4lassarljusrtt3 3nstiiuir of (Errljnology
Physics Department
8.13-814
Ctttiwtiirwrii 76
Side Light From a Helium- Neon Laser
READ APPENDIX I BEFORE BEGINNING!
I.Theory:
In 1917, Einstein made an investigation of the thermodynamics of an
assembly of atoms in equilibrium with a radiation field. Elementary
arguments based on the Boltzman distribution law and on Planck's
radiation law led him to several conclusions. We will consider here the
simple case involving transitions between two states, the upper one
labeled 2, and lower labeled 1. Suppose there are n t atoms
instantaneously in the upper state and n2 in the lower. Then: ,
1. The rate at which energy is absorbed from the field by the atoms
going from I up to 2 is given by:
-dp(co)/dt = Ai2n l
where p(co) is the energy density of radiation at the transition
frequency, and A 12 is called the coeffient of induced absorption.
2. The rate at which energy is emitted into the field by the atoms
going from 2 down to 1 is given by:
dp(o>)/dt = A21n2p(a>)fta> + B2ln2 1Ta>
where A21 is the coeffient of induced emission and B21 is the coeffient
Page 16-2
of spontaneous emission.
3. A
= A 12
Thus, neglecting spontaneous emission for the moment, we see that
the total energy added to the radiation field will be proportional to (n2
-DI), This gives us our first requirement for lasing
in order to
amplify light by stimulated (i.e. induced) emission, we must keep more
atoms in the upper state than in the lower, that is n2 > nt. This state
of affairs is called a population inversion, since under conditions of
thermodynamic equlibrium, n2/nj = exp[-15a)/kT] < 1.
u
To get the condition for amplification, we must consider the
properties of both the induced and the spontaneously emitted radiation.
The induced radiation is emitted in the same phase and direction as the
wave which stimulates it. However, spontaneous-emitted radiation has a
random phase and direction relative to the incident.
(
In the lasers used in the laboratory, population inversion is
produced by collisions between helium and neon atoms. The discharge tube
is filled with 90% helium and 10% neon. A DC discharge through the tube
excites the helium atoms to metastable excited states
metastable
because angular momentum selection rules prohibit electric dipole
transitions
and they can deliver their excitation energy to the neon
atoms by collisions. The lower state of the laser transition decays very
rapidly once reached, so the net effect is a population inversion
between the upper and lower laser and therefore amplifying power ('gain')
at the frequency corresponding to the energy difference between the
states. See Figure 1 for an energy level diagram.
By providing feedback, a system with gain can be made into an
oscillator. In this laser, the feedback is provided by putting the laser
inside of a high Q Fabry-Perot resonator.
A standing wave then builds up between the mirrors of the
Fabry-Perot. Considering the standing wave as two beams traveling in
opposite directions, one of these beams inside a typical laser cavity may
reach an intensity of 5 watts/cm 2, or more than 30 times the intensity of
visible sunlight striking the earth. Less than 1% of this light is
transmitted through the mirrors as output, since if much more were
brought out, the losses would exceed the gain and it would not oscillate.
}»
^~^
Helium-Neon Laser
K'ellum
Upper Neon
laser levels
r.ietustable states
3.39^
(5s)
20,6 oV
20.3 eV
19.3 eV
(| 5 )(2s)
(strong infrared)
Collisi on
Transfer
He-^Ne
( 3 S)
(4s)
6328 A
(strongest
visible)
(3p)
l8.7eV
f
(strong infrared)
Electron
Collisiona!
'Excitation
5S45 A
(3s)
16,6 cV
Lacer
Transition
Cround
States
FIGURE
I
Page 16-3
When the discharge is on, but the system is not lasing, the He-Ne
collisions will give rise to a high population of atoms in the upper
laser level of neon (the 5s'01* level for a laser operating in the
visible). The side-light spectrum of such a discharge is the normal one
for the given operating, with fairly intense lines representing
transitions originating at the 5s'ol level. During the lasing process
however, most of the transitions originating at the 5s'01 level will
terminate at the 3p'l2 level as a result of stimulated emission, giving
= 6328 A). The side-light spectrum
rise to the intense laser output (X
•
should now show far weaker spontaneous transitions originating at the
upper laser level. Correspondingly, many more atoms now reach the level,
so the side-light spectrum should show increased intensity in those lines
representing transitions originating at the lower laser level.
%
-s
* Modified Racah notation. See AIP Handbook, p.7 - 46.
II. Experimental Procedure.
The purpose of the experiment is to compare the side light spectra
when the discharge tube is lasing (L) and when it is not lasing (NL). It
may seem that all the data needed for comparison would be contained in
two data runs, i.e. lasing and not lasing. However, the difference in
the two spectra is fractionally very small, of the same order as noise in
this experiment. This is not at all an uncommon case in experimental
physics, so here you will learn techniques for using a Phase-Lock
Amplifier to extract small signals.
•• v
1) Using the setup in Figure 2, take spectra with the tube lasing
and not lasing. Use the high speed on the recorder. Take two spectra
for not lasing at different sensitivities by controlling the slit size on
the monochromator. One spectrum should have the largest lines on scale;
the other should have higher sensitivity to show the smaller lines.
Stay within the range 200 to 900 on the monochromator, and mark your
spectra when you begin and end with the appropriate setting. These
numbers are supposed to relate to nanometers, but the calibration can
easily be thrown off by running over range, and linearity is not very
good besides. Therefore, use your spectrum (NL) to calibrate the
monochromator using the Handbook Tables.
The Phase-Lock Amplifier. The small signal difference between lasing and
not lasing should be obvious in your two spectra. The Phase-Lock
^
^-^
Helium-Neon Laser
iL
</)
4-
o
c
0
•^
o
D
d
(A
it
tf
X.
^-^^"^
LL
t/t
}
16-4
amplifier can extract and amplify this difference, which is what
you're
really interested in. Here's how it works.
By chopping the laser beam, we turn the laser on and off.
the signal around 5400A. You should see this:
Observe
J.c.
This is an a.c. signal riding on a much larger d.c.signal. A satura
ted
photodiode provides a reference signal at the chopping frequency:
from
T, determine F. First, the PLA puts both signal and reference
through a
narrow bandpass filter which passes only the fundamental frequen
cy. The
monitor allows you to observe both filtered signal and
filtered
reference. Tune for maximun amplitude around F.
signal
Next the reference goes through a zero crossing detector to giv
e a
square wave. Note that regardless of the shape or symmetry
of the
reference fed in, at this point there is a perfect square wave.
This
5
square wave ^ multiplied with the signal. Ths result depends on the
relative phase. Tune For a rectified sine wave. This can be observed
with the monitor on mix.
Next, the signal goes through an integrator with variable time
constant. This gives the r.m.s. dc value which is plotted. This r.m.s.
value is proportional to the signal difference which we want to measure.
It can go positive or negative. You may also want two different
sensitivity spectra here. The sensitivity knob controls signal
amplification.
After tuning and adjusting the phase of the phase-lock amplifier,
connect the output from the rear of the phase-lock amplifier to the
recorder. Since the output of the PLA is a current proportional to the
signal and the chart recorder is a voltage measuring device, a resistor
must be put across the PLA output. To make the recorder sensitivity
adjustable, use a potentiometer. Observe grounds. R.un over the same
spectral range as you did for the ordinary spectrum. Again, obtain two
spectra, one with all the lines on scale and one with a higher
sensitivity. Try different slit widths and different settings of the
time constant control.
The rnonochromator is accurate to ±300A or so, but fitting a straight
line to chart position vs wavelength should be accurate to ±15A or
better. Identify the strongest lines first, then use a preliminary fit
to identify others. Remember that the gas mixture is 90% Helium.
V
%
Page 16-6
IMPORTANTIf the laser will not lase, do not attempt to adjust it,
it will
only make it worse.
III. Analysis:
Using the American Institute of Physics Handbook
, or some other
suitable source:
1) Find the transitions corresponding to observed lin
es in the
side-light spectrum. Explain all the changes (or lack
thereof) in their
intensity when the lasing is stopped.
2] Describe quantitatively your main sources of error.
What is the
source (or sources] of noise in the cignal? What
factors limit the
resolution of the system?
3] The percentage change in intensity of several of the
Ne lines
(between L and NL conditions] can be determined ap
proximately with the
oscilloscope. Set the diffraction grating to a wa
velength whose
intensity has been found to change with lasing. Judiciou
s use of both AC
and DC coupling on the oscilloscope will permit you
to measure this
change. How is this small fractional change in intensit
y explained?
4] How does the relative response of the photomultip
lier vary with
wavelength?
5] What is the strong line at ~ 7800 A in the DC spectrum
?
6] What is the natural width of the 6328 K line? What
is the width
of the sidelight in this line? What is the width of the
laser line?
What is the spacing between cavity modes?
7) What fraction of the neon atoms in the upper state
of the laser
line decay by stimulated emission? What is the spectr
al energy density
of the laser line in the cavity?
(Optional] With the guidance of a TA, measure the spe
ctrum of the direct
laser beam.
Page 16-7
Hopefully Helpful Hints
g
Remember: The most important part of the analysis is identifyin
not
the transitions which change intensity when the laser is lasing/
do
lasing, and explaining the change using population arguments. To
The
this, it helps to understand the notation in the AIP handbook.
to the
complications of the Systematic (modified Racah) notation are due
the
pattern of electrons in an excited Neon state. In addition to
ation
electron which has been excited to an upper level, a complete not
se
must keep track of the five outer electrons left behind. Each of tho
angular
electrons has an orbital angular momentum of 1 and a spin
inary
momentum of 1/2. (All angular momenta are in units of-ft.) Ord
r
ula
ang
l
tota
e
sibl
pos
to
lead
ld
wou
m
ntu
me
mo
r
ula
ang
of
addition
after
momentum of the five electrons of 1/2, 3/2, 5/2, ... 15/2, however,
3/2
taking into the Pauli exclusion principle, we find the only states of
mentum
mo
r
ula
ang
the
h
wit
te
sta
a
s
ote
den
e
prim
The
.
wed
allo
are
1/2
and
ntum
of the whole shell = 1/2. Now, if we denote the orbital angular mome
ntum
of the valence electron by L, we find that K, "the total angular mome
ume
of the atom exclusive of the spin of t.he valence electron", can ass
the following values:
- *NW
(L+3/2X (IX3/2H .... |L-3/2|, |L-1/2|
The first subscript is (K-l/2). The second subscript is the total
angular momentum, J, of the atom with possible values:
(K-l/2),
or
|K-1/2|
The rest of the notation is standard and is explained in any
and
spectroscopy textbook (see, for example, Hertzberg Atomic Spectra
Atomic Structure).
Appendix I:
Effect of Output Beam of Laser on Human Eye:
In this appendix, we will estimate the effect of a laser beam on the
might
e
On
.
eye
the
on
ctly
dire
fall
to
e
wer
m
bea
a
h
suc
if
eye
an
hum
rce, its
expect that if any eye damage were to be caused by an intense sou
the
severity would be proportional to the power incident per unit area on
\
""""'
retina. As a point of comparison, let us consider the flux of light on
the retina for an eye focused on the sun on a clear day, :;ince this is a
light of intolerably high intensity with wKick we are all familiar.
Sun
z^ Image
At the earth's orbit, the sun subtends and angle of about 1/2 degree and
the solar power incident on an area of 1 cm2 is about 0.14 watts. The
diameter of the pupil under normal outdoor conditions is about 0.4 cm.
Thus, if one were to look directly at the sun, about 0.018 watts would
enter the eye. The image formed by the lens of the eye on the retina
will cover an area of about 7T(L sin i?/2)2, where 1? is the angle subtended
by the sun and L is the distance in the eye from the lens to the retina,
about 2.5 cm. This implies an average power per unit area of retina of
P = 0.018 watts/(7rL2 sin2 tf/2) = 40 watts/cm2
For a He-Ne gas laser, to a good approximation, we may assume a
point source. An output of Imw from the exit mirror is about correct for
the unit we are using. At the furthest distance that one could get in
from the laser in the lab (several meters) at least 25% of this power
would enter the pupil of the eye, about 0.5 cm in diameter under normal
room lighting. To find the size of the image on the retina, diffraction
must be taken into account and so neglecting all but the zero order part
of the diffraction pattern, the size of the image has a radius R=1.22LX/a
where L is the wavelength, a is the diameter of the lens, and L is given
above. Taking a = 0.5cm, X = 6328 A, we have R = 3.86xlO~ 4 cm or we
find an average flux of P = 533 watts/cm2 at least 13 times the
corresponding figure for the sun. This is certainly enough the cause a
severe burn on the retina of the eye. DO NOT look directly into the
beam, or at its reflection from a polished surface.
Page 16-9
References:
1. 8.14 Optical Pumping write-up (exp #11). Informatioa on the
process of population inversion. See especially Appendix on Lasers,
available in 4-348.
2. R. Feynman et al., Lectures on Physics. Addison-Wesley, 1965.
3. Appendix II (on rack in 4-348) on cavity modes.
4. Reference booklet with various articles on lasers etc. In
reference drawer rm 4-352.
5. American Institute of Physics Handbook.
wavelength tables.
Neon and helium
j