The light reflected from scarab beetles illuminated with unpolarized white light is analyzed ellipsometrically and displayed as the sum of an elliptically polarized spectrum I(p) and an unpolarized spectrum I(u). A chirped stack of chiral resonators, each with a characteristic Bragg wavelength and partial realignment of birefringent material to a fixed axis, is proposed as a model for simulation of both reflection and polarization spectra. Possible mechanisms that effectively eliminate impedance mismatch at the air-elytron interface and allow some beetles to exhibit nearly perfect circularly polarized reflections are discussed. Results are presented for three representative beetles, Ischiosopha bifasciata, which is shown to be a narrowband left-circular polarizer; Chrysophora chrysochlora, a broadband left-circular polarizer; and Chrysina woodi, an elliptical polarizer. The methods that are developed are applicable to the more general problem of synthesis of reflectors with prescribed reflection and polarization spectra.