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We report an optical method of generating arbitrary polarization states bymanipulating the thicknesses of a pair of uniaxial birefringent plates, theoptical axes of which are set at a crossing angle of {\pi}/4. The method hasthe remarkable feature of being able to generate a distribution of arbitrarypolarization states in a group of highly discrete spectra without spatiallyseparating the individual spectral components. The target polarization-statedistribution is obtained as an optimal solution through an exploration. Withina realistic exploration range, a sufficient number of near-optimal solutionsare found. This property is also reproduced well by a concise model based on adistribution of exploration points on a Poincar\'e sphere, showing that thenumber of near-optimal solutions behaves according to a power law with respectto the number of spectral components of concern. As a typical example of anapplication, by applying this method to a set of phase-locked highly discretespectra, we numerically demonstrate the continuous generation of a vector-likeoptical electric field waveform, the helicity of which is alternated within asingle optical cycle in the time domain.

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