R. Beravat

Helically twisted photonic crystal fibres

Recent theoretical and experimental work on helically twisted photonic crystal fibres (PCFs) is reviewed. Helical Bloch theory is introduced, including a new formalism based on the tight-binding approximation. It is used to explore and explain a variety of unusual effects that appear in a range of different twisted PCFs, including fibres with a single core and fibres with N cores arranged in a ring around the fibre axis. We discuss a new kind of birefringence that causes the propagation constants of left- and right-spinning optical vortices to be non-degenerate for the same order of orbital angular momentum (OAM). Topological effects, arising from the twisted periodic ‘space’, cause light to spiral around the fibre axis, with fascinating consequences, including the appearance of dips in the transmission spectrum and low loss guidance in coreless PCF. Discussing twisted fibres with a single off-axis core, we report that optical activity in a PCF is opposite in sign to that seen in a step-index fibre. Fabrication techniques are briefly described and emerging applications reviewed. The analytical results of helical Bloch theory are verified by an extensive series of ‘numerical experiments’ based on finite-element solutions of Maxwells equations in a helicoidal frame. This article is part of the themed issue ‘Optical orbital angular momentum’.

Twist-induced guidance in coreless photonic crystal fiber: A helical channel for light

Twisting the periodic “space” within a coreless photonic crystal fiber creates gravitation-like forces that trap light. A century ago, Einstein proposed that gravitational forces were the result of the curvature of space-time and predicted that light rays would deflect when passing a massive celestial object. We report that twisting the periodically structured “space” within a coreless photonic crystal fiber creates a helical channel where guided modes can form despite the absence of any discernible core structure. Using a Hamiltonian optics analysis, we show that the light rays follow closed spiral or oscillatory paths within the helical channel, in close analogy with the geodesics of motion in a two-dimensional gravitational field. The mode diameter shrinks, and its refractive index rises, as the twist rate increases. The birefringence, orbital angular momentum, and dispersion of these unusual modes are explored.

Current sensing using circularly birefringent twisted solid-core photonic crystal fiber

Continuously twisted solid-core photonic crystal fiber (PCF) exhibits pure circular birefringence (optical activity), making it ideal for current sensors based on the Faraday effect. By numerical analysis, we identify the PCF geometry for which the circular birefringence (which scales linearly with twist rate) is a maximum. For silica-air PCF, this occurs at a shape parameter (diameter-to-spacing ratio of the hollow channels) of 0.37 and a scale parameter (spacing-to-wavelength) of 1.51. This result is confirmed experimentally by testing a range of different structures. To demonstrate the effectiveness of twisted PCF as a current sensor, a length of fiber is placed on the axis of a 7.6 cm long solenoid, and the Faraday rotation is measured at different values of dc current. The system is then used to chart the wavelength dependence of the Verdet constant.

Higher-order mode suppression in twisted single-ring hollow-core photonic crystal fibers

A hollow-core single-ring photonic crystal fiber (SR-PCF) consists of a ring of capillaries arranged around a central hollow core. Spinning the preform during drawing introduces a continuous helical twist, offering a novel means of controlling the modal properties of hollow-core SR-PCF. For example, twisting geometrically increases the effective axial propagation constant of the LP01-like modes of the capillaries, providing a means of optimizing the suppression of HOMs, which occurs when the LP11-like core mode phase-matches to the LP01-like modes of the surrounding capillaries. (In a straight fiber, optimum suppression occurs for a capillary-to-core diameter ratio d/D=0.682.) Twisting also introduces circular birefringence (to be studied in a future Letter) and has a remarkable effect on the transverse intensity profiles of the higher-order core modes, forcing the two-lobed LP11-like mode in the untwisted fiber to become three-fold symmetric in the twisted case. These phenomena are explored by means of extensive numerical modeling, an analytical model, and a series of experiments. Prism-assisted side-coupling is used to measure the losses, refractive indices, and near-field patterns of individual fiber modes in both the straight and twisted cases.

Excitation of modes in twisted single-ring PCF by prism-grating-coupling

Single-ring hollow core photonic crystal fibre (SR-PCF) has created much interest over the past several years because of the simplicity of the structure, relatively low transmission losses and broad guidance bands. SR-PCF consists of a ring of thin-walled capillaries (inner diameter d) arranged symmetrically around a central hollow core (diameter D). It has been shown that if d/D = 0.682, the LPci-like core mode is strongly confined by anti-resonant reflection at the capillary ring, whereas higher order modes (HOMs), such as the LP11-like mode, are resonant with the capillaries and leak strongly away [1]. This condition for HOM suppression can be tuned by spinning the fibre preform during drawing, so as to produce a helical structure. This extends the length of the spiralling capillaries, slowing down the axial speed of the light and permitting HOM suppression at values of d/D < 0.682 [2].

Single-circular-polarisation twisted single-ring hollow-core PCF

Recent developments in single-ring hollow-core photonic crystal fibre (SR-PCF) have made possible robust single-mode guidance over a broad bandwidth [1]—an important attribute in many applications, for example high power delivery of laser light and ultrafast gas-based nonlinear optics. Here we report for the first time that these fibres can be designed to transmit just one circular polarisation state if they are twisted continuously during fibre drawing [2], forming a helical structure.