Radiation in bent asymmetric coupled waveguides.

A numerical study of the radiation in coupled bent waveguides is presented. Such arrangements of curved waveguides in reduced radiation-loss configurations can be used to enhance the quality factor of integrated microresonators. 3D full vector computations of the complex modal fields (and propagation constants) and the transient propagation effects have been performed. The results obtained agree qualitatively with former 2D finite-difference time-domain (FDTD) analyses. At the same time, the calculations presented meet the accuracy requirements for the design of practical implementations that are unattainable with 2D approaches.

On the asymptotic evolution of finite energy Airy wave functions.

In general, there is an inverse relation between the degree of localization of a wave function of a certain class and its transform representation dictated by the scaling property of the Fourier transform. We report that in the case of finite energy Airy wave packets a simultaneous increase in their localization in the direct and transform domains can be obtained as the apodization parameter is varied. One consequence of this is that the far-field diffraction rate of a finite energy Airy beam decreases as the beam localization at the launch plane increases. We analyze the asymptotic properties of finite energy Airy wave functions using the stationary phase method. We obtain one dominant contribution to the long-term evolution that admits a Gaussian-like approximation, which displays the expected reduction of its broadening rate as the input localization is increased.

Spatiotemporal dispersion and wave envelopes with relativistic and pseudorelativistic characteristics.

A generic nonparaxial model for pulse envelopes is presented. Classic Schrödinger-type descriptions of wave propagation have their origins in slowly-varying envelopes combined with a Galilean boost to the local time frame. By abandoning these two simplifications, a picture of pulse evolution emerges in which frame-of-reference considerations and space-time transformations take center stage. A wide range of effects, analogous to those in special relativity, then follows for both linear and nonlinear systems. Explicit demonstration is presented through exact bright and dark soliton pulse solutions.

Fast and slow light in zigzag microring resonator chains.

We analyze fast- and slow-light transmission in a zigzag microring resonator chain. In the superluminal case, a new light-transmission effect is found whereby the input optical pulse is reproduced in an almost-simultaneous manner at the various system outputs. When the input carrier is tuned to a different frequency, the system permits to slow down the propagating optical signal. Between these two extreme cases, the relative delay can be tuned within a broad range. We propose, and analyze numerically, a laser-array configuration for the stable operation of active devices.

Helmholtz solitons at nonlinear interfaces.

Reflection and refraction of spatial solitons at dielectric interfaces, accommodating arbitrarily angles of incidence, is studied. Analysis is based on Helmholtz soliton theory, which eliminates the angular restriction associated with the paraxial approximation. A novel generalization of Snell's law is discovered that is valid for collimated light beams and the entire angular domain. Our new theoretical predictions are shown to be in excellent agreement with full numerical simulations. New qualitative features of soliton refraction and limitations of previous paraxial analyses are highlighted.

Spatial Kerr soliton collisions at arbitrary angles.

The theory of spatial Kerr solitons is extended to colliding beams that are neither almost-exactly copropagating nor almost-exactly counterpropagating. Our new Helmholtz formalism yields results that are consistent with the inherent symmetry of the collision process and that are not predicted by existing paraxial descriptions. Full numerical and approximate analytical results are presented. These show excellent agreement. In particular, Kerr solitons are found to be remarkably robust under nonparaxial collisions.

Helmholtz-Manakov solitons.

A different spatial soliton-bearing wave equation is introduced, the Helmholtz-Manakov (HM) equation, for describing the evolution of broad multicomponent self-trapped beams in Kerr-type media. By omitting the slowly varying envelope approximation, the HM equation can describe accurately vector solitons propagating and interacting at arbitrarily large angles with respect to the reference direction. The HM equation is solved using Hirota's method, yielding four different classes of Helmholtz soliton that are vector generalizations of their scalar counterparts. General and particular forms of the three invariants of the HM system are also reported.

Helmholtz dark solitons.

A general dark-soliton solution of the Helmholtz equation (with defocusing Kerr nonlinearity) that has on- and off-axis, gray and black, paraxial and Helmholtz solitons as particular solutions, is reported. Modifications to soliton transverse velocity, width, phase period, and existence conditions are derived and explained in geometrical terms. Simulations verify analytical predictions and also demonstrate spontaneous formation of Helmholtz solitons and transparency of their interactions.