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Strutt, JW (Lord Rayleigh). On the Maintenance of Vibrations by Forces of Double Frequency, and on the Propagation of Waves Through a Medium Endowed with a Periodic Structure. Phil. Mag., S.5, vol.24, no.147, August 1887, pp.145-59. Please see the discussion that begins on page 156 and the formula for the stop-band-width, equation (74).

Strutt, JW (Lord Rayleigh). On the Remarkable Phenomenon of Crystalline Reflexion described by Professor Stokes. Phil. Mag., S.5, vol.26, no.160, September 1888, pp. 256-65.

Darwin CG. The Theory of X-ray Reflection, Part II. Phil. Mag., vol.27, 1914, pp.675-690. Darwin applied Rayleigh's ideas to "Dynamical X-ray Diffraction", i.e. the theory which includes the effect of X-ray standing waves, finite mini-gaps, etc. X-ray index contrast is too small to allow for a 3-d photonic bandgap.