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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Bifurcations of optical transverse solitary waves

Jeffrey W. Grantham, G. Khitrova, Hyatt M. Gibbs, John F. Valley, J. Xu

Published Dec 16, 1992• 0 citations
Publisher

Abstract

Bifurcations of optical transverse solitary waves are studied for one-way propagation through a sodium vapor cell. Two types of phase encoding seed transverse bifurcations resulting in cell- exit profiles with beauty rivaling that of a kaleidoscope. The cell-exit profiles are stationary in time, reproduce completely when the power or frequency is scanned, and agree well with one- way computations. Temporal and longitudinal development of the cell-exit profiles is shown, demonstrating both the instability nature of this phenomenon and its solitary wave nature. The first evidence is also presented for a double-peaked Raman gain

DOI
10.1117/12.131793

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IEEE Journal of Quantum Electronics•Sep 1, 1985•18 citations
Bifurcations of optical transverse solitary waves are studied for one-way propagation through a sodium vapor cell. Two types of phase encoding seed transverse bifurcations resulting in cell- exit profiles with beauty rivaling that of a kaleidoscope. The cell-exit profiles are stationary in time, reproduce completely when the power or frequency is scanned, and agree well with one- way computations. Temporal and longitudinal development of the cell-exit profiles is shown, demonstrating both the instability nature of this phenomenon and its solitary wave nature. The first evidence is also presented for a double-peaked Raman gain
This dissertation investigates three different optical instabilities: cw conical emission, bifurcations of optical transverse solitary waves, and asymmetric gain modification in a vertical cavity surface emitting laser (VCSEL). The first two instabilities occur in sodium vapor while the third occurs in a new type of semiconductor laser. For the conical emission instability, the first comparison and agreement between theory and experiment is given. The conical emission process is modeled as a series of nonlinear effects including self-trapping of the pump beam, Doppler-broadened Raman-gain amplification of Doppler-broadened resonance fluorescence, propagational four-wave mixing, and diffraction and pump-induced refraction of the new frequencies. Each step of the emission process is thoroughly examined and explained. Detailed comparisons are made between experimental observables and numerical calculations including near-field and far-field spatial profiles, frequency spectra, and cone angles. All comparisons show good agreement. In a different but related experiment, bifurcations of optical transverse solitary waves are studied for one-way propagation through a sodium vapor cell. Two types of phase encoding seed transverse bifurcations which result in transverse cell-exit profiles with the beauty rivaling that of a kaleidoscope. The cell-exit profiles are stationary in time, reproduce completely when the power or frequency is scanned, and agree well with one-way computations. Evidence is also presented for the first observation of a double-peaked Raman gain. In the third experiment, a temporal instability is examined in a GaAs VCSEL. Strong evidence is presented for an asymmetric gain modification induced when a strong optical signal is injected into the Fabry-Perot transmission peak of the VCSEL while it is lasing. This gain modification results in increased absorption on the high frequency side of the injected signal and increased gain on the low frequency side as manifested by the formation of an optical sideband. The frequency of the sideband depends on the intensity of the injected signal with frequencies (> 50 GHz) well beyond the predicted relaxation oscillation frequency being observed. Very efficient nondegenerate four-wave mixing is also observed.
Computational results show that the conical emission and Rabi sidebands observed when a nearly resonant laser pulse propagates through an atomic vapor are the result of pulse breakup into temporal-spatial (2-D) solitary waves. The temporal modulation associated with pulse breakup appears as Rabi sidebands in the spectrum. Because the process of pulse breakup depends on the pulse area, the 2-D solitary waves are curved in the time-radius plane due to the transverse profile of the pulse. The curvature of the solitary waves in the time-radius plane results in a transverse spatial oscillation and a corresponding transverse wave vector that leads to conical emission in the far field.
A transverse optical bistability is defined here as a bistability that would not occur with a plane-wave input, i.e., it depends crucially upon the radial variations in the input. Such bistabilities are characterized by much more pronounced changes in transverse profiles than in total transmission. An optical cavity is not required, making such systems good candidates for continuous wave studies of delayed-feedback instabilities which require a round-trip time longer than the medium response time. Trapping bistability and diffraction-free-encoding bistability are two limiting cases of transverse optical bistabilities. Trapping bistability occurs only for a long self-focusing nonlinear medium and arises from self-trapping of a single beam with a single feedback mirror or from cross trapping of two counterpropagating beams. In the diffraction-free-encoding case, diffraction is negligible through the portion of the nonlinear medium performing the encoding, but it is significant through any remaining medium and in the free-space propagation to the mirror and back. This paper is organized as follows: The physics of transverse optical bistabilities is summarized in Section I. Theoretical models are presented in Section II. A thin-sample-encoding (TSE) rings model is defined and shown not only to predict transverse bistability but also to account for the interference rings observed to accompany TSE bistability; it also yields delayed-feedback instabilities with a rich bifurcation sequence. Transverse bistability using a short length of sodium vapor is reported under TSE and DFE conditions in Section III. Recently it was discovered that TSE bistability has been seen only when the feedback beam is displaced from the input by about one beam diameter at the sodium. It remains to be determined just how much the nonconcentric feedback assists the concentric bistability predicted by the TSE rings model. A delayed-feedback instability with a period of twice the round-trip time is also seen.
Computational results show that the conical emission and Rabi sidebands observed when a nearly resonant laser pulse propagates through an atomic vapor are the result of the breakup of the pulse into solitary waves. For an incident pulse with a transverse as well as a temporal profile, the crests and troughs of the 2-D solitary waves are curved in a time-radius plane. The temporal modulation associated with pulse breakup appears as Rabi sidebands in the spectrum, while the curvature of the solitary waves in the time-radius plane results in a transverse spatial modulation, resulting in conical emission in the far field. These results were obtained by performing detailed numerical calculations of the time-dependent paraxial propagation of a cylindrically symmetric laser pulse through a vapor of two-level atoms. Our results can be interpreted readily in terms of optical nutation on the Bloch sphere and in terms of noncollinear phase matching through the curvature of the solitary waves rather than through additional parametrically generated waves. The cone opening angle depends on the initial transverse profile of the pulse and the process of beam breakup as well as self-focusing.
The dynamical evolution of a two transverse dimensional laser beam profile is monitored as it switches from a low to a high transmission state in a bistable optical resonator. Sharp gradients appearing at the edge of the switched-on central portion of the beam initiate a train of solitary waves which grow inwards towards the beam center. In a high finesse resonator, strong saturation of the beam in the on state tends to stabilize the solitary waves as concentric rings. Unlike earlier one transverse dimensional studies, the central part of the beam undergoes a slow periodic oscillation, but the shapes of the outer rings are consistent with earlier one transverse dimensional predictions. Numerical evidence is provided for filamentation of lower amplitude rings.