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

Applied Physics Letters

Phase noise of four-wave mixing in semiconductor lasers

Rongqing Hui, Antonio Mecozzi

Published May 18, 1992• 65 citations
Publisher

Abstract

A simple theoretical analysis shows that the linewidth of the conjugate wave produced in four-wave mixing in semiconductor lasers is equal to the linewidth of the probe plus four times the linewidth of the pump. Experimental results in good agreement with the theory are presented. This result implies an enormous enhancement in the phase noise of the conjugate wave and sets a limitation on some practical applications of four-wave mixing.

DOI
10.1063/1.106931

Related papers

Nonfrequency-shifted phase conjugation based on Brillouin scattering

Mark D. Skeldon, Paul Narum, Robert W. Boyd

It has previously been shown that Brillouin enhanced four-wave mixing can lead to large phase conjugate reflectivities for moderate laser powers.1,2 However, in the geometry considered by previous workers the pumps have equal frequency and hence the conjugate signal is shifted in frequency with respect to the probe. We have conducted an experimental and theoretical study of Brillouin-enhanced four-wave mixing for the different case in which the two pump waves differ in frequency by twice the Brillouin frequency of the four-wave mixing medium, and in which the probe wave frequency is halfway between those of the pump waves. In this case, the phase conjugate wave has the same frequency as the probe. Reflectivities > 100 % have been measured. Experimental results are compared to those of a theory that includes the effects of phase mismatch, pump depletion, and the finite response time of the medium.

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

Optical Phase Conjugation Using Four-Wave Mixing in Laser Diodes Subject to Strong Probe Injection Power

Yanhua Hong, Jianming Tang, K. Alan Shore

Optical phase conjugation through nearly degenerate four-wave mixing (NDFWM) in semiconductor lasers has attracted considerable attention in recent years since being first demonstrated by Nakajima and Frey[ 1 ]. Such interest arises due to the very high conjugate reflectivity of order 30-40dB which can be achieved owing to the amplifying effect of the semiconductor gain medium and cavity enhancement of mixing process. However, most previous experimental and theoretical work has placed emphasis on the weak signal case, where the injection signal acts only as a small perturbation of free-running laser diode. It is only very recently that a theoretical analysis of NDFWM in a semiconductor laser subject to strong probe injection power has been presented[2].

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•Jan 1, 1998•0 citations

Four-wave mixing and phase conjugation in semiconductor laser media

Govind Prasad Agrawal

A theory of four-wave mixing in semiconductor laser media is developed by considering the contributions of both the gain and index gratings created by the carrier-density modulation occurring at the beat frequency of the pump and the probe waves. The general formalism can be applied to semiconductor lasers operating below or above threshold. As an illustration, we consider the case in which the semiconductor laser is operated as a traveling-wave amplifier. The results show that the dominant contribution to the four-wave mixing process comes from the index grating. Further, the index grating makes the probe transmission asymmetric with respect to the pump-probe detuning.

Optics Letters•Apr 1, 1987•99 citations

Nearly degenerate four-wave mixing in distributed feedback semiconductor lasers operating above threshold

Antonio Mecozzi, Alessandro D’Ottavi, Rongqing Hui

Nearly degenerate four-wave mixing in distributed feedback semiconductor lasers above threshold in investigated theoretically and experimentally. The experimental results reveal an almost symmetric amplification of probe and conjugate fields versus frequency with respect to zero pump-probe detuning, in contrast with observations in traveling wave amplifiers. The result of the theory, based on the coupled mode formalism, is a set of nonlinear differential equations which are solved in the mean field approximation. The theory is shown to match well with the experimental results when the effect of the nonlinear gain compression is taken into account.>

IEEE Journal of Quantum Electronics•Jun 1, 1993•45 citations

Phase conjugate reflectivity of 165% using four-wave mixing in a broad-area laser diode

Peter Kürz, R. Nagar, T. Mukai

Optical phase conjugation using semiconductor gain media promises several advantages. It is expected to be fast (nanosecond response times) and the phase conjugator can be easily integrated with other semiconductor devices. Here, we demonstrate experimentally a third advantage. It can be highly efficient, since both the pump and the probe beams are optically amplified. Our phase conjugation experiment is based on spatially nondegenerate four-wave mixing in a broad-area laser diode.

IEEE Lasers and Electro-Optics Society Annual Meeting (LEOS)•Nov 19, 2002•0 citations

Quantum theory of noise in phase conjugation by four-wave mixing in a two-level system

Robert W. Schirmer, Mary Yvonne Lanzerotti, Alexander L. Gaeta +1 more

A quantum theory of nearly degenerate backward four-wave mixing in a two-level atomic system is developed. The theory is used to calculate the quantum noise produced by a phase-conjugate mirror based on this system. The results indicate that in the case of pure radiative broadening the ideal quantum-noise limit is reached for relatively small pump-wave strengths and for relatively large probe-pump and pump-resonance detunings, so that the phase-conjugate reflectivity is far from its maximum value. Conversely, in the collisionally broadened case, operation closest to the quantum-noise limit occurs near the point of maximum reflectivity.

Physical Review A•Apr 1, 1997•5 citations
A simple theoretical analysis shows that the linewidth of the conjugate wave produced in four-wave mixing in semiconductor lasers is equal to the linewidth of the probe plus four times the linewidth of the pump. Experimental results in good agreement with the theory are presented. This result implies an enormous enhancement in the phase noise of the conjugate wave and sets a limitation on some practical applications of four-wave mixing.
It has previously been shown that Brillouin enhanced four-wave mixing can lead to large phase conjugate reflectivities for moderate laser powers.1,2 However, in the geometry considered by previous workers the pumps have equal frequency and hence the conjugate signal is shifted in frequency with respect to the probe. We have conducted an experimental and theoretical study of Brillouin-enhanced four-wave mixing for the different case in which the two pump waves differ in frequency by twice the Brillouin frequency of the four-wave mixing medium, and in which the probe wave frequency is halfway between those of the pump waves. In this case, the phase conjugate wave has the same frequency as the probe. Reflectivities > 100 % have been measured. Experimental results are compared to those of a theory that includes the effects of phase mismatch, pump depletion, and the finite response time of the medium.
Optical phase conjugation through nearly degenerate four-wave mixing (NDFWM) in semiconductor lasers has attracted considerable attention in recent years since being first demonstrated by Nakajima and Frey[ 1 ]. Such interest arises due to the very high conjugate reflectivity of order 30-40dB which can be achieved owing to the amplifying effect of the semiconductor gain medium and cavity enhancement of mixing process. However, most previous experimental and theoretical work has placed emphasis on the weak signal case, where the injection signal acts only as a small perturbation of free-running laser diode. It is only very recently that a theoretical analysis of NDFWM in a semiconductor laser subject to strong probe injection power has been presented[2].
A theory of four-wave mixing in semiconductor laser media is developed by considering the contributions of both the gain and index gratings created by the carrier-density modulation occurring at the beat frequency of the pump and the probe waves. The general formalism can be applied to semiconductor lasers operating below or above threshold. As an illustration, we consider the case in which the semiconductor laser is operated as a traveling-wave amplifier. The results show that the dominant contribution to the four-wave mixing process comes from the index grating. Further, the index grating makes the probe transmission asymmetric with respect to the pump-probe detuning.
Nearly degenerate four-wave mixing in distributed feedback semiconductor lasers above threshold in investigated theoretically and experimentally. The experimental results reveal an almost symmetric amplification of probe and conjugate fields versus frequency with respect to zero pump-probe detuning, in contrast with observations in traveling wave amplifiers. The result of the theory, based on the coupled mode formalism, is a set of nonlinear differential equations which are solved in the mean field approximation. The theory is shown to match well with the experimental results when the effect of the nonlinear gain compression is taken into account.>
A quantum theory of nearly degenerate backward four-wave mixing in a two-level atomic system is developed. The theory is used to calculate the quantum noise produced by a phase-conjugate mirror based on this system. The results indicate that in the case of pure radiative broadening the ideal quantum-noise limit is reached for relatively small pump-wave strengths and for relatively large probe-pump and pump-resonance detunings, so that the phase-conjugate reflectivity is far from its maximum value. Conversely, in the collisionally broadened case, operation closest to the quantum-noise limit occurs near the point of maximum reflectivity.