  We study nanofibers with Bragg gratings from equidistant holes. We calculate
analytically and numerically the reflection and transmission coefficients for a
single grating and also for a cavity formed by two gratings. We show that the
reflection and transmission coefficients of the gratings substantially depend
on the number of holes, the hole length, the hole depth, the grating period,
and the light wavelength. We find that the reflection and transmission
coefficients of the gratings depend on the orientation of the polarization
vector of light with respect to the holes. Such a dependence is a result of the
fact that the cross section of the gratings is not cylindrically symmetric.
