Question

Comparison of Stimulated and Spontaneous Emission. An atom with two energy levels corresponding to a transition with characteristics: λο 0.7 μιη, 4 3 ms, Δν 50 GHz, and Lorentzian lineshape, is placed in a resonator of volume V 100 cm3 and refractiven dex n-: 1 . Two radiation modes (one at the center frequency vo and the other at Urt Δν) are excited with 1000 photons each. Determine the probability density for stimulated emission (or absorption). If N2 such atoms are excited to energy level 2, determine the time constant for the decay of N2 due to stimulated and spontaneous emission. How many photons (rather than 1000) should be present so that the decay rate due to stimulated emission equals that due to spontaneous emission?

Check S&T Foundamental of Photonics

Answer 1

SOLUTION:

Given that

Given that The spontaneous emission rate is 1/tsp = 1/3ms stimulated emission rate is P_st = N - c/v sigma(v) sigma(v_0) = pi^2/8 pi tsp g(v_0) g(v_0) = delta v/2 pi/(delta v/v)^2 = 2/pi delta v sigma(v_0) = lambda^2/4 pi^2 tsp delta^2 = (0.7 mu m)62/4 pi^2 times 3ms times 50 GHZ = 8.28 times 10^-19 cm^2 \r\n N = 1/tsp v/c^sigma = 1/3 ms 100 cm^3/3 times 10^10 cm/s middot 83 times 10^-19 cm N = 1.34 times 10^12 photons W = I sigma/h v_o = 1/tsp I = hv_0/sigma tsp