Dispersion Engineering for Integrated Nanophotonics E-Book

Olivier Vanbésien

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 162

Veröffentlichungsjahr: 2014

Beschreibung

This book shows how dispersion engineering in two dimensional dielectric photonic crystals can provide new effects for the precise control of light propagation for integrated nanophotonics.
Dispersion engineering in regular and graded photonic crystals to promote anomalous refraction effects is studied from the concepts to experimental demonstration via nanofabrication considerations. Self collimation, ultra and negative refraction, second harmonic generation, mirage and invisibility effects which lead to an unprecedented control of light propagation at the (sub-)wavelength scale for the field of integrated nanophotonics are detailed and commented upon.

Leseprobe

Contents

Introduction

1 Two-Dimensional Dielectric Photonic Crystals

1.1. Context

1.2. Concepts: photonic band structures and equi-frequency curves

1.3. Fundamental dispersion effects

1.4. From concepts to reality

1.5. Conclusion

2 Flat Lenses

2.1. Context

2.2. Negative refraction based flat lenses

2.3. Gradient index lenses

2.4. Conclusion

3 Towards Transform Optics Based Devices

3.1. Context

3.2. From transform Optics to Hamiltonian optics

3.3. 1D graded photonic crystals

3.4. Cloaking devices

3.5. Conclusion

Conclusion

Bibliography

Index

First published 2014 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.

Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:

ISTE Ltd27-37 St George’s RoadLondon SW19 4EUUKwww.iste.co.uk

John Wiley & Sons, Inc.111 River StreetHoboken, NJ 07030USAwww.wiley.com

©ISTE Ltd 2014The rights of Olivier Vanbésien and Emmanuel Centeno to be identified as the author of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988.

Library of Congress Control Number: 2013957303

British Library Cataloguing-in-Publication DataA CIP record for this book is available from the British LibraryISSN 2051-2481 (Print)ISSN 2051-249X (Online)ISBN 978-1-84821-564-1

Introduction

To be able to control the velocity and direction of light propagation over very short distances (of the order of a wavelength) with absolute precision... To be able to manipulate the properties of individual photons at will... To be able to trap these photons, for a greater or lesser time, in a very small region of space... To be able to render invisible objects of macroscopic size in the visible or infrared wavelength ranges... There have been so many “dreams” from physicists and writers over the centuries, with many achievements imagined by the latter but viewed with skepticism by the former.

Yet, in recent decades, many topics previously relegated to the fiction shelves of libraries have emerged in research laboratories. Indeed, many imaginary concepts have been theorized, for example, using the tools of transformation optics, which enable us to manipulate at will the wave trajectories and structural material parameters of the propagation media. An almost infinite number of new functions can then be created as long as the principle of reality is ignored. Accounting for the technological constraints of fabrication, often at the nanometer scale when exploring the field of optics, remains the main limiting factor for the emergence of these extraordinary devices.

However, recent decades have been marked by remarkable progress in the fabrication (top down) or synthesis (bottom up) processes of heterogeneous materials, regularly labeled as “artificial”, leading to a true “dispersion engineering”. Whether modulating the electric permittivity–magnetic permeability couple or the refractive index–surface impedance couple, the common goal is to tailor the material constituents in order to prevent or enable particular electromagnetic states. In general, the achievable structuring scale fixes the spectral range impacted (or conversely: the spectral range targeted fixes the structuring scale needed).

Progressively, over time, these structuring techniques have evolved. Initially, they consisted mainly of modulating the bulk (or surface) material parameters by changing the permeability and/or permittivity properties of periodic arrangements of metallic or dielectric elements to reach unusual values in the frequency or wavelength range targeted. For example, by diluting a metal as a thin wire cubic lattice and associating it with a network of resonant metallic particles of more or less complex geometries, it has been proved possible to generate several decades under the plasma frequency of the metal used, effective permittivity and permeability both negatives leading to the non-trivial concept of negative refraction. Such artificial material has been baptized “left-handed”, referring to the indirect trihedron thus formed by the wave vector and the electric and magnetic fields in this case. In this area, two broad classes of “artificial materials” can be distinguished depending on the fact that the structuring scale appears very small compared with the wavelength (metamaterials) or the order of the wavelength (electromagnetic or photonic crystals).

More recently, the bulk (or surface) engineering of material parameters has become too complex for either metamaterial or electromagnetic/photonic crystals to move towards localized engineering (uni-, bi-or three-dimensional), via the notions of graded crystals (geometrical modulation of crystal properties) or via the principles of transformation optics, to offer more original functionalities from optical mirages to invisibility cloaks...

If, from a spectral point of view, we focus on the infrared range (up to the visible domain), it appears that the majority of the new proposed devices come from the field of dielectric photonic crystals with a progressive extension to “graded” photonic crystals or a-periodic structures... “Metallic” approaches are used extremely rarely, even under high dilution, due to loss levels often incompatible with the required performance. Furthermore, if we are interested in the very promising and competitive applications in the area of integrated (nano-)photonics, it appears that the field of two-dimensional dispersion engineering represents the largest part of the current research.

The main purpose of this book is to give an exhaustive review of dispersion engineering principles in dielectric artificial materials in the optical domain (wavelengths of a few micrometers or less). As most of the applications will concern integrated photonics, mainly two-dimensional designs will be considered in detail, but constant attention will be paid to the third dimension of space which will automatically reappear in prototype processing or characterization steps, often with undesired collateral detrimental effects on optimal performances.

To allow a progressive immersion in this quite large field of research, the first chapter gives the basic tools to understand the dispersion properties of photonic crystals, with special attention paid to two-dimensional dielectric lattices. A parametric study of the band diagrams of various crystal geometries will help us to understand the anomalous propagation regimes afforded by such periodic arrangements. More specifically, it will be seen that the extensive use of equi-frequency contours extracted from the band diagram will help us to gain a profound understanding of unexpected effects such as collimation, ultra or negative refraction which appears when such crystals of finite thickness are interfaced with air or a homogenous medium. The various approaches followed to bring these concepts to reality will be detailed in Chapter 1. As regards optics, the dielectrics used are mainly semiconductors. The fabrication processes use intensively advanced nano-electronics tools. The different strategies used to produce the two-dimensional dispersion engineering-based applications in real space (intrinsically three-dimensional) are also reviewed in the chapter.

Chapter 2 addresses the various functionalities that can be obtained using flat lenses. Such approaches have regained popularity since it has been expected that flat lenses based on artificial material can easily overcome the limitation of classical optics: the concept of the “perfect lens” with an infinite resolution has arrived! After much debate in the scientific community over the last 10 years, fed by experiments carried out worldwide, the “super-lens” concept still remains extremely interesting even if less close to the ideal. In this area, we first examine how a point source can be focused by a photonic crystal-based flat lens using negative refraction. Secondly, plane wave focusing is shown using photonic crystal-based flat gradient index (GRIN) lenses. These two applications are detailed from the design stage up to near field optical characterization, along with the necessary trade-offs made to build a measurable prototype.

The third and final chapter addresses more fanciful and prospective applications based on the generalization of localized dispersion engineering using the tools of Hamiltonian or transformation optics. Key words for the chapter include: optical mirages, cloaking or bypass devices, invisibility... a series of topics situated at the cutting edge of state-of-the-art research. Here again, various proposals (along with practical realizations when available) made to create advanced functionalities for integrated nano-photonics are analyzed pragmatically. We start from graded photonic crystals (with one and two dimensional gradients, a natural extension of the GRIN approaches developed in Chapter 2), with the prospect of ultra-miniaturized complex optical functions required, for example, in dense wavelength division multiplexing applications. Finally, preliminary two-dimensional cloaking devices or bypass systems are presented as potential candidates for the integration of future three-dimensional optical circuits.

Among the literature that has been written on these subjects for more than a decade, and which is sometimes fiercely debated, one goal of this book is to present, with pragmatism, realistic applications of “dispersion engineering” in optics which can be achieved with the current state-of-the-art theoretical knowledge and fabrication capabilities. Indeed, it is one thing to propose intriguing and fancy new devices based on complex material parameter engineering, and another thing to fabricate and characterize prototypes compatible with large scale integration or production. Based on a rigorous analysis of light propagation in highly complex heterogeneous materials, always keeping in mind their technological feasibility, it is hoped to give readers (engineers, physicists or post-graduate students, whether specialists in the field of optics or not) who are just curious or want to increase their field of interest, the basic tools of “dispersion engineering”, which they can use themselves in the future to develop new ideas...

1

Two-dimensional Dielectric Photonic Crystals

In Chapter 1, the fundamental concepts for the exploitation of light propagation in photonic crystals are reviewed, based on the exploitation of band structures and equi-frequency surfaces. Special attention is devoted to hole and pillar dielectric lattice nanofabrication techniques, aiming to operate for wavelengths at the micron scale.