1. (Optical communications laser) You are designing a VCSEL laser based on InxGal_„AsyPi.y - InP, for which In.Gai_xAsyPI p 52 micrometers thick, is the active layer, while alternating layers of Iti„Gal_.AsyPi_y (of the same composition as the active layer) and InP form the dielectric mirrors. 'The bandgap and index of refraction for InxGal,AsyPi..), (with y = (1-x)/0.465) are given by the equations below, while the absorption is given by the curve on the right:
(a) What is the composition of the active layer for a design wavelength of 1300 nm?
(b) What is the thickness of the layers forming the dielectric mirrors?
(c) What is the mode number of the peak radiation?
(d) What is the spectral separation between the modes of the cavity at around 1300 nm?
(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.
2. (Si pin photodiodes) A Si pin photodiode has the following characteristics and responsivity:
| Wavelength range[nm] |
Active area diameter[mm] |
Rise time [ps] |
Junction capacitance[pF |
Dark current[pA] |
NEP[WHz-1/2] |
| 400-1100 |
1.25 |
300 |
24 |
40 |
9x10-14 |
(a) Calculate the i-layer thickness for this device and the internal electric field for a reverse bias of 100 V (Er - 11).
(b) Given that for the electric field at point (a) the drift velocity for the charge carriers, is around - 6 x 104 mis, calculate the maximum drift time of the carriers across the i - layer.
(c) Compare the drift time of the carriers with the rise time specified for this device. Explain the discrepancy.
(d) What is the optimal load resistance to be used with this photodiode?
(e) What is the quantum efficiency of the device at 400 nm, 800 nm, and 1000 nm? (0 Calculate the minimum light intensity for the three wavelengths that would produce a photocurrent signal at least equal with the dark current.
(g) This detector is used across the specified wavelength range to detect signals with a bandwidth of 100 MHz. What is the minimum power required for a SNR equal with at least 1?