Spin-orbit-interaction-induced generation of optical vortices in multihelicoidal fibers

C. N. Alexeyev, A. N. Alexeyev, B. P. Lapin, G. Milione, and M. A. Yavorsky

Phys. Rev. A 88, 063814 – Published 5 December 2013

Abstract

We have studied the effect of the spin-orbit interaction on generation and conversion of optical vortices in multihelicoidal fibers, that is, the fibers possessing a multihelical refractive index profile. On the basis of a fully analytical approach we have obtained the spectra of coupled modes and their structure. Specifically, we have established selection rules, under which the spin-orbit interaction mediates the conversion of optical vortices into vortices with the topological charge changed by $\pm (ℓ \pm 2)$ , $ℓ$ being the number of helical branches in refractive index distribution. Also, we have shown that the spin-orbit interaction can lead to generation of radially and azimuthally polarized TE and TM modes from optical vortices. We have also demonstrated that if such generation is mediated by a scalar-type perturbation of the fiber's form, it is possible only for weakly deformed fibers. For strongly deformed fibers such perturbation can result only in generation of vortices with zero total angular momentum. Additionally, we have studied the possibility of polarization control over the orbital angular momentum of the generated state in such a system.

Received 6 September 2013

DOI:https://doi.org/10.1103/PhysRevA.88.063814

Authors & Affiliations

C. N. Alexeyev^1,*, A. N. Alexeyev², B. P. Lapin¹, G. Milione^3,4,5, and M. A. Yavorsky¹

¹Taurida National V. I. Vernadsky University, Vernadsky Prospekt, 4, Simferopol, 95007, Crimea, Ukraine
²National Academy of Sciences of Ukraine, Karadag Nature Reserve, 24 Nauki strasse, Kurortnoe, Feodosia, 98188, Crimea, Ukraine
³Institute for Ultrafast Spectroscopy and Lasers, Physics Department, City College of New York of the City University of New York, 160 Convent Avenue, New York, New York 10031, USA
⁴Graduate Center of New York of the City University of New York, 365 Fifth Avenue, New York, New York 10016, USA
⁵New York State Center for Complex Light, 160 Convent Avenue, New York, New York 10031, USA

^*Corresponding author: c.alexeyev@yandex.ua

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Vol. 88, Iss. 6 — December 2013

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Images

Figure 1
The model of an $ℓ = 4$ MHF. Note that the pitch $H$ is 4 times greater than the minimal distance, at which the refractive index is restored. Shown schematically is the generation of an OV from $m$ = 0 Gaussian beam (intensity distribution is given).Reuse & Permissions
Figure 2
Plots of zero-approximation spectral curves and resonance points. (a) illustrates the statement that the scalar-perturbation term enables transitions with both the raising and the lowering of the orbital index of the incident mode ( $| 1, 3 〉$ , black solid line) by $ℓ$ (here $ℓ = 1$ , which stands for a helical-core fiber). In the point (a) it can be converted into the mode $| 1, 2 〉$ (blue dotted line) with the lowering of the orbital index, whereas in the point (c) it can be converted into the mode $| 1, 4 〉$ (red dashed line) with the raising of the orbital index. In the point (b), although the resonance conditions are met, no conversion between the modes $| 1, 2 〉$ and $| 1, 4 〉$ takes place since the dynamical selection rule [Eq. (11)] is not satisfied. (b) shows the spectral curves for the mode family $| m | = 1$ . Note a double degeneracy of $J = 0$ curves for $| 1, - 1 〉$ and $| - 1, 1 〉$ OVs. Inset shows degeneracy lifting due to the SOI with the forming of the $| TE 〉$ and $| TM 〉$ modes spectral curves.Reuse & Permissions
Figure 3
Transmission coefficient $T$ plotted in the reflectionless approximation for the SOI-induced conversion of the OV $| 1, 1 〉$ into the OV $| - 1, 5 〉$ in an elliptical spun fiber ( $ℓ = 2$ ). Fiber parameters: $n_{co} = 1.5$ , $Δ = 10^{- 2}$ , $δ = 5 \times 10^{- 2}$ , $r_{0} = 10 λ_{0}$ , $λ_{0} = 6.328 \times 10^{- 7} m$ .Reuse & Permissions
Figure 4
Controlling the OAM state of the outcoming beam by controlling the polarization state of the input field. By changing the circular polarization of the input OV with the topological charge 2 from right (red dashed line $| 1, 2 〉$ ) to left (blue dotted line $| - 1, 2 〉$ ) one can generate OVs of either charge 7 or 3 (black solid labeled lines). The SOI-induced conversion $| 1, 2 〉 \to | - 1, 7 〉$ ( $M = + 3$ ) occurs at $q_{01}$ , whereas the transformation process $| - 1, 2 〉 \to | 1, 3 〉$ ( $M = + 3$ ) takes place at $q_{02}$ (here $ℓ = 3$ ). Insets show repulsion of spectral curves due to mode coupling [see also Eq. (18)].Reuse & Permissions
Figure 5
Hybridization of spectral curves with nearly degenerate $J = 0$ curves. For the case where the width of the coupling area is much less than the distance between the $| TE 〉$ and $| TM 〉$ spectral curves (a) the two-mode coupling scheme is implemented and the transitions in such well-separated points run between the corresponding input mode $| α 〉$ (red line) and the $| TE 〉$ or $| TM 〉$ modes (blue lines) leading to transformation of spectral curves (see inset). In the opposite case (b) the mode coupling affects the input mode $| α 〉$ and one of the OVs $| 1, - 1 〉$ , $| - 1, 1 〉$ , which form the hybrid modes with the spectral curves $| 1 〉$ and $| 2 〉$ (see inset). The remaining OV of the pair $| 1, - 1 〉$ , $| - 1, 1 〉$ is uncoupled and its spectral curve (middle blue line in inset) does not hybridize.Reuse & Permissions
Figure 6
Schematic plot of the spectral curves in the intermediate case of comparable coupling constants $Q$ , $b_{1}$ in Eq. (29).Reuse & Permissions

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