Local-Field Theory for Optical Phase Conjugation byDegenerate Four Wave Mixing in Mesoscopic Interaction Volumes ofCondensed Media

Abstract

A local-field theory describing optical phase conjugation incondensed media in the special case of degenerate four wave mixing isestablished. The aim of the theory is to form the framework formicroscopic studies of optical phase conjugation (i) ofevanescent fields in the context of near-field optics, (ii)in mesoscopic films and quantum wells, (iii) in smallparticles, and (iv) in lossy media where the fieldpenetration depth is comparable to or (substantially) less than thevacuum wavelength of the driving field. The aforementioned goal makesit necessary to abandon both the slowly varying envelope- and theelectric dipole approximations usually adopted in phase conjugationstudies where spatially slowly decaying or modulated fields are mixed.By keeping in the interaction Hamiltonian the term of second order inthe vector potential and in the current-density operator the term offirst order in the vector potential new microscopic field-matterinteraction processes of particular importance in the present contextare included. The physics of the various nonlinear microscopicprocesses is analysed, and systematised by presenting in diagrammaticform the nonlocal electrodynamics hidden in the nonlinear constitutiverelation. A new nonlocal conductivity tensor, enabling one to describethe degenerate four wave mixing process among the prevailing localfields, is presented and the eigensymmetries of its various parts areanalysed. Starting from the general local-field theory a degeneratefour wave mixing response tensor of relevance for media exhibitingtwo-dimensional translational invariance is established and discussed.In the last part of the paper an integral equation allowing one toobtain the phase conjugated local field inside and outside thenonlinear medium is established, discussed and formally solved, and itis pointed out that this equation for systems with two-dimensionaltranslational invariance often can be analysed analytically andnumerically using methods previously developed in theoretical studiesof the linear local-field electrodynamics of mesoscopicfilms.