Photonic crystals and photon gaps - Fundamental aspects

Controlling electromagnetic waves in photonic circuits in the same way as we control electronic currents in integrated circuits - that's the objective we can envisage by exploiting the various "facets" of artificial structures such as photonic crystals, from concepts to applications. The terms "crystal", "photon gaps" and "photonic band gaps" clearly evoke analogies with semiconductor crystals and electronic band gaps. Obtained by periodically structuring dielectric or metallic materials in one, two or three directions in space, photonic crystals offer the prospect of producing optical or electromagnetic devices capable of storing, filtering and guiding light on the wavelength scale. In addition to the race for miniaturization required to process an ever-increasing amount of information, this prospect may also lead to new optical components with ultimate properties.

This paper on "photonic crystals" is divided into two parts. In the first part (article [AF 3 710]), we first recall the motivations behind the photonic crystal concept, with a brief summary of the first results that triggered the scientific craze we know today. We then move on to the electron-photon analogy that gave rise to the notions of photon gaps and photonic band gaps. This borrowing of electromagnetism and optics from solid-state physics can be seen as a fair return, since since the advent of quantum mechanics, physics in general had never failed to borrow from optics, treating electronic excitations in terms of matter waves. The electron-photon analogy is simply illustrated using the well-known one-dimensional systems of semiconductor quantum wells and Bragg mirrors. Starting from Maxwell's equations, we then describe the models that allow us to determine the photonic band diagrams of periodic, infinite and defect-free structures. Illustrations are given in order of increasing complexity, from one-dimensional to three-dimensional photonic crystals. The final paragraphs are devoted to finite-size crystals and their modeling.

Particular attention is paid to the description of periodicity defects and their influence on the electromagnetic properties of photonic crystals. The analogy with the crystalline defects of real solid crystals is repeated, except that the defects are useful, like the dopants in a semiconductor. The insertion of defects will, in fact, make it possible to introduce optical resonators and waveguides into photonic crystals.

The various optical properties of photonic crystals, the new effects that can be expected from them, the technological progress required to develop them in the visible and infrared range, and their first applications in both microwaves and optics, will be developed in the second part of this presentation (article...