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Journal de Physique III

Semiconductor laser with dispersive loss : Quantum noises and amplitude squeezing

Rashit F. Nabiev, Yuri M. Popov, Amnon Yariv

Published Sep 1, 1992• 2 citations
Publisher

Abstract

We carried out the quantum mechanical treatment of the amplitude and phase noise characteristics of internal and output light of semiconductor laser with dispersive loss inside the resonator and found the quantum limits for the noise power spectra and compared with the characteristics of the semiconductor laser without dispersive loss. In the case of noise suppressed pumping it is possible to get considerably deeper squeezing in the semiconductor laser with dispersive loss than in the laser without dispersive loss.

DOI
10.1051/jp3:1992100

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We carried out the quantum mechanical treatment of the amplitude and phase noise characteristics of internal and output light of semiconductor laser with dispersive loss inside the resonator and found the quantum limits for the noise power spectra and compared with the characteristics of the semiconductor laser without dispersive loss. In the case of noise suppressed pumping it is possible to get considerably deeper squeezing in the semiconductor laser with dispersive loss than in the laser without dispersive loss.
In the recent paper 1 semiclassical treatment of semiconductor laser (SL) with dispersive loss element (DLE) inside the cavity was presented. In SL with frequency dependent photon life time τ p ( τ p −1=τp0−1+2Cφ, φ is the slowly varying phase of an electromagnetic field) phase and amplitude noises were shown to be decreased (1 + Cα)2 / (l +α2) and (1 + Cα)2 / (1 + C2) (α is the linewidth enhancement factor) times, respectively, comparing to the conventional SL (C=0). At the same time, he low frequency portion of current modulation response is unchanged. Possible values of parameter C 1 can be ~10 and some dozens in the case of atomic absorption cell and the weak coupling of SL to an external high-finesse Fabry-Perot etalon, respectively.
This thesis describes the phase and amplitude noise properties of semiconductor lasers subjected to weak, dispersive optical feedback. In the first half, experiments demonstrating reductions in the laser frequency noise power spectrum and spectral linewidth by several orders of magnitude are presented. Weak optical feedback is applied to the laser by an external cavity containing an atomic vapor. The presence of the vapor adds to the dispersion of the cavity and simultaneously locks the laser to a fixed frequency reference. The role of 1/f frequency noise in limiting the effectiveness of this linewidth reduction technique is investigated and 1/f noise is found to be the dominant contribution to the linewidth under strong optical feedback conditions. An electronic feedback scheme utilizing FM sideband locking is then implemented alongside the optical feedback, and an additional reduction in the low frequency 1/f frequency noise power spectrum by over two orders of magnitude is obtained. With both systems operating simultaneously, the spectral linewidth is narrowed from its free-running value of about 20 MHz to 1.4 kHz. Excellent absolute frequency stability is also achieved. In the second half, the effects of optical feedback on the quantum mechanical amplitude noise properties of the laser are examined. A fully quantum mechanical theory of amplitude and phase noise for a semiconductor laser with weak optical feedback is developed, and the nature and limits of the noise reduction using this technique are established. Particular attention is given to the feedback-induced enhancement of the amplitude squeezing which can be obtained in a pump-suppressed semiconductor laser: an improvement in the squeezing by 3 dB is predicted under moderate pumping. Somewhat larger noise reductions are expected when the laser is operating closer to threshold. Measurements performed on a laser biased close to threshold are then described and a reduction in the low frequency amplitude noise power spectrum by 7 dB is obtained. An experimental investigation of the effects of optical feedback on the amplitude squeezing in a semiconductor laser is then discussed. The low frequency squeezing in a room temperature device is increased from 3% below the standard quantum limit (SQL) under free-running conditions to 19% below the SQL with optimal feedback. The experimental results are found to agree poorly with the single-mode model and a multi-mode model including the effects of asymmetrical cross-mode non-linear gain is developed to explain the discrepancy. Finally, further experimental investigation into the generation of amplitude squeezed light is presented using a commercial laser with no intentional external modifications. Squeezing as large as 29% below the SQL is measured using a balanced homodyne detector with the laser operating near room temperature, corresponding to 41% below the SQL at the output facet of the laser.
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.
Amplitude-squeezed states are generated from a room-temperature semiconductor laser using a combination of pump suppression and dispersive optical feedback. The laser amplitude noise is found to be sensitive to extremely weak feedback levels, of the order of 10-8 of the output power. a reduction of the noise from 2% below the standard quantum limit (SQL) under free-running conditions to 19% below the SQL under optimal feedback conditions is obtained. A single mode theory is presented but is found to be inadequate in explaining the measured dependence of the noise reduction on the feedback power. A multimode theory including asymmetrical cross-mode nonlinear gain is proposed to explain this discrepancy.
A second-order correlation function approach is adopted to focus on the mechanism for generating amplitude-squeezed light in a semiconductor diode laser pumped with suppressed amplitude fluctuations. Second-order correlation functions between the electromagnetic field intensities and between the electromagnetic field intensities and the charge carrier numbers are calculated. Sub-Poissonian statistics and antibunching effects inside the laser cavity are analyzed; the analysis focuses on various quantities responsible for generating this state of the field. The influence of these quantities on the noise spectra of the detected field and conditions for quantum-noise reduction are considered.