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Physical Review A

Effects of gain saturation on polarization switching in vertical-cavity surface-emitting lasers

Franco Prati, P. Caccia, F. Castelli

Published Dec 26, 2002• 26 citations
Publisher

Abstract

Starting from a fully microscopic spin-flip model for a vertical cavity surface emitting laser, we derive a macroscopic model that includes the frequency dependence of the complex gain and the gain nonlinearities due to spectral hole burning. The macroscopic model reproduces well the predictions of the microscopic one. The gain nonlinearities affect especially the switching from the higher to the lower frequency, and their effects are more manifest when the spin-flip rate is large.

DOI
10.1103/physreva.66.063811

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Starting from a fully microscopic spin-flip model for a vertical cavity surface emitting laser, we derive a macroscopic model that includes the frequency dependence of the complex gain and the gain nonlinearities due to spectral hole burning. The macroscopic model reproduces well the predictions of the microscopic one. The gain nonlinearities affect especially the switching from the higher to the lower frequency, and their effects are more manifest when the spin-flip rate is large.
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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].
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.