Frequency-angular distributions of signal wave intensity are calculated for spontaneous parametric down-conversion and parametric frequency conversion in spatially nonuniform nonlinear media. Wave reflection from interfaces is taken into account, and both regular and irregular nonuniform distributions of second-order nonlinear susceptibility are considered. A unified approach using a scattering matrix and a generalized Kirchhoff law is applied in calculations of spontaneous and stimulated processes in dissipative nonlinear media. Interference of electromagnetic zero-point fluctuations of the vacuum, nonlinear interference, and nonlinear diffraction are examined for media with various absorptive properties. Theoretical foundations are developed for diagnostics of nonuniform distributions of the second-order susceptibility, based on measurement of the line profiles of nonlinear signals.
The Scharnhorst effect in quantum electrodynamics predicts a superluminal velocity shift
δc>0 at low photon frequencies due to vacuum fluctuations between two mirrors. Although theoretically robust (no causality violation), the effect is extraordinarily small (
δc/c≈10−32 for mirrors
1μm apart) and outside current experimental reach. Here we propose a condensed matter analogue, replacing the photons in the electromagnetic vacuum by phonon excitations of a Bose-Einstein condensate. In an idealized geometry, the two-dimensional surface of a cylinder (circumference
L) at zero temperature, the axial speed of sound is increased due to zero-point fluctuations of the condensate by
δc/c≃5×10−3g~ at
L≃2ξ, to first order in the dimensionless interaction constant
g~≃10−1 of the Bose gas of healing length
ξ≃1μm. This is 28 orders of magnitude larger than the photonic effect, basically because phonons have a self-interaction while photons only interact via massive electrons. We discuss the prospects for observation of the acoustic Scharnhorst effect, the main restriction being the low-temperature requirement.