(a) Clearly state the conditions required for the electric field in a medium with a spatially varying index of refraction to satisfy the equation

(b) Let the index decrease radially away from a central axis according to n(ρ) = n₀[1 − α²ρ²]. Ensure that the foregoing applies and show that a solution E = E(ρ) exp[i(hz − ωt)]ϕ̂ exists where the electric field decreases very rapidly away from the central axis. This is a technique used to produce wave guiding in an optical fiber.

Transcribed Image Text:

V²E- n²(r) 3²E c² at² î = 0.