Generating arbitrary polarization states by manipulating the thicknesses of a pair of uniaxial birefringent plates

We report an optical method of generating arbitrary polarization states by manipulating the thicknesses of a pair of uniaxial birefringent plates, the optical axes of which are set at a crossing angle of {π}/4. The method has the remarkable feature of being able to generate a distribution of arbitrary polarization states in a group of highly discrete spectra without spatially separating the individual spectral components. The target polarization-state distribution is obtained as an optimal solution through an exploration. Within a realistic exploration range, a sufficient number of near-optimal solutions are found. This property is also reproduced well by a concise model based on a distribution of exploration points on a Poincar\'e sphere, showing that the number of near-optimal solutions behaves exponentially with respect to the number of spectral components of concern. As a typical example of an application, by applying this method to a set of phase-locked highly discrete spectra, we numerically demonstrate the continuous generation of a vectorlike optical electric field waveform, the helicity of which is alternated within a single optical cycle in the time domain.