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Journal of the Optical Society of America B

Spatial resonance in an anisotropic medium with modulated gyrotropy

Levon S. Aslanyan, H. H. Hovakimyan

Published Jan 22, 2020• 4 citations
Publisher

Abstract

The problem of the propagation of linearly polarized light in an optically anisotropic medium with spatially modulated gyrotropy is considered. The analysis has been carried out using optical Bloch equations in the approximation of a rotating wave. For clarity, the results are interpreted on the Poincaré sphere. It is demonstrated that under the resonance conditions, i.e., when the spatial frequency of modulation of gyrotropy coincides with the spatial frequency of polarization beats, a resonant increase in the amplitude of these beats is observed.

DOI
10.1364/josab.378809

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The optical-pumping theory of the passage of polarised radiation through a resonant medium was developed in the irreducible tensorial formalism. Transitions with arbitrary momenta J 1.2 are considered in the cubic approximation. For transitions with small values of momenta (J 1 =1 to J 2 =0; J 1 = 1 / 2 to J 2 = 1 / 2 ) the vector form of the equation system in density-matrix notation allows the problem to be solved exactly for light intensity. In the general case of an elliptically polarised wave, the equation systems for the interaction between circular components of polarisation of light in a resonant medium are obtained. Numerical calculations for deformation and rotation of the polarisation ellipse in a medium subject to saturation effects are also carried out. Irrespective of the initial state the polarisation tends either to a linear or to a circular form as it propagates, depending on times of collisional relaxation of orientation and alignment. The polarisation of linearly and circularly polarised waves does not change as the waves propagate, but the values of the saturation power for these polarisations differ considerably.
On-resonance self-action of a beam with periodically modulated amplitude in a two-level saturable absorber is studied numerically. When the period of modulation is comparable with relaxation times, one cannot describe the medium by means of susceptibility, and the response of the medium to the amplitude variation is not immediate. We solve the Bloch equations in each point of the medium to find this response correctly. Transient behavior followed by stable oscillations of population difference and polarization vector is shown to depend strongly on the frequency and amplitude of modulation. Beam propagation is considered using a simplified model of a thin absorber followed by free space, the propagation distance being small compared with the modulation wavelength. Manifestations of non-stationary response of the medium in the output intensity behavior are analyzed.
Optical bistability in resonators containing a nonlinear gyrotropic isotropic medium is analyzed by studying the dependence of the bifurcation intensity of the incident radiation on its ellipticity. It is found that if the gyrotropy is weak, this dependence may have symmetry-induced singular points or turning points. The stable radiation states in the resonator formed near a singular or turning point differ in respect of the polarization and are due to the evolution of the polarization instability. Bifurcation curves are plotted for a ring resonator containing a medium with a cubic nonlinearity. The form of these curves changes appreciably as the gyrotropy is increased. The change in the resonator transmission accompanying changes in the gyrotropy is studied.