Reflection of light by composite volume holograms: Fresnel corrections and Fabry-Perot spectral filtering

Abstract

Effects in composite volume Bragg gratings (VBGs) are studied theoretically and experimentally. The mathematics of reflection is formulated with a unified account of Fresnel reflections by the boundaries and of VBG reflection. We introduce the strength S of reflection by an arbitrary lossless element such that the intensity of reflection is R=tanh(2) S. We show that the ultimate maximum/minimum of reflection by a composite lossless system corresponds to addition/subtraction of relevant strengths of the sequential elements. We present a new physical interpretation of standard Fresnel reflection: strength for TE or for TM reflection is given by addition or by subtraction of two contributions. One of them is an angle-independent contribution of the impedance step, while the other is an angle-dependent contribution of the step of propagation speed. We study an assembly of two VBG mirrors with a thin immersion layer between them that constitutes a Fabry-Perot spectral filter. The transmission wavelength of the assembly depends on the phase shift between the two VBGs. Spectral resolution Deltalambda(FWHM)=25 pm at lambda=1063.4 nm is achieved with the device of small total physical thickness 2L=5.52 mm.

More on analyzing the reflection of a laser beam by a deformed highly reflective volume Bragg grating using iteration of the beam propagation method

“…For validation, an ideal VBG with very large grating strength has been analyzed and the numerical calculations were compared to analytical formula [16]. A VBG with a z-dependent background index change has also been analyzed with the z axis perpendicular to the grating planes and the results were compared to calculations using a matrix approach described in [17], in which the distorted VBG is represented by a large number of ideal gratings. These validation calculations demonstrate that the methods presented here are very accurate.…”

Optical elements containing semitransparent wavelike films

“…The optimal value of h corresponds to the first maximum of the Bessel function Jn(Ph) in (20). The diffraction efficiency DEn in the n-th diffraction order is defined similarly to expression (40) in [25]: where the asterisk means complex conjugation.…”

Modeling of phase volume diffractive gratings, part 2: reflecting sinusoidal uniform gratings, Bragg mirrors

“…2, which considers Fresnel reflections and the added effects of composite VBGs such as using two VBGs to form a Fabry-Perot cavity, but also does not address a reduction to practical formulae for designers. In spite of Kogelnik's theory of coupled waves 1 developed about 40 years ago, no reduction to practical formulae enabling precise design of VBGs has been provided up to today.…”