Generalization of the effective index design approach to the diffracting surface relief photonic structures

Effective refractive index method is widely used for subwavelength photonics structures. Resonance domain photonic structures, wherein the grating period slightly exceeds the wavelength, deserve similar analytical treatment for theory and design. Proposed effective grating theory provides analytical solutions for rigorous light diffraction with arbitrary angles of incidence at periodic surface relief structures in the resonance domain of diffraction. Generalized TE and TM polarization modes for the conical diffraction are defined. Solutions with diffractive efficiency approaching to 100% are found and verified by numerical simulations. Now rigorous diffraction effects for resonance domain surface relief gratings at arbitrary 3D “conical” angles of incidence may be evaluated in an analytical form with almost the same simplicity as customary in the scalar diffraction. Optimization of the diffraction efficiency and coupling coefficients for high contrast photonics structures is discussed.