## Abstract

We present a single-channel photonic band gap fiber design allowing for guiding light inside a water core, which is surrounded by solid microstructured cladding, consisting of an array of high refractive index strands in silica. We address all relevant properties and show that the microstructure substantially reduces loss. We also introduce a ray reflection model, matching numerical modelling and allowing for time-effective large-scale parameter sweeps. Our single channel fiber concept is particularly valuable for applications demanding fast and reliable injection of liquids into the core, with potential impact in fields such as optofluidics, spectroscopy or bioanalytics.

© 2017 Optical Society of America

## 1. Introduction

All-solid photonic band gap (PBG) fibers rely on the confinement of an optical mode inside a defect core which is surrounded by a regular array of high refractive index (RI) strands embedded in a low RI host. The confinement in such leaky waveguides is associated with the PBG effect, resulting from the close-to-unity reflection of the microstructured cladding at wavelengths at which the density of photonic cladding states (DOS) is small or even vanishes [1]. The RI contrast between strands and host impose strong interference of light propagating in the structured section, leading to the formation of distinct photonic band structures with varying DOS [2, 3] and giving rise to bandgaps which allow guiding an optical mode inside a defect core. Examples of all-solid PBG fibers with silica as host material include arrays of cylindrical strands made from GeO_{2}-doped silica [4, 5], tellurite [6], metaphosphate [7, 8], polymers [9, 10], chalcogenide [11] or even metals [12, 13]. PBG fibers made from low melting compound glasses have also been implemented, examples of which include silicate (e.g., SF6/LLF1 [14]) or chalcogenide (e.g. Te_{20}As_{30}Se_{50}/As_{38}Se_{62} [15]) systems. Due to the strong wavelength dependence of the PBG effect such fibers are highly suitable for spectral filtering of multiple selected wavelengths, with extinction ratios as high as 60 dB/cm [11], or for observing sophisticated nonlinear optical effects (e.g., trapped solitons [16]).

Currently used all-solid PBG fibers employ the same material for host and defect core, including a hexagonal lattice of cylindrical high RI strands with a defect defined by omitting one or more strands in the array’s centre. This particular geometry imposes limitations on the application of all-solid PBG fibers, as the solid core prevents introducing desired media into the light-guiding section. Based on this restriction, the application of all-solid PBG fibers is rather limited particular within spectroscopy, and therefore this design has thus not been widespread. Replacing the solid core by a liquid analyte or even a gas would greatly extend the range of potential application of all-solid PBG fibers, with the outstanding example of a water core which would yield immediate spectroscopic application within bioanalytics [17] or environmental science [18].

In contrast to all-solid PBG fibers, hollow core fibers (HCFs) include the ability for the introduction of various media into the holey fiber sections. Driven by promising application in areas such as nonlinear light generation [19], particle guidance [20], chemical microreactor [21, 22] or acousto-thermal detection [23] the interest in HCFs has regained substantial attention during recent times. Beside well-established platforms such as the PBG [24] or the Kagome [25, 26] designs, the anti-resonant geometry has been identified to be highly relevant due to simplified fabrication, low optical loss over large spectral bandwidth [27–30] and low susceptibility to bending [31]. All mentioned HCF designs rely on holey microstructures, which require having comparably complex cladding structures to sufficiently reduce the modal attenuation. For instance, hollow core PBG fibers demand hundreds of as-equal-as-possible thin-wall capillaries to be used during the stacking process. From the bioanalytical perspective, using HCFs with liquid analytes is challenging as liquid are typically injected into both core and microstructured cladding, making applicability of this platform with regard to biosensing questionable. The most widely used solution resolving this issue is to collapse the cladding holes via heating while keeping the core section open. Post-processing has been successfully shown [32, 33], but represents an additional and sometimes hard-to-reproduce implementation step, which should be avoided to make sample preparation as-straightforward-as-possible. For spectroscopic application, an ideal fiber geometry would combine the advantages of all-solid PBG fibers with a hollow or liquid core. One example geometry with such properties consists of one ring of densely-packed metallic nanowires surrounding an air core, leading to indefinite metamaterial cladding HCF [34, 35].

Here we introduce a novel fiber design which allows guiding low-loss modes in a water-filled core inside a PBG fiber consisting of an entirely solid microstructured cladding. The design relies on a hexagonal array of high RI strand embedded in a silica matrix surrounding a hexagonal water core, which allows for low modal attenuation over a substantial spectral bandwidth. The structure only includes one single hole in the array’s centre and thus water only enters the core section, avoiding the mentioned bottlenecks of the HCF design. Here we discuss all relevant optical properties, including PBG structure, modal discrimination and the dependency of modal attenuation on various structural parameters. We also introduce a planar reflection model which allows understanding the observed guidance by planar interface reflection of a single ray, matching full numerical calculations and yielding a fast and straightforward calculation approach for optimizing PBG designs.

## 2. Design

The cladding geometry considered here consists of an array of high RI strands embedded in a low RI matrix with a defect core of even lower RI [Fig. 1(a) and (b)]. The RIs of strands, matrix and core (*n _{s}*,

*n*and

_{c}*n*) have been chosen such to match those of arsenic trisulphide (As

_{w}_{2}S

_{3}), silica (SiO

_{2}) and water (H

_{2}O) at 900 nm (

*n*= 2.5,

_{s}*n*= 1.47 and

_{c}*n*= 1.33). It is important to note that the implementation of hybrid chalcogenide/silica fibers with strand of sub-micrometre diameter has been experimentally demonstrated in numerous works [11, 36–39], placing the implementation of the proposed design on solid grounds (more details on feasibility can be found before the conclusion section). The main structural parameters characterizing the solid cladding are the strand diameter

_{w}*d*, the centre-to-centre pitch

*Λ*and the number of rings

*N*. Our study assumes all materials to have no material attenuation, allowing scaling the geometry, i.e., normalize the various quantities to

*Λ*. Most of the simulations conducted assume

*d*/

*Λ*= 0.44, which is in accordance with typically capillary dimensions used in the stack-and-draw method.

The low RI core (i.e., water core) is formed by omitting entire rings of strands in the central section, maintaining the hexagonal geometry and leading to a hexagonal-shaped core, which can be characterized by either the shortest or longest possible discrete radius (*R _{s}* and

*R*) with

_{l}*R*=

_{s}*√(3)*/

*2*·

*R*[Fig. 1(b)]. The thickness of the inner silica wall facing the water (labelled as

_{l}*g*in Fig. 1b) is assumed to be half of the pitch (

*g*=

*Λ*/

*2*), which is in accordance with the stack-and-draw process. The realization of hexagonal shaped cores in microstructured fibers fabricated using stack-and-drawing is challenging but was experimentally demonstrated in various publications including HCFs [24] or Kagome-design [25, 40]. We believe that our proposed concept defines a novel motivation for the implementation of fibers with hexagonal core, which can substantially widen the application range of PBG fibers.

## 3. Photonic band gap simulations

As first step we calculated the density of cladding state (DOS) of the photonic crystal in the cladding using the Bloch Finite Elements Method (BFEM). This method works as follows: we build up the unit cell of the photonic crystal geometry with periodic boundaries, then calculate the propagation constant for each angular frequency with discrete Bloch vectors and add up the weighted number of modes for certain propagation constant and angular frequency [13, 41–43]. The spectral distribution (with regard to the normalized frequency *Λ*/*λ* with the vacuum wavelength *λ*) of the real part of the effective mode index (Re(*n _{eff}*)) reveals that our geometry exhibits several regions of zero DOS below the RI of the silica [Fig. 2(a)], which can be used for PBG guidance in case the water is replaced by silica. Within the region 0.53 <

*Λ*/

*λ*< 0.59 the domain of zero DOS falls below the RI of water [Fig. 2(b)], yielding the unique opportunity for guiding a fundamental mode inside the defect core of an all-solid cladding PBG fiber. Our simulations reveal that the appearance of this region is associated with high RI contrast between strands and host, which is hard if not impossible to obtain for typically used all-solid PBG fibers. Higher-order PBGs, which have been highlighted in other works (e.g., in [44]) are also visible here [Fig. 2(a)] but are not considered, as they support higher-order defect modes with practically difficult-to-excite mode profiles. Here we concentrate on the region of the fundamental PBG below the RI of water (magenta region in Fig. 2(b)).

## 4. Planar single interface reflection model

The low modal attenuation of PBG fibers originates from the high reflectivity of the microstructured cladding, which strongly reduces for increasing core diameters. In case of hollow core PBG fibers it was observed that the loss scales with inverse cubed of the core radius [45], which suggest a route towards ultralow loss guidance. As we have shown for the situation of an indefinite metamaterial cladding HCF with an air core diameter being much larger than the wavelength (*d* >> *λ*) [34, 35], it is possible to approximate the properties of the leaky modes by the reflection of a single wave on a planar interface. At sufficiently large core diameters, the model excellently approximates both real and imaginary part of *n _{eff}* (i.e., modal dispersion and modal attenuation) over a large span of parameters. The key feature of this model is that the calculation of the reflection properties is independent of the core radius and only demands a simulation volume which is a fraction of that required in full FEM calculations, yielding a straightforward simulation tool with substantially reduced computational effort. The calculations only involve understanding the reflection of a single wave at the core/microstructured cladding interface, making complex and time- and memory-intensive simulation of the entire geometry obsolete.

Similar to the mathematical derivation used in the reference [34] here we obtain the amplitude reflection coefficient of the microstructured cladding *r* by simulating the corresponding planar interface (Fig. 3) using FEM.

We found that a linear approximation of *r* with regard to small incidence angles *ψ* (*ψ* ≪ 1, Fig. 3) is not sufficient as in the case described in the reference [34], requiring to include the quadratic term, i.e., *r* = −1 + *V∙ψ* + *W*∙*ψ ^{2}* +

*O(ψ)*. Here we use a ray model that correlates modal loss and dispersion to power loss per reflection

^{3}*A*and reflection phase

*ϕ*, respectively. Both quantities are obtained by fitting the numerical data of

_{ref}*A*and with the following second order approximations:

*κ*of the supported modes is given by

*j*is the n

_{mn}^{th}zero of the Bessel function

*J*. From that we obtain the effective index of the specific situation of a perfectly reflection cladding using the relation

_{m}*k*=

_{w}^{2}*β*+

^{2}*κ*(

^{2}*k*=

_{w}*n*):

_{w}k_{0}*A*for a single reflection process and the distance

*L*between two reflections which is given by

*L*=

*4β∙R*/

*κ*≈

*4k*/

_{w}∙R^{2}*j*. From these relations we obtain the imaginary part of the effective index:

*β∙L*. In contrast to the situation of an ideal reflector, the microstructured cladding causes an additions phase shift

*ϕ*according to Eq. (2) which can be treated as an additional contribution

_{ref}*Δβ*=

*ϕ*/

_{ref}*L*to the propagation constant

*β*and leads to an additional term in the real part of the effective index:

## 5. Results

The behaviour of the complex effective index of the fundamental guided defect mode in the water-core all-glass cladding PBG fiber has been analysed here using FEM and the introduced ray model. The spectral distribution of *n _{eff}* qualitatively shows the same features generally observed in PBG fibers, which are low-loss transmission bands surrounded by regions of high loss, originating from a coupling of the defect mode to the supermodes formed in the microstructured cladding [1, 11]. For the structural parameters considered here a pronounced low-loss band is found for 0.47 <

*Λ*/

*λ*< 0.60, which is in accordance with PBG region observed the DOS calculations (magenta region in Fig. 2(b)). Both Re(

*n*) and Im(

_{eff}*n*) are fully reproduced by the ray model [Fig. 3(a) and 3(b)] across all regions of low loss. Close to the resonances, i.e., to the wavelengths the defect mode couples to the cladding supermodes, the assumption of a high cladding reflectivity is not fulfilled, leading to deviations of our model. These regions, however, are associated with unfeasible high attenuation and are therefore not relevant for practical applications. It is important to note that hexagonal shaped core makes the definition of the core radius required for the planar model to some extended undefined. Here we consider the two extreme values of core radius (

_{eff}*R*and

_{s}*R*, defined in Fig. 1(b)), showing that the evolution of Im(

_{l}*n*) of the hexagonal geometry (points in Fig. 4(a) and 4(b)) lies in-between the two curves calculated using the model (solid and dashed lines in Fig. 4(a) and 4(b)), revealing that guidance in water-filled all-solid cladding PBG fibers can be understood on the basis of the reflection of a ray at a planar interface.

_{eff}The relevance of the microstructure, i.e., the improvement of loss originating from PBG cladding can be quantified by comparing Im(neff) with the corresponding loss values of a water-filled silica capillary (i.e., a fiber with no microstructure, Fig. 4(c)), showing that the PBG effect for the particular example shown in Fig. 2 (6 rings included) reduces losses by a factor of about 45 at mid-gap frequency.

The results presented in Fig. 4(b) suggest that changing the water core radius significantly modifies modal attenuation, allowing adjusting the fiber geometry considered here to the demands imposed by the respective application. To quantify this dependency, we have analyzed the dependence of Im(*n _{eff}*) on the core radius at the mid-gap frequency (

*Λ*/

*λ*= 0.545) for a fixed number of rings by calculating the effective index at four different core radii (triangles in Fig. 5(a), data refer to

*R*) and fitting data points by a polynomial with the exponent being one fitting parameter. This procedure reveals that modal loss of the water-core all-solid PBG fibers scales with the inverse cubed of the core radius (FEM (red line in Fig. 5(a)): Im(

_{s}*n*) = 0.00178·

_{eff}*R*

^{-2.932}, model (purple line in Fig. 5(b)): Im(

*n*) = 0.00243·

_{eff}*R*

^{-2.99}), yielding a radius dependency which similar to that of hollow core PBG or metamaterial fibers [34, 45].

Another key aspect to understand is the influence of the number of rings on modal loss. Using a similar fitting procedure, we find that the imaginary part of the effective index scales exponentially (FEM (red line in Fig. 5(b)): Im(*n _{eff}*) = 1.275·10

^{−5}·10

^{-0.252∙}

*, model (purple line in Fig. 5(b)): Im(*

^{N}*n*) = 1.317·10

_{eff}^{−5}·10

^{-0.245·}

*) showing that adding one more ring of strands reduces loss by about 5 dB.*

^{N}Based on the match of model and FEM calculations for the various combinations of geometric parameters discussed (Figs. 4 and 5), the ray model can be used as a tool for fast and straightforward large scale parameter sweeps for optimizing modal properties. It is important to note that the model allows calculating the loss via analyzing the reflection of a ray at the boundary of the water core only, i.e., it requires a simulation volume which is only a fraction of that used in FEM, speeding up simulation times by orders on magnitude. Moreover, once the reflection parameters of the interface are determined, the modal loss can be determined for any core diameter without the necessity for further numerical calculations, allowing to solely concentrating on optimizing the reflection properties of the microstructured cladding. Here we analyze the loss behavior of the fundamental mode over a wide range of normalized frequencies and *d*/*Λ*-ratios (Fig. 6(a)), showing that for any configuration (i.e., *d*/*Λ*-ratio, y-axis in Fig. 6(a)), a low-loss transmission window with a particular spectral bandwidth can be found (yellow region in Fig. 6(a)). The spectral distribution of the modal attenuation investigated in the configuration discussed in Figs. 4 and 5 is shown in Fig. 6(b). Interestingly, the map of Fig. 6(a) contains all structural parameters of the microstructured cladding in dimensionless units, meaning that for a given combination of RIs (i.e., materials) this map can be used to identify experimentally feasible combinations of structural parameters.

Due to the comparably large core diameter considered here our design supports several leaky modes, requiring understanding how mode order affects the complex effective index. Here we calculated the real and imaginary parts of *n _{eff}* for the three lowest order modes (namely HE

_{11}, TE

_{01}and TM

_{01}) using both FEM and the ray model [Fig. 7(a) and 7(b)]. The phase index (Re(

*n*)) follows the overall expected behaviour of increasing values towards higher frequencies [Fig. 7(a)], with the HE

_{eff}_{11}mode showing the largest phase index at all frequencies considered, suggesting that this mode is the fundamental mode. The dispersions bend when approaching the resonances – an effect, which is particular pronounced in the case of the TM

_{01}mode – resulting from the anti-crossing of a cladding supermode with the guided defect mode [1, 11]. Towards the edges of the transmission bands the modes extend more into the microstructured regions, whereas the mode is well confined within the center domain of the bands (examples of corresponding spatial mode profiles are shown on the right side Fig. 7(b)). The spectral distribution of Im(

*n*) shows an interesting feature: Outside the PBG domain, the HE

_{eff}_{11}mode has the lowest loss of all modes as expected. Within the PBG, however, FEM simulations reveal that the TE

_{01}mode exhibits losses below the HE

_{11}mode – a phenomenon which was also observed for other types of HCFs such as the Omniguide design [46]. This particular behaviour distinguishes our design from typical all-solid PBG fibers, and reveals that the water-core PBG geometry yields a sophisticated waveguide combining different guidance principles. We believe that in contrast to all-solid PBG fibers, the additional water-silica interface, which itself has a close-to-unity reflection in case of large core radii, modifies the reflection properties of the cladding substantially yielding a situation which is different from regular all-solid PBG fibers.

The spectral distributions of the effective indices calculated with the ray model matches to those determined by FEM for the HE_{11} and TM_{01} modes, whereas an obvious discrepancy, which is particular pronounced for Im(*n _{eff}*), is found for the TE

_{01}mode. It is evident that the model incorrectly suggests lower loss within the PBG domain and disregard the anti-crossing at around

*Λ*/

*λ*= 0.6. This effect emerges because the model does not include the spatial profiles of the electromagnetic fields, i.e., neglects the actual shape of the core. A precise analysis of the mode fields shows that particular in the vicinity of the corners of the hexagonal core the fields are not entirely TE-polarized and include a significant fraction of TM components. The latter components are not included into the calculation of the TE-mode dispersion, as only the TE-related reflection parameters enter Eqs. (5) and (6).

To understand the influence of the silica wall thickness we simulated the spectral distribution of the complex effective index for various *Λ*/*g* ratios (HE_{11} mode). No significant spectral shift of the characteristic features (e.g., resonances or loss minima) was found in case the Λ/g ratio is changed by ± 25% (relative to *Λ*/*g* = 2). By analyzing *n _{eff}* at mid-gap frequency (

*Λ*/

*λ*= 0.54), we found that Re(

*n*) remains unaffected, whereas Im(

_{eff}*n*) changes by maximal a factor of two (relative to

_{eff}*Λ*/

*g*= 2) towards smaller

*Λ*/

*g*ratios (i.e., thicker walls), indicating a reduced influence of the microstructured cladding (inset of Fig. 7(b)). For larger ratio (i.e., thinner walls), the influence of the silica wall thickness on modal attenuation is substantially less pronounced in the attenuation distribution.

From the practical perspective, an obvious issue to be addressed is the experimental feasibility of the proposed design, i.e., is the fabrication of this geometry, which mainly concerns the inclusion of high RI materials into fibers and the realization of a hexagonal shaped core. Here one needs to take into account recent advancements in multimaterial fiber fabrication [47]: Various types of materials such as chalcogenides [11, 36–39], tellurites [6], semiconductors [48] or even metals [49–52] have been recently integrated into silica fibers mostly in the form of cylindrical micro- or nanowires using either post-processing (e.g., pressure-assisted melt filling [53] or high-pressure chemical vapour deposition [54]) or direct fiber drawing [49, 55]. Both techniques yield samples of metre scales, which are sufficient for many applications particular with regard to spectroscopy, placing fabrication on solid grounds. The implementation of a hexagonal shaped core remains challenging, whereas we are confident that our design can indeed be implemented since geometries with higher complexities, such as the Kagome fibers [56] or PBG fibers [24], have been experimentally realized.

It is important to note that our design includes core diameters of the order of a few tens of micrometers, which allows either using free-beam excitation via lens coupling or butt coupling using commercially available delivery fibers. Efficient and mode-selective free-beam excitation of the fundamental mode of highly nonlinear liquid-core fibers (carbon-disulfide filled silica capillaries) with coupling efficiencies of around 50% using optofluidic mounts was recently demonstrated by the authors [57]. Moreover, our design allows producing fibers with outer diameters matching those of commercially available fibers, enabling to butt couple our design to multimode fibers and therefore allowing interfacing the water-core all-solid cladding design with microfluidic technology.

## 6. Conclusion

Photonic band gap fibers rely on guiding light in a defect core within arrays of high refractive index strands, representing a geometry with great potential in many fields, whereas the use of solid cores has prevented widespread application of this type of fiber, particular within fields such as spectroscopy, bioanalytics or medicine. Here we introduce a novel fiber design allowing for guiding a leaky waveguide mode in the water core of an all-glass cladding photonic band gap fiber, effectively combining the advantages of photonic band gap fibers with those of tube-type waveguides. Our geometry includes one single central channel, whereas the remaining cladding entirely consist of solid material, yielding a flexible and low-loss light-pipe-type fiber waveguide with low optical attenuation. We reveal all relevant optical properties (e.g., spectral distribution of complex effective index, dependency of loss on number of rings and water core radius) and show that the microstructure substantially reduces loss by more than one order of magnitude compared to a capillary. We additionally introduce a single interface ray model, matching both real and imaginary parts of the complex effective index of the fundamental mode and revealing that guidance in water-filled band gap fibers can be described by the reflection of a single ray at the core/microstructured cladding boundary. The model demands extremely small simulation volumes and only requires studying the reflection at the water interface without the necessity to include the entire core section, yielding a straightforward and fast simulation approach for large-scale parameters sweeps.

The particular features of having an entirely solid cladding and a single channel in the structure’s centre at comparably small core diameters is of great relevance particular for the field of fiber-based optofluidics: Compared to large-core tube-type waveguides such as leaky capillaries, Teflon based tubes and metal-coated tube waveguides, our design provides long light/liquid interaction lengths at low modal attenuation levels even at core diameters of a few tens of micrometre only, whereas the other mentioned waveguides can have core dimensions in the millimetre range (e.g., the Teflon AF waveguide discussed in [58] has a 1mm core diameter). Another advantageous of our design is the potentially small outer diameter of the final fiber, which allows straightforwardly integrating the design into microfluidic chip-based devices. The solid cladding and the single central channel represent key features of our design, as they avoid several problems of optofluidic hollow core fibers such as undesired penetration of liquid into the side channels (and thus avoids the risk of bubble formation in the cladding), uncertainties in the optical characterization, and a change of the spectral characteristics of the filled fiber. All these points clearly show that the water core all-solid cladding photonic band gap fiber design gives rise to a unique device with improved properties compared to tube-type waveguides and holey hollow core fibers with regard to optofluidic application, as it allows using samples “directly from the spool” and thus having the potential to substantially enhance the field of tube-waveguide and fiber-based optofluidics.

The concept of guiding light in a water core using a fiber structure with only one single hole intrinsically suggests application within absorption [18] or Raman [59] spectroscopy to measure, e.g., extremely small concentrations of analytes, yielding a practically-relevant motivation for the implementation of such kind of sophisticated PBG fibers. Future research will target to clarify if the presented concept can be transferred to fibers with an air core to allow for studying gas-light interaction in the guiding core section only.

## Funding

German Research Foundation (Grant SCHM2655/6-1, SCHM2655/8-1); Thuringian State Projects (2015FGI0011, 2015-0021, 2016FGR0051); European Regional Development Fund (ERDF); European Social Funds (ESF).

## Acknowledgments

We thank Dr. Ron Fatobene for the discussion and kind support on FEM simulation with COMSOL and the research group Fiber Sensors of the Leibniz Institute of Photonic Technology for the encouraging working environment.

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**24. **R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. S. Russell, P. J. Roberts, and D. C. Allan, “Single-mode photonic band gap guidance of light in air,” Science **285**(5433), 1537–1539 (1999). [CrossRef] [PubMed]

**25. **F. Couny, F. Benabid, and P. S. Light, “Large-pitch kagome-structured hollow-core photonic crystal fiber,” Opt. Lett. **31**(24), 3574–3576 (2006). [CrossRef] [PubMed]

**26. **P. Ghenuche, S. Rammler, N. Y. Joly, M. Scharrer, M. Frosz, J. Wenger, P. S. Russell, and H. Rigneault, “Kagome hollow-core photonic crystal fiber probe for Raman spectroscopy,” Opt. Lett. **37**(21), 4371–4373 (2012). [CrossRef] [PubMed]

**27. **F. Poletti, J. R. Hayes, and D. Richardson, “Optimising the Performances of Hollow Antiresonant Fibres,” in *37th European Conference and Exposition on Optical Communications*, OSA Technical Digest (CD) (Optical Society of America, 2011), Mo.2.LeCervin.2. [CrossRef]

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**29. **A. Hartung, J. Kobelke, A. Schwuchow, J. Bierlich, J. Popp, M. A. Schmidt, and T. Frosch, “Low-loss single-mode guidance in large-core antiresonant hollow-core fibers,” Opt. Lett. **40**(14), 3432–3435 (2015). [CrossRef] [PubMed]

**30. **B. Debord, A. Amsanpally, M. Chafer, A. Baz, M. Maurel, J. M. Blondy, E. Hugonnot, F. Scol, L. Vincetti, F. Gérôme, and F. Benabid, “Ultralow transmission loss in inhibited-coupling guiding hollow fibers,” Optica **4**(2), 209–217 (2017). [CrossRef]

**31. **S. F. Gao, Y. Y. Wang, X. L. Liu, W. Ding, and P. Wang, “Bending loss characterization in nodeless hollow-core anti-resonant fiber,” Opt. Express **24**(13), 14801–14811 (2016). [CrossRef] [PubMed]

**32. **H. P. Gong, C. C. Chan, Y. F. Zhang, W. C. Wong, and X. Y. Dong, “Miniature refractometer based on modal interference in a hollow-core photonic crystal fiber with collapsed splicing,” J. Biomed. Opt. **16**(1), 017004 (2011). [CrossRef] [PubMed]

**33. **G. Fu, W. Jin, X. Fu, and W. Bi, “Air-Holes Collapse Properties of Photonic Crystal Fiber in Heating Process by CO2 Laser,” IEEE Photonics J. **4**(3), 1028–1034 (2012). [CrossRef]

**34. **M. Zeisberger, A. Tuniz, and M. A. Schmidt, “Analytic model for the complex effective index dispersion of metamaterial-cladding large-area hollow core fibers,” Opt. Express **24**(18), 20515–20528 (2016). [CrossRef] [PubMed]

**35. **A. Tuniz, M. Zeisberger, and M. A. Schmidt, “Tailored loss discrimination in indefinite metamaterial-clad hollow-core fibers,” Opt. Express **24**(14), 15702–15709 (2016). [CrossRef] [PubMed]

**36. **S. Wang, C. Jain, L. Wondraczek, K. Wondraczek, J. Kobelke, J. Troles, C. Caillaud, and M. A. Schmidt, “Non-Newtonian flow of an ultralow-melting chalcogenide liquid in strongly confined geometry,” Appl. Phys. Lett. **106**(20), 201908 (2015). [CrossRef]

**37. **S. Xie, F. Tani, J. C. Travers, P. Uebel, C. Caillaud, J. Troles, M. A. Schmidt, and P. S. J. Russell, “As2S3-silica double-nanospike waveguide for mid-infrared supercontinuum generation,” Opt. Lett. **39**(17), 5216–5219 (2014). [CrossRef] [PubMed]

**38. **K. F. Lee, N. Granzow, M. A. Schmidt, W. Chang, L. Wang, Q. Coulombier, J. Troles, N. Leindecker, K. L. Vodopyanov, P. G. Schunemann, M. E. Fermann, P. S. J. Russell, and I. Hartl, “Midinfrared frequency combs from coherent supercontinuum in chalcogenide and optical parametric oscillation,” Opt. Lett. **39**(7), 2056–2059 (2014). [CrossRef] [PubMed]

**39. **N. Granzow, M. A. Schmidt, W. Chang, L. Wang, Q. Coulombier, J. Troles, P. Toupin, I. Hartl, K. F. Lee, M. E. Fermann, L. Wondraczek, and P. S. J. Russell, “Mid-infrared supercontinuum generation in As2S3-silica “nano-spike” step-index waveguide,” Opt. Express **21**(9), 10969–10977 (2013). [CrossRef] [PubMed]

**40. **C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Müller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, “Low-loss hollow-core silica/air photonic bandgap fibre,” Nature **424**(6949), 657–659 (2003). [CrossRef] [PubMed]

**41. **P. S. J. Russell, “Photonic-crystal fibers,” J. Lightwave Technol. **24**(12), 4729–4749 (2006). [CrossRef]

**42. **J. M. Pottage, D. M. Bird, T. D. Hedley, J. C. Knight, T. A. Birks, P. S. Russell, and P. J. Roberts, “Robust photonic band gaps for hollow core guidance in PCF made from high index glass,” Opt. Express **11**(22), 2854–2861 (2003). [CrossRef] [PubMed]

**43. **J. C. Flanagan, R. Amezcua, F. Poletti, J. R. Hayes, N. G. R. Broderick, and D. J. Richardson, “The effect of periodicity on the defect modes of large mode area microstructured fibers,” Opt. Express **16**(23), 18631–18645 (2008). [CrossRef] [PubMed]

**44. **A. F. Oskooi, J. D. Joannopoulos, and S. G. Johnson, “Zero-group-velocity modes in chalcogenide holey photonic-crystal fibers,” Opt. Express **17**(12), 10082–10090 (2009). [CrossRef] [PubMed]

**45. **P. Roberts, F. Couny, H. Sabert, B. Mangan, D. Williams, L. Farr, M. Mason, A. Tomlinson, T. Birks, J. Knight, and P. St J Russell, “Ultimate low loss of hollow-core photonic crystal fibres,” Opt. Express **13**(1), 236–244 (2005). [CrossRef] [PubMed]

**46. **S. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, T. Engeness, M. Soljacic, S. Jacobs, J. Joannopoulos, and Y. Fink, “Low-loss asymptotically single-mode propagation in large-core OmniGuide fibers,” Opt. Express **9**(13), 748–779 (2001). [CrossRef] [PubMed]

**47. **M. A. Schmidt, A. Argyros, and F. Sorin, “Hybrid optical fibers – an innovative platform for in-fiber photonic devices,” Adv. Opt. Mater. **4**(1), 13–36 (2016). [CrossRef]

**48. **H. K. Tyagi, M. A. Schmidt, L. Prill Sempere, and P. S. J. Russell, “Optical properties of photonic crystal fiber with integral micron-sized Ge wire,” Opt. Express **16**(22), 17227–17236 (2008). [CrossRef] [PubMed]

**49. **H. K. Tyagi, H. W. Lee, P. Uebel, M. A. Schmidt, N. Joly, M. Scharrer, and P. S. Russell, “Plasmon resonances on gold nanowires directly drawn in a step-index fiber,” Opt. Lett. **35**(15), 2573–2575 (2010). [CrossRef] [PubMed]

**50. **C. Jain, A. Tuniz, K. Reuther, T. Wieduwilt, M. Rettenmayr, and M. A. Schmidt, “Micron-sized gold-nickel alloy wire integrated silica optical fibers,” Opt. Mater. Express **6**(6), 1790 (2016). [CrossRef]

**51. **P. Uebel, M. A. Schmidt, S. T. Bauerschmidt, and P. S. J. Russell, “A gold-nanotip optical fiber for plasmon-enhanced near-field detection,” Appl. Phys. Lett. **103**, 021101 (2013). [CrossRef]

**52. **P. Uebel, M. A. Schmidt, H. W. Lee, and P. S. J. Russell, “Polarisation-resolved near-field mapping of a coupled gold nanowire array,” Opt. Express **20**(27), 28409–28417 (2012). [CrossRef] [PubMed]

**53. **H. W. Lee, M. A. Schmidt, R. F. Russell, N. Y. Joly, H. K. Tyagi, P. Uebel, and P. S. J. Russell, “Pressure-assisted melt-filling and optical characterization of Au nano-wires in microstructured fibers,” Opt. Express **19**(13), 12180–12189 (2011). [CrossRef] [PubMed]

**54. **R. He, P. J. A. Sazio, A. C. Peacock, N. Healy, J. R. Sparks, M. Krishnamurthi, V. Gopalan, and J. V. Badding, “Integration of GHz bandwidth semiconductor devices inside microstructured optical fibres,” Nat. Photon .**6**, 352 (2012).

**55. **J. Ballato, T. Hawkins, P. Foy, R. Stolen, B. Kokuoz, M. Ellison, C. McMillen, J. Reppert, A. M. Rao, M. Daw, S. R. Sharma, R. Shori, O. Stafsudd, R. R. Rice, and D. R. Powers, “Silicon optical fiber,” Opt. Express **16**(23), 18675–18683 (2008). [CrossRef] [PubMed]

**56. **B. Debord, A. Amsanpally, M. Chafer, A. Baz, M. Maurel, J. M. Blondy, E. Hugonnot, F. Scol, L. Vincetti, F. Gerome, and F. Benabid, “Ultralow transmission loss in inhibited-coupling guiding hollow fibers,” Optica **4**(2), 209–217 (2017). [CrossRef]

**57. **M. Chemnitz, M. Gebhardt, C. Gaida, F. Stutzki, J. Kobelke, J. Limpert, A. Tünnermann, and M. A. Schmidt, “Hybrid soliton dynamics in liquid-core fibres,” Nat. Commun. **8**(1), 42 (2017). [CrossRef] [PubMed]

**58. **L. Kröckel, T. Frosch, and M. A. Schmidt, “Multiscale spectroscopy using a monolithic liquid core waveguide with laterally attached fiber ports,” Anal. Chim. Acta **875**, 1–6 (2015). [CrossRef] [PubMed]

**59. **D. Yan, J. Popp, M. W. Pletz, and T. Frosch, “Highly Sensitive Broadband Raman Sensing of Antibiotics in Step-Index Hollow-Core Photonic Crystal Fibers,” ACS Photonics **4**(1), 138–145 (2017). [CrossRef]