<![CDATA[A numerical study has been carried out on the effects of shallow sinusoidal modulation on the refractive index of linear and nonlinear medium. The result on the linear system demonstrates generally the existence of a transmission band gap at acertain range of wavelength as usually revealed by analytic solution obtained with strictly nonreflecting boundary condition. It is shown in the numerical results that a more general boundary condition leads to similar transmission characteristics as the device length becomes much larger than the modulation period. A further description is given on the variation of gap characteristics with the system parameters. The extension by including the nonlinear term representing the intensity dependent refractive index (IDRI) effect gives rise to a new feature of the transmission gap, exhibiting imperfect reflection characterized by the appearance of transmission channels in the gap. As the input intensity increases, further modification of the gap feature occurs in conjunction with the appearance and growth of hysteretic effect featuring multistable states useful for logic functions. The variations of hysteretic characteristics with respect to the system parameters are also described.]]>
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