Optical Heterodyne Reception Within Atmosphere

9009-002

In this analysis of Optical SETI it has been assumed that because of atmospheric turbulence effects, both the receiving and transmitting telescopes had to be outside planetary atmospheres.

In the case of the transmitting telescope, atmospheric turbulence would cause the transmitted beam to wander all over the cosmos. In the case of the receiving telescope, atmospheric turbulence would destroy the spatial coherence of the received signal, thereby drastically reducing the heterodyne efficiency.

We shall now describe a method by which the heterodyning efficiency may be maintained even in the presence of atmospheric turbulence.  In order to employ this technique we must have the cooperation of the Aliens!  Let us assume that an alien civilization might decide that the receiving civilization (us) would like to use telescopes within its planetary atmosphere.  What can the aliens do to facilitate this mode of reception?

If, and only if it is possible for the aliens to generate very high power narrow-band beacon signals, then they could transmit such a signal along with the modulated signal, so that the former acted like a pilot-tone.  The pilot-tone reference carrier would be spaced very close to the data signal as illustrated in diagram (9009-003).

Any wavefront distortion induced on the signal would also be induced on the reference tone.  By optically mixing the reference tone with the signal, we could extract a beat signal with all the intelligence superimposed, unimpaired by the turbulence.  In this system, the pilot-tone would effectively act as the first optical local oscillator

Consider two optical beams mixing on a photodiode (square-law detector).  Let the beams be given by:

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

Received pilot-tone beam electric field = E_plcos(w_plt)

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

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

     + ½E_o²[1 + cos2w_ot]

The three main frequency components are:

1.    E_rE_ocos{(w_r - w_o)t + ø}

2.    E_plE_ocos{(w_pl - w_o)t + ø}

3.    E_rE_plcos{(w_r - w_pl)t + ø}

The first two difference frequencies are much stronger than the third, since E_o >> E_pl.  Thus, we may ignore the third term.

Taking the first two terms and multiplying them together, we extract a signal:

I  ~ E_rE_plE_ocos{(w_r - w_pl)t + ø}

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

Each of these contributions from each photodetector that receives a bit of this signal will be in phase.  Thus coherent combining of these signal may be achieved.