Photorefractive Phase Conjugate Mirror Research Articles

Stabilization of photorefractive phase conjugate mirror

Stabilization of photorefractive phase conjugate mirror

Self-oscillation in a photorefractive phase-conjugate mirror with linear absorption I Isotropic four-wave mixing

The effects of linear absorption on the degenerate and nondegenerate self-oscillation conditions of a photorefractive phase-conjugate mirror are explored. In this study, phase-conjugation results from nonlinear mixing of two strong undepleted parallel-polarized counterpropagating pump waves with a probe wave. Numerical results are presented that illustrate that the linear absorption tends to increase the value of the coupling coefficient required for self-oscillation. It is also found that the pump intensity ratio r is almost independent of the linear absorption for positive normalized detuning Δωτ between the probe and the pump frequencies and of the zero phase shift, ϕ, between the gratings and the light interference patterns when the gratings are stationary. For ϕ = ±π/2, the variation of r with respect to absorption is symmetric for positive and negative detunings.

Self-oscillation in a photorefractive phase-conjugate mirror with linear absorption II Anisotropic four-wave mixing

The effects of linear absorption on the degenerate and nondegenerate self-oscillation of a photorefractive phase-conjugate mirror under condition of anisotropic four-wave mixing are considered. The phase conjugation results from nonlinear mixing of two strong undepleted orthogonally polarized counterpropagating pump waves with a probe wave. We consider two types of situation for orthogonally polarized pump beams corresponding to two crystal families: one such as the Bi12SiO20 crystal family (sillenite family) and the other such as the BaTiO3 and strontium barium niobate crystal family. In both of these crystal families the degenerate and nondegenerate self-oscillations are shown to occur in the presence of linear absorption, which tends to increase the value of the coupling coefficient required for self-oscillation. Numerical results are presented that exhibit various features of degenerate and nondegenerate self-oscillation in both crystal families for different values of the phase ϕb of the backward grating.

Image transmission with a pair of graded-index optical fibers and a BaTiO_3 phase-conjugate mirror

One-way transmission of images was achieved with two graded-index multimode optical fibers and a phase-conjugate mirror. Two fibers were made to have the same shape and the same property. A distorted output beam from the first fiber was reflected by a photorefractive self-pumped BaTiO3 phase-conjugate mirror and was launched to the second fiber. Images were restored in the output beam of the second fiber. Graded-index fibers showed better image recovery than did step-index fibers.

Effects of linear absorption on the steady-state behavior of a photorefractive phase-conjugate mirror

A photorefractive phase-conjugate mirror with linear absorption is examined. An objective of this study is to identify possible effects of absorption on the self-oscillation conditions of the mirror and the properties of the excited conjugate wave. It has been found that self-oscillation is still possible in the presence of absorption. However, the coupling coefficient required for self-oscillation must increase in magnitude with increasing absorption coefficient to counteract the depressing effects of absorption. A consequence of self-oscillation in the presence of absorption is enhancement of the mirror reflectivity. A parametric study of the absorption-enhanced mirror is presented.

ロジウムをドープしたＢａＴｉＯ３結晶のフォトリフラクティブ効果

Photorefractive effect with Rh-doped BaTiO3 crystals are more sensitive to near infared light, compared with nominally non-doped crystals. The reflectivity of photorefractive phaseconjugate mirrors was measured for several wavelengths in the nearinfrared. The reflectivity of about 25% was obtained at the wavelength of 780nm in a ring configuration.

Effect of phase mismatch on the transverse dynamics of a phase-conjugate resonator at low Fresnel number

The dynamics of a resonator using an externally pumped photorefractive phase-conjugate mirror is studied experimentally as a function of the phase mismatch introduced by an angular tilt of the pump beam. At the lowest Fresnel number allowing transverse structures ( F∼2.5), it is observed that spatially inhomogenous patterns are time dependent, periodic in this case, with a diverging period as phase matching is approached. The transverse beam pattern is analyzed using a singular value decomposition revealing two significant eigenmodes oscillating in phase quadrature.

Double phase-conjugate mirror: to oscillate, or not to oscillate?

A physical picture of the differences in operation of the photorefractive double phase-conjugate mirror for TM versus TE polarization is presented.

Theoretical Investigation of Photorefractive Ring Passive Phase-conjugate Mirror in the Presence of Asymmetric Transmission

Abstract The performance of a photorefractive ring phase-conjugate mirror is found to be determined by the combined effect of coupling the strength (ΓL), the product (T 1 T 2) and the ratio (T 1/T 2) of the cavity transmissivities along the two directions. The threshold phase-conjugate reflectivity of the device can be changed or controlled by the variation of these three parameters.

Operation of the double phase conjugate mirror for TE polarization: exact solution and failure of the slowly varying envelope approximation

The steady-state two-dimensional coupled wave equations describing the photorefractive double phase conjugate mirror with TE-polarized pumps, and which are derived directly from Maxwell's equations without employing the slowly varying envelope approximation (SVEA), are solved analytically in the undepleted pumps approximation for equal pump intensities and angles of incidence. The solutions are compared with those obtained using the SVEA, and the predictions of each approach with regard to the operation of the double phase conjugate mirror are discussed.

Observation of chaos in off-Bragg photorefractive four-wave mixing

Large-amplitude oscillations in the phase conjugate intensify have been observed when one of the pumping beams of an externally pumped photorefractive phase conjugate mirror deviates slightly from the Bragg angle. The Fourier transform of the experimental time series data exhibits the broad frequency spread characteristics of a chaotic signal. A phase space plot is constructed, and is found to exhibit some of the features associated with strange attractors. The fractal dimension of the attractor is determined to be approximately 5.7, indicating chaotic behavior. The number of dynamical dimensions for this attractor is found from Takens' theorem to be approximately 13, considerably greater than what is predicted by the standard scalar four-wave mixing equations, and an explanation for such high dimensionality is presented in terms of a vector field description of photorefractive four-wave mixing. Additionally, evidence is presented to support the conclusion that the chaotic behavior results from the off-Bragg detuning of one of the pumping beams.

Threshold for conjugation of speckle beams by a double phase conjugate mirror

We find the theoretical threshold for phase conjugation of a pump beam with speckle structure by a double photorefractive phase conjugate mirror based on transmitting and reflecting gratings of a diffusion type. For a speckle beam the nonlinear dependence of the profile of light-induced optical nonuniformity on the local intensity profile reduces the readout efficiency and raises the threshold by as much as a factor of 1.5.

Theory of photorefractive phase-conjugate oscillators. I. Isotropic four-wave mixing.

A theory of the photorefractive phase-conjugate oscillator (PCO) is developed. A PCO consists of an optical resonator made up of two planar mirrors (a Fabry-P\'erot cavity) containing an intracavity photorefractive phase-conjugate element that is pumped externally by a pair of off-axis counterpropagating laser beams of the same frequency. The two pumps are assumed to be parallel polarized. Phase conjugation of an input beam of slightly higher or lower frequency occurs because of nondegenerate isotropic four-wave mixing. The conjugation process generates a beam of slightly lower or higher frequency so that six waves coexist in the resonator. In the absence of the mirrors, the PCO simply reduces to a photorefractive phase-conjugate mirror (PCM), and in the absence of one of the mirrors, it reduces to a photorefractive phase-conjugate resonator (PCR). Degenerate and nondegenerate self-oscillations are shown to occur for several different cases of practical importance, and the threshold conditions for these cases are derived analytically under the assumption of the undepleted pumps. It is shown that the PCM can exhibit nondegnerate self-oscillations for \ensuremath{\varphi}=\ensuremath{\pi}/2, where \ensuremath{\varphi} is the phase shift between the gratings and the light interference patterns when the gratings are stationary. The coupling coefficient required for degenerate self-oscillation in the PCR is found to be one-half of that for the PCM if the mirror is perfectly reflecting and if the pump beams have equal powers (r=1). It is also shown that one cannot have degenerate self-oscillation in PCO for r=1 and \ensuremath{\varphi}=\ensuremath{\pi}/2, and nondegenerate self-oscillation for r=1 and \ensuremath{\varphi}=0. The self-oscillation conditions for the PCO do not depend upon the position of the photorefractive crystal inside the cavity.

Experimental investigation of a system of two coupled double phase conjugate mirrors

The results of an investigation of a nonlinear resonator formed by two coupled photorefractive double phase conjugate mirrors are presented. In steady-state the resonator exhibits bistable behavior versus both pumping beam power ratio and the Fresnel number of the cavity. The dynamics of the development of the scattering is characterized by the relatively long “silence” zone preceding the appearance of conjugate beams.

Multigrating phase conjugation: chaotic results

Slowly varying envelope wave equations describing degenerate four-wave mixing (4WM) in photorefractive phase-conjugate mirrors are solved exactly, in terms of quadratures. Multigrating 4WM geometry is assumed, with the transmission and reflection gratings contributing equally and with the counterpropagating pump–pump interaction accounted for. The original boundary-value problem is transformed into an initial-value problem, which is treated by an iteration procedure. It is shown that within the iterative boundary-fitting procedure the multistability of solutions takes place and that the intensity reflectivity of the mirror may become chaotic. The strange attractor thus arising is analyzed with the use of standard methods of nonlinear dynamics.

Passive transverse-mode organization in a photorefractive oscillator with saturable absorber

We present and demonstrate a self-transverse-mode organization effect (passive transverse mode locking?) in a cavity that contains a saturable absorber. It gives narrowing and filamentation of the oscillating beam in the region of the absorber. In the demonstration, we have used a resonator formed by two photorefractive phase conjugate mirrors. The saturable absorber was bacteriorhodopsin in a polymer film. Light powers of 1–100 mW were used.

Mode locking and frequency tuning of a laser diode array in an extended cavity with a photorefractive phase conjugate mirror

We demonstrate active mode locking and a tunable narrow spectrum under cw conditions in an extended cavity laser which uses an AlGaAs/GaAs array gain medium and an external feedback from a self-pumped photorefractive phase conjugate mirror. The mirror ensures self-aligned, spatially matched feedback. The mode-locked pulses are 92 ps wide. The tuning, obtained by an intracavity grating, has a range of 70 Å under cw conditions.

Lateral and focal shifts of phase-conjugated beams in photorefractive materials

It is predicted that when a dc electric field is present or when a probe beam contains temporal frequencies different from that of the pump waves a beam reflected from a photorefractive phase-conjugate mirror will experience lateral and focal shifts. These shifts are a consequence of angular dependence of the phase of the reflectivity and are similar to the Goos-Hänchen effect. The phenomenon becomes more pronounced near resonance.

Real-time optical Wiener–Kolmogorov and novelty filtering with phase conjugation

Real-time all-optical Wiener-Kolmogorov filtering is demonstrated by using two coupled photorefractive phase-conjugate mirrors. A novelty filtering system based on the combination of the present operation and the operation of real-time image subtraction previously presented [Opt. Lett. 13, 503 (1988)] is outlined. By comparing an input signal pattern with a set of known stored patterns, all known information in the input would be eliminated from the output, while any novel information would appear. This latter scheme could also be used in image-synthesis applications.

Coupling pulsed dye oscillators using a phase conjugate resonator

Four pulsed dye oscillators are coherently combined into a single phase conjugate resonator through the selfpumped conjugation process in a single crystal of BaTiO(3). We have measured the locking range and energy scaling behavior of the system. The locking range is of the order of hundreds of wavelengths. Our best results are close to the theoretical limit and show that one can obtain output energy approximately proportional to N, the number of dye gain cells. Since the N output beams are locked in phase, this implies that the peak far-field intensity would scale as N(2). We also report two properties of the photorefractive phase conjugate mirror that are relevant to such a system: the fluence required for start-up (9 J/cm(2)) and the field of view (0.0 sr).