Show explicitly that the diffraction grating made by two beams interfering in a medium will give diffracted
Question:
Show explicitly that the diffraction grating made by two beams interfering in a medium will give diffracted output of a third beam consistent with momentum conservation of the photons. In other words, first calculate the interference pattern for two beams with the same wavelength and wave vectors k(vectors)1 and k(vectors)2 interfering in a planar medium. Assume that the medium then has index of refraction proportional to the intensity of the interference pattern in the plane. Last, calculate the Fraunhofer (far-field) diffraction pattern for a third beam with the same wavelength, and wave vector k(vectors)3 impinging on this medium. Show that the output pattern corresponds to beams with 
One can also show this for non-equal wavelengths, but then one must perform a volume interference pattern instead of just an interference pattern in a two-dimensional plane.
Step by Step Answer:
Let the electric fields of the two beams be Eewt and E2e2wt where we have already mad...View the full answer
