We investigate the optical response of one-dimensional photonic crystal slabs for an incident wave from free space. The Maxwell equation is solved in an analytic manner using the eigenmodes for the empty lattice case (without periodic gratings), and compact formulas for transmittivity of the incident wave and excitation efficiency of waveguide modes are obtained. These formal results are visualized at certain parameters. The effect of width in the wave vector of incident wave is also discussed.
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Kazuki Koshino (2003) studied this question.