Flat-band localization and self-collimation of light in photonic crystals

We investigate the optical properties of a photonic crystal composed of a quasi-one-dimensional flat-band lattice array through finite-difference time-domain simulations. The photonic bands contain flat bands (FBs) at specific frequencies, which correspond to compact localized states as a consequence of destructive interference. The FBs are shown to be nondispersive along the $\Gamma\rightarrow X$ line, but dispersive along the $\Gamma\rightarrow Y$ line. The FB localization of light in a single direction only results in a self-collimation of light propagation throughout the photonic crystal at the FB frequency.Comment: 18 single-column pages, 7 figures including graphical to

Wave propagation in ordered, disordered, and nonlinear photonic band gap materials

Photonic band gap materials are artificial dielectric structures that give the promise of molding and controlling the flow of optical light the same way semiconductors mold and control the electric current flow. Their basic property is the photonic gap, a frequency range in which wave propagation is not allowed in any direction, in a close analogy with the electronic energy band gap in semiconductors;In this dissertation we study two areas of photonic band gap materials. The first area is focused on the properties of one-dimensional PBG materials doped with Kerr-type nonlinear material. Such systems have been shown to exhibit bistability, an essential feature for an all-optical switching mechanism. Here, we will study an approximate structure model, in which the nonlinear material is concentrated in very thin, or delta-function, layers. We will derive analytical solutions, and compare with the finite-width nonlinear layer case, in order to find it\u27s limitations and the physical mechanisms behind them. Also, by using numerical simulations, we will study the dynamics of an externally-controlled switching mechanism for such systems, which is pulse injection while they are illuminated by a constant wave. Finally, we will develop a model for the nonlinear response of colloidal crystals, which will reveal a light-lattice coupling similar to the electron-phonon in semiconductors;The second area of study is focused on the mechanisms responsible for the gap formation, as well as other properties of two-dimensional PBG materials. We will show that in one case, the dominant gap-forming mechanism is the excitation of single scatterer Mie resonances and not Bragg-like multiple scattering, and that the photonic states are analogous to the localized atomic orbitals in semiconductors. We will develop a tight-binding model based on a linear combination of Mie resonances, that will successfully reproduce the photonic band structure of any lattice arrangement, with and without defects, thus proving the validity of a strongly localized photon picture. Then, using ab initio numerical techniques, we will study the effects of disorder for various realizations of two-dimensional photonic band gap materials, and identify the cases for which the strongly localized photon picture applies, and those for which a nearly free photon picture is a more proper one

Robustness of One-Dimensional Photonic Bandgaps Under Random Variations of Geometrical Parameters

The supercell method is used to study the variation of the photonic bandgaps in one-dimensional photonic crystals under random perturbations to thicknesses of the layers. The results of both plane wave and analytical band structure and density of states calculations are presented along with the transmission cofficient as the level of randomness and the supercell size is increased. It is found that higher bandgaps disappear first as the randomness is gradually increased. The lowest bandgap is found to persist up to a randomness level of 55 percent.Comment: Submitted to Physical Review B on April 8 200

Nonlinear guided waves and spatial solitons in a periodic layered medium

We overview the properties of nonlinear guided waves and (bright and dark) spatial optical solitons in a periodic medium created by a sequence of linear and nonlinear layers. First, we consider a single layer with a cubic nonlinear response (a nonlinear waveguide) embedded into a periodic layered linear medium, and describe nonlinear localized modes (guided waves and Bragg-like localized gap modes) and their stability. Then, we study modulational instability as well as the existence and stability of discrete spatial solitons in a periodic array of identical nonlinear layers, a one-dimensional nonlinear photonic crystal. Both similarities and differences with the models described by the discrete nonlinear Schrodinger equation (derived in the tight-binding approximation) and coupled-mode theory (valid for the shallow periodic modulations) are emphasized.Comment: 10 pages, 14 figure

Gap deformation and classical wave localization in disordered two-dimensional photonic band gap materials

By using two ab initio numerical methods we study the effects that disorder has on the spectral gaps and on wave localization in two-dimensional photonic band gap materials. We find that there are basically two different responses depending on the lattice realization (solid dielectric cylinders in air or vise versa), the wave polarization, and the particular form under which disorder is introduced. Two different pictures for the photonic states are employed, the ``nearly free'' photon and the ``strongly localized'' photon. These originate from the two different mechanisms responsible for the formation of the spectral gaps, ie. multiple scattering and single scatterer resonances, and they qualitatively explain our results.Comment: Accepted for publication in Phys. Rev.

Laser Annealing as a Platform for Plasmonic Nanostructuring

Nanoconstruction of metals is a significant challenge for the future manufacturing of plasmonic devices. Such a technology requires the development of ultra‐fast, high‐throughput and low cost fabrication schemes. Laser processing can be considered as such and can potentially represent an unrivalled tool towards the anticipated arrival of modules based in metallic nanostructures, with an extra advantage: the ease of scalability. Specifically, laser nanostructuring of either thin metal films or ceramic/metal multilayers and composites can result on surface or subsurface plasmonic patterns, respectively, with many potential applications. In this chapter, the photo‐thermal processes involved in surface and subsurface nanostructuring are discussed and processes to develop functional plasmonic nanostructures with pre‐determined morphology are demonstrated. For the subsurface plasmonic conformations, the temperature gradients that are developed spatially across the metal/dielectric structure during the laser processing can be utilized. For the surface plasmonic nanoassembling, the ability to tune the laser\u27s wavelength to either match the absorption spectral profile of the metal or to be resonant with the plasma oscillation frequency can be utilised, i.e. different optical absorption mechanisms that are size‐selective can be probed. Both processes can serve as a platform for stimulating further progress towards the engineering of large‐scale plasmonic devices

Mesoscopic magnetism in dielectric photonic crystal meta materials: topology and inhomogeneous broadening

We consider meta materials made from a two-dimensional dielectric rod-type photonic crystal. The magnetic response is studied within the recently developed homogenization theory and we in particular study the effects of topology and inhomogeneous broadening. While topology itself mainly affects the Mie resonance frequency we find that the dispersion in the topological radius R of the dielectric rods may lead to significant inhomogeneous broadening and suppression of the negative-mu phenomena for dR/R0 >> epsilon''/epsilon', with epsilon=epsilon'+i*epsilon'' being the relative dielectric function of the rods.Comment: 13 pages including 1 table and 5 figure