The narrow slot in TM mode. Derive the update equations for the narrow slot problem of Section 12.2.3, only for the 2D TM mode. Start by drawing a similar diagram to that of Figure 12.7, but with
components.
(a) Write an FDTD simulation of a narrow slot for the 2D TM mode. Create a slot whose width can be varied from 0.1?x to ?x, and a material whose length in y is 10?y. Launch a sinusoidal plane wave from the y = 0 plane toward the slot, with a wavelength equal to 20?x. What is the amplitude of the wave that passes through the slot? How does it vary with the slot width?
(b) Repeat (a), but this time hold the slot width to 0.5?x and vary the slot length from ?y to 10?y. How does the transmitted amplitude vary with the slot length?