Question

Question 3 An electromagnetic wave is coupled into a ring resonator. The resonance condition of the ring is that ma-nL, where m is an integer, λ is the wavelength, n is the refractive index of the medium and L is the geometrical length of the resonator path. a) If the resonator is made of glass, n = 1.46, and has a radius of 50pm, calculate the wavelengths of radiation that would meet the resonance condition for m =295 and m=296 b) If the ring resonator was converted into a linear resonator with mirrored end facets, what length of cavity would be required to match the m 295 and m 296 resonance conditions in (a) at the same wavelengths. (Hint: what is the new resonance condition equation?) In the linear resonator in part (b), what is the longest wavelength that can meet the resonance condition? c)

Answer 1

The answers are in the pictures along with explanations

(a) n = 1.46 r = 50mm therefore L = 2 pi r = 2 times pi times 50mm m lambda = nL lambda = nL/m for m = 295 lambda = 2 times pi times 50 times 10^-6 times 1.46/295 = 1.555 times 10^-6m = 1555nm for m = 296 lambda = 2 times pi times 50 times 1.46/296 = 1.550 times 10^-6m = 1550nm \r\n b) when light reflects of a mirror, it experiences a Phase change of 180 degrees. For a resonant mode, if should from a standing wave within the cavity eqn for resonant mode a lambda/2 = m L where L is the lengthy of the cavity now, for lambda = 1555 nm a = 295 n = 1.46 L = a lambda/2n = 295 times 1555 times 10^-9/2 times 1.46 = 157.1 times 10^-6m for lambda = 1550m a = 295 n = 1.46 L = 296 times 1550 times 10^-9/2 times