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Japanese Journal of Applied Physics

Transient Behavior of a Saturable Optical Resonator with Distributed Bragg-Reflectors

Masahiro Okuda, Kiyoshi Onaka, Takashi Sakai

Published Dec 1, 1978• 5 citations
Publisher

Abstract

Transient behaviors of a saturable optical resonator with distributed Bragg-reflectors are analyzed in the scheme of time-dependent coupled wave equations. The up and down switching times of the saturable optical resonators are calculated for various values of the optical intensity, the width of incident pulse, and the relaxation time and the length of the saturable absorber. It is shown that the switching time of a saturable resonator has an optimum value for the optical intensity and the width of the incident pulse. Also, the switching time becomes shorter, as increasing the normalized length of the saturable absorber. However, even if the optimum values of the optical intensity and the width of the incident pulse are employed, the switching time is much larger than the transit time in the saturable resonator, because the transmission pulse is constructed by multiple reflections in the reflector.

DOI
10.1143/jjap.17.2123

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Transient behaviors of a saturable optical resonator with distributed Bragg-reflectors are analyzed in the scheme of time-dependent coupled wave equations. The up and down switching times of the saturable optical resonators are calculated for various values of the optical intensity, the width of incident pulse, and the relaxation time and the length of the saturable absorber. It is shown that the switching time of a saturable resonator has an optimum value for the optical intensity and the width of the incident pulse. Also, the switching time becomes shorter, as increasing the normalized length of the saturable absorber. However, even if the optimum values of the optical intensity and the width of the incident pulse are employed, the switching time is much larger than the transit time in the saturable resonator, because the transmission pulse is constructed by multiple reflections in the reflector.
Bistability of an optical resonator with distributed Bragg-reflectors is analyzed by using the coupled-mode theory. Hysteresis and nonlinear properties are given as a function of the quantities characterizing the Kerr medium (the quadratic electrooptic coefficient n 2 and the length of the Kerr medium l ) and the propagation characteristics of the corrugated waveguide (the coupling coefficient k and the optical loss in the corrugated waveguide Γ). We show that the optical resonator with distributed Bragg-reflectors has a multi-valued transmission characteristic by the Kerr effect. From the numerical calculations, the up-switching and down-switching power intensities of bistable operation are estimated.
The effect of the bleaching property of a saturable absorber and the optical loss in a corrugated waveguide on bistability is analyzed by using the coupled-mode theory. Hysteresis and nonlinear properties are given as a function of the quantities characterizing the saturable absorber (the absorption coefficient Γ 0 , and the length of saturable absorber l ) and the propagation characteristics of the corrugated waveguide (the coupling coefficient k and the optical loss in waveguide Γ). It is clear, by selecting the optimum values of these parameters., that the saturable optical resonator has a bistable property which is useful as an optical gate, an optical amplifier, and an optical memory in integrated optical circuits.
Optical bistability in a CO2 infrared laser containing SF6 as a saturable intracavity absorber has been studied under dynamic conditions as a function of a time-dependent laser control parameter. The width of the optical bistability region, the fluctuations in the bistability switching values, and the dependence on the initial conditions have been investigated in this transient optical bistability. A numerical solution of the laser rate equations provides a good interpretation of the experimental results, but some experimental observations cannot be completely explained.
The coupled Maxwell-Schrodinger equations are used to describe propagation of a pulse in a nonlinear absorbing medium. The absorber is assumed to be comprised of a homogeneously broadened system of two-level atoms that are exactly resonant with the field. Numerical calculations have been performed for incident pulses of hyperbolic-secant shape and of duration that is long compared to the atomic phase-memory time. Selected values of input intensity are considered. For intensities below a certain level the calculations nearly agree with rate-equation predictions, but as the incident intensity is increased we find that optical nutation comes into play. The nutation effect leads to pulse breakup as the packet penetrates into the medium. An analytical calculation, for the case of an applied optical field of step-function form, has been performed in order to provide additional insight about the intensity threshold for nutation.
The transient behavior of degenerate four-wave mixing (DFWM) in a three-level saturable absorber is analyzed and verified experimentally. A sharp peak of phase-conjugated reflectivity is predicted and observed at high pump intensities for pulsed beams. The influence of the time-dependent behavior of the conjugate wave signal on results of pulsed-beam experiments is studied. It is shown that transient effects could account for discrepancies between previous experimental results and steady-state theory.