Problem Set 2

Collimated rays of light, with wavelength λ, shines on a square periodic structure at an angle Θ relative to the structure normal. Assume that every surfaces of this structure, except the tops, are absorptive. The light rays are scattered off the top surface as spherical wavelets as described by the Huygen’s principle.

1. Find exit angles where the scattered light intensity is maximized as a function of λ, a, and Θ. Explain how you come to this conclusion. (Hint, exit angle Θ is one such angle where the exit rays are interfered in phase. The other exit angles, such as &Theats;₂, correspond to the condition that the scattered rays are interfering constructively.)

1. If λ is 500 nm, a is 200 nm, and Θ is 10 degrees, calculate the smallest three exit angles where the scattered light intensity is maximized. The scattered light exiting at angle Θ is called the 0^th order diffraction spot, the light scattered at the next larger angle is called the 1st order diffraction, and so on.

1. If the incident light is a mixture of two colors, &lambda₁ = 500 nm, &lambda₂ = 600 nm, what is the angular separation of the 0th order diffraction from rays of these two colors. What are the angular separations of the 1st and 2nd order diffractions of these two color rays?