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New Materials and Processing Methods for Microstructured Optical Fibres

A special issue of Materials (ISSN 1996-1944).

Deadline for manuscript submissions: closed (15 June 2014) | Viewed by 112008

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Foundation for Research and Technology - Hellas (FORTH), Institute of Electronic Structure and Laser (IESL), N. Plastira 100, 70013 Vasilika Vouton, Greece

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Guest Editor
Photonics and Optical Sensing Research Laboratory, Cyprus University of Technology, Limassol 3036, Cyprus
Interests: bragg grating and optical fibre sensors; femtosecond laser microfabrication of photonic devices; microfluidics; plasmonics and laser material interactions

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Keywords

  • New Materials and Microstructured Optical Fibres Drawing/Growth Techniques
    • Soft glasses  and crystalline materials for microstructured optical fibre drawing
    • Multi-component glasses optical fibres
    • Nanomaterials with tailored optical/physical and affinity properties for specialty optical fibres, including carbon related materials
    • Materials growth techniques inside microstructured optical fibres
    • Random geometry/aperiodic microstructured optical fibres
  • Novel Processing Methods
    • Laser, Chemical and Lithographic techniques for structuring microstructured optical fibres
    • Advanced infusion and infiltration techniques
  • Applications
    • Biological, chemical and medical sensors
    • Sensors for harsh environments
    • Terahertz related sensing applications
    • Non-linear switching and laser emission devices
    • Optofluidics, Acoustics, Optomechanics

Published Papers (16 papers)

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Research

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1207 KiB  
Article
Microfluidic Flows and Heat Transfer and Their Influence on Optical Modes in Microstructure Fibers
by Edward Davies, Paul Christodoulides, George Florides and Kyriacos Kalli
Materials 2014, 7(11), 7566-7582; https://doi.org/10.3390/ma7117566 - 24 Nov 2014
Cited by 8 | Viewed by 6322
Abstract
A finite element analysis (FEA) model has been constructed to predict the thermo-fluidic and optical properties of a microstructure optical fiber (MOF) accounting for changes in external temperature, input water velocity and optical fiber geometry. Modeling a water laminar flow within a water [...] Read more.
A finite element analysis (FEA) model has been constructed to predict the thermo-fluidic and optical properties of a microstructure optical fiber (MOF) accounting for changes in external temperature, input water velocity and optical fiber geometry. Modeling a water laminar flow within a water channel has shown that the steady-state temperature is dependent on the water channel radius while independent of the input velocity. There is a critical channel radius below which the steady-state temperature of the water channel is constant, while above, the temperature decreases. However, the distance required to reach steady state within the water channel is dependent on both the input velocity and the channel radius. The MOF has been found capable of supporting multiple modes. Despite the large thermo-optic coefficient of water, the bound modes’ response to temperature was dominated by the thermo-optic coefficient of glass. This is attributed to the majority of the light being confined within the glass, which increased with increasing external temperature due to a larger difference in the refractive index between the glass core and the water channel. Full article
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737 KiB  
Article
New Methods of Enhancing the Thermal Durability of Silica Optical Fibers
by Karol Wysokiński, Tomasz Stańczyk, Katarzyna Gibała, Tadeusz Tenderenda, Anna Ziołowicz, Mateusz Słowikowski, Małgorzata Broczkowska and Tomasz Nasiłowski
Materials 2014, 7(10), 6947-6964; https://doi.org/10.3390/ma7106947 - 13 Oct 2014
Cited by 31 | Viewed by 6117
Abstract
Microstructured optical fibers can be precisely tailored for many different applications, out of which sensing has been found to be particularly interesting. However, placing silica optical fiber sensors in harsh environments results in their quick destruction as a result of the hydrolysis process. [...] Read more.
Microstructured optical fibers can be precisely tailored for many different applications, out of which sensing has been found to be particularly interesting. However, placing silica optical fiber sensors in harsh environments results in their quick destruction as a result of the hydrolysis process. In this paper, the degradation mechanism of bare and metal-coated optical fibers at high temperatures under longitudinal strain has been determined by detailed analysis of the thermal behavior of silica and metals, like copper and nickel. We furthermore propose a novel method of enhancing the lifetime of optical fibers by the deposition of electroless nickel-phosphorous alloy in a low-temperature chemical process. The best results were obtained for a coating comprising an inner layer of copper and outer layer of low phosphorous nickel. Lifetime values obtained during the annealing experiments were extrapolated to other temperatures by a dedicated model elaborated by the authors. The estimated copper-coated optical fiber lifetime under cycled longitudinal strain reached 31 h at 450 °C. Full article
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1546 KiB  
Article
Diffusion and Interface Effects during Preparation of All-Solid Microstructured Fibers
by Kobelke Jens, Bierlich Jörg, Wondraczek Katrin, Aichele Claudia, Pan Zhiwen, Unger Sonja, Schuster Kay and Bartelt Hartmut
Materials 2014, 7(9), 6879-6892; https://doi.org/10.3390/ma7096879 - 25 Sep 2014
Cited by 7 | Viewed by 6960
Abstract
All-solid microstructured optical fibers (MOF) allow the realization of very flexible optical waveguide designs. They are prepared by stacking of doped silica rods or canes in complex arrangements. Typical dopants in silica matrices are germanium and phosphorus to increase the refractive index (RI), [...] Read more.
All-solid microstructured optical fibers (MOF) allow the realization of very flexible optical waveguide designs. They are prepared by stacking of doped silica rods or canes in complex arrangements. Typical dopants in silica matrices are germanium and phosphorus to increase the refractive index (RI), or boron and fluorine to decrease the RI. However, the direct interface contact of stacking elements often causes interrelated chemical reactions or evaporation during thermal processing. The obtained fiber structures after the final drawing step thus tend to deviate from the targeted structure risking degrading their favored optical functionality. Dopant profiles and design parameters (e.g., the RI homogeneity of the cladding) are controlled by the combination of diffusion and equilibrium conditions of evaporation reactions. We show simulation results of diffusion and thermal dissociation in germanium and fluorine doped silica rod arrangements according to the monitored geometrical disturbances in stretched canes or drawn fibers. The paper indicates geometrical limits of dopant structures in sub-µm-level depending on the dopant concentration and the thermal conditions during the drawing process. The presented results thus enable an optimized planning of the preform parameters avoiding unwanted alterations in dopant concentration profiles or in design parameters encountered during the drawing process. Full article
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696 KiB  
Article
Anthracene Fibers Grown in a Microstructured Optical Fiber for X-ray Detection
by Stanton DeHaven, Russell Wincheski and Sacharia Albin
Materials 2014, 7(9), 6291-6303; https://doi.org/10.3390/ma7096291 - 03 Sep 2014
Cited by 5 | Viewed by 8674
Abstract
Anthracene fibers are grown inside a microstructured quartz matrix to form a multicore optical fiber for X-ray detection. A modified fiber growth method for single crystal anthracene from the melt via the Bridgman-Stockbarger technique is presented. The anthracene fiber is characterized by using [...] Read more.
Anthracene fibers are grown inside a microstructured quartz matrix to form a multicore optical fiber for X-ray detection. A modified fiber growth method for single crystal anthracene from the melt via the Bridgman-Stockbarger technique is presented. The anthracene fiber is characterized by using spectrophotometry, Raman spectroscopy, and X-ray diffraction. These results show the anthracene grown in fiber has high purity and a crystal structure similar to anthracene grown from liquid, vapor, and melt techniques. As an X-ray detector, the output is 12%–16% efficient between the energy ranges of 40 and 10 keV. The effect of materials and fiber processing are discussed. Full article
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941 KiB  
Article
Photonic Bandgap Propagation in All-Solid Chalcogenide Microstructured Optical Fibers
by Celine Caillaud, Gilles Renversez, Laurent Brilland, David Mechin, Laurent Calvez, Jean-Luc Adam and Johann Troles
Materials 2014, 7(9), 6120-6129; https://doi.org/10.3390/ma7096120 - 26 Aug 2014
Cited by 26 | Viewed by 6618
Abstract
An original way to obtain fibers with special chromatic dispersion and single-mode behavior is to consider microstructured optical fibers (MOFs). These fibers present unique optical properties thanks to the high degree of freedom in the design of their geometrical structure. In this study, [...] Read more.
An original way to obtain fibers with special chromatic dispersion and single-mode behavior is to consider microstructured optical fibers (MOFs). These fibers present unique optical properties thanks to the high degree of freedom in the design of their geometrical structure. In this study, the first all-solid all-chalcogenide MOFs exhibiting photonic bandgap transmission have been achieved and optically characterized. The fibers are made of an As38Se62 matrix, with inclusions of Te20As30Se50 glass that shows a higher refractive index (n = 2.9). In those fibers, several transmission bands have been observed in mid infrared depending on the geometry. In addition, for the first time, propagation by photonic bandgap effect in an all-chalcogenide MOF has been observed at 3.39 µm, 9.3 µm, and 10.6 µm. The numerical simulations based on the optogeometric properties of the fibers agree well with the experimental characterizations. Full article
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999 KiB  
Article
Modified Powder-in-Tube Technique Based on the Consolidation Processing of Powder Materials for Fabricating Specialty Optical Fibers
by Jean-Louis Auguste, Georges Humbert, Stéphanie Leparmentier, Maryna Kudinova, Pierre-Olivier Martin, Gaëlle Delaizir, Kay Schuster and Doris Litzkendorf
Materials 2014, 7(8), 6045-6063; https://doi.org/10.3390/ma7086045 - 22 Aug 2014
Cited by 23 | Viewed by 7285
Abstract
The objective of this paper is to demonstrate the interest of a consolidation process associated with the powder-in-tube technique in order to fabricate a long length of specialty optical fibers. This so-called Modified Powder-in-Tube (MPIT) process is very flexible and paves the way [...] Read more.
The objective of this paper is to demonstrate the interest of a consolidation process associated with the powder-in-tube technique in order to fabricate a long length of specialty optical fibers. This so-called Modified Powder-in-Tube (MPIT) process is very flexible and paves the way to multimaterial optical fiber fabrications with different core and cladding glassy materials. Another feature of this technique lies in the sintering of the preform under reducing or oxidizing atmosphere. The fabrication of such optical fibers implies different constraints that we have to deal with, namely chemical species diffusion or mechanical stress due to the mismatches between thermal expansion coefficients and working temperatures of the fiber materials. This paper focuses on preliminary results obtained with a lanthano-aluminosilicate glass used as the core material for the fabrication of all-glass fibers or specialty Photonic Crystal Fibers (PCFs). To complete the panel of original microstructures now available by the MPIT technique, we also present several optical fibers in which metallic particles or microwires are included into a silica-based matrix. Full article
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984 KiB  
Article
Optical Spectra Tuning of All-Glass Photonic Bandgap Fiber Infiltrated with Silver Fast-Ion-Conducting Glasses
by Ioannis Konidakis and Stavros Pissadakis
Materials 2014, 7(8), 5735-5745; https://doi.org/10.3390/ma7085735 - 07 Aug 2014
Cited by 16 | Viewed by 5824
Abstract
Silver iodide metaphosphate glasses of the xAgI + (1−x)AgPO3 family are embedded inside the air capillaries of a commercial silica photonic crystal fiber (PCF) by means of vacuum-assisted infiltration technique. In this paper, we report on tuning the photonic [...] Read more.
Silver iodide metaphosphate glasses of the xAgI + (1−x)AgPO3 family are embedded inside the air capillaries of a commercial silica photonic crystal fiber (PCF) by means of vacuum-assisted infiltration technique. In this paper, we report on tuning the photonic bandgap (PBG) guidance characteristics of the fabricated all-glass photonic bandgap fibers, by varying the composition of the fast-ion-conducting phosphate glass infiltration medium. Doping AgPO3 metaphosphate glass with AgI significantly alters the PBG guidance patterns in the examined range between 350 and 1750 nm, as it leads to the introduction of numerous additional transmission stop-bands, while affecting scattering dependant losses. The effect of phosphate glass cooling method during sample fabrication on the transmission behavior of the xAgI + (1−x)AgPO3/PCFs is also considered. Full article
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750 KiB  
Article
High Power Spark Delivery System Using Hollow Core Kagome Lattice Fibers
by Ciprian Dumitrache, Jordan Rath and Azer P. Yalin
Materials 2014, 7(8), 5700-5710; https://doi.org/10.3390/ma7085700 - 07 Aug 2014
Cited by 20 | Viewed by 7197
Abstract
This study examines the use of the recently developed hollow core kagome lattice fibers for delivery of high power laser pulses. Compared to other photonic crystal fibers (PCFs), the hollow core kagome fibers have larger core diameter (~50 µm), which allows for higher [...] Read more.
This study examines the use of the recently developed hollow core kagome lattice fibers for delivery of high power laser pulses. Compared to other photonic crystal fibers (PCFs), the hollow core kagome fibers have larger core diameter (~50 µm), which allows for higher energy coupling in the fiber while also maintaining high beam quality at the output (M2 = 1.25). We have conducted a study of the maximum deliverable energy versus laser pulse duration using a Nd:YAG laser at 1064 nm. Pulse energies as high as 30 mJ were transmitted for 30 ns pulse durations. This represents, to our knowledge; the highest laser pulse energy delivered using PCFs. Two fiber damage mechanisms were identified as damage at the fiber input and damage within the bulk of the fiber. Finally, we have demonstrated fiber delivered laser ignition on a single-cylinder gasoline direct injection engine. Full article
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2236 KiB  
Article
Nanomechanical Optical Fiber with Embedded Electrodes Actuated by Joule Heating
by Zhenggang Lian, Martha Segura, Nina Podoliak, Xian Feng, Nicholas White and Peter Horak
Materials 2014, 7(8), 5591-5602; https://doi.org/10.3390/ma7085591 - 31 Jul 2014
Cited by 8 | Viewed by 5727
Abstract
Nanomechanical optical fibers with metal electrodes embedded in the jacket were fabricated by a multi-material co-draw technique. At the center of the fibers, two glass cores suspended by thin membranes and surrounded by air form a directional coupler that is highly temperature-dependent. We [...] Read more.
Nanomechanical optical fibers with metal electrodes embedded in the jacket were fabricated by a multi-material co-draw technique. At the center of the fibers, two glass cores suspended by thin membranes and surrounded by air form a directional coupler that is highly temperature-dependent. We demonstrate optical switching between the two fiber cores by Joule heating of the electrodes with as little as 0.4 W electrical power, thereby demonstrating an electrically actuated all-fiber microelectromechanical system (MEMS). Simulations show that the main mechanism for optical switching is the transverse thermal expansion of the fiber structure. Full article
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989 KiB  
Article
Fabrication of an Optical Fiber Micro-Sphere with a Diameter of Several Tens of Micrometers
by Huijuan Yu, Qiangxian Huang and Jian Zhao
Materials 2014, 7(7), 4878-4895; https://doi.org/10.3390/ma7074878 - 25 Jun 2014
Cited by 21 | Viewed by 9000
Abstract
A new method to fabricate an integrated optical fiber micro-sphere with a diameter within 100 µm, based on the optical fiber tapering technique and the Taguchi method is proposed. Using a 125 µm diameter single-mode (SM) optical fiber, an optical fiber taper with [...] Read more.
A new method to fabricate an integrated optical fiber micro-sphere with a diameter within 100 µm, based on the optical fiber tapering technique and the Taguchi method is proposed. Using a 125 µm diameter single-mode (SM) optical fiber, an optical fiber taper with a cone angle is formed with the tapering technique, and the fabrication optimization of a micro-sphere with a diameter of less than 100 µm is achieved using the Taguchi method. The optimum combination of process factors levels is obtained, and the signal-to-noise ratio (SNR) of three quality evaluation parameters and the significance of each process factors influencing them are selected as the two standards. Using the minimum zone method (MZM) to evaluate the quality of the fabricated optical fiber micro-sphere, a three-dimensional (3D) numerical fitting image of its surface profile and the true sphericity are subsequently realized. From the results, an optical fiber micro-sphere with a two-dimensional (2D) diameter less than 80 µm, 2D roundness error less than 0.70 µm, 2D offset distance between the micro-sphere center and the fiber stylus central line less than 0.65 µm, and true sphericity of about 0.5 µm, is fabricated. Full article
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1128 KiB  
Article
Ytterbium-Phosphate Glass for Microstructured Fiber Laser
by Ryszard Stępień, Marcin Franczyk, Dariusz Pysz, Ireneusz Kujawa, Mariusz Klimczak and Ryszard Buczyński
Materials 2014, 7(6), 4723-4738; https://doi.org/10.3390/ma7064723 - 19 Jun 2014
Cited by 20 | Viewed by 7228
Abstract
In the paper, we report on the development of a synthesis and melting method of phosphate glasses designed for active microstructured fiber manufacturing. Non-doped glass synthesized in a P2O5-Al2O3-BaO-ZnO-MgO-Na2O oxide system served as [...] Read more.
In the paper, we report on the development of a synthesis and melting method of phosphate glasses designed for active microstructured fiber manufacturing. Non-doped glass synthesized in a P2O5-Al2O3-BaO-ZnO-MgO-Na2O oxide system served as the matrix material; meanwhile, the glass was doped with 6 mol% (18 wt%) of Yb2O3, as fiber core. The glasses were well-fitted in relation to optical (refractive index) and thermal proprieties (thermal expansion coefficient, rheology). The fiber with the Yb3+-doped core, with a wide internal photonic microstructure for a laser pump, as well as with a high relative hole size in the photonic outer air-cladding, was produced. The laser built on the basis of this fiber enabled achieving 8.07 W of output power with 20.5% slope efficiency against the launched pump power, in single-mode operation M2 = 1.59, from a 53 cm-long cavity. Full article
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611 KiB  
Article
Two Octaves Supercontinuum Generation in Lead-Bismuth Glass Based Photonic Crystal Fiber
by Ryszard Buczynski, Henry Bookey, Mariusz Klimczak, Dariusz Pysz, Ryszard Stepien, Tadeusz Martynkien, John E. McCarthy, Andrew J. Waddie, Ajoy K. Kar and Mohammad R. Taghizadeh
Materials 2014, 7(6), 4658-4668; https://doi.org/10.3390/ma7064658 - 19 Jun 2014
Cited by 13 | Viewed by 6995
Abstract
In this paper we report a two octave spanning supercontinuum generation in a bandwidth of 700–3000 nm in a single-mode photonic crystal fiber made of lead-bismuth-gallate glass. To our knowledge this is the broadest supercontinuum reported in heavy metal oxide glass based fibers. [...] Read more.
In this paper we report a two octave spanning supercontinuum generation in a bandwidth of 700–3000 nm in a single-mode photonic crystal fiber made of lead-bismuth-gallate glass. To our knowledge this is the broadest supercontinuum reported in heavy metal oxide glass based fibers. The fiber was fabricated using an in-house synthesized glass with optimized nonlinear, rheological and transmission properties in the range of 500–4800 nm. The photonic cladding consists of 8 rings of air holes. The fiber has a zero dispersion wavelength (ZDW) at 1460 nm. Its dispersion is determined mainly by the first ring of holes in the cladding with a relative hole size of 0.73. Relative hole size of the remaining seven rings is 0.54, which allows single mode performance of the fiber in the infrared range and reduces attenuation of the fundamental mode. The fiber is pumped into anomalous dispersion with 150 fs pulses at 1540 nm. Observed spectrum of 700–3000 nm was generated in 2 cm of fiber with pulse energy below 4 nJ. A flatness of 5 dB was observed in 950–2500 nm range. Full article
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361 KiB  
Article
Superlattice Microstructured Optical Fiber
by Ming-Leung Vincent Tse, Zhengyong Liu, Lok-Hin Cho, Chao Lu, Ping-Kong Alex Wai and Hwa-Yaw Tam
Materials 2014, 7(6), 4567-4573; https://doi.org/10.3390/ma7064567 - 16 Jun 2014
Cited by 13 | Viewed by 5974
Abstract
A generic three-stage stack-and-draw method is demonstrated for the fabrication of complex-microstructured optical fibers. We report the fabrication and characterization of a silica superlattice microstructured fiber with more than 800 rhomboidally arranged air-holes. A polarization-maintaining fiber with a birefringence of 8.5 × 10 [...] Read more.
A generic three-stage stack-and-draw method is demonstrated for the fabrication of complex-microstructured optical fibers. We report the fabrication and characterization of a silica superlattice microstructured fiber with more than 800 rhomboidally arranged air-holes. A polarization-maintaining fiber with a birefringence of 8.5 × 10−4 is demonstrated. The birefringent property of the fiber is found to be highly insensitive to external environmental effects, such as pressure. Full article
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705 KiB  
Article
Materials Development for Next Generation Optical Fiber
by John Ballato and Peter Dragic
Materials 2014, 7(6), 4411-4430; https://doi.org/10.3390/ma7064411 - 11 Jun 2014
Cited by 51 | Viewed by 8325
Abstract
Optical fibers, the enablers of the Internet, are being used in an ever more diverse array of applications. Many of the rapidly growing deployments of fibers are in high-power and, particularly, high power-per-unit-bandwidth systems where well-known optical nonlinearities have historically not been especially [...] Read more.
Optical fibers, the enablers of the Internet, are being used in an ever more diverse array of applications. Many of the rapidly growing deployments of fibers are in high-power and, particularly, high power-per-unit-bandwidth systems where well-known optical nonlinearities have historically not been especially consequential in limiting overall performance. Today, however, nominally weak effects, most notably stimulated Brillouin scattering (SBS) and stimulated Raman scattering (SRS) are among the principal phenomena restricting continued scaling to higher optical power levels. In order to address these limitations, the optical fiber community has focused dominantly on geometry-related solutions such as large mode area (LMA) designs. Since such scattering, and all other linear and nonlinear optical phenomena including higher order mode instability (HOMI), are fundamentally materials-based in origin, this paper unapologetically advocates material solutions to present and future performance limitations. As such, this paper represents a ‘call to arms’ for material scientists and engineers to engage in this opportunity to drive the future development of optical fibers that address many of the grand engineering challenges of our day. Full article
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722 KiB  
Article
Fabricating Nanoporous Silica Structure on D-Fibres through Room Temperature Self-Assembly
by John Canning, Lucas Moura, Lachlan Lindoy, Kevin Cook, Maxwell J. Crossley, Yanhua Luo, Gang-Ding Peng, Lars Glavind, George Huyang, Masood Naqshbandi, Martin Kristensen, Cicero Martelli and Graham Town
Materials 2014, 7(3), 2356-2369; https://doi.org/10.3390/ma7032356 - 19 Mar 2014
Cited by 2 | Viewed by 6971
Abstract
The room temperature deposition of self-assembling silica nanoparticles onto D-shaped optical fibres (“D-fibre”), drawn from milled preforms fabricated by modified chemical vapour deposition (MCVD), is studied. Vertical dip-and-withdraw produces tapered layers, with one end thicker (surface coverage >0.85) than the other, whilst horizontal [...] Read more.
The room temperature deposition of self-assembling silica nanoparticles onto D-shaped optical fibres (“D-fibre”), drawn from milled preforms fabricated by modified chemical vapour deposition (MCVD), is studied. Vertical dip-and-withdraw produces tapered layers, with one end thicker (surface coverage >0.85) than the other, whilst horizontal dip-and-withdraw produces much more uniform layers over the core region. The propagation of induced fracturing over the core region during drying is overcome using a simple protrusion of the inner cladding. Thick coatings are discernible through thin film interference colouring, but thinner coatings require scanning electron microscopy (SEM) imaging. Here, we show that fluorescence imaging, using Rhodamine B, in this example, can provide some qualitative and speedy assessment of coverage. Full article
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Review

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1019 KiB  
Review
Transverse Anderson Localization in Disordered Glass Optical Fibers: A Review
by Arash Mafi, Salman Karbasi, Karl W. Koch, Thomas Hawkins and John Ballato
Materials 2014, 7(8), 5520-5527; https://doi.org/10.3390/ma7085520 - 28 Jul 2014
Cited by 8 | Viewed by 5762
Abstract
Disordered optical fibers show novel waveguiding properties that can be used for various device applications, such as beam-multiplexed optical communications and endoscopic image transport. The strong transverse scattering from the transversely disordered optical fibers results in transversely confined beams that can freely propagate [...] Read more.
Disordered optical fibers show novel waveguiding properties that can be used for various device applications, such as beam-multiplexed optical communications and endoscopic image transport. The strong transverse scattering from the transversely disordered optical fibers results in transversely confined beams that can freely propagate in the longitudinal direction, similar to conventional optical fibers, with the advantage that any point in the cross section of the fiber can be used for beam transport. For beam multiplexing and imaging applications, it is highly desirable to make the localized beam radius as small as possible. This requires large refractive index differences between the materials that define the random features in the disordered fiber. Here, disordered glass-air fibers are briefly reviewed, where randomly placed airholes in a glass matrix provide the sufficiently large refractive index difference of 0.5 for strong random transverse scattering. The main future challenge for the fabrication of an optimally disordered glass-air fibers is to increase the fill-fraction of airholes to nearly 50% for maximum beam confinement. Full article
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