Holography, coherent light amplification and optical phase conjugation with photorefractive materials

The theory of nondegenerate four-wave mixing (NDFWM) in semiconductor lasers and amplifiers is presented with particular emphasis on the physical processes that lead to population pulsations. In the case of nearly degenerate four-wave mixing, modulation of the carrier density at the beat frequency Ω of the pump and probe waves creates a dynamic population grating whose effectiveness is governed by the spontaneous carrier lifetime τs. Such a grating affects both the gain and the refractive index of the probe wave. In particular, the probe gain exhibits features analogous to those observed in a detuned atomic system arising from the optical Stark effect. Both the gain grating and the index grating contribute to NDFWM, with the dominant contribution coming from the index grating. For detunings such that Ωτs ≫ 1, population pulsations correspond to modulation of the intraband population arising from spectral hole burning. Our results show that NDFWM is then limited by the phase-mismatch effects governed by the transit time τ rather than by the intraband population-relaxation time T1. Significant NDFWM is expected to occur for detunings up to about 300 GHz for typical transit-time values of 3 psec in semiconductor lasers.

Population pulsations and nondegenerate four-wave mixing in semiconductor lasers and amplifiers

The real-time information processing and manipulation of electromagnetic waves using nonlinear Qptical techniques has resulted in a myriad of new applications in diverse fields such as quantum electronics, image processing, optical computing, adaptive optics, and nonlinear spectroscopy. In this paper, we review and explore the field, provide a historical perspective, analyze several of the nonlinear interactions useful for the generation of phase-conjugate replicas, and conclude with a brief survey of potential applications and suitable nonlinear media.

Nonlinear Optical Phase Conjugation

In this article active non-linear optical effects in semiconductors are reviewed. These processes arise because of the dynamics of excited populations of charge carriers temporarily created in otherwise empty states when a beam of laser radiation is incident on the material. A large number of different effects have been observed in different semiconductor materials recently and the non-linearities cover a wide range of magnitudes both in time-scale and size of non-linearity. The theory and physical concepts relevant to these processes are described and experimental observations using both high power pulsed and low power c.w. lasers are reviewed. Applications in optical bistability, phase conjugation, optical gating and optoelectronic gating are discussed.

Dynamic non-linear optical processes in semiconductors

We present an analysis of resonator properties for a cavity bounded by a phase conjugate mirror, which is generated by a degenerate four-wave nonlinear optical interaction. Using a ray matrix formalism to describe the conjugate mirror, resonator stability conditions are derived. Longitudinal and transverse mode characteristics are discussed. Results are compared with an experiment where laser oscillation was observed at 6943 A using carbon disulfide as the nonlinear interacting medium comprising the phase conjugate mirror.

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A theoretical and experimental investigation of the modes of optical resonators with phase-conjugate mirrors

We present the first reported observation in the infrared of nonlinear phase-conjugated reflection. This was achieved via degenerate four-wave mixing in polycrystalline germanium. The observation was facilitated by taking advantage of the counterpropagating (strong) waves internal to a pulsed CO2 laser cavity. The measured effective reflectivity was 2% with a 10-mm interaction length. This simple intracavity technique is generally applicable to any nonlinear material transparent at the wavelength of the laser into which it is inserted.

High-efficiency pulsed 10.6-Mu m phase-conjugate reflection via degenerate four-wave mixing.

We have obtained phase-conjugate reflection and amplification with an effective reflectivity exceeding unity by redirecting the output of a TEA CO(2)-laser oscillator into its own gain medium. The intense counterpropagating waves within the laser were coupled through the saturated medium to provide the nonlinearity in a process analogous to degenerate four-wave mixing.

On-resonant phase-conjugate reflection and amplification at 10.6 microm in inverted CO(2).

We report efficient, diffraction-limited, phase conjugation of an XeF (3511-A) laser beam using stimulated Brillouin scattering. Approximately 70% of the 1-GHz bandwidth-locked portion of an injection-locked XeF laser output is phase conjugated by focusing the laser beam at 5 GW/cm2 into hexane or isopropanol.

Efficient phase conjugation of an ultraviolet XeF laser beam by stimulated Brillouin scattering

In this paper we develop the interrelationships between the steady-state and transient behavior for cw-pumped Kerr-like conjugators in which the optical Kerr effect is considered to respond instantaneously. We use Laplace-transform techniques to develop an expression for the conjugate response to input pulses of arbitrary form. For stable conjugator operation (in which the cw conjugate reflectivity is finite for all input frequencies), the expression reduces to an antilinear Fourier-transform relationship, which is readily adaptable to computer simulation. The cw filter function of Pepper and Abrams (Opt. Lett. 3, 312 (1978)) is found to play a central role. We show, both numerically and analytically, that our calculated delta-function response agrees with that previously published. We numerically demonstrate temporal spreading and reshaping when the conjugator transit time becomes equal to or longer than the duration of the input pulse, and we show numerically the perfect chirp reversal for sufficiently thin conjugators and the deviations from perfect chirp reversal upon increasing the thickness of the conjugator. These numerical results can be understood in terms of the bandwidth of the associated cw filter function.

B. J. Feldman

Papers

High-efficiency pulsed 10.6-Mu m phase-conjugate reflection via degenerate four-wave mixing.

On-resonant phase-conjugate reflection and amplification at 10.6 microm in inverted CO(2).

Efficient phase conjugation of an ultraviolet XeF laser beam by stimulated Brillouin scattering

Transient analysis of Kerr-like phase conjugators using frequency-domain techniques

Effect of CO2 laser-pulse mode quality on multiple photon absorption in SF6