Coherence collapse in semiconductor lasers with phase-conjugate feedback

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.

Experimental and theoretical studies of coherence collapse in GaAs/AlGaAs laser diodes with weak optical feedback show two distinct routes to chaos. In each case we observe undamped relaxation oscillations, then external cavity mode beating, and finally coherence collapse. When there is frequency locking between the relaxation oscillations and external cavity modes, a period doubling sequence is followed, otherwise the route to chaos is via quasiperiodicity.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

We report the first experimental observation of the route to chaos for semiconductor lasers with weak optical feedback. For increasing feedback level, the laser undergoes a quasiperiodic route interrupted by frequency locking, which is also predicted by a comprehensive numerical analysis. Experiments further demonstrate the occurrence of quantum-noise-induced transitions between two attractors with different relaxation oscillation frequencies. The attractors are created by two subsequent Hopf bifurcations of the same external cavity mode.

Spin-polarized vertical-cavity surface-emitting lasers (spin-VCSELs) with birefringence-induced polarization oscillations have been proposed to generate desired photonic microwave signals. Here, we numerically investigate the generation of photonic microwave signals in an optically pumped quantum dot (QD) spin-VCSEL. First, the influence of intrinsic key parameters on period-one (P1) oscillations and microwave properties is discussed. Second, the difference between microwave generation based on the quantum well (QW) and QD spin-VCSELs is analyzed by controlling the carrier capture rate that is described in the spin-flip model. The QD spin-VCSEL shows superior microwave quality in the low-frequency range (e.g., 10 GHz~20 GHz) compared with the QW spin-VCSEL. Finally, to boost the performance of the generated photonic microwave signal, optical feedback is introduced. The results show that dual-loop feedback can simultaneously narrow the microwave linewidth and suppress the side modes that are derived from the external cavity mode.

An external cavity lasing system, which operates at 2.4 μm and involves an InGaAsSb Fabry-Perot gain chip, was developed and characterized. The system was set up in a Littrow configuration to achieve a tuning range of about 100 nm. Continuous, mode-hope free tuning was observed with variation of grating angle. The threshold current of the lasing chip varied from 86 mA down to 70 mA for lasing in Fabry-Perot (FP) and external cavity (ECL) modes, respectively. A dependence of the threshold current on lasing wavelength was observed. The tuning range was found to depend on the semiconductor gain profile and also on the intensity of the optical feedback through the collimation-dispersion system. Drifting of the wavelength, as observed in intra cavity semiconductor lasers, was not observed for drive currents of up to 350 mA in regions close to the gain peak. Single mode ECL lasing could be sustained in this range at a significantly weaker optical feedback. Traces of FP lasing were, however, observed at currents in the range of 100-200 mA for wavelengths in the shoulder regions of the gain profile. In these cases, an increase of drive current resulted in mode hopping to multi-mode FP lasing. Our results confirm the competing nature of FP lasing with that of ECL mode of lasing. The onset of multi-mode FP lasing, and eventual hopping to these modes, can be correlated with the gain profile, drive current, and optical feedback.

Compact, efficient, diode-laser-based blue light sources are useful for many applications including optical storage and laser printing. Blue light can be generated by frequency doubling the output of reliable, high-power 860-nm lasers in potassium niobate. The Second Harmonic Generation (SHG) conversion efficiency can be substantially increased by placing the nonlinear crystal inside of a resonator in order to increase the infrared intensity in the crystal.1,2,3,4 The build-up of a high infrared intensity and efficient generation of blue output requires precise frequency matching of the diode laser and the SHG resonator. Previously, electronic locking1 and weak optical feedback techniques2,3,4 have been used to maintain this frequency matching. Electronic locking has the disadvantage of requiring an optical isolator to prevent destabilization of the laser frequency by light scattered from the resonator. Weak optical feedback has the disadvantage of requiring electronic control of the phase of the optical feedback as well as precise control of the feedback amplitude.3,4 We describe the operation of an antireflection-coated GaAlAs diode laser in an extended laser cavity that contains the SHG resonator as an intracavity element. The use of an antireflection coating on the laser and strong optical feedback is intended to suppress coupled-cavity effects and produce stable operation of the laser at a single frequency that is resonant with the SHG resonator. With the extended cavity we have obtained blue output powers of up to 12.5 milliwatts.

The transient dynamics of a single-mode semiconductor laser subjected to both weak optical feedback and light injection is studied. Even at detuning values for which injection locking is not effective, turn-on jitter and frequency jitter can still be strongly reduced by adjusting either the length of the external cavity or the detuning.

We report on an experiment to study the properties of nonlasing subthreshold sidemodes in a semiconductor laser operating in an external grating cavity configuration. We measure optical spectra consisting of the lasing mode and subthreshold nonlasing sidemodes, as well as radio frequency spectra at low frequency (0-100MHz) and at high frequency near the external grating cavity mode frequency. As the laser frequency is varied, the features of the rf spectra and the optical sidemode spectra all vary systematically. We present results on how these variations depend upon the external grating cavity mode frequency. Our results are compared with previous experiments and with theoretical predictions based upon four-wave mixing between the lasing mode and the adjacent sidemodes.

Through the use of analytical and numerical techniques, we investigate the interaction between the trivial off-state and the continuous-wave (CW) operation of a semiconductor laser subject to conventional optical feedback. More specifically, using numerical continuation tools, the stability and bifurcations of the CW states, or external-cavity modes (ECMs), are analyzed in dependence on the parameters of feedback phase, feedback strength, pump current, and the linewidth enhancement factor. In this way, curves of codimension-one Hopf bifurcations are shown to destabilize the off-state and lead to stable ECM operation. Moreover, self-intersections of these Hopf curves in codimension-two Hopf-Hopf bifurcation points are seen to give rise to curves of codimension-one torus bifurcations (Hopf bifurcations of the ECMs), and degenerate-Hopf points to the birth of saddle-node bifurcations of the ECMs, as parameters are varied. These codimension-two points are shown to come together at a codimension-three degenerate Hopf-Hopf point (a Bogdanov-Takens bifurcation of the ECMs): a limiting point for which a stable off-state can exist.

Because the ring and semilinear passive phase conjugate mirrors use dynamic transmission holograms, they are insensitive to vibration and may be pumped with light of short coherence length or with picosecond mode-locked laser light. Experimental demonstrations of these modes of operation are described.

We present a systematic study of the complex dynamics of a quantum dot (QD) laser subjected to optical feedback from a short external cavity. Our model consists of a Lang–Kobayashi like model for the electric field combined with a microscopically based rate equation system. We separately treat electron and hole dynamics in the QDs and the surrounding wetting layer (WL). By tuning the phase–amplitude coupling and the optical confinement factor we are able to discuss various scenarios of the dynamics on the route towards conventional quantum well (QW) lasers. Due to the optical feedback, multistability occurs in our model in form of external cavity modes (ECMs) or delay‐induced intensity pulsations. In dependence of the feedback strength we analyze complex bifurcation scenarios for the intensity of the emitted laser light as well as time series, power spectra, and phase portraits of all dynamic variables in order to elucidate the internal dynamics of the laser.

We analyze the dynamics of a laser diode subject to optical feedback from a short external cavity (EC), i.e. with an EC round-trip time much smaller than the period of the laser relaxation oscillations (RO). Our numerical simulations are based on the Lang-Kobayashi (LK) equations for single mode edge-emitting lasers subject to weak/moderate optical feedback. A new, detailed, Hopf bifurcation analysis shows that LK equations admist both supercritical and subcritical Hopf bifurcation points. Subcritical Hopf points lead to time-periodic pulsating intensity solutions with a frequency close to half the RO frequency. In contrast, from supercritical Hopf bifurcatiosn emerge harmonic intensity oscillations with a frequency either close to the RO frequency or to the EC frequency. Microwave oscillations are obtained, as a result of a beating between two EC modes. In general, these high frequency dynamics are stable only for a small range of feedback parameters. However, we find that decreasing the α factor largely improves the stability of the microwave oscillations and makes it possible to observe pulsating intensity solutions for a larger range of EC length. The high frequency intensity solutions of laser diodes with short EC are thought to be of great interest for new applications in all optical signal handling. Our results motivate new theoretical studies of LK equations with short EC.

It is commonly believed that the dynamics responsible for low-frequency fluctuations (LFF's) in external cavity semiconductor lasers is stochastic or chaotic. A common approach to address the origin of LFF's is to investigate the dynamical behavior of, and the interaction among, various external cavity modes in the Lang-Kobayashi (LK) paradigm. In this paper, we propose a framework for understanding of the LFFs based on a different set of fundamental solutions of the LK equations, which are periodic or quasiperiodic, and which are characterized by a sequence of time-locked pulses with slowly varying magnitude. We present numerical evidence and heuristic arguments, indicating that the dynamics of LFF's emerges as a result of quasiperiodic bifurcations from these solutions as the pumping current increases. Regular periodic solutions can actually be observed when (1) the feedback level is moderate, (2) pumping current is below solitary threshold, and (3) the linewidth enhancement factor is relatively large.

We calculate the field power spectrum of a Semiconductor Laser in a finite time window in presence of weak feedback and compare it with numerical simulations. The asymmetry of the side peaks, their frequency shift and the linewidth reduction are characterized. We consider the limit of very weak feedback, in which only side peaks associated with relaxation oscillations modified by the feedback appear in the spectrum.

Coexisting attractors, which arise from different external-cavity modes of the same longitudinal mode of the solitary laser, retain distinct stability properties, particularly when the laser is biased far above threshold and subjected to moderately strong optical feedback from a distant reflector. When the laser is modeled by the Lang and Kobayashi equations with additional gain nonlinearity, the dynamics is limited to external-cavity attractors that develop from the external-cavity modes which have a positive but not too large frequency shift with respect to the solitary laser emission frequency v 0 . Although relaxation oscillations about these externalcavity modes are the first to become undamped as the feedback intensity increases, the attractors that arise from these modes remain stable over the largest range of feedback strengths. Stronger feedback destabilizes the individual attractors, creating new solutions which form from their ruins. At the beginning of the merging, the attractor ruins are not equally visited; the most visited ruins are those of the attractors last destabilized. We explore and explain these results by examining the dynamics of the laser when operating on a single externalcavity attractor. @S1050-2947~98!08101-3#