GAIN/FEEDBACK APPROACH TO OPTICAL INSTABILITIES IN SODIUM VAPOR

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GAIN/FEEDBACK APPROACH TO OPTICAL INSTABILITIES IN SODIUM VAPOR

G. Khitrova, J. Valley, H. Gibbs

To cite this version:

G. Khitrova, J. Valley, H. Gibbs. GAIN/FEEDBACK APPROACH TO OPTICAL INSTABIL- ITIES IN SODIUM VAPOR. Journal de Physique Colloques, 1988, 49 (C2), pp.C2-483-C2-486.

�10.1051/jphyscol:19882113�. �jpa-00227624�

GAIN/FEEDBACK APPROACH T O OPTICAL I N S T A B I L I T I E S I N SODIUM VAPOR

G. KHITROVA, J.F. VALLEY and H.M. GIBBS

Optical Sciences Center, University of Arizona, Tucson, AZ 85721, U.S.A.

Abstract

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The gainlfeedback approach to lasing and optical instabilities has been applied to sodium vapor driven by a near-resonant intense field. The observed lasing fre- quencies agree with the two-beam-coupling gain curve calculated for a Doppler- broadened two-level medium. Rayleigh-gain lasing is seen with no external cavity using counterpropagating beams, and Raman gain lasing is seen in a ring cavity.

We use the gain-feedback approach1 to explain a number of instabilities observed in sodium vapor with the laser frequency vL .tuned to the defocusing side of line center at v,. _{The gain} curve, which includes motion of the atoms, predicts two regions of possible gain: Rayleigh gain for frequencies v just above v, and Raman gain for v 1- vL - v,, where v, is the on-resonance Rabi frequency; see Fig. 1.2 Lasings based on these two gain mechanisms have been seen in two different feedback configurations. The new observations are: Rayleigh-gain lasing with no external mirrors using the distributed feedback of counterpropagating pump beams, Rayleigh- gain lasing without a foreign gas, Raman-gain lasing in a ring cavity (see Fig. 21, and both Rayleigh and Raman lasing using a single feedback mirror.

The gain curve f o r a stationary Na atom has already been derived3 and verified4 using an atomic beam of Na. For moving atoms, one must integrate this curve over the velocity d i s t r i b ~ t i o n . ~ Figure 1 shows the stationary-atom and the Doppler-broadened curves showing the ac-Stark shift of the absorption peak and the shift and broadening of the Raman gain. If the intense pump frequency vL is detuned from the stationary-atom weak-pump resonance frequency v0 by SvL

-

= vL

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v0, then the peak of the Raman gain occurs at a frequency v given by v r vL T

(1

^{SvL1 2}

+

^vR2)1/2 for a stationary atom, where T is given by 6vL/1 6vLl and v, is the on- resonance Rabi frequency. For moving atoms and when the Doppler broadening is roughly equal to Sv,, as in Fig. Ib, the Raman gain is much broader and its peak shifts to almost vL - ^v,.

In contrast, the Rayleigh gain is Doppler-free and hardly affected.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19882113

JOURNAL DE PHYSIQUE

PROBE DETUNING FROM PUMP (GHz)

Figure 1. Calculations of (a) the stationary-atom and (b) the Doppler-broadened probe-gain profiles for an intense pump at vL detuned by vL

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v0 = -2.6 GHz (defocusing side) from the low- field line center vo. The Rabi frequency is v, = 2.4 GHz and the argon pressure 0.3 Torr.

(a) This shows the well-known ac-Stark-shifted absorption at v,

+

v,. The 500X enlargement at the left shows Raman gain (peak value 14) at v,

-

v , and Rayleigh gain peaked at about (2nT,)-1 to the right of vL. (b) For a Doppler width of 2 GHz, one sees that the high-intensity absorption dsolid curve) is shifted from the low-intensity absorption (dashed curve). (The 10X enlargement at the left has the same scale as the enlargement in (a), showing that the Rayleigh gain near v, is harclly affected.) But the Raman gain has a lower peak and greater width enabling several modes to lase as shown in Fig. 2.

occurs, but in only one direction in the cavity, namely in the forward direction with respect to the pump. For 6vL = -5 GHz, the lasing begins at

I

^v

-

^{vLl =} 4.1 GHz, just slightly larger than

the V R Y 3.7 GHz calculated from the 680-mW input power, 112-pm waist, and the dipole

moment4 of Na. The Raman lasing is much closer to v, than it would be if the atoms were stationary. Because of the broadened gain curve, several longitudinal modes of the ring cavity may be above the Raman lasing threshold, as shown in Fig. 2 for SvL = -3.5 GHz. Figure 1 shows the corresponding calculated plane-wave gain curve, where vR = 2.4 GHz gives a better fit because of absorption and defocusing.

For the counterpropagating-beams case, 300 mW beams were focused by two 30-cm-focal- length AR-coated lenses. Using counterpropagating-beams distributed feedback (DFB), an optical instability was seen by means of Rayleigh-gain lasing with no external cavity. The zero-order DFB modes of our short samples are broad and essentially flat over the Rayleigh-gain region which peaks at about 10 MHz from vL; consequently, lasing occurs at the peak of the gain curve.

The lengths L here, 0.9 cm for the flow cell and 10 cm for the quartz cell, are both short compared to the long lengths proposed in Ref. 1 where the next higher-order DFB mode at c/2L is made to coincide with the Rayleigh-gain curve. The ~10-MHz frequency shift facilitates detection by the heterodyne technique even for exact counterpropagation.

In summary, the gainlfeedback approach is a powerful tool for studying the onset of optical instabilities.'

The authors are grateful to P. Berman, Y. Silberberg, G. Giusfredi, S. L. McCall, E.

Ressayre, M. LeBerre, and A. Tallet for fruitful discussions, and to NSF for support.

Figure 2. Raman-gain lasing in Na in a ring cavity (see inset) for 6vL r -3.5 GHz (defocusing side). Fabry-Perot spectrum showing laser light at v

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^{vL =} 0 and Raman-gain lasing in four ring-cavity modes for v - v, r -3 GHz.

JOURNAL DE PHYSIQUE

References

1. Silberberg, Y. and Bar Joseph, I., Phys. Rev. Lett. 48 (1982) 1541; Bar-Joseph, I. and Silberberg, Y., Phys. Rev. A 36 (1987) 1731, and refs. contained therein.

2. Khitrova, G., Ph.D. dissertation (New York University, 1986); Khitrova, G., Berman, P. and Sargent 111, M., J. Opt. Soc. Am. B 5 (1988) 160.

3. Haroche, S. and Hartman, F., Phys. Rev. A 6 (1972) 1280; Mollow, B.R., Phys. Rev. A 5 (1972) 2217.

4. Wu, F.Y., Ezekiel, S., Ducloy, M. and Mollow, B.R., Phys. Rev. Lett. 38 (1977) 1077.

5. See also Khitrova, G., Valley, J.F. and Gibbs, H.M., Phys. Rev. Lett. 60 (1988) 1126.