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

@article{Azzam1986RelationshipBT, title={Relationship between the p and s Fresnel reflection coefficients of an interface independent of angle of incidence}, author={Rasheed M. A. Azzam}, journal={Journal of The Optical Society of America A-optics Image Science and Vision}, year={1986}, volume={3}, pages={928-929} }

The Fresnel reflection coefficients rp and rs of p- and s-polarized light at the planar interface between two linear isotropic media are found to be interrelated by (rs − rp)/(1 − rsrp) = cos 2β, independent of the angle of incidence ϕ, where tan2β = ∊ and ∊ is the (generally complex) ratio of dielectric constants of the media of refraction and incidence. This complements another relation (found earlier), (rs2 − rp)/(rs − rsrp) = cos 2ϕ, which is valid at a given ϕ independent of ∊ (i.e., for…

## 33 Citations

Fresnel's interface reflection coefficients for the parallel and perpendicular polarizations: global properties and facts not found in your textbook

- MathematicsOptics & Photonics
- 1994

This paper reviews recently obtained results related to Fresnel's reflection coefficients which play a central role in the optics of light reflection by surfaces and thin films. Topics include…

Relations for the Fresnel reflection coefficients of a bimaterial interface independent of the angle of planewave incidence

- Physics
- 1988

A relation between the Fresnel reflection coefficients, for parallel and perpendicular planewave incidence, applicable to a dielectric-dielectric interface has been given by Azzam, the relationship…

Analytical determination of the complex refractive index and the incident angle of an optically isotropic substrate by ellipsometric parameters and reflectance.

- PhysicsApplied optics
- 2021

The proposed method provides a simple way to measure the AOI and the complex refractive index of nonplanar samples without extra or complicated hardware.

Reflection and transmission ellipsometry of a uniform layer

- Physics
- 1987

We examine the general properties of the ellipsometric quantities ρ = rp/rs and τ = tp/ts for a nonabsorbing uniform film. At fixed angle of incidence and for variable thickness, τ moves periodically…

Infrared reflectivity of metallic surfaces

- Mathematics
- 1988

We propose simple and good approximate equations for the reflectance of the perpendicular and parallel polarizations of light upon an isotropic absorbing medium deduced from the Fresnel coefficients…

Three polarization reflectometry methods for determination of optical anisotropy.

- PhysicsApplied optics
- 1998

Three novel methods for the determination of optical anisotropy are proposed and tested and the use of the Azzam universal relationship between the Fresnel s- and p-reflection coefficients is suggested.

Novel approaches in polarized optical reflectometry

- PhysicsOther Conferences
- 1998

Due to its simplicity polarization reflectometry technique have some advantages over the ellipsometric methods. We demonstrate this claim in the threefold manner suggesting three novel polarization…

Polarization Conversion for Specular Components of Surface Reflection

- PhysicsIEEE Geoscience and Remote Sensing Letters
- 2013

A combination of the Hong and ASH approximations is suggested to improve upon previous studies that used only the Hong approximation in a variety of applications.

Integral solution for diffraction problems involving conducting surfaces with complex geometries. I. Theory

- Mathematics
- 1988

For an arbitrary conducting surface Z(x, y) we obtained an analytical expression for the local refractive index ν as a function of Z, ∂Z/∂x, ∂Z/∂y, and the Drude conductivity σ by using the complex…

## References

SHOWING 1-10 OF 12 REFERENCES

Direct relation between Fresnel’s interface reflection coefficients for the parallel and perpendicular polarizations

- Physics
- 1979

We have found a significant relation, rp = rs(rs − cos2ϕ)/(1 − rs cos2ϕ), between Fresnel’s interface complex-amplitude reflection coefficients rp and rs for the parallel (p) and perpendicular (s)…

Simple and direct determination of complex refractive index and thickness of unsupported or embedded thin films by combined reflection and transmission ellipsometry at 45° angle of incidence

- Physics
- 1983

Measurements of the polarization states (represented by complex numbers χr and χt, respectively) of light reflected and transmitted by an unsupported or embedded thin film, for totally polarized…

Relations between amplitude reflectances and phase shifts of the p and s polarizations when electromagnetic radiation strikes interfaces between transparent media.

- GeologyApplied optics
- 1979

Simple and direct determination of complex refractive index and thickness of unsupported or embedded thin films by combined reflection and transmission ellipsometry at 450 angle of incidence,

- J. Opt. Soc. Am
- 1983

Principles of Optics (Pergamon

- New York,
- 1975

Definitions and conventions in ellipsometry," Surf

- Sci. 16,
- 1969

Un theoreme r6latif A la r6flexion m6tallique

- C. R. Acad. Sci
- 1950

Un theoreme r6latif A la r6flexion m6tallique," C

- R. Acad. Sci
- 1950