Mitigation of dynamical instabilities in laser arrays via non-Hermitian coupling

Arrays of coupled semiconductor lasers are systems possessing complex dynamical behavior that are of major interest in photonics and laser science. Dynamical instabilities, arising from supermode competition and slow carrier dynamics, are known to prevent stable phase locking in a wide range of parameter space, requiring special methods to realize stable laser operation. Inspired by recent concepts of parity-time ($\mathcal{PT}$) and non-Hermitian photonics, in this work we consider non-Hermitian coupling engineering in laser arrays in a ring geometry and show, both analytically and numerically, that non-Hermitian coupling can help to mitigate the onset of dynamical laser instabilities. In particular, we consider in details two kinds of nearest-neighbor non-Hermitian couplings: symmetric but complex mode coupling (type-I non-Hermitian coupling) and asymmetric mode coupling (type-II non-Hermitian coupling). Suppression of dynamical instabilities can be realized in both coupling schemes, resulting in stable phase-locking laser emission with the lasers emitting in phase (for type-I coupling) or with $\pi/2$ phase gradient (for type-II coupling), resulting in a vortex far-field beam. In type-II non-Hermitian coupling, chirality induced by asymmetric mode coupling enables laser phase locking even in presence of moderate disorder in the resonance frequencies of the lasers.Comment: revised version, changed title, added one figure and some reference

Non-exponential decay via tunneling in tight-binding lattices and the optical Zeno effect

An exactly-solvable model for the decay of a metastable state coupled to a semi-infinite tight-binding lattice, showing large deviations from exponential decay in the strong coupling regime, is presented. An optical realization of the lattice model, based on discrete diffraction in a semi-infinite array of tunneling-coupled optical waveguides, is proposed to test non-exponential decay and for the observation of an optical analog of the quantum Zeno effect

A study of the interests of high school boys in their physical activity program

Thesis (M.A.)--Boston University, 1949. This item was digitized by the Internet Archive

Nonlinear directional coupler for polychromatic light

We demonstrate that nonlinear directional coupler with special bending of waveguide axes can be used for all-optical switching of polychromatic light with very broad spectrum covering all visible region. The bandwidth of suggested device is enhanced five times compared to conventional couplers. Our results suggest novel opportunities for creation of all-optical logical gates and switches for polychromatic light with white-light and super-continuum spectrum.Comment: 3 pages, 3 figure

Zitterbewegung of optical pulses in nonlinear frequency conversion

Pulse walk-off in the process of sum frequency generation in a nonlinear $\chi^{(2)}$ crystal is shown to be responsible for pulse jittering which is reminiscent to the Zitterbewegung (trembling motion) of a relativistic freely moving Dirac particle. An analytical expression for the pulse center of mass trajectory is derived in the no-pump-depletion limit, and numerical examples of Zitterbewegung are presented for sum frequency generation in periodically-poled lithium niobate. The proposed quantum-optical analogy indicates that frequency conversion in nonlinear optics could provide an experimentally accessible simulator of the Dirac equation.Comment: to be published in Journal of Physics B: Atomic, Molecular & Optical Physic

Spectral singularities and Bragg scattering in complex crystals

Spectral singularities that spoil the completeness of Bloch-Floquet states may occur in non-Hermitian Hamiltonians with complex periodic potentials. Here an equivalence is established between spectral singularities in complex crystals and secularities that arise in Bragg diffraction patterns. Signatures of spectral singularities in a scattering process with wave packets are elucidated for a PT-symmetric complex crystal.Comment: 6 pages, 5 figures, to be published in Phys. Rev.

Nonlinearity-induced broadening of resonances in dynamically modulated couplers

We report the observation of nonlinearity-induced broadening of resonances in dynamically modulated directional couplers. When the refractive index of the guiding channels in the coupler is harmonically modulated along the propagation direction and out-of-phase in two channels, coupling can be completely inhibited at resonant modulation frequencies. We observe that nonlinearity broadens such resonances and that localization can be achieved even in detuned systems at power levels well below those required in unmodulated couplers.Comment: 14 pages, 4 figures, to appear in Optics Letter

Quantization of a generally covariant gauge system with two super Hamiltonian constraints

The Becci-Rouet-Stora-Tyutin (BRST) operator quantization of a finite-dimensional gauge system featuring two quadratic super Hamiltonian and m linear supermomentum constraints is studied as a model for quantizing generally covariant gauge theories. The proposed model ``completely'' mimics the constraint algebra of General Relativity. The Dirac constraint operators are identified by realizing the BRST generator of the system as a Hermitian nilpotent operator, and a physical inner product is introduced to complete a consistent quantization procedure.Comment: 17 pages. Latex file. Minor changes, two references adde

Classical realization of two-site Fermi-Hubbard systems

A classical wave optics realization of the two-site Hubbard model, describing the dynamics of interacting fermions in a double-well potential, is proposed based on light transport in evanescently-coupled optical waveguides.Comment: 4 page

Multistable Pulse-like Solutions in a Parametrically Driven Ginzburg-Landau Equation

It is well known that pulse-like solutions of the cubic complex Ginzburg-Landau equation are unstable but can be stabilised by the addition of quintic terms. In this paper we explore an alternative mechanism where the role of the stabilising agent is played by the parametric driver. Our analysis is based on the numerical continuation of solutions in one of the parameters of the Ginzburg-Landau equation (the diffusion coefficient $c$), starting from the nonlinear Schr\"odinger limit (for which $c=0$). The continuation generates, recursively, a sequence of coexisting stable solutions with increasing number of humps. The sequence "converges" to a long pulse which can be interpreted as a bound state of two fronts with opposite polarities.Comment: 13 pages, 6 figures; to appear in PR