Directional Coupler Model

The Directional Coupler model is an analytical model that simulates an ideal 4-port directional coupler. Its S matrix is modeled as:

$S = \begin{bmatrix} r & i & t & c \\ i & r & c & t \\ t & c & r & i \\ c & t & i & r \end{bmatrix}$

The first and second ports in the S matrix (ports A₀ and B₀ in the schematic) are connected by an isolation coefficient $i$, similarly to the third and fourth ports (A₁ and B₁ in the schematic).

Direct transmission exists between the first and the third ports, as well as between the second and fourth ones, with transmission coefficient $t$.

The first and fourth ports are coupled through a coupling coefficient $c$, same as the second and third.

Finally, all ports have the same reflection coefficient $r$.

Multimode ports

In the case of multimode ports, the 4 ports must support the same number of modes. All coefficients must be specified as sequences with one value for each port mode. This model does not include mode mixing, i.e., all cross-coupling coefficients are zero.