Nonlinear active Huygens metasurfaces for reflectionless phase conjugation of electromagnetic waves in electrically thin layers

A possibility of almost perfect phase conjugation in electrically thin nonlinear sheets is shown for the normal incidence of the signal wave, using either symmetrical or asymmetrical particles and nondegenerate interaction with slightly different frequencies of the incident and phase-conjugated waves. Under these conditions, the use of linear and nonlinear Huygens sources for both linear (signal) and nonlinear (phase-conjugated) waves ensures zero or very small reflection for both of them. In perspective, this can lead to realization of reflectionless superlens based on three-wave interactions, as well to other applications based on reflection-free and electrically thin nonlinear layers.