Picosecond Third Harmonic Generation
in /?-BaB 2 0 4 and Calcite
A. Penzkofer, P. Qiu *, and F. Ossig
Naturwissenschaftliche Fakultat H-Physik, Universitat Regensburg,
D-8400 Regensburg, Fed. Rep, of Germany
*On leave from Shanghai Institute of Optics and Fine Mechanics,
Academia Sinica, Shanghai, Peop.Rep.of China
1. I n t r o d u c t i o n
Phase-matched t h i r d harmonic g e n e r a t i o n has been a c h i e v e d i n metal vapors [ 1 , 2 ]
i n e r t gases [ 3 ] , o r g a n i c dyes [ 4 - 6 ] , l i q u i d c r y s t a l s [ 7 ] and b i r e f r i n g e n t c r y s t a l s [ 8 - 1 4 ] . T h i r d harmonic l i g h t may be generated by t h e d i r e c t t h i r d - o r d e r
n o n l i n e a r i n t e r a c t i o n , v L +v L +v L +v 3 , due t o t h e t h i r d - o r d e r n o n l i n e a r s u s c e p t i b i lity X ^ G *
9
a t e d by c a s c a d i n g t h e second harmonic g e n e r a t i o n ,
v L +v L -^v 2 , and t h e frequency m i x i n g , v 2 + v L + v 3 . The second harmonic g e n e r a t i o n and
the frequency m i x i n g a r e due t o the second-order n o n l i n e a r s u s c e p t i b i l i t i e s X J H G
and X F M • Phase-matching, Ak=0, i s necessary f o r e f f i c i e n t t h i r d harmonic l i g h t :
g e n e r a t i o n . I n b i r e f r i n g e n t c r y s t a l s i t i s achieved by c r y s t a l o r i e n t a t i o n and
angle t u n i n g . In c r y s t a l s w i t h i n v e r s i o n c e n t e r o n l y d i r e c t t h i r d harmonic gener a t i o n i s a l l o w e d w h i l e i n c r y s t a l s w i t h o u t i n v e r s i o n c e n t e r c a s c a d i n g and mixed
( d i r e c t and c a s c a d i n g ) t h i r d harmonic g e n e r a t i o n a r e p o s s i b l e . A double phasematching o f t h e second harmonic g e n e r a t i o n and t h e frequency m i x i n g r e q u i r e s two
s e p a r a t e l y o r i e n t e d c r y s t a l s i n s e r i e s . The subsequent phase-matched second h a r monic g e n e r a t i o n and phase-matched frequency m i x i n g i s most e f f i c i e n t and i s
w i d e l y used [ 1 5 ] . The v a r i o u s phase-matching schemes f o r t h i r d harmonic generat i o n i n n e g a t i v e u n i a x i a l b i r e f r i n g e n t c r y s t a l s a r e summarized i n Table 1.
O
R
I
T
M
A
Y
B
e n e r
E
Table 1 S i n g l e and double phase-matched angle-tuned g e n e r a t i o n o f t h i r d - h a r m o n i c
l i g h t i n negative uniaxial b i r e f r i n g e n t c r y s t a l s (n <n ). D = d i r e c t . C = casc a d i n g . D+C = mixed. IC = i n v e r s i o n c e n t e r .
e
Crystal
Process
Phase-matching
o
Interaction
Contribution
s i n g l e c r y s t a l , s i n g l e phase-matched
w i t h IC
D
THG
=
0
type I
OlOL°L e
type II
type I I I ° L L L " 3
type I
°L°L* 2
type II
+
3
e
w i t h o u t IC
C
A k
SHG . FM*
= 0
A k
0
V
C
e
type I
o o -*e
type II o e L - e
type I I I 2 < V 3
type I
° °L L 3
type I I
type I I I ° L L e i + e
L
3
2
Ak
THG
=Ak
SHG
+Ak
FM
=0
(2)
* eff,SHG
v
vX eff,FM
( 2 )
3
e
D+C
X eff,THG
e
e
2
Y
e
0
> e
L
(3)
(2)
X eff, THG *eff,cas
Y
+ Y
e
3
two c r y s t a l s , double phase-matched
w i t h o u t IC
C
s H G , i =0 and
A k , =0
Ak
ra
2
type I
type I I
a) Cascading t h i r d harmonic g e n e r a t i o n w i t h A k
t o Ak =0 [ 1 3 ] .
312
oo+e
oe-»-e
S H G
1: Xe1f, HG
2: x
* eff.FM
=0 i s l e s s e f f i c i e n t compared
a
n
d
S
( 2 )
Springer Proceedings in Physics, Vol. 36
Nonlinear Optics of Organics and Semiconductors
Editor T. Kobayashi © Springer-Verlag Berlin, Heidelberg 1989
In t h i s paper the s i n g l e phase-matched t h i r d harmonic g e n e r a t i o n i n s i n g l e
c r y s t a l s o f c a l c i t e and e-BaB 0 i s s t u d i e d . C a l c i t e i s a n e g a t i v e u n i a x i a l c r y s t a l w i t h i n v e r s i o n c e n t e r ( t r i g o n a l system, space group R3c, p o i n t group 3m).
B-BaB 0 i s a newly developed n e g a t i v e u n i a x i a l c r y s t a l w i t h o u t i n v e r s i o n c e n t e r
[16,17] ( t r i g o n a l system, space group R3, p o i n t group 3; a h i g h e r symmetry o f
R3c and 3m i s s t a t e d i n [18]). The l a r g e e f f e c t i v e second harmonic c o e f f i c i e n t s ,
the wide t r a n s p a r e n t waveband (190 - 3500 nm), and the high damage t h r e s h o l d
make BBO very important f o r second harmonic g e n e r a t i o n and frequency mixing i n
the u l t r a v i o l e t s p e c t r a l r e g i o n [19-24]. e-BaB 0- was a p p l i e d s u c c e s s f u l l y i n
the second harmonic g e n e r a t i o n o f femtosecond pulses [25,26].
2
2
4
4
2
Table 2 g i v e s a l i s t o f c r y s t a l s t h a t have been a p p l i e d t o t h e phase-matched
t h i r d harmonic g e n e r a t i o n i n a s i n g l e c r y s t a l .
Table 2 R e a l i z e d phase-matched t h i r d harmonic g e n e r a t i o n i n s i n g l e
A l l c r y s t a l s a r e n e g a t i v e u n i a x i a l . D = d i r e c t . D+C = mixed.
Crystal
Class
References
Laser
Interaction
crystals.
[nm]
Calcite
t r i g o n a l , R3c
KDP
ADP
6-BaB 0
2
4
D
Q-switched
Q-swi tched
Mode-locked
694.3
1060
1054
8,9
11,14
t h i s work
t e t r a g o n a l , 42m
D+C
Q-switched
1064
11
t e t r a g o n a l , 42m
D+C
Q-switched
Mode-locked
1060
1060
10
10
t r i g o n a l , R3(R3c)
D+C
Mode-locked
1054
t h i s work
2. Fundamentals
The g e o m e t r i c a l arrangement o f phase-matched t h i r d harmonic g e n e r a t i o n i n a
s i n g l e c r y s t a l i s sketched i n F i g ^ l . The angle 0 between the c r y s t a l f i x e d z - a x i s
( o p t i c a x i s ) and wave-vector ic (||ic ) i s a d j u s t e d t o phase-matching. a and a a r e
the w a l k - o f f angles between t h e r a y d i r e c t i o n s o f e x t r a o r d i n a r y and o r d i n a r y
polarized l i g h t .
L
3
L
3
Col l i n e a r phase-matching o f mixed o r d i r e c t THG r e q u i r e s
A
k
=
k
e 3 -
a L -
k
k
b L -
k
c L
=
0
»
(1
a,b,c i n d i c a t e t h e p o l a r i z a t i o n s o o r e o f t h e
of t y p e - I I phase-matching i t i s k3e-2k L-k L=0.
to t h e r e f r a c t i v e i n d i c e s n by k=27rnv/c where
vacuum l i g h t v e l o c i t y . The o r d i n a r y r e f r a c t i v e
s t a l o r i e n t a t i o n . The e x t r a o r d i n a r y r e f r a c t i v e
by
O
e
0
n n
= —y—5—
n (0)
p
n
0
and n
o
o
1/2
(n cos 0 + n s i n 0 )
e
Z
e
Z
Z
Z
5
fundamental waves. In the case
The wave-vectors a r e r e l a t e d
v i s the frequency and c i s t h e
index n i s independent o f c r y index depends on t h e p o l a r angle 0
0
0
( )
2
1 / z
are t h e p r i n c i p a l r e f r a c t i v e
>
indices.
l
Fig.l
L.eff
Schematic geometrical
arrangement
The w a l k - o f f angle a l i m i t s the o v e r l a p length o f the o und e pump l a s e r
components i n the case o f t y p e - I I and t y p e - I l l phase-matching t o
L
Ad
A
L
(3)
L e f f * 2S[
f
where A d i s the pump pulse beam diameter. The w a l k - o f f angle a a l l o w s t h i r d
harmonic g e n e r a t i o n over the whole c r y s t a l l e n g t h but a m p l i f y i n g i n t e r a c t i o n
between pump and t h i r d harmonic l i g h t occurs o n l y w i t h i n an e f f e c t i v e l e n g t h
L
l
3
(4)
3 , e f f * 2£
3
For femtosecond pulses the temporal o v e r l a p o f the o and e pump p u l s e components o f t y p e - I I and t y p e - I l l phase-matched c r y s t a l s may be l i m i t e d by the group
v e l o c i t y d i s p e r s i o n . The group r e f r a c t i v e index i s
v
°9 " i
(5)
M
n 3v
The time d e l a y between o r d i n a r y and e x t r a o r d i n a r y rays i s given by ( 6 t / 6 j , )
[ g o L ~ g e L ( ) ] / o and t h e . o v e r l a p l e n g t h i s l i m i t e d t o
n
n
0
o L e L
At,
o
(6t/6£)
2
=
c
(6)
oLeL
The d u r a t i o n o f t h e generated t h i r d harmonic p u l s e i s given approximately by
At3 .
where il
+ («t/a£)23o|_£f j
1
^ ;
i s the shorter length o f
(7)
iQ,
and « .
.
Lfeff
The energy c o n v e r s i o n e f f i c i e n c y o f t h i r d harmonic g e n e r a t i o n i s given by
112,13]
n
E
_
K
2.2- i
,2 s i n (Ala/2) -,.
.
.
v
OlJ eff I
)
2
f(Ad ,AOL,Av ,At )
A
x
U
|
a
2
)
L
n
A
L
t
L
k comprises constant f a c t o r s . The f u n c t i o n f takes care o f t h e r e d u c t i o n o f conv e r s i o n e f f i c i e n c y due t o the f i n i t e beam diameter A d L , the divergence A O , t h e
s p e c t r a l width A v L , and t h e p u l s e d u r a t i o n A t L o f t h e pump p u l s e .
l
3. C r y s t a l
data
The d i s p e r s i o n o f the p r i n c i p l e r e f r a c t i v e i n d i c e s n and n o f c a l c i t e [271
and BBO [19] are d e p i c t e d i n F i g . 2 . The t r a n s m i s s i o n s T a r e shown i n F i g . 3 .
The t y p e - I , I I , and I I I phase-matching angles o f d i r e c t THG i n c a l c i t e and o f
mixed THG i n BBO a r e p l o t t e d i n F i g . 4 . The corresponding w a l k - o f f angles a
and a are diagrammed i n F i g . 5 .
0
e
L
3
The angular dependence n ( ) / n ( O p M )
shown i n Fig.6a f o r X =
1.054 um (A0 =O, Av =0, A d L = « ) . AG
i s t h e FWHM o f the a n g u l a r detuning curve.
0
o
E
L
L
Fig. 2
B
B
0
i
s
L
1 / 2
0.5
WAVELENGTH
f
E
1
2
x
turn]
Q2
3
0.5
WAVELENGTH
R e f r a c t i v e i n d i c e s o f 6-BaB 0
2
( s o l i d ) [19] and c a l c i t e
4
Fig.3 S p e c t r a l t r a n s m i s s i o n o f 6-BaB 0
dashed)
2
4
{i
3
1
WAVELENGTH X [um]
= 6 mm, s o l i d ) and c a l c i t e (i - 33 mm,
Fig.4
2
3
WAVELENGTH
L
turn]
(dashed)[27].
j
2
X
Type-I, I I , and I I I phase-matching i n 6-BaB 0
2
4
i i i i i i i i i i i i
1
2
x
[|im]
L
(a) and c a l c i t e (b).
Fig.5 Walk-off angles a ( a ) and a ( b ) o f BBO ( s o l i d and dotted) and c a l c i t e
(dashed, only t y p e - I I i s shown).
L
3
i/2
"inverse p r o p o r t i o n a l t o t h e c r y s t a l l e n g t h i. A G
* versus wavelength
i s p l o t t e d i n Fig.7 f o r c a l c i t e and BBO. The i n t e r n a l divergence o f t h e pump
i n order t o a v o i d remarkl a s e r r a d i a t i o n , A? L0, i^nft >» should be l e s s than A G
A 0
1
S
1 / 2
A
J\/2
T
_
r
able l o s s o f e f f i c i e n c y ( e x t e r n a l divergence angle
AG,
n
oL L,int)A 0
The frequency dependence n ( v ) / n ( v ) a t a f i x e d angle i s s i m i l a r t o the
angular dependence a t a f i x e d wavelength. n ( v ) / n ( v ) o f BBO i s d e p i c t e d i n
Fig.6b ( A G = 0 , A V = 0 , A d = « ) . Phase-matching i s a d j u s t e d t o V~l = X = 1.054 nm.
i/2
P
l detuning curve. Av w i s i n v e r s e p r o p o r t i o n a l
to t h e c r y s t a l l e n g t h i. A $ £ , versus wavelength i s d i s p l a y e d i n F i g . 8 . The
s p e c t r a l width o f t h e pump l a s e r A v should be l e s s than A v
i n order t o
avoid remarkable l o s s o f e f f i c i e n c y .
E
E
L
E
l
A v
i
s t
h
l
e F
W
H
M
o
f t
E
L
L
h
e s
e
c
L
t
r
a
?
1 / 2
L
1 / 2
The group v e l o c i t y d i s p e r s i o n l i m i t s t h e temporal o v e r l a p (Eqs.6 and 7 ) .
The curves o f (&t/6i)
and (<$t/<5£)
a r e d e p i c t e d i n Fig.9a and 9b, r e spectively.
oLeL
e3oL
1
|
A
1 1 '•'"•TV|VI
1—» 1 |
'
- (a)
UJ
F
c
a
Z
z
:
-1
10
/
jOL
•
ui
" , A
i
PM
li
'
I
•
11 • / 1
-10
1
0-0
' ii
i
10
Cmrad]
[cm" ]
9-\
1
.6 Angular (a) and s p e c t r a l (b) detuning curves o f 3-BaB 0. a t x.
f o r t y p e - I I phase-matched mixed THG (i = 0.72 mm).
2
0»-—I
1 1 1 1 1 I
1
I
I
I
2
WAVELENGTH
I
1.054 um
I L
3
x
L
dm]
Fig.7 H a l f w i d t h o f angular t u n i n g curves f o r BBO ( s o l i d ) and c a l c i t e
o n l y t y p e - I I ) . Mixed THG.
(dashed,
WAVELENGTH x, [|tin]
F i q . 8 H a l f w i d t h o f s p e c t r a l t u n i n g curves f o r BBO ( s o l i d and d o t t e d ) and c a l c i t e (dashed, o n l y t y p e - I I i s shown). Mixed THG.
8
I V
\\\
£
-Si
•
-
(b)
w
o
-f> 0
mm,
' -^^^ -
i
£
41
-I
i
.
.
.
,
i
.
_JL-——
"
mmm
+-*
«o
S 0
1
1 — J
1
J
1
1
WAVELENGTH x
1
L
1
'
1
»
'
'
'
l^ml
Fig.9 Time d e l a y s (&t/6i)oLqL
(a) and ( 6 t / 6 £ )
(b) f o r mixed THG i n BBO
( s o l i d ) and d i r e c t THG i n c a l c i t e ( o n l y t y p e - I I i s shown).
e 3 o L
4. Experimental
The experimental setup i s shown i n Fig.10. S i n g l e picosecond l i g h t pulses o f
a p a s s i v e l y mode-locked Nd-phosphate g l a s s l a s e r ( A t - 5 p s , A = 1.054 Mm)
are used as pump p u l s e s . The energy c o n v e r s i o n e f f i c i e n c y o f t h i r d harmonic
l i g h t versus i n p u t pump p u l s e peak i n t e n s i t y i s measured and the angular detuning
curves a r e determined. The c a l c i t e c r y s t a l i s 2 cm long and the l e n g t h o f t h e
B-BaB 0 c r y s t a l i s i = 7.2 mm. In some c a l c i t e measurements a c y l i n d r i c a l l e n s
i s i n s e r t e d t o generate a l i n e - f o c u s which i n c r e a s e s t h e l i g h t i n t e n s i t y a t t h e
c r y s t a l w i t h o u t i n c r e a s i n g the r e l e v a n t l a s e r divergence A G i n t h e plane spanned by the o p t i c a x i s and the l i g h t propagation d i r e c t i o n .
L
2
L
4
l
M.L.LASER 1
— | SWITCH [
\
PM
CR
F
- HAMPLIFIERI
\
— '*
i
/
i
cjn SA
6
[J]PD2
PD1
Fig.10 Experimental setup. PD1, PD2, p h o t o d e t e c t o r s . SA, s a t u r a b l e absorber
(Kodak No.9860) f o r peak i n t e n s i t y d e t e c t i o n [28]. CR, c r y s t a l . F, f i l t e r . PM,
photomultiplier.
5. R e s u l t s
Type-II phase-matched mixed (BBO) and d i r e c t
angular d e t u n i n g curves n ( o ) / n ( O p ) o f BBO
For BBO the s p e c t r a l width o f t h e pumg l a s e r
c a l c i t e two curves a r e d e p i c t e d f o r A v L = 10
modulated p u l s e s ) .
E
E
M
( c a l c i t e ) THG a r e i n v e s t i g a t e d . The
and c a l c i t e are shown i n Fig.11.
i s A v L = 10 cm" . In the case o f
cm" and A V L = 40 cm" ( s e l f - p h a s e
1
The phase-matched THG energy c o n v e r s i o n e f f i c i e n c y versus pump pulse peak i n t e n s i t y i s d e p i c t e d i n Fig.12. A t t h e h i g h e s t i n t e n s i t i e s a p p l i e d c o n v e r s i o n
e f f i c i e n c i e s o f n » 0.01 ( I
= 5xl0
W/cm )-and n * 8 x l 0 " ( I
= 1 0 W/cm )
have been obtained f o r BBO and c a l c i t e , r e s p e c t i v e l y . The damage t h r e s h o l d o f
c a l c i t e i s I h,c > 10 W/cm and t h e damage t h r e s h o l d o f BBO i s I t h , B " 10 W/cm
[18,22] f o r s i n g l e pulses o f 5 ps d u r a t i o n . A t pump pulse i n t e n s i t i e s s l i g h t l y
below t h e damage t h r e s h o l d very high c o n v e r s i o n e f f i c i e n c i e s a r e expected i n
both c r y s t a l s .
1 0
E
0
2
5
L
E
1 1
0
2
L
2
2
t
The e f f e c t i v e n o n l i n e a r s u s c e p t i b i l i t i e s xlW a r e determined by comparison o f
the measured energy c o n v e r s i o n e f f i c i e n c i e s n w i t h c a l c u l a t i o n s (Eq.5). The obt a i n e d values are l i s t e d i n Table 3 t o g e t h e r w i t h other c r y s t a l parameters. A
E
3
4
2
1
o
INTERNAL DETUNING ANGLE 0-e
1
pM
2
[mrad]
Fig.11 THG c o n v e r s i o n e f f i c i e n c y versus detuning angle f o r BBO o f 0.72 cm l e n g t h
(a) and c a l c i t e o f 2 cm l e n g t h ( b ) . A 0 L =5x10
r a d . ( l , o ) , A v L = 10 cm" .
( 2 , A ) , A V = 40 cm" . Type-II phase-matching.
1
1
l
d e t a i l e d a n a l y s i s o f the e f f e c t i v e s u s c e p t i b i l i t i e s i n d i c a t e s t h a t x !L ™,
x >
a r e o f t h e same order o f magnitude f o r BBO [ 1 3 ] .
"'
(
(2
r
and
e
6 £ f fCclS
~ i — i
10
z
o
i
11—r—
i i |
-
QC
HI
> 10
z
o
u
1
/
2
V)
\
i
y\ 11
i
/
/
\\y\\
1
Ith.C '
-
y
4 _
—
-
-
6
UJ
LLt
10
i
i i i t
10*
i
i
10*
i i i
i
i
11
i
10"
INPUT PEAK
1
I
10"
INTENSITY
i f f
1
10°
TW/cm ]
I
2
0L
Fig*12 Energy c o n v e r s i o n e f f i c i e n c y o f BBO (curve 1 , 0 ; i = 7.2 mm) and c a l c i t e
(curve 2,A; % • 2 cm). Type-II phase-matching. A 0 L = 10" r a d . A\>L = 20 c n r .
The damage t h r e s h o l d s I
(BBO) and I
( c a l c i t e ) are i n d i c a t e d .
4
t h / B
1
t h f C
Table 3 Phase-matched t h i r d harmonic g e n e r a t i o n o f picosecond pulses o f a
Nd-phosphate g l a s s l a s e r i n c a l c i t e U = 2 cm) and 6-BaBpO- (i = 7.2 mm).
A t = 5 ps, X = 1.054 nm.
L
L
Parameter
Calcite
System
trigonal
trigonal
P o i n t group
3m
3 (3m)
Space group
R3c
R3 (R3c)
Process
(ooe+e)
[rad cm]
°l/2 *
Av
£
2.3x10
1 / 2
[°]
[°]
(6t/6£)
e3oL [ps cm' ]
< /6A)
1
5 t
o L e L
x
[m V ]
Y
[m V- ]
Y
[m V- ]
2
eff,THG
(2)
* eff,cas
(3)
* eff
2
2
3x10-24
3.7
6.75
4.45
5.85
4.05
1.7
2.0
[W cm" ]
1 1
2 4
(2.1x10-16 esu)
- 5
a )
2
OL
- 2 3
6.6xl0
- 2 3
1.3x10-22 (9.2x10 "
0.01
- 10
* 1
+ 1
1 3
W/cm . b: I
6.4xl0
> 10
n(I
5x10
10
-4
2.1
8xl0
2
10
3.4xl0
4
2
2
(ooe+e)
8.8
3x10 "
- 2
^ E
OL
_
2.2
[ p s cm" ]
1
type-II
47.4
35.96
A
4
D +C
type-II
PM
a: I
2
D
Phase-matching
0
6-BaB 0
W/cm .
2
b )
1 2
1 S
esu)
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