Question

2. Lasers (20 points) A He-Ne laser operating atA-632.8 nm produces 50 mW of multimode power as its output. It has an inhomogeneously broadened gain profile with a Doppler linewidth Av1.5 GHz FWHM. The spectral profile of the gain coefficient in this case is given (V-Vo)2 y the Gaussian form Yo(v)-Yo(Vo) exp | WIth ΔνD_ ー resonator is 30-cm-long, and the refractive index of the He-Ne gas mixture is very close to that of the air: n-1 a). If the maximum small-signal gain coefficient is twice the loss coefficient α determine the number of the longitudinal modes of the laser b). Assuming that the laser resonator is optimized in such a way that one of the longitudinal modes is matched with the frequency vo (the maximum of the gain profile), find the fraction of the total output power emitted into a side-frequency (the mode with the frequency v- vo VF)

Answer 1

(a) The expression for the frequency between the adjacent longitudinal modes is as follows: с Δυν = 2nl Here, n is the refractive index, l is the length, and c is the speed of light. From the given data, the frequency between the adjacent longitudinal modes is as follows: с Δυ, = 2nl 3x108 m/s 2(1)(30x10-2 m) = 5x108 Hz Hence, the number of longitudinal modes of laser is as follows: Δυο N = Δυν 1.5 GHz 5x108 Hz 1.5x10° Hz 5x108 Hz = = 3