Analytical solution of the fundamental waveguide mode of one-dimensional transmission grating for TM polarization

This article presents an analytical solution of the effective index of the fundamental waveguide mode of one-dimensional (1D) metallodielectric grating for TM polarization. In contrast to the existing numerical solution involving a transcendental equation, it is shown that the square of the effective index (n(Eff)) of the fundamental waveguide mode of 1D grating is inversely proportional to the slit width (w) and the refractive index (n(m)) of the ridge material and varies linearly with the incident wavelength (lambda). Further, it has also been demonstrated that the dependence of n(Eff) on the grating period (P) and the incidence angle (0) is minimal. Agreement between the results obtained using the solution presented in this article and published data is excellent. (C) 2011 Optical Society of America