The Poincaré sphere representation is used to analyze the operation of wavelength-dependent birefringent optical networks. A broadband input signal is spread on the sphere into a linear spectral density of states locus, which is in general further deformed on passage through subsequent birefringent elements. Unlike alternative mathematical procedures, this representation gives a clear visualization of the evolution of the state of polarization within an element, the dependence of that state on optical wavelength, and the requirements of a practical device design. Finally, it makes possible the synthesis of a new class of networks not previously considered. © 1981, Optical Society of America.