Designing broadband and ultra broadband half wave plate by composite pulse control

Broadband and ultra-broadband half-wave plates with composite design were previously experimentally demonstrated by E. Dimova et. al., in Opt. Commun. 366, 382 (2016). To achieve broadband and ultra-broadband performance, the authors utilized the relative rotation between the individual identical half-wave plates as control parameters, thus simulating the well-known control technique of composite pulses from quantum optics. In this paper, we extend the broadband and ultra-broadband designs by relaxing the condition of having identical constituent half-wave plates and allow for their thicknesses to also be variable control parameters. We further relax the condition of having symmetric rotation angles and solve numerically for both control parameters - rotation angles and thicknesses of the birefringent plates. We show that the presented design is broadband over a much wider range of the wavelengths, compared to the original design, when using the same number of constituent half-wave plates.