Homodyne Detection Theory

9008-045

Consider two optical beams mixing on a photodiode (square-law detector), as illustrated in 9008-047. Let the beams be given by:

Received signal beam electric field = E_rcos(w_rt + ø),

Local-oscillator beam electric field = E_ocosw_ot.

The photodetector current is given by:

I ~ (E_r + E_o)²

I ~ [E_rcos(w_rt + ø) + E_ocosw_ot]²

I ~ E_r²cos²(w_rt + ø) + 2E_rE_ocos(w_rt + ø).cosw_ot + E_o²cos²w_ot

Replacing w_r by w_o,

I ~ ½E_r²[1 + cos2(w_ot + ø)] + E_rE_o[cos(2w_ot + ø) + cos ø]

+ ½E_o²[1 + cos2w_ot]

I ~ ½(E_r + E_o)² + E_rE_ocos ø