Cholesteric cored photonic fibre as a narrow optical filter

ABSTRACT

We consider an electromagnetic wave propagating in a cylindrical waveguide filled with a cholesteric liquid crystal whose helical axis is along the cylinder axis. Maxwell equations are established and analytically solved by imposing the appropriated boundary conditions for the Transverse Electric fields. We calculate the dispersion relation of the cholesteric fibre, from the transcendental equation given by the boundary conditions, for three components of the $TE$ modes. This involves to reconcile the simultaneous restrictions imposed by the cholesteric band gap and the wavelength tuning of the cylindrical structure. We found that the cholesteric fibre can be used as an optical filter from the infrared to ultraviolet spectrum, where it is a narrow frequency filter from the visible to ultraviolet. The wavelength of light travelling into the fibre could be selected by choosing the appropriate parameter values of the cholesteric fibre and the $TE$ mode.

Graphical Abstract

KEYWORDS:

• Cholesteric liquid crystal
• optical waveguide
• optical filter
• transversal electric modes
• dispersion relation

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Dirección General de Asuntos del Personal Académico, Universidad Nacional Autónoma de México [grant number IN101316 PAPITT].