A. S. Rodrigues

Photonic bandgap materials and structures by sol–gel processing

The sol–gel method is an inexpensive and flexible liquid phase processing technique that is suitable for the fabrication of 1-D photonic bandgap structures, such as multilayer dielectric mirrors. In the present work, we started by preparing highly reflecting quarter-wave multilayer stacks, composed of alternating films of high refractive index material (TiO2) and low refractive index material (SiO2), possessing well-defined stop bands. For example, for a 11-layer stack, a stop band was obtained with more than 96% reflectance (at near-normal incidence) between ∼600 and 700 nm, with a gap to mid-gap ratio Δλ/λmax=15.4%. Fabry–Perot micro-cavities, containing high or low index defects within the quarter-wave stack, were also prepared and tested. Such structures were optimized with the help of suitable modeling, using transfer matrix techniques. Various experimental techniques were used to characterize these multilayers, including ellipsometry, visible spectroscopy, X-ray diffraction and atomic force microscopy.

Interaction of dual-frequency pulses in passively mode-locked lasers

Abstract We have found, numerically, that three stable pulses of different shapes can exist in systems described by the complex Ginzburg–Landau equation, such as passively mode-locked lasers with a fast saturable absorber. At the same cavity parameter values, however, only two of them can coexist, which two depending on the particular values of the parameters. The region of existence for each pulse is investigated numerically. The interaction between each pair of pulses is studied numerically. Using the interaction plane technique, we have found stable bound states of composite pulses.

From nodeless clouds and vortices to gray ring solitons and symmetry-broken states in two-dimensional polariton condensates

We consider the existence, stability and dynamics of the nodeless state and fundamental nonlinear excitations, such as vortices, for a quasi-two-dimensional polariton condensate in the presence of pumping and nonlinear damping. We find a series of interesting features that can be directly contrasted to the case of the typically energy-conserving ultracold alkali-atom Bose-Einstein condensates (BECs). For sizeable parameter ranges, in line with earlier findings, the nodeless state becomes unstable towards the formation of stable nonlinear single or multi-vortex excitations. The potential instability of the single vortex is also examined and is found to possess similar characteristics to those of the nodeless cloud. We also report that, contrary to what is known, e.g., for the atomic BEC case, stable stationary gray ring solitons (that can be thought of as radial forms of Nozaki-Bekki holes) can be found for polariton condensates in suitable parametric regimes. In other regimes, however, these may also suffer symmetry-breaking instabilities. The dynamical, pattern-forming implications of the above instabilities are explored through direct numerical simulations and, in turn, give rise to waveforms with triangular or quadrupolar symmetry.

FEMTOSECOND PULSE PROPAGATION NEAR A TWO-PHOTON TRANSITION IN A SEMICONDUCTOR QUANTUM-DOT WAVEGUIDE

We have studied femtosecond pulse propagation in CdS quantum-dot-doped waveguides produced by the solgel and ion-exhange methods. The observed two-photon absorption and asymmetric spectral modulation of the transmitted pulses are explained by our theoretical model, which incorporates a near-resonant two-photon transition.

Interaction of discrete nonlinear Schr¨ odinger solitons with a linear lattice impurity

The interaction of moving discrete solitons with a linear Gaussian defect is investigated. Solitons with profiles varying from hyperbolic secant to exponentially localized are considered such that the mobility of soliton is maintained; the condition for which is obtained. Studies on scattering of the soliton by an attractive defect potential reveal the existence of total reflection and transmission windows which become very narrow with increasing initial soliton amplitude. Transmission regions disappear beyond the small-amplitude limit. The regions of complete reflection and partial capture correspond to the windows of the existence and nonexistence of solution of the stationary problem. Interaction of the discrete soliton with a barrier potential is also investigated. The critical amplitude of the defect at which splitting of the soliton into two parts occurs was estimated from a balance equation. The results were confirmed through direct numerical integration of the dynamical equation showing very good agreement with the analytical prediction.

Symmetry-Breaking Effects for Polariton Condensates in Double-Well Potentials

We study the existence, stability, and dynamics of symmetric and anti-symmetric states of quasi-one-dimensional polariton condensates in double-well potentials, in the presence of nonresonant pumping and nonlinear damping. Some prototypical features of the system, such as the bifurcation of asymmetric solutions, are similar to the Hamiltonian analog of the double-well system considered in the realm of atomic condensates. Nevertheless, there are also some nontrivial differences including, e.g., the unstable nature of both the parent and the daughter branch emerging in the relevant pitchfork bifurcation for slightly larger values of atom numbers. Another interesting feature that does not appear in the atomic condensate case is that the bifurcation for attractive interactions is slightly sub-critical instead of supercritical. These conclusions of the bifurcation analysis are corroborated by direct numerical simulations examining the dynamics of the system in the unstable regime.

Femtosecond pulse propagation and optical solitons in semiconductor-doped glass waveguides in the vicinity of a two-photon resonance

The propagation of ultrashort optical pulses in semiconductor-doped glass waveguides is investigated theoretically for wavelengths below the half bandgap. The linear and non-linear properties of the composites are obtained and a field equation for pulse propagation is derived. This equation yields a new family of sub-picosecond optical solitons which are observed in numerical simulations. Interesting applications are anticipated for ultrafast all-optical signal processing.

Interactions and scattering of quantum vortices in a polariton fluid

Quantum vortices, the quantized version of classical vortices, play a prominent role in superfluid and superconductor phase transitions. However, their exploration at a particle level in open quantum systems has gained considerable attention only recently. Here we study vortex pair interactions in a resonant polariton fluid created in a solid-state microcavity. By tracking the vortices on picosecond time scales, we reveal the role of nonlinearity, as well as of density and phase gradients, in driving their rotational dynamics. Such effects are also responsible for the split of composite spin–vortex molecules into elementary half-vortices, when seeding opposite vorticity between the two spinorial components. Remarkably, we also observe that vortices placed in close proximity experience a pull–push scenario leading to unusual scattering-like events that can be described by a tunable effective potential. Understanding vortex interactions can be useful in quantum hydrodynamics and in the development of vortex-based lattices, gyroscopes, and logic devices.Superfluid flow around a vortex is quantized so that vortices become discrete, particle-like defects, with interactions mediated by the surrounding fluid. Here, the authors use a polariton system to experimentally investigate the behavior and scattering of vortices in a two-component superfluid.

Transverse instability of solitons in nonlinear systems

We study the transverse instability associated with higher-dimensional nonlinear systems. For this, a cubic–quintic-nonlinear system is considered wherein the coefficients of cubic and quintic terms are allowed to be of either focusing or defocusing nature. It is found that focusing-cubic and defocusing-quintic nonlinearity can suppress the transverse instability growth rate. The addition of guiding potentials can also suppress the instability growth rate for all kinds of solitons with the same propagation constant.