Numerical calculation of the operation wavelength range of a polarization controller based on rotatable wave plates

We calculate the operation wavelength range of polarization controllers based on rotating wave plates such as paddle-type optical fiber devices. The coverages over arbitrary polarization conversion or arbitrary birefringence compensation are numerically estimated. The results present the acceptable phase retardation range of polarization controllers composed of two quarter-wave plates or a quarter-half-quarter-wave plate combination, and thereby determines the operation wavelength range of a given design. We further prove that a quarter-quarter-half-wave-plate combination is also an arbitrary birefringence compensator as well as a conventional quarter-half-quarter-wave-plate combination, and show that the two configurations have the identical range of acceptable phase retardance within the uncertainty of our numerical method.