Constructing Fresnel reflection coefficients by ruler and compass

1 4 N ov 2 00 1 Constructing Fresnel reflection coefficients by ruler and compass

A simple and intuitive geometical method to analyze Fresnel formulas is presented. It applies to transparent media and is valid for perpendicular and parallel polarizations. The approach gives a graphical characterization particularly simple of the critical and Brewster angles. It also provides an interpretation of the relation between the reflection coefficients for both basic polarizations as...

مهندسی گاف نوار فوتونی در بلورهای فوتونی یک بعدی با استفاده از ضرایب فرنل و مقایسه آن با نتایج روش ماتریس انتقال

In this paper photonic band gaps of 1D photonic crystal are compared by using transfer matrix method and Fresnel coefficients method. In Fresnel coefficients method, the refractive indices of each layer and incidence light angle to the surface are used for calculating Fresnel coefficients, and then the necessary and sufficient condition for a 100% reflection from the surface of double layer die...

Herbrand’s theorem and non-Euclidean geometry

We use Herbrand’s theorem to give a new proof that Euclid’s parallel axiom is not derivable from the other axioms of first-order Euclidean geometry. Previous proofs involve constructing models of nonEuclidean geometry. This proof uses a very old and basic theorem of logic together with some simple properties of ruler-and-compass constructions to give a short, simple, and intuitively appealing p...

Relationship between the p and s Fresnel reflection coefficients of an interface independent of angle of incidence

On Casimir Forces for Media with Arbitrary Dielectric Properties

We derive an expression for the Casimir force between slabs with arbitrary dielectric properties characterized by their reflection coefficients. The formalism presented here is applicable to media with a local or a non-local dielectric response, an infinite or a finite width, inhomogeneous dissipative, etc. Our results reduce to the Lifshitz formula for the force between semi-infinite dielectri...