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Problem 2.3 (37.5 points) (Optical communications laser) You are designing a VCSEL laser based on In Gai-xAsyP1-y- InP, for which In,Gar-xAsyP1-y, 52 micrometers thick, is the active layer, while alternating layers of In,Gar-AsyPy (of the same composition as the active layer) and InP form the dielectric mirrors. The bandgap and index of refraction for In, Ga1-xAsyP1-y (with y = (1-x)/0.465) are given by the equations below, while the absorption is given by the curve on the right: 1×108 In Ga As P 1x 100 E. (y)(eV) = 1.35-0.72y+0.12y² 2.054 1x106 n(y) = 6.287+ 1.35 1-0.6245 -0. 2[um] Eg(y)[eV] 0.8 1.0 12 Wavelength (um) (m-1) 1x 105 1x10⁰4 8-NO---- 0.6 1.4 1.6 13
(e) If the gain curve of the active layer has a width of about 30 nm how many modes are emitted by the laser? (f) If the reflectivity of the back dielectric stack is about ~100% and the reflectivity of the output dielectric stack is ~90 % calculate the threshold gain for this laser. (g) If the carrier lifetime is Tsp 10 ps, calculate the threshold population inversion.