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 $\mathrm{\Delta }\lambda \left(\mathrm{FWHM}\right)=25\mathrm{pm}$ at $\lambda =1063.4\mathrm{nm}$ is achieved with the device of small total physical thickness $2L=5.52\mathrm{mm}$ .

© 2008 Optical Society of America

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