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

Chinese Physics B

Theoretical study on phase conjugation in weakly injected vertical-cavity surface-emitting lasers

Zhang Wei-Li, Wei Pan, Luo Bin, Li Xiao-Feng, Zou Xi-Hua, Wang Meng-yao

Published May 1, 2008• 1 citation
Publisher

Abstract

This paper gives a detailed theoretical investigation on phase conjugation induced by nearly degenerate four-wave mixing in single mode vertical-cavity surface-emitting lasers (VCSELs) with weak optical injection. Considering VCSELs that can work in linearly polarized or elliptically polarized states, it derives the theoretical expression of the conjugated field by small signal analysis based on the vectoral rate equations—the spin-flip model. For linearly polarized state, VCSELs show similar conjugate spectra to edge-emitting semiconductor lasers. For the elliptically polarized state, dichroism and birefringence parameters as well as the spin-flip rate can change the conjugate spectra. Especially, when frequency detuning of the probe and pump waves is between the positive and negative relaxation oscillation frequency, changes are evident. For specific values of parameters, conjugate efficiency between 20dB to 40dB are obtained.

DOI
10.1088/1674-1056/17/5/045

Related papers

Analysis of elliptically polarized states in vertical-cavity-surface-emitting lasers

Franco Prati, Morten Bache, F. Castelli

A detailed analysis of the properties of the elliptically polarized state in spin flip model is essential for a full understanding of the experimental results. This paper studies the stationary properties of this state and its stability, considering both birefringence and dichroism. Results show that for small values of the /spl alpha/ parameter the transition from the lower frequency mode to the elliptical state may be subcritical. As a consequence, bistability between the linearly and the elliptically polarized modes exists, with jumps from one state to the other when the injected current is varied. In an experiment, the existence of such a bistable domain could lead to noise induced hopping from one state to the other, close to the instability threshold of the lower frequency mode. The authors checked that gain nonlinearities due to spectral hole burning favors subcriticality.

European Quantum Electronics Conference (EQEC)•Oct 19, 2004•1 citation

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

Quantum spin-flip model of vertical-cavity surface-emitting lasers

Jean‐Pierre Hermier, Mikhail I. Kolobov, Isabelle Maurin +1 more

We present a theoretical and experimental investigation of quantum fluctuations in vertical-cavity surface-emitting lasers (VCSELs) having one longitudinal and transverse linearly polarized mode above threshold. We develop the quantum version of the broadly used four-level spin-flip model to take into account the quantum statistics of the pumping process of the active atoms. Our theory allows for arbitrary pumping statistics varying from Poissonian to regular. We compare experimental results obtained with single-mode VCSELs with predictions of our theory and find very good agreement. We demonstrate that the quantum fluctuations of the subthreshold field component polarized orthogonally to the lasing mode have to be taken into account for adequate description of quantum fluctuations in VCSELs. In particular, we show that when the laser light passes through a polarizer, the two orthogonal polarization components of the light wave after passing through the polarizer can be strongly anticorrelated.

Physical Review A•May 13, 2002•11 citations

Spin-flip model of spin-polarized vertical-cavity surface-emitting lasers: Asymptotic analysis, numerics, and experiments

Hadi Susanto, Kevin Schires, M.J. Adams +1 more

The spin-flip model describing optically pumped spin-polarized vertical-cavity surface-emitting lasers is considered. The steady-state solutions of the model for elliptically polarized fields are studied. Asymptotic analysis for the existence and stability of the steady-state solutions is developed, particularly in the presence of pump polarization ellipticity. The expansion is with respect to small parameters representing the ellipticity and the difference between the total pump power and the lasing threshold. The analytical results are then confirmed numerically, where it is obtained that generally one of the steady-state solutions is stable while the other is not. The theoretical results are shown to be in qualitative agreement with the experiments.

arXiv:1601.00831•Physical Review A•Dec 23, 2015•28 citations

Optical Instabilities in Sodium Vapor and Vertical Cavity Surface Emitting Lasers

Jeffrey W. Grantham

This dissertation investigates three different optical instabilities: cw conical emission, bifurcations of optical transverse solitary waves, and asymmetric gain modification in a vertical cavity surface emitting laser (VCSEL). The first two instabilities occur in sodium vapor while the third occurs in a new type of semiconductor laser. For the conical emission instability, the first comparison and agreement between theory and experiment is given. The conical emission process is modeled as a series of nonlinear effects including self-trapping of the pump beam, Doppler-broadened Raman-gain amplification of Doppler-broadened resonance fluorescence, propagational four-wave mixing, and diffraction and pump-induced refraction of the new frequencies. Each step of the emission process is thoroughly examined and explained. Detailed comparisons are made between experimental observables and numerical calculations including near-field and far-field spatial profiles, frequency spectra, and cone angles. All comparisons show good agreement. In a different but related experiment, bifurcations of optical transverse solitary waves are studied for one-way propagation through a sodium vapor cell. Two types of phase encoding seed transverse bifurcations which result in transverse cell-exit profiles with the beauty rivaling that of a kaleidoscope. The cell-exit profiles are stationary in time, reproduce completely when the power or frequency is scanned, and agree well with one-way computations. Evidence is also presented for the first observation of a double-peaked Raman gain. In the third experiment, a temporal instability is examined in a GaAs VCSEL. Strong evidence is presented for an asymmetric gain modification induced when a strong optical signal is injected into the Fabry-Perot transmission peak of the VCSEL while it is lasing. This gain modification results in increased absorption on the high frequency side of the injected signal and increased gain on the low frequency side as manifested by the formation of an optical sideband. The frequency of the sideband depends on the intensity of the injected signal with frequencies (> 50 GHz) well beyond the predicted relaxation oscillation frequency being observed. Very efficient nondegenerate four-wave mixing is also observed.

•Jan 1, 1991•0 citations

Semiconductor surface emitting lasers for photon pairs generation

Luc Vanbever, Evgueni Karpov, Krassimir P. Panajotov

We study the feasibility of generating photon pairs in a resonant Vertical-Cavity Surface-Emitting Laser (VCSEL) as a result of a third-order non-linear, four wave mixing interaction. We focus on degenerate four wave mixing in the spontaneous regime where two pump photons are annihilated to create a pair of signal and idler photons. Using the methods of quantum optics, we calculate the two-photon production rate, the spectrum of the generated photons, and the signal-idler cross-correlations. We highlight how the dispersion of the medium in the VCSEL cavity (a regular GaAs configuration) significantly diminishes the two-photon production rate. Based on our results, we enumerate the characteristics of a VCSEL that would be suitable for photon pair generation.

Chaos An Interdisciplinary Journal of Nonlinear Science•Sep 15, 2017•1 citation
This paper gives a detailed theoretical investigation on phase conjugation induced by nearly degenerate four-wave mixing in single mode vertical-cavity surface-emitting lasers (VCSELs) with weak optical injection. Considering VCSELs that can work in linearly polarized or elliptically polarized states, it derives the theoretical expression of the conjugated field by small signal analysis based on the vectoral rate equations—the spin-flip model. For linearly polarized state, VCSELs show similar conjugate spectra to edge-emitting semiconductor lasers. For the elliptically polarized state, dichroism and birefringence parameters as well as the spin-flip rate can change the conjugate spectra. Especially, when frequency detuning of the probe and pump waves is between the positive and negative relaxation oscillation frequency, changes are evident. For specific values of parameters, conjugate efficiency between 20dB to 40dB are obtained.
A detailed analysis of the properties of the elliptically polarized state in spin flip model is essential for a full understanding of the experimental results. This paper studies the stationary properties of this state and its stability, considering both birefringence and dichroism. Results show that for small values of the /spl alpha/ parameter the transition from the lower frequency mode to the elliptical state may be subcritical. As a consequence, bistability between the linearly and the elliptically polarized modes exists, with jumps from one state to the other when the injected current is varied. In an experiment, the existence of such a bistable domain could lead to noise induced hopping from one state to the other, close to the instability threshold of the lower frequency mode. The authors checked that gain nonlinearities due to spectral hole burning favors subcriticality.
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].
We present a theoretical and experimental investigation of quantum fluctuations in vertical-cavity surface-emitting lasers (VCSELs) having one longitudinal and transverse linearly polarized mode above threshold. We develop the quantum version of the broadly used four-level spin-flip model to take into account the quantum statistics of the pumping process of the active atoms. Our theory allows for arbitrary pumping statistics varying from Poissonian to regular. We compare experimental results obtained with single-mode VCSELs with predictions of our theory and find very good agreement. We demonstrate that the quantum fluctuations of the subthreshold field component polarized orthogonally to the lasing mode have to be taken into account for adequate description of quantum fluctuations in VCSELs. In particular, we show that when the laser light passes through a polarizer, the two orthogonal polarization components of the light wave after passing through the polarizer can be strongly anticorrelated.
The spin-flip model describing optically pumped spin-polarized vertical-cavity surface-emitting lasers is considered. The steady-state solutions of the model for elliptically polarized fields are studied. Asymptotic analysis for the existence and stability of the steady-state solutions is developed, particularly in the presence of pump polarization ellipticity. The expansion is with respect to small parameters representing the ellipticity and the difference between the total pump power and the lasing threshold. The analytical results are then confirmed numerically, where it is obtained that generally one of the steady-state solutions is stable while the other is not. The theoretical results are shown to be in qualitative agreement with the experiments.
This dissertation investigates three different optical instabilities: cw conical emission, bifurcations of optical transverse solitary waves, and asymmetric gain modification in a vertical cavity surface emitting laser (VCSEL). The first two instabilities occur in sodium vapor while the third occurs in a new type of semiconductor laser. For the conical emission instability, the first comparison and agreement between theory and experiment is given. The conical emission process is modeled as a series of nonlinear effects including self-trapping of the pump beam, Doppler-broadened Raman-gain amplification of Doppler-broadened resonance fluorescence, propagational four-wave mixing, and diffraction and pump-induced refraction of the new frequencies. Each step of the emission process is thoroughly examined and explained. Detailed comparisons are made between experimental observables and numerical calculations including near-field and far-field spatial profiles, frequency spectra, and cone angles. All comparisons show good agreement. In a different but related experiment, bifurcations of optical transverse solitary waves are studied for one-way propagation through a sodium vapor cell. Two types of phase encoding seed transverse bifurcations which result in transverse cell-exit profiles with the beauty rivaling that of a kaleidoscope. The cell-exit profiles are stationary in time, reproduce completely when the power or frequency is scanned, and agree well with one-way computations. Evidence is also presented for the first observation of a double-peaked Raman gain. In the third experiment, a temporal instability is examined in a GaAs VCSEL. Strong evidence is presented for an asymmetric gain modification induced when a strong optical signal is injected into the Fabry-Perot transmission peak of the VCSEL while it is lasing. This gain modification results in increased absorption on the high frequency side of the injected signal and increased gain on the low frequency side as manifested by the formation of an optical sideband. The frequency of the sideband depends on the intensity of the injected signal with frequencies (> 50 GHz) well beyond the predicted relaxation oscillation frequency being observed. Very efficient nondegenerate four-wave mixing is also observed.
We study the feasibility of generating photon pairs in a resonant Vertical-Cavity Surface-Emitting Laser (VCSEL) as a result of a third-order non-linear, four wave mixing interaction. We focus on degenerate four wave mixing in the spontaneous regime where two pump photons are annihilated to create a pair of signal and idler photons. Using the methods of quantum optics, we calculate the two-photon production rate, the spectrum of the generated photons, and the signal-idler cross-correlations. We highlight how the dispersion of the medium in the VCSEL cavity (a regular GaAs configuration) significantly diminishes the two-photon production rate. Based on our results, we enumerate the characteristics of a VCSEL that would be suitable for photon pair generation.