Theory of noise in semiconductor lasers in the presence of optical feedback

Spanó, P.; Piazzolla, S.; Tamburrini, M.

doi:10.1109/jqe.1984.1072403

Cited by 112 publications

(24 citation statements)

References 20 publications

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“…where the characteristic functions of the external cavity are given as The expression for the double sideband frequency fluctuation spectrum is derived following the procedure of [21]:…”

Section: A + ( T ) = Ia+(t)le~'(~)mentioning

confidence: 99%

Phase noise reduction by self-phase locking in semiconductor lasers using phase conjugate feedback

Petersen

Gliese

Nielsen

1994

IEEE J. Quantum Electron.

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Abstruct-A theoretical analysis of the behavior of the frequency/phase noise of semiconductor lasers with external phase conjugate feedback is presented. It is shown that the frequency noise is drastically reduced even for lasers with butt-coupled phase conjugate mirrors. In this laser system, the phase noise takes a finite-low value corresponding to a state of first-order self-phase locking of the laser. As a result, the spectral shape of the laser signal does not remain Lorentzian but collapses around the carrier to a delta function with a close to carrier noise level of less than -137 dBcMz. The total phase variance of this laser signal, in a 20 GHz noise bandwidth, is less than 0.002 rad'.

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“…where the characteristic functions of the external cavity are given as The expression for the double sideband frequency fluctuation spectrum is derived following the procedure of [21]:…”

Section: A + ( T ) = Ia+(t)le~'(~)mentioning

confidence: 99%

Phase noise reduction by self-phase locking in semiconductor lasers using phase conjugate feedback

Petersen

Gliese

Nielsen

1994

IEEE J. Quantum Electron.

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“…The corresponding solution for n is given by n = --cos(w0+w)r. (11) In order to discuss the noise and stability properties of a particular solution given by (8), (10) and (11) we add noise sources FE(t) and F(t) in the r.h. sides of (6A) and (6B) respectively. These stochastic forces model the quantum noise due to spontaneous emission.…”

Section: 'Yarmentioning

confidence: 99%

“…It is reasonable to assume Gaussian distributions for FE and F with S-correlations only8"t. We express the fluctuating field as E(t) = 'T+M(t). exp[iLwt + iq5(t)] and the carrier number as n(t) = n + Ln(t), substitute these expressions in (6A,B) and use (8), (10) and (11). Then, assuming that the fluctuating quantities LXI, n and remain small, linearization leads to…”

Section: 'Yarmentioning

confidence: 99%

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<title>Feedback noise in single-mode semiconductor lasers</title>

Lenstra

Cohen

1991

SPIE Proceedings

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In nearly every application of semiconductor lasers some externally reflected light is coupled back into the laser with a certain time delay. The noise and coherence properties are very sensitive to optical feedback. Coupling to external cavity modes induces frequency shifts, line-narrowing and broadening, competition among different external cavity modes, or dynamical instabilities. Strongly dispersive gain makes instabilities efficiently generate phase noise, leading to coherence collapse. We present an overview of these phenomena and their theoretical descriptions.

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“…External-cavity semiconductor lasers are a feasible means of meeting this requirement. The intensity and phase-noise power spectral densities of semiconductor lasers in the presence of weak optical feedback have been studied by Spano et al 1 However, recent experimental and theoretical research indicates that strong externalcavity optical feedback is preferred. 2 4 Tkach and Chraplyvy experimentally distinguished the various operating reigmes according to the level of feedback in long external-cavity lasers.…”

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confidence: 99%

Noise and frequency chirping in external-cavity semiconductor lasers

Hui

Yizun

1989

Opt. Lett.

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The noise spectra and frequency chirping of semiconductor lasers in the presence of arbitrary amounts of optical feedback are analyzed. Short external cavities with strong optical feedback are found to reduce the noise dramatically in semiconductor lasers, especially in the high-frequency regime. Frequency chirping is shown to be closely related to the nonlinear gain effect.Coherent light-wave transmission and high-bit-rate single-mode fiber communication systems require stable lasers with narrow linewidths. External-cavity semiconductor lasers are a feasible means of meeting this requirement. The intensity and phase-noise power spectral densities of semiconductor lasers in the presence of weak optical feedback have been studied by Spano et al. 1 However, recent experimental and theoretical research indicates that strong externalcavity optical feedback is preferred. 2 4 Tkach and Chraplyvy experimentally distinguished the various operating reigmes according to the level of feedback in long external-cavity lasers. 4 In the strong-feedback regime (regime V in Ref. 4) the laser operates stably with narrower linewidths for all phases of the feedback. The linewidth dependence for and dynamic stability of semiconductor lasers with weak and strong optical feedback are known.5 ' 6 However, a unified study of the intensity and phase-noise spectra and frequency chirping in lasers with arbitrary amounts of optical feedback has not been developed. This Letter presents a theoretical derivation of simple formulas that describe these effects. This analysis also incorporates the effect of nonlinear gain. We show that short external cavities with strong optical feedback dramatically reduce the intensity and phase noises, especially in the high-frequency regime, and that nonlinear gain has a significant impact on frequency chirping but not on the Lorentzian linewidth. The external-cavity semiconductor laser investigated here is a three-mirror-cavity model (Fig. 1). By taking into account multiple random reflections in the external cavity, the rate equations of semiconductor lasers in the presence of arbitrary amounts of optical N(t) = -GI(t) _ N(t) + M(t) + FN(t),where I(t) is the number of photons, N(t) is the number of minority carriers, G is the gain coefficient, AG is the net gain coefficient, 4n(t) is the optical phase noise, Q and wo are the optical frequency with and without feedback, respectively, a is the linewidth enhancement factor, and F,(t) (x = I, X, N) represent the Langevin noises. r = noLic and ri = ni/c are the round-trip time delays in the passive and active cavities, respectively, R, is the rate of spontaneous emission, re is the electron lifetime, M(t) is the injection current, and T dwoHere r 2 is the amplitude reflectivity of the diode facet facing the external cavity and R 3 is the effective amplitude reflectivity, including coupling loss, of the external mirror.Equations (1)- (3) are now linearized, and thus limited to the case of relatively short external-cavity lasers. Linearized versions of 1(t), N(t...

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Theory of noise in semiconductor lasers in the presence of optical feedback

Cited by 112 publications

References 20 publications

Phase noise reduction by self-phase locking in semiconductor lasers using phase conjugate feedback

Phase noise reduction by self-phase locking in semiconductor lasers using phase conjugate feedback

<title>Feedback noise in single-mode semiconductor lasers</title>

Noise and frequency chirping in external-cavity semiconductor lasers

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