Download NEW INFRARED NOBLE GAS LASER TRANSITIONS BETWEEN 3y

NEW INFRARED NOBLE GAS LASER TRANSITIONS
BETWEEN 3y AND 18y
by
EDDIE L. BROWN, B.S. in E.E.
A THESIS
IN
ELECTRICAL ENGINEERING
Submitted to the Graduate Faculty
of Texas Tech University in
Partial Fulfillment of
the Requirements for
the Degree of
MASTER OF SCIENCE
IN
ELECTRICAL ENGINEERING
Approved
Accepted
December, 19 79
/ ' ^—
•j
^
-y^
ACKNOWLEDGl^NTS
I w o u l d l i k e t o t h a n k Dr. M a r t i n Gundersen f o r
his
t i r e l e s s p a t i e n c e and g u i d a n c e t h r o u g h o u t my i m d e r g r a d u a t e and g r a d u a t e s t u d i e s and f o r h i s h e l p i n
p r e p a r a t i o n of t h i s t h e s i s .
the
I am a l s o i n d e b t e d t o Dr.
P . F . W i l l i a m s f o r h i s h e l p and a d v i c e .
11
TABLE OF CONTENTS
ACKNOWLEDGMENTS
ii
ABSTRACT
^^
LIST OF TABLES
v
LIST OF FIGURES
^^
Chapter
I.
INTRODUCTION
^
II.
LASER DESIGN
^
III.
IV.
EXPERIMENTAL RESULTS
^^
CONCLUSION
2^
LIST OF REFERENCES
^^
APPENDIX
2^
111
ABSTRACT
Nineteen new infrared laser transitions observed in
Kr, Ar and Xe ranging from 3.631u to 17.233y are reported
and identification of all but one of these transitions
has been made.
An identification of a previously ob-
served but unidentified transition is given along with a
method for assigning term assignment to observed transitions.
The design and construction of a high power
noble gas laser capable of operating at gas pressures as
low as 5y and electric currents as high as 2KA is discussed.
IV
LIST OF TABLES
Table
Page
1.
New Laser Transitions
12
2.
Term Assignments
^^
V
LIST OF FIGURES
Figure
Page
1.
Model of a three level laser system
2.
Diagram of the noble gas laser used in
2
the study
5
3.
Liquid nitrogen dewar
7
4.
Graph of the atomic energy levels of Kr
showing new laser transitions
Graph of the atomic energy levels of Ar
showing new laser transitions
Graph of the atomic energy levels of Xe
showing new laser transitions
5.
6.
VI
18
19
20
CHAPTER I
INTRODUCTION
Noble gas lasers are of interest for many applications because they exhibit long-term frequency stability,
a wide range of wavelengths, and useful power levels.
The
first pure noble gas laser transitions were observed by
W. R. Bennett et al.^"*"^ in 1962. Patel et al.^^^ continued the work producing CW oscillations on 14 noble gas
transitions in Ar,
(3)
by Faust et al.^ ^
lengths between 2y
on 158 transitions
Kr, Xe and Ne.
Other work was done
who studied transitions with waveand 35y and produced CW oscillations
in Ne, Ar, Kr, and Xe.
The pure noble gas laser uses electron impact as
the main excitation mechanism.
Pure noble gas lasers
can be modeled as a three level system (Figure 1). An
electron with energy well above the excitation energy may
collide with the noble gas atom and excite it to level 1
thus creating a population inversion between levels 1 and
a lower level 2.
If the radiative life time of level 1
is less than the collisional relaxation time, the atom
may relax to level 2 while emitting a photon of light.
LEVEL I
PHOTON EMISSION
ELECTRON
IMPACT
EXCITATION.
LEVEL
COLLISIONAL
RELAXATION
GROUND
STATE
Figure 1.
Model of a three laser system
2
The following chapters discuss problems and
parameters in laser design including electrical, optical,
mechanical, and vacuum requirements.
Experimental results
are given including a discussion of the theory explaining the results.
CHAPTER II
LASER DESIGN
The longitudinal discharge laser is shown in
Figure 2.
This laser was designed to operate at pres-
sures down to 5y, and at currents exceeding 2,000 A.
A 3m plasma tube was constructed from 19 mm i.d.
pyrex tubing and contains three groups of electrodes.
The center group contains two molybdenum electrodes which
are held at ground potential and used as the anode.
The
group of electrodes at either end of the plasma tube contains one indium and one molybdenum electrode.
When used
as a cathode indium absorbs most gases, acting as a
getter, but the absorption of noble gases is very low.
Indium is therefore a very useful cathode material in
noble gas lasers.
However, when gas other than the
noble gases are being studied the indium electrodes become undesirable and the molybdenum electrodes may be
used.
High repetition rate noble gas lasers tend to have
the problem of instability in the gas pressure.
phenomena contribute to this instability.
cataphoresis pumping.
Two
The first is
The second is absorption of the
4
CM
-K
^
lO
W
tn
is
II
Z UJ
m
d
r^
J^'"
6
noble gas by the cathode and walls of the plasma tube.
The pressure difference between the ends of the plasma
tube cause by cataphoresis pumping is described by ^ ^
^
= 6.7 X 10"^^ I T f L (D)"^
(1)
where I is the current in amperes, T is the length of the
current pulse in ysec, f is the repetition rate in Hz,
L is the length of the plasma tube in cm, and D is the
diameter of the plasma tube in cm.
Using the parameters
of the laser used, I = 2 x 10^ A, T = 3 ysec, f = 30 Hz,
- "^
AP
L = 200 cm, and D = 1.8 cm, ^
becomes 4.14 x 10
.
This result implies the instability due to cataphoresis
pumping may be neglected.
The instability caused by the absorption of noble
gases into the cathode and walls of the plasma tube without correction would soon greatly reduce the cavity
pressure.
To correct this situation a liquid nitrogen
dewar was constructed (Figure 3).
The outer chamber of
the dewar is connected to the plasma tube.
The inside
chamber is filled with liquid nitrogen which condenses
out droplets of gas in the outside chamber.
The tem-
perature of the liquid nitrogen and thus the vapor pressure of the gas droplets may be controlled by controlling
the pressure of the liquid nitrogen.
equivalent to a large gas ballast.
These droplets are
7
FILLER CAP
PRESSURE GAGE — 2 -
o
an..
•PRESSURE RELIEF VALVE
^—NEEDLE VALVE
1.5-
r
3 1/2
5 7/8-
—
Figure 3.
1/2
Liquid nitrogen dewar
8
For the optical cavity silver mirrors coated with
thorium oxyfluoride were chosen because of their high
reflectivity in the infrared, visible and ultraviolet
regions.
The thorium oxyfluoride coating is necessary
to prevent the silver from tarnishing.
These mirrors are
placed at either ends of the plasma tube to feed signal
back into the cavity analogous to the way a feedback loop
in an electrical oscillator feeds some of the output
signal back into the amplifier.
One of the mirrors was
chosen to be a flat with a 3 mm pinhole to couple out
energy.
A stable two mirror optical cavity will satisfy
0 f (1 - |-) (1 - |~) < 1
a
(2)
b
where L is the mirror separation, R^ and R, are the
radius of curvature of mirrors A and B.
R
Using L = 10 m,
= °o, and R, = 20 m, this equation yields 0.5.
The
result is well within the limits and therefore, the
curvatures of the cavity mirrors were chosen to be <» and
20 m.
KCl windows were chosen to seal off the ends of
the plasma tube because of high transmission of signals
from O.ly to 20y.
However the optical quality of windows
commercially available hinders lasing at wavelenghts
below ly.
The equation for Brewsters angle as a function of
index of refraction is
9
is the index of refraction
where 9^ is Brewsters angle, N
D
W
of the window and Ng is the index of refraction for air.
The refractive index for KCl at 16y is 1.48.
Substitut-
ing into equation 3 gives the Brewsters angle for KCl
to be 56 . Using this result the ends of the plasma
tube were cut at 56 .
Each of the two sections of the laser were driven by
identical networks.
The 0.1 yF capacitors are charged
to a voltage of 16 to 20 KV using the IKfi resistors as a
charging path (Figure 2). When the spark gap is closed
the capacitor of each network is placed in parallel with
a section of the plasma tube and the 1 K^ resistor.
The
RC time constant is 0.1msec which is much longer than the
time it takes for the discharge to occur in the gas. An
EG6tG gas filled spark gap was used because of its ability
to operate at repetition rates up to approximately 20 Hz.
The spark gap was placed in transformer oil to cool it.
The spark gap was triggered by a lab built pulser producing a 600 V pulse which was stepped up to 30 KV by a
EG&G pulse transformer.
10
The vacuum station contains an Edwards mechanical
pump, a cryogenic pump and two 8 liter/sec ion pumps.
A mechanical pump was used mainly to clean out the
cryogenic pump.
Limited use of the mechanical pump on
the laser is considered advisable in order to reduce
possibilities of contamination by the backstreaming oil.
The cryogenic pump is used to bring the pressure of the
laser down to roughly 0.5y and the ion pumps are then
used to bring the pressure down to about 10
torr.
Rough wavelength measurements were made with the
use of various filters, and more accurate measurements
were made using a half meter double spectrometer with
600 grooves/mm gratings blazed at 16y.
The laser
radiation was detected by a HgCdTe detector with sensitivity extending to 18y.
With this apparatus, measure-
ments accurate to .005y could be made between 2y and 18y.
CHAPTER III
EXPERIMENTAL RESULTS
Nineteen new infrared laser transitions were observed in Kr, Ar, and Xe.
The transitions ranged in wave-
length from 3.631y to 17.233y.
Table 1 gives a listing
of the new laser transitions observed in each of the
noble gases.
The pressure listed beside the laser wave-
length in Table 1 is the pressure at which the transition
was observed and is not necessarily the optimum pressure
for the laser.
The relative strength of the lines are
given in Table 1.
The light pulse occurred typically
100 nsec after the beginning of the current pulse and had
a pulse length of 200 to 400 nsec depending on pressure
and gas used.
In order to make term assignments, a computer program was written to calculate the energy differences
between known energy levels^ ^ satisfying the jl coupling
selection rules (Al = +1 and AJ = 0, +1). The measured
wavelengths were then c'ompared to those calculated.
This
procedure was followed not only for neutral species, but
also for the known ionized species.
All but one of the
observed wavelengths were identified with neutral tran11
12
TABLE 1
NEW LASER TRANSITIONS
Observation
Niimber
Wavelength
(Xvac)
Pressure
Observed
at
Current
Density
Relative
Line
Strength
90^/2
cm
ti
medium
Kr
1
5.000y
2
8.115y
3
9.637y
4
50y
weak
It
weak
10.937y
M
medium
5
17.070y
II
medium
6
17.233y
M
medium
Ar
weak
1
3.631y
250
2
3.702y
II
II
medium
3
3.715y
II
II
weak
4
5.021y
ti
n
weak
5
6.S12y
M
M
weak
6
7.956y
20
M
medium
7
11.042y
20
II
weak
8
13.475y
250
II
medium
cm
13
TABLE 1--Continued
Observation
Number
Wavelength
(Avac)
Pressure
Observed
at
Current
Density
Relative
Line
Strength
Xe
1
3.725y
2
7.767y
3
7.782y
150y
150^/ 2
cm
"
M
"
M
II
M
weak
strong
strong
4
8.404y
strong
5
11.582y
20y
"
medium
14
sitions.
No term assignment could be given to the 13.475y
line observed in Ar, even after including all known
ionized transitions.
Term assignments obtained in this manner are given
in Table 2 using Racah jl notation with the upper levels
given first.
The energy levels are denoted by nl [k]. with
2
an unprimed 1 value indicating a P^/o core state and a
2
primed 1 value indicating a
^-^j^
core.
Transitions ap-
pear to occur in groups sharing initial levels.
Because
transitions from common or similar upper levels involve
the same pump mechanism, the term assignments in Table 2
are grouped by similar configurations of upper levels.
A term assignment for the previously observed i 8)
but unidentified 5.804y line in Ar is given in Table 2.
Three d'-p transition in Kr and two transitions in Xe have
been listed in Table 2.
Although transitions involving
a change in the parent core configuration are forbidden
by selection rules for jl coupling, similar transitions
have been previously reported.^ ^ Also, since the density
of states increases for the high lying levels, for an
equal distribution of electron energies, these levels
have a lower probability of attaining sufficient population to produce an inversion.
Therefore, transitions with
upper levels above about 8s, 7p, 6d are neglected.
Figures
15
TABLE 2
TERM ASSIGNMENTS
Configuration Observation
(Racah.)
Number
Calculated
Wavelengths
(Xvac)
Levels
Upper
Lower
Kr
5d[%]^-6p[%]^^
5d-6p
4
10.9337y
4d'-6p
1
4.9997y
4 d ' [l%]3_-6p[%]^_
5
17.0709y
4d'[2%]3-6p[2%]3^
6
17.2328y
4d'[2%]3-6p[2%]2_
6d-7p
3
9.639 y
6d[l%]3_-7p[l%]3_^
8s-7p
2
8.1151y
8s[l%]3_-7p[2%]2_
Ar
4
5.0220y
4d[%]3_-5p[%]^
6.
5.8037y
4d[l%]2-3p[l%]2
5
6.8129y
4d[%];L
' 1
3.6312y
6 s ' [%]^-5p'[l%]3_^
2
3.7013y
6s'[%]^-5p'[k]i^
3
3.7143y
6 s ' [%]3_-5p' [1%]2_
7p-7s
7
11.0415y
7p[%]Q-7s[l%]^
5^-60
6
7.955 y
5d[l%]T-6p[l%]
4d-5p
6s'-5p'
-^V['^^^2
16
TABLE 2--Continued
Configuration Observation
(Racah)
Number
Calculated
Wavelengths
Levels
Upper
Lower
(Avac)
Xe
2
2
7.7665y
7.7665y
6d [ l % ] ^ - 7 p [1%]^
4
8.4042y
6d[l%]^-7p[%]Q_
5d'-7p
1
1
3.7265y
3.7265y
5d'[2%]2-7p[2%]^
5d'-8p
3
3
7.7813y
7.7813y
5 d ' [1%] ^^-Sp [1%] ^
9p-9s
55
11.5821y
11.5821y
6ci-7p
9P[%]Q-9S[1%]^
17
4, 5 and 6 show the atomic energy levels and the new
laser transitions for Ar, Kr, and Xe respectively.
Longitudinal discharge lasers, such as the one
used in this work, rely on electron impact for the main
excitation mechanism.
For electrons with energy well
above threshold the electron excitation cross sections are
very broadly resonant (E = 8 x 10
to 8 x 10
cm" ) . This
broad resonance allows an electron with energy above the
atomic dissociation limit of the gases studied, to excite
the atom from ground state to many energy levels.
This
may be seen as follows.
The differential cross-section for excitation from
the ground state to the n
state is given by Bom's
approximation to be ^ '^
2 2k
I
= 4Trm
n .^ ^ (R)exp{i(k5 -k S) .R}
on
,4
k ' on^ ^ ^
o n
4^/(?)i|^n(?)dJdRl^
(1)
^here ^
,— are the wavelengths of the incident electron
' n
before and after impact, n and n are unit vectors in the
direction of incidence and of scattering, and V is the
coulomb interaction between the colliding electron and
the atom electrons, £ /(r-R).
(kit^-k^n)
^ o n
Therefore
18
10.9-1
10.7E
u
O
O
O
o
>•
an
UJ
z
UJ
10.5*-
4d'
10.3 -
i^igure
Graph of the atomic energy levels of Kr
showing new laser transitions
19
Figure 5
Graph of the atomic energy levels of Ar
showing new laser transitions
20
9.3 -
5d"
8p
9.2 -
E
o
O
O
S 9.1
88
>UI
z
Ui
9.0-
8.9-
7p
8.8 -
Figure 6
Graph of the atomic energy levels of Xe
showing new laser transitions
21
is the change of momentum of the incident election.
Choos
ing the axis of a system of polar coordinates along this
vector gives
exp {i(kn -k^n).r} = e ^ ^
(2)
where K = Ikn -k nl.
' o n '
Equation 1 becomes
This expression may be simplified by performing the integration over the coordinates of the colliding electron.
/ Ve^^dR = e^
E / j ^ ^ dS
s=l
IS-r^l
In many cases the transition can be thought of as involving only one electron therefore the summation may be
dropped.
Using the formula
/ exp(iKn.r')
^'^^=^'^ ^iKn.r
ixp (^iKn
I r-r'
K
give J
/ V e ^ ^ dl = ^
K
e^^s
22
E q u a t i o n (3) now becomes
2 2k
2
-r
_ 4'n' m n I 47T£ r
^on - - ^
T^ ' 7 ^
iKxc,..- . ^^ ,2
"r-^^^drl
//, \
(4)
Now consider the integral of equation (4)
_ . ^iKXe ..- -.^
on
^o ^
iKx
This integral will be small when e
s make many oscillations over the range of the wave functions ii^'^^,ii^ .
°
^ o'^n
Therefore when
K >> — = K
a
o
o
that is if the change in momentum is large compared to
the inverse of the Bohr radius the scattering crosssection is negligible. Now to evaluate e , eiKx may be
expanded
e ^ ^ = 1 + iKx - ^^^^ • •
2!
Now if K << —Z the second order and higher terms may be
ao
neglected so that
e
on
= / i|;* ip dr + iK / XT|;^'^I|; dr,
^ on
but since / ^* i) dr = 0
on
o' '^n
o^n
23
Substituting into equation (4) gives
.2_4 k
=
4
m
£
n l , , | | ,
I
on
H^
^ K'
|2
Therefore for small changes in the momemtum of the incident electrons the probability of excitation from the
ground state to state n is proportional to the probability
of an optical transition.
Because the allowed optical
transition must satisfy the selection rule Al = ±1, the
closed shell-p ground state of the noble gases has a
much larger probability of being excited to an s or d
state rather than p or f state.
Therefore a strong in-
version between the s-p and d-p states may be obtained
by electron impact excitation in noble gases.
All of the
Kr transitions observed, and all but one of the Ar and
Xe transitions have upper levels in the s or d states.
From a calculation of line strengths, it may be shown
(3)
that the strongest transitions satisfy Ak = AJ. ^
All of the transitions in Xe, all but one transition in
Ar and half of the new transitions in Kr satisfy this
condition.
CHAPTER IV
CONCLUSION
Nineteen new infrared laser transitions have been
observed in Kr, Ar, and Xe and term assignments have been
given to all new transitions with the exception of the
13.475y line observed in Ar.
A term assignment has also
been made for the 5.804y line which was previously observed^ ^ but not identified.
Although it had been
anticipated that new transitions at high current densities and lower pressures would be ionized species,
identification of all but one of the transitions were
made in terms of neutral species.
A list of wavelengths
of possible infrared transitions show that the number of
these transitions for ionized species is approximately
0.1 percent of that of the neutral species.
24
LIST OF REFERENCES
(1) W. R. Bennett, Jr., Bull. Am. Phys. Ser. 7, 15
(1962).
(2)
C. K. N. Patel, W. R. Bennett, Jr., W. L. Faust,
and R. A. McFarlane, Phys. Rev. Letters J.
102 (1962).
(3) W. L. Faust, R. A. McFarlane, C. K. N. Patel, and
C. G.B. Garrett, Phy. Rev., Vol. 133, pp.
A1476-A1486.
(4) W. W. Simmons and R. S. Witte, IEEE J. Quantum
Electronics, OE-6, p. 648.
(5)
C. P. Harper, and M. Gundersen, Rev. Sci. Instriom,
Vol. 45, pp. 400-402, 1974.
(6)
Amnon Yariv, Quantum Electronics. New York;
John Wiley and Sons, 1967, p. 196.
(7)
Charlotte E. Moore. Nat. Stand Ref. Data Ser.,
Nat. Bur. Stands (U.S.), 35/Vol. I, Vol. II,
Vol. III.
(8)
0. R. Wood, E. G. Burkhardt, M. A. Pollack and
T. J. Bridges, Appl. Phys. Lett. 18, 261 (1971)
(9)
H. S. W. Massey, and E. H. S. Binhop, "Electronic
and Ionic Impact Phenomena," Oxford at the
Clarendon Press, 1952, pp. 136-140.
25
APPENDIX
PROCEDURES FOR IDENTIFYING OBSERVED LASER
TRA^TSITIONS IN THE NOBLE GASES
In order to give term assignments to the observed
laser transitions two computer programs were written for
each species of each noble gas studied.
Program I cal-
culated all the possible infrared transitions with wavelengths between 2y and 18y which satisfy the jl coupling
selection rules (Al = ±1 and AJ = 0,
on magnetic tape.
±1) and stored them
Program II matched an observed wave-
length, which had been corrected to its vacuum wavelength,
to calculated wavelengths within experimental error.
The
two program system was used to reduce computer time.
Energy levels and their n, J, and 1 quantum numbers
for Kr I, Kr II, Kr III, Xe I, Xe III, Ar I, Ar II, Ar III,
Ar IV, Ar V, Ar VI, and Ar VII were obtained from the
National Standards Reference Series 35 Vol. I, Vol. II
and Vol. III.
This information for each species was
stored on magnetic tape in three arrays.
held all known energy levels.
Array E (A)
Array J(A) held the J
quantum numbers for energy levels E(A). Array L(A) held
a code which contained the n and 1 quantum number.
26
This
27
code contained three numbers.
number.
The first was the n quantum
The second was the 1 quantum number, and the
third held a 0 for unprimed 1 valves are a 1 for a primed.
Program I contained a pair of loops which took one
energy level and determined the wavelength of the transition to every other level.
When a transition was foiand
with a wavelength between 2y and 18y AJ and Al for the
transitions were calculated.
If they satisfied the jl
coupling selection rules, that wavelength and the two
array numbers corresponding to the two energy levels were
coded together and loaded on magnetic tape.
In order to
code the information together only four significant
digits of the wavelength were kept.
then multiplied by 10
the decimal.
The wavelength was
so that it appeared to the left of
The first three places to the right of the
decimal contain the array number of one energy level and
the fourth, fifth and sixth places to the right of the
decimal contained the array number of the second level of
the transition.
Program II asked the operator to input the observed
wavelength and experimental error and printed out all
calculated wavelengths within experimental error and the
n, 1, and J quantum numbers for the two energy levels.
Following are Program I and Program II written for
Kr I transitions.
28
PROGRAM I
Statement: This program calculates a wavelengths in Kr I between 2y and 18y which
satisfies the jl coupling selection rules.
100 Dimension L(220), J(220), E(220),WC(IOOO)
Statement:
Array L contain the n and 1 quantum
number, Array J contains the J quantum number. Array E
contains the Energy levels in cm
, and WC is for the
calculated wavelengths.
Statement:
Find and Read Array L, J, and E.
110 Find 1
120 Read (§33: L, J. E
130 For I = 1 to 220
140 For T = I to 220
150 Kl = ABS ( K(I) - K(T) )
160 M = 10000/Kl
Statement: M is the wavelength for the transition.
Statement: cheack to is if M is between 2y and 18y.
170 IF INT (M) > 2 Then 190
180 Go To 310
190 IF INT (M) < 18 Then 210
200 Go To 310
210 IF ABS ( L(I) - L(T) )= 1 Then 230
220 Go To 310
230 IF ABS ( J(I) - J(T) )<> 1 Then 250
240 Go To 260
29
250 IF ABS ( J(I) - J(T) )<> 0 Then 310
Statement: In Code I, T, and M
260 II = I/IOOO
270 TI = T/1,000,000
280 M= INT ( M * 10000 )
290 S = S + 1
300 WC(S) = M + II -f TI
310 Next T
320 Next I
Statement: write Array WC in file 2.
330 Find 2
340 Write @ 33: WC
PROGRAM II
Statement: This program matches observed wavelengths in KrI to calculated wavelengths.
100 DimWC(lOOO), L(220), J(220)
Statement: Find and Read L, J, and WC
110 Find 1
120 Read (§33: L, J
130 Find 2
140 Read (§ 33: WC
150 Print "This Program matches Lines in KrI"
160 Print "Input wavelength"
170 Input Wl
30
180 Print "Input experimental error"
190 Input D
200 For I = 1 to 1000
Statement: decode WC
210 M = (INT (WC(I)))/10000
220 kl = Int (WC(I) - Int (WC(I))nOOO)
230 k2 = (wc(i)nooo = Int (wc(i)nooo))nooo
Statement: compare wavelength to experimental error
240 IF ABS (M-W1)> D Then 280
Statement: Print array numbers
250 Print "The Transition is Kr(";kl;") to Kr(";k2;")
Statement: Print n, 1, and J numbers
260 Print L(kl); J(kl);" To "•L(k2);J(k2)
270 Print "wavelength = "; M
280 Next I
290 Print "Finished"