We perform a quantitative numerical calculation of the steady-state radiation spectrum in a slab of cold electrons which is illuminated by unpolarized collimated, high brightness temperature radiation. The process of induced Compton backscattering can dramatically increase the intensity of radiation reflected from the slab over the level predicted by spontaneous scattering when the incident radiation spectrum has a spectral index alpha > 1 (where the flux density S(n)u proportional to nu(alpha)). In this case, the reflected spectrum has a spectral index alpha greater than or equal to 1 up to a cutoff at the peak frequency (nu(0)) of the illuminating radiation spectrum. When the incident spectrum has a spectral index alpha < 1, the intensity of the reflected radiation is instead strongly reduced and a broad absorption-like feature appears in the reflected spectrum at nu greater than or similar to nu(0). In agreement with previous order of magnitude estimates, we find that induced Compton backscattering limits the brightness temperature at the peak of the transmitted flux density spectrum to (kT(B)/m(e)c(2))tau(T)(2) theta(2) = 1.0, where theta is the opening angle of the beam and tau(T), is the Thomson depth of the slab. The polarization of the backscattered flux can be exponentially magnified if the incident radiation has a small net polarization. Induced Compton backscattering also rapidly transfers momentum from the incident radiation beam to the scattering electrons and can significantly enhance the radiation pressure force on the illuminated side of the scattering plasma. Applying these results to a simple spherically symmetric model of a magnetized pulsar wind, we find that the pulsed emission from radio pulsars with P less than or similar to 0.1Pover dot(-15)(1/5) scattering. We argue that the electron density along the path of the radio emission must be substantially underdense relative to the predictions of the simplest wind model, perhaps as the result of a large induced radiation pressure force. Stimulated backscattering enhances the reflected flux density from the parsec scale material in the centers of radio-loud active galactic nuclei, and the flux from the reflection nebulae could be as much as a few percent of the total observed flux. The reflected flux density is characterized by S-nu proportional to nu and strong frequency-dependent polarization.
