Optical spectra of graded pitch structurally chiral media

We study optical spectra when circularly polarized light normally impinges on a structurally chiral medium (SCM) with variable pitch which locally has a [Formula: see text] point group symmetry. In this case, a structural period is defined as a length along the nonhomogeneity axis, where the director rotates a full turn. We considered three different pitch gradients: (a) The pitch value is constant in each structural period and it uniformly increases or decreases in subsequent periods. (b) The pitch value linearly increases or decreases from the initial to the final structural period. (c) The pitch value linearly increases or decreases in a period, with identical periods in the slab. In the first and second case, spectra show a Bragg-type broad-band. It is broader as the difference between the initial and final pitch value in the SCM increases. However, for the third case, there are regions where waves are mainly transmitted as right circularly polarized (RCP) or left circularly polarized (LCP) waves. Inside these regions there are multiple narrow bands for both RCP and LCP waves. Meanwhile, reflexion is almost absent in the spectra except for the optical bands, where there is reflexion for RCP and LCP waves. Thus, spectra exhibit conversion of RCP waves in LCP (LCP in RCP) waves. Moreover, we found that the center frequency of the bands are harmonics of the center frequency of the first band.