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

Physical Review Letters

Observation of Bistable Reflectivity of a Phase-Conjugated Signal through Intracavity Nearly Degenerate Four-Wave Mixing

Hisao Nakajima, Robert Frey

Published Apr 22, 1985• 43 citations
Publisher

Abstract

Experimental results are presented regarding the generation and bistable behavior of a conjugated signal obtained through intracavity nearly degenerate four-wave mixing in a semiconductor laser amplifier injected with both pump ($\ensuremath{\omega}$) and probe ($\ensuremath{\omega}\ensuremath{-}\ensuremath{\delta}\ensuremath{\omega}$) frequencies. Conjugated reflectivities at $\ensuremath{\omega}+\ensuremath{\delta}\ensuremath{\omega}$ larger than 500% with 35% efficiency together with bistable behavior in the three signals (pump, probe, and conjugated) are reported.

DOI
10.1103/physrevlett.54.1798

Related papers

Collinear nearly degenerate four-wave mixing in intracavity amplifying media

Haruto Nakajima, Robert Frey

Intracavity nearly degenerate four-wave mixing in amplifying media has been demonstrated to be a powerful technique to get very high conjugated reflectivities. A physical interpretation of this process is given in terms of interactions among pump (ω), probe (\omega- \delta\omega), or conjugated (\omega + \delta\omega) waves with optically induced refractive index modulations or gratings. Mixing experiments performed at the milliwatt level inside a (GaAl)As semiconductor laser operating above or below threshold have demonstrated very high conjugated reflectivities (a factor of 103-104) together with a 10 percent energy conversion efficiency. The appearance of additional peaks related to the ac Stark effect and observation of bistability on probe and conjugated beams also make this mixing process interesting for the study of instabilities occurring in lasers.

IEEE Journal of Quantum Electronics•Aug 1, 1986•60 citations

Bistable behavior of pump, probe, and conjugate signals through collinear intracavity nearly degenerate four-wave mixing

Nitin C. Kothari, Robert Frey

Theoretical calculations regarding the collinear intracavity nearly degenerate four-wave mixing are presented when a Fabry-Perot cavity is externally driven by a strong pump and probed by a weak signal. The calculations are performed for two different limits: the mean-field and the small-signal gain approximations. The results suggest the bistable behavior for all the three signals (pump, probe, and conjugate) with several different shapes of the hysteresis loops. Furthermore, for certain values of the parameters in the mean-field approximation, calculations show a resonance behavior of probe and conjugate signals with respect to the incident pump intensity, with probe and conjugate transmittance as high as ${10}^{3}$--${10}^{4}$ in the case when the pump transmission does not exhibit bistability. In the small-signal gain approximation, theory also demonstrates strong dependence of probe amplification on the normalized detuning when it is smaller than the probe-cavity mistuning.

Physical Review A•Sep 1, 1986•7 citations

Bistable reflectivity of phase-conjugated signal through intracavity degenerate four-wave mixing

Govind Prasad Agrawal, Christos Flytzanis, Robert Frey +1 more

Through intracavity degenerate four-wave interaction the reflectivity of the phase-conjugated signal is shown to exhibit bistability and hysteresis when the driving pump field is varied in a continuous matter. The nonlinear medium inside the Fabry-Perot cavity may be in one- or two-photon resonance with the pump. We suggest suitable materials and discuss possible applications of the bistable response of the reflectivity.

Applied Physics Letters•Apr 1, 1981•28 citations

Generation of Phase Conjugate Wave from a Visible InGaAlP Laser

Yoshinari Awaji, Shuji Sayama, Hiromasa Suzuki +1 more

This paper presents the first quantitatively measured results of detuning and spatial characteristics of the phase conjugate wave which is emitted from a Fabry-Perot cavity-type InGaAlP laser. Bandwidth of a nearly-degenerate four-wave mixing was confirmed to be due to the relaxation oscillation frequency of the laser. The reflectivity of the phase conjugate mirror and the amplification gain were larger than 10 and 100, respectively. By the off-axial injection of the probe beam to a broad stripe laser, the emitted phase conjugate wave was separated spatially from the pump beam. Non-degenerate four-wave mixing characteristics of an AlGaAs laser were also measured for the first time. Its 3-dB cutoff frequency was as large as 0.1 THz, which was determined by the reciprocal of the half-cycle time of the intracavity light-wave.

Japanese Journal of Applied Physics•Mar 1, 1993•1 citation

Intracavity resonant degenerate four-wave mixing: bistability in phase conjugation

Govind Prasad Agrawal

A general formalism is developed to study intracavity phase conjugation through resonant degenerate four-wave mixing. The effects of spatial hole burning, arising from interference of the counterpropagating pump waves, are fully incorporated. The analysis is applied to discuss intracavity phase conjugation in nonlinear media that can be modeled using either a two-level system or a Λ-type three-level system. In both cases, the phase-conjugate reflectivity exhibits bistability for an appropriate choice of the input parameters. For a two-level system, the tuning characteristics of the Fabry–Perot cavity significantly affect the phase-conjugate spectrum that displays hysteresis when the cavity is detuned from the applied laser frequency.

Journal of the Optical Society of America•May 1, 1983•18 citations

Optical Logic Functions Using Nearly Degenerate Four-Wave Mixing In Laser Diodes

Bruno J. Thedrez, Hisao Nakajima, Robert Frey

Optical logic functions can be obtained through nearly-degenerate four-wave mixing in laser diodes operating above as below threshold. In this nonlinear mixing process the pump frequency w is given either by laser oscillation or by amplification of an external pump signal. The conjugate frequency w + δw is then obtained by intracavity nearly-degenerate four-wave mixing when a probe beam of frequency w - δw is injected through the laser diode colinearly with the pump beam. Several examples using this technique are discussed including high contrast bistable memory, AND, OR, and INV gates.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Jan 8, 1987•0 citations
Experimental results are presented regarding the generation and bistable behavior of a conjugated signal obtained through intracavity nearly degenerate four-wave mixing in a semiconductor laser amplifier injected with both pump (\ensuremathω\ensuremath{\omega}\ensuremathω) and probe (\ensuremathω\ensuremath−\ensuremathδ\ensuremathω\ensuremath{\omega}\ensuremath{-}\ensuremath{\delta}\ensuremath{\omega}\ensuremathω\ensuremath−\ensuremathδ\ensuremathω) frequencies. Conjugated reflectivities at \ensuremathω+\ensuremathδ\ensuremathω\ensuremath{\omega}+\ensuremath{\delta}\ensuremath{\omega}\ensuremathω+\ensuremathδ\ensuremathω larger than 500% with 35% efficiency together with bistable behavior in the three signals (pump, probe, and conjugated) are reported.
Intracavity nearly degenerate four-wave mixing in amplifying media has been demonstrated to be a powerful technique to get very high conjugated reflectivities. A physical interpretation of this process is given in terms of interactions among pump (ω), probe (\omega- \delta\omega), or conjugated (\omega + \delta\omega) waves with optically induced refractive index modulations or gratings. Mixing experiments performed at the milliwatt level inside a (GaAl)As semiconductor laser operating above or below threshold have demonstrated very high conjugated reflectivities (a factor of 103-104) together with a 10 percent energy conversion efficiency. The appearance of additional peaks related to the ac Stark effect and observation of bistability on probe and conjugated beams also make this mixing process interesting for the study of instabilities occurring in lasers.
Theoretical calculations regarding the collinear intracavity nearly degenerate four-wave mixing are presented when a Fabry-Perot cavity is externally driven by a strong pump and probed by a weak signal. The calculations are performed for two different limits: the mean-field and the small-signal gain approximations. The results suggest the bistable behavior for all the three signals (pump, probe, and conjugate) with several different shapes of the hysteresis loops. Furthermore, for certain values of the parameters in the mean-field approximation, calculations show a resonance behavior of probe and conjugate signals with respect to the incident pump intensity, with probe and conjugate transmittance as high as 103{10}^{3}103--104{10}^{4}104 in the case when the pump transmission does not exhibit bistability. In the small-signal gain approximation, theory also demonstrates strong dependence of probe amplification on the normalized detuning when it is smaller than the probe-cavity mistuning.
This paper presents the first quantitatively measured results of detuning and spatial characteristics of the phase conjugate wave which is emitted from a Fabry-Perot cavity-type InGaAlP laser. Bandwidth of a nearly-degenerate four-wave mixing was confirmed to be due to the relaxation oscillation frequency of the laser. The reflectivity of the phase conjugate mirror and the amplification gain were larger than 10 and 100, respectively. By the off-axial injection of the probe beam to a broad stripe laser, the emitted phase conjugate wave was separated spatially from the pump beam. Non-degenerate four-wave mixing characteristics of an AlGaAs laser were also measured for the first time. Its 3-dB cutoff frequency was as large as 0.1 THz, which was determined by the reciprocal of the half-cycle time of the intracavity light-wave.
A general formalism is developed to study intracavity phase conjugation through resonant degenerate four-wave mixing. The effects of spatial hole burning, arising from interference of the counterpropagating pump waves, are fully incorporated. The analysis is applied to discuss intracavity phase conjugation in nonlinear media that can be modeled using either a two-level system or a Λ-type three-level system. In both cases, the phase-conjugate reflectivity exhibits bistability for an appropriate choice of the input parameters. For a two-level system, the tuning characteristics of the Fabry–Perot cavity significantly affect the phase-conjugate spectrum that displays hysteresis when the cavity is detuned from the applied laser frequency.
Optical logic functions can be obtained through nearly-degenerate four-wave mixing in laser diodes operating above as below threshold. In this nonlinear mixing process the pump frequency w is given either by laser oscillation or by amplification of an external pump signal. The conjugate frequency w + δw is then obtained by intracavity nearly-degenerate four-wave mixing when a probe beam of frequency w - δw is injected through the laser diode colinearly with the pump beam. Several examples using this technique are discussed including high contrast bistable memory, AND, OR, and INV gates.