Optical Communications, 2nd Edition

5.5 MULTIMODE HETERODYNING

In Eq. (5.1.3), we wrote the general expression for heterodyning with a received field and a local field. We then specialized to the case where the signal was confined to a single diffraction pattern and the local field mode was spatially matched to it. In this section, we examine several generalizations of this case.

Let the received field produce the general expansion in Eq. (5.1.5), and assume the local field is itself expanded into the same set of orthogonal diffraction functions,

This corresponds to a multimode version of the local field, with each mode having power P_L = . The heterodyned waveform is again given by Eq. (5.1.3), with the crossterm now being

This represents the generalized crossterm produced from multimode heterodyning. When expanded in this way, we see that n_RL(t) is now the sum of envelope time functions, one from each mode. If the local field existed in only one mode, only the crossterm from that one mode would appear. Hence multimode heterodyning adds in contributions from all other heterodyned signal modes.

We now examine some special cases. Consider a strong local field occupying D_L spatial modes, heterodyned with a single mode signal ...