Scattering over Varying Amplification Grating

The scattering pattern from a narrow absorbing/amplifying grating is investigated. A simple model of a narrow amplifying grating is solved exactly numerically and approximately analytically for the regime where the beam’s wavelength is much shorter than the grating’s wavelength. The main results are: The incident angle divides the scattering pattern into two regimes: below and above the incident angles. The former regime has a weak dependence on the incident angle but has a strong dependence on the scattering one. In this regime, a new grating formula is derived. The opposite occurs in the latter regime, which is very sensitive to the incident angle, but has only weak dependence on the scattering angle. Consequently, at certain incident angles, all the scattering is concentrated in the first regime, i.e., all scattering angles are lower than the incident angle.