Light Beam Propagation in complex Crystals

Author: Nikhil Pradeep Kumar
Title: Light Beam Propagation in Complex Crystals
Director: Prof. Muriel Botey i Cumella, Prof. Ramon Herrero Simon and Prof. Kestutis Staliunas
Presentation date: July 13, 2017
Link to text: http://www.tdx.cat/handle/10803/405772

Abstract: Recent advancement in Photonics have brought about a new era of miniaturisation. Along came a need for technology to allow the manipulation of light at the micrometer scale, with precise control over beam propagation. The past decades have seen numerous studies devoted to periodic nanophotonic structures, Photonic Crystals (PhCs), which brought out different temporal and spatial functionalities such as frequency bandgaps, waveguiding, or managing diffractive properties of the beam. More recently, attention was paid to equally accessible artificial nanophotonic structures, where gain and losses are modulated on the wavelength scale: Gain Loss Modulated Materials (GLMMs). Therefore, the aim of my PhD was providing a deep analysis on beam propagation in GLMMs, identifying the spatial propagation effects they held and proposing realistic scenarios in which they could be implemented, in existing and evolving technology and devices. We built our studies from a solid understanding of GLMMs of prior works performed, however, using a paraxial approximation, which reduces the predictions accuracy by excluding propagation at large angles. The methodology adopted is a combination of analytical predictions and numerical confirmation of the predicted effects. We initially investigated the high anisotropy of beam amplification/attenuation within GLMMs. As predicted by the plane wave expansion method, the propagation of light beams within such structures is sensitive to the propagation direction. We provided a numerical proof in 2D periodic Loss Modulated Materials (LMM) with square and rhombic lattice symmetry, by solving the full set of Maxwell¿s equations, using the finite difference time domain method, which entails no approximation. Anisotropy of amplification/attenuation leads to the narrowing of the angular spectrum of beams with wavevectors close to the edges of the first Brillouin Zone. The effect provides a novel tool to filter out high spatial harmonics from noisy beams, while being amplified. A later study lead us to analyse the focalisation performance of a flat LMM slab. Flat lensing was analytically predicted by the dispersion curves obtained from a coupled mode expansion of Maxwell¿s equations, and then numerically confirmed. For a range of frequencies coinciding with a high transmission window at resonant Bragg frequencies (bandgap frequencies for PhCs), light beams undergo negative (anomalous) diffraction through LMMs. The phase shifts accumulated within the structure are then compensated by normal diffraction in free space, leading to a substantial focalization beyond it. The predicted phenomena are generic for spatially modulated materials and other kinds of waves. Thus, we also discussed, for the first time, propagation in LMM acoustic crystals, predicting high angular transmission bands. While these initial studies assumed hypothetical LMM materials, in a realistic scenario, loss modulations are always accompanied by refractive index modulations, as predicted by Kramers-Kronig relations. During the final phase of my PhD, we focused on more realistic structures exhibiting both index and loss modulations, namely metallic photonic crystals (MPhCs), made of 2D rhombic arrays of metallic cylinders embedded in air. We explored their ability to tailor the spatial propagation of light beams. Indeed, MPhCs support self-collimated propagation and negative diffraction. In this later case, flat lensing was demonstrated, leading to the focalization of beams behind MPhCs slabs. Also, the anisotropic attenuation of light within MPhCs enables spatial filtering. Finally, we initiated studies towards the implementation of GLMMs as an intrinsic mechanism to improve the beam quality from Broad Area Semiconductor (BAS) amplifiers. Along the development of my PhD, we proposed, analysed and established spatial beam propagation effects in GLMM, from purely ideal LMM structures to more realistic structure as MPhCs or BAS amplifiers.