Heterodyne Detection Theory

9008-046

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 = E_rcos(w_rt + ø),

Local-oscillator beam = 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

I ~ ½E_r²[1 + cos2(w_rt + ø)] + E_rE_o[cos{(w_r - w_o)t + } + cos{(w_r + w_o)t + ø)}] + ½E_o²[1 + cos2w_ot]

I ~ E_rE_ocos{(w_r - w_o)t + ø}

where (w_r - w_o) is the difference (intermediate) frequency.