Investigations of superfluorescent cascades

1 July 1994

OPTICS COMMUNICATIONS

ELSEVIER Optics Communications 109 (1994) 348-360

Full length article

Investigations of superfluorescent cascades

A. Kumarakrishnan ’

Department ofPhysics, V-46, University of Connecticut, Storrs, CT 06269, USA

X.L. Han Department ofphysics, Butler University, Indianapolis, IN 46208, USA

Received 19 July 1993; revised manuscript received 24 November 1993

Abstract

We report our studies of superfluorescent cascades in atomic calcium which result from two-photon excitation of several levels reasonably close to the ionization limit. We have observed significant conversion efficiencies for some of these transitions which result in subnanosecond pulses particularly in the visible wavelengths. We report the discovery of a novel two-photon scattering mechanism which could prove to be a useful method for determining collisional broadening rates. In addition, a hyper Raman transition near 17 pm is discovered which appears to be a promising candidate for a tunable source.

1. Introduction

A collection of N excited atoms usually decays radiatively through incoherent spontaneous emission. The emitted intensity is proportional to N and decays exponentially in a time T12 where r,, is the radiative lifetime of the transition involved. Alternatively, the atoms may evolve from spontaneous emission into a coherent state in which their dipole moments are coupled to the common electromagnetic field of the emitted radiation. This process, termed superflu- orescence (SF) [ 11, results in an intense, highly di- rectional burst of radiation whose peak intensity scales as N’. It is characterized by a temporal pulse width which scales as TJN and a time delay T,,K l/

N in which the coherence builds up (Fig. 1 a). In most

’ Present address: Department of Physics, New York University, 4 Washington Place, New York, NY 10003, USA.

0030-4018/94/$07.00 0 1994 Elsevier Science B.V. All rights reserved XTDI0030-4018(93)E0609-J

experiments, a population inversion is created between levels I 1) and I 2) of a three level system of atoms contained in a cylindrical column or atomic beam. The atoms are pumped with a pulsed laser which couples levels IO) and I 1) (Fig. 1 b). SF then evolves from quantum fluctuations on the I 1) + I 2) transition.

1.1. Regimes of interest

The nature of SF can be quantified [ 2-5 ] in terms of the propagation time of light through the medium &=L/c and the dipole coupling time rR= 1 /Nr,,,u. Here, L is the sample length, N the number of participating atoms, r I2 = 1 IT,, the spontaneous emission rate for the SF transition andp is a geometrical factor which defines the diffraction solid angle of the inter- acting volume.

A. Kumarakrishnan. X. Han /Oplics Communication 109 (1994) 348-360 349

$g =D (a)

? ;-_a N*

c- 5.

B (R s I

ko Time (Arb: Units)

12)

IO> I

4S4P’P’O)

lb)

45215 0

ICI

Fig. 1. (a) SF Intensity as a function of time. (b) Three-level system. (c) Ca three-level system.

ti) rE<TR

SF experiments are usually done either in an atomic beam or in a Doppler broadened column of excited atoms in a cell. Pumping an atomic beam corresponds to transverse or instantaneous excitation. Pumping an atomic column, on the other hand, is referred to as longitudinal or swept excitation. In the case of swept excitation, no upper limit on the number of atoms which can couple radiatively is expected [6] since SF initiated in time rR follows the pump pulse at nearly the same speed. In the case of transverse excitation we have the possibility of pure cooperative emission SO long as rE < ?R. This would en- able atoms at one end of the column to communicate with atoms at the other end during the evolution of

the system. This yields an upper limit [ 71 for the maximum cooperation number NC which is the larg- est number of atoms which can emit cooperatively. Thus, NC<c/NL’,,p. In this regime, the SF peak intensity is a N2, the time delay rpa 1 /N and the SF pulse width scales as T,,/N.

(ii) rE-‘rR The effects of stimulated emission are expected to

become important in this regime. The SF peak intensity is expected to vary nonlinearly with N and begin to scale less than quadratically.

(iii) rE> rR Since N> NC, we have in essence the basis for a sin-

gle-pass laser. Gross and Haroche [ 21 have proposed that’in this case, one can consider the column of length L to be divided into S slices, each of length L, con- tainingN’atOmssuchthat S=L/L,=N/N'=rRT/zR. Here, the dipole coupling time in each slice satisfies the condition rR’=LC/c. The number of slices can then be calculated to be S=L/L,= (+E/rR) '12. For this proposition to hold, the evolution time of each slice is rR< = rRrE) ‘12. The SF pulse width for the en- tire sample can be shown to scale as ( 1/N”2r,2) while the delay time being proportional to rR,, scales as ( 1 /N ‘I’). We can now describe the system as the evolution of S independent sets of dipoles with the result that the peak intensity is a N.

It must be noted however, that SF from a collection of uncorrelated slices is fundamentally different from pure stimulated emission. Whereas in the for- mer situation all N atoms in 11) can be transferred to level 12)) in the latter the emission ends when the populations of the two levels are equalized.

The threshold for SF occurs [ 8 ] when rR = T2 where T2 is the dipole dephasing time which in general has separate contributions from natural, Doppler and collisional dephasing. Under ideal conditions of pre- vious SF experiments (such as those in Refs. [ 9- 1 1 ] ), 7E -c 7, e 7,, < T2. However, SF is a fairly ro- bust phenomenon that can take place under unfavor- able conditions of rapid collisional and radiative re- distribution (such as those in Refs. [ 12- 161 and in our experiment ) even when T2 < r,,. The experimental delay times and pulse widths will then be larger than in the absence of dephasing.

350 A. Kumarakrishnan, X. Han /Optics Communication 109 (1994) 348-360

1.2. Effects qfcoherent excitation

It has been implicitly assumed that the initiation of SF begins after an incoherent excitation of level 11) , i.e., there is no initial dipole moment at the SF frequency o,~. This actually corresponds to a very re- strictive condition that a pump pulse of area 71 and infinitesimally small duration rp, such that r, < rn be used. This was pointed out by Bowden and Sung [ 17 ] who showed that if r, > rR, &R > 1, QT,, s2T, > 1, the pump pulse characterized by a Rabi frequency 52 could produce initial coherence in the form of seed photons at the Raman frequency wL- oo2. Here, o,_ is the frequency of the pump laser and T, is the radiative lifetime of 1 1) . The system then evolves collec- tively from this initial dipole moment and the emission is therefore more analogous to superradiance [ 18,19 ] than to SF. As a result, the pulse shapes, delay times and statistics of the fluctuations of SF pulses are expected to be modified considerably.

1.3. The context and results of the Ca-SF experiment

The purpose of our experiment was to study the competition between SF and Stimulated Raman Scattering (SRS) with the goal of creating tunable sources of radiation in the mid IR. The group IIA ele- ments Ca and ST which had the potential to generate fast pulses at 5.5 urn and 6.5 urn were therefore of interest. It was found that SRS could not be induced at all whereas SF occurred readily. These media are optically thick for very low number densities at their principal resonance transitions (4227 A in Ca and 460 1 A in Sr ). In this regard, they are very similar to systems like the copper vapor laser where radiation trapping can aid the frequency conversion process.

Our studies of SF (described in detail in Ref. [ 20 ] ), were centered on nanosecond SF pulses at 5.5 urn generated from a 50 cm column of calcium vapor buffered with argon by optically pumping the Ca ( 4s2 ‘So - 4s4p ‘P, - 3d4s ‘D2) Raman amplifier scheme (Fig. 1 c). Power broadening due to an intense 13 ns pump pulse precludes the evolution of SF for essentially this duration. As a result, the scaling laws introduced earlier which govern the characteristic properties of SF (peak heights, pulse shapes and delay times), in a transversely excited system are shown to apply in our situation in which the conditions resem-

ble swept excitation [ 211. In addition, measurements of the densities of the three levels, the absolute IR photon yield, and the spatial distribution of the excited states indicate that the system has a quantum yield of unity. An appreciable modification of time delays at high values of N was also observed on ac- count of the coherence established in the medium by the pump pulse in the form of seed photons at the SRS frequency. These measurements were consistent with the predictions of Bowden and Sung [ 171.

Evidence for the role of dephasing parameters and transverse effects is presented [ 221 by comparing the pulse shapes of the 5.5 urn SF with those of an SF emission at 1.9 urn involving Ca (3d4s 3DJ - 4s4p 3P.,_, ), generated by spin changing collisions. The results of a numerical simulation which examines the effect of radiation trapping on the expected temporal ringing in SF is considered in Refs. [ 23,241.

We have also studied [25] the effects of mJ level degeneracy of the 4s4p ‘P, level on the polarization of the 5.5 urn SF. The ellipticity of the polarization undergoes an abrupt rotation through 90” when mon- itored as a function of the detuning of the pump laser. The distribution of populations in the magnetic sub- levels are known to depend on optical cross sections which are modified by the presence of sizable AC Stark shifts created by the pump laser. However, it is necessary to invoke a quantum interference effect due to the presence of coherence in the medium at the SRS frequency in order to explain the observed polarization flip.

We present the results of a survey of SF cascades generated by means of a novel two photon scattering mechanism [26] in this article. The generation of subnanosecond pulses at visible wavelengths is demonstrated and possibilities of obtaining tunable radiation near 17 urn are considered.

This paper is divided into five sections. A brief review of relevant literature is presented in Sect. 2. The details of the experiment are described in Sect. 3 and Sect. 4 contains a discussion of our results.

2. Review of literature

Gain coefftcients for nonlinear processes such as third harmonic generation and parametric conversion were originally calculated by Armstrong et al.

A. Kumarakrishnan, X. Han /Optics Communication 109 (1994) 348-360 351

[ 271. The work of Hodgson et al. [ 28 ] showed that these gain coefficients were greatly enhanced by resonant two-photon absorption. Coherent two-photon effects were studied experimentally by Brewer and Shoemaker [29] who showed that two-photon absorption of counterpropagating beams could result in Doppler-free spectra. Grischkowsky et al. [ 301 de- rived a vector model for two-photon processes and pointed out that the enhancement of gain coefficients was pronounced when the input frequencies were well separated from intermediate resonances. They also remarked that since a large transfer of population to the two photon state was achieved, the possibility of achieving high gains for laser action between this state and one or more of the intermediate states existed. Grischkowsky [ 3 1 ] later showed in an elegant article that two-photon absorption was the result of a coherent excitation process which was proportional to the intensity of the pump pulse (for small fields) as op- posed to incoherent excitation of an intermediate state which results from atomic relaxation processes and is hence proportional to the integral of the same pump pulse.

Lasing action from a two-photon state to intermediate levels as suggested by Grischkowsky et al. [ 301 is now a well-known method of frequency conversion and has been achieved through the mechanism of hyper Raman scattering or through the production of fast SF cascades.

Komine and Byer [ 321 proposed a frequency conversion scheme in atomic mercury where population stored on the radiatively trapped 6 ‘Pi level could be used by anti-Stokes or two-photon processes to create an inversion with respect to the 6 ‘P levels. They also pointed out the possibility of electron excitation of the 6 ‘P1 and subsequent quenching of the 6 ‘P levels by a buffer gas as a method of improving the gains for these processes. Kung and Itzkan [ 33 ] used a combination of SRS and SF cascades to populate the radiatively trapped 4 PllZ level in Potassium with a priming laser and then used a second laser to produce hyper Raman scattering at 16 pm and 8.5 pm. They achieved tuning ranges of 2 to 4 cm-i but very small energy conversion efficiencies. Vrehen et al. [ 341 observed SRS at 14 pm in cesium following two-photon excitation. Hanna et al. [ 35 ] also observed SRS in cesium in the wavelength range 2.5-4.8 pm, 5.7-8.7 pm and 11.7- 15 urn by pumping various two-photon

transitions. Both groups reported a high degree of tunability (several tens of wavenumbers) and rea- sonable energy conversion efficiencies ( l-2%).

Okada et al. [ 36 ] observed very narrow ( 100-200 ps) SF pulses at 8126 A with a streak camera in a cascade in atomic lithium. The 3 S1,Z two-photon state was pumped by the absorption of two photons from the same nanosecond pump laser. This group, as well as Malcuit et al. [ 15 1, demonstrated the transition from the regime of ASE (amplified spontaneous emission), where dephasing processes curbed cooperative emission and resulted in highly spiked and broadened pulses, to the regime of SF where cooperative emission dominates dephasing.

SF cascades at visible wavelengths were observed by Cahuzac et al. [ 371 in europium and by Brechig- nac et al. [ 381 in strontium. Chang-Mao [ 391 pumped several levels which were well below the ionization limit in atomic calcium by two-photon excitation and observed laser action at several visible wavelengths.

3. Experimental details

The experiments reported here were performed in a 50 cm Ca vapor column which was buffered with Ar and contained in a stainless steel cell. The ground state density, measured by the curve of growth method, was in accordance with data from vapor pressure curves and ranged between 3 x lOI cme3 and 2x 1015 crnp3. The buffer gas pressure, measured to within 0.25% by a capacitance manometer, varied between 1 Torr and 100 Torr. The column was excited by a homemade pulsed dye laser ( 1 to 2 GHz bandwidth) which had a tuning range of several hundred wavenumbers around the wavelength of the principal resonance line at 4227 A. The dye laser consists of a double grating oscillator cavity (Litt- man design), which is transversely pumped, and three amplifying stages. A set of pinholes spatially filters the light and minimizes the ASE. The measured ratio of total laser light to the broad ASE pedestal was = 6 : 1. The pulses had a duration of 13 ns and the average energy per pulse N 1.5 mJ as measured with an Epply Thermopile ( & 2%). Its transverse profile was a gaussian and the beam was collimated to have a confocal parameter greater than the length of the

352 A. Kwnarakrishnan, X. Han /Optics Communication 109 (1994) 348-360

cell. A well defined column length was assured since the pump beam’s fluence was high enough to com- pletely “burn through” the column.

In the first set of experiments, the two photon states were excited by the absorption of two photons from this single pump beam. The second set of experiments involved the use of two copropagating pulsed dye lasers, the first tuned to the vicinity of the principal resonance line at 4227 A and the second tuned to the vicinity of the 4s4p ‘P,-4s4d ID2 transition at 7328 A. In both experiments, most of the resultant cascades exhibited the characteristic property of SF- emission at the atomic frequency with a time delay which could be varied by controlling the number of participating atoms N. This was achieved by detuning the laser(s) from resonance.

The cascades were detected at the back end of the cell in the IR ( 1.8- 12 pm ) by a homebuilt Ge : Hg detector ( N 400 MHz bandwidth) and in the visible ( 3000 A- 1.1 pm) by a silicon pin photodiode (2 GHz bandwidth, Optoelectronics) after passing through a Spex 0.75 m Czerny-Turner spectrometer installed with appropriate gratings (75 grooves mm-‘, 10 pm blaze for IR, 1200 grooves mm-’ for visible). The output of these detectors was connected to a 1 GS s- ’ digitizing oscilloscope (one channel of a Tektronix DSA 602 ) . The scope was triggered by the pump pulse hitting a homemade photodiode assembly (N 500 MHz bandwidth) (see Fig. 2 ).

The CaF, window at the exit end of the cell was replaced by a BaF, window to extend the transmis- sion out to = 14 pm. When greater detectivity was required, an Ge:Au detector (Judson, 200 MHz bandwidth and coupled to a charge-to-voltage con- verter) or a photomultiplier tube (Hamamatsu) was used at the exit slit of the spectrometer to cover the infrared and visible parts of the spectrum, respectively. The output of these detectors was connected to a boxcar averager which was in turn connected to a chart recorder.

Fig. 2. Schematic diagram of experimental setup.

A survey of the SF emissions was first established with this system. Since the spectral response of the monochromator was not available, apparent strong or interesting emissions were later restudied with the aid of calibrated bandpass filters. The absolute photon yield (which is the number of participant SF atoms IV) of these emissions was measured with a LiTaO, pyroelectric detector (Molectron) which had been calibrated ( f 15%) against the Epply Thermo- pile. The relative intensities of any multiple emissions in a particular bandpass region were corrected for the known detector response, making the reason- able assumption that the grating response varied smoothly over the wavelength excursions of a bandpass filter.

Although we did not study emissions from the front end of the cell in detail, it was possible to ascertain that their intensity was approximately the same as that measured at the back end of the cell. A comparison of pulses from both ends of the cell obtained on a single shot showed that the pulse shapes and time delays were nearly identical. The same was true for the time averaged pulses. We therefore assume that the photon yield from either end of the cell was nearly the same.

4. Discussion of results

4.1. A novel two-photon scattering mechanism

In the first set of experiments involving a single

pump laser, a number of upper levels close to the ionization limit could be excited by two-photon transitions with the laser detuning A ranging between 65 cm-’ and 250 cm-’ on either side of the 4s4p ‘PI level. These are summarized in Table 1. Of these levels, three upper levels, 4s 1 OS *So, 3d5s ‘DZ, and 3d5s 3D2 produced the strongest emissions which were studied in detail. It was discovered that these levels could be excited by two different pathways.

The first pathway is referred to as a direct two-photon process and is shown in Fig. 3a. This is the coherent excitation described by Grischkowsky [ 3 11. The first photon connects the ground state ( IO) ) with a virtual level which is connected to the final state ( 13) ) by a second photon. The detuning from the intermediate level ( 11) ) is denoted by A. AC Stark

A. Kumarakrishnan. X. Han /Optics Communication 109 (1994) 348-360 353

Table 1 Summary of two-photon transitions studied.

Transition Mechanism Pump detuning (cm-‘)

1 4s4p ‘P, - 4s9s ‘S* two-photon 2 4s4p ‘P, - 4s8d ‘Dz two-photon 3 unknown unknown 4 4s4p ‘P, - 4slOs ‘s, two-photon

and two-step 5 4s4p ‘P, - 3dSs ‘Dr two-photon

and two-step 6 4s4p ‘P, - 3d5s 3Dz two-photon

and two-step

-241.4 - 181.6 -77.8 +65.8

+131.6 +71.8

+ 143.6 +79.8

+ 159.6

2-PHOTON

I

26

452 ‘so L-

4-bCOLLISIONS

a) TWO-PHOTON b) TWO-STEP

Fig. 3. Mechanism of two-photon and two-step pathways.

shifts created by the pump laser are not shown in this figure.

The second pathway leading to the two-photon level is through an incoherent excitation shown in Fig. 3b. The detuning is now 24. Once again, the first photon connects the ground state to a virtual level. Collisions with the buffer gas then transfer population to the 4s4p ‘Pr level. The second photon then connects the two-photon state to this intermediate level.

The collisional line strengths and line shapes which correspond to the two processes was studied for the case of two pump lasers by Liao et al. [ 40 ] on the basis of the theory developed by Bjorkholm et al. [ 411 and by Berman [ 42,43 1. Berman’s theory describes the effect of two independent, near-resonant, weak laser fields. It gives the relative amplitudes of the two- photon and two-step processes in terms of the plasma dispersion function which is parametrized by c= J+ iK and given by

such that

’ (2)

Im(Z)=(1/7r)*/2 ’ (3)

The amplitude of the two-photon process is given by

c, (u)LLIC) p33(2-phoWa ,~2,c_-oL,Ic, (‘w”djc’vJ

x ZInl ( i[YO3 +iM +A21 1 I~L*/c-%lIcIv >p

and that of the two-step process is given by

(4)

P33(2-steP)a (wL2,c)

c, (WL1/C) (,,i”“)’ (;Ed g

xz i[713+iWl

( Irn I(%*lcM > . (5)

Here, Cr is a constant, v is the relative thermal velocity between atom and perturber, wL, and oL2 are the frequencies of the two lasers, A1 =q, -ool and AZ= wLz- or3 are their respective detunings and

701 = 1/2(YOrad +Y1rad)+Yc(ol), ~03=1/2(yOrad+

Y3rad)+k(O3)? ~13=1/2(Y,,=d+Y3rsd)+yC(13) are

the collisional broadening rates. These are expressed in terms of the buffer gas pressure P and a constant

Cd as k (ob) = c,bp.

The two-photon excitation is responsible for narrow spectral lines whereas the two-step incoherent excitation gives broader spectral components. The ratio of the amplitude of the two processes is independent of detuning and depends only on the pressure of the buffer gas which affects the collisional broadening rates yccol), ycco3), and yc(r3). These predictions were confirmed experimentally by Liao et al. [ 401 and later by Comey et al. [ 441.

It may be possible to use the discovered resonances shown in Fig. 3 to extract collisional broadening rates of the transitions involved. Figures 4a and 4b show the predictions of theory for the intensity of the two processes using wL2/c--,/c=O.25 cm-‘,

354 A. Kumarakrishnan, X. Han /Optics Communication 109 (1994) 348-360

0.00 20.00 40.00 60.00 80.00 100.00 Buffer Gas Pressure (Torr)

= 6 aB d- G

zi-s lb) cil k

0.00 20.00 40.00 60.00 80.00 100.00

Buffer Gas Pressure (Torr)

Ii \-----i 0.00 20.00 40.00 60.00 60.00 100.00

Buffer Gas Pressure (Torr)

Fig. 4. (a) Two-photon intensity (theory) as a function of buffer gas pressure. (b) Two-step intensity (theory) as a function of buffer gas pressure. (c) Two-photon intensity/two-step intensity (theory) as a function of buffer gas pressure.

w,,/c=23652 cm-‘, A,/c=66.5 cm-’ yO’orad=O, y,,=2.18x108s-1,y,,,=1x106s-‘,Col=3x106 s-’ Torr-‘, CL3= 1 x lo7 s-‘To~-1,C03=1x105s-1 Torr- ‘, and V* 5 x IO4 cm s-’ for a buffer gas pressure range of ,O- 100 Tot-r. The ratio of intensities in Fig. 4c indicates the dominance of the two-photon component. Our experiment involved a study of the total peak intensity of the resultant SF cascades in the IR produced by the two mechanisms as a function of Ar pressure in the range 3 Torr to 100 Torr at

a ground state density of - 3 x 1014 cm-3. It is to be noted that the two processes were of comparable magnitude.

When tuned to either type of resonance, two SF pulses were observed in the absence of the spectrometer. The first was the sum of all the IR cascade emissions which resulted in a relatively intense pulse occurring under the pump pulse. The second was a weak SF pulse at 5.5 urn which was delayed by about 25 ns (see Fig. 5).

In our case, oL1 = oL2 and the estimated Rabi frequency for the 10) + 11) transition was about 20 cm-‘. As a result, the weak field theory of Berman et al. [42,43] cannot be applied in this situation. We show the peak intensity of the cascade emission (averaged over 5 12 shots) recorded for the two-photon and two-step cases in figs. 6a and 6b when the upper level was the 4~1 OS ‘So level. As expected, the magnitude of the two-photon process decreases as a function of buffer gas pressure, whereas that of the two- step process increases. It is to be noted that the two- photon process saturates at a finite nonzero value at high pressures. This is attributable to the fact that collisions can actually enhance SF by aiding the transfer of population to the intermediate level (Fig. 3b). Likewise, the two-step process starts out at a nonzero value at the lowest buffer gas pressures. We attribute this behavior to the 10%-l 5% ASE in our pump laser which can populate several of the closely spaced upper levels (the effect of three-photon scattering in populating level 1 1) has not been discussed

5 nsecldiv Fig. 5. IR cascade emissions without spectral resolution; [‘So]-3x10’4cm-‘.

A. Kumarakrishnan, X. Han /Optics Communication 109 (1994) 348-360 355

g s c R c

3 (a)

B s - g-+ zs z $_

+ f

+ + + +-

k Y 8

dr r 0.00 20.00 40.00 60.00 80.00 100.00

Ar Pressure (Torr)

s p

=o (b)

=9 - T nz-

a + -8 $$ + +

T + 28 ++

6 r 0.00 20.00 40.00 60.00 80.00 100.00

Ar Pressure (Torr)

^08 al* G (d

28 = i-

F + 58 ‘p c-i-

I

%!o +

0 f + + 61 r

0.00 20.00 40.00 60.00 80.00 ioo.00 Ar Pressure (Tom)

Fig. 6. (a) Two-photon intensity (experiment) as a function of Ar pressure; [‘So] _ 3 x 10” cme3. (b) Two-step intensity (experiment) as a function of Ar pressure; [‘So] . 3 x lOI cmm3. (c) Two-photon intensity/two-step intensity (experiment) as a function of Ar pressure; [ ‘$] - 3x lOI cme3.

since the pump laser detuning from this level is N 70 cm-‘). The ratio of intensities is shown in Fig. 6c and shows that the contribution of each process is at best an order of magnitude larger at either extreme.

These results, however, are quite novel and may be a suitable method for measuring collisional broadening rates if low laser intensities are employed. It has been shown [ 45 ] that it is not possible to separate the individual contributions of the two reso-

nances for values of the field strengths used here (IE] -2xlO’V/m).

4.2. SF cascades

Figs. 7a and 7b show the cascades detected as a result of populating the 3d5s ‘Dz level via two-photon and two-step pathways, respectively, at a buffer gas pressure of 3 Tot-r. When spectrally separated, the time delays of these pulses were seen to vary as a function of pump laser detuning, thereby confirming their SF nature. None of the observed emissions showed any tunability. The wavelengths of these cascades is summarized in Table 2.

It was noticed that the estimated photon yields cor- responding to population transfer in and out of the various levels showed smaller discrepancies (within a factor of two) for levels lower down the energy ladder. This suggests that some of the cascades, espe- cially those with wavelengths longer than 14 urn may not have been detected. Such transitions usually correspond to the first steps in the cascades out of the excited two-photon state and may be candidates for obtaining tunable radiation.

In Ref. [ 2 11, we have discussed the buildup of the 5.5 urn SF under conditions when power broadening due to an intense 13 ns pump pulse precludes the evolution of SF for essentially this duration. As a result, the scaling laws which govern the properties of SF in a transversely excited system apply in our situation in which the conditions resemble swept excitation. After the pump pulse turns off, SF evolves under conditions when the Doppler width of the transition is much larger than the natural width. At low densities, it was suggested that only atoms from a single velocity group (of the order of the natural linewidth) take part directly in the initiation. Other atoms contribute indirectly by velocity reshufIling [ 23,241 due to radiation trapping. At high densities, the presence of SRS seed photons was found to mod- ify the evolution of SF. The SF cascades originating from levels other than the upper state thus provide an opportunity to study the scaling laws which govern SF delay times, pulse shapes and peak heights in the absence of the dephasing effects of the pump pulse. These cascades would also be isolated from the effects of seed photons at various SRS frequencies if it

356 A. Kumarakrishnan. X. Han /Optics Communication 109 (1994) 348-360

Energy ( cm-’ )

48000 -_I

46000

42000

36000

32000

26000

24000

3

(a) ‘1 0 3pi23p0,;p; 3D,233D,;3 ‘“2 D2 ‘S

I 03F03

234 F234 ‘F3” 3G ‘G

Fig. 7. (a) SF cascades as a result of pumping the 3d5s ‘D2 level via the two-photon pathway. [‘So] - 1 X lOI cm-‘; 3 Torr Ar.

is ensured that the spectral content of the pump pulse is devoid of ASE.

It is notable that we find that SF transitions with radiative rates r- 1 06- 10’ Hz evolve well under the pump pulse with high efficiency on very short time scales in the presence of Doppler broadening which is the dominant dephasing mechanism. For the IR cascades shown in Table 2, the delay time (measured from the leading edge of the pump pulse) and pulse widths were typically 7 ns and 10 ns, respectively (Fig. 8a) and for the visible cascades these were 5 ns and N 1 ns, respectively (Fig. 8b). The apparent shorter delay time shown in Fig. 8b for the SF pulse at 5043 8, (which occurs lower down the energy ladder than the IR pulse at 3.8 pm in Fig. 8a) is probably just an

artifact due to the fact that the IR and visible cascades were recorded separately on different data runs when the shape of the pump pulse was slightly different (the positioning of the independent time bases of the upper and lower traces displayed on the oscilloscope are accurate to within 0.5 ns). The fact that they are different may be something which should be checked in future work by simultaneously monitor- ing the upper IR emissions and their resulting optical cascades.

Dominant visible transitions which result in pulses whose temporal fwhm is less than a nanosecond oc- cur at 4528.2 A, 45 13.5 A, 5043.0 A and 6719.5 A (see Table 2). These have estimated photon yields of > 5 x 1 0L2 and offer possibilities for excellent conver-

A. Kumarakdshnan, X. Han /Optics Communication 109 (1994) 348-360 351

Energy ( cm- ’ )

48OOOJ

4s8f 4s8f

4S7f 457f

4S6f 4s6f 460004

44000 1 i

42000_

36000_

32000_

455s 30000_

28000_

26000_

24000_

20000_ 344s

15000_

O_ 4s4p

452 3

'S 3Po 3P (b) 'I 0 012 0,:': 3D123 123 D2 2

3Do I IDO 3FO 3

234 F234 3 'F" 3G 'G

Fig. 7. (b) SF cascades as a result of pumping the 3d5s ‘D2 level via the two-step pathway. [‘So] - 1 x lOIs crnd3; 3 Torr Ar.

sion efficiencies if pumped directly with picosecond lasers which would limit the dephasing effects during the pumping process. Calculations based on the scaling laws introduced in Sect. 1 indicate that possibilities exist for producing narrow pulses N 100 ps in duration at these wavelengths. It may also be possible to make such sources have a relatively narrow pulse width by seeding the SF emission with an external broadband source [ 46 1. The role of the ASE from the pump pulse in seeding these transitions is yet to be investigated.

The strongest visible transitions in Table 2 also ex- hibit multiple pulses (see Fig. 9 ) , presumably due to regenerative pumping, and are in agreement with ex- pectations [ 38 ] (population transfer to the upper

levels of this cascade occurs over approximately the duration of the pump pulse). Multiple pulses would stop occurring when the number density of the upper level becomes smaller than the threshold density for SF.

4.3. Generation of I7pm radiation

When two copropagating lasers, the first tuned to the principal resonance line at 4227 A and the second tuned to 7328 A, were used to excite the 4s4d ‘Dz transition, SF cascade emissions were recorded on the 4s4d ‘Dz - 3d4p ‘F3 (6.7 urn), 4s5p ‘Pi - 4~5s *So (2.9 urn), and 4s5p ‘Pi - 4~5s 3S1 (1.9 pm) transitions as shown in Fig. 10. The SF pulse at 6.7 pm

358 A. Kumamkrishnan, X. Han /Optics Communication 109 (1994) 348-360

Table 2

Wavelengths of SF cascades obtained by pumping the 3d5s ‘D1

level via two-photon and two-step pathways; [‘Se] _ 1 X 1015

cme3; 3 Torr Ar; + and - indicate the occurrence or absence of

a transition, respectively.

Transition Wavelength A (vacuum)

24

1 4s9d ‘Dz - 4s5p ‘P, 2 3d5s ‘Dz - 3d4p ‘P,

3 4s9p ‘P, - 4s7s ‘Se

4 4s7f ‘Fs - 3d4s ‘Dz

5 4s8d ‘Dz - 3d4p ‘P,

6 4s9s 3s’ - 4s5p 3Pe 7 4s8p ‘P, - 4~7s ‘Se

8 4s8p ‘P, - 3d4s ‘D2

9 4s7d ‘D1 - 4s6p ‘P,

10 4s7d ‘DZ - 4s6p ‘P’

11 4~8s ‘Se - 4s4p ‘P,

12 4s7p ‘P, - 4s7s ‘Se

13 4s7p ‘P, - 4~6s ‘Se

14 4s6d ‘Dz - 4s6p ‘P,

15 4s6d ‘Dz - 4s4p ‘P,

16 4s5g ‘G4 - 4s4f ‘Fs

17 4s5f ‘Fs - 4s5d ‘D*

18 4~7s ‘Se - 4s6p ‘P,

19 4s7s ‘Se - 4s4p ‘P,

20 3d4p ‘P, - 4~6s ‘Se 21 3d4p ‘P’ - 3d4s ‘Dz

22 4s5d ‘Dz - 4s6p ‘P,

23 4s5d ‘D2 - 4s4p ‘P,

24 4s4f ‘F3 - 4s4d ‘DZ

25 4s4f ‘Fs - 3d4s ‘Dz

26 4s6p 3Pz - 3d4s 3D,

27 4s6p ‘P, - 4s4d ‘Dz

28 4s6p ‘P, - 3d4s ‘D2

29 4p* ‘Se - 4s4p ‘P,

30 4~6s ‘Se - 4s5p ‘P,

31 4s4d ‘Dz - 4s4p ‘P,

32 4s5p ‘P’ - 4sss ‘So

33 4s5p ‘P’ - 3d4s ‘D2

34 4s4p ‘P, - 3d4s ‘D2

35 3d4s )Dg - 4s4p 3P,

9024.6 8,

2.8 pm

3.4 pm

3973.7 A

3.3 urn

9803.3 A

4.5 pm

4060.1 8,

2.16 urn

2.21 pm

4497.4 A

8.7 pm

2.11 urn

3.0 pm

4686.9 A

3.9 urn

5.3 pm

3.8 urn

4848.7 A

3.1 urn

4528.2 8,

8.1 urn

5190.3 A

1.98 pm

4879.5 8,

4513.5 A

4380.7 A

5043.0 A

5514.5 A

2.5 urn

7328.2 8,

2.9 pm

6719.5 8,

5.5 urn

1.97 urn

- + + + + + + + _ + - + + + + + + + + + + + + + + + + + + + + + + + +

+ + + - - - - - + - + + + + - + + + + + + + - + - - + + - + - + - + +

began evolving only at the tail end of the pump pulses (which overlapped in time), consistent with our ex- pectations for the evolution of SF from a power

broadened transition. The 2.9 ym emission, which appeared to be dominant, occurred well under the

pump pulse suggesting that emission at 17.6 urn on the 4s4d ‘Dz - 4s5p ‘PI occurred via a hyper Raman

transition. This is a potential candidate for a tunable source and remains to be explored.

5 nsecldiv

5 nsecldiv

Fig. 8. (a) 4~7s ‘Se- 4s6p ‘P, SFcascade at 3.8 pm. (b) 4s6p ‘P,

- 3d4s ‘Dz SF cascade at 5043 A.

5 nsecldiv

Fig. 9.4~6~ ‘P’ - 3d4s ‘D2 SF cascade at 5043 A showing multi-

ple pulses.

A. Kwnarakrishnan, X. Han /Optics Communication 109 (1994) 348-360 359

PUMP 4227 A

4s2 ‘s 0

Fig. 10. Generation of 17 pm radiation,

5. Conclusions

The novel two-photon scattering mechanism reported here may prove useful in measuring collisional broadening rates. The dominant SF cascades may be ideally suited for obtaining ultrashort pulses at high conversion efftciencies by pumping with picosecond lasers. The scaling laws which govern their evolution and the effect of seeding these transitions at appropriate wavelengths are topics which remain to be studied in detail. A study of the conversion efficiencies of emissions at long wavelengths may also prove to be useful in the context of obtaining tunable sources. In addition, a detailed study of any asym- metry between emissions in the forward and back- ward directions remains to be carried out. We con- clude by noting that some striking asymmetries have recently been reported for ASE [ 47 1.

Acknowledgements

This work was done by A. Kumarakrishnan in par- tial fulfillment of the requirements for the degree of Ph.D. in Physics (1992) at the University of Idaho under the guidance of Jim Kelly. This work was sup- ported by Jim Kelly’s grants from NSF PYI, NSF EPSCOR (Idaho ) and AFWL.

A. Kumarakrishnan would like to thank Phillip L. Gould and Timothy P. Dineen of the University of Connecticut for helpful comments on the manuscript.

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