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Journal of the Optical Society of America B

Semiclassical description of noise and generation of amplitude squeezed states with vertical cavity surface-emitting semiconductor lasers

Jean-Luc C. Vey, Wolfgang Elsäßer

Published Jun 1, 1997• 11 citations
Publisher

Abstract

Theoretical investigations of the generation of light with sub-shot-noise intensity fluctuations by vertical cavity surface-emitting lasers are performed with a semiclassical model. From these results we conclude that, because of their dimensions and structure, vertical cavity surface-emitting lasers are promising candidates for generation of amplitude squeezed states. Finally, the influence of internal loss, distributed reflection coefficients, and gain suppression is emphasized and discussed.

DOI
10.1364/josab.14.001299

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IEEE Journal of Quantum Electronics•Jan 1, 1997•10 citations
Theoretical investigations of the generation of light with sub-shot-noise intensity fluctuations by vertical cavity surface-emitting lasers are performed with a semiclassical model. From these results we conclude that, because of their dimensions and structure, vertical cavity surface-emitting lasers are promising candidates for generation of amplitude squeezed states. Finally, the influence of internal loss, distributed reflection coefficients, and gain suppression is emphasized and discussed.
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.
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 $(M\ensuremath{\approx}1)$ 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.
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.
A semiclassical model of semiconductor laser noise, based on the Green's function method, is used to derive analytical formulas for the amplitude and frequency noise spectra taking into account incoming vacuum fluctuations and noise due to internal loss. This formalism also takes into account phenomena such as gain suppression as well as spatial hole burning (SHB). The amplitude noise squeezing is studied for Fabry-Perot structures pointing out the influence of the laser structural parameters. A complete agreement with already existing quantum mechanical models is found. However, extension of the model to SHB induces limitations in the squeezing performances, which are very important for more complex structures as will be pointed out in detail, in Part II.
For pt.I see ibid., vol.33, no.11, p.2097-2104 (1997). We present noise studies of distributed feedback (DFB) laser structures, where spatial hole burning (SHB) plays a key role performed using the model described in part I of this paper with particular emphasis on the influence of SHB, on the coupling coefficient /spl kappa/L, and on the laser facet reflectivities. These structures exhibit high amplitude noise and the possible noise reduction is strongly reduced compared to Fabry-Perot structures. Distributed Bragg reflector (DBR) lasers are better candidates even if their performances are also strictly determined by SHB and the loss in the Bragg reflector. Finally, limitations due to gain suppression are demonstrated for such complex lasers structures. We conclude on the optimum laser structure for amplitude squeezed states generation.