Programmable universal photonic array

An N-port system, comprising:

• a plurality of N ports (N-port system);
• a plurality of DFrFTs;
• and
• a plurality of diagonal phase shifts, wherein the diagonal phase shifts and DFrFTs are arranged as alternating layers.

A photonic integrated circuit comprising:

• a plurality of (N+1) phase shifter arrays each comprising N phase shifters;
• a plurality of (N+2) waveguide arrays comprising N optical dielectric waveguides that are positioned in parallel and in proximity such that light from each optical dielectric waveguide evanescently couples to adjacent optical dielectric waveguides, the optical dielectric waveguides each having a length (L) given by
• L
• =
• π
• 2
• ⁢
• κ
• 0
• the proximity being such that coupling coefficients κi,i+1 between adjacent optical dielectric waveguides obeys:
• κ
• i
• ,
• i
• +
• 1
• =
• κ
• 0
• 2
• ⁢
• (
• N
• -
• i
• )
• ⁢
• i
• ⁢
• for
• ⁢
• i
• =
• i
• ,
• …
• ,
• N
• -
• 1
• ;
• where κ0 is a reference coupling value for suitably scaling all coupling coefficients κi,i+1 and the length L;
• each phase shifter in the plurality of phase shifters is directly cascaded with adjacent waveguide in the plurality of waveguides such that the phase shifters and waveguides alternate.