Counterpropagating Plane Waves Research Articles

Band gaps and group velocity in optical lattices

We study the optical properties of a periodic array of thin layers, as a model of an optical lattice carried by two counterpropagating plane waves. In particular we evaluate the dependence of the stationary waves on the polarization and the incidence angle of a probe beam. Also the effect of the dispersion relation and the photonic band gaps on the group velocity of wave packets is analyzed.

Resonances of a dielectric sphere illuminated by two counterpropagating plane waves

We consider the scattering of light by a spherical particle illuminated by two counterpropagating plane waves. Destructive and constructive interference of the two incident fields modifies the resonance contribution to the scattered and internal fields. The resonance contribution can vary between zero and twice the value of that associated with ordinary Mie scattering; the amount of the contribution is a function of the relative phase between the two beams.

Study of a parallel plate thermoacoustic prime mover

The frequency response of a resonance tube including parallel plate heat exchangers and prime mover stack has been measured. The results are given in terms of the quality factor Q of the prime mover. As the temperature gradient across the prime mover stack is increased, the Q increases indicating a decrease in attenuation across the stack. When the temperature difference is sufficiently large (∼300 K), the resonator goes into self-sustained oscillation indicating negative attenuation. Observations of Q approaching the onset of self-oscillation are reported in helium gas at pressures from 170–500 kPa. The observed Q's and the resonance frequency are explained in terms of counterpropagating plane waves. [Work supported by ONR and the NPS Research Program.]

Nonlinear polarization dynamics. III. Spatial polarization chaos in counterpropagating beams.

The steady-state spatial polarization distribution of counterpropagating plane waves in a ${\ensuremath{\chi}}^{(3)}$ medium is numerically investigated using a Stokes vector formalism. We consider all those material symmetry classes whose equations of motion are thought to be nonintegrable. Poincar\'e plots indicate that all these cases exhibit chaotic behavior. We also identify new analytic solutions for certain initial conditions. This completes the classification of the polarization dynamics of counterpropagating beams for all rotation symmetries about the axis of propagation, in parity- and non-parity-invariant media.

Isolas in four-wave mixing optical bistability

Optical bistability based on the cross-interaction of two counterpropagating plane waves in a Kerr-like medium is considered. It is shown that the input-output characteristics of such a system have not only multivalued hysteretic response (which was demonstrated by Winful and Marburger in 1980), but also multiple isolated branches (so called isolas) with nonhysteretic jumps from these branches to the main curve (but not vice versa). The isolas were found both in the case in which the problem can be solved analytically (particularly for electrostriction mechanism of optical nonlinearity) and in the general case of arbitrary light-induced anisotropy.

Degenerate two-wave mixing in the collinear geometry

Differential equations are derived for the propagation of two counterpropagating plane waves of arbitrary polarization in an optical medium having a cubic nonlinearity in dielectric susceptibility. It is shown that a simple analytic solution exists when both waves are circularly polarized. For waves polarized linearly, but with an angle θ between the polarizations at incidence, numerical solutions are found leading to elliptically polarized waves. Numerical solutions are also plotted for the reflection coefficient in the case when the pump waves are of equal amplitude and of the same polarization and an object wave of arbitrary amplitude (up to 30% of the pump amplitude) is incident with the orthogonal polarization.

Interaction of four counterpropagating plane waves in a medium with an instantaneous cubic nonlinearity

A theoretical analysis is made of the energy exchange between four counterpropagating plane waves during their interaction in a medium having an instantaneous cubic reactive nonlinearity. A solution of a complete system of equations in terms of Jacobi elliptic functions is obtained. The interaction pattern is constructed using concepts of dynamic holography. It is shown that the high energy exchange efficiency of a local nonlinear response of the medium is due to a shift of a hologram with respect to the interference pattern of the diffracted waves.