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 . 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 at is achieved with the device of small total physical thickness .
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