Excitation Mechanisms and Characterization of a Multi-Ionic Xenon Laser

The emission characteristics of an ultraviolet-visible pulsed multi-ionic xenon laser were studied through time-resolved spectroscopy and the results were interpreted using a collisional radiative theoretical model. This analysis includes more than 20 laser lines belonging to several ionic species (Xe III VIII). Depending on the experimental conditions, different temporal distributions of the laser lines and their corresponding sponta neous emissions can be observed. In particular, laser emission presents temporal oscillations near threshold. Pumping processes for the laser transitions have been analyzed by using this model. Relativistic Hartree Fock calculations of laser level lifetimes and radiative transition probabilities were performed. Experimental laser gain for several transitions were obtained and compared with the theoretical values derived from the calculations. Index Terms Collisional-radiative model, gas discharge, gas lasers, xenon laser. I. In t r o d u c t i o n SINCE THE advent o f the laser, capillary discharges have been used to produce laser action in the ultraviolet (UV), visible, and infrared (IR) range [l]-[4 ] . In particular, lowpressure xenon plasm a excited by pulsed high-current-highvoltage electrical discharges produces high gain laser transi tions in the near U V and visible range. This laser output has been used for pumping dye lasers [5] [7] and for studying injection locking phenom ena in CW dye lasers [8 ], [9]. Both from a basic and practical point o f view, it is im portant to know which are the levels and ionic species involved in laser emission. D uchowicz et al. [10] showed that m ost visible laser emissions belong to Xe V while UV emissions belong in general to Xe VTI. In recent works, most o f the unresolved laser lines were attributed to Xe V [11], Xe VII [12], and Xe VIII [13]. Manuscript received December 9, 1998; revised June 7, 1999. This work was supported by the Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), by the Comisión de Investigaciones Científicas de la Provincia de Buenos Aires (CICBA), and by the Facultad de Ciencias Exactas, Universidad Nacional de La Plata. H. Sobral and D. Schinca are with Centro de Investigaciones Opticas, 1900 La Plata, Argentina. They are also with CICBA, 1900 La Plata, Argentina, and with the Physics Department, Universidad Nacional de La Plata, 1900 La Plata, Argentina. M. Raineri is with Centro de Investigaciones Opticas, 1900 La Plata, Argentina. He is also with CICBA, 1900 La Plata, Argentina. M. Gallardo is with the Centro de Investigaciones Opticas, 1900 La Plata, Argentina. He is also with CONICET, 1916 Buenos Adres, Argentina. R. Duchowicz is with the Centro de Investigaciones Opticas, 1900 La Plata, Argentina. He is also with CONICET, 1916 Buenos Aires, Argentina, and with the Physics Department, Universidad Nacional de La Plata, 1900 La Plata, Argentina. Publisher Item Identifier S 0018-9197(99)06785-8. Following another line o f research, Papayoanou et al. [14] reported on the param etrization o f a xenon plasm a laser including observations about the tem poral distribution o f the output. Sasaki and Saito [15] have obtained double pulsed output when the plasma was excited w ith a long current pulse. In a previous work [16], we presented experimental results about the temporal evolution o f visible laser lines together w ith a simple model to simulate this behavior. A fter that, we perform ed an extensive study on the tem poral characteristics o f the spontaneous emission o f a low density pulsed discharge plasm a. The results were interpreted through a collisional radiative theoretical model [17]. This paper extends the previous tem poral study o f the laser emission to more than 20 lines in the UV visible re gion. Based on our previous plasm a m odel that considers the population behavior o f Xe I IX species [17], we have now also included stim ulated emission term s to take into account different laser transitions. On the basis o f this model, we analyze the population mechanism s responsible for m ost o f the classified laser xenon transitions corresponding to Xe III, X e V, Xe VII, and Xe VIII, in this region. We also perform ed laser gain analyses for several lines by using level param eters (lifetimes and radiative transition rates) obtained from relativistic H artree Fock calculations; these results are com pared w ith the corresponding experim ental values. II. E x p e r i m e n t a l S e t u p a n d R e s u l t s The experimental setup is sim ilar to that used in [16]. The discharge tube was 1.3 m long and has a 5 m m bore, w ith cold electrodes in side arms at the ends. Excitation was achieved using a capacitor bank having an overall capacitance ranging from 100 to 420 nF and charged to a voltage up to 18 kV, w hich yields peak current pulses o f about 3 kA having a tem poral w idth between 1-3 fxs full-w idth at half-m axim um (FW H M ). X enon pressure was varied betw een 5 100 mtorr. The resonant cavity consisted o f tw o m ultilayer coated spher ical m irrors o f 1.5 m radius o f curvature located in a nearly confocal configuration. The light em itted longitudinally was focused into a 0.5 m focal length scanning monochrom ator and detected w ith a U V visible photom ultiplier. Its output was amplified and displayed by a 200 M Hz digital oscilloscope and recorded by a plotter. The temporal study carried out previously in the visible region was extended into the UV region as far as 2 0 0 0 A, studying more than 2 0 transitions corresponding to different ionic degrees (Xe III-V III). 0018 9197/99$ 10.00 © 1999 IEEE

F ollow ing another line o f research, Papayoanou et al. [14] reported on the param etrization o f a xenon plasm a laser including observations about the tem poral distribution o f the output.Sasaki and Saito [15] have obtained double pulsed o u tput w hen the plasm a w as excited w ith a long current pulse.In a previous w ork [16], w e presented experim ental results about the tem poral evolution o f visible laser lines together w ith a sim ple model to sim ulate this behavior.A fter that, w e perform ed an extensive study on the tem poral characteristics o f the spontaneous em ission o f a low density pulsed discharge plasm a.The results were interpreted through a collisional radiative theoretical m odel [17].
T his paper extends the previous tem poral study o f the laser em ission to m ore than 20 lines in the U V visible re gion.B ased on our previous plasm a m odel that considers the population behavior o f X e I IX species [17], w e have now also included stim ulated em ission term s to take into account different laser transitions.O n the basis o f this m odel, w e analyze the population m echanism s responsible for m ost o f th e classified laser xenon transitions corresponding to X e III, X e V, X e VII, and X e V III, in this region.W e also perform ed laser gain analyses for several lines by using level param eters (lifetim es and radiative transition rates) obtained from relativistic H artree F o ck calculations; these results are com pared w ith the corresponding experim ental values.
II. E x p e r i m e n t a l S e t u p a n d R e s u l t s T he experim ental setup is sim ilar to th at used in [16].The discharge tube w as 1.3 m long and has a 5 m m bore, w ith cold electrodes in side arm s at the ends.E xcitation w as achieved using a capacitor bank having an overall capacitance ranging from 100 to 420 nF and charged to a voltage up to 18 kV, w hich yields peak current pulses o f about 3 kA having a tem poral w idth betw een 1-3 fxs full-w idth at half-m axim um (FW H M ).X enon pressure w as v aried betw een 5 1 0 0 m torr.The resonant cavity consisted o f tw o m ultilay er coated spher ical m irrors o f 1.5 m radius o f curvature located in a nearly confocal configuration.The light em itted longitudinally w as focused into a 0.5 m focal length scanning m onochrom ator and detected w ith a U V visible photom ultiplier.Its output w as am plified and displayed by a 200 M H z digital oscilloscope and recorded by a plotter.
T he tem poral study carried out previously in the visible region w as extended into the U V region as far as 2 0 0 0 A, studying m ore than 2 0 transitions corresponding to different ionic degrees (Xe III-V III).D epending on the m irro r reflectivity and experim ental con ditions, several ions can lase sim ultaneously.A s the stage o f ionization increases, the onset o f lasing is delayed further w ith respect to the beginning o f the current pulse.T hese results w ere also observed in previous studies o f the spontaneous em ission [10], [17].
W e have analyzed the tem poral distribution o f the laser and the corresponding spontaneous em ission o f each line studied under different experim ental conditions.In these situations, w e rem oved the output m irro r to com pare the form er (that depends on both the upper and low er laser level p o pulation) w ith the latter (proportional to the upper level p o pulation only).N ear threshold, laser em ission oscillations o ccurs in m o st o f the observed lines, especially for h igh ionic degrees.Fig. 1 show s the tem poral distribution o f the laser em ission n ear threshold for a line belonging to X e V III (A 3 350.03Â ) together w ith the corresponding spontaneous em ission output and the current pulse for reference.D uring the tem poral region around the spontaneous peak, the laser em ission exhibits oscillations.A fter that, the ion population and the spontaneous and laser em ission decay.
W hen pum ping is increased eith er by increasing the dis charge voltage or by decreasing the pressure, oscillations tend to disappear and laser em ission follow s the tem poral shape o f the spontaneous em ission.T his behavior is show n in Fig. 2 for the 3645.48A line (X e V ll), w here laser and spontaneous tem poral distributions are sim ilar.T his p articular line presents, w hen pum ping is above threshold, a flat tem poral profile during alm ost all o f the current pulse.
Well above laser threshold, the output consists o f a sin gle pulse appearing at the beginning o f the corresponding spontaneous pulse.The large initial gain obtained u n d er these conditions p roduces a depopulation o f the up p er laser level w hich usually cannot reco v er to generate a p ositive population inversion.Fig. 3  .is the dielectronic recom bination coeffi cient from the kth level o f the ion z + 1 to the level j o f the ion 2 .The excitation and ionization rates were calculated using the sem i em pirical form ulas o f Van R egem orter and Lotz, respectively, cited in [18]; D z{ is calculated through its relation w ith the excitation rate [18] giR fj 9 jD j{ e x p ( A E /T e), w here gi and gj are the statistical w eights o f levels i and j , and Te is the electron tem perature.Since our plasm a has a m oderate electron density [17], the tw o body recom bination process (dielectronic and radiative recom bination) prevails.B oth processes can be calculated by Sobelm an [18, pp.118 and 1 2 2 ] and show th at dielectronic recom bination is the dom inant term.We w ill restrict the num ber o f ions to z < 9 since no experim ental evidence o f the existence o f X e X w as found under our conditions.The system m ust also satisfy the initial condition that N l takes on a value o f about 1 0 l 0 cm 3 (depending on the filling pressure), w hile the rest o f populations are zero.
W hen the cavity is taken into account, the tem poral evolu tion o f the levels that give rise to laser action are also affected by the stim ulated em ission term s.I f N z and N f represent the population densities for the upper and low er levels corre sponding to each laser line, and n z is the corresponding total num ber o f photons inside the cavity, their tem poral evolution m ust satisfy the follow ing set o f equations [19]: w here 7 C is the inverse lifetim e o f the photons in the cavity, Vc is the cavity volum e, and K is the coupling constant given by w here A is the w avelength o f the transition and A A /A is its relative linewidth.I V .

IV. S p e c t r o s c o p i c P a r a m e t e r s
To analyze the excitation processes that give rise to stim u lated em ission, the lifetim e and transition probability for the m ain laser transitions in the U V visible region w ere calculated.F or this purpose, theoretical determ inations from relativistic H artree F o ck (R H F) ab initio calculations and energy m atrix diagonalization [20] w ere used.In order to obtain the best values for lifetim es and spontaneous transition probabilities, sem i em pirical calculations using energy param eters adjusted from least squares calculations w ere perform ed.R ydberg se ries interactions w ere also included for a better fit o f the theoretical values o f the experim ental energy level values.
U nder our experim ental conditions, w e did n o t observe any X e II laser lines.For X e III, R H F calculations w ere carried out using energy param eters from Persson et al. [21], A lthough X e IV laser lines do exist, they appear w ith w eak intensity [22] and seem to be o f little practical interest.D espite this fact, the m odel does take into account the dynam ics o f these transitions.For Xe V, sim ilar calculations w ere perform ed w ith param eters taken from [ 1 1 ] for the even parity levels and from [23] for the odd parity levels.Spectroscopic results do n o t show any laser lines belonging to X e V I. F o r X e V II, alm ost all the experim ental energy levels o f the 5 s 4 / configuration are unknow n.In such a case, it is n o t possible to optim ize the param eters using the previously m entioned technique; therefore, ab initio calculations w ere carried out.
Since X e V III has a single electron out o f a closed shell, inclusion o f the Rydberg series becom es im portant [20].Ab initio calculations w ere also used in this case including the ns and np series up to n 15 and nd and n f series to n 12. Table I show s the results obtained for the m ain classified transitions in these ions.In general, the spontaneous transition probability is about 1 0 7 -1 0 8 s -1 , and the lifetim e o f the upper level lies betw een 3 4 0 ns, w hile the lifetim e o f the low er level is one or tw o orders o f m agnitude low er.

V . P u m p i n g P r o c e s s e s
A ccording to [17], w e assum e that the m ain excitation and deexcitation processes are radiative and collisional.In order to understand the population inversion m echanism s, the set o f equations ( 1 ) w as solved for typical discharge conditions.R H F ab initio calculations w ere carried out for each one o f the ions.They included all the relevant configurations that show interaction w ith those to w hich the laser levels belong.F rom these results, the levels that show ed larger oscillator strengths w ith the laser transition levels w ere determ ined and their param eters included in equation set ( 1 ).L aser levels are m ainly populated by electron im pact and cascade recom bination, and their relative w eights differ for different ions.We w ill restrict o u r analysis to the optically allow ed transitions since their cross sections m aintain a large value for a m uch broader range than the optically forbidden ones [25].B esides, calculations show that the upper laser level has a stronger transition probability to the low er laser level than to the rest o f the levels.T he upper level h as also a strong connection w ith higher levels that populate it, w ith an oscillator strength value o f about unity.B ased on these facts, a four level m odel turns out to be th e m o st favorable schem e to describe the excitation processes that lead to laser action for the different ions.
Fig. 4 show s a sim plified diagram o f the excitation m ech anism s that give rise to inversion population.C ontributions o f electronic im pact, radiative and collisional decay, and recom bination cascade processes w ere taken into acco u n t in all cases for the optically allow ed transitions.The p o pulation is transferred by electron im pact from the ground level o f each ion E \ to higher excited levels £ | .The latter m ay receive (depending on the configuration) cascade contributions due to recom bination processes [18].£ f and £ | p opulations are connected by radiative decay and e x citatio n d eex citatio n electron collision processes [17].Since, in all cases, the £ f lifetim e is m uch larger than £ f , the population o f state 3 exceeds that for state 2. B ased on these assum ptions, w e w ill analyze in detail som e o f the laser transitions belo n gin g to different ions.
C alculations show ed that the upper laser level o f the 4060.45A laser line belonging to X e TIT is p opulated m ainly by dielectronic recom bination from the ground X e IV level: T he upper level £ 3 o f X e V laser transitions is filled m ainly by cascading from the 5s5p2 4 f and 5s2 5p7d configurations ( £ 4 ) , and these are populated b y electron im pact from the ion ground level in a m ultistep process.The upper laser level £ 3 o f the X e V II (5 s 4 / 1 F s), is pop ulated b oth by radiative d ecay from £ 4 and by recom bination from the Xe V III ground level.O u r calculations show ed that the latter process is dom inant for the Te peak values considered here.
Finally, for X e V III, the £ 3 levels are m ainly p opulated by a strong radiative decay from the up p er configurations, w ith transition probabilities o f th e order o f 1012 s 1 .In turn, these levels are populated m ainly by recom bination from th e 4 d 10 configuration belonging to X e IX.

V I. L a s e r G a i n
The gain coefficient p e r unit length for different lines appearing in Table II can be calculated u sing the follow ing relation [26]: w here A 32 is the radiative transition rate, N i and gi are the density population and th e statistical w eights corresponding to level i, A A/A is the relative linew idth, and c is the speed o f light.
T he linew idth is given b y D op p ler broadening and b y colli sions betw een electrons an d ions.T he form er can be calculated from [25], and the latter from an expression p roposed by G riem [27].U nder our experim ental conditions, calculations show that th e last term is dom inant.
A 3 2 values w ere obtained from R H F calculations.The p o pulation densities N 3 an d N 2 w ere d eterm ined by solving ( l ) ( 5 ) for typical ex citation values [17] and in cluding the m ain levels that interact w ith each laser level.The electron tem perature (Te) is increased until laser th resh o ld is reached for each line.The population densities T3 and N 2 obtained u n d er these conditions are in troduced in (6 ).
T he sm all signal laser gain for the m ain know n transitions w as m easured in the usual w ay, introducing a know n loss into the cavity until threshold w as reached for a particular line.
T he results can be seen in Table II, together w ith values from other authors for com parison [14], [28].
T heoretical results are in general agreem ent w ith experim en tal data.For X e V III, the spontaneous transition probabilities are low er than those corresponding to other ions, although it is com pensated for by the large radiative collisional decay rate m entioned previously.VII.T e m p o r a l A n a l y s i s In order to analyze the tem poral characteristics o f the em is sion, ( 1 ) w as solved num erically for typical discharge param e ters.A ll the levels that take place in the excitation deexcitation processes giving rise to laser action w ere included.The elec tron tem perature is increased until the shape o f the calculated spontaneous em ission reproduces the experim ental results.A fter that, the stim ulated em ission term s (2) and (3) w ere included in ( 1 ), and the w hole system w as solved together w ith (4) and (5).
C alculations show s that laser oscillations are dependent on the pum ping rate o f the levels.A s expected, they appear n ear threshold, in agreem ent w ith previous w ork [16].This fact w as m ore clearly observed in lines belonging to higher ionization stages such as X e V II and X e V III, since, u n d er our experim ental conditions, they operate near threshold.This is theoretically supported by the low er transition probability for the upper laser levels belonging to several o f these lines.N ear threshold, the calculated em ission presents a large n um ber o f oscillations.This situation holds, for exam ple, w hen A 32 is low , as in the typical case for X e V III.Fig. 5 show s the tem poral evolution o f the spontaneous and stim ulated em ission for the 3350.03À line o f the X e V III.The result agrees w ith that show n in Fig. 1 for the sam e line.
W hen the electron tem perature is increased from threshold, oscillations disappear and the stim ulated em ission follow s the tem poral shape o f the spontaneous em ission.This agrees w ith the fact that the low er laser level radiative decay rate is m uch larger than that for the upper laser level (Table I).Fig. 6 show s the tem poral shape o f the spontaneous em ission for a X e V II transition and the 3645.48À stim ulated em ission, reproducing the experim ental observation o f Fig. 2. Further increases o f the electron tem perature produce an intense single laser pulse, as w as show n in previous w orks [ 1 0 ], [16].

V III. C o n c l u s i o n s
The tem poral evolution o f m ore than 20 U V visible xenon laser lines and their corresponding spontaneous em ission from a m ulti-ionic low -pressure plasm a is analyzed using tim eresolved spectroscopy.R H F calculations on X e III to X e IX w ere carried out to determ ine spontaneous transition proba b ilities and lifetim es o f relevant levels involved in the laser em ission.R esults show that the upper laser spontaneous tran sition rate to the low er laser level is larger than to the rest o f the levels.M oreover, the u p p er level lifetim e is one o r tw o orders o f m agnitude greater than that for the low er state.U sing a collisional radiative m odel based on electron im pact and cascade processes, w e studied the dynam ics o f the plasm a.The num erical solution o f this m odel, including the stim ulated term s, predict the observed oscillations near threshold w hich agrees w ith experim ental results.It can also be u sed to determ ine the optim um lasing conditions for each line.The results also indicated that, u n d er certain experim ental conditions, the strong 3645.48A line can also be m ade to lase in an extended m ode, giving rise to a quasi C W tem poral profile, sim ilar to the visible lines reported in [29].We found in m ost o f the laser lines that b oth the electron im pact and recom bination m echanism s are responsible for population inversion.The agreem ent betw een experim ental sm all signal m easured gain and the calculated gain values supports the proposed m odel.The m odel is being applied to other m ulti ionic rare gas laser system s.-" -

5 0
show s this b ehavior for the 4060.45A line, belonging to X e III.I I I .III. M o d e l w here th e electron d ensity n e can be calculated from the charge b alance equation, R f is the excitation rate coefficient from level i to lev el j o f the ion z (corresponding to the z 1 tim es ionized xenon), D z is the deexcitation rate coefficient, A ji is th e radiative transition rate, is the electron im pact 2 The m odel u se d to analyze the tem poral evolution o f the population d ensities is sim ilar to th at used in[17].I f N? is the population density o f the j t h level o f ion z in a plasm a w ith no cavity effects, the set o f equations that describe its tem poral evolution is the follow ing: a yth level o f the ion 2 to the level i o f the ion (z + 1 ), and
C a l c u l a t e d a n d M e a s u r e d La s e r G a in

Fig. 5 .Fig. 6 .
Fig. 5. Calculated temporal distribution o f the spontaneous and stimulated emission near threshold for a Xe VIII (A 3350.03A) line.

TABLE 1 M
a in Cl a s s if ie d Io n ic X e n o n La s e r Tr a n s it io n s in t h e U V V is ib l e Re g io n : T h e o r e t ic a l U p p e r Lif e t im e t 3 , L o w e r L if e t im e T2, a n d Spo n t a n e o u s T r a n s it io n Pr o b a b il it y A 32