User:Mcgarc/sandbox

Summary/actions: 1) DONE: Name change to ARF. (Should this page be about hollow core fibres in general? Or just anti-resonant fibres? If the former, then there should be a section on PBGFs and their operating principle and history, followed by a section on ARFs including Kagomé, single ring and nested. If the latter, then any reference to PBGFs should be removed.)

2) DONE Fix 'no dispersion' to low dispersion.

3) History: touching tubes, to icecream cone, to nodeless, to nested.

4) ADDED, but could probably be done better? Link ARROW model.

5) Can we use images in papers that have CC license.

6) Spell fibre the correction way.

7) Add eqn from David Bird's paper about anti-res from 2017

Anti-resonant hollow core fibre (ARF), also shortened to hollow core fibre (HCF), is a class of optical fiber where centre of the fibre is hollow, with a thin glass microstructure surrounding. The core, where the majority of the light propagates, does not contain any glass. The first design of such fibres were a variation on Photonic-crystal fiber, and as such the term technically is applied to any such fibre where the light guided in the centre is hollow. However, over time the core surrounding glass structures have become less complex and are variations of surrounding tubes. Although there are many types of hollow core fibres, this class of hollow core fibres are defined by the thin struts of glass in the cross section being antiresonant with guided wavelengths. The most commmon designs are the 'tubular' (also known as 'revolver') and Nested Antiresonant Nodeless fibre (NANF) designs.

Hollow core fibers can perform different functions to conventional optical fiber. The absence of dielectric medium in the core means that the optical mode can propagate without any dispersion..., wavelengths can be guided that are otherwise opaque or largely lossy in glass cores, transmit high-power laser light over long distances and they can be filled with gas for long interaction lengths. Due to the attenuation of silica being higher than air, they can also provide lower loss transmission for better telecommunication purposes, although there are many fabrication challenges of hollow core fibre to be addressed that increase the attenuation. In 2020 hollow core fibres have overcome the attenuation limit of standard optical fibers, by exhibiting NANFs that have losses comparable or lower in technologicall relevant wavelengths of 660, 850 and 1060 nanometers.

Description
Hollow core fibres have a central core, absent of any glass or structure, surrounded by microstructres which form the cladding. The surrounding structure is typically made of silica consisting of an outer most solid cylinder, which forms the outer diameter of the fiber. The inner structure surrounding the hollow centre is formed of nanometer thick silica structures. The guided light overlaps very little with the surrounding structure. And their refractive indicides.

Although hollow silica capillaries are a class of hollow optical fiber, including Bragg optical fibres where the inner capillary is formed of a distributed bragg reflector surface, they are not often considered when using the nomenclature of 'hollow core fiber' in the field. An inner structure of thin microstructured cladding is often expected when refering to 'hollow core fibers'. They are also known as 'anti-resonant fibre' (ARF).

There are many different designs which have evolved through refined understanding and fabrication capabilities: photonic band gap fibre, Kagomé, tubular and nested.

Uses
The absense of material in the core of the fibre allows for much lower interaction of the guided light with the surrounding glass. This makes the fibres very attractive in a much wider range of uses than conventional optical fibres due low latency, low attenuation, and low loss guidance at unconventional wavelengths. However, although hollow core fibres are well established in academic literature and hold lots of promise in a wide array of applications, their commercial avaliability is much more limited than solid core optical fiber.

Similar to conventional optical fibres, the biggest market of interest is in telecommunications. Hollow core fibres in particular could offer advantages in high-frequency securities trading, low-latency 5G services or transmitting at high optical powers. However, it is still a challenge to mass manufacture these fibres at in repeatable large yields of anti-resonant fibres at losses that are comparative to conventional optical fiber. Companies such as Comcast and Microsoft are investigating. Internet service provider Comcast announced plans to deploy end to end hollow core fibre connections. Shortly after, Microsoft acquired University of Southampton's hollow core fibre Corporate Spin-off company, Lumenisity.

The high damage threshold of air compared to silica allows anti-resonant fibres to carry higher laser powers. This could offer transformative benefits in medical ablation and surgery, manufacturing, construction and drill oil wells.

The hollow core also offers benefits in Raman spectroscopy where optical fibres are often used to carry data and signals from remote locations. Traditional solid core fibres can obscure the wanted signals with a large silica background as the light has interacted with long lengths of silica glass from travelling through the fibre. Hollow core fibres have very little overlap with the surrounding glass (~10-4), so are naturally free of silica background. These fibres have been shown to create sensitive gas sensing devices.

Commerically, there has been an increased interest in using hollow core fibres for quantum technologies, such as quantum computing. Low-loss hollow core fibres could become a key component in quantum memories

Operating principles
A conventional solid core optical fibre operates by total internal reflection of the light. This relies on the core having a higher refractive index than the cladding, which is not possible for a HCF as the core necessarily has a refractive index $$n_\text{co} = 1$$. Instead, they confine light through'anti-resonant guidance' described in the ARROW waveguide model.

Anti-resonant fibres
ARFs are HCFs which guide light through the anti-resonance effect. Because they cannot guide using total internal reflection, and there is no photonic band-gap forcing the light to propagate in the core of ARFs, they are inherently leaky, meaning that each time light in the hollow core of an ARF interacts with the glass microstructure surrounding it, a some light is lost. The loss can be minimised by ensuring that the walls are anti-resonant with respect to the wavelength of the light being guided.

When light propagating in the core of an ARF interacts with the thin glass of the cladding at the core boundary, some is reflected back into the core at the first boundary. The rest is transmitted through the glass and upon encountering the interface at the far edge of the glass, is either transmitted through to the rest of the cladding, or is reflected and makes m round-trips through the glass before also being transmitted to the rest of the cladding. The thickness of the glass bounding the core and the wavelength of the light determines the value of m and therefore whether the light that has made m round-trips through the through the glass constructively or destructively interferes with the light that was initially transmitted through. When constructive interference occurs, the bounding glass is highly transmissive and a lot of light is lost from the core, causing the fibre to have high loss, when destructive interference occurs, the bounding glass is highly reflective and the amount of light lost through the glass is minimised

This is analagous to the operation of a Fabry–Pérot interferometer. The transmission of a Fabry–Pérot interferometer for light at angle of incidence, $$\phi$$, is given by

$$T_\text{FP} = \frac{1}{1+F\sin^2(\delta/2)}$$

where

$$F = \frac{4R}{(1-R)^2}$$

is the coefficient of finesse and

$$ \delta = 2tn_\text{cl}\cos\phi$$

is the phase difference between successively transmitted rays.

Light is guided at wavelengths where the $$T_\text{FP}$$ is low, i.e. when the resonators are highly reflective and so confine the light to the core. This occurs for wavelengths satisfying $$\delta=m\lambda_m$$, where $$m \in \mathbb{Z}$$ and $$\lambda_m$$ is the $$m^\text{th}$$ order propagation wavelength. This gives rise to a series of transmission windows where light of a given wavelength can propagate along the HCF. This is shown in figure for a given fibre thickness. It is necessary to account for the refractive index of silica varying with the wavelength.



For a given wavelength, the resonator thickness required for propagation can be found by considering a ray propagating inside the fibre core. When the ray reaches the interface with the resonator at angle $$\theta$$ it is refracted according to Snell's law so that, $$ \sin\theta = n_\text{cl}\sin\phi$$. Taking the paraxial approximation, $$\sin\theta \approx 1$$ and therefore the path difference can be re-written $$ \delta = 2t\sqrt{n_\text{cl}^2 - 1}$$. It is therefore possible to write the resonance wavelengths as

$$ \lambda_m = \frac{2t}{m}\sqrt{n_\text{cl}^2 - 1}. $$