Abstract
We investigate numerically the effect of weak Kerr nonlinearity on the transmission spectrum of a one-dimensional (1D) $\ensuremath{\delta}$-function photonic crystal. A new and interesting phenomenon is observed. It is found that, for weak defocusing nonlinearity, a defect-mode-like (DML) resonance peak is obtained inside the photonic band gap (PBG). That means that a weak nonlinearity acts as a defect introduced in a 1D perfect photonic crystal. A total transmission of this peak is found for a critical value of nonlinearity strength $|{\ensuremath{\alpha}}_{c}|$, while above this value a splitting of the DML resonance peak is observed. Calculations of the spatial dependence of the electric-field intensity reveal that DML resonance peaks have a similar origin as the well-known gap solitons appearing in nonlinear systems. The influences of nonlinearity strength, refractive index, incident angle, number of periods, and polarization on this DML resonance peak are analyzed.
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