Dark and bright solitons in resonantly absorbing gratings

Saturation and stability of nonlinear photonic crystals

We consider a one-dimensional photonic crystal made by an infinite set of nonlinear nematic films immersed in a linear dielectric medium. The thickness of each equidistant film is negligible and its refraction index depends continuously on the electric field intensity, giving rise to all the involved nonlinear terms, which joints from a starting linear index for negligible amplitudes to a final saturation index for extremely large field intensities. We show that the nonlinear exact solutions of this system form an intensity-dependent band structure which we calculate and analyze. Next, we ponder a finite version of this system; that is, we take a finite array of linear dielectric stacks of the same size separated by the same nonlinear extremely thin nematic slabs and find the reflection coefficients for this arrangement and obtain the dependence on the wave number and intensity of the incident wave. As a final step we analyze the stability of the analytical solutions of the nonlinear crystal by following the evolution of an additive amplitude to the analytical nonlinear solution we have found here. We discuss our results and state our conclusions.

Non-Bragg resonance of surface water waves in a trough with periodic walls

The non-Bragg resonance of surface water waves is investigated, both theoretically and experimentally, in a trough with square-wave corrugated sidewalls. Unlike the familiar Bragg resonances, the non-Bragg resonances occur far from the edges of the Brillouin zone and open additional forbidden bands. The experimental observations confirm the existence of these resonances, and the measurements for the transmission properties showing both Bragg and non-Bragg band gaps agree fairly well with the theoretical predictions obtained by the plane-wave expansion method. It is shown that both Bragg and non-Bragg resonances highly depend on the symmetry of the corrugations on the opposite sidewall. As the relative shift between the two corrugations increases from zero to the half period of the corrugations, the Bragg gap shrinks and vanishes, but the non-Bragg gap varies in the opposite way, reaching its maximum, which is impressively wide and much more efficient in reflecting water waves.

Solitons in a linearly coupled system with separated dispersion and nonlinearity

We introduce a model of dual-core waveguide with the cubic nonlinearity and group-velocity dispersion (GVD) confined to different cores, with the linear coupling between them. The model can be realized in terms of photonic-crystal fibers. It opens a way to understand how solitons are sustained by the interplay between the nonlinearity and GVD which are not "mixed" in a single nonlinear Schrodinger (NLS) equation, but are instead separated and mix indirectly, through the linear coupling between the two cores. The spectrum of the system contains two gaps, semi-infinite and finite ones. In the case of anomalous GVD in the dispersive core, the solitons fill the semi-infinite gap, leaving the finite one empty. This soliton family is entirely stable, and is qualitatively similar to the ordinary NLS solitons, although shapes of the soliton's components in the nonlinear and dispersive cores are very different, the latter one being much weaker and broader. In the case of the normal GVD, the situation is completely different: the semi-infinite gap is empty, but the finite one is filled with a family of stable gap solitons featuring a two-tier shape, with a sharp peak on top of a broad "pedestal." This case has no counterpart in the usual NLS model. An extended system, including weak GVD in the nonlinear core, is analyzed too. In either case, when the solitons reside in the semi-infinite or finite gap, they persist if the extra GVD is anomalous, and completely disappear if it is normal.

Effects of the near-dipole-dipole interaction on gap solitons in resonantly absorbing gratings

Gap solitons can exist in a periodic refractive-index grating modified by periodic layers of near-resonant two-level systems. In this work, we include the effect of the density-dependent near-dipole-dipole (NDD) interaction in order to generalize this model. For certain values of the grating parameters, we find that the NDD interaction significantly modifies the frequency bands in which gap solitons can exist. The difference between the model with and without the NDD interaction is discussed. The stability of gap solitons is studied numerically.

Solitary waves in systems with separated Bragg grating and nonlinearity

The existence and stability of solitons in a dual-core optical waveguide, in which one core has Kerr nonlinearity while the other one is linear with a Bragg grating written on it, are investigated. The system's spectrum for the frequency omega of linear waves always contains a gap. If the group velocity c in the linear core is zero, it also has two other, upper and lower (in terms of omega) gaps. If c not equal to 0, the upper and lower gaps do not exist in the rigorous sense, as each overlaps with one branch of the continuous spectrum. When c=0, a family of zero-velocity soliton solutions, filling all the three gaps, is found analytically. Their stability is tested numerically, leading to a conclusion that only solitons in an upper section of the upper gap are stable. For c not equal to 0, soliton solutions are sought for numerically. Stationary solutions are only found in the upper gap, in the form of unusual solitons, which exist as a continuous family in the former upper gap, despite its overlapping with one branch of the continuous spectrum. A region in the parameter plane (c,omega) is identified where these solitons are stable; it is again an upper section of the upper gap. Stable moving solitons are found too. A feasible explanation for the (virtual) existence of these solitons, based on an analytical estimate of their radiative-decay rate (if the decay takes place), is presented.

Parametric Bragg resonances in waves on a shallow fluid over a periodically drilled bottom

Bragg resonances involving strong interactions among Fourier wave components of a periodically drilled bottom and parametrically driven surface waves on a shallow liquid are experimentally shown to break down the secular dispersion relation of surface waves. When the fluid is sufficiently shallow, wave components that match reciprocal wave vectors of the bottom topography are dominant. Experimental evidence of band-gap phenomena in these surface waves are also shown. Moreover, the prevalence of Bragg resonances is so strong that one of them is excited anomalously within the band gap.

Spatiotemporally localized solitons in resonantly absorbing bragg reflectors

We predict the existence of multidimensional solitons that are localized in both space and time ("light bullets") in two- and three-dimensional self-induced-transparency media embedded in a Bragg grating. These fully stable light bullets suggest new possibilities of signal transmission control and self-trapping of light.