Star coupler
A star coupler joins each of M inputs to each of N outputs. With as many inputs as outputs it is lossless, and each output takes 1/N of each input.
Ports
Inputs in 1 to in M on one side, outputs out 1 to out N on the other (each 1 to 32).
The model
The coupler is the \(M \times N\) corner of a \(K\)-point discrete Fourier transform, with \(K = \max(M, N)\). From input \(i\) to output \(j\), counting from zero,
\[\mathbf S_{ij} = \frac{a}{\sqrt K}\, e^{\,i 2\pi\, i j / K}\;\mathbf I,\]with \(a = 10^{-\ell/20}\) for an excess loss \(\ell\) (dB), the same both ways.
- With \(M = N\), the matrix is unitary when \(a = 1\). Each output takes \(1/N\) of each input’s power, and none is lost. A 2 × 2 star coupler is a 50:50 coupler, with a phase convention of its own.
- With fewer inputs than outputs, each input is still shared equally among all \(N\) outputs.
- With more inputs than outputs, each input reaches the outputs with only \(N/M\) of its power in all.
The DFT’s phases are what make the outputs of one input interfere as they should: light of one laser into all the inputs, with the right phases, can be steered into a single output.
Settings
| Field | Default | Meaning |
|---|---|---|
ins | 2 | Inputs |
outs | 4 | Outputs |
loss | 0.3 | Excess loss (dB) |
From the tool's own tables, file format version 1: the names are those in a .jekray file.
Assumptions
- The split is ideal and flat in wavelength and polarisation, with the DFT’s phases exactly.
- No light passes between inputs, or between outputs.
Related
- Splitter and combiner, 1 × N.
- 2×2 coupler.