### optics - Relation between intensity of light and refractive index - Physics Stack Exchange

refractive index;. Maxwell-Bloch equations; finite-difference time-domain. 1. Introduction permittivity ε, permeability µ and refractive index n – to the point of even allowing for an of Engineering and the Leverhulme Trust. Appendix A. By equation (6), this current density is produced by the electric field e(r) of the PC .. We should note that the diagonal form of the permittivity and permeability tensors . This results in an imaginary effective refractive index, as corresponds to regions (kx> π /2a) where our long-wavelength expansion cannot be trusted. Negative Dielectric Permittivity and Magnetic Permeability . .. Dispersion relation of the periodic microstrip model equivalent CRLH TLs in (a) Purely .. (b) negative refractive index and (c) magnetic permeability response . encouragement, and especially for his trust all throughout this thesis journey.

List of refractive indices For visible light most transparent media have refractive indices between 1 and 2. A few examples are given in the adjacent table.

**Module - 4 Lecture -7**

These values are measured at the yellow doublet D-line of sodiumwith a wavelength of nanometersas is conventionally done. Almost all solids and liquids have refractive indices above 1. Aerogel is a very low density solid that can be produced with refractive index in the range from 1. Most plastics have refractive indices in the range from 1.

### DoITPoMS - TLP Library Dielectric materials - The dielectric constant and the refractive index

Moreover, topological insulator material are transparent when they have nanoscale thickness. These excellent properties make them a type of significant materials for infrared optics. The refractive index measures the phase velocity of light, which does not carry information.

This can occur close to resonance frequenciesfor absorbing media, in plasmasand for X-rays. In the X-ray regime the refractive indices are lower than but very close to 1 exceptions close to some resonance frequencies. Since the refractive index of the ionosphere a plasmais less than unity, electromagnetic waves propagating through the plasma are bent "away from the normal" see Geometric optics allowing the radio wave to be refracted back toward earth, thus enabling long-distance radio communications.

See also Radio Propagation and Skywave. Negative index metamaterials A split-ring resonator array arranged to produce a negative index of refraction for microwaves Recent research has also demonstrated the existence of materials with a negative refractive index, which can occur if permittivity and permeability have simultaneous negative values.

## From photonic crystals to metamaterials: the bianisotropic response

The resulting negative refraction i. Ewald—Oseen extinction theorem At the atomic scale, an electromagnetic wave's phase velocity is slowed in a material because the electric field creates a disturbance in the charges of each atom primarily the electrons proportional to the electric susceptibility of the medium.

Similarly, the magnetic field creates a disturbance proportional to the magnetic susceptibility. As the electromagnetic fields oscillate in the wave, the charges in the material will be "shaken" back and forth at the same frequency.

The light wave traveling in the medium is the macroscopic superposition sum of all such contributions in the material: This wave is typically a wave with the same frequency but shorter wavelength than the original, leading to a slowing of the wave's phase velocity. The aforementioned homogenization theories all limit the generality to one or more of the following aspects: Also available are two approaches to homogenization that are of much wider generality: On the other hand, the FA method is based on the averaging of the PC's electromagnetic fields in a unit cell.

Both the EPR method and the FA method are numerical methods for the determination of effective parameters, rather than mean-field homogenization theories. There exist, in principle, many ways of defining the effective parameters by suitably relating the macroscopic constitutive fields, namely the dielectric displacement D and the magnetic field H, to the physical macroscopic fields, namely the electric field E and the magnetic induction B.

In this paper, we present a mean-field theory of PCs that goes beyond conventional ones. By assuming that the Bloch wavelength is much greater than the lattice constant of the periodic artificial structure, we derive analytic results on the effective tensors of both the bianisotropic response and the nonlocal dielectric response. These are determined for arbitrary periodicity one- 1Dtwo- 2D or three-dimensional 3D of the PC, for an arbitrary Bravais lattice and for arbitrary structure of the unit cell.

### Refractive index - Wikipedia

Considering isotropic and nonmagnetic materials in the unit cell of the photonic crystal, we show that the use of the bianisotropic response allows us to distinguish clearly the magnetic effects and, consequently, to characterize more properly the electromagnetic metamaterial properties. This paper derives the bianisotropic response from the PC or 'micro-level', for the first time on the basis of a very general set of assumptions. The effective permittivity and permeability for specific dielectric and metallo-dielectric photonic crystals are calculated, analyzed and, in some cases, compared with other theories in the literature.

The paper is organized as follows. Finally, the proofs of several formulae have been relegated to the appendices. Mean-field theory Let us consider a boundless PC composed, in general, of metallic and dielectric components. The form of the inclusions in the unit cell and the Bravais lattice are assumed to be completely arbitrary. In addition, the inclusions can be either isolated or in contact.

For simplicity, we also assume that the component materials are isotropic and that the metal has no magnetic properties.