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Physical Review A

Response of a phase-conjugate mirror to an incident photon

Z. Y. Ou, Samir Bali, L. Mandeļ

Published Mar 1, 1989• 19 citations
Publisher

Abstract

The response of a phase-conjugate mirror (PCM) based on nondegenerate four-wave mixing to an incident photon wave packet has been calculated. In the monochromatic limit the phase-compensating property of the PCM, which makes the response independent of optical path length, is recovered. However, for a photon wave packet of nonzero bandwidth, the response of the PCM varies in a fairly complicated manner with the wave-packet length. In particular, the length of the pulse reflected from the PCM becomes independent of the length of the incident pulse for sufficiently short pulses.

DOI
10.1103/physreva.39.2509

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Europhysics Letters (EPL)•Jan 14, 1992•6 citations
The response of a phase-conjugate mirror (PCM) based on nondegenerate four-wave mixing to an incident photon wave packet has been calculated. In the monochromatic limit the phase-compensating property of the PCM, which makes the response independent of optical path length, is recovered. However, for a photon wave packet of nonzero bandwidth, the response of the PCM varies in a fairly complicated manner with the wave-packet length. In particular, the length of the pulse reflected from the PCM becomes independent of the length of the incident pulse for sufficiently short pulses.
Phase conjugation is an nonlinear effect that results from the four-wave-mixing process. This peculiar effect, in analogy to a mirror, reflects an incident beam in a way that the reflection constitutes the time-reversal of the original beam. By combining the phase conjugate mirror with ordinary mirrors, a special resonator, called phase conjugate resonator (PCR), is constructed. The phase conjugate resonator has been used in a wide range of applications, including phase aberration correction, image transmission, holography, and phase sensing using interferometers. Here, we explore theoretically the properties of phase conjugate mirror by investigating its action upon a variety of quantum states. In addition, we analyze the input-output relations of a phase conjugate resonator. Experimental results are reported that faithfully verify PCR's enhanced stability as compared to normal resonators. Furthermore, we observe a linewidth narrowing effect that is only present in the phase conjugate resonator.
We investigate theoretically the quantum-noise properties of optical phase conjugation via four-wave mixing of nonclassical signal fields. We show that while the field generated at a phase-conjugate mirror (PCM) can be in a nonclassical state, the generated field is not necessarily useful within the context of phase conjugation. For the case in which a quadrature-squeezed signal field is incident at a PCM, we determine that the signal-to-noise ratio of one of the quadrature components of the generated field can approach the signal-to-noise ratio of the corresponding quadrature component of the signal field as the amount of squeezing of the vacuum field injected at the rear of the PCM is increased. For the case in which the signal field is amplitude squeezed, we determine that the signal-to-noise ratio of the conjugate field is always much smaller than that of the signal field. These results demonstrate that the phase-conjugation process can preserve the desirable quantum-noise properties of quadrature-squeezed fields but not those of amplitude-squeezed fields.
We have repeated the classic experiment of Wiener,1 which established the nature of the standing-wave pattern produced by reflection at the surface of a metallic mirror, with the metallic mirror used in his experiment replaced by a phase-conjugate mirror. We find that the positions of the fringes produced by interference between the wave incident on the phase-conjugate mirror and the wave leaving the mirror depends on the phase of the incident wave. This result is in contrast to that obtained through the use of a metallic mirror, in which case the interference pattern is found to be independent of the phase of the incident wave. The origin of the different behavior in these two cases lies in the fact that the phases of the waves that pump the PCM provide a reference through which phase information carried by the signal wave can be obtained. The experimental results are in excellent quantitative agreement with recent theoretical predictions.2
This paper is the second in a series describing propagation of electromagnetic radiation in phase-conjugate oscillators. We apply the formulation developed in the first paper to study the phase-conjugate resonator (PCR) and the Fabry–Perot cavity with an intracavity phase-conjugate mirror (PCM). Our results show that nondegenerate oscillation occurs in the PCR for large parametric gains and fixed separation between the conventional reflector and the PCM. The bandwidth is considerably reduced from that of a PCM alone. In the phase-conjugate oscillator, oscillation will occur at the pump frequency only if there is no separation between the conventional mirrors and the phase-conjugate element and if the nonlinear medium fills the entire Fabry–Perot cavity.