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Optics Letters

Natural modes for the analysis of optical bistability and laser instability

Lloyd W. Hillman, Robert W. Boyd, Carlos R. Stroud

Published Sep 1, 1982• 45 citations
Publisher

Abstract

A self-consistent description is given for the propagation of a weak optical probe beam through a homogeneously broadened two-level medium in the presence of a strong, collinear, near-resonant pump beam. The propagation of the probe beam is given in terms of bichromatic natural modes, which contain frequency components symmetrically displaced from that of the pump beam. The two frequency components have a definite relative amplitude and phase, which are determined solely by the frequency detunings of the optical fields from the atomic resonance and by the intensity of the pump field. A simple method for calculating these natural modes is derived, and their importance in describing nearly degenerate four-wave mixing, optical bistability, and the stability of homogeneously broadened ring lasers is discussed.

DOI
10.1364/ol.7.000426

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A self-consistent description is given for the propagation of a weak optical probe beam through a homogeneously broadened two-level medium in the presence of a strong, collinear, near-resonant pump beam. The propagation of the probe beam is given in terms of bichromatic natural modes, which contain frequency components symmetrically displaced from that of the pump beam. The two frequency components have a definite relative amplitude and phase, which are determined solely by the frequency detunings of the optical fields from the atomic resonance and by the intensity of the pump field. A simple method for calculating these natural modes is derived, and their importance in describing nearly degenerate four-wave mixing, optical bistability, and the stability of homogeneously broadened ring lasers is discussed.
We review and extend the theory of instabilities in absorptive optical bistability for ring cavities containing homogeneously broadened two-level media. The instabilities occur in the high-transmission branch and result in either a precipitation to the low-transmission branch or in pulsed multimode operation. Two numerical approaches are used to predict operation away from the simple mean-field limit. First, an iterative method is used to solve the general field eigenvalue equation for cavity modes with frequencies displaced from the input frequency. This work shows that the instability region decreases in size as the mirror transmission increases. These calculations are confirmed by the second numerical technique, consisting of direct integrations of the coupled Maxwell-Bloch equations. This second approach also provides time histories of the instability evolutions, and divides the instability range into a precipitation regime and a self-pulsing regime. The results are discussed in terms of first- and second-order phase transitions, and agree with the analytical results obtained within the dressed-mode description of optical bistability. They show that when the incident field is adiabatically decreased along the high-transmission branch, the spiking behavior always appears abruptly. By further decreasing the incident intensity, the self-pulsing disappears either continuously if the system remains in the high-transmission branch, or discontinuously if the system precipitates to the low-transmission branch. Connection is made with induced probe gain known in the saturation spectroscopy of absorbers (uninverted media), in which population pulsations transfer energy from a saturating wave to the probe waves. The very close relationship with multimode operation in homogeneously broadened unidirectional ring lasers is also established.
The interaction of a strong nearly resonant cw pump laser and a weak cw probe laser in a medium consisting of two-level atoms was studied by numerical integration of the Maxwell-Bloch equations. With propagation into the optically thick medium, the numerically calculated probe gain spectrum deviates substantially from one calculated by a four-wave-mixing formulation of coupled-wave theory with an undepleted pump. For probe frequencies inside the modified gain region, the laser field, initially in an unstable steady-state condition, evolves to a stable solution of the sine-Gordon equation.
A mean field theory of nearly-degenerate four-wave mixing is developed for the optical bistability, which has recently been found in a phase-conjugate resonator consisting of a normal mirror and a phase-conjugate mirror under relatively strong pumping. The bistability in transmission of the probe beam occurs as the mirror separation or the probe offset frequency is changed, but for a limited range of probe beam intensity. This behavior is explained as occurring under injection-locked conditions because of combined effects of tilting and broadening, or narrowing of the resonance curves due to nonlinearities in the phase-conjugate reflectivity arising from pump depletion.
Abstract : This thesis describes theoretical and experimental studies of a homogeneously broadened ring dye laser; particularly the two frequency instability in which a bichromatic field emerges from the laser above the instability threshold. The interaction of a bichromatic field with an isolated atomic resonance is examined. The time averaged inversion and the saturated gain exhibit structure in the form of a series of subharmonic resonances. The stability of a strong bichromatic laser field to the growth of a subharmonic probe field is examined. The gain of the subharmonic bichromatic probe field in the presence of the strong bichromatic laser field is calculated. The strong bichromatic field is stable to the growth of the subharmonic fields when the modulation frequency of the strong field coincides with the Rabi frequency of the lasing transition. The existence of chaos in a strongly driven nonlinear system is experimentally investigated in a multimode ring dye laser. A dye laser is pumped with a modulated pump source. The response of the dye laser to commensurate and incommensurate modulations is reported. For commensurate modulations, the dye laser responds in a periodic fashion and the rf spectrum of the dye is composed of a series of harmonics. For incommensurate modulations, the dye laser responds in a quasiperiodic fashion with a broadband rf spectrum.
The propagation of a weakly modulated light beam through a nonlinear material is treated. The optical field representing such a beam consists of a strong carrier-frequency component and two weak, symmetrically displaced sidebands that combine to form a field, which may be purely amplitude modulated (AM), frequency modulated (FM), or some combination of these two modulation forms. It is shown that, for any optical nonlinearity, two modulation forms exist that have the property that the form of modulation is invariant under propagation of the beam. If a modulation form other than one of these natural modes is injected into the nonlinear medium, the modulation form will change as the beam propagates, asymptotically approaching the natural mode that experiences the lower attenuation. Explicit expressions for these natural modes are presented for the case in which the nonlinear medium can be modeled as a collection of two-level atoms. For the special case of an on-resonance pump beam, the natural modes correspond to pure amplitude modulation and pure frequency modulation. This formalism provides a general description of saturation spectroscopy for both AM and FM fields. Formulas are derived for the rate at which a pure FM beam is converted to an AM beam owing to its interaction with a two-level atomic medium. We also consider the variation that is due to propagation of the depth of modulation of an AM wave interacting resonantly with two-level atoms. The formalism predicts the existence of spectral features whose shape depends sensitively on the internal relaxation processes of the material. Experimental spectra are presented for ruby, alexandrite, and fluorescein in glass and are interpreted.