Cool. There are still areas where optical analogue computing is a in a
performance class of its own. I haven't looked up the papers, but I
gather that you get one butterfly per 3 dB coupler, so you'd need N
log2(N) couplers, and the whole thing would need to be phase coherent.

That could probably be done with silicon photonics, which would have the
additonal advantage of allowing heaters and circuitry to tweak all the
phase delays and coupling coefficients.

Would that approach have any advantages over the arrayed waveguide
grating approach?

Any reference to (a) Fourier Optics textbook(s) hich would go beyond the
paraxial domain (high NA) and include polarization effecs?

Peter Kuemmel's earlier list:
- Gu Min, "Advanced Optical Imaging Theory" (Springer Series in
Optical Sciences)
He uses Debye's approximation (stationary phase) for high NA systems.
- Masud Mansuripur, "Classical Optics and Its Applications"
There is a chapter which describes his technique to numerically
calculate
high NA systems. He has found a way to also sample high NA fields with
a processable number of sample points.
Papers:
- B. Richards and E. Wolf, "Electromagnetic diffraction in optical
systems. II,"
Maybe the first investigation of high NA diffraction with polarization
- Peter Török
http://www.imperial.ac.uk/research/photonics/pt_group/pubsconf/pubs.htm

W. Watson wrote:

I've looked over some optics texts that use FTs to solve problems.
With my very basic understanding of the physics behind optics, it's
something of a puzzle how they do get used.
[snip]

The most profound application of FT in optics imo, is that of a prism or grating
dispersing a ray of light:

The produced spectrum is just the Fourier transform of the original signal in
the frequency domain.

It's also possible to do an inverse Fourier, by passing the spectrum backwards
into a second prism and recovering the original signal.

In other words, dispersing prisms (and gratings) are mini Fourier and inverse
Fourier transform devices ;o)