A new approach is developed to calculate diffraction efficiency for a dielectric grating with an arbitrary refractive index profile. By treating a one-dimensional grating as a segment of a virtual two-dimensional (2D) photonic crystal, we exploit a rigorous theory of photonic crystal refraction and calculate the diffraction efficiencies. We expand, analytically in many cases, the dielectric function of the grating into 2D Fourier series. We find the eigenmodes for the virtual photonic crystal, and then use these eigenmodes to match the boundary conditions by solving a set of linear equations. In two such simple steps, the diffraction efficiencies can be computed rigorously without slicing the grating into thin layers.
© 2006 Optical Society of America
Diffraction and Gratings
Original Manuscript: February 10, 2006
Revised Manuscript: April 4, 2006
Manuscript Accepted: April 4, 2006
Wei Jiang and Ray T. Chen, "Rigorous analysis of diffraction gratings of arbitrary profiles using virtual photonic crystals," J. Opt. Soc. Am. A 23, 2192-2197 (2006)