The effect of optical feedback on the relaxation oscillation in semiconductor lasers

Cohen, Jeffrey P.; Drenten, R.R.; Verbeeck, B.H.

doi:10.1109/3.8533

Cited by 42 publications

(17 citation statements)

References 7 publications

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“…1,4,5 We report on a stability analysis without any such approximation, the results of which are valid for arbitrary laser parameters. This method was also used by Cohen et al 6 in analyzing a diode laser with COF.…”

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confidence: 99%

Stability of a diode laser with phase-conjugate feedback

1998

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An exact analysis is presented of the steady-state stability of a semiconductor laser subjected to feedback from a phase-conjugate mirror. Reduced stability occurs at low feedback whenever the effective external delay time is an integer multiple of the relaxation oscillation period. The role of a finite response time of the mirror is to enhance drastically the steady-state stability. © 1998 Optical Society of America OCIS codes: 140.2020, 140.3430, 140.3570, 140.5960, 190.5040. Optical feedback is known to affect severely the properties of a semiconductor laser. For stabilization purposes feedback from a phase-conjugate mirror is preferred over conventional optical feedback (COF), since in the latter case the laser suffers from extreme sensitivity to mirror-distance variations within an optical wavelength. This sensitivity is due to the fact that with an ordinary mirror the phase of the returning light depends strongly on the mirror position, whereas in phase conjugation there is no such dependence. 2 However, in the case of phase-conjugate feedback (PCF) one is always confronted with a certain sluggishness of the ref lector owing to the f inite response time, which should be taken into account when one is analyzing the stability of the laser operation with a phase-conjugate mirror. Most of the previous stability analyses disregarded this sluggishness. 3,4 In this Letter we present a linear stability analysis of the steady state of single-frequency operation of a single-mode diode laser with PCF, including the finite response-time effect. Owing to the time-delay term in the rate equations an exponential appears in the characteristic equation D͑s͒, the roots of which determine the stability of the laser. This exponential, which also shows up in the case of COF, complicates the analysis, and several kinds of approximation have been made in stability analysis. 1,4,5We report on a stability analysis without any such approximation, the results of which are valid for arbitrary laser parameters. This method was also used by Cohen et al. 6 in analyzing a diode laser with COF.When multiple external round trips can be ignored, the rate equations for a single-mode semiconductor laser with sluggish PCF are given bywhere E is the slowly varying amplitude of the optical field with respect to the optical carrier exp͑iv 0 t͒, with v 0 as the emission frequency of the solitary laser (i.e., the same laser without feedback) at threshold. E is normalized such that jEj 2 P equals the number of photons inside the cavity. N N th 1 DN is the number of electron -hole pairs (inversion) in the active layer, and N th is the inversion at threshold of the solitary laser. j is the differential gain, e is the nonlinear gain parameter, G 0 is the photon decay rate, a is the linewidth-enhancement factor, g p is the feedback rate, t m is the response time of the mirror, d 0 is the detuning of the mirror pump beam with respect to v 0 , t is the external-cavity round-trip time, J is the number of carriers injected into the active layer per un...

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Stability of a diode laser with phase-conjugate feedback

1998

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“…With increasing external feedback, the real part of each mode increases and the laser becomes less stable important frequency of laser oscillations besides these modes is the frequency of the relaxation oscillation. Since chaos is a nonlinear phenomenon, many modes are not only related to the internal and external modes and the relaxation oscillation modes but also their sums and differences, and higher harmonics are excited (Cohen et al 1988;Helms and Petermann 1990;Levine et al 1995). For a chaotic bifurcation, the laser first becomes unstable with a frequency close to the relaxation oscillation, which is called period-1 oscillation.…”

Section: Linear Mode and Stability And Instability In Semiconductor mentioning

confidence: 98%

Theory of Optical Feedback in Semiconductor Lasers

Ohtsubo

2012

Springer Series in Optical Sciences

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A semiconductor laser with optical feedback is an excellent model for generating chaos in its output power and the system has proven to be very useful in practical applications. This chapter concerns the theoretical background for instability and chaos induced by optical feedback in narrow-stripe edge-emitting semiconductor lasers, such as Pabry-Perot lasers, multi-quantum well (MQW) lasers, and distributed feedback (DFB) lasers. Particular dynamics of feedback-induced instability and chaos in semiconductor lasers are separately discussed in the following chapter. In this chapter, we focus on the theoretical treatment of optical feedback effects in semiconductor lasers. Lasers show the same or similar dynamics as far as rate equations are described by the same equations. We here assume single mode operations for semiconductor lasers. The dynamics for multimode cases will be discussed in

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“…The determinant D in (16) determines the stability of the harmonic solutions of (6A,B). The stationary solution considered is stable if and only if all zeroes of D are located in the upper half complex Ill-plane.…”

Section: 'Yarmentioning

confidence: 99%

<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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The effect of optical feedback on the relaxation oscillation in semiconductor lasers

Cited by 42 publications

References 7 publications

Stability of a diode laser with phase-conjugate feedback

Stability of a diode laser with phase-conjugate feedback

Theory of Optical Feedback in Semiconductor Lasers

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

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