Exact envelope solitons in topological Floquet insulators.

The existence of new types of four-wave mixing Floquet solitons were recently realized numerically through a resonant phase matching in a photonic lattice of type-I Dirac cones; specifically, a honeycomb lattice of helical array waveguides imprinted on a weakly birefringent medium. We present a wide class of exact solutions in this system for the envelope solitons in dark-bright pairs and a "molecular" form of bright-dark combinations. Some of the solutions, red or blue detuned, are mode-locked in their momenta, while the others offer a spectrum of allowed momenta subject to constraints amongst the system and solution parameters. We show that the characteristically different solutions exist at and away from the band edge, with the exact band edge possessing a periodic pair of sinusoidal excitations akin to that of two-level systems apart from localized solitons. These could have possible applications for designing quantum devices.

Variation of self-imaging length in multimode waveguides beyond the paraxial approximation.

We demonstrate the precise variation of self-imaging distance with width of a Gaussian input, centrally fed into a symmetric dielectric slab waveguide of width ∼20λ0. The width of the Gaussian is varied from the paraxial to completely nonparaxial domain. Unlike the paraxial case, the self-imaging distance is found to depend on the beam width and change with the number of excited modes in the waveguide. These features should be useful in designing devices that exploit self-imaging for improved efficiency, especially in nanophotonic circuits.

Quasi-Gaussian output from dual case I waveguide resonators with mirrors of step-index reflectivity profiles.

There are three recognized low-loss configurations for waveguide laser resonators in which the waveguide is either closed at each end by a plane mirror (dual case I design) or one of the plane mirrors is replaced by a curved mirror at some distance from the guide exit. Some time ago, a variant of the latter design was proposed by exploiting the self-imaging properties of multimode waveguides. The resonator was predicted to produce a TEM(00)-like output with very low round-trip loss and excellent mode discrimination even though the curved mirror was placed much nearer to the guide exit (making the resonator more compact) than was conventional for achieving those results. In the present work, we show that the desirable features of the above design can be achieved even in a dual case I configuration by using end mirrors with suitable reflectivity profiles. Since there is no free space region between the waveguide and the mirrors, the resonator will have the additional advantages of being compact and portable. Furthermore, the absence of curved mirrors will also facilitate its realization in semiconductor integrated optics technology.