We investigate numerically the effect of weak Kerr nonlinearity on the transmission spectrum of a one-dimensional (1D) $\delta$-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 $|{\alpha }_c|$, 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.

• Received 30 August 2019
• Accepted 26 February 2020

DOI:https://doi.org/10.1103/PhysRevA.101.043830