David M. Bird

We report a method to experimentally estimate the effective number of modes guided by multi-mode anti-resonant hollow core optical fibres using their far field intensity distributions. With a simple experimental setup and incoherent illumination, an arbitrary number of modes can be measured quickly and accurately.

Scattering from the microscopic roughness of glass-air interfaces that arises from frozen-in surface capillary waves is often the limiting factor in minimization of the propagation loss of hollow-core optical fibers. The strength of this scattering is typically modelled through calculation of the normalized electric field intensity, F, of the core-guided modes at the glass-air interfaces. An alternative formulation of F is proposed that resolves an ambiguity arising from the discontinuity of the normal component of the electric field across each interface. Theoretical analysis of a concentric-layers model of antiresonant, hollow-core fibers, backed up by numerical simulations of realistic fiber designs, shows that, for a given wavelength, F can be minimized by using a core surround of antiresonant thickness and that, to a good approximation, other structural features of the cladding make no significant difference to the value of F.

Antiresonant, hollow-core optical fibers are currently challenging or even exceeding the loss performance of conventional solid-core fibers. Despite this progress, there are aspects of the guidance mechanism in these fibers that are still not understood. For example, a physical mechanism to explain why negative curvature of the core surround is correlated with low loss remains elusive. It is shown that the glass elements of the cladding structure with an approximately radial orientation play a crucial role in determining the confinement loss by strongly shaping the wave fields in the azimuthal coordinate. This shaping, described as azimuthal confinement, can result in an evanescent field in the radial direction through the cladding, and this leads to a confinement loss that is substantially lower than would be the case without azimuthal confinement. A comprehensive theory of azimuthal confinement is developed, yielding an expression for the confinement loss of any fiber structure with a single antiresonant glass layer between the core and the outer glass jacket. This is tested by comparison with large-scale numerical simulations on two types of cladding structure. It is shown that negative curvature of the core surround has little or no intrinsic role in reducing confinement loss in fibers with a nodeless cladding structure. The power of azimuthal confinement is demonstrated in model structures where the confinement loss drops by more than two orders of magnitude as the radial width of the cladding is increased. It is anticipated that the concept of azimuthal confinement will be valuable in interpreting confinement loss in a wide range of existing antiresonant, hollow-core fibers and in the design of novel, low loss cladding structures.

A systematic analysis of the dependence of the confinement loss of an anti-resonant capillary on the curvature of the core surround is presented. The core boundary is described by circular arcs and the construction allows for a wide range of core shapes to be considered. It is found that both negative and positive curvatures substantially reduce the confinement loss relative to that of a circular anti-resonant capillary and that this effect is insensitive to the size of the core relative to the wavelength and to the properties of the glass capillary wall. In contrast, for a solid core surround there is a small increase in the confinement loss with curvature. Results of scalar and vector calculations are shown to be similar. A qualitative explanation of the results is proposed based on azimuthal confinement of the wave fields generated by the curved boundaries.

The dependence of the confinement loss of unjacketed and jacketed single-ring fibres on structural parameters and the wavelength is analysed with reference to an anti-resonant model for which an analytic expression for the loss is available. Provided leakage through the gaps between the cladding capillaries is suppressed, the loss of unjacketed structures follows the prediction of the analytic model closely in terms of the scaling with respect to the radius and glass thickness of the capillaries, and the ratio of the wavelength to the core radius. The absolute value of the confinement loss and its dependence on the dielectric constant differ significantly from the analytic model; these differences are discussed in terms of the negative curvature of the core-cladding boundary. The loss of jacketed structures does not follow the anti-resonant model as closely, but there is sufficient similarity to conclude that anti-resonance in the glass and air regions of the cladding is key to understanding the guidance mechanism.

We study the mid-infrared attenuation of antiresonant hollow-core fiber made of fused silica glass. The role of absorptive losses increases with wavelength but can be minimized by reducing the overlap of the trapped light with the silica. We show that this overlap is least at the lowest-order antiresonance condition, corresponding to the thinnest core wall, and for higher resonances scales with the core wall thickness. A record-low minimum attenuation of 18 dB/km measured in our fiber at 3.1 µm wavelength is not limited by silica absorption. We measured 40 dB/km attenuation at 4 µm wavelength, where the attenuation of bulk silica is 860 dB/m. We show that this corresponds to a modal overlap of 2.81 × 10⁻⁵ which is in good agreement with simulations, suggesting that at this wavelength, attenuation is limited by silica absorption. This enables us to predict the achievable attenuation at longer wavelengths as well. Extrinsic losses due to gaseous molecular absorption may make demonstration of such losses difficult in some spectral bands. In contrast to shorter wavelengths, where leakage loss is the primary attenuation mechanism, introducing additional elements into the cladding design is unlikely to reduce the attenuation further, and further loss reduction would require a larger core size.

Motivated by the recent development of hollow-core, microstructured optical fibres without a translationally-periodic cladding structure, an analysis of the symmetry-induced properties of the modes of a uniform fibre with C_Mv point group symmetry is presented. Modes are classified according to the irreducible representations of the longitudinal components of the electric and magnetic fields; the radial component of the electric field and azimuthal component of the magnetic field share the symmetry of the longitudinal component of the electric field, while the radial component of the magnetic field and the azimuthal component of the electric field have the same symmetry as the longitudinal magnetic field. The symmetry class of the lowest order modes in fibres with point group C_Mv with M from 1 to 10 is given. The work is closely related to previous analyses, but clarifies the symmetry relationship between the two orthogonal modes in a degenerate pair and how the different symmetries of the longitudinal electric and magnetic field components emerge from the governing equations.

An analytic expression is obtained for the confinement loss of model anti-resonant fibres consisting of concentric regions of air and glass. Hankel functions in the regions surrounding the air core are approximated by their asymptotic form; apart from this, results are correct to leading order in the small parameter 1/(k₀r_c), where r_c is the core radius and k₀ the free space wavenumber. The results extend and generalise previous solutions for propagation in a hollow glass tube and a thin-walled capillary. Comparison with exact numerical calculations shows that the analytic expression provides an accurate description of the loss, including its dependence on the mode, the core radius and the widths of the surrounding glass and air regions. The relevance of the results to the recent generation of hollow-core, anti-resonant photonic crystal fibres is discussed.