Frequency locking of modulated waves

We consider the behavior of a modulated wave solution to an $\mathbb{S}^1$-equivariant autonomous system of differential equations under an external forcing of modulated wave type. The modulation frequency of the forcing is assumed to be close to the modulation frequency of the modulated wave solution, while the wave frequency of the forcing is supposed to be far from that of the modulated wave solution. We describe the domain in the three-dimensional control parameter space (of frequencies and amplitude of the forcing) where stable locking of the modulation frequencies of the forcing and the modulated wave solution occurs. Our system is a simplest case scenario for the behavior of self-pulsating lasers under the influence of external periodically modulated optical signals

Few-cycle optical solitary waves in nonlinear dispersive media

We study the propagation of few-cycle optical solitons in nonlinear media with an anomalous, but otherwise arbitrary, dispersion and a cubic nonlinearity. Our approach does not derive from the slowly varying envelope approximation. The optical field is derived directly from Maxwell's equations under the assumption that generation of the third harmonic is a nonresonant process or at least cannot destroy the pulse prior to inevitable linear damping. The solitary wave solutions are obtained numerically up to nearly single-cycle duration using the spectral renormalization method originally developed for the envelope solitons. The theory explicitly distinguishes contributions between the essential physical effects such as higher-order dispersion, self-steepening, and backscattering, as well as quantifies their influence on ultrashort optical solitons

Sasa-Satsuma hierarchy of integrable evolution equations

We present the infinite hierarchy of Sasa-Satsuma evolution equations. The corresponding Lax pairs are given, thus proving its integrability. The lowest order member of this hierarchy is the nonlinear Schrödinger equation, while the next one is the Sasa-Satsuma equation that includes third-order terms. Up to sixth-order terms of the hierarchy are given in explicit form, while the provided recurrence relation allows one to explicitly write all higher-order terms. The whole hierarchy can be combined into a single general equation. Each term in this equation contains a real independent coefficient that provides the possibility of adapting the equation to practical needs. A few examples of exact solutions of this general equation with an infinite number of terms are also given explicitly.The authors gratefully acknowledge the support of the Australian Research Council (Discovery Projects DP140100265 and DP150102057) and support from the Volkswagen Stiftung. N.A. is a recipient of the Alexander von Humboldt Award. U.B. acknowledges support by the German Research Foundation in the framework of the Collaborative Research Center 787 “Semiconductor Nanophotonics” under project B5. Sh.A. acknowledges support of the German Research Foundation under Project No. 389251150

Infinite hierarchy of nonlinear Schrödinger equations and their solutions

We study the infinite integrable nonlinear Schrödinger equation hierarchy beyond the Lakshmanan-Porsezian-Daniel equation which is a particular (fourth-order) case of the hierarchy. In particular, we present the generalized Lax pair and generalized soliton solutions, plane wave solutions, Akhmediev breathers, Kuznetsov-Ma breathers, periodic solutions, and rogue wave solutions for this infinite-order hierarchy. We find that “even- order” equations in the set affect phase and “stretching factors” in the solutions, while “odd-order” equations affect the velocities. Hence odd-order equation solutions can be real functions, while even-order equation solutions are always complex

Demonstration of a self-pulsing photonic crystal Fano laser

Semiconductor lasers in use today rely on mirrors based on the reflection at a cleaved facet or Bragg reflection from a periodic stack of layers. Here, we demonstrate an ultra-small laser with a mirror based on the Fano resonance between a continuum of waveguide modes and the discrete resonance of a nanocavity. The Fano resonance leads to unique laser characteristics. Since the Fano mirror is very narrow-band compared to conventional lasers, the laser is single-mode and in particular, it can be modulated via the mirror. We show, experimentally and theoretically, that nonlinearities in the mirror may even promote the generation of a self-sustained train of pulses at gigahertz frequencies, an effect that was previously only observed in macroscopic lasers. Such a source is of interest for a number of applications within integrated photonics

Physics and Applications of Laser Diode Chaos

An overview of chaos in laser diodes is provided which surveys experimental achievements in the area and explains the theory behind the phenomenon. The fundamental physics underpinning this behaviour and also the opportunities for harnessing laser diode chaos for potential applications are discussed. The availability and ease of operation of laser diodes, in a wide range of configurations, make them a convenient test-bed for exploring basic aspects of nonlinear and chaotic dynamics. It also makes them attractive for practical tasks, such as chaos-based secure communications and random number generation. Avenues for future research and development of chaotic laser diodes are also identified.Comment: Published in Nature Photonic

Dynamics and stability improvement of DFB tapered master-oscillator power-amplifiers

We consider theoretically the lasing properties of distributed-feedback master-oscillator poweramplifiers which are compact semiconductor laser devices capable of emitting a high brilliance beam at an optical power of several Watts. Based on a traveling wave equation model we calculate emitted optical power and spectral maps for increasing current injections of the power amplifier. We show that a proper choice of the coupling coefficient of the Bragg grating allows to optimize the laser operation, so that the laser emits a high intensity continuous wave beam without previously observed mode jumps or dynamic instabilities when injection currents are tuned

Early Adversity and the Prospective Prediction of Depressive and Anxiety Disorders in Adolescents

The current study was a prospective exploration of the specificity of early childhood adversities as predictors of anxiety and depressive disorders in adolescents. Participants were 816 adolescents (414 males, 402 females) with diagnostic information collected at age 15; information on early adversities had been collected from the mothers during pregnancy, at birth, age 6 months, and age 5 years for a related study. Adolescents with "pure" anxiety disorders were compared with adolescents with "pure" depressive disorders (major depressive disorder, dysthymia), and these groups were compared to never-ill controls. Analyses controlled for gender and maternal depression and anxiety disorders. Results indicated that adolescents with anxiety disorders were more likely than depressed youth to have been exposed to various early stressors, such as maternal prenatal stress, multiple maternal partner changes, and more total adversities, whereas few early childhood variables predicted depressive disorders. Even when current family stressors at age 15 were controlled, early adversity variables again significantly predicted anxiety disorders. Results suggest that anxiety disorders may be more strongly related to early strees exposure, while depressive disorders may be related to more proximal stressors or to early stressors not assessed in the current study

Modeling and simulations of beam stabilization in edge-emitting broad area semiconductor devices

A 2+1 dimensional PDE traveling wave model describing spatial-lateral dynamics of edge-emitting broad area semiconductor devices is considered. A numerical scheme based on a split-step Fourier method is presented and implemented on a parallel compute cluster. Simulations of the model equations are used for optimizing of existing devices with respect to the emitted beam quality, as well as for creating and testing of novel device design concept