Generation of cylindrically symmetric modes and orbital-angular-momentum modes with tilted optical gratings inscribed in high-numerical-aperture fibers.

Optical fiber with high numerical aperture (NA) can efficiently relieve the degeneracy of higher-order linearly polarized modes. The degeneracy relief is investigated in two types of high-NA fibers, i.e., low-index-cladding fiber and high-index-core fiber. A naked-core fiber, as with low-index cladding, can be used theoretically to generate the orbital-angular-momentum mode (OAMM) HE21 and the cylindrically symmetric modes (CSMs) TM01 and TE01. A high-index-core fiber incorporated with high-contrast-index structure can be used similarly to obtain OAMM HE31. The generation of both CSMs and OAMMs required tilted optical gratings to couple the fundamental core mode HE11 into these modes. The tilt angle and modulation period of the grating fringes can be calculated simply and visually with the method proposed in this article.