Detectors and System Mar. 28, 2018

• Photodetection: Photoconductive effect is fast and used in communication.
Photovoltaic effect is slow and used in solar cells.
Exchange photons for electrons.
• Photo-current: I_{ph} = ccR P_{"in"} where ccR is responsivity ( A/W) and P_{"in"} is input optical power. Note - current I = I_{ph} + I_d where I_d is the dark current.
• Responsivity: ccR = (eta q )/(h nu) = eta {lambda (mum)}/1.24
Current is generated by excitation of electrons to upper level, i.e. h nu > E_g -> cut-off wavelength lambda_{th} = 1.24/E_g
Absorption of photons generates charges (electrons and holes)

Photodiode: Reverse biased to photoconductive regime of a diode. Electrons need to travel across the depletion layer to be excited. Output voltage V_{"out"} = I_{ph} R_L where R_L is the load resistor.
• Modulation response: two factors control it.
Transit time - Delta f = 0.35/tau_r where tau_r is the rise time or the time to travel across depletion layer.
Circuit time - tau_{"cr"} = 2.19 (R_L)_{eq} C_d and Delta f = 1/{2 pi (R_L)_{eq} C_d where C_d is the junction capacitance.
Example on calculation with detector response time

• Mean square value of noise current: Shot noise bar {i_S^2} = 2 q (bar{I_{ph}} + I_d) Delta f
Note: noise is proportional to signal
Thermal noise bar {i_T^2} = (4kT)/(R_L)_{eq} Delta f
Note: noise increases as R_L decreases.
Example for SNR calculation with DC signal
Comment on SNR calculation with AC signal

• Overall bandwidth budget: total system delay Delta tau_{sys} = sqrt(tau_r^2 + tau_t^2 + tau_f^2} and R_b = 1/(4 Delta tau_{sys})
tau_r -- delay of detector, tau_t -- delay of source, tau_f -- delay of fiber.