Transmission Through a Diffraction Grating (a) The thickness of a thin transparent plate varies sinusoidally in the x direction, d(x, y) = [1 + cos(2x/A), as illustrated in Fig. 2.4-11. Show that the complex amplitude transmittance is (x, y) = ho exp[-j(n - 1)kdo cos(2wx/A)] where ho = exp[−j(n + 1)kodo] (b) Show that an incident plane wave traveling at a small angle ; with the z direction is transmitted in the form of a sum of plane waves traveling at angles 0 given by (2.4-9). Hint: Expand the periodic function (x, y) in a Fourier series. 0 = 0; q- + እ " (2.4-9) Grating Equation