Question

Q6) Photon lifetime. Calculate the photon lifetime for a semiconductor cavity in air which is fabricated by cleaving the two ends of the material to flat surfaces. The semiconductor has a refractive index of n -3.7 and a cavity length of L-300 μm. Express your answer in picoseconds.

Answer 1

Refractive index of semi conductor, n = 3.7 cavity length, L = 300 mu m Reflectance at each surface is same R = (n - 1)^2/(n + 1)^2 (R_1 = R_2) = (3.7 - 1)^2/(3.7 + 1)^2 = 0.33 Total attenuation coefficient is (alpha_t) alpha_t = alpha_s + 1/2L ln (1/R_1 R_2) = 20 cm^-1 + 1/(2 times 300 times 10^-4 cm) ln (1/(0.33) (0.33)) = 57.0 cm^-1 The photon cavity lifetime T_ph = n/c alpha_t = 3.7/3 times 10^8 m/s) (57 cm^-1) T_ph = 2.1637 ps