s. e. harris and j. f. young 00 core-excited metastable...

Vol. 4, No. 4/April 1987/J. Opt. Soc. Am. B 547

Core-excited metastable levels: application to spectroscopy,to the generation of picosecond extreme-ultraviolet pulses,

and to lasers

S. E. Harris and J. F. YoungEdward L. Ginzton Laboratory, Stanford University, Stanford, California 94305

Received October 13, 1986; accepted December 18, 1986The paper reviews both the properties and the applications of core-excited metastable atoms. The production ofthese atoms by microwaves, pulsed hollow-cathode discharges, and laser-produced x rays is described. We discussthe application of these atoms to several new types of spectroscopy that allow autoionizing linewidths as narrow as0.1 cm' to be measured. The application of these metastables to the generation of picosecond-time-scale soft-x-ray pulses and to XUV lasers is also discussed.

1. INTRODUCTIONMetastable levels of atoms and ions have played an impor-tant and traditional role in atomic spectroscopy, in photo-chemical studies, and in the kinetics of several of the mostimportant visible and infrared lasers. Their role should beespecially important in the extreme-ultraviolet (XUV) andsoft-x-ray regions of the spectrum, where the lifetimes ofnonmetastable levels are limited both by autoionization andby increasingly fast spontaneous emission.

For almost 10 years now' we have been developing tech-niques for using metastable levels for the generation of shortXUV pulses, for new types of very-high-resolution core-excited spectroscopy, and for the construction of short-wavelength lasers. Our earlier efforts were based on excita-tion by high-power microwaves and by both cw and pulsedhollow-cathode techniques. Though sufficient to showsome of the basic principles, these techniques were not suffi-cient to produce practical devices. About four years agoCaro et al.2 learned how to use laser-produced x rays toproduce densities of core-excited metastables that exceed1015 cm-3. This technique for the production of core meta-stables can be reasonably simple and shows promise forapplication in each of the above areas.

In the following sections of this paper we will review thespectroscopy of core-excited metastables, their method ofproduction, their application to new types of ultrahigh-resolution spectroscopy, to the generation and measurementof XUV and soft-x-ray picosecond pulses, and to the con-struction of short-wavelength lasers.

2. SPECTROSCOPIC CONSIDERATIONS

A. Inert-Gas-Like MetastablesThe paper will be concerned with two types of core-excitedmetastables.3 The first are the inert-gas-like metastablesthat are produced by electron ionization or soft-x-ray photo-ionization of column I metals. The second are the class ofmetastable levels of alkali atoms and alkalilike ions that lieabove the lowest continuum and are metastable against auto-ionization and sometimes against radiation.

Of these, the inert-gas-like metastables are the easiest toproduce. Figure 1 shows an energy-level diagram for theproduction of Li+(ls2s) 'S and 3S metastables. Soft-x-rayphotons with an energy greater than 64 eV ionize a is elec-tron and thereby produce the excited metastable ion; thepumping process thereby compresses broadband pumpingenergy into nearly monochromatic (Doppler-limited) storedenergy. The population of the excited singlet or triplet ioncan be determined by measuring the absorption of a laserprobe beam at 958 or 549 nm, respectively.

Though the inert-gas metastables are quite easy to pro-duce, they are difficult to invert. As was noted quite earlyby Hyman and co-workers,4 the essential problem is that,when an excited ion is produced, the simultaneously pro-duced hot electron has an energy that is more than sufficientto ionize collisionally a 2s electron, thereby producing aground-level ion and destroying the inversion. A possiblesolution to this problem is to work at low ambient density,but this greatly increases the required laser pumping energy.

B. Core-Excited DoubletsTo overcome the above problem, we have become interestedin the class of core-excited levels that lie above the lowestcontinuum and are metastable against autoionization.'Perhaps the simplest of these are the even-parity 2P levels ofneutral Li (Fig. 2) where autoionization is prevented by thesimultaneous conservation of parity and angular momen-tum. Table 1 shows the wavelengths and relative intensitiesof the transitions from this manifold.6 The strongest ofthese at 20.75 nm has an Einstein A coefficient of A = 2 X101 sec'1, which corresponds to a Doppler-broadened gaincross section at 7000 C of 3 X 10-14 cm2. The lower level ofthese transitions are valence levels of the atom that may beemptied by laser photoionization, thereby providing a four-level laser system.

C. Core-Excited Metastable QuartetsThough the core-excited Li doublets do not autoionize, theydo radiate rapidly and therefore require rapid pumping.Figure 3 shows a prototype laser system7 in which energy is

0740-3224/87/040547-16$02.00 © 1987 Optical Society of America

00WCD

0

O

Ca

0le+

S. E. Harris and J. F. Young

548 J. Opt. Soc. Am. B/Vol. 4, No. 4/April 1987

Li

SOFT X RAYS(t 264 eV)

FROM PLASMA

534861

519522

Li+

545296 -Is2p'P/958 nm 3

534861 Is2s'S 5 3 7 750 - Is2p P/549 nm

519522- s2s3 S

43487 I i+ Is 2 S 43487--Is2 S

0_ Is22 2S

Fig. 1. Energy-level diagram for producing metastable Li+(ls2s)S and Li+(ls2s) 3S ions.

first stored in a metastable quartet level and then trans-ferred to a radiating doublet level by a picosecond-time-scale laser pulse. Even in the heavier alkalies, quartet levelsthat have the highest J in a configuration have no doubletcomponent and therefore require a spin-spin interaction toautoionize. In the absence of electrons, levels of this typeare metastable for many microseconds.

There are, however, two problems associated with the Lisystem of Fig. 3. The first is the small intercombinationoscillator strength (f = 2.5 X 10-8) on the 295-nm quartet-doublet transition, and the second is the need to empty theresonance level of the atom. These problems may be over-come by using heavier alkalies such as Na and K, for whichthe intercombination oscillator strengths are about 4 ordersof magnitude greater than in Li, and for which the lowerlevel of the laser transition is closer to the valence continu-um.8

545296 cmI """ Is2p 'PO ION

530195 cm 1 -IIS2p) 3 P4p-(Is2p)1 P3p] 2p528441 cm' I (IS2p) 3 P4p+(IS2p)lP3p] 2P520944 cml (s 2p) 3p3p 2P

496943cm , 1S2p 2 2 p

207.5 A

43487 cm I ,,,, , S2 ION

30925 cml - S 2 3p 2pO14904 cm'1 is 2p 0

O IS22 2S0 is 2S SFig. 2. Energy-level diagram of neutral Li.6

D. Quasi-Metastable QuartetsWe have recently found that there is a subclass of quartetlevels that even in the heavier elements retain metastabilityagainst autoionization and radiate quite strongly in theXUV.9 The distinguishing property of these quartets isthat the selection rules on the spin-orbit matrix elementspermit nonzero matrix elements only to doublet basis levels,which are themselves prohibited from autoionizing but areradiatively allowed. For alkali atoms, the condition for suchquasi-metastability is that the level have parity and orbitalangular momentum that are both odd or both even, that IJ -LI = 3/2, and that the level not be a pure (highest-J) quartet.Table 2 lists the quasi-metastable levels for the lower config-urations of the alkalilike atoms that obey this selection rule.9Note, however, that this selection rule is weak and holds bestfor lower levels such as 4S3/2 and 4P5/2, which have the great-est energy separation from their neighbors and, therefore,have the weakest second-order coupling to autoionizing dou-blets.

Figure 4 shows an energy-level diagram for the 109.1-nmtransition in neutral Cs. Figure 5 shows the emission spec-

Table 1. Transitions from Core-Excited 2 p States in Neutral LiObserved Calculated

Relative Wavelengtha WavelengthbTransition Intensitya (nm ± 0.01) (nm)

ls2p2 2 p - S2 2p 2Po 62 20.75 20.745- 1s23p 2 P1 12 21.46 21.458

- ls24p 2P0 6 21.71 21.716- 1s25p 2P0 2 21.84 21.837

s2 S + e 22.05

(1s2p)3 P3p2P 1S22p2po 8 19.78 19.761[(ls2p) P 4p + (s2p) P 3p] 2P - s22p 2 o 3 19.48 19.472

- ls2 3p 2P0 10 20.10 20.099- 1s24p 2P0 0.3 20.33 20.326- 1 25p 2P0 0.2 20.43 20.432

[(ls2p) 3P 4p - (s2p) P 3p] 2P - ls23p 2P0 8 20.03 20.0292s4p 2P0 1.5 20.25 20.254

a Ref. 6.b Ref. 34.

0

0

C2

0



4348s/ Is2 S CONTINUUM

2949A -

14904 c u. 1s22p 2 o

0 1s22 2S

Energy-level diagram for a possible 207-A laser in neutral

Table 2. Quasi-Metastable and Metastable QuartetLevels of Alkalilike Configurations

Configuration Quasi-Metastable Metastable

p5 sp 4S3/24D1/2 4D7/2

p5sd 4P5 /24F3/2 4F92

p5 pd 4S3/2 4D1/24D7/2

4 G,/2 4G11/2p5 d2 4P5/2p5d2 4P5 /2

4F3/ 24F9 /2

138799 ZZ/Z/'"" Cs 5p5 6s [I ]

106248. 1 5p5 5d6s 4 P5 /2

trum of neutral Cs taken in a pulsed hollow-cathode dis-charge by Holmgren et al.10 As is the case in each of thealkali atoms, the emission from the quasi-metastable levelsdominates the neutral emission spectrum." Table 3 givesthe radiative and autoionizing rates for the lowest quasi-metastable level of each of the alkali atoms. Table 4 givesthe transition wavelengths and designations of each of thequasi-metastable lines."1

In a recent experiment, Pedrotti et al.12 have used a pulsedhollow-cathode discharge and tunable VUV radiation gener-ated by four-wave mixing to measure the oscillator strengthand hyperfine structure of the 109.1-nm transition (Fig. 4) inneutral Cs. Their value of 7.2 X 10-3 is in good agreementwith the value predicted by the RCN/RCG atomic physicscode.' 3

Because of their large doublet component, the quasi-metastable levels permit quartet-doublet transfer schemesat large intercombination oscillator strength and may alsoallow direct lasing in the XUV. As will be discussed inSection 5, they also permit a new type of core-excited laserspectroscopy.

3. PRODUCTION AND MEASUREMENT OFMETASTABLES

A. Metastable Production by MicrowavesDuring the course of this program, we have used three meth-ods to produce metastable atoms and ions. These are high-power microwaves, pulsed hollow-cathode discharges, andphotoionization by laser-produced x rays. The microwavemethod is simple, and the repetition rate of 400 Hz is espe-cially well suited for observing emission spectra at relativelylow atom density (about 1014 cm- 3). Under typical condi-tions, about 300 kW of 9.4-GHz radiation in a 2-,usec pulse isapplied to a ridged waveguide emission cell. In apparatus of

Cs+927 A

Cs901 A

Cs1091 A

90 950 100 1050X A)1091 A

1100 1150

Fig. 5. Emission scan of Cs from pulsed hollow-cathode discharge.

347//,//// "/ s+ 5p Iso3107 C 5 S0

14597 IF 5p6 5d 2 D5 /2

0 5p6 6 2sFig. 4. Energy-level diagram for quasi-metastable emission in neu-tral Cs.10

Table 3. Radiative and Autoionizing Rates for theLowest Quasi-Metastable Levels of the Alkali Metals

Autoionizing Rate Radiative RateLevel (sec1) (sec-1)

Na 2p53s3p 4S3 /2 6.8 X 105 9.7 106K 3p53d4s 4P5 /2 1.8 X 105 3.5 X 106Rb 4p55s5p 4S3/2 8.5 X 107 2.6 X 107Cs 5p55d6s 4P5/2 1.0 108 5.4 X 107

545303 "Z =1 Is2p Po CONTINUUM

5 1 9 5 2 2 ///4// Is2s S CONTINUUM

496970 ,PUMP LASER

-2949 A|

463061-1

- 1s2p 2 P

- Is 2s 2p 4 PO

, 207 A, LASER TRANSITION

nCD

e4FP

W0

14

Fig. 3.Li.7

. . . . . . . .



Table 4. Quasi-Metastable Lines Observed with Microwave ExcitationaX Relative Upper-Level

Element Transition (nm) Intensity Energy (cm-')Na 2p53s3p 4S3/2 - 2p63p 2P312,1/2 40.52 7.0 263 789 + 120K 3p54s4p 4S3/2 - 3p64p 2P3/2 67.39 23.0 161 426 60

- 3p64p 2p,/2 67.36 6.03p53d4s 4F3/2 - 3p63d 2D3/2,5/2 69.17 2.0 166 092 : 603p53d4s 4P5 /2 - 3p63d 2D3/2,5/2 72.10 27.0 160 227 d 60

Rb 4p 55s5p 4S3/2 - 4p65p 2P3/2 82.37 30.0 134 220 40_ 4p65p 2P1/2 82.20 12.0_ 4p66p 2P3/2,/2 90.53 0.5

4p54d5s 4P5/2 - 4p64d 2D5/2,3/2 85.18 6.0 136 756 40Cs 5p55d6s 4P5/2 _ 5p65d 2D5/2 109.10 24.0 106 256 30

_ 5p65d 2D3/2 108.98 2.0- 5p66d 2DS/2,3/2 119.58 3.0_ 5p67d 2D5/23/2 124.72 1.0

a Ref. 11.

y5 SUPPORT ROD-

CATHODE i0)ANODE 9\4t

GLOW DISCHARGE .10'Al

WINDOW WATER

Fig. 6. Schematic of pulsed hollow-cathode discharge.'

TANTALUMT ARGET f

\ fTPROBELASER

LITHIUM VAP(1017 c 3 )

SOFT-X-RAY/ RADIATION

x . l , ~ 2

'OR _ q L- (IS 22s)2 S+1w

I I Ii i II I I1.0 I II.O t 6i (l~smS

the incoming microwaves, which occurs as the electron den-sity rises above the plasma frequency. Willison et al.6 haveused this method to take the emission spectrum of the even-parity levels of Li. Mendelsohn et al.11 have used it toexamine the column I quasi-metastable emission spectrum,and Dimiduk"' is now using it to study singly ionized columnII quasi-metastable emission.

B. Pulsed Hollow-Cathode DischargeTo overcome the limitations on neutral pressure of the mi-crowave method, Falcone and co-workers' 5 developed thepulsed hollow-cathode discharge shown schematically inFig. 6. A 5-cm-diameter stainless-steel tube contains themetal vapor and serves as the discharge anode. Inside andconcentric with this tube is a 30-cm-long stainless-steel tubeof 1.9-cm diameter, which functions as the cathode. Thedevice operates in a heat-pipe mode at a vapor pressure ofabout 6 Torr, an applied voltage of about 5 kV, and a currentof about 1500 A. The pulse length is about 1 psec, and thedischarge runs at a rate of 10 Hz. Using this type of dis-charge, Holmgren et al.'6 measured populations of the meta-stable (ls2s2p) 4P level of Li, and of the analogous (2p53s3p)

e

Fig. 7. Metastable production by soft x rays.

this type, electrons heat reactively; i.e., during successivehalf-cycles of the microwave field they first gain energy fromthe field and then return it to the field. For these conditionsthe peak reactive electron energy is about 100 eV. As elec-trons experience collisions with atoms and ions, they de-phase with the microwave field and gain energy in incre-ments of the reactive energy. The electron temperature islimited by electron atom and ion cooling, and by shielding of

C

.0 106

0I-

U

U) 0U)

-'

00

I 10 100PHOTON ENERGY (ev)

Fig. 8. Photoionization cross sections of Li (solid curve); emissionspectrum of a 30-eV blackbody (dashed curve).22

0

0co

0Qa)

PoV

Zia)(j)a)

NE

zI0a.

110231000


SnVol. 4, No. 4/April 1987/J. Opt. Soc. Am. B 551

electrons (Fig. 1). Figure 8 shows the absorption cross sec-tion as a function of soft-x-ray energy for ionization of a Li isor a 2s electron (1 barn = 10-24 cm 2 ) and also the spectrum ofa 30-eV blackbody. For an operating pressure of 1017 cm-3 ,the stopping distance for 100-eV x rays is about 10 cm.From a somewhat different point of view, a 30-eV blackbody,with an area of 10-3 cm2 , radiating for 1 nsec produces aspectrally integrated x-ray flux of 6.4 X 10'5 photons, or0.08 J. For the K-shell absorption cross section of Fig. 8 anda perpendicular distance from target of 0.5 cm, the spectrallyintegrated transition probability for a neutral atom equals

S e

o 25

'350

75 ~~~~~~~~~(b)-30 -20 -10 0 10 20 30

Fig. 9. (a) Spectral profile of the dye-laser probe pulse in thevicinity of 548.5 nm. (b) Absorption trace of the Li+(1s2s) 3S-Li+(1s2p) 3P transition at 548 nm.23

4D7/2 level of Na, of 3 X 1010 and 1011 cm-3 atoms, respective-ly. These populations were about a factor of 20 smaller thanwere those obtained in the ionic metastable levels of thesame element under similar conditions. This type of dis-charge has also been used by Holmgren et al.17 to obtain apartial Grotrian diagram for core-excited Na and to studyquasi-metastable emission from neutral Cs.10 Pedrotti etal.18 used a similar technique to take the emission spectra ofcore-excited Na and Mg. A higher-voltage pulsed hollow-cathode discharge was also recently constructed by King andCaro.19

C. Metastable Production by Laser-Produced Soft XRaysWhen a laser is focused onto a solid target at an intensity of1012-1014 W cm-2, a dense plasma is formed at the surface ofthe target that absorbs laser radiation and is heated by it.The plasma is often black over much of the XUV and soft-x-ray region and converts laser energy to soft-x-ray energy atan efficiency that is often as high as 50%.20 The use of suchradiation to pump x-ray lasers was first suggested by Du-guay 2l and was extended to the production of metastables byHyman and co-workers.4

Figure 7 shows the experimental configuration that wehave employed for using this radiation to produce metasta-ble ions and atoms.2 22 In this geometry the Li vapor sur-rounds the Ta target that emits the soft x rays. These x raysare omitted into about 7r sr and decrease in intensity as theinverse square of the distance from the target. For theconstruction of lasers and for many types of spectroscopicexperiments, the more pertinent quantity is the product ofdensity times perpendicular distance, which varies as theinverse of the first power of the distance from target.

Ionic metastables are produced by photoionization of core

1ole I

E

n01

I 10 50DISTANCE FROM TARGET (mm)

Fig. 10. N*L [Li+(ls2s) 3S] as a function of distance from thetarget at a time 1.9 nsec after the peak of the 1064-nm pulse. Lidensity, 1017 cm-3; energy incident upon each of three targets, 2.3J.23

016

- 1015'E

cIn

-JJZ IOI4

l0 13-I 0 1 2 3 4 5 6

TIME (nsec)Fig. 11. N*L [Li+(js2s) 3S] as a function of time with respect to thepeak of the 1064-nm laser pulse. Distance from targets, 7 mm; Lidensity, 1017 cm-3; energy incident upon each of three targets, 2.3J.23

0

0'3

[- ° l ]

A/ ,

- i-i:1i



64.4 ' E1(Is2s S)60.8 - -i Is2p 2 4 P

371 nm57.4-i, Is2s2p 4 P0

ELECTRONS

° 2pP ° I- s 22s 2S

Fig. 12. Energy-level diagram showing photoionization of the ab-sorber atom and the subsequent electron excitation of the targetatom. The laser-probe transition is also indicated.24

7.1 X 10-3; i.e., for a ground-level Li density of 107 cm3, 7.1 X1014 cm-3 metastable ions will beproduced.

The ionic metastable density as a function of both dis-tance and time is determined by measuring the absorption ofa picosecond-time-scale probe laser tuned to an appropriatetransition. For incident laser energies in the range of a jouleor more, the spectral absorptions are sufficiently broad thatthese measurements can be made with an optical multichan-nel analyzer on a single-shot basis.23 Figure 9 shows a typi-cal absorption trace for a probe near 549 nm. The probelight for this trace was first smoothed by stimulated Ray-leigh wing scattering in CS 2. Figures 10 and 11 show theLi+(Is2s) 3S density-times-length product obtained by Caroet al. for a three-spot target cell with 2.3 J of 1064-nm energyincident per spot, both as a function of the distance fromtarget and as a function of time.23 The electron density forthe conditions of these figures varied between 1015 and 1016cm- 3, depending on the distance from target. Even at thiselectron density, metastability of at least several nanosec-onds is apparent.

D. Production of X-Ray-Produced Hot ElectronsThere is a second method2 4 for using x rays from a laser-produced plasma for the production of metastable atomsand ions. In this method an additional absorber gas isphotoionized so as to produce an impulsive burst of hotelectrons. These electrons, in turn, excite core levels in thesystem. We have used this method to produce population inthe Li(ls2s2p) 4 P level and also to measure the metastabilityof this level in the presence of about 10l5 cm-3 electrons andions. Figure 12 shows an energy-level diagram for this ex-periment, with Ne used as the additional absorber gas. Fig-ure 13 shows the initial energy distribution of the ejectedelectrons for excitation with a 30-eV blackbody. At a Nedensity of 1018 cm-3, these electrons cool, primarily by exci-tation of the Ne resonance line, at a mean rate of about720 eV nsec-1. This allows one to use a few-hundred-pico-second probe laser, in this case at 371 nm, to measure themetastability of the target level.

Using this method, we have produced excited Li(ls2s2p)4P densities of 1013 cm- 3 . This density is about 2 orders of

magnitude larger than that produced in our hollow cathodesbut 2 orders smaller than the Li+ metastable density pro-duced by direct photoionization. Figure 14 shows the meta-stable times-length product density of these metastables asa function of the time delay between the 600-psec-long 1064-nm laser pulse and the probe pulse of about the same length.The observed decay time of about 2.5 nsec can be attributedto electron dipole-dipole collisional deexcitation and showsthat there is not an anomalously large electron decay rate forlevels that are embedded in a continuum.2 4

E. Production by Charge TransferAnother method by which core-excited alkali metastablesmay be produced is by exothermic charge transfer from the

0

0

E 2

oz

0I0EI

100PHOTON ENERGY (eV)

(a)

,E8

2

00Ia

20C

ELECTRON ENERGY (eV)

Fig. 13. (a) Photoionization cross section of Ne and the x-rayspectrum 1 mm from the target. (b) Predicted ejected electrondistribution for a Ne density of 3 X 1017 cm- 3.24

E

Z0\

10 12 l

0 1 2 3 4 5TIME DELAY (nsec)

Fig. 14. N*L for Li(ls2s2p) 4P 0 versus the time delay between thepeaks of the probe and 1064-nm pulses. The solid line is a fit to thedata yielding Tdecay = 2.5 nsec.2 4

Ne Li

SOFT X RAYSFROM PLASMA

eV

0

0

QPoCd

eV22 ! Do .Go Z ' E(2p5 )

, PHOTOIONIZATION _ .8 X CROSS SECTION OF NEON

/ En 30 eV BLACK BODY, 4 _ / \6 PHOTON FLUX

4 iI

/ .C2 /

l I I I I

.11


5.4 .... + .... EI(IS2)

0


Table 5. Metastable Production by Charge TransferParent Ion Donor Metastable Exothermicity (cm71)

Li+(ls2s) So Li(ls22s) 2S1/2 Li(ls2s2p) 4P5i/2 12 985Na+(2p53s)/2[3/2]a=2 Na(2p63s) 2S1/2 Na(2p'3s3p) 4S3/2 1139K+(3p4s)/%[%13/2=2 K(3p64s) 2S1/2 K(3p54s4p) 4S3/2 1081Rb+(4p15s)/%[3/j]5=j Rb(4p65s) 2S1/2 Rb(4p'5s5p) 4S3/2 650Cs+(5p5 6s)/,['/2 J=2 Cs(5p66s) 2S1/2 Cs(5p'5d6s) 4P3/2 1 149

ground neutral to the parent core-excited ion. For example,atoms in the Cs(5p5 5d6s) 4P5/2 level may be produced by thereactionCs(5p 66s) 2S1/2 + Cs+(5p'6s)'/ 2['/2]J=2 - Cs+(5p6) lSo

+ Cs(5p55d6s) 4P5/2 + 1149 cm-'. (I)

For a typical charge-transfer cross section of about 10-15cm2, and a neutral Cs density of 1017 cm-3, about 5% of thecore-excited parent ions would transfer to this level in10 nsec. Since core-excited parent densities in excess of 1015cm-3 are readily obtainable by x-ray photoionization, it isexpected that this method should produce densities greaterthan 103 atoms cm-3.

Table 5 lists the exothermicity for charge transfer betweenthe core-excited parents and some of the metastable levelsand quasi-metastable levels of the alkali atoms. In both Naand Rb we have some early evidence that charge transfer isthe operative populating mechanism. In Na, Holmgren etal.'7 note enhancement of fluorescence from neutral corelevels when population is transferred to higher ion levels. InRb, Spong et al.25 note reduction in the quasi-metastableradiation at 82.4 nm when the Rb+ level is depleted by atunable laser.

4. GENERATION AND MEASUREMENT OFPICOSECOND PULSES

A. GenerationOne of the applications of stored metastable energy is to thegeneration of short pulses of XUV and soft-x-ray radiation.This is accomplished by anti-Stokes scattering of picosec-ond-time-scale visible or ultraviolet laser pulses off metasta-ble atoms.26 Figure 15 shows an energy-level diagram forsuch scattering in He-like carbon. In this case near-UVradiation at 354.7 nm will scatter into 4.03-nm radiation.This scattering will be either stimulated or spontaneous,depending on whether the metastable atoms are, or are not,inverted with respect to ground. The cross section for spon-taneous anti-Stokes scattering, i.e., the ratio of scatteredXUV photons to incident laser photons, varies as the inversesquare of the detuning from resonance and, at fixed XUVoscillator strength and detuning, varies as W3. For scatter-ing of 354.7-nm radiation to 4.03 nm in C v, the detuningfrom resonance is 168 cm-', and the spontaneous anti-Stokes scattering cross section for the incident laser beam is5.5 X 10-19 cm2 .

A limitation on the intensity of this type of radiator isposed by its nature as a two-photon blackbody.26 This isperhaps easiest seen by describing the process in terms of alaser-induced per-atom emission rate, A(w), and a laser-induced cross section for the absorption of XUV radiation,a(w). That is, the incident laser beam not only causes the

metastable atoms to couple through virtual levels to emitXUV radiation but also causes ground-level atoms to absorbradiation by coupling through these same virtual levels.Both A(c) and a(w) increase linearly with incident laserintensity and are related to each other in the same manner asare the emission and absorption coefficients for single-photon processes, i.e.,

72c22() A(0.

=ic

The brightness of the radiation source B(w) (power perbandwidth in radians/second per solid angle) and area isdetermined by the interplay of the emissive and absorptiveprocesses and, for a sample of a length L, is given by

B(co) = - [exp(hW21 kT) -1-187r 3c2

X 1 - exp[-(co)(Nj - N2)L] 1,

6c 3 LT \W2illil + iil 2pa(@)~~ ~~ = ~ + -g(O)6C2ht3 _ ,z oi-(' COi + (Jovis _A

(2)

(MKS units). In this expression, T is the equivalenttemperature of the metastable level, i.e., N/N, =exp(-hW2i/kT); yujj are matrix elements; wi are the frequen-cies of the intermediate levels; Pp/A and wvi, are the intensityand frequency of the pump laser; is the frequency of thescattered radiation; and g(w) is the line shape for the two-photon absorptive process.

In the optically thin case, -(M)(N - N2 )L << 1, B(c)increases linearly with the incident laser power density andis the same as obtained from the spontaneous-scatteringviewpoint of the preceding paragraph. As the laser powerdensity is increased and the medium becomes nominallytwo-photon opaque, the brightness approaches a constant

2,383,361 cn' Is2p'P__

354.7 nm

2,455,006 ci' Is2s'O

nm

Is2 ISO

Fig. 15. Anti-Stokes scattering in C v.



Table 6. Anti-Stokes Scattering at Soft-X-RayWavelengthsa

ls2s S ls2p P X(2s - 2p) X(2p - is)Species (cm-') (cm-') (nm) (nm)

He I 166 277 171 135 2,058.7 58.43339Li II 491 372 501 806 958.4 19.9280Be III 981 175 997 454 614.3 10.02552B IV 1 635 752 1 657 979 449.9 6.03144C v 2455 006 2 483 367 352.6 4.02679N vi 3439 390 3 473 790 290.7 2.8787O VII 4 588500 4 629 200 245.7 2.16020F VIII 1 228 460 5 949 900 211.8 1.6807Ne IX 7382 890 7 436 600 185.2 1.3447

Experimental values are from Ref. 44; theoretical results, in italics, arefrom Ref. 45.

Co

li w 34 eV

Ca,

PICOSECOND XUVPULSE

49305 ... Co'(39645)

3p6452 15 _

PICOSECOND VISIBLE 3P'3d4p 4I/2PULSE

/X 7206 X ' 3872 AftC- 1.1 X 1-4

273167 3d2

261221 3p5

3d4, 4F312

) < ~~~~49305'''''''"' C." (3p6)rA E .x10-1

2

3p64S 2S

Fig. 16. Correlation of picosecond XUV pulses.

value equal to that of a blackbody radiator at the tempera-ture T of the metastable level. In general, and especially atshort wavelengths, the temperature of the metastable levelwill be much higher than that of a radiating level.

Although the maximum power per bandwidth is deter-mined by the ratio of metastables to ground-level atoms, thetotal emitted power may be increased by using a broadbandpump laser to increase the spectral range of two-photonopacity.

In an experiment in 1978, Zych et al.26 used a He-Ne glowdischarge and a 100-psec-long pulse of 1064-nm radiation toverify the two-photon blackbody nature of the source. Inthat experiment they found a per-bandwidth intensity ratioof laser-induced 56.9-nm light to He resonance-line 58.4-nmlight of 140.

We believe that it may be possible to use soft-x-ray photo-ionization to produce quite high densities of He-like meta-stable ions through species as high as Ne IX. For thesespecies the necessary laser wavelength to reach the XUVresonance transition is within the range of frequency-doubled dye lasers, and the generated wavelength is as shortas 1.3 nm (Table 6).

The reason why it may be possible to produce a relativelyhigh density of a particular species is that, as an element isstripped down, the energy that is necessary for photoioniza-tion rises abruptly as the He-like species is encountered.For example, the successive ionization potentials for C are11.3,24.4,47.9,64.5, and 392.1 eV. Therefore, for a correctlychosen radiation flux and temperature, the ambient atomswill be stripped to predominantly He- and Li-like ions. In-ner-shell photoionozation of the latter species will then pro-duce the desired metastable.

For the generated XUV pulse to be as short as the incidentlaser pulse, it will be necessary for the detuning from theresonance line to be large compared with the bandwidth ofthe pulse. For the 168-cm-l detuning of 354.7 nm in C v,this would permit generation of pulses as short as about 0.03psec. For this detuning, the laser saturation energy at which1/e of the stored metastable energy will be scattered is 0.34 Jcm-2 . At a metastable density of 1014 cm-3 ions about 1011photons will be scattered from a 1-mm3 volume into 4ir sr. Ifthis occurs in 1 psec, the scattered power will be about 4.9MW. This radiation will come from a small enough regionthat grazing-incidence optics, such as those discussed inSubsection 6.C, may be used to focus it into a reasonablycollimated beam.

B. MeasurementMetastable levels may also bear on the measurement of thelength of picosecond-time-scale soft-x-ray pulses.2 7 Oneapproach is shown schematically in Fig. 16. Here, broad-band XUV radiation with photon energy greater than 34 eVphotoionizes neutral Ca and, because of configuration mix-ing, produces Ca II ions in the 3p 53d 2 2p level. These ionsautoionize in about 2 psec. A picosecond-tunable laser willtransfer these ions to a radiating quasi-metastable level onlywhen the broadband XUV pulse and the tunable laser pulseoverlap in time. The system, therefore, provides a means tocorrelate XUV pulses with optical pulses, with the minimumcorrelation time determined by the autoionizing time of theion. For appropriate levels, this time may be as short as10-14 sec. Note that the energies of the levels in Fig. 16 areRCN/RGN code values' 3 and have not been experimentallydetermined.

5. SPECTROSCOPIC APPLICATIONOver the past several years we have developed three spectro-scopic techniques that are based on core-excited metasta-bles. These new methods allow one to obtain level positionsand autoionizing linewidths to the accuracy of visible lasersand, therefore, at a resolution that is about 10 times greaterthan that previously obtainable.

A. Anti-Stokes Radiation SourceThe first of these techniques is absorption spectroscopy us-ing the anti-Stokes source that was described in Section 4.Metastable atoms are produced, and a tunable visible laser isscattered off these atoms to produce tunable XUV radiationthat is incident upon the sample cell. The linewidth of thetunable radiation is the wider of the Doppler width of themetastable transition or the linewidth of the incident laser.In two related sets of experiments using this source Rothen-berg et al.2 8 ,29 examined a portion of the core-excited spec-trum of neutral K. Figure 17 shows the apparatus used inthe first of these experiments. A tunable laser is scatteredoff He metastables produced in a cw hollow-cathode dis-charge. The tunable spontaneous radiation counterpropa-gates through a K cell and, after passing through an Al filter,is incident onto a photomultiplier. The spontaneous anti-Stokes scattering cross section for visible photons at 600 nmto XUV photons in the 50-nm spectral region is 4 X 10-23cm2. For typical conditions this resulted in the generationof about 108 XUV photons. The available solid angle of the



rELECTRON POTASSIUM rXUV SCATTERED5 MULTIPLIER CELL /RADIATION

LALUMINUM 1 FILTER +

TUNABLE HOLLOW CATHODELASER HELIUM DISCHARGE

Fig. 17. Schematic of apparatus used for absorption spectroscopyof K.28

detector and the Al filter reduced the effective count rate toabout 800 photons per pulse, or 8,000 photons per second.

Figure 18 shows the result of a typical absorption scan.Table 7 summarizes the spectral information that was ob-tained.2 8 A second set of experiments used high-power-pulsed microwaves for the production of the He metasta-bles.29 This produced an anti-Stokes signal that was muchstronger than was the case with the pulsed hollow-cathodebut also resulted in a high level of spurious XUV radiation.A spectrometer was used to reject this radiation; this in turnresulted in a net count rate that was only about a factor of 10greater than with the cw hollow-cathode. Table 8 summa-rizes the spectral information that was obtained with themicrowave apparatus. The designations in both Tables 7and 8 were obtained from the work of Mansfield. 30

A different, more limited, experiment that used anti-Stokes radiation was the measurement of the isotopic shiftof the ls2s So of 3He and 4He. In this experiment Falconeet al.3 1 used visible fluorescence in Ne as an internal detectorfor 58.37-nm radiation and measured the difference in theoptical parametric oscillator wavelength that was necessaryto excite the Ne from metastables from 3He and 4He. The

,1.0I-I

Wa 0.5

U) N1&11_ BACKGROUNDZ CALIBRATIONI-r I

result was a measured shift of the isotopic singlet metastablelevels of 7.8 1 0.5 cm-'.

B. Laser-Generated FluorescenceThe second of the techniques that have been developedmakes use of laser-produced fluorescence from atoms storedin metastable levels. Because fluorescence must be ob-served, the technique is most applicable to levels that auto-ionize sufficiently slowly to have a good fluorescence yield.In the first of these experiments Willison et al.32 used pulsedmicrowaves to produce Li(ls2s2p) 4P5/2 quartets and tun-able laser radiation to transfer these atoms to the Li(1s2p2 )2P level. Radiation at 20.7 nm (Fig. 3) was observed as afunction of the tunable laser wavelength. In close accord tothe predictions of Bunge33 ' 34 and Jauregui and Bunge,3 5 thistransition was found to be at 33 872 + 2 cm-', thus providingthe first experimental connection between the quartet anddoublet manifolds of neutral Li. This technique may be

Table 7. Potassium Absorption FeaturesPreviouslyObserved

Energy Linewidth Designation Energya

183 320 + 1 cm-' 8.4 cm-1 3p 53d(3P)5s 2P1/2 183 322 cm-183 530 10.5 3p53d(3P)5s 2P3/2 183 532184 008 2.6184 076 3.4 184 076184 321 2.5184 344 15.0 3p54s(1P)5s 2P3/2 184 342184 465 7.8185 806 1.9186 659 5.0 3p54d('D)4s 2D3/2 186 656

a Ref. 28.

183200 183300 183400 183500 183600FREQUENCY (Cm')

, 1.0I-(n

z

M 0.5I-

z

184000 184100 184200 184300 184400FREQUENCY (cm')

Fig. 18. Absorption scans of K. Vapor pressure is JO15 cm 3, and cell length is 5 cm.28

nOWM

eF

X

$aW0O+

>d9012PC+Oa0

0


_ . _ _ _ _ .. _ _ _ _ _ ...

v


Table 8. Linewidths and Positions of PotassiumAbsorption Features Observed with the Microwave

Apparatus -

Energy Linewidth Previously Observed(cm-') (cm-') Designation Energy (cm- 1)a

179 885 4.0 3p53d(3D)4s 2D?/2 179 886

179 918 2.1 179 920

180 547 43.0 3p53d(P)4s 2P/2 180 551

180 794 55.0 3p55d('P)4s 2P?/2 180 791

180 840 11.0 180 850

181519 2.7 181517

181 745 5.5 3p53d5s 4P?/2 181 742

182 152 8.8 182 152

182 652 .5.6 182 651

a Ref. 29.

used for transitions that have very small oscillator strengths.For example, for the ls2s2p 4P - 1s2p2 2P transition, withan oscillator strength of 2.5 X 10-8, 36% of the populationwithin the 0.2-mm 2 beam was transferred with 10 mJ of laserenergy.

Using a related method, Holmgren et al.17 used metasta-ble population to develop a partial Grotrian diagram forcore-excited Na. In this experiment a pulsed hollow cath-ode was used to excite the metastable 2p53s3p 4D7/2 and the2p53s3p 4S3/2 quasi-metastable levels, and a tunable laserwas used to transfer this population to other core-excitedlevels. Visible and near-UV fluorescence from these latterlevels was observed, and loops were established betweeninterconnected levels. Branching ratios were also measuredand found to agree to within a factor of 3.5 with calculated

values based on the RCN/RCG atomic physics code.'3 Re-cently, Engstr6m et al.36 have given further confirmation ofthese ratios. Tables 9 and 10 summarize the results ofHolmgren et al., and Fig. 19 shows the brighter lines of theNa spectrum.

C. Laser-Depletion SpectroscopyIn quite recent work Spong et al.2 5 have demonstrated whatmay be the most powerful of the laser spectroscopic meth-ods. In this technique the XUV radiation from a quasi-metastable level is monitored, and a tunable laser is scannedover the region where other autoionizing lines are expectedto be present. When one is encountered, the quasi-metasta-ble radiation is depleted, thereby determining its autoioniz-ing linewidth and its position relative to the quasi-metasta-ble level. By using a curve-fitting method, which is in one-to-one correspondence with the curve-of-growth method,the transition oscillator strength may also be determined.

In this work the 4p55s5p 4S 3 /2 quasi-metastable level of Rbis excited by laser-produced x rays (Fig. 20), and radiation at82.4 nm is monitored with a wide-slit spectrometer. Table11 gives the linewidth, transition energy, and tentative des-ignations of the depletion transitions that we have thus farobserved. These first results give linewidths, and thereforeautoionizing times, to an accuracy that is at least 20 timesgreater than given previously.

In an earlier experiment, using pulsed hollow-cathodetechnology, Pedrotti3 7 observed radiation at 20.7 nm in Liand used this depletion technique to obtain a width of 25.5cm-' for the Li ls(2s2p 3p) 2P autoionizing line at 475 163cm'.

By observing the radiation from an appropriate quasi-metastable level, this technique permits observation ofautoionizing lines of both even and odd parity and with Jvalues that make them inaccessible by optical absorptionfrom ground. The observation of Rydberg transitions andinterferences should also be possible.

Table 9. Relative Term Energies, Designations, and Coulombic Autoionizing Rates of Na I Core-Excited QuartetLevels

AutoionizingConfiguration Energy (cm-')a Composition Rate (sec-1)

2p53s3p 0 0.98 4S3/2 - 0.13 4P3/2 4.15 X 1052 841 0.99 4D7/2 03 187 0.94 4D5/2 - 0.21 4P5/2 + 0.18('P) 2D5/2 1.25 X 10103 536 -0.92 4D3/2 + 0.23 4P3 /2 - 0.22('P) 2D3/2 1.79 X 10103 830 -0.94 4D1/2 + 0.22('P) 2P,/2 + 0.20 4P1/2 1.06 X 1094 768 0.91 4P5/2 + 0.32(P) 2D5/2 + 0.20(3P) 2 D5/2 3.84 X 10105 152 0.76 4P3 /2 + 0.48('P) 2D3/2 + 0.30(3P) 2D3/2 8.59 X 1010

+ 0.22('P) 2P3122p53s4s 22 555 -1.0 4P5 2 2.93 X 10-3

2p53s3d 28474 0.97 4P 1/2 - 0.24 4D1/2 2.02 X 10628 543 0.86 4P3 /2 - 0.49 4D3/2 1.76 X 10828 595 -1.0 4F9/2 028 654 0.72 4D5/2 - 0.60 4P5/2 - 0.33 4F5 /2 1.02 X 10628 703 0.71 4F7 /2 - 0.70 4D7/2 1.76 x 10829 168 -0.73 4F5/2 + 0.58 4P5/2 + 0.26('P) 2D5/2 5.08 X 10929 264 -0.65 4D3/2 + 0.54 4F3/2 - 0.42 4P3/2 1.55 X 109

+ 0.22(lP) 2P3/2 - 0.21(lP) 2D3/2

a 42 cm- 1.



Table 10. Na I Quartet Transition Wavelengths, Transitions, Probabilities, Branching Ratios (B R), andObserved Line Intensities

ExperimentalUpper Level Lower Level X (A)- Aik (108 sec-1) gjB R Intensity

(2p53s3d) 4P/ 2 (2p5 3s3p) 4S3/2 3511.0 1.15 1.3 1.34P3 /2 4286.7 0.28 0.32 0.464D3/2 4008.8 0.15 0.18 0.27

"P3/2 4S3/2 3502.5 0.88 1.0 1.6"P3/2 4273.9 0.16 0.18 0.234P 5/2 4204.9 0.25 0.28 0.464D 3/2 3997.7 0.08 0.09 0.144D5/2 3942.6 0.21 0.24 0.32

4D3/2 4S3/2 3416.2 0.15 0.034D1/2 3930.6 0.25 0.05 0.154D3/2 3885.7 0.62 0.12 0.36

4D5/2 4S3/2 3489.0 0.42 1.5 1.34P3/2 4253.8 0.05 0.18 0.174P5/2 4185.5 0.49 1.8 1.54D3/2 3980.3 0.05 0.18 0.144D5/2 3925.6 0.45 1.6 0.854D7/2 3872.9 0.12 0.45 0.19

4F5/2 4S3/2 3427.3 0.28 0.11 0.094D5/2 3848.0 0.28 0.03 0.054D3/2 3900.4 0.77 0.08 0.15

4F7/2 4P 5 2 4176.7 0.35 0.83 0.824D5/2 3917.9 0.66 1.5 1.64D7/2 3865.5 0.58 1.4 1.3

4F9/2 4D7 /2 3881.8 1.63 10.0 4.2(2p 53s4s) 4P5/2 4S3/2 4432.3 0.14 0.91 3.1

4P3/2 5744.2 0.04 0.23 0.124P5/2 5621.0 0.14 0.91 0.424D3/2 5256.4 0.02 0.16 0.074D5/2 5162.5 0.15 1.0 0.834D7/2 5071.2 0.41 2.7 2.7

a Air wavelengths, 0.2 A.

6. LASERSOf the several applications of core-excited metastable levels,the application to the construction of lasers has thus farproven the most elusive. The essential difficulty is that theinert gaslike metastables, i.e., Li+(ls2s) S, which we knowhow to produce in large densities, are difficult to invert;while on the other hand the column I metastables and quasi-metastables, which are invertable with regard to valencelevels of the atom, are more difficult to produce. The lack ofknowledge of the spectroscopy of these latter species alsomakes population measurement difficult and forces the useof less-than-optimum systems.

A. Power and Energy RequirementsWe begin by considering the requirements on pumping pow-er and energy for reasonably well-chosen laser systems in the10-100-nm spectral region. Table 12 lists the species, tran-sition, and Doppler-limited gain cross section for several ofthe species that we have studied. The table includes notonly the metastable systems discussed thus far but also somesystems that are based on selective Auger decay, which willbe discussed somewhat further below.

Since the metastable store-and-transfer approach will noteasily allow the use of resonators, lasers of this type willrequire a single-pass gain of about exp(20) to saturate fully.For a gain cross section of 10-13 cm 2, this requires an exciteddensity times length product of NL = 2 X 10"4 cm 2. By oneof several approaches it should become possible to confinethe pumped area to about 1 cm2, thereby requiring a total of2 X 1014 excited atoms. For atoms with an energy of 100 eV,this requires a total stored energy of about 3 mJ.

We next assume that pumping occurs by photoionizationby laser-produced x rays. Though conversion efficiencies ashigh as 80% from laser energy to x-ray energy have beenreported, 10% conversion efficiency into the useful band-width is more typical. If these x rays can be completelyabsorbed, then in the ideal case a laser pumping energy ofabout 30 mJ will be required. For the metastable store-and-transfer systems this energy can be deposited in about 1nsec, while in direct pumped systems with large oscillatorstrength and, therefore, small spontaneous-emission time, itwill have to be deposited in less than 100 psec.

In a realistic system there will be additional inefficiencies.In a photoionization-pumped system, x rays are often



3s3d 4 F 33n 3S3D 4 P 3s3O 4 D

NUMBERS BESIDE LEVELS INDICATETOTAL ANGULAR MOMENTUM J

7/2

3/2Fig. 19. Na I core-excited Grotrian diagram.'7

167032 """'"" IAUTOIONIZING__ LEVELS

DYE LX

134220 5p 4s3/2

X=82.4nm

46 SO33691 "I'll"/// 4p6 s

12817 4p65p 2 P3 /20 4p65s 2

1/2

Fig. 20. Laser depletion spectroscopy in Rb.

Table 11. Depletion Spectroscopy of Neutral Rb

PreviouslyObserved Linewidth Tentative Observed

Energy (cm-') (cm-,) Designationa Energy (cm1)b

148 874 <0.5 4p 54d5s D3/2 148 880150 559 2.3 4p55s6s 4P5/2 150 583151 282 <0.5152 287 2.6 152 348153 384 1.4 153 356154 016 36.0 4p54d5s 4P312 154 082

a RCN/RCG atomic physics code, Ref. 13.b Ref. 46.

stopped by electrons in shells other than the desired one; inan Auger-pumped system the yields to a particular level willnot often exceed 20%; in other systems pumping by second-ary processes such as charge transfer will be necessary, andthe efficiencies of these processes are not yet known. Evenso, it appears that photoionization pumping of metastablelevels offer the prospect of a class of lasers that are bothefficient and have a threshold pumping energy of under ajoule.

B. Laser SystemsWhen possible, direct photoionization by laser-produced xrays is the preferred pumping mechanism. This approachwas proposed by Duguay2 l and extended to metastable sys-tems by Mahr and Roeder and Hyman and co-workers.4

Using the geometry of Caro et al.,2 Silfvast and colleaguesconstructed a photoionization-pumped 442-nm Cd laser38

and also used a tunable laser to transfer population to higherlevels to construct several near-UV lasers.39

Though direct photoionization readily leads to inversionon intermediate transitions, it is not yet clear if it may beused to produce an inversion with respect to ground. Prob-lems include the production of ground-level ions by longer-wavelength x rays, by x-ray-produced electrons, and throughautoionization.4 By operating at much lower pressure, andby using appropriate filters, it may well be possible to over-come these problems but probably at the expense of muchhigher pumping energy.

Another way to use photoionization pumping is throughselective Auger processes. 40-42 The potential advantage ofsuch systems is that lasing may occur to high-lying levels inthe second ion, thereby avoiding the problems of direct pho-

3s3d 4 P 3s3d 4D294x IO3

293 x 103 k

292 x 103

0

0Cd.

0a)

3s4s 4 P

287 x o3J

286 x103

7

E-

-J>

-J

zI 270 xIO3

269 x 103

268 x 103

267 x 103

266 x 103

265 x10 3

264 x 103



Table 12. Possible Laser SystemsSpecies Process XLASER (nm) CGAIN (cm2)

Metastable transferLi I ls2s2p 4P0 + hw (295 nm) -

ls2p2 2p - ls22p 2P020.7 9.7 X 10-14

NaI 2p53s3p 4S3/2 + hw (342 nm) -2p'3s3p 4 D3/2 - 2p6 3d 2D3/2,5/2 37.9 6.9 X 10-15

Quasi-metastableK I 3p53d4s 4P,5/2 - 3p63d 2D5 /2 72.1 4.9 X 10-16Rb I 4p55s6p 4S312 - 4p6 5p 2P3 /2 82.3 5.1 X 10-15Cs I 5p55d6s 4p5/2 - 5p 65d 2D5/2 109.1 4.9 X 10-14

Shake-upLi II ls3s 3S - ls2p 3

P 165.3 1.0 X 10-3

AugerZn III 3d84s2 G4 - 3d94p F3 133.2 8.8 X 10-13Cs III 5s25p4 6s 2D5/2 - 5s25p5 2P3/2 63.8 5.6 X 10-13Rb III 4s24p 45s 2S1/ 2 4s24p5 2P3/2 49.0 5.7 X 10-13

toionization. One example4 i of such a system is shown inFig. 21. Here, photoionization of a 3p electron in neutral Znleads, through super-Coster-Kronig decay, to inversion ofthe 3p53d8 4s2 1G4 level of Zn III with regard to several levelsin the 3d94p and 3d94s configurations. Possible lasing tran-sitions are shown in Fig. 22. The Einstein A coefficient ofthe 133.2-nm transition results from configuration mixing,and the metastability of this level is therefore uncertain.We have not yet been able to identify a selective Augersystem, with good yield, to a completely metastable level.

We turn next to the metastable and quasi-metastable sys-tems of column I. Much has been said of these systems inthe previous sections. An example of a metastable transfersystem in Na, which overcomes the small intercombinationoscillator strength difficulty of the earlier Li system, isshown in Fig. 23. The parameters of this system, as well asthose of two related systems, are shown in Table 13. Inthese systems it is intended to create an inversion by photo-ionization of the valence 3d electron. We are also interestedin systems in which transfer would be to a Rydberg level andwhere, therefore, photoionization of the lower level may notbe necessary. As compared with the Auger systems, thesesystems have the advantage that they typically have muchlower loss at the lasing wavelength, and the disadvantagethat, at least to date, that they are excited much less effi-ciently.

C. GeometryMost of the work to date on photoionization-pumped lasershas made use of a single-spot or multispot transverse geome-try (Fig. 7) in which the laser beam propagates through theambient vapor and is incident onto a heavy metal target.The generated x rays are emitted into about 7 sr, and theirintensity reduces as the square of the distance from thetarget. The NL product, which is the pertinent quantity forpumping lasers, therefore decreases linearly as the perpen-dicular distance. In practice, for any laser system there willbe a maximum x-ray power density at which it may operate.At a given laser energy per spot, this density, or perhapsplasma blowoff, will limit the distance of closest approach tothe target. If more laser energy is available, one uses multi-

ple spots or, at high enough energy, a cylindrical lens and aline focus.

As a means for obtaining additional length at a givenpower density, we have recently suggested43 the alternativegeometry shown in Fig. 24. Here, a section of a prolateellipsoid is used to reflect at grazing incidence the radiationfrom a laser-produced plasma located at one focus to a targetcell in the region of the second focus. The effective f-num-ber and optical efficiency of this type of nonimaging opticmay be very large. For example, at a wavelength of 10 nm,the grazing-incidence reflectivity of a Au surface is greaterthan 75% for all rays with grazing angles less than 10 deg. Inthe transverse plane, rays are collected over the full surfaceof revolution, yielding a total solid-angle collection ap-proaching 1 sr. Figure 25 shows the fraction of collected softx rays as a function of the ratio of the minor half-axis to thehalf-focal separation (b/c) for a point source placed at thefirst focus.

For a point source and a perfectly accurate surface, theradiation is focused into an annular cone that converges witha half-angle of about 1/2(b/c). For a finite source dimen-

3p53dlo 45296eV

/

/ 3d9 42

/ _ s -3d4s 91 eV

3p6 3d 1452-OeV

ZnI ZnI

3p6 3d84s 2

G4- 54.8eV

3d9 4p- 45.2 eV

3d94 37.3eV

- 27.4eV

Zn=

--- 4 * PHOTOIONIZATION= SUPER COSTER-KRONIG DECAY

Fig. 21. Population of 3d84s2 G4 level by super-Coster-Kronigdecay.41



Zn m

3d8 4s4p 3G3~254121 cm

X = 302.4 nmTW

3d8 4s 2 G4221052 cnf1

3d8 4s2 G4

X = 133.2 nmA = 8.2 X io8 sec-'

0= 8.8 X 10-13 cm 2

3d9 4p 1F3-145967cm'

3d9 5d 3G5 1_d95d _G5 261829.8 cm-X=366.9nm

3d9 5p 3 F4 234576 cm

739Anm/

3d8 4s 2 G4

X = 56.8 nmA =7.7 X IO8 sec'l

-=6.2X10-1 4 cm 2

3d9 4s 3D3- 78096 cmI

3d10 15o

X = 82.9nmA = 4.5 X 08 sec-

Q-= 1.3 x 10-13 cm2

3d9 4p 3F4m- 141327cmI

3d10 5~0

(b)Fig. 22. Energy-level diagrams for three possible systems in Zn II.41

306378 cm 2p5 3s [3/212

293037

341

2637732p 5 3s3p

2P5 3s3d 23/

379 A

41450 j (Na+) 2p 6 SO

29173 T 2p63d 2D3/2, 5/2

o-22p63S 2 S 1/2Fig. 23. Energy-level diagram for a 379-A laser in Na.

sion, the qualitative nature of the focus is determined by theconservation of optical etendue, i.e., A101 = A202, where Qand A are solid angle and area, respectively. The solid angleQ, intercepted by the short section of the eccentric ellipsoidis typically about 7r/3 sr, and the focal area is given approxi-mately by A2 = Al/(b/c) 2 . For a b/c = 0.1, the optic will

produce a linear magnification of the source of about 10,with an aspect ratio of approximately 25.

The comparison of the elliptical end-pumping geometrywith the transverse pumping geometry is dependent on theparameters of the particular laser system. To the extentthat the laser may be focused to a sufficiently small spot ontarget, the end-pumping geometry has a substantial powerdensity times length, and therefore gain, advantage over thetransverse pumping geometry. For example, at a 50-,smtarget spot size, this advantage is about a factor of 20. Onthe other hand, in many systems such a small spot is not ableto radiate at a sufficient rate to pump the system, and inorder for the available laser energy to be used maximally the

ELLIPSOIDALREFLECTOR

SOFT x

TaTARGET

.RAYS LASEROUTPUT

PUMPED MEDIUM

PLASMA-PRODUCINGLASER

Fig. 24. Schematic of longitudinal pumping using a prolate ellip-soidal reflector.43

Table 13. Possible XUV Lasers in Na I

Upper T AI Transfer Transfer Laser again LaserLevel (psec) gf X (nm) gf (cm2) X (nm)

2p53s3d 4D3/2 645 0.10 341.6 0.038 6.9 X 10-'5 37.902p53s3d 4F5/2 196 0.30 342.7 0.055 6.5 X 10-15 37.912p53s3d 2D5/2 45 0.011 -314 0.485 5.6 X 10-14 37.53

3dt0 SO-0

(a) (C)



0.5

z0

U-IL

0Luj-J

-JLu0U-

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Fig. 25. Fraction F of source energy delivered to the focal planeversus ellipsoid shape; b/c is the ratio of the semiminor to the half-focal separation.43

target spot size must be enlarged. At a spot size of about 1mm2, the end-pumping and transverse geometries haveabout the same gain. Even here, the end-pumping geometryhas the advantage of permitting a small target cell with aninherently improved aspect ratio.

ACKNOWLEDGMENTSThis is a review paper that incorporates the contributions ofmany of our colleagues, former students, and present stu-dents. These include Richard Caro, Roger Falcone, SteveWallace, Guang-Yu Yin; Douglas Holmgren, Andrew Men-delsohn, Ken Pedrotti, Joshua Rothenberg, Joe Wang, JohnWillison, Jeffrey Wisoff; Chris Barty, David Dimiduk, JeffKmetic, David King, John Macklin, Mark Sher, JackieSpong, and David Walker. The many contributions of eachof these people are gratefully acknowledged. We also thankour sponsors: the U.S. Air Force Office of Scientific Re-search, the U.S. Army Research Office, the U.S. Office ofNaval Research, the Lawrence Livermore National Labora-tory, and the Strategic Defense Initiative Organization.

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