Optical Activity in Twisted Solid-Core Photonic Crystal Fibers

In this Letter we show that, in spectral regions where there are no orbital cladding resonances to cause transmission loss, the core mode of a continuously twisted photonic crystal fiber (PCF) exhibits optical activity, and that the magnitude of the associated circular birefringence increases linearly with twist rate and is highly reproducible. In contrast to previous work on twist-induced circular birefringence, PCF has zero linear birefringence and an on-axis core, making the appearance of circular birefringence rather unexpected. A theoretical model based on symmetry properties and perturbation theory is developed and used to show that both spin and orbital angular momentum play a role in this effect. It turns out that the degenerate left- and right-circularly polarized modes of the untwisted PCF are not 100% circularly polarized but carry a small amount of orbital angular momentum caused by the interaction between the core mode and the hollow channels.

Figure 1

(a) Cut-back measurements (circles) and linear regression (lines) of the rotation angle of linear polarization at a fixed wavelength of 800 nm for PCFs with twist rates of 3.1, 6.3, and $10.1\mathrm{rad}/\mathrm{mm}$, with corresponding beat lengths of 57.1, 27.6, and 16.9 cm. (Inset) Scanning electron micrograph of the PCF. (b) Relative rotation angle deviation of the output polarization state as a function of input polarization angle.

Figure 2

(a) Circular birefringence as a function of twist rate at a wavelength of ${\lambda }_0=800\mathrm{nm}$. The error is the difference between the numerically modeled (by solving the full Maxwell equations with a finite element method) and the values of $B_C$ calculated using perturbation theory; (b) $B_C$ as a function of wavelength for a twist rate of $10.1\mathrm{rad}/\mathrm{mm}$.

Figure 3

(a) Axial component of spin angular momentum density, normalized so that the total energy flux is unity. (b) Normalized axial component of OAM density. Note the small OAM contribution in the vicinity of the fiber core, which leads to a non-negligible contribution to the total angular momentum density and becomes dominant when circular birefringence is considered.