Selective reflection by helicoidal liquid crystals. results of an exact calculation using the 4 x 4 characteristic matrix method

The exact calculation of the reflection from single domain aligned samples of helicoidal liquid crystals (SmC* or cholesterics) is performed using the 4 multiplied by 4 matrix formulation of Maxwell equations in anisotropic media. We show that the expansion, approximation up to the 1st order of Berreman and Scheffer, is not adequate to describe the real situation, especially concerning the short wavelength region (heights of peaks, number of branches in the reflection band and their dependence on the different parameters).