Finite high-contrast grating, 2D, schematically
Finite high-contrast gratings,
2D simulations of corrugated dielectric membranes with the following specification [1, 2]: background refractive index nb = 1.0, refractive index of the guiding regions ng = 3.48, slab thickness h = 1.494µm, (sub-wavelength) grating period Delta = 0.716µm, "tooth" width a = 0.5012µm.  

Excitation by Gaussian beams with a full width at half maximum of 10µm (field, at x = 10µm, top of the computational window), at a vacuum wavelength of 2.0968µm, for normal incidence; TE polarization, the principal electric field component Ey is perpendicular to the x-z-plane of the computational window.

Transmission properties:
QUEP simulations of configurations with varying number N of periods; N = 0 indicates a structure with a single hole of width Delta-a. Transmittance T, reflectance R, and the power G carried away laterally by guided slab modes are evaluated.

N = 0 N = 1 N = 2 N = 5 N = 10 N = 15 N = 20

The links at the positions indicated by the bold upper tick marks lead to animations of the time harmonic electric field, and of the field modulus. Compare with corresponding simulations of what happens for a non-corrugated slab, and in case the membrane is absent.

[1]   C.J. Chang-Hasnain and W. Yang, High-contrast gratings for integrated optoelectronics, Advances in Optics and Photonics (4) 379-440, 2012
[2]   M. Maksimovic, Resonances in high-contrast gratings with complex unit cell topology, International Workshop on Optical Waveguide Theory and Numerical Modeling (OWTNM 2013), Enschede, The Netherlands, proceedings, paper O-1.2