Please give me detailed and step by step solutions Discuss the diffraction of an
ID: 1838216 • Letter: P
Question
Please give me detailed and step by step solutions
Discuss the diffraction of an optical plane wave of wavelength lambda from the following periodic structures, indicating in each case the geometrical configuration and the frequency shift(s): An acoustic traveling wave of wavelength. An acoustic standing wave of wavelength. A graded-index transparent medium with refractive index varying sinusoidally with position (period). A stratified medium made of parallel layers of two materials of different refractive indexes, alternating to form a periodic structure of period (see Sec. 7.1C).Explanation / Answer
(a)In the progressive acoustic wave of wavelength the separation between two consecutive maxima is and the width of each maxima is and hence the pattern of the progressiove acpoustic wave is equivalent to a plane diffraction grating with width of each slit as and the separation between two consecutive slits as . Thus grating element is(
Using the theory of plane transmission grating we get the condition of occurrence of princi[al maxima in the diffraction pattern as
Or
Or (i)
Where represent the order of interference maxima. The sign indicates that there are two principal maxima of the same order lying on either side of the zero order maximum
If the number of maxima in the progressive sound wave in path of the optical wave is N, then we get the series of minima of the diffraction pattern for
Where m has all integral values except 0,N,2n,,-----nN.
This condition gives
0r
Or (ii)
Secondary maxima will given by
(b) in case of standing accoustic wave the system will be equivalent to a plane transmission grating of the width of each slit as half of wavelength of the soundwave and the separation of two consecutive slits will also be the half of this wave lenth and then the above mentioned conditiond of principal maxima, minima and the secondary maxima will be written in the similar manner