Locking bandwidth of two laterally coupled semiconductor lasers subject to optical injection

We report here for the first time (to our knowledge), a new and universal mechanism by which a two-element laser array is locked to external optical injection and admits stably injection-locked states within a nontrivial trapezoidal region. The rate equations for the system are studied both analytically and numerically. We derive a simple mathematical expression for the locking conditions, which reveals that two parallel saddle-node bifurcation branches, not reported for conventional single lasers subject to optical injection, delimit the injection locking range and its width. Important parameters are the linewidth enhancement factor, the laser separation, and the frequency offset between the two laterally-coupled lasers; the influence of these parameters on locking conditions is explored comprehensively. Our analytic approximations are validated numerically by using a path continuation technique as well as direct numerical integration of the rate equations. More importantly, our results are not restricted by waveguiding structures and uncover a generic locking behavior in the lateral arrays in the presence of injection

Two Dimensional Analysis on Nonlinear Interferometer and Decay of Spirals

Our two dimensional analysis on Vorontsov’s nonlinear interferometer model reveals how to construct complex patterns with unstable eigenmodes and how spirals decay into petals.</jats:p

Encoded and Spontaneous Dark and Bright Solitary Wave Patterns in a Nonlinear Optical Feedback System

Spatially robust dark/bright solitary wave patterns can be induced on a switched-on 2D beam, either through external phase encoding or a spontaneous modulational instability.</jats:p

Spontaneous Spatial Symmetry Breaking in Passive Nonlinear Optical Feedback Systems

In an earlier paper [1] we derived a formula describing a modulational instability on the plane or quasi-plane wave background of the field in a passive nonlinear optical ring cavity. This formula was applied to the specific case of the eigenvalue of the linearization of the fixed point going through -1 signifying a period doubling bifurcation. The Ikeda plane wave instability analysis was shown to be invalid, indicating that such fixed points are unstable to transverse fluctuations. We will show that this formula is universally applicable to feedback systems exhibiting strong nonlinear dispersion. We recover, as a special case, the recent mean field result of Lugiato et al. [2] in the case where the above eigenvalue approaches +1, signifying a saddle-node bifurcation. The modulational instability is of widespread occurrence even in situations where the plane wave solution (K T = 0) is strongly damped. It explains the occurrence of upper bistable branch solitary wavetrains [3] and shows that the dynamical switching from a low to high transmission state with transverse spatial rings occurs via nonlinear generation of higher harmonics in K T space.</jats:p

SPONTANEOUS SPATIAL SYMMETRY BREAKING IN PASSIVE OPTICAL FEEDBACK SYSTEMS

On montre qu'une formule d'instabilité modulationelle dérivée auparavant est universellement applicable aux systèmes optiques non linéaires feedback. Un nouveau type de structure d'évolution complexe en temps et en espace est identifié à deux dimensions d'espace transverse et est associé avec un récurrent écrasement des larges amplitudes de filaments saturés dans des structures d'anneaux et de crêtes.We show that a previously derived modulational instability formula is universally applicable to nonlinear optical feedback systems. A new type of complex spatio-temporal pattern evolution is identified in two-transverse space dimensions and is associated with the recurrent collapse of large amplitude saturated filaments into ring-like and ridge-like structures