Helical core optical fibers maintaining propagation of a solitary optical vortex

We study theoretically the mode structure of few-mode helical core optical fibers with small (up to a wavelength order) values of the helix pitch. We demonstrate that in such fibers, at certain values of pitch the fundamental $H{E}_{11}$ mode strongly hybridizes with $l=1$ optical vortices and the forbidden zone appears in the spectra of such hybrid modes, which results in their attenuation. We have shown that within the spectrum gap, the only forward-propagating guiding modes are represented by two circularly polarized optical vortices with opposite polarization and the same topological charge so that upon excitation of such a fiber with a circularly polarized beam, only a solitary optical vortex could be excited in it. Such “monovortex” fibers are found to be analogous to conventional monomode fibers that maintain the propagation of the $H{E}_{11}$ mode.

Figure 1

(Color online) One of the models of a helical core fiber: the spiral core is surrounded by an infinite cladding. The offset of the core’s helix is strongly exaggerated.

Figure 2

To the derivation of the refractive index modification in a small-offset helical core fiber. In a $z$ cross section, the bending is accomplished in the plane $z{x}^{\prime }$. The change in the refractive index in a point $(x,y)$ depends on the $x^{\prime }$ coordinate of that point.

Figure 3

Refractive index distributions for the models of helical core step-index fibers: (a) implied by Eq. (3), transversal refractive index variation along the $x^{\prime }$ axis (see Fig. 2), the dashed lines show $n$ for a straight fiber; (b) transversal variation of refractive index for the standard model (see Fig. 1) along the line connecting the central line of the core’s helix and the fiber’s axis, $d$ is the offset value; (c) equi-index lines for refractive index (3). While plotting (c), it is assumed that $n_{\mathrm{co}}=1.5$, $\Delta ={10}^{-3}$, $r_0=10\lambda$, and the effective curvature radius is $\rho =r_0∕\Delta$.

Figure 4

The solutions ${\beta }_i^{\left(0\right)}$ of the zeroth-approximation secular equation (13) versus $q$. The spectra of the forward-propagating modes are plotted by thick lines; dotted lines correspond to backward-propagating fields. The type of mode is indicated near the line.

Figure 5

Repulsion of spectral lines caused by intermodal hybridization near points (a)–(c). Note that near point (a), no forbidden spectral zone is formed due to coupling of two forward-propagating modes. In contrast, the coupling between forward- and backward-propagating fields near the points (b),(c) leads to the appearance of the spectrum gap located near $q_{b,c}$. Spectral lines in the zeroth approximation are plotted by dashed lines.

Figure 6

(Color online) Principal scheme of excitation of the OV in the few-mode helical core fiber with an oblique Gauss beam. If the wavelength of the incident circularly polarized Gauss beam GB is such that the band-gap condition (33) is satisfied, the only nondamping guided mode will be represented by a circularly polarized vortex OV. Note that the incidence angle is strongly exaggerated.