Question

A holographic transmission grating imposes phase modulation of (pi/2)*sin (2*pi*x/d) on incident plane wave beam, where d=1000 nm is time of the grating. An observation screen is located 5 cm from the grating and the input wavelength is 300 nm.

(a) Believe the radiation from just one period of the grating from x=-d/2 to d/2. Huygens principle states that the electric field amplitude at a point p is sum of the field amplitudes of an infinite number of point sources at the source plane. Taking N=200 point sources, calculate numerically and plot the amplitude and phase of the field amplitude at the observation screen in the region of (0 cm <=x<= 4 cm). utilize a 1 micrometer grid spacing to calculate p.

(b) with result from part (a) compute the amplitude and phase at the observation screen for a grating of 100 periods extending from x=-50 d to x=+50 d. Then compute the net intensity at the observation screen and plot it as a function of x in the region 0.01<=x<=3.99 cm. final field amplitude is just the addition of 100 slit radiations patterns as compute in (a) each shifted all along the x-axis by displacement of that slit from the origin x=0