ECE 212CN – Nanophotonics
Homework #2
For this homework, it will be useful to refer to the following literature on Rigorous Coupled Wave Analysis (RCWA): Moharam et al., J. Opt. Soc. Am. A, 12, 1068 (1995). Also refer to the Au dispersion information used in the attached file.
a) Using your favorite technical computing environment (e.g. Matlab, Fortran, BASIC, etc.), write your own code for performing RCWA. Your code should have the capability of solving the problem of the diffraction of both s- and p-polarized electromagnetic waves by periodic structures.
b) Referring to the literature cited above, recreate the four plots in Fig. 2 using your code. You should do this for both s- and p-polarizations; however, you may skip the conical mount. Note that this should serve as a decent confirmation of the accuracy of your code.
c) Consider the two-dimensional setup in Fig. A below. The grating is periodic to ±∞ in the x- direction with a period of Λ=550 nm. The grey boxes are composed of gold and the remainder of the area is free space. A plane wave is incident from the left side. Plot the diffraction efficiency as a function of kx for diffraction into the zeroth and first orders (kx is the x-component of the incident wavevector). Do this for both s- and p- polarizations and for both 400 nm and 500 nm wavelengths. Take the range of kx to be 0 ≤ kx ≤ 2w/c, where wis the angular frequency of the electromagnetic wave and c is the velocity of light. Make separate plots for the zeroth and first order efficiencies (i.e. you should end up with two plots containing four curves each). Briefly discuss your results.
d) Repeat part ‘d’ for a grating period of Λ= 150 nm. Briefly discuss your results and compare them to those from part ‘d. ’
Fig. A