENGINEERING // October
OPTICALENGINEERING
1140
1140 / /OPTICAL
October 1989
1989 // Vol.
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LASER-INDUCED
DAMAGE AND
ANDTHE
THEROLE
ROLEOF
OFSELF
SELF-FOCUSING
LASERINDUCED DAMAGE
-FOCUSING
IUU
100
24
E
20
14µm
IB
.. 1 06m
16
4
Ó
12
10
ó
ff
B
s
Ips
10ps
10ps
lOOps
Ins
100ps
Ins
PULSE
DURATION, ttp
p
PULSE DURATION,
10ns
IOns
For the low field
field limit,
limit, i.e.,
i.e., longer
longer pulses,
pulses, the
the ionization
ionization rate is
is
exponentially
exponentially dependent
dependent on
on E and the
the resulting
resulting pulsewidth
pulsewidth
dependence
dependence isis relatively
relatively weak.4
weak.4In
In Fig.
Fig. 6,6, we
we reproduced
reproduced the
the
theoretical curves
curves derived
derived by Sparks et al.4
al.4 showing the predicted
dicted dependence
dependence of
of the
the breakdown field EB
EB on pulsewidth
and have
have extended
extended the
the pulsewidth
pulsewidth scale
scaleto
to longer
longerand
and shorter
shorter
pulses.
of the
the data
data for
pulses. The overall dependence
dependence of
foraa given
given spot
spot size
size
is
is in
in remarkably
remarkably good
good agreement
agreement with
with this
this theory using
using no
adjustable
intrinsic avalanche
adjustable parameters. However, intrinsic
avalanche ionizaionizapredict aa spot
spotsize
size dependence,
dependence, which
tion does not predict
which isis clearly
clearly
seen
seen in
in the
the data. This relatively
relatively large spot size
size dependence
dependence
may
may well
well be
be due
due to extrinsic materials
materials parameters
parameters such
such as
as
multiphoton ionization of impurities
impurities or defects
defects that provide
the starter
starter electrons
electronsfor
forthe
theavalanche
avalancheN0.3,32
N0 . 3' 32
While
While the
the observed
observed temporal
temporal dependence is consistent with
spot size
an intrinsic avalanche, the wavelength and spot
size dependdependence strongly
phenomena is
ence
strongly indicate
indicate that
that the phenomena
is an
an extrinsic
extrinsic
of materials. In
In addition,
addition,the
thestrong
strongsampleproperty of
to -samsample-to-samin thresholds
thresholdssupport
supportthis
thisconclusion.12,29
ple variations in
conclusion. 12' 29 The
extrinsic nature
damage makes
makes quantitative,
quantitative, first
extrinsic
nature of bulk damage
first
principle descriptions
damage process
process very
principle
descriptions of the damage
very difficult.
difficult.
One problem is
is that
that the good optical materials of
of interest have
very low
low levels
levelsof
ofdefects
defectsand
and impurities.
impurities. One
One solution to this
problem
do experiments
experiments with
with samples
samples prepared with
problem isis to do
with
known type and densities of defects and impurities. This is the
approach we take below.
below.
6.
CONTROLLED DEFECT STUDIES
6. CONTROLLED
The
(which produces,
produces, among other
The effects
effects of
of y irradiation (which
defects,
60 on
defects, E' centers)
centers)60
onthe
the ELID
ELID thresholds of fused silica,
were
were investigated.
investigated. Samples
Samples were
were sliced
slicedinto
into four
four quadrants.
One
was kept as
One quadrant was
as aa control
control (i.e.,
(i.e., no
no irradiation),
irradiation), and
the remaining three quadrants
quadrantswere
weresubjected
subjectedtoto106,
107,, and
106 ,107
10
8 rad
108
rad of
of cobalt
cobalt y irradiation
irradiation from
from the
the Naval
Naval Research
Research
Laboratory
source. Unfortunately,
Unfortunately, the
density of
Laboratory cobalt
cobalt source.
the density
defects
defects cannot
cannot be determined,60
determined,ó0 although
although their effects
effects on linlinear absorption and ELID
ELID can
can be
be measured.
measured. Single
Single specimens
specimens
of three types
types of fused
fused silica
silica were
were tested:
tested: Spectrasil A, B, and
WF
performedwith
with1818nsns(F(FWHM)
W F(water
(water free).
free). Damage
Damage was performed
W H M)
pulses at 1.06
1.06 p,m
Amand
and0.53
0.53/zm
µmfocused
focused into
into the bulk of three 3
mm thick samples using a 40
40 mm focal length lens. Each site
was
was irradiated
irradiated only
only once.
once. The
The ELID
ELID thresholds
thresholds were
were found
found to
to
be
at the
be independent
independent of
of y irradiation at
the1.06
1.06 µm
jumwavelength.
wavelength.
However,
However, significant
significant reduction
reduction in
in damage
damage thresholds
thresholds (up to
40%)
40
%)was
wasmeasured
measuredfor
forthe
the irradiated
irradiated samples
samples at
at 0.53
0.53 µm.61,62
jum. 61 ' 62
effects of selfself-focusing
Again, the effects
focusing were
weredetermined
determined to be negligible by
ligible
by performing
performing polarization dependent
dependent damage
damage meamea-
V
(a)
I
266
532
266 532
100ns
100ns
Fig. 6.
Pulsewidth dependence
dependence of
Fig.
6. Pulsewidth
of the
the rms
rms breakdown
field E8
for
breakdown field
EB for
NaCI at
/urn for
different spot
spot sizes.
sizes. Data
Data are
are scaled
scaled for
NaCI
at 1.06 .em
for three different
self-focusing
. 43 The
self- focusing using
using P2
P243
Thesolid
solidline
linewas
wasobtained
obtained from
from the electron avalanche
avalanche ionization
of Sparks
Sparks et
et al.4
al. 4
ionization theory of
i /^'N'
— WF
--- A
..... B
0Q
0
__...—-*.._„
"^
#= a—*"
90
90
80
80
70
70
60
60
50
50
40
40
30
30
20
20
10
10
5.0µm
7.2µm
22
J
1064
1064
r*
IUU
100
90
90
80
80
70
70
60
60
50
50
40
40
30
30
20
10
n
e=>
ST
-A f^
/ V
v'
— WF
-—A
.......... B
i
!
(b)
1
266
532
266 532
1064
\|nm)
X Inml
Alnml
X Inml
Fig.
Fig. 7.7. Transmission
Transmissionas
asaafunction
function of
of wavelength
wavelength AX for
for the
the three
three
samples of
(a) unirradiated
samples
of SiO2
Si02 (a)
unirradiated and
and (b)
(b) yy irradiated
irradiated with
with 108
10 8 rad.
of the
the various
various fluorozirconate
f luorozirconateglasses
glasses studied.
TABLE V.
V. Composition
Composition of
studied.
Sample
Sample
A
A
BB
CC
DD
EE
FF
Color
Color
Clear
Clear
Green
Green
Green
Green
Green
Green
Violet
Violet
Yellow
Yellow
ZrF4
ZrF4
(mol°/o)
(mot %)
BaF2
BaF,
(mol%)
(mol %)
57
57
34.5
34.5
34.25
34.25
34
34
34
34
33.75
33.75
34.25
34.25
56.75
56.75
56.5
56.5
56.5
56.5
55.75
55.75
56.75
56.75
LaF3
LaF,
AIF3
AIF,
CrF,
CrF3
MnF2
MnF,
(mol %)
(mol"/o)
(mol°/o)
(moth)
(mol%)
(mol %)
(mol%)
(mol
%)
4.5
4.5
44
44
44
44
44
44
4.5
4.5
4.5
4.5
4.5
4.5
4.5
4.5
4.5
4.5
NiF,
NiF2
(mol°/o)
(mol %)
NdF3
NdF,
(mol°/o)
(mol %)
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
11
1
1
0.5
0.5
surements.
jum are substantially
surements. The ELID thresholds at 0.53 µm
lower than those at 1.06
1.06 µm
/zm even for the unirradiated witness
witness
samples.
samples. Avalanche ionization predicts an
an increase
increase in threshold
reduced wavelength.
wavelength. Thus, the ELID
ELID process
old for reduced
process is
is not
not
simply
even for
for the
the witness
witness sample.
simply avalanche breakdown even
sample.
spectra of
Figure 7 shows
shows the linear transmission spectra
of the unirradiated and
and irradiated
irradiated(108
(108rad)
rad)samples.61.62
samples.61 ' 62 Note that this
this
figure
figure shows
shows no
no observable change in transmission at either
either
1.06
show a substantial
substantial change
1.06 urn
µm or
or 0.53
0.53 jitm
µm but does show
change at
0.266 jum
irradiated samples.
0.266
µm for the irradiated
samples. This
This suggests
suggests that the
the
decrease in
at 0.53 µm
jum may be associated with
in ELID
ELID threshold
threshold at
with
the change in transmission
at the
the harmonic
harmonic0.266
transmission at
0.266µm.
^m. We
We will
will
examine
examine this
this relation
relation after
after presenting
presenting data
data that
that shows
shows aa
similar
linear absorption
absorption at
similar dependence
dependenceofofELID
ELID on
on linear
at aa
harmonic.
We also performed
series of LID
performed a series
LID experiments on fluorozirconate (FZ) glasses,
glasses, undoped
undoped and
and doped with Cr, Mn, Ni,
Ni, and
and
Nd. 63 Table
Nd.ó3
Table VVshows
showsthe
theglass
glasscompositions.
compositions. The linear absorpabsorption spectra are given
given in
in Ref.
Ref. 63.
63. The
The doped
doped and undoped FZ
glasses were
were studied
studied at 1.06 jum
µm using 45 ps and 18 ns pulses
pulses and
and
a calculated 5.3
5.3 jum
Measurementsatat0.53
µm focused spot size. Measurements
0.53 Am
jum
were performed
18 ns pulses
performed using 18
pulses and
and a calculated focused spot
size,
size, assuming
assuming negligible
negligible aberrations,
aberrations, equal
Polarequal to
to 2.7
2.7 µm.63
jum. 63 Polarization dependent studies
studies confirmed
confirmedthe
theabsence
focusabsenceofofselfself-focusing effects.
effects.The
The breakdown
breakdown fields decreased significantly at both
wavelengths
FZ glasses
glasses when
when compared
wavelengthsfor
for all
all of
of the doped FZ
compared
with the undoped sample
sample A.
A.
We
present below
below aa two
two-photon
assisted electron
We present
-photon assisted
electron avaavalanche breakdown
model as
as given
given in
in Refs.
Refs. 62
62 and
and 63
63 that
breakdown model
that we
we
justify primarily on
on the
the basis
basis of
of its
its surprisingly good fit of the
data.
experimental results
results for both the irradiated
irradiated silica
data. Our experimental
silica
and FZ glass materials were found to be
be in
in good
good agreement
agreement
with this very simplified
simplified model in which two-photon
two -photon absorption by impurities or defects provides the starter electrons for
an avalanche.
avalanche. In
In this
this model
modelwe
weassume
assumethat
thatlaserlaser-induced
induced
breakdown occurs
occurs when
when the
the density
density of
breakdown
offree
free carriers
carriers generated
generated
combination of
oftwo
two-photon
and avalanche
by aa combination
-photon and
avalanche processes
processes
OPTICAL
/ October
1989
/ Vol.
OPTICALENGINEERING
ENGINEERING
/ October
1989
/ Vol.2828No.
No.1010
/ / 1141
1141
Downloaded From: http://proceedings.spiedigitallibrary.org/ on 01/30/2015 Terms of Use: http://spiedl.org/terms
SOILEAU,
MANSOUR, VAN
VAN STRYLAND
STRYLAND
SOILEAU, WILLIAMS,
WILLIAMS, MANSOUR,
500
1BU
180
i5
S
Nl_
• Spectrasil
A
Spectrasil A
160
160
• tp
tp == 15ns
1 5ns
140
\ff
O
i
jWm
120
100
Fluorozirconate Glass
Gbss
Fharozirconate
X-1064nm
a=
1084 nm
J-'
• À
\ == 532nm
532nm
400 -
tp
tp «
45 ps
=45ps
A
c
/f ;
CO
o 300
S
300
O 200
- >X
•1
>
W loo
«n
80
0
2
1
33
4
-In
(of | at 266m
266nm
In krPI
012345
o
3
2
4
Fig.
Square of
nm versus
versus the
Fig. 8.
8. Square
of the
the damaging
damaging electric
electric field
field at 532 nm
the
negative
negative natural
natural logarithm
logarithm of
of the
the linear
linear absorption
absorption at 266
266 nm for the
irradiated
irradiated and
and unirradiated
unirradiated Spectrasil
Spectrasil A Si02
SiO2 samples.
samples.
reaches some
reaches
some critical
critical value
value Nc
Ne.. In
In the avalanche process the
buildup of free carrier density
density is
is given
given by Eq.
Eq. (10),
(10), where
where we
we
assumed
assumed the
the high
high field
field limit
limit with
with an
an ionization
ionization rate
rate proportional to El.
E|. The
The model
model assumes
assumes that
that the
the initial
initial free
free carriers
carriers
are generated
generated by
by two-photon
two -photonabsorption
absorption from
from impurity states
states
within the bandgap. Therefore,
Therefore, No
N0 can
can be
be written
writtenasasNo
N0 cc
oc n,
where
is the density
density of
of two
two-photon
allowed impurity
where nn is
-photon allowed
impurity or
defect
logarithm of
ofEq.
defect states.
states. Taking
Taking the natural logarithm
Eq. (10)
(10) yields
yields
ln(n) ++ constant
constant
aEB == -ln(n)
.
(12)
The
final assumption
assumption is
that the
the density
density ofoftwo
The final
is that
-photon
two-photon
allowed
wavelength (X)
allowed states
states at
at the fundamental wavelength
is propor(A) is
tional to the linear absorption
at the
thesecond
second harmonic
harmonic(X
(X/2).
absorption at
/2).
For that assumption
assumption Eq.
Eq. (12)
(12) gives
gives
EBla[
X
a -1n(aPi)Iat
lat X/2
A/2
(13)
(13)
where
the linear
linear absorption
absorption coefficient
coefficient at the
where aa is the
the second
second
harmonic
harmonic wavelength
wavelength and
and It is the sample length.
Figure 8 isis aa plot
field at 532
plot of
ofthe
the square
square of the
the breakdown
breakdown field
nm
\n(at) atat266
266 nm
nm for
forthe
theSpectasil
Spectasil A
nm as
as aa function
function of
of -1n(at)
A
sample.
increasing irradiation dosage
dosage goes
goes from
sample. Note
Note that increasing
from
right to left
left in
in this
this figure.
figure. A
A linear
linear relation
relation is
is also
also seen
seen for
for the
the
other samples (B and WF), although
althoughsample
sampleBB shows
shows aa signifisignificant increase
increase in
in absorption
absorption for only the highest
highest y irradiation
level.
level. Figure
Figure 99 isisaaplot
plotof
ofthe
thesquare
square of
ofthe
the breakdown
breakdown field at
1.06
ln(a£) at
at 0.53
0.53 µm
p,m using
using picosecond
picosecond pulses
1.06 /zm
µm versus
versus -ln(a2)
pulses
for
updoped and doped
doped FZ
FZ glasses.
glasses. A similar
for the updoped
similar plot for
for
nanosecond
nanosecond pulses
pulses also
also yields
yieldsaa linear
linear relation.
relation. Plotting
Plotting the
breakdown
ln(a:£) at
breakdown field
fieldsquared
squaredatat0.532
0.532jum
µmversus
versusthe
the -1n(at)
0.266
gives a linear rela0.266 fjLm
µm using
using nanosecond pulses again gives
tion. Similar plots of damage versus linear
linear losses
losses at the damaging
aging wavelength
wavelength show
show no
no systematic
systematic trends.
trends. The
The agreement
agreement
with
with the
the prediction of Eq. (13) is quite good considering the
extreme
extreme simplicity
simplicity of
of the
the model
model and
and the
the assumptions made.
Note that even in cases
cases in
in which
which nanosecond
nanosecond pulses were used
where
is expected
from the
where the
the ionization
ionization rate
rate is
expected to depart from
the EB
E|
dependence
what pulsewidth
pulsewidth or
dependencegood
goodfits
fits are
are obtained.
obtained. At what
irradiance
from an
anEB
E| dependence
dependence becomes
becomes
irradiance the
the deviation from
large isis not
not well
wellestablished.
established. However,
However, we
we found
found that
that for all of
the FZ glasses
glasses where
picosecond data
where both
both nanosecond
nanosecond and picosecond
were
were taken,
taken, the
the reduction
reduction in
in ELID
ELID threshold
threshold for
for the
the doped
doped
samples
samples was
was nearly
nearlyaa factor
factor of
of two
two larger
larger for the picosecond
picosecond
irradiation.
expected in this model
model where
where the
irradiation. This
This trend
trend is expected
starter
avalanche are created
created by
by nonlinear
nonlinear
starter electrons
electrons for
for an avalanche
-In
532nm
-In Joff)
Iarl at 532nm
Fig.
Fig. 9.
9. Square of the damaging
damaging electric
electric field
field at 1064 nm versus the
of the
the linear
linear absorption
absorption at
at 532
532 nm
nm for
negative natural logarithm
logarithm of
for the
the
Fluorozirconate glass samples listed in Table V.
absorption since
since the breakdown
breakdown field
field isis substantially
substantially larger
larger
for picosecond pulses.
pulses.
In spite
spite of
of the
thecomplexity
complexityassociated
associatedwith
withlaserlaser-induced
induced
damage mechanisms for dielectric materials, our
our experimenexperimenare consistent
consistent with
with aatwo
two-photon-assisted
tal results are
-photon- assisted electron
avalanche process.
this model
model is
is corprocess. We
We should
should note that ifif this
implication is
is that
that the
the witness
witness samples
samples at
at 0.53
0.53 µm,
jitm, in
in
rect, the implication
the case of the fused
fused silica
silica samples,
samples, and the
the undoped
undoped glass
glass
(sample A) in the
glass samples are
the case
case of
ofthe
the fluorozirconate
fluorozirconate glass
also
dominated by
by extrinsic
extrinsic defect
defect (or
(or impurity)
impurity) initiated
initiated
also dominated
This conclusion
conclusion comes
comes from
from the
the fact
fact that
thatthese
these samples
samples
ELID. This
are included in
in the
the curves
curvesof
ofELID
ELIDversus
versus In
-ln absorption, and
they fit.
how far we
we can
can take
take this
this simple
simple model
model is not
they
fit. Just how
in presenting
presenting itit is that the data
clear. The primary justification
justification in
fits the prediction. One conclusion,
conclusion, however,
however, is
is certainly true;
these materials
materials is
is dependent
dependent on
on defects
defects and
and
the damage in these
impurities.
CONCLUSION
7. CONCLUSION
clarified the
therole
roleofofself
self-focusing
laser-inducedWe have clarified
-focusing ininlaserinduceddamage experiments
experiments and
and can
can readily
readily account
accountfor
forits
its effects
effects on
With this
this knowledge
knowledge we
we have carefully
measured thresholds. With
examined both our data and
and the
the data
data of
ofothers
others to
to determine
determine
examined
that intrinsic avalanche ionization theory cannot account for
the parametric
parametricdependencies
dependenciesobserved.
observed.Sample
Sample-to-sample
-to- sample
variations, wavelength
wavelength dependence,
dependence, and
and spot
spotsize
size dependence
suggest that damage to transof damage thresholds strongly suggest
dielectric materials
materials isis an
an extrinsic
extrinsic process.
process. In
In aa sense,
sense,
parent dielectric
is good
this is
good news
news in
in that
that the implication is that ELID thresholds
increased as
progress is
is made
made in the materials
materials
olds can
can be
be increased
as progress
areas.
growth and preparation areas.
8.
ACKNOWLEDGMENTS
8 ACKNOWLEDGMENTS
We
of the Office of Naval
We gratefully
gratefully acknowledge
acknowledge the support
support of
Naval
Research,
Research, the
the Florida High Technology and Industry Council,
cil, and
and the
the Defense
Defense Advanced
Advanced Research Projects Agency, and
we wish
we
wish to
to thank
thank D. Griscom of the Naval Research Laborairradiating samples.
samples.
tory for irradiating
9.
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1142
OPTICAL ENGINEERING
/ /October
ENGINEERING
October1989
1989// Vol.
Vol. 28
28 No.
No. 10
10
1142 // OPTICAL
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-FOCUSING
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28 No.
No. 10
10 // 1143
1 143
Downloaded From: http://proceedings.spiedigitallibrary.org/ on 01/30/2015 Terms of Use: http://spiedl.org/terms
STRYLAND
VAN STRYLAND
MANSOUR, VAN
SOILEAU,
SOILEAU, WILLIAMS,
WILLIAMS, MANSOUR,
Martin,
D. Martin,
Bendow, and
B. Bendow,
Soileau, B.
J. Soileau,
M. J.
Guha, M.
S. Guha,
Mansour, S.
N. Mansour,
63. N.
63.
and D.
glass,"
"Laser-induced
"Laser- induceddamage
damageinin doped
doped and
and undoped fluorozirconate glass,"
Natl. Bureau
Bureau of
of Standards
Standards Special
Special Pub.
Pub. 746,108-119,
746,108-119, U.S.
U.S. Government
S
(1985).
Printing Office,
Office, Washington,
Washington, D.C. (1985).
Printing
received
He received
1944. He
in 1944.
born in
was born
Soileau was
M. J. Soileau
the Ph.D.
degree in
in quantum
quantum electronics
in
electronics in
Ph.D. degree
the
Cali­
Southern Caliof Southern
University of
1979
1979 from
from the University
fornia, Los
Angeles, where
where he worked
worked at the
Los Angeles,
fornia,
laser-induced
onlaserCenter for Laser
induced
Studies on
Laser Studies
Center
to wide-bandgap
wide -bandgap optical
optical materials. He
He
damage to
and
Force and
Air Force
U.S. Air
the U.S.
spent
spent six
six years
years in
in the
worked for
seven years at the Navy Michelson
for seven
^m^Mmjm: •of the
faculty of
Laboratory. Dr. Soileau joined the faculty
Texas State
North Texas
Physics of North
Department
Department of Physics
founding member
and was a founding
1 980 and
University in 1980
became the
he became
1987 he
In 1987
Center for
for Applied
Applied Quantum
Quantum Electronics. In
of the Center
Electro-Optics
in ElectroResearch in
for Research
Center for
Optics
first director of the newly formed Center
is a professor
he is
where he
and Lasers
Lasers at
atthe
the University
University of Central
Central Florida, where
professor of
and
interests
research interests
Soileau's research
Dr. Soileau's
electrical engineering
engineering and
and physics.
physics. Dr.
electrical
induced damage
damageto
tooptical
optical materials,
materials, nonlinear
nonlinear absorption
absorption
laser-induced
include laserand
and refraction,
refraction, and
and optical
optical limiting.
degree
BS degree
hisBS
received his
Williamsreceived
E. Williams
William E.
Texas, in
Beaumont, Texas,
University, Beaumont,
Lamar University,
from
from Lamar
1978. He
He then
then attended
school at
graduate school
attended graduate
1978.
North Texas
Texas State
State University,
University, Denton,
Denton, where
where
North
and his
he received
his MS
MS degree
degree in
in 1981
1981 and
his
received his
he
Ph.D. degree
degree in
in 1984,
1984, both
both in physics.
physics. His
His dis­
disPh.D.
sertation, "Parametric studies
picosecond
of picosecond
studies of
sertation,
laserinduced breakdown
breakdown in
in fused quartz and
laser-induced
self-focusing
of selfwith the influence
focusing
influence of
NaCI," dealt with
In
liquids. In
and liquids.
solids and
damage in
on optical
in solids
optical damage
on
984 Dr.
11984
Dr. Williams
Williams joined
joined the
the technical
technical staff
staff of
of
Texas Instruments,
Instruments, Inc.
Inc. (Tl),
(TI), Defense
Defense Systems
Systems and
and Electronics
Electronics Group.
Group.
Texas
While at
evaluated aa number
number of
of optical
optical limiting
limiting technologies for
he evaluated
Tl he
at TI
system level
level applications
applications and was
was cofounder of aa dedicated
dedicated laboratory
laboratory at
at
system
TI
for development
development of
of optical
optical lirniters.
limiters. Since
Litton
at Litton
been at
has been
he has
1987 he
Since 1987
Tl for
Laser Systems,
Systems, Orlando,
Orlando, as aa member
member of
of the
the research
research staff.
staff. His research
Laser
interests include laserinduced damage,
damage, optical
optical lirniters,
limiters, optical phase
phase
laser-induced
processes.
optical processes.
nonlinear optical
by nonlinear
conjugation, and frequency conversion by
Dr. Williams
Williams is currently
and
Laser and
IEEE Laser
the IEEE
OSA, the
the OSA,
of the
member of
currently aa member
Dr.
Electro- OpticsSociety,
Society,SPIE,
SPIE,and
andthe
theAssociation
Association of
of Old
Old Crows.
Crows.
Electro-Optics
(first class honors) in physics from
BS (first
receivedaa BS
Mansourreceived
Nastaran
Nastaran Mansour
from the
the
from
physics from
in physics
(honors) in
MS (honors)
an MS
National
National University,
University, Tehran,
Tehran, Iran,
Iran, an
physics
in physics
Ph.D. in
and aa Ph.D.
Texas, and
Dallas, Texas,
University, Dallas,
Methodist University,
Southern
Southern Methodist
Texas, DenNorth Texas,
of North
Universityof
the University
from the
1988 from
(quantum
(quantum electronics) in 1988
DenResearch
Center for Research
ton.
ton. She
She then
then worked as aa research
research scientist at the Center
Florida,
Central Florida,
of Central
University of
Electro-Optics
in
in ElectroOpticsand
and Lasers
Lasers at
at the
the University
physics at the
of physics
professor of
assistant professor
Orlando.
Orlando. Dr.
Dr. Mansour
Mansour is currently
currently assistant
also on
ran. She
id Baheshti),
National
National University
University (Shah
(Shahid
Baheshti), Teh
Tehran.
She isis also
on the
Laser Division, in
Energy, Laser
Atomic Energy,
of Atomic
research
research staff of the Organization of
dielec­
in dielecTehran. Her
Tehran.
Her research
research interests
interests include optical nonlinearities in
optical
to optical
damage to
laser-induced
materials,lasersemiconductor materials,
and semiconductor
tric and
induced damage
is a member
Mansour is
Dr. Mansour
physics. Dr.
laser physics.
and laser
limiting, and
materials, optical limiting,
member
APS.
and APS.
IEEE, and
OSA, IEEE,
the OSA,
of the
He
1947. He
in 1947.
born in
was born
Stryland was
Van Stryland
W. Van
E. W.
E.
Ph.D. degree
received
received the Ph.D.
degree in
in physics
physics in
in 1976
of Arizona, Tucson,
University of
from the University
Tucson, where
where
on
Center on
Sciences Center
Optical Sciences
the Optical
he worked at the
he
He worked
optical
optical coherent transients. He
worked in
in the
the
multi-production, multi
areas of femtosecond pulse production,
laser-induced
and lasersolids, and
in solids,
photon absorption in
induced
Laser Studies at the
damage
damage at
at the Center for Laser
Los Angeles.
University of Southern California, Los
Angeles.
depart­
physics departthe physics
Stryland joined the
Dr.
Dr. Van
Van Stryland
n 1978
n ivers ity iin
Texas State
Nortih Texas
ment at North
State UUniversity
Elec­
Center for Applied Quantum Electhe Center
informing
and
and was
was instrumental
instrumental in
forming the
in
Research in
forResearch
Centerfor
formedCenter
newlyformed
the newly
joined the
he joined
1987 he
In 1987
tronics there. In
Orlando,
Florida, Orlando,
Central Florida,
of Central
Electro-Optics
Electro- Optics and
and Lasers
Lasers at
at the
the University of
where he is aa professor
professor of
ofphysics
physicsand
andelectrical
electricalengineering,
engineering, working
working in
in
the area
area of
of nonlinear optics.
No. 10
Vol. 28 No.
ENGINEERING /October
1144 / /OPTICAL
OPTICAL ENGINEERING
/ October 1989
1989 // Vol.
1144
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