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Light scattering by a phase conjugator in the four-wave mixing configuration

Henk F. Arnoldus, Thomas F. George

Published Jun 1, 1988• 0 citations
OpenAlex

Abstract

Abstract Reflection of travelling and evanescent plane waves by a four-wave mixing phase-conjugator is studied in detail. No restrictions are imposed on the nonlinear interaction strength, the angle of incidence or the frequency mismatch between the pump-beams and the incoming waves. We only assume that the incident field is weak compared to the pump fields, which justifies a classical field description of the pumps. The wave-vectors, amplitudes and phases for the various waves are evaluated, without the slowly-varying amplitude approximation. Familiar phase-matching resonances for certain values of the interaction length are recovered, and in addition strong resonances are found if the angle of incidence is finite and the incident light is not in perfect resonance with the pumps. The latter resonances appear at the transitions from a travelling to an evanescent wave. The significance of finite angles of incidence and evanescent waves for spectroscopic applications is pointed out.

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Light Scattering by a Phase Conjugator in the Four-wave Mixing Configuration

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Reflection of travelling and evanescent plane waves by a four-wave mixing phase-conjugator is studied in detail. No restrictions are imposed on the nonlinear interaction strength, the angle of incidence or the frequency mismatch between the pump-beams and the incoming waves. We only assume that the incident field is weak compared to the pump fields, which justifies a classical field description of the pumps. The wave-vectors, amplitudes and phases for the various waves are evaluated, without the slowly-varying amplitude approximation. Familiar phase-matching resonances for certain values of the interaction length are recovered, and in addition strong resonances are found if the angle of incidence is finite and the incident light is not in perfect resonance with the pumps. The latter resonances appear at the transitions from a travelling to an evanescent wave. The significance of finite angles of incidence and evanescent waves for spectroscopic applications is pointed out.

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The phase-conjugate mirror realized by means of degenerate four-wave mixing in a Kerr-like medium is investigated using the angular spectrum representation of interacting fields. The analysed model is based on the nonlinear mixing of two infinite plane pump waves with the spatially limited probe and signal waves. Relations among harmonic components of the probe and signal fields are derived assuming non-depleted pumping and neglecting the evanescent waves. The influence of the injected signal field on the frequency spectrum of the generated phase-conjugate field is also examined.

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Phase conjugation by nondegenerate four-wave mixing with excited-state Zeeman coherences

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Nondegenerate four-wave mixing on the j=0\ensuremath{\rightarrow}j=1 transition, in a ``V '' system, using orthogonal, circularly polarized pump beams is used to study theoretically the generation of the phase-conjugate signals. The efficiency of generation of the conjugate wave is studied as a function of the various system parameters such as pump-probe detuning, Zeeman splitting, pump-atom detuning, collisional parameters, and the intensities of the pump beams. The origin of the various resonances in the reflectivity is explained. For weak pump fields, some resonances are shown to have subnatural linewidths. In the degenerate case, the reflectivity as a function of pump-atom detuning has, in contrast to a two-level system, a doublet structure for moderate absorption-length parameters and field strengths. The reflectivity is shown to have additional resonances due to pump imbalance. The phase-conjugate signal is also shown to exhibit the pressure-induced extra resonances.

Physical Review A•Feb 1, 1985•7 citations
Abstract Reflection of travelling and evanescent plane waves by a four-wave mixing phase-conjugator is studied in detail. No restrictions are imposed on the nonlinear interaction strength, the angle of incidence or the frequency mismatch between the pump-beams and the incoming waves. We only assume that the incident field is weak compared to the pump fields, which justifies a classical field description of the pumps. The wave-vectors, amplitudes and phases for the various waves are evaluated, without the slowly-varying amplitude approximation. Familiar phase-matching resonances for certain values of the interaction length are recovered, and in addition strong resonances are found if the angle of incidence is finite and the incident light is not in perfect resonance with the pumps. The latter resonances appear at the transitions from a travelling to an evanescent wave. The significance of finite angles of incidence and evanescent waves for spectroscopic applications is pointed out.
Reflection of travelling and evanescent plane waves by a four-wave mixing phase-conjugator is studied in detail. No restrictions are imposed on the nonlinear interaction strength, the angle of incidence or the frequency mismatch between the pump-beams and the incoming waves. We only assume that the incident field is weak compared to the pump fields, which justifies a classical field description of the pumps. The wave-vectors, amplitudes and phases for the various waves are evaluated, without the slowly-varying amplitude approximation. Familiar phase-matching resonances for certain values of the interaction length are recovered, and in addition strong resonances are found if the angle of incidence is finite and the incident light is not in perfect resonance with the pumps. The latter resonances appear at the transitions from a travelling to an evanescent wave. The significance of finite angles of incidence and evanescent waves for spectroscopic applications is pointed out.
Optical phase conjugation by four-wave mixing is examined in detail. The Fresnel coefficients for reflection and transmission of a plane wave irradiating the surface of the phase conjugator are calculated. It appears that for normal incidence and a weak nonlinear interaction the device produces the phase-conjugated beam with respect to the incoming beam. For finite angles of incidence or stronger nonlinearities in the crystal, the generated wave deviates from the ideal conjugated wave, and also a second, specularly reflected, wave appears.
We present a plane-wave analysis of a recently demonstrated self-pumped phase conjugator. This device uses four-wave mixing to produce the phase-conjugate replica of an incident optical wave. All the waves are derived from the single incident wave: there are no externally supplied pumping beams. We consider the case of four-wave mixing in two interaction regions coupled by simple reflection. We calculate the phase-conjugate reflectivity as a function of coupling strength, taking into account imperfect coupling between the two interaction regions, and show that there is a threshold coupling strength below which the reflectivity is zero and above which the reflectivity is multiple valued. We also compute the coupling strength per unit length for a photorefractive crystal of barium titanate.
Optical phase conjugation by four-wave mixing in a Kerr medium is considered. Two strong counterpropagating lasers pump a nonlinear medium in which they excite the third-order polarization. Mixing with a weak incident field then generates the phase-conjugated image of that field. It is shown how the polarization of the pumps and the tensorial nature of the nonlinear interaction can be accounted for by a geometrical polarization tensor. The electric field is shown to obey two coupled wave equations, which couple a positive- and negative-frequency component of the field. These wave equations allow plane-wave solutions, and we derive the dispersion relation for the wave vectors of these modes. By matching the field of such a mode across the boundaries of the medium to an external incident field, we are able to obtain analytically the Fresnel coefficients for reflection and transmission. Our expressions reduce to earlier results in the appropriate limits.
The phase-conjugate mirror realized by means of degenerate four-wave mixing in a Kerr-like medium is investigated using the angular spectrum representation of interacting fields. The analysed model is based on the nonlinear mixing of two infinite plane pump waves with the spatially limited probe and signal waves. Relations among harmonic components of the probe and signal fields are derived assuming non-depleted pumping and neglecting the evanescent waves. The influence of the injected signal field on the frequency spectrum of the generated phase-conjugate field is also examined.
Nondegenerate four-wave mixing on the j=0\ensuremath{\rightarrow}j=1 transition, in a ``V '' system, using orthogonal, circularly polarized pump beams is used to study theoretically the generation of the phase-conjugate signals. The efficiency of generation of the conjugate wave is studied as a function of the various system parameters such as pump-probe detuning, Zeeman splitting, pump-atom detuning, collisional parameters, and the intensities of the pump beams. The origin of the various resonances in the reflectivity is explained. For weak pump fields, some resonances are shown to have subnatural linewidths. In the degenerate case, the reflectivity as a function of pump-atom detuning has, in contrast to a two-level system, a doublet structure for moderate absorption-length parameters and field strengths. The reflectivity is shown to have additional resonances due to pump imbalance. The phase-conjugate signal is also shown to exhibit the pressure-induced extra resonances.