  We investigate numerically the effect of Kerr nonlinearity on the
transmission spectrum of a one dimensional $\delta$-function photonic crystal.
It is found that the photonic band gap (PBG) width either increases or
decreases depending on both sign and strength of Kerr nonlinearity. We found
that any amount of self-focusing nonlinearity $(\alpha >0)$ leads to an
increase of the PBG width leading to light localization. However, for
defocusing nonlinearity, we found a range of non-linearity strengths for which
the photonic band gap width decreases when the nonlinearity strength increases
and a critical non-linearity strength $|\alpha_{c}|$ above which the behaviour
is reversed. At this critical value the photonic crystal become transparent and
the photonic band gap is suppressed. We have also studied the dependence on the
angle of incidence and polarization in the transmission spectrum of our
one-dimensional photonic crystal. We found that the minimum of the transmission
increases with incident angle but seems to be polarization-independent. We also
found that position of the photonic band gap (PBG) shifts to lower wavelengths
when the angle of incidence increases for TE mode while it shifts to longer
wavelengths for TM mode.

Optics;Materials Science