The Fresnel Fibre Story: a personal perspective, J. Canning
During a short visit to Melbourne University to work with Shane Huntington regarding the etching of the ends of optical fibres, I observed that the deposited layers highlighted by etching represented annuli of decreasing width the further away from the centre. This was analogous to the optimum phase ring layout of chirped linear Fresnel grating lenses. It was obvious immediately that the condition imposed by classical Fresnel analysis – namely that the area of each annuli be approximately equal – was automatically satisfied by the MCVD fabrication process used to make this fibre. The idea that one could readily make Fresnel lenses on the end of an optical fibre was attractive and although the central core was at odds with the rings in terms of phase matching, it was possible that even the humble fibre before us could achieve lensing. Upon my return to Sydney we confirmed that indeed there was focusing even if the coupling efficiency was low. We both patented and published this technology and Shane came up with one of the catchiest slogans in photonics I have come across: “by 2010 every house will have a Fresnel lens!”
Personally, this episode necessitated revaluation fibre optics completely. I now examined fibre propagation from the perspective of local coherent scattering leading to constructive interference in the forward propagating direction in an optical fibre. Further reading and I soon realised that fibres could in fact be treated purely as achieving a phase condition that one dreams of in the field concerned with diffractionless free space beam propagation. A fundamental analogy was raised: that the mathematical description of free space beams and waveguides was essentially describing the same attempt to control diffraction. In other words, despite the presence or not of a solid medium the goal is to achieve localised and sustained coherent interference to enable a “quantised” light to propagate without loss. A fibre is thus one solution to this problem that relies on continuous control of the near field. Diffractive axicons and lenses are another approach that aim to control the far field by effectively “coding” the near field to ensure a desired beam profile is achieved – sophisticated holographic filters nowadays can achieve marvellous things such as capillary beams that extend a few meters.
It was therefore intuitively obvious that by appropriate fibre design both the near field and the far field can be controlled in a fibre – thus the term Fresnel fibre was born. The first proof of principle experiment confirming that this new “paradigm” in fibre technology can be made real was carried out in our labs in 2002. We used a revitalised approach to fibre engineering based on Lucent Technologies air- structured fibres of the 1970s to achieve both propagation within an air hole and focussing at the far field. We patiently drilled a crude Fresnel design into a 10cm silica glass preform that was then drawn into optical fibre. This marked the first major transition in fibre theory and design. Such was the large transition that since our demonstrated results, simple Fresnel fibres based on Bragg grating assisted propagation (commonly known as Bragg fibres) have been made but almost no work has been carried out to examine the design impact on the far field or even optimal coupling into the fibre. I eventually convinced a colleague to have their student model chirped Bragg fibres, the simplest of the optimised Fresnel fibres, predicting superior performance to linear Bragg fibres. Several other groups have confirmed the concept of the Fresnel fibre theoretically but its implementation beyond the level we have demonstrated has been difficult. It therefore remains a new field where much technological innovation is required before it is exploited in practical low loss devices.
From a fundamental perspective the new approach to the fibre problem has tremendous repercussions for how we look at things. Coming from a different background, Sergei Khuklevsky, a theoretician from the PTFE Institute in Hungary, independently also realised the fundamental analogy between waveguide modes and free space beam propagation. The reason why this is more important than is currently recognised, I argue as follows: the same rigorous coherent mode scattering analysis used in the analysis of holographic apertures for creating diffractionless beams can also be applied to waveguides because it is a model soley dependent on the phase relations of the shaped light regardless of the mechanism that local interference arises, to give rise to a self compensating solution that ensures a “spatial non-linear soliton” propagates in the direction of choice. (The concept of a linear soliton is intriguing given that Allen Snyder was able to show that even the most non-linear solitons can be described by linear mathematics and should not be dismissed as easily as some have done so). Philosophically, dare I say there is an element here of David Bohm’s holographic universe theory – if we know all the phase perturbations in a system we can predict the movement and shaping of light without knowing that there is anything there other than interference. In other words this description dispenses with the concept of matter altogether and it is only when we operate within the confined parameters of our limited perception of the universe that we then proceed to conjure up the physical terms we are so bound to and which therefore define what we observe rather than define what is actually there.
Since the Fresnel fibre encapsulates near field control of all fibre types to date by local interference regardless of the mechanism it is in fact a generic description of all fibres to date including step-index, Bragg, chirped Bragg, and various bandgap fibres, for example. More specifically, since it is easier to absorb things slowly, I have applied the Fresnel concept to these fibres deliberately designed with recognition of the role of the virtual zones reflecting the desired phase jumps necessary to achieve the propagation one needs within an arbitrarily shaped waveguide. The first example was, therefore, a crude air hole version of a chirped Bragg fibre, where the holes were distributed roughly within the classical zone plates of the cylindrical waveguide.
Returning to a practical perspective, I have proposed several new areas of research:
1) A new approach to modelling all fibres based on coherent mode analysis such as that summarised compactly by Andrey S. Ostrovsky and others as a general representation of optics. This will take some time and require the initiative of a good theoretician.
2) Completely new “wild” fibre designs such as hyperbolic fibres that are the analogy of hyperbolic Fresnel lenses. These can now be designed using existing hole structured fibre technology.
3) Generation of novel structures that permit holographic beam shaping in the far field beyond the fibre (e.g. a capillary beam described by Andrey Ostrovsky).
There clearly remains a huge gulf between experiment and concept and it will be some time before the impact of this genuine new paradigm shapes fibre optics research. Similar concepts, however, are likely to be emerging within other existing fields that exploit advanced lithography and planar technologies - the "new" area of meta materials comes to mind (I propose there is an analogous "meta" material concept in fibres where the mode solution of a waveguide can be defined by a spatial "unit" independent of the actual photon wavelength of its constituent parts - this unit is significantly larger than the surrounding structure and will therefore display analogous metamaterial properties but on a macro scale that can be significantly larger than the photon wavelength - macro optics with large structured metamaterials.This in turn will lead to an optical example of complexity theory where the individual photons cannot predict this macro behaviour, another area of intriguing research).
Fortunately, our recent demonstrations of preserving structure in the nano domain suggests that in the not too distant future the refinement will lead to one day true low loss arbitrary Fresnel fibres designed and adapted for very specific functionality. However, funding will likely prove to be the major determinant of the progress in this field. In the meantime Fresnel fibres visibly remind us that the optical fields and modes we exploit in the fibre community and with which we are all intimately familiar with are determined by the geometry of the waveguide, a reflection of the quantised nature of the problem and the importance of classical phase – Bessel modes are a product of a radial symmetry whether it be in free space to confine a beam in all but the forward direction, or in the containment within cylindrical optical fibres. The way things interact subsequently determines the rules of engagement dragging us away from the eternal urge to find simple reductionist descriptions of everything that probably portray very little of the actual detail of the world around us.
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