928 OPTICS LETTERS / Vol. 21, No. 13 / July 1, 1996

Observation of a critical concentration inlaser-induced transparency and multiphoton excitation

and ionization in rubidium

Lu Deng,* W. R. Garrett, and M. G. Payne*

Chemical Physics Section, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831

D. Z. Lee

Department of Physics, The University of British Columbia, Vancouver, British Columbia, Canada V5K 2T3

Received January 29, 1996

We report the behavior of Autler–Townes splitting and production of a four-wave mixing (FWM) field inrubidium in the context of laser-induced transparency. Gain saturation of the FWM and simultaneoussuppression of Autler –Townes splitting above a critical concentration are interpreted in terms of the odd-photondestructive interference effect. The results demonstrate that, when multimode lasers are used, odd-photondestructive interference significantly limits the high-efficiency and high-intensity FWM generation promisedby early studies of laser-induced transparency. 1996 Optical Society of America

Laser-induced transparency (LIT) and related studieshave been an active field of research since LIT was firstdiscussed by Kocharovskaya and Khanin.1 The firstLIT scheme that could operate in a steady-state modewas later proposed by Harris.2 It was hoped that anovel process such as LIT might lead to a promisingmethod for generating intense coherent radiation withhigh eff iciency.

In this Letter we report measurements of four-wavemixing (FWM) field production and multiphoton ioni-zation (MPI) line shapes obtained with multimodelasers under conditions in which one form of LIT oc-curs (see Fig. 1 for the relevant energy-level diagramand laser couplings). This FWM scheme is of inter-est because, once the second laser is suff iciently in-tense to drive the medium transparent, it results inphase-matched FWM with a large third-order suscep-tibility and relatively little absorption of the generatedwave. We show, however, that at sufficiently high con-centrations the generated FWM field eventually startsto be absorbed. This absorption of the FWM field pro-vides a second pathway to the level j3l. However, thisexcitation, which is due to the internally generatedfield, is 180 deg out of phase with the excitation of thesame level by two lasers (i.e., by the first excitationpathway to level j3l through 2vL1 2 vL2d and henceresults in a destructive interference in which the po-larization at the FWM frequency decreases and finallyapproaches zero at suff icient depths into the medium.Consequently the FWM intensity becomes concentra-tion independent. We also show that the Autler–Townes splitting produced by the second laser de-creases when the critical concentration is reached andcompletely vanishes in the same region where the gainof the FWM field goes to zero. However, when thetwo beams are counterpropagating, the Autler–Townessplitting returns and is seen in MPI line shapes atall concentrations. These observations and theoreti-cal results that predict this outcome3 have lead us toconclude that the physical mechanism for the reduction

0146-9592/96/130928-03$10.00/0

of the Autler–Townes splitting and the saturation ofthe FWM field is a result of the odd-photon destructiveinterference effect.4,5

The familiar three-photon destructive interferencedoes not usually occur in situations in which there isa lower-order resonance, such as the one studied here,because of the incoherence introduced by storing popu-lation in the intermediate resonance. Although simi-lar LIT schemes were studied by other researchers6

from the viewpoint of nonlinear-optical generation, tothe best of our knowledge there have been no previ-ous attempts to include systematically the possibilityof odd-photon interference under circumstances whenlaser-induced transparency is expected. Such a treat-ment requires that multiphoton coupling and the cou-pling involving the generated FWM field be treated onequal bases. Because of space limitations we presentonly the experimental data here. A detailed theoreti-cal treatment can be found in Ref. 3.

Fig. 1. Relevant rubidium energy-level diagram withlaser coupling schemes. Level assignments: j1l, 5s1/2;j2l, 6d5/2; j3l, 5p3/2. Splittings are exaggerated.

1996 Optical Society of America

July 1, 1996 / Vol. 21, No. 13 / OPTICS LETTERS 929

The second-harmonic (pulse length 7 ns) of aSpectra-Physics DCR-2A Q-switched Nd:YAG laserwas used to pump two Lumonics dye lasers (bandwidth.0.1 cm21). The output of the f irst dye laser wasfocused to a beam waist of 0.6 mm by an f ­ 1 m lens.This laser was tuned to the two-photon resonancebetween the ground state 5s1/2 and the excited state6d5/2 of rubidium. The output of the second dye laserwas unfocused, with a beam waist of ,0.8 mm. Thislaser was tuned onto the resonance between the 6d5/2state and the 5p3/2 fine-structured level. The energiesof the two beams were 60 mJ and 6 mJ, respectively,and both beams were linearly polarized. By keepingthe intensity of the f irst laser low, we avoided pos-sible competition from processes such as parametricfour-wave mixing and hyper-Raman generation. Thetwo laser beams stayed completely overlapped insidea rubidium heat pipe operated in a non-heat-pipingmode. The heating region was ,20 cm (Ar typicallyat 4 Torr was used as a buffer gas). In the actualexperiment the temperature of the rubidium vaporwas measured. We then calculated the correspondingvapor pressure and the concentration n s cm23d of therubidium atoms, using ideal gas law. This is validbecause of the non-heat-piping mode operation. AKeithley 480 picoammeter with proper electronics wasused to collect photoelectrons.

The ionization measurements depend on the factthat electron–ion recombination is very slow in al-kali metals, so recombination does not occur beforethe charge is collected. Thus, despite space-chargeeffects, the electrons and ions produced by multi-photon ionization can eventually be collected. TheFWM signal was measured with a Jarrell-Ashe82000 monochromator (resolution 0.01 nm) coupledwith a RCA C30134 photomultiplier.

Rubidium was chosen because of the large fine-structure splitting between the 5p3/2 and 5p1/2 levelssdfs . 240 cm21d. With such large splitting one canstudy the FWM process involving the 5p3/2 level up toconcentrations at which the interference occurs whileneglecting the phase mismatch that is due to the 5p1/2fine-structure level, provided that the Autler–Townessplitting remains sufficiently small compared with thefine-structure splitting. (See Ref. 3 for discussions ofthe effect of a nearby fine-structure level.) In ourexperiments the condition jV23j ,, jdfsj was alwaysobserved.

First we measured MPI profiles at different con-centrations with the second laser turned off. Theseprofiles have two well-defined peaks, separated by1.2 cm21 on the one-photon scale, corresponding to ioni-zation out of the two 6d f ine-structure levels, i.e., 6d5/2and 6d3/2 [see Fig. 2(a)]. These two levels are sepa-rated by ,2.3 cm22.7 We then turned on the secondlaser and adjusted it to produce symmetric Autler–Townes splitting in a counterpropagating-beam geome-try by scanning the f irst laser across the two-photonresonance. The oscillator strengths for transitions6d5/2 ! 5p3/2 and 6d3/2 ! 5p3/2 are 0.028 and 0.0029,respectively. We neglected the transitions from 6dstates to 5p1/2 for the reasons described above.

At low concentration the sharp MPI peak that is dueto level 6d5/2 was altered significantly. We observed

a widely separated twin-peak structure with much de-creased amplitude, representing the well-known Aut-ler–Townes splitting. However, the line shape of thepeak that represents the contribution from the transi-tion 6d3/2 ! 5p3/2 did not change appreciably becausethe oscillator strength for the this transition is small(0.0029) [see Fig. 2(b)]. Notice that once the intensityof the second laser is high enough to drive the mediumtransparent, further increase in the intensity of thislaser does not increase the ionization eff iciency becausethe photoionization cross section of the state j2l is largeenough that the ionization probability for any popula-tion of the state is already close to unity.8 Althoughthe intensity of the second laser was 6 mJ, it is the op-timum intensity somewhere in the beam profile that isresponsible for the largest part of the MPI signal. Thehigh-intensity part of the beam will produce a largeAutler–Townes split with low excitation probability,leading to a diminished signal buried in the wing ofthe MPI signal. Figure 2(b) indicates that the Aut-ler–Townes splitting is ,2jV23j . 3.2 cm21. Noticethat this split is much smaller than the f ine-structuresplit, dfs . 240 cm21, yet many times larger than thebandwidth of lasers s.0.1 cm21d. At higher concentra-tions the Autler–Townes split became much smaller.We observed a critical concentration n . 6 3 1014 cm23

above which Autler–Townes splitting disappears com-pletely [see Fig. 2(c)] and the MPI profile exhibits a lineshape similar to that without the second laser. Thismeasurement agrees well with the theoretical estimateof n . 5 3 1014 cm23.3

Fig. 2. Multiphoton ionization signal versus the wave-length of the first laser. (a) First laser only. (b) Aut-ler–Townes splitting is clearly seen at T ­ 105 ±C s5.8 31012 cm23d. (c) Autler–Townes splitting disappears com-pletely at T ­ 230 ±C s2.3 3 1015 cm23d.

930 OPTICS LETTERS / Vol. 21, No. 13 / July 1, 1996

Fig. 3. Plot of the FWM signal versus P sTorrdyTsKd.Dashed curve, theoretical curve based on theory of thethree-photon destructive interference (see Ref. 3). Inset:the low-concentration behavior. Curve fit, constant 3sPyT d2.

When the second laser was counterpropagated, awell-defined twin-peak structure was again observedat all concentrations, showing the persistence ofAutler–Townes splitting for this beam propagationgeometry.

An independent confirmation of the critical concen-tration was obtained through a series of measurementsof the FWM field as a function of concentration.This was done simultaneously with the ionizationmeasurements. When both lasers were tuned to exactresonance and propagated collinearly, and the secondlaser was suff iciently intense to induce Autler–Townessplitting that was much larger than the laser band-width, high-efficiency FWM was observed at 780 nm.In particular, in the range n # 2.7 3 1013 cm23

[,2.6 3 1026sTorryKd] the FWM intensity is propor-tional to n2 and the conversion efficiency is in goodagreement with the theory of Harris9 and Harriset al.10 In Fig. 3 we have plotted the peak height ofthe FWM signal against the pressureytemperatureratio of the rubidium vapor sPyT d. We have alsoplotted (dashed curve) the theoretical curve obtainedfrom Ref. 3 for comparison. The peak height growsquadratically in the low-concentration region (see theinset of Fig. 3). However, above a critical concentra-tion the FWM field plateaus. The region where thecurve deviates from the n2 behavior was estimatedat , 3.2 3 1026sTorryKd s, 3.0 3 1013 cm23d, andthe output became limited at , 6.5 3 1025sTorryKds, 6.2 3 1014 cm23d. These observations agree wellwith theoretical predications based on a three-photondestructive interference.3 This theory predicts that,for the parameters given above, a destructive interfer-ence will occur for n . 2.9 3 1013 cm23 and the FWMintensity will stop increasing at .5 3 1025 sTorryKd.This theory also predicts that in the same concentra-tion region the line shape of the two-photon resonantlyenhanced multiphoton ionization, obtained by scanningthe f irst laser across the two-photon resonance, will

gradually decrease in width until no Autler–Townessplitting can be seen and the width of the MPI profileis limited by the laser bandwidth. Our experimentalobservations agree well with these predictions.

In conclusion, we have investigated the effect of theodd-photon destructive intereference on one form oflaser-induced transparency in rubidium. Both theMPI profiles and the FWM intensity agree well withthe theoretical predictions. The key observation isthe critical concentration above which Autler–Townessplitting induced by the second laser disappearedcompletely and the FWM field became concentrationindependent. These observations confirm that theodd-photon destructive interference is complete anddominant in the high-concentration region. Theseresults demonstrate that odd-photon destructiveinterference signif icantly limits the much-hoped-forhigh-eff iciency and high-intensity nonlinear-opticalgeneration promised by early studies of LIT, atleast for the multimode laser system used in thepresent study.

This research was partly sponsored by NationalScience Foundation grant PHY-9505468, the GeorgiaSouthern Foundation Fellowship, and the U.S. Depart-ment of Energy Office of Health and Environmen-tal Research under contract DE-AC05-84OR21400 withLockheed-Martin Energy Systems, Inc. L. Deng ob-tained summer support from Oak Ridge AssociatedUniversities/Oak Ridge Institute of Sciences and Engi-neering, and experiments were carried out at the OakRidge National Laboratory.

*Permanent address, Department of Physics, Geor-gia Southern University, Statesboro, Georgia 30460.

References

1. O. Kocharovskaya and Y. Khanin, Soviet Phys. JETP63, 945 (1986); Soviet Phys. JETP Lett. 48, 630 (1988);also see P. Mandel, Contemp. Phys. 34, 235 (1993), andreferences therein.

2. S. E. Harris, Phys. Rev. Lett. 62, 1033 (1989).3. M. G. Payne, L. Deng, and W. R. Garrett, ‘‘Theory of

the effect of the odd-photon destructive interferenceon optical shifts in resonantly enhanced multiphotonexcitation and ionization,’’ submitted to Phys. Rev. A.

4. M. G. Payne, J. Y. Zhang, and W. R. Garrett, Phys. Rev.A 48, 2334 (1993), and references therein.

5. L. Deng, J. Y. Zhang, M. G. Payne, and W. R. Garrett,Phys. Rev. Lett. 73, 2035 (1994). (E2 should be 2–3 mJin this paper.)

6. K. Hakuta, L. Marmet, and B. P. Stoicheff, Phys. Rev.A 45, 5152 (1990).

7. C. E. Moore, Atomic Energy Levels, Natl. Stand. Ref.Data Ser. Natl. Bur. Stand. 35 (1958), Vol. III.

8. G. S. Hurst and M. G. Payne, Principles and Applica-tions of Resonance Ionization Spectroscopy (IOP Pub-lishing, Philadelphia, Pa., 1988).

9. S. E. Harris, Phys. Rev. Lett. 62, 1033 (1989); A.Imamoglu and S. E. Harris, Opt. Lett. 14, 1344 (1989).

10. S. E. Harris, J. E. Field, and A. Imamoglu, Phys. Rev.Lett. 64, 1107 (1990).