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Journal of the Optical Society of America B

Measurement of the spectral reflectivity of a self-pumped phase conjugator

D. A. Noraev, Patrick Lambelet, Jack Feinberg

Published Sep 1, 1998• 3 citations
Publisher

Abstract

We measure the spectral reflectivity of a Cat (so named because its first conjugated image was that of a cat) self-pumped conjugator. We find that the transmission and the phase-conjugate reflectivity of the conjugator always vary periodically with wavelength and that the periodicity is caused by a resonator loop that springs up and self-adjusts inside the crystal. Depending on the spectral width of the incident beam, the conjugator will have either a minimum or a maximum reflectivity at the center of the writing spectrum. We show that the sign of the coherence function after one round trip of the internal resonator determines the spectral behavior of the conjugator, and we experimentally map out the dependence of the conjugator’s reflectivity and transmission on the spectral content of the incident beam.

DOI
10.1364/josab.15.002376

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We measure the spectral reflectivity of a Cat (so named because its first conjugated image was that of a cat) self-pumped conjugator. We find that the transmission and the phase-conjugate reflectivity of the conjugator always vary periodically with wavelength and that the periodicity is caused by a resonator loop that springs up and self-adjusts inside the crystal. Depending on the spectral width of the incident beam, the conjugator will have either a minimum or a maximum reflectivity at the center of the writing spectrum. We show that the sign of the coherence function after one round trip of the internal resonator determines the spectral behavior of the conjugator, and we experimentally map out the dependence of the conjugator’s reflectivity and transmission on the spectral content of the incident beam.
Dispersion compensation for a photorefractive self-pumped phase conjugator with femtosecond pulses is analyzed. The self-pumped phase conjugator consists of a pair of dynamic gratings coupled by total internal reflections at the crystal surfaces (cat conjugator). The negative angular dispersions of refraction at the air-crystal interface and the gratings inside the crystal compensate for the positive dispersion of the finite crystal path. The experimental results show that with partial dispersion compensation the width of the self-pumped phase conjugation at 450 nm of femtosecond pulses is narrower than that of the transmitted pulses.
Abstract The properties of the phase‐conjugate reflectivity are analyzed anew for the self‐pumped four‐wave mixing in which only the two waves, i.e., the forward pump wave and the probe wave, are incident on the photo‐refractive crystal and the phase‐conjugate wave of the forward pump wave is used as the backward pump wave. First, by means of a model in which a Cat‐type phase conjugator is placed outside the interaction region, the equation for the phase‐conjugate reflectivity of self‐pumped four‐wave mixing using a transmission grating is derived. Next, the numerical calculations have been used for the first time to determine the effects of the coupling strength, the probe ratio as the incident intensity ratio of the forward pump wave to the probe wave, and the reflectivity of the Cat‐type phase conjugator on the entire phase conjugate reflectivity. Since the equation describing the phase‐conjugate reflectivity has multiple solutions, the strict analysis of the equation shows that the phase‐conjugate reflectivity has multiple values. Further, the conditions for high phase‐conjugate reflectivity has been studied.
Photorefractive self-pumped phase conjugation is attractive for its simplicity and high reflectivity with low-power light sources. In order to realize its potential applications, it is important to study its response. So far the response of a phase-conjugate wave has been described with its rise time. It has not studied how the phase-conjugate wave responds when the spatial structure of an input probe wave is changed dynamically. We investigated the response of the phase conjugate wave by using two mutually coherent input beams, which can be regarded as components of a probe wave, and by introducing sinusoidal phase changes into one of them with varied frequencies. Each input beam has a power of 6 mW at the wavelength of 515 nm. A BaTiO3 crystal was employed as a self-pumped phase-conjugate mirror.1 By measuring relative phase between the two output beams, which can be regarded as components of a phase-conjugate wave, we found the response characteristic represented by a time-lag of first order, which is similar to RC circuit. The response time thus determined was 0.32 s, which was much shorter than the rise time of 30 s obtained with the same condition.
We have studied both experimentally and numerically the role of resonant refractive index gratings in a self-pumped phase conjugate mirror based on an Nd:YAG amplifier with nonreciprocal feedback loop. In experiment the generation of the phase-conjugating laser was delayed with respect to recording of a holographic nonlinear mirror by an external beam. An increase in the phase-conjugate reflectivity at a delay time of about 3 microseconds was measured. The numerical calculation confirmed the additional contribution of the resonant refractive-index grating, which is formed in the pumped Nd:YAG crystal due to excitation of a higher-lying level of Nd3+ ions, to efficiency of phase conjugation.
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.