Gain-feedback approach to optical instabilities in sodium vapor

Abstract

The gain-feedback approach to lasing and optical instabilities has been applied to sodium vapor driven by a nearly resonant intense field. The observed lasing frequencies agree with the two-beam-coupling gain curve calculated for a Doppler-broadened two-level medium. Rayleigh-gain lasing is seen for no external cavity with use of counterpropagating beams, and Raman-gain lasing is seen in a ring cavity. PACS numbers: 42.65.Ma, 32.80.Wr, 42.50. Tj, 42.65.Ky Silberberg and Bar-Joseph' have analyzed the onset of an optical instability as the simultaneous occurrence of sufficient gain and feedback to permit lasing at a new frequency.The instability observed on the transmitted light is then merely the beat between the pump field and the newly generated "lasing. " We have used this gainfeedback approach in sodium vapor using the Rayleigh gain to generate sideband lasing displaced from the driving laser field by 8 to 14 MHz. Raman-gain lasing is also seen, but it is displaced by the on-resonance Rabi frequency, typically 4 6Hz or less here, rather than by the effective Rabi frequency which is larger because of the detuning. The new observations are Rayleigh-gain lasing with no external mirrors with use of counterpropagating pump beams, ' Rayleigh-gain lasing without a foreign gas, and Raman-gain lasing in a ring cavity.The pump-probe or two-beam-coupling gain curve for a stationary Na atom has already been derived and verified.Here we adopt the nomenclature of Haroche and Hartman and refer to the dispersion-shaped resonance at the laser frequency vL, as "Rayleigh" (called 1/T~in Ref. 4) and the gain peak at vL, -vttE as "Raman" (sometimes called Rabi or three-photon ' gain).Here the effective Rabi frequency is vaE (~BvL+ va) ', where va is the on-resonance Rabi frequency, pvL =vLvo, and vo is the two-level-atom frequency.For moving atoms, one must integrate this curve over the velocity distribution; this has been expressed as easily calculable sums of plasma dispersion functions. " ' Figure 1 compares the detuned stationary-atom curve in Fig. 1(a) with the Doppler-broadened curve in Fig. 1(b) showing the ac Stark shift of the absorption peak and the shift and broadening of the Raman gain. The peak of the Raman gain occurs at a frequency v given by v=-vL~v&E for a stationary atom, where~is given by &vL/I&vL~. For moving atoms and when the Doppler broadening is roughly equal to b'vL, as in Fig. 1(b), the Raman gain is much broader and its peak shifts to almost vL -vR. In contrast, the Rayleigh gain is Doppler free and hardly affected. Lasing will be described on the basis of these two gain mechanisms with use of two different feedback configurations.The experimental apparatus consists of a cw ring dye laser and sodium cell. The =-900-mW single-mode output power of the dye laser is diffracted from an acoustooptic Bragg cell so that any feedback is shifted by 80 MHz and has no effect on the dye-laser frequency. The beam is then spatially filtered, collimated, and focused by a 30or 45-cm focal-length lens into the sodium wit...

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