Question

4. (a)A GaAlAs laser diode has a 500 micron cavity length which has an effective absorption coefficient of 10 cm . For uncoated facets the reflectivities are0.32 at each end. What is the optical gain at the lasing threshold? (b) If one end of the lasers is coated with a dielectric reflector so that its reflectivity is now 90%, what is the optical gain at the lasing threshold? -1 Notice that required gain to overcome the loss can be reduced by coating on one side of the cavity and take the useful output on the otherside)

Answer 1

a) write the expression for gain thershold. g_th = alpha + 1/2L ln [1/R^2] Here alpha is the effective absorption coefficient of the material Ga A/As. L rightarrow is the length of cavity R_1 and R_2 are the mirror reflectivity's OR Fresnel reflection coefficients. Substitute 500 or 500 times 10^-4 cm for 2L R = 0.32 alpha = 10cm^-1 gth = 10 cm^-1 + 1/2(500 times 10^-4) ln [1/0.32^2] = 10cm^-1 + 1/(500 times 10^-4) ln [1/0.32^2] = 10cm^-1 + 22.78 = 32.78 cm^-1 Thus, optical gain at lasing threshold is 32.78 cm^-1 \r\n (b) Write the expression for gain threshold g_th = alpha + 1/2L ln [1/R_1 R_2] substitute corresponding values gth = alpha + 1/2 (500 times 10^-4) ln 1/(0.9) (0.32) = 10 + 12.44 = 22.44 cm^-1 Thus, optical gain at lasing threshold is 22.44 cm^-1