Inhibition of dipolar radiation in a momentum nonconserving nonlinear interaction

It has been shown in many occasions that the spontaneous emission rate of a dipolar radiative system can be strongly modified by the environment that surrounds it. Recently, it has been suggested that these changes could also be seen in very simple systems where the radiation is emitted only m one or two directions, as in surface second harmonic generation. In an experiment of SHG in front of a mirror, corresponding to the radiation of a sheet of dipoles at a variable distance from a surface boundary, Kauranen et al. [1998] observed that even when the total rate of radiation was suppressed, the field between the dipolar sheet and the boundary was finite and independent of this total rate. In this work, we have shown that this apparent contradiction can only be explained if the quadratic nonlinear interaction includes terms not conserving momentum, such as the term that considers the transfer of energy from the reflected SHG field to the incident fundamental and vice-versa.