Vertical Modes on Snake Gratings

In a waveguide, vertical (or transverse) modes are specific configurations of the electric and magnetic fields whose properties can be finely tuned using periodic structures. In this study, we investigate the excitation and propagation of vertical modes on a sinusoidal grating, periodically repeated along another spatial direction, referred to as a snake grating. This type of structure enables a significant enhancement of the coupling between incident light waves and vertical modes. Using the method of moments, in which a tensor product of a Fourier basis and Legendre polynomials serves as the expansion and projection functions, we demonstrate a strong sensitivity of vertical modes to the geometric parameters of the grating. The expected result is the excitation of vertical modes for both transverse magnetic (TM) and transverse electric (TE) polarizations on the snake grating, thus allowing more flexible light manipulation and the development of more efficient optical devices.