Transition radiation in cholesteric liquid crystal

ABSTRACT

We consider a constant velocity charged particle travelling in an arbitrary direction by a cholesteric liquid crystal. We calculate the time-dependent-induced polarisation in the cholesteric by the electric field generated by the charged particle. Thus, we express the radiation field originated by the induced dipole distribution in the cholesteric in terms of the cholesteric susceptibility. To simplify our procedure, we write Maxwell equations and the constitutive non-local equation for the cholesteric, in the Fourier space since in this representation the equations turn to be simple difference equations. We solve these equations iteratively by assuming small values for the cholesteric birefringence to find the first-order electric field produced by the charge particle immersed in the cholesteric. This allows us to obtain the dominant contributions of the radiation field one of which is the usual Cherenkov effect. We focus in the terms occurring for hypoluminic charged particle and calculate the radiated energy as a function of observing angle, frequency, velocity and direction with respect to the cholesteric axis.

Graphical Abstract

Acknowledgement

We ackowledge partial support from Conacyt and grant DGAPA-PAPITT IN 101316.

Disclosure statement

No potential conflict of interest was reported by the authors.