Relaxation-oscillation phenomena in an injection-locked semiconductor laser

Jagher, P. C. De; Graaf, W.A. van der; Lenstra, D.

doi:10.1088/1355-5111/8/4/004

Cited by 35 publications

(20 citation statements)

References 12 publications

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“…Putting (15) and (18) into (7), we have (22) Since is a positive real number, the phase of can be deduced from (22). However, we only consider the magnitude of (22) in the following. By using the known results of , , , and…”

Section: Tuning Characteristicsmentioning

confidence: 99%

Analysis of an Optically Injected Semiconductor Laser for Microwave Generation

Chan

2010

IEEE J. Quantum Electron.

146

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Abstract-The nonlinear dynamical period-one oscillation of an optically injected semiconductor laser is investigated analytically. The oscillation is commonly observed when the injection is moderately strong and positively detuned from the Hopf bifurcation boundary. The laser emits continuous-wave optical signal with periodic intensity oscillation. Since the oscillation frequency is widely tunable beyond the relaxation oscillation frequency, the system can be regarded as a high-speed photonic microwave source. In this paper, analytical solution of the oscillation is presented for the first time. By applying a two-wavelength approximation to the rate equations, we obtain mathematical expressions that characterize the oscillation. The analysis explains the physical origin of the periodic intensity oscillation as the beating between two wavelengths, namely, the injected wavelength and the cavity resonance wavelength. As the injection strength increases, the optical gain reduces, the cavity is red-shifted through the antiguidance effect, and so the beat frequency increases continuously. The theoretical analysis is useful for designing the system for photonic microwave applications.

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Section: Tuning Characteristicsmentioning

confidence: 99%

Analysis of an Optically Injected Semiconductor Laser for Microwave Generation

Chan

2010

IEEE J. Quantum Electron.

146

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“…The bifurcation diagram is similar to that of a laser diode with monochromatic external optical injection [18,19]. In the (input field frequency, input field amplitude) plane, the curve above which relaxation oscillations become undamped 'touches' the line below which locking cannot be achieved in the positive frequency region, while it is above and almost parallel to this line in the negative frequency region (see, for example, figures 4 and 5 of [18], or figure 1 of [19]). To display the stability of the steady-state solutions in more detail, figure 2(b) shows the evolution in the (tan(ω i τ ), γ ) plane of the solutions with i < 0, and figure 2(c) shows the evolution of the solutions with i > 0.…”

Section: Stability Of the External Cavity Modesmentioning

confidence: 78%

Stability and modulation properties of a semiconductor laser with weak optical feedback from a distant reflector

Masoller

Abraham

1998

Quantum Semiclass. Opt.

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Abstract. We analyse the stability of the steady-state solutions of the compound system formed by a single-longitudinal-mode semiconductor laser and an external reflector. Of the large number of these external cavity modes (ECMs) created in pairs of modes and antimodes by moderate feedback, the antimodes are always unstable, while the modes may be stable or unstable when created. The ECMs that have a large positive frequency shift with respect to the emission frequency of the solitary laser are unstable when created. In contrast, the ECMs that have a large, negative frequency shift are stable on creation and remain stable over a relatively large feedback range. For sufficiently large feedback an ECM that is created stable gives way to a time-dependent solution (limit cycle or torus) that is localized in phase space around the ECM; several time-dependent attractors may coexist. Approximating the dynamical equations, taking into account terms up to second order, we obtain relations for the amplitudes of the oscillations of the laser variables for these attractors. The external cavity length and the injection current are key parameters which determine these amplitudes. Our approximations are in good agreement with numerical simulations, and hold even far from the bifurcation points where these attractors originate.

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“…In a similar vein, a two-dimensional vector field approximation of the injection laser was derived in Ref. [47], and then studied in Ref. [48] with normal form theory near the SNH point.…”

Section: The Optically Injected Lasermentioning

confidence: 99%

Bifurcations ofn-homoclinic orbits in optically injected lasers

Wieczorek

Krauskopf

2005

Nonlinearity

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Abstract.We study in detail complex structures of homoclinic bifurcations in a threedimensional rate-equation model of a semiconductor laser receiving optically injected light of amplitude K and frequency detuning ω. Specifically, we find and follow in the (K, ω)-plane curves of n-homoclinic bifurcations, where a saddle-focus is connected to itself at the n-th return to a neighborhood of the saddle. We reveal an intricate interplay of codimension-two double-homoclinic and T-point bifurcations. Furthermore, we study how the bifurcation diagram changes with an additional parameter, the so-called linewidth enhancement factor α of the laser. In particular, we find folds (minima) of T-point bifurcation and double-homoclinic bifurcation curves, which are accumulated by infinitely many changes of the bifurcation diagram due to transitions through singularities of surfaces of homoclinic bifurcations.The injection laser emerges as a system that allows one to study codimensiontwo bifurcations of n-homoclinic orbits in a concrete vector field. At the same time, the bifurcation diagram in the (K, ω)-plane is of physical relevance. An example is the identification of regions, and their dependence on the parameter α, of multi-pulse excitability where the laser reacts to a single small perturbation by sending out n pulses.

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Relaxation-oscillation phenomena in an injection-locked semiconductor laser

Cited by 35 publications

References 12 publications

Analysis of an Optically Injected Semiconductor Laser for Microwave Generation

Analysis of an Optically Injected Semiconductor Laser for Microwave Generation

Stability and modulation properties of a semiconductor laser with weak optical feedback from a distant reflector

Bifurcations ofn-homoclinic orbits in optically injected lasers

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