Global coupling of QCLs: inclusion of dynamics.

A theoretical nonlinear treatment of coupled quantum cascade lasers (QCLs) by a monolithic Talbot cavity all grown on the same chip is presented, analyzed and the results are compared to recent experiments. The model is capable of computing numerically the stability or instability of the supermodes of the coupled system and can capture possible bifurcations into pulsating intensities. The model is derived by using an equivalent ring laser model that contains several separated gain section all coupled by an integrated Talbot cavity. In the small signal gain limit it captures the threshold gain of the various supermodes and matches the results of previous calculations in the literature in the same limit.

Experimental investigation of broad area quantum cascade lasers under external feedback.

Mode creation and temporal response of broad-area quantum cascade lasers (BA-QCL) placed within an external feedback cavity are described in this publication. The critical feedback parameter becomes the mirror angle relative to the BA-QCL facet. With judicious angle choices, a plethora of curious modes can be created, each with their particular threshold and slope efficiency. These range from a nearly single far-field intensity peak to highly multimode emission similar to their diode counterparts. Dynamics are strongly dominated by transverse mode competition ranging for less than 20MHz to greater than 100MHz. When the mirror is parallel to the facet, higher frequency external cavity oscillations become undamped.

A poly-epoxy surface explored by Hartree-Fock ΔSCF simulations of C1s XPS spectra.

Whereas poly-epoxy polymers represent a class of materials with a wide range of applications, the structural disorder makes them difficult to model. In the present work, we use good experimental model samples in the sense that they are pure, fully polymerized, flat and smooth, defect-free, and suitable for ultrahigh vacuum x-ray photoelectron spectroscopy, XPS, experiments. In parallel, we perform Hartree-Fock, HF, calculations of the binding energies, BEs, of the C1s electrons in a model molecule composed of the two constituents of the poly-epoxy sample. These C1s BEs were determined using the HF ΔSCF method, which is known to yield accurate values, especially for the shifts of the BEs, ΔBEs. We demonstrate the benefits of combining rigorous theory with careful XPS measurements in order to obtain correct assignments of the C1s XPS spectra of the polymer sample. Both the relative binding energies-by the ΔSCF method-and relative intensities-in the sudden approximation, SA, are calculated. It results in an excellent match with the experimental spectra. We are able to identify 9 different chemical environments under the C1s peak, where an exclusively experimental work would have found only 3 contributions. In addition, we observe that some contributions are localized at discrete binding energies, whereas others allow a much wider range because of the variation of their second neighbor bound polarization. Therefore, HF-ΔSCF simulations significantly increase the spectral resolution of XPS and thus offer a new avenue for the exploration of the surface of polymers.

Two-parameter study of square-wave switching dynamics in orthogonally delay-coupled semiconductor lasers.

We perform a detailed numerical analysis of square-wave (SW) polarization switching in two semiconductor lasers with time-delayed, orthogonal mutual coupling. An in-depth mapping of the dynamics in the two-parameter plane coupling strength versus frequency detuning shows that stable SWs occur in narrow parameter regions that are localized close to the boundary of stability of the pure-mode solution. In this steady state, the two coupled lasers emit orthogonal polarizations. We also show that there are various types of SW forms and that stable switching does not need the inclusion of noise or nonlinear gain in the model. As these narrow regions of deterministic and stable SWs occur for quite different combinations of parameters, they could potentially explain the waveforms that have been observed experimentally. However, on the other hand, these regions are narrow enough to be in fact considered as experimentally unreachable. Therefore, our results indicate that further experimental statistical studies are needed in order to distinguish deterministic and stationary square waveforms from long transients because of noise.

Hopf bifurcation to square-wave switching in mutually coupled semiconductor lasers.

Using advanced continuation techniques for dynamical systems, we elucidate the bifurcations leading to asymptotically stable square-wave pulsing and polarization mode switching in semiconductor lasers with mutual time-delayed and polarization rotating coupling. We find that the increase of coupling strength leads to a cascade of Hopf bifurcations on a mixed-mode steady state up to a transcritical bifurcation on a so-called pure-mode steady state where both lasers emit with the injected polarization state. From these successive Hopf bifurcations emerge time-periodic solutions that have a period close to the laser relaxation oscillation for weak coupling but a period close to twice the time delay for large coupling strength. The wave form of the time-periodic solutions also evolves from harmonic pulsing up to square-wave pulsing as has been observed recently in experiments.

ASE in thin disk lasers: theory and experiment.

We derive equations for the ASE intensity, decay time, and heat load. The crux of our development is frequency integration over the gain lineshape followed by a spatial integration over the emitters. These integrations result in a gain length that is determined from experiment. We measure the gain as a function of incident pump power for a multi-pass pumped Yb:YAG disk doped at 9.8 at.% with an anti-ASE cap. The incident pump powers are up to 3kW. Our fit to the measured gain is within 10% of the measured gain up to pump powers where the gain starts to flatten out and roll over. In this comparison we extract the gain length that turns out to be 43% of the pump spot size of 7mm.

Coherent combining of spectrally broadened fiber lasers.

We demonstrate that fiber lasers spectrally broadened by cross mode coupling can be coherently combined with high efficiency. The spectral broadening that it induces suppresses stimulated Brillouin scattering. Using long cavity length lasers, > 800 m, we induce spectral broadening of > 50 GHz and show mode by mode coherence in the output of four intracavity coupled fiber lasers.

SBS threshold for single mode and multimode GRIN fibers in an all fiber configuration.

We investigate stimulated Brillouin scattering (SBS) threshold in single mode and multimode fibers in an all fiber network. The pump is a single mode fiber pigtail attached to a diode. We find the theory and experiment agree for both single mode and multimode GRIN fibers. We modify the bulk SBS threshold equation for use with fibers by properly accounting for mode sizes and modal dispersion.

Delay dynamics of semiconductor lasers with short external cavities: bifurcation scenarios and mechanisms.

We present a comprehensive study of the emission dynamics of semiconductor lasers induced by delayed optical feedback from a short external cavity. Our analysis includes experiments, numerical modeling, and bifurcation analysis by means of computing unstable manifolds. This provides a unique overview and a detailed insight into the dynamics of this technologically important system and into the mechanisms leading to delayed feedback instabilities. By varying the external cavity phase, we find a cyclic scenario leading from stable intensity emission via periodic behavior to regular and irregular pulse packages, and finally back to stable emission. We reveal the underlying interplay of localized dynamics and global bifurcations.

Bistability of pulsating intensities for double-locked laser diodes.

Rate equations for semiconductor lasers subjected to simultaneous near-resonant optical injection and microwave current modulation are examined by combined analytical-numerical bifurcation techniques. Simple qualitative criteria are given for a bistable response. These results compare well with experimental measurements.

Extraction characteristics of a dual fiber compound cavity.

We study experimentally the time dependence, steady state behavior and spectra of a dual fiber-laser compound cavity. Theoretically we confirm the CW and spectral characteristics. This particular cavity is formed with two Er-doped fiber amplifiers, each terminated with a fiber Bragg grating, and coupled through a 50/50 coupler to a common feedback and output coupling element. The experiment and theory show that a low Q, high gain symmetric compound cavity extracts nearly 4 times the power of a component resonator. This extraction is maintained even when there is significant difference in the optical pathlengths of the two component elements. Further, our measurements and theory show that the longitudinal modes of the coupled cavity are distinct from the modes of the component cavities and that the coherence is formed on a mode-by-mode basis using these coupled-cavity modes. The time behavior of the compound cavity shows slow fluctuations, on the order of seconds, consistent with perturbations in the laboratory environment.

Dynamics of semiconductor lasers subject to delayed optical feedback: the short cavity regime.

We give experimental and numerical evidence for a new dynamical regime in the operation of semiconductor lasers subject to delayed optical feedback occurring for short delay times. This short cavity regime is dominated by a striking dynamical phenomenon: regular pulse packages forming a robust low-frequency state with underlying fast, regular intensity pulsations. We demonstrate that these regular pulse packages correspond to trajectories moving on global orbits comprising several destabilized fixed points within the complicated phase space structure of this delay system.

Regular dynamics of low-frequency fluctuations in external cavity semiconductor lasers.

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.

Stability and bifurcations of periodically modulated, optically injected laser diodes.

Recent experiments using lasers subject to external injection [T. B. Simpson, Opt. Commun., 170, 93 (1999)] have shown remarkable locking performances when a small reference current modulation is added to the dc-bias current. The locking problem is studied analytically by using a multiple scale perturbation method. We derive a slow time amplitude equation for the laser rapid limit-cycle oscillations. The solution of this equation is then investigated both analytically and numerically using a continuation method. We find that the intensity of the laser field can be time periodic (locking) or quasiperiodic (unlocking) and that there exist two distinct bifurcation mechanisms leading to locking. Finally, we compare bifurcation diagrams based on our amplitude equation with diagrams obtained from the laser original equations and find a good quantitative agreement.

Extraction characteristics of a one dimensional Talbot cavity with stochastic propagation phase.

We study the near- and far-fields of a linear array of fiber lasers in an external Talbot cavity. Each emitter has a random optical path difference (OPD) phase due to length and dispersion differences. The individual emitter fields are described by forward and reverse differential equations in the Rigrod approximation with the Talbot cavity coupling all emitters through boundary conditions. We analytically determine the effect of the rms phase on the increase in the threshold, the decrease in the emitter amplitude, and the decrease in the far-field intensity. These results are confirmed numerically by using a Monte Carlo technique for the phase. This leads to a locking probability, a coherence function, and the on-axis intensity as functions of the rms phase. Another issue which we investigate is the cavity performance for inter-cavity and external cavity phasing and find the latter preferable. We also determine the strong coupling limit for the fill factor.

Extraction characteristics of a cw double-hexagonal Talbot cavity with stochastic propagation phase.

We solve the coupled cw electric field differential equations for an hexagonal array of fiber gain elements all sharing a common monolithic Talbot cavity mirror. A threshold analysis shows that the lowest gains are nearly equal, within 10% of one another, and that one of these corresponds to an in-phase supermode. Above threshold we study the extraction characteristics as a function of the Talbot cavity length, and we also determine the optimum outcoupling reflectivity. These simulations show that the lasing mode is an in-phase solution. Lastly, we study extraction when random linear propagation phases are present by using Monte Carlo techniques. This shows that the coherence function decreases as $\exp(-\sigma;2)$, and that the near-field intensity decreases faster as the rms phase $\sigma;2$ increases. All of the above behaviors are strongly influenced by the hexagonal array rotational symmetry.

Experimental demonstration of suppression of low-frequency fluctuations and stabilization of an external-cavity laser diode.

We demonstrate experimentally all-optical stabilization of a single-mode laser diode subject to external optical feedback operating in the low-frequency fluctuations (LFF) regime, by the technique of applying a second delayed optical feedback. We interpret our results as suppression of LFF through destruction of the antimodes responsible for the LFF crises and stabilization of the laser through creation of new maximum gain modes, in agreement with recent theoretical predictions.

Pulse train characterisitcs of a passively Q-switched microchip laser.

A study of passively Q-switched microchip laser pulse trains yields approximate, yet reliable, formulae for the peak power, pulse energy, half-width, period, and the pulse shape in time. The pulse gain differential equation is made integrable by assuming that the laser absorption cross sections for the gain and saturable absorber are equal. We compare our predictions with an experiment which uses Nd:YAG as a gain medium and Cr:YAG as a saturable absorber. The agreement between theory and experiment for the period, pulse width, and the pulse energy is within 10%.

Experimental control of a chaotic semiconductor laser.

We have experimentally controlled the chaotic output of a single-mode semiconductor laser pumped near threshold and subject to optical feedback. We used a novel technique called dynamic targeting, which was theoretically proposed by Wieland et al. [Opt. Lett. 22, 469 (1997)]. Optical feedback causes the semiconductor laser to undergo a bifurcation cascade that exhibits regions of stability, periodicity, chaos, and coherence collapse. By adjusting the feedback phase simultaneously as the feedback strength was varied we steered the laser into the stable maximum gain mode, and thus we stabilized the system at maximum intensity.