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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"