An optical device includes a first and a second splitting device. Each of the first and second splitting devices have respective first and second input ports, respective first and second output ports, and a respective transfer matrix. A first optical waveguide is optically coupled to the first output port of the first splitting device and the first input port of the second splitting device. A second optical waveguide is optically coupled to the second output port of the first splitting device and the second input port of the second splitting device. The first and second optical waveguides are configured to introduce a phase shift of .pi. radians to the optical radiation propagating through the first optical waveguide with respect to the optical radiation propagating through the second optical waveguide. The transfer matrix of the second splitting device is the diagonal transpose of the transfer matrix of the first splitting device and the transfer matrix of the second splitting device is substantially different from the transfer matrix of the first splitting device.