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Physical Review A

Linear anisotropies and polarization properties of vertical-cavity surface-emitting semiconductor lasers

Martino Travagnin

Published Nov 1, 1997• 44 citations
Publisher

Abstract

The polarization properties of the light emitted by vertical-cavity surface-emitting semiconductor lasers are studied by means of a four-level scheme which includes misaligned linear phase and amplitude anisotropies. First we investigate the system stability characteristics, demonstrating that upon increasing the pumping level a polarization switching may take place both from the lower- to the higher- and from the higher- to the lower-frequency states. Then we study the laser stationary states identifying the role played by nonlinear effects and demonstrating that noticeable deviations from linear behavior are induced by the simultaneous presence of misaligned phase and amplitude anisotropies with comparable magnitude.

DOI
10.1103/physreva.56.4094

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The polarization properties of the light emitted by vertical-cavity surface-emitting semiconductor lasers are studied by means of a four-level scheme which includes misaligned linear phase and amplitude anisotropies. First we investigate the system stability characteristics, demonstrating that upon increasing the pumping level a polarization switching may take place both from the lower- to the higher- and from the higher- to the lower-frequency states. Then we study the laser stationary states identifying the role played by nonlinear effects and demonstrating that noticeable deviations from linear behavior are induced by the simultaneous presence of misaligned phase and amplitude anisotropies with comparable magnitude.
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Semiconductor lasers are normally used as single-photon sources in most commercial and research quantum key distribution (QKD) systems [1]. These lasers are also used for quantum random number generation (QRNG) that is a necessary security requirement for QKD. In device-dependent QRNGs unpredictability is guaranteed by comparing experimental measurements with simulation data obtained from a model of the physical entropy source [2]. The characterization of phase fluctuations in a gain-switched edge-emitting semiconductor laser for QRNG has been recently performed [2]. Very recently a QRNG based on the random excitation of the linearly polarized modes of a gain-switched vertical-cavity surface-emitting laser (VCSEL) has also been proposed [3]. In this work we characterize the polarization fluctuations found in this system by comparing experimental measurements with the results obtained from the simulation of a VCSEL's model that incorporates the device intrinsic parameters found using state-of-the-art experimental techniques [4].
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.