Answer Happy

8.3 Use the result from Problem 8.1 a reflectivity R to determine the full width at half maximum (FWHM) of the center peak in the grating reflectivity spectrum. Show that this is approximately equal to the width an given in Eq. (8-13). Textbook : Photonics and Lasers An Introduction An R= ( ) sin?(N8/2) sin?(8/2) n t Δλ λο = 1 N (spectral half-width, weak grating) (8-13)
8.1 The sum in Eq. (8-8) was determined graphically by adding vectors in the complex plane. An alternative is to use the mathematical identity 1 + x + x2 + ... + 1 - 1-X taking x = exp(-id). Show that this approach leads to a reflectivity An sin (N8/2) sin (8/2) R - ( ) n