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

Highly nondegenerate four-wave mixing in semiconductor lasers due to spectral hole burning

Govind Prasad Agrawal

Published Aug 3, 1987• 40 citations
Publisher

Abstract

Spectral hole burning in semiconductor lasers manifests as a nonlinear suppression of the mode gain by a few percent. In the presence of a probe wave, the same mechanism can lead to highly nondegenerate four-wave mixing (NDFWM) by creating the dynamic gain and index gratings at the beat frequency of the pump and probe waves. Since the grating efficiency is governed by the intraband relaxation time (typically <1 ps), significant NDFWM can occur even for a pump-probe detuning ∼100 GHz. We present the results for the conjugate reflectivity and the probe transmittivity when an InGaAsP laser is used as a traveling-wave amplifier.

DOI
10.1063/1.98450

Related papers

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

Govind Prasad Agrawal

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.

Journal of the Optical Society of America B•Jan 1, 1988•396 citations

Observation of highly nondegenerate four-wave mixing in 1.5 mu m traveling-wave semiconductor optical amplifiers and estimation of nonlinear gain coefficient

Kazuro Kikuchi, Motoki KAKUI, Chung-En Zah +1 more

Nondegenerate four-wave mixing is measured in the 1.5 mu m traveling-wave semiconductor optical amplifier medium as a function of the pump-probe detuning frequency ranging from a few GHz to 400 GHz. It is found that two different sources are responsible for the four-wave mixing: the carrier density modulation and the nonlinear gain effect. The latter is clearly observed when the detuning frequency increases above 100 GHz. The nonlinear gain coefficient epsilon , which induces a gain grating through the pump-probe beating, is estimated to be 1.75*10/sup -23/ m/sup 3/. The change in the real refractive index associated with the nonlinear gain effect, which generates an index grating, is negligibly small. The relaxation time involved in the nonlinear gain effect is found to be less than 0.3 ps. These results support the role of the spectral hole burning rather than the carrier heating in the nonlinear gain effect.>

IEEE Journal of Quantum Electronics•Jan 1, 1992•132 citations

Resonantly enhanced non-degenerate four wave mixing in semiconductor travelling wave amplifiers

Martin W. McCall, K.A. Shore

Nearly degenerate four wave mixing (NDFWM) in semiconductor laser amplifiers has received attention recently as a means of efficiently generating phase conjugate beams. The high efficiency is due to two factors: (i) intracavity geometry enhances pump efficiency; (ii) an amplifying nonlinear medium results in high coupling efficiency. These factors have combined to give observed conjugate reflectivities of approximately 30/40 dB. The NDFWM process in semiconductor lasers is also very fast ( tau approximately 10/sup -9/s) being limited primarily by the interband relaxation time. Recent theoretical studies, however, have suggested that temporal gratings with THz frequencies may be supportable. It should be noted that NDFWM in semiconductor lasers is quite different from four wave mixing in most other media in that to a first approximation the gratings formed are purely temporal. Spatial effects are normally neglected, both for computational convenience and because carrier diffusion tends to wash out spatial holes. Previously, the authors demonstrated how the temporal nature of the wave mixing process could be exploited to produce a resonant enhancement in a two wave mixing geometry. In this paper, they examine a novel scheme for enhancing the phase conjugate reflectivity via pumping the device resonantly at the detuning frequency. They demonstrate that on resonance, conjugate reflectivities several orders of magnitude greater than those previously reported are possible. >

•May 20, 1992•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

Detuning characteristics and conversion efficiency of nearly degenerate four-wave mixing in a 1.5- mu m traveling-wave semiconductor laser amplifier

T. Mukai, Tadashi Saitoh

The optical nonlinearity in a semiconductor laser gain medium is investigated through copropagating nearly degenerate four-wave mixing (NDFWM) in a 1.5- mu m InGaAsP traveling-wave laser amplifier (TWA). The FWM signal output powers vary symmetrically with the sign of probe detuning with respect to the pump frequency, while the pump and probe output powers vary asymmetrically. The NDFWM conversion efficiency from the probe input to the FWM signal output is a maximum of 8.3 dB around zero detuning and has positive gain in the range of +or-6 GHz. This demonstrates highly efficient nonlinear interaction due to both large optical gain and large third-order susceptibility. The NDFWM efficiency is also investigated in connection with the TWA gain saturation characteristics and is found to be a maximum for operation around the saturation intensity of the TWA.>

IEEE Journal of Quantum Electronics•May 1, 1990•81 citations

Nearly degenerate four-wave mixing in a traveling-wave semiconductor laser amplifier

Kyo Inoue, Takaaki Mukai, Tadashi Saitoh

Nearly degenerate four-wave mixing (NDFWM) in a traveling-wave semiconductor laser amplifier is demonstrated by simultaneously injecting two lights of slightly different frequencies in the same direction. A new frequency light at an expected frequency for NDFWM is observed with the same order of output as that of the injected light. The output power ratio of the three beams is strongly dependent on the sign of the frequency detuning. Theoretical analysis, in which the carrier rate equation is coupled with nonlinear Maxwell’s equations, explains the experimental results well. The observed behaviors are attributed to a unique third-order nonlinearity stemming from saturation-induced refractive index change in the semiconductor gain medium.

Applied Physics Letters•Oct 5, 1987•94 citations
Spectral hole burning in semiconductor lasers manifests as a nonlinear suppression of the mode gain by a few percent. In the presence of a probe wave, the same mechanism can lead to highly nondegenerate four-wave mixing (NDFWM) by creating the dynamic gain and index gratings at the beat frequency of the pump and probe waves. Since the grating efficiency is governed by the intraband relaxation time (typically <1 ps), significant NDFWM can occur even for a pump-probe detuning ∼100 GHz. We present the results for the conjugate reflectivity and the probe transmittivity when an InGaAsP laser is used as a traveling-wave amplifier.
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.
Nondegenerate four-wave mixing is measured in the 1.5 mu m traveling-wave semiconductor optical amplifier medium as a function of the pump-probe detuning frequency ranging from a few GHz to 400 GHz. It is found that two different sources are responsible for the four-wave mixing: the carrier density modulation and the nonlinear gain effect. The latter is clearly observed when the detuning frequency increases above 100 GHz. The nonlinear gain coefficient epsilon , which induces a gain grating through the pump-probe beating, is estimated to be 1.75*10/sup -23/ m/sup 3/. The change in the real refractive index associated with the nonlinear gain effect, which generates an index grating, is negligibly small. The relaxation time involved in the nonlinear gain effect is found to be less than 0.3 ps. These results support the role of the spectral hole burning rather than the carrier heating in the nonlinear gain effect.>
Nearly degenerate four wave mixing (NDFWM) in semiconductor laser amplifiers has received attention recently as a means of efficiently generating phase conjugate beams. The high efficiency is due to two factors: (i) intracavity geometry enhances pump efficiency; (ii) an amplifying nonlinear medium results in high coupling efficiency. These factors have combined to give observed conjugate reflectivities of approximately 30/40 dB. The NDFWM process in semiconductor lasers is also very fast ( tau approximately 10/sup -9/s) being limited primarily by the interband relaxation time. Recent theoretical studies, however, have suggested that temporal gratings with THz frequencies may be supportable. It should be noted that NDFWM in semiconductor lasers is quite different from four wave mixing in most other media in that to a first approximation the gratings formed are purely temporal. Spatial effects are normally neglected, both for computational convenience and because carrier diffusion tends to wash out spatial holes. Previously, the authors demonstrated how the temporal nature of the wave mixing process could be exploited to produce a resonant enhancement in a two wave mixing geometry. In this paper, they examine a novel scheme for enhancing the phase conjugate reflectivity via pumping the device resonantly at the detuning frequency. They demonstrate that on resonance, conjugate reflectivities several orders of magnitude greater than those previously reported are possible. >
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.
The optical nonlinearity in a semiconductor laser gain medium is investigated through copropagating nearly degenerate four-wave mixing (NDFWM) in a 1.5- mu m InGaAsP traveling-wave laser amplifier (TWA). The FWM signal output powers vary symmetrically with the sign of probe detuning with respect to the pump frequency, while the pump and probe output powers vary asymmetrically. The NDFWM conversion efficiency from the probe input to the FWM signal output is a maximum of 8.3 dB around zero detuning and has positive gain in the range of +or-6 GHz. This demonstrates highly efficient nonlinear interaction due to both large optical gain and large third-order susceptibility. The NDFWM efficiency is also investigated in connection with the TWA gain saturation characteristics and is found to be a maximum for operation around the saturation intensity of the TWA.>
Nearly degenerate four-wave mixing (NDFWM) in a traveling-wave semiconductor laser amplifier is demonstrated by simultaneously injecting two lights of slightly different frequencies in the same direction. A new frequency light at an expected frequency for NDFWM is observed with the same order of output as that of the injected light. The output power ratio of the three beams is strongly dependent on the sign of the frequency detuning. Theoretical analysis, in which the carrier rate equation is coupled with nonlinear Maxwell’s equations, explains the experimental results well. The observed behaviors are attributed to a unique third-order nonlinearity stemming from saturation-induced refractive index change in the semiconductor gain medium.