By R. E. Slusher, B. J. Eggleton (auth.), Richard E. Slusher, Benjamin J. Eggleton (eds.)
Nonlinear optical reviews of periodic dielectric buildings have blossomed some time past twenty years. New fabrication concepts are generating fiber grating and multidimensional photonic crystals in fabrics the place the refractive index may be diverse through mild pulses and beams. hole solitons that may propagate at any speed from 0 to the rate of sunshine and spatial solitons that hinder the diffractive unfold of sunshine in waveguide arrays are examples of the recent phenomena defined during this booklet. Microstructured optical fibers enable regulate of the guided mode dispersion for broadband mild new release and new soliton phenomena. Many new fabrics and constructions are being built that would effect new optical units with purposes in optical communications and optical information processing. all of the above subject matters are addressed intimately during this book.
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Defining v to be the group velocity in units of V we find 1 ow aLl 2 aQ = v = ±J1- li: jLl2 . 20) Thus, consistent with Fig. 1, v = 0 at the edges of the photonic band gap (I Lli -+ Ii:), whereas far from the band gap (I Lli -+ 00), the group velocity is essentially that of the underlying uniform medium. For intermediate values of the detuning, the group velocity smoothly varies between these extreme values. 19) in a manner convenient for the discussion of Bloch functions below: Q = li:l'lvl, Ll± = ±li:I', I' = 1- v 2 - 1 2 .
Thus, although the equations for the two polarizations are ofthe same form, their dispersion relations will be different. Because we expect the coupled mode equations to give a good description of light near the Bragg wave number, we can use them to approximate the dispersion relation in the region close to ko. In fact, although we have stipulated that c5ni « ni, we could relax that restriction and the resulting coupled mode equations, based on the underlying Bloch functions of the periodic medium, would still provide a good approximation for the dispersion relation of the system near the Bragg wave number [16].
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