Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Conference on Lasers and Electro-Optics

Mode theory and fidelity of Kerr-type phase conjugate mirrors

Erik J. Bochove

Published Jan 1, 1984• 0 citations
Publisher

Abstract

The fidelity of the image beam produced by a phase conjugate mirror (PCM) is less when pump beams are not plane waves. On the other hand, high fidelity is a desirable property for most proposed applications, while energy or power should also be economized. We show that PCM fidelity may be characterized in terms of eigenfunctions—and values—of the reflection operator, and optimization may be achieved through use of an appropriate phase filter.1,2 In the present view, the filter has the role of transforming the incident object field into a (near) eigenfunction of the reflectivity operator. An equivalence theorem is presented which demonstrates parallels between the PCM and a certain kind of optical cavity. Perturbation theory applied in the small distortion case leads to an alternative approach to characterization and calculation technique.

DOI
10.1364/cleo.1984.thq5

Related papers

Eigenmodes of Kerr-type phase-conjugate mirrors

Erik J. Bochove

The equivalence of the reflection-invariant modes of an imperfect phase-conjugate mirror to the transverse modes of a particular type of optical cavity is demonstrated. The reflection-invariant modes are shown to satisfy an approximate minimum-volume condition when the pump and the probe beams are well aligned.

Journal of the Optical Society of America B•Oct 1, 1984•3 citations

Applications of a semi-self-pumped phase conjugate mirror

Mark Cronin‐Golomb, Amnon Yariv

We introduce a semi-self-pumped phase conjugate mirror (PCM) in which one pump is externally injected into a ring resonator while the other is self-induced as in a unidirectional ring resonator. One application is in one-way imaging through optical distortions using a phase conjugate window.1 The original realization of the phase conjugate window was similar to an externally pumped PCM and had the disadvantage of requiring a clean pump beam coherent with the distorted probe. This meant that the clean beam had to bypass the distortion, thus limiting the practical utility of the device. By replacing the externally pumped PCM portion of the device with a semi-self-pumped PCM, the clean beam can be self-induced as an oscillation beam. The second application is as a thresholding phase conjugate mirror which would be useful, for example, in some optical associative memories.2 In the semi-self-pumped phase conjugator, the presence of the externally injected pumping beam suppresses buildup of the self-induced pumping beam until the signal reaches a certain threshold intensity.

Annual Meeting Optical Society of America•Jan 1, 1986•0 citations

Optical phase conjugation with very weak continuous-wave signals

Mary Yvonne Lanzerotti, Robert W. Schirmer, Alexander L. Gaeta

Summary form only given. We use a high-reflectivity phase-conjugate mirror (PCM) to demonstrate that optical phase conjugation can be performed on continuous-wave signal beams having power spectral densities as low as 5 x 10/sup -18/ W/Hz (i.e., 19 photons/sec.Hz). Our high-reflectivity (>600%), wide-bandwidth (90 MHz) PCM is formed by performing four-wave mixing in a potassium vapor cell using a frequency-stabilized Ti:sapphire laser that is tuned near the D/sub 2/ line. We have measured the noise spectra of the conjugate beam as functions of pump detuning from resonance, probe-pump detuning, pump-probe angular separation, and the number density of potassium atoms.

Quantum Electronics and Laser Science Conference•Jun 7, 1996•0 citations

Theory of phase conjugation by degenerate four-wave mixing using spatially varying pump beams

Erik J. Bochove

Phase-conjugate beam fidelity is studied in degenerate four-wave mixing with spatially varying pump beams. The theory includes long-cell-length (or high-gain) effects, diffraction, and nonlinear phase variation, focusing of the probe beam, and, finally, losses. Relatively simple algebraic expressions for the reflectivity are given that cover the cases of collinear or near-collinear beam geometries. An easily calculated parameter is defined that characterizes phase-conjugate fidelity and is applied to study focusing effects. It is shown that focusing effects may be useful in greatly reducing the principal distortion of the phase-conjugate beam over a considerable range of variation of beam parameters.

Journal of the Optical Society of America•Oct 1, 1983•17 citations

Quantum noise properties of phase conjugate mirrors

Alexander L. Gaeta, Robert W. Boyd

We investigate theoretically the quantum electrodynamic properties of the phase conjugation process. Based on the requirement that the reflected (conjugate) field must obey proper communication relations,1 we find that the reflected field contains a noise contribution due to the phase conjugate mirror (PCM). To calculate the statistical properties of the field leaving the PCM, we use the diagonal coherent state representation for the density operator of the reflected field.

Quantum Electronics and Laser Science Conference•Apr 24, 1989•0 citations

Nature of the interference pattern produced on reflection at a phase-conjugate mirror

Arturo A. Jacobs, Wayne R. Tompkin, Robert W. Boyd

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

Annual Meeting Optical Society of America•Jan 1, 1986•0 citations
The fidelity of the image beam produced by a phase conjugate mirror (PCM) is less when pump beams are not plane waves. On the other hand, high fidelity is a desirable property for most proposed applications, while energy or power should also be economized. We show that PCM fidelity may be characterized in terms of eigenfunctions—and values—of the reflection operator, and optimization may be achieved through use of an appropriate phase filter.1,2 In the present view, the filter has the role of transforming the incident object field into a (near) eigenfunction of the reflectivity operator. An equivalence theorem is presented which demonstrates parallels between the PCM and a certain kind of optical cavity. Perturbation theory applied in the small distortion case leads to an alternative approach to characterization and calculation technique.
We introduce a semi-self-pumped phase conjugate mirror (PCM) in which one pump is externally injected into a ring resonator while the other is self-induced as in a unidirectional ring resonator. One application is in one-way imaging through optical distortions using a phase conjugate window.1 The original realization of the phase conjugate window was similar to an externally pumped PCM and had the disadvantage of requiring a clean pump beam coherent with the distorted probe. This meant that the clean beam had to bypass the distortion, thus limiting the practical utility of the device. By replacing the externally pumped PCM portion of the device with a semi-self-pumped PCM, the clean beam can be self-induced as an oscillation beam. The second application is as a thresholding phase conjugate mirror which would be useful, for example, in some optical associative memories.2 In the semi-self-pumped phase conjugator, the presence of the externally injected pumping beam suppresses buildup of the self-induced pumping beam until the signal reaches a certain threshold intensity.
Summary form only given. We use a high-reflectivity phase-conjugate mirror (PCM) to demonstrate that optical phase conjugation can be performed on continuous-wave signal beams having power spectral densities as low as 5 x 10/sup -18/ W/Hz (i.e., 19 photons/sec.Hz). Our high-reflectivity (>600%), wide-bandwidth (90 MHz) PCM is formed by performing four-wave mixing in a potassium vapor cell using a frequency-stabilized Ti:sapphire laser that is tuned near the D/sub 2/ line. We have measured the noise spectra of the conjugate beam as functions of pump detuning from resonance, probe-pump detuning, pump-probe angular separation, and the number density of potassium atoms.
Phase-conjugate beam fidelity is studied in degenerate four-wave mixing with spatially varying pump beams. The theory includes long-cell-length (or high-gain) effects, diffraction, and nonlinear phase variation, focusing of the probe beam, and, finally, losses. Relatively simple algebraic expressions for the reflectivity are given that cover the cases of collinear or near-collinear beam geometries. An easily calculated parameter is defined that characterizes phase-conjugate fidelity and is applied to study focusing effects. It is shown that focusing effects may be useful in greatly reducing the principal distortion of the phase-conjugate beam over a considerable range of variation of beam parameters.
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