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Annual Meeting Optical Society of America

Transient optical phase conjugation in dynamic media

J. A. Tataronis, George C. Papen, Bahaa E. A. Saleh

Published Jan 1, 1987• 1 citation
Publisher

Abstract

We explore dynamic media, such as plasmas and photorefractive materials, as generators of phase conjugated replicas of transient optical signals via four-wave mixing. The characterizing element of dynamic media is a population of free charge carriers that leads to induced charge density gratings on probe illumination. In steady-state conditions, phase conjugation in such media normally appears with smaller pump intensities than are required in Kerr media but at the expense of potentially slow response times.1

DOI
10.1364/oam.1987.mf14

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We explore dynamic media, such as plasmas and photorefractive materials, as generators of phase conjugated replicas of transient optical signals via four-wave mixing. The characterizing element of dynamic media is a population of free charge carriers that leads to induced charge density gratings on probe illumination. In steady-state conditions, phase conjugation in such media normally appears with smaller pump intensities than are required in Kerr media but at the expense of potentially slow response times.1
A general solution to a linearized transient problem is presented and is shown to be valid for Kerr materials, photorefractive materials, and plasmas. The solution is expressed in terms of a transfer function that relates the complex frequencies of the probe and the conjugate field. Using this solution, the parameters that govern the overall time behavior are identified and compared. These parameters are then used to discuss the distortion characteristics of the conjugate signal for each of the three materials.>
Nonlinear optics normally involves the change in the susceptibility of a material due to the presence of optical radiation. In many cases, the light-matter interaction produces a change in the refractive index of the medium, as occurs in photorefractive media, as well as in Kerr-like media, Brillouin-active media and absorbing media with thermallyinduced refractive index changes. Such nonlinear refractive index variation corresponds to a change in the real part of the optical susceptibility %. In resonant materials, the optical radiation induces stimulated emission (or absorption) causing transfer of population between different energy states of the medium. This can lead to saturation of the amplification (or absorption) corresponding to changes in the imaginary part of the susceptibility x= i2odk where the amplitude gain coefficient a(I) is a saturable function of the intensity /, and k is the magnitude of the wavevector of the optical radiation. The interference of two (or more) coherent beams I(x) in the laser amplifier can cause a modulation of the population inversion N(x). This modulation of the inversion is commonly known as spatial hole burning in lasers and leads to formation of a gain-grating a(x) = 1/2GN(X) where G is the stimulated emission cross-section. The gain grating can act as a very efficient diffractive optical element exhibiting high diffraction efficiency that may be even greater than unity [16] and also very high phase conjugate reflectivity using four-wave mixing (FWM) geometries [5-7].
Recent interest in degenerate four-wave mixing in artificial Kerr media to produce phase conjugate waves has concentrated on the visible and infrared spectra. Attempts to extend this technique to the millimeter wave and microwave spectral regions encounter severe difficulties arising from the requirements of medium nonlinearity and high beam intensities. The former problem may be solved by the use of artificial Kerr media and the latter by confinement in a waveguide. In a single-mode waveguide, however, wavefront perturbations cannot propagate. Phase conjugation therefore reduces in this case to a 1-D conjugation capable only of correcting for longitudinal phase error. Observation of this conjugate wave with a slow response medium is made possible by using a sequential method. The general concept is to first write the nonlinear refractive index grating using counterpropagating pump and probe waves. Subsequently, both waves are turned off, and a pump wave approaching from the opposite side reads (scatters from) the grating to produce the phase conjugate wave.
The generation of phase conjugated replicas of optical signals has been the subject of many theoretical and experimental studies. Phase conjugation of harmonic signals is a byproduct of certain nonlinear processes such as degenerate four- wave mixing and stimulated Brillouin scattering. Although conjugation of steady signals is well established, the possibility and the effectiveness of conjugating unsteady signals remain largely unexplored. When the envelope of an optical signal varies, new physical phenomena in the conjugation process arise. As previously shown,1 dispersion in the conjugation process distorts the phase conjugate replica of a pulsed signal. Distortion appears even if the response of the medium to the applied optical signal is instantaneous.
Transient phase conjugation by degenerate four-wave mixing in saturable dyes is investigated theoretically and experimentally. Two special cases are examined: (1) the case in which two pump waves and a probe wave are simultaneously turned on and (2) the case in which the pump waves are turned on well before the incidence of the probe wave. For case (1) a peak appears in the transient reflectivity for high pump intensity, while for case (2) the reflectivity increases monotonically with time up to the steady-state value irrespective of the value of the pump intensity.
In the case of disordered nonlinear media, it is shown that in four-wave mixing a phenomena analogous to phase conjugation may occur. In contrast to the case of transparent media in which two counterpropagating pump waves (with frequency ${\ensuremath{\omega}}_{p}$) are required, phase conjugation may occur in the presence of a single pump wave injected into the disordered nonlinear material. We find that in the angular distribution of radiation of frequency ${\ensuremath{\omega}}_{s}$ (${\ensuremath{\omega}}_{s}$=2${\ensuremath{\omega}}_{p}$-${\ensuremath{\omega}}_{i}$, where ${\ensuremath{\omega}}_{i}$ is the frequency of probe wave) there is a narrow peak in the backscattered direction associated with the probe wave. The intensity of this peak may be some orders of magnitude larger than the diffuse background at the frequency ${\ensuremath{\omega}}_{s}$.