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Physical Review A

Quantum noise and polarization properties of vertical-cavity surface-emitting lasers

Jean-Luc C. Vey, Christian Degen, Karsten Auen, Wolfgang Elsäßer

Published Oct 1, 1999• 30 citations
Publisher

Abstract

We present theoretical and experimental results on the quantum noise performances of vertical-cavity-surface-emitting-lasers (VCSELs). Using a semiclassical laser noise approach, we demonstrate that the ratio $M=\overline{S}/\overline{P}$ of the powers in the two polarization modes of the laser is one of the essential parameters governing the VCSELs quantum noise behavior. The generation of amplitude squeezed states of light is only possible for two well-selected cases which are the ideal two-polarization-mode laser $(M\ensuremath{\approx}1)$ and the ideal single-polarization-mode laser $(M\ensuremath{\approx}0),$ respectively. Furthermore, we show that gain suppression, as well as other relevant semiconductor parameters, have also to be taken into account to model realistically the VCSEL's quantum noise. These theoretical investigations are very well supported by our experimental results. We demonstrate experimentally that indeed there exists a direct link between the parameter M and the shot noise normalized amplitude noise. In a two-polarization-mode laser as, e.g., represented by a large diameter air-post VCSEL, squeezed states could not be generated because of insufficiently low values of M even though a strong anticorrelation between the two modes exists. With a single-polarization-mode laser, as realized with small diameter oxide confined VCSELs, we have been able to demonstrate the generation of single-mode squeezed light with a VCSEL. A squeezing level of 0.9 dB has been measured, which with the detection efficiency corrected, results in 1.3 dB at the VCSEL upper facet.

DOI
10.1103/physreva.60.3284

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We present theoretical and experimental results on the quantum noise performances of vertical-cavity-surface-emitting-lasers (VCSELs). Using a semiclassical laser noise approach, we demonstrate that the ratio M=S‾/P‾M=\overline{S}/\overline{P}M=S/P of the powers in the two polarization modes of the laser is one of the essential parameters governing the VCSELs quantum noise behavior. The generation of amplitude squeezed states of light is only possible for two well-selected cases which are the ideal two-polarization-mode laser (M\ensuremath≈1)(M\ensuremath{\approx}1)(M\ensuremath≈1) and the ideal single-polarization-mode laser (M\ensuremath≈0),(M\ensuremath{\approx}0),(M\ensuremath≈0), respectively. Furthermore, we show that gain suppression, as well as other relevant semiconductor parameters, have also to be taken into account to model realistically the VCSEL's quantum noise. These theoretical investigations are very well supported by our experimental results. We demonstrate experimentally that indeed there exists a direct link between the parameter M and the shot noise normalized amplitude noise. In a two-polarization-mode laser as, e.g., represented by a large diameter air-post VCSEL, squeezed states could not be generated because of insufficiently low values of M even though a strong anticorrelation between the two modes exists. With a single-polarization-mode laser, as realized with small diameter oxide confined VCSELs, we have been able to demonstrate the generation of single-mode squeezed light with a VCSEL. A squeezing level of 0.9 dB has been measured, which with the detection efficiency corrected, results in 1.3 dB at the VCSEL upper facet.
We present comprehensive investigations on the polarization resolved quantum noise behavior of vertical cavity surface emitting lasers (VCSELs) with various cavity designs. These experiments are accompanied by detailed studies using a semiclassical approach, first, to calculate and model theoretically the amplitude fluctuations and correlations of a two orthogonal polarization-mode semiconductor laser as realized by a VCSEL, and second, to explore theoretically the squeezing potential of VCSELs. First, we find that the possible amount of squeezing with VCSELs should be superior as compared to edge emitting lasers for ideal single mode operation and under comparable pumping conditions. Second, we demonstrate that there exists the possibility of squeezing also in the two-mode regime besides sub-shot noise emission in the well known ideal single-mode operation regime configuring the recently published first experimental demonstration of the generation of amplitude squeezed light with VCSELs. Third, we demonstrate for the first time the generation of amplitude squeezed light by a lateral and polarization single mode VCSEL with the achievement of a maximum squeezing of 0.9 dB. Finally the future trends, the applications and the limitations of these non-classical states of light with respect to metrology applications are discussed.
Using a theoretical semiclassical approach, we study in detail the amplitude fluctuations and correlations of a two-orthogonal polarization-mode semiconductor laser as obtained from a vertical-cavity surface-emitting laser (VCSEL). We demonstrate that there exists the possibility of squeezing in the two-mode regime besides sub-shot-noise emission in the well-known ideal single-mode operation regime. These theoretical results confirm a recent experimental demonstration of the generation of amplitude-squeezed light with VCSEL's.
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.
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].