Generalization of Pancharatnam-Berry phase interference theory for fabricating phase-integrated liquid crystal optical elements

ABSTRACT

In this paper, we extended the methods for fabricating phase-integrated liquid crystal optical elements by interfering of orthogonal circularly polarised beams with different PB phase and generalised those methods as Pancharatnam-Berry (PB) phase interference theory. The generalised theory exhibits two kinds of interference ways. The first way takes place when various PB optical elements (PBOEs) are sequentially illuminated by a linearly polarised light in half-wave condition. The second way happens when the first PBOE is illuminated by a circularly polarised light in quarter-wave condition while the following PBOEs are in half-wave condition. The fabrication of fork polarisation gratings based on this generalised theory is used to confirm the two different interference ways. The generalised theory can better describe the interference of orthogonal circularly polarised beams with different PB phase and can be widely used for fabricating phase-integrated liquid crystal optical elements using existing PB phase device, which may promote the development and extensive applications of the PBOEs.

GRAPHICAL ABSTRACT

KEYWORDS:

• Pancharatnam-Berry phase interference
• phase-integrated liquid crystal optical elements
• forked polarisation grating
• vortex beam

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China under Grant [61605046, 61704053, 11574079]; Natural Science Foundation of Hunan Province under Grant [2018JJ3069]; and Fundamental Research Funds for the Central Universities of China