Reciprocal optical activity in multihelicoidal optical fibers

We have studied manifestation of optical activity for higher-order modes that propagate in optical fibers with multihelical distribution of the refractive index profile. We have shown that due to form-induced intermodal coupling between the fundamental modes and the higher-order modes the hybrid modes of such fibers are symmetric (antisymmetric) combinations of circularly polarized optical vortices with opposite orbital angular momentum. We have demonstrated that because of the spin-orbit interaction the system features circular birefringence for such hybrid modes. We have obtained analytical expressions for the coefficients of optical activity related to propagation of such hybrid higher-order modes. We have shown that for those modes the effect of optical activity greatly surpasses the one exhibited for the fundamental modes. The obtained results might be useful for predicting possible new phenomena concerned with propagation of higher-order fields in twisted photonic crystal fibers and for understanding the nature of optical activity for fundamental modes in them.

Figure 1

The model of a MHF ($\ell =5$) and the geometry of the problem. In a cross-section $z$ the frame $X^{\prime }{Y}^{\prime }$ rotated by an angle $qz$ with respect to laboratory frame $XY$ is introduced, in which a point $A$ has polar coordinates $\tilde{r}=r, \tilde{\phi }=\phi -qz$ (also $\tilde{z}=z$). There are shown the pitch $H$ and rotation of the electric vector ${\mathbf{E}}_{\mathrm{out}}$ of the outcoming field by an angle $\gamma$ with respect to the vector ${\mathbf{E}}_{\mathrm{in}}$ of the incoming field.

Figure 2

The difference $n_{+}-n_{-}$ in refractive index units (RIU) for higher-order modes at various orders of fiber symmetry $\ell$ (a) and the ratio of optical activities $A/A_{\mathrm{FM}}$ of higher-order modes and the fundamental mode (b). Fiber parameters: $n_{\mathrm{co}}=1.5, r_0=20{\lambda }_0, {\lambda }_0=800\mathrm{nm}, \delta =0.05, q=5{\mathrm{m}}^{-1}, \mathrm{\Delta }=0.05$.

Figure 3

The difference $n_{+}-n_{-}$ (in RIU) vs the height of refractive index profile $\mathrm{\Delta }$ (a) and the ratio of optical activities $A/A_{\mathrm{FM}}$ vs $\mathrm{\Delta }$ for higher-order modes and the fundamental mode (b); $\ell =5$, other parameters as in Fig. 2.

Figure 4

The difference $n_{+}-n_{-}$ (in RIU) vs wavelength (a) and the ratio of optical activities $A/A_{\mathrm{FM}}$ vs wavelength (b); $\ell =5$, other parameters as in Fig. 2.