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Conference on Lasers and Electro-Optics

Dynamical picture of quantum fluctuations in semiconductor lasers: the role of noise modulation and squeezing hindering by pump-blocking

Martino Travagnin, Luigi A. Lugiato

Published Aug 29, 2005• 1 citation
Publisher

Abstract

Summary form only given. The noise properties of semiconductor lasers are studied by using the equations for the photon and carrier number fluctuations extended to include the blocking of the injected carriers induced by the Pauli principle.
DOI
10.1109/iqec.2000.907793

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Summary form only given. The intensity noise properties of single-mode semiconductor lasers at zero-frequency are studied on the basis of an operator set of equations for the field, the material polarization, the microscopic carrier distribution and the total carrier number in each band. The theory includes the noise effects of (i) Coulomb scattering processes, which tend to drive the carriers into intraband Fermi-Dirac quasi-equilibrium, (ii) spectral hole burning, i.e. the carrier deviation from quasi-equilibrium induced mainly by light-matter interaction, (iii) pump-blocking, which, in conformity with the Pauli exclusion principle, prevents the pumped carriers whose k-state is already occupied from entering the active layer. All these phenomena are not considered in the standard theory, which starts from a macroscopic set of equations for the field and the total carrier population only. Our analysis shows that Coulomb scattering and spectral hole burning have only negligible effects on the noise properties of the laser, while pump-blocking can bring a sizable increase of intensity noise. Under certain parametric conditions this increase can raise the noise level above the shot noise limit, thus destroying any squeezing. We show that the pump-blocking induced additional noise originates from the field and the material polarization. Since the suppression of field and polarization noise is ensured respectively by destructive interference of field fluctuations at the output mirror and by gain saturation, we conclude that pump-blocking hampers both these phenomena.
In this paper we derive the intensity and phase noise spectra of a single-mode semiconductor laser on the basis of an operatorial Langevin set of equations that includes the dynamics of the microscopic variables, i.e., the carrier polarization and their distribution over the k states. In particular we take into account the fact that the carriers pumped into the active layer are subject to the blocking determined by Pauli exclusion principle. We demonstrate that, due to the fastness of the carrier scattering and polarization dephasing processes, the noise spectra can be determined on the basis of a macroscopic linearized set of three equations for the two quadrature components of the laser intensity and the total carrier number. A formal comparison with the paradigmatic results of [Yamamoto et al. Phys. Rev. A 34, 4025 (1986)] allows to deduce that the only essential difference arises from Pauli-induced pump blocking, which has the effect of increasing the low-frequency branch of the intensity noise spectrum. We demonstrate that, even for very small amounts of pump blocking, the low-frequency intensity noise steeply rises with the stationary value of the carrier density in the active layer, which depends on a great number of parameters. This result can explain the erratic behavior of the experimental findings and their discrepancy with the standard theoretical predictions.
We analyze the zero-frequency intensity noise of a single-mode semiconductor laser on the basis of a full quantum-mechanical model which takes into account the carrier distributions over the k states. The theory includes the effects of (i) Coulomb scattering processes, which tend to drive the carriers into intraband Fermi-Dirac quasiequilibrium; (ii) spectral hole burning, i.e., the carrier deviation from quasiequilibrium induced mainly by light-matter interaction; (iii) pump blocking, which, in conformity with the Pauli exclusion principle, prevents the pump carriers whose k state is already occupied from entering the active layer. Our analysis shows that Coulomb scattering and spectral hole burning have only negligible effects on the noise properties of the laser, while pump blocking can bring, under appropriate parametric conditions, a sizable increase of noise intensity. This additional noise can explain why quietly pumped semiconductor lasers fail to reach the perfect squeezing which is expected on the basis of the theory so far available. The squeezing-hindering effect of pump blocking is confirmed as different pumping schemes are employed.
We study in detail the influence of pumping statistics on the laser dynamics. We apply the technique of quantum Langevin operators and generalize the corresponding noise operators to incorporate the statistical properties of the pump mechanism. These equations are then used to derive expressions for the phase and intensity fluctuations of lasers with various pump statistics. We find that a reduction of pump noise can lead to a significant squeezing of the photon number noise below the shot-noise limit. This is in complete agreement with our previous analysis, which used a density-operator approach.
The quantum noise properties of injection-locked semiconductor laser oscillators are investigated. Included in the analysis are pump-noise suppression and squeezing of the injection signal. It is shown that the main effect of injection locking is the reduction of the phase noise of the outgoing laser light field. The influence that squeezing of the injection signal state has on the output state is shown to be strongly dependent on the value of the linewidth enhancement factor. In general, little or no noise reduction stands to be gained by squeezing the injection signal. It is also shown that under idealized conditions, the spectral uncertainty product of the outgoing field will approach, but never go below, the minimum uncertainty value given by the Heisenberg uncertainty relation.