Light propagation in deterministic aperiodic waveguide arrays

Abstract

Over the past two decades, the light transport properties in regular (periodic) and disordered coupled waveguides have been extensively scrutinized. These two, in a sense, opposite types of ordering lead to two dierent phenomena - discrete diraction in regular arrays, where light energy spreads linearly along propagation direction, and transverse localization in disordered, where light energy is distributed between nite number of adjacent waveguides. Still an open question remains whether light behavior in intermediate domain is between fully periodic and fully disordered structures - deterministic structures with no periodicity. In this thesis the impact of deterministic aperiodic one-dimensional (1D) and two-dimensional (2D) coupled waveguide arrays (photonic lattices) on transverse light transport has been investigated both experimentally and numerically. Several types of lattices were considered: 1D and 2D position modulated Fibonacci lattices, 1D refractive index contrast modulated Fibonacci lattice, 1D regular lattice and regular lattice with defect. The aim is to explore the possibility of using these structures as a tool for light diraction suppression. In the experiment, waveguide arrays were generated in photorefractive crystals, lithium-niobate and strontium-barium-niobate, by direct laser writing and incoherent Bessel beam induction technique, respectively. Gaussian and Airy beam were used as excitation beams. A series of numerical simulations were conducted using Beam Propagation Method. It is found that the position modulated Fibonacci lattice can suppress light diraction in comparison to the regular one. This is more pronounced in 1D than in 2D lattice. In 1D case, for relatively high refractive index contrasts, the propagating beam becomes almost completely localized in transverse plane. In 1D refractive index contrast modulated Fibonacci lattice the similar result is obtained - diraction is suppressed considerably comparing to regular lattice. Furthermore, the stronger modulation leads to strongly localized states, so the light propagation in Fibonacci lattice resembles the propagation in disordered one. Besides, it is shown that the slightly disordered Fibonacci lattice with relatively small refractive index contrast modulation enhances diraction. In addition, it is shown that a regular lattice can reduce a self-bending of Airy beam trajectory. The research presented in the thesis provides additional standpoint in understanding of light transport in complex optical structures and imposes new ways for control of light diraction and engineering of the optical response of devices.

U prethodne dve decenije, prostiranje svetlosti u regularnim (periodič- nim) i neuređenim spregnutim talasovodima je intenzivno proučavano. Ova dva, na neki način suprotna tipa uređenja, odgovorna su za dva različita fenomena - diskretnu difrakciju u regularnim nizovima, gde se energija svet- losti širi linearno duž pravca propagacije, i transverzalnu lokalizaciju u neuređenim nizovima, gde je svetlosna energija raspoređena u konačnom broju susednih talasovoda. Još uvek je otvoreno pitanje ponašanja svetlosti u oblasti između sasvim periodičnih i sasvim neuređenih struktura - determinističkim strukturama bez periodičnosti. U ovoj tezi je eksperimentalno i numerički proučavan uticaj determin- ističkih aperiodičnih jednodimenzionih (1D) i dvodimenzionih (2D) nizova spregnutih talasovoda (fotonskih rešetki) na transverzalnu propagaciju svet- losti...