Fresnel Transmission Coefficients Research Articles

New Green-function formalism for surface optics

A new Green-function formalism is developed for calculating fields generated by sources in the presence of a multilayer geometry. The approach is to formulate the problem immediately in terms of s- and p-polarized waves generated, so that the calculation of the effect of interfaces proceeds by the introduction of Fresnel reflection and transmission coefficients and parallels the simple physical picture of light progressing through the structure.

Reply to "Comments on intensity enhancement in textured optical sheets"

The recent comments on the above paper are self-contradictory and are physically incorrect. The comments violate the principle of time-reversal invariance for the Fresnel transmission and reflection coefficients of light rays. The proposed alternate formula for the intensity enhancement in optical media is an overestimation that violates the first and second laws of thermodynamics.

Scattering of scalar waves from a rough interface using a single integral equation

Using Green's function methods we consider the problem of scattering from a rough interface separating two semi-infinite homogenous media. We derive a single coordinate-space integral equation of the first kind for the generalized reflection coefficient R. A second integral equation of the first kind is derived for the generalized transmission coefficient T. The two equations are new results. In the limiting cases corresponding to Dirichlet and Neumann boundary conditions, we recover the usual boundary integral equations from the R-equation. In the flat surface limit, R and T reduce to the usual Fresnel reflection and transmission coefficients. The latter are derived from these more general results rather than assumed as in perturbation methods.

Refraction at a Curved Dielectric Interface: Geometrical Optics Solution

The transmission of a spherical or plane wave through an arbitrarily curved dielectric interface is solved by the geometrical optics theory. The transmitted field is proportional to the product of the conventional Fresnel's transmission coefficient and a divergence factor (DF), which describes the cross-sectional variation (convergence or divergence) of a ray pencil as the latter propagates in the transmitted region. The factor DF depends on the incident wavefront, the curvatures of the interface, and the relative indices of the two media. We give explicit matrix formulas for calculating DF, illustrate its physical significance via examples.

Transformation of Fresnel’s interface reflection and transmission coefficients between normal and oblique incidence

If w denotes an interface Fresnel reflection or transmission coefficient for s - or p -polarized light at an oblique angle of incidence ϕ, and z denotes the same coefficient at normal incidence, we find that w is an analytic function of z, w = f(z), that depends on ϕ but not on the specific optical properties of the two media on both sides of the interface. All four functions that correspond to the four distinct Fresnel coefficients and their inverses are determined. We single out for detailed examination, as an example, the relationship between the reflection of s -polarized light at 45° angle of incidence and at normal incidence for any transparent medium/absorbing medium interface by considering the mapping properties of the associated transformation and its inverse between the z and w planes. A useful byproduct of this investigation is a technique for the determination of the optical properties of isotropic and uniaxially and biaxially anisotropic absorbing media from measurement of reflectance at normal and oblique incidence.

Reflection at a Curved Dielectric Lnterface - Electromagnetic Tunneling

The reflection of a locally plane wave from a curved interface between two nonabsorbing dielectric media is investigated. Our analysis is applicable to an interface of general shape, defined at each point by the two principal radii of curvature. When the wave is incident from the denser medium at angles greater than the critical angle it is only partially reflected, due to a form of electromagnetic tunneling. Generalized Fresnel transmission coefficients and an extension of Snell's law are derived to account for this transmission into the less dense medium. Ray tracing can then be applied to determine such phenomena as the bending losses in optical slab waveguides, and the curvature loss of skew rays within straight optical waveguides of circular cross section.

Bending losses of multimode optical fibres

The bending loss of rays within circular and slab multimode optical waveguides is determined using only Snell's laws, the generalised Fresnel transmission coefficient and the Goos-Haenchen shift. The generalised transmission coefficient accounts for radiation losses, due to curvature, not included in Fresnel's classical laws.

Generalised Fresnel's law for loss due to curvature

Many rays, predicted by Fresnel's laws to be totally reflected from a curved interface between two dielectric media, are only partially reflected. We derive a generalised Fresnel transmission coefficient to account for this loss. Our transmission coefficient applies to an arbitrary surface; e.g. one defined by two arbitrary radii of curvature. It can be used to determine radiation loss from bent and straight circular optical fibres.

Mueller-Stokes Matrix Formulation of Fresnel's Equations

The Mueller-Stokes matrices for Fresnel's reflection and transmission equations at a dielectric surface are derived and the basic properties of these matrices are discussed. A corresponding pair of matrices for Fresnel's reflection and transmission coefficients are also derived. The matrix forms are shown to simplify considerably at the Brewster angle and their special properties are demonstrated. In order to simplify matrix multiplications a diagonal matrix is constructed. The significance of the eigenvalues and the eigenvectors of the Mueller-Stokes polarizing matrix is noted. The relationship between the Mueller-Stokes polarizing matrix and the diagonal polarizing matrix is developed. Finally, Chandrasekhar's phase matrix is shown to be a special case of the diagonal polarizing matrix.