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Optics Express

Optics Express

  • Editor: J. H. Eberly
  • Vol. 9, Iss. 7 — Sep. 24, 2001
  • pp: 319–327
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Microstructured polymer optical fibre

Martijn A. van Eijkelenborg, Maryanne C. J. Large, Alexander Argyros, Joseph Zagari, Steven Manos, Nader A. Issa, Ian Bassett, Simon Fleming, Ross C. McPhedran, C. Martijn de Sterke, and Nicolae A.P. Nicorovici  »View Author Affiliations


Optics Express, Vol. 9, Issue 7, pp. 319-327 (2001)
http://dx.doi.org/10.1364/OE.9.000319


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Abstract

The first microstructured polymer optical fibre is described. Both experimental and theoretical evidence is presented to establish that the fibre is effectively single moded at optical wavelengths. Polymer-based microstructured optical fibres offer key advantages over both conventional polymer optical fibres and glass microstructured fibres. The low-cost manufacturability and the chemical flexibility of the polymers provide great potential for applications in data communication networks and for the development of a range of new polymer-based fibre-optic components.

© Optical Society of America

1. Introduction

Polymer optical fibre (POF) technology has advanced rapidly in recent years, with the expectation that POF will form an integral part of datacom networks. POF may be one technology that will provide the backbone of the critical last mile of the telecommunications networks, offering a high-bandwidth, easy to install, fibre-optic replacement for copper cables. In contrast to a glass optical fibre, a thick polymer fibre will remain mechanically flexible, which, in combination with a large core, allows easy and inexpensive connectivity of the fibres during installation. Data transmission rates of 11 Gbits/sec over 100 meters at 1300 nm in POF have been demonstrated, and a POF-based local-area network has been installed at Keio University in Japan [1

1. M. Sato, T. Ishigure, and Y. Koike, “Thermally stable high-bandwidth graded-index polymer optical fiber”, J. Lightwave Tech. 18, 952–8 (2000). [CrossRef]

].

In this paper, we report the fabrication of the first microstructured polymer optical fibre (MPOF). This new type of POF is likely to be of great importance, because all of the disadvantages of conventional POF are potentially addressed by the use of MPOF. The light guiding mechanism in MPOF is fundamentally different from conventional POF. It arises from a pattern of microscopic air channels that run along the length of the fibre, rather than from variations in the refractive index of the fibre material. This mechanism was demonstrated in recent years in microstructured silica optical fibres, also called photonic crystal fibres (PCFs) [2

2. T.A. Birks, J.C. Knight, and P. St. J. Russell, “Endlessly single-mode photonic crystal fibre,” Opt. Lett. 22, 961–963 (1997). [CrossRef] [PubMed]

,3

3. H. Kubota, K. Suzuki, S. Kawanishi, M. Kakazawa, M. Tanaka, and M. Fujita, “Low-loss, 2 km-long photonic crystal fibre with zero GVD in the near IR suitable for picosecond pulse propagation at the 800 nm band,” Postdeadline paper CPD3, Conference on Lasers and Electro-Optics CLEO2001, Baltimore, MD, USA.

]. The application of this guiding mechanism to POF offers a range of unique new properties and benefits. These include the possibility to combine single-mode behavior with large mode areas [4

4. J.C. Knight, T.A. Birks, R.F. Cregan, P.St.J. Russell, and J.-P. de Sandro, “Large mode area photonic crystal fibre,” Electron. Lett. 34, 1347 (1999). [CrossRef]

], which is the ideal combination for easy-to-install transmission fibre. In addition, the recently developed photonic band gap fibres [5

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

] offer the promise of guidance in air rather than in the fibre material, allowing the problem of absorptive losses of polymers to be addressed. The potential benefits of MPOF will be discussed further in section 4, after the presentation of the experimental results in section 2 and the theoretical results in section 3.

2. The single-mode microstructured polymer optical fibre

MPOF preforms were fabricated using commercially available extruded polymethyl methacrylate, PMMA. The details of the fabrication methods will be described in a subsequent paper. The PMMA was of poor optical quality, and attenuation tests on an unstructured fibre drawn from this material indicated an absorption loss of about 32 dB/m at a wavelength of 632.8 nm. MPOF was drawn on a polymer fibre draw tower at a rate of 10 m/min at a temperature of approximately 175°C and to an outer diameter of 250 µm.

Fig.1. Electron micrographs of the microstructured polymer optical fibre (MPOF).

Electron microscope images of the fibre are shown in Figure 1. It can be seen that the air hole microstructure consists of four rings of holes in a hexagonal pattern, embedded in an outer sleeve. Small deformations are visible, such as in the hole diameters and shapes. Compared to the preform that the fibre was drawn from, the hole structure in the fibre has a slightly reduced hole diameter to hole spacing ratio, d/Λ=0.46, whereas in the preform d/Λ=0.67. The optical experiments reported below were performed on a piece of this fibre, with an average hole diameter d=1.3 µm and an average hole spacing Λ=2.8 µm, which defines a core size of 4.3 µm.

To demonstrate that the MPOF effectively guides only a single mode, three independent experiments were conducted, identical to those reported to confirm the single-mode operation of glass microstructured fibres [4

4. J.C. Knight, T.A. Birks, R.F. Cregan, P.St.J. Russell, and J.-P. de Sandro, “Large mode area photonic crystal fibre,” Electron. Lett. 34, 1347 (1999). [CrossRef]

,6

6. J.C. Knight, T.A. Birks, P.St.J. Russell, and D.M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. 21, 1547–1549 (1996). [CrossRef] [PubMed]

,7

7. J. K. Ranka, R.S. Windeler, and A.J. Stentz, “Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm,” Opt. Lett. 25, 25–27 (2000). [CrossRef]

]. In the first experiment, HeNe laser light of 632.8 nm was launched into a 1-m length of MPOF by butt-coupling to a multi-mode silica fibre. The fibre output was observed, both in the near field and far field. It was found that both patterns were independent of the launching conditions from the multimode fibre (both angle and position) and independent of any bends or twists in the fibre. This is strong evidence of single-mode guiding [4

4. J.C. Knight, T.A. Birks, R.F. Cregan, P.St.J. Russell, and J.-P. de Sandro, “Large mode area photonic crystal fibre,” Electron. Lett. 34, 1347 (1999). [CrossRef]

].

In the third experiment, a spatial interference measurement was performed, between the collimated output mode of the MPOF and the output of a standard single-mode glass fibre. The resulting stable interference pattern is shown in Fig. 2 d). A translation of the fringes could be observed due to thermal and mechanical disturbances, and as a function of fibre bending. The clear fringe pattern with a visibility close to unity indicates that only a single mode was guided in the microstructured fibre [7

7. J. K. Ranka, R.S. Windeler, and A.J. Stentz, “Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm,” Opt. Lett. 25, 25–27 (2000). [CrossRef]

].

Fig.2. Optical testing of the single mode guiding of the microstructured polymer optical fibre (MPOF). a) the mode pattern in the near field, b) a contour plot of the near field pattern, c) the far field mode pattern d) the interference pattern between a standard single-mode fibre and the MPOF. The white patches in the images a) and c) are due to overexposure of the camera.

As verified experimentally in three different ways, the MPOF consistently behaves as a single-mode guiding structure at a wavelength of 632.8 nm. The near field and far field mode patterns, though distorted, showed no evidence of the structure associated with higher-order modes (see also section 3). It is important to mention that in addition to the single-mode fibre, we also fabricated a multi-mode MPOF. The different behavior of this multi-mode fibre in the experiments described above is striking. The details of the multi-mode MPOF will be reported elsewhere.

Bending of both the single-mode and multi-mode MPOF to a radius of about 3 mm showed no significant change in transmitted power, indicating a low critical bending radius. Unfortunately the high losses of the PMMA made it difficult to perform further optical tests such as a determination of the bending losses and dispersion measurements. In future experiments, the poor quality PMMA will be replaced with a low-loss optical-quality PMMA and other low-loss polymers.

3. Modeling of the structure

We modeled the MPOF using a recently developed multipole method [8

8. T.P. White, R.C. McPhedran, C.M. de Sterke, L.C. Botten, and M.J. Steel, “Confinement losses in microstructured optical fibres,” Opt. Lett., in press (2001). [CrossRef]

,9

9. T.P. White, B.T. Kuhlmey, R.C. McPhedran, D. Maystre, G. Renversez, C. Martijn de Sterke, and L.C. Botten, “Multipole method for microstructured optical fibres I: Formulation,” in preparation (2001).

]. Compared with other modeling techniques, it has advantages in terms of speed, accuracy, and the ability to calculate confinement losses [8

8. T.P. White, R.C. McPhedran, C.M. de Sterke, L.C. Botten, and M.J. Steel, “Confinement losses in microstructured optical fibres,” Opt. Lett., in press (2001). [CrossRef]

], although at present it is restricted to holes of circular cross-section. Using this method, we modeled regular structures composed of varying numbers of rings of holes of diameter d=1.3 µm and spacing Λ=2.8 µm, inserted in a lossless matrix of index n=1.4897 for PMMA at 632.8 nm. The dimensions correspond to the fibre parameters reported in section 2. We found the structure to have three bound modes, two of which are doubly degenerate, together with a nondegenerate mode located in close proximity to the second degenerate mode. In terms of the effective indices neff=β/k0, where β is the propagation constant and k0 is the free space wave number, we find Re(neff)=1.48655 for the fundamental mode, independent of the number of rings. For both higher order modes Re(neff)=1.48240 for a four-ringed structure, with a weak dependence on the number of rings. The beat length between the fundamental and higher order modes is only 150 µm at 632.8 nm, essentially precluding internal mode coupling due to random perturbations inside the fiber. The energy flow in the fiber direction for the two degenerate modes in a two-ringed structure is shown in Fig. 3.

It is important to note that the modes’ confinement losses, which are associated with the finite number of rings [8

8. T.P. White, R.C. McPhedran, C.M. de Sterke, L.C. Botten, and M.J. Steel, “Confinement losses in microstructured optical fibres,” Opt. Lett., in press (2001). [CrossRef]

], are vastly different. The reduction of confinement loss with an increasing number of rings is quite different for the fundamental mode and the first two higher-order modes. For two, three and four rings, the losses for the fundamental mode are respectively 2.4, 5×10-3 and 3×10-6 dB/m. The losses of all the higher-order modes are roughly equal, and they decrease much more slowly: 2×103, 5×102 and 2×102 dB/m respectively. In the four-ring case (which corresponds to the MPOF in section 2) the fundamental mode thus exhibits a loss of 3×10-6 dB/m, which is much smaller than the absorption loss of 32 dB/m, and is therefore essentially negligible. In contrast, the higher-order modes have a loss around 200 dB/m. Not only is this confinement loss much larger than the absorption loss, it also precludes any light that was originally in these modes being transmitted through the 1-m length of fiber. The MPOF structure therefore behaves as if it is single moded at λ=632.8 nm for 2, 3, 4 and probably more rings. These theoretical results are entirely consistent with the experimental demonstration of single-mode behavior.

Fig.3. Axial component of the Poynting vector for the first two degenerate modes of a two-ring MOF (d=1.3 µm, Λ=2.8 µm, matrix index n=1.4897, λ=632.8 nm). The holes of the fibre are located at the positions where indents are observed in the mode profile of the second mode.

4. Advantages of microstructured polymer optical fibre

Microstructured optical fibres have, to date, only been fabricated in glass, which usually entails the stacking of circular glass capillaries to form a preform with a close packed hexagonal arrangement of air holes. With this technique, it is difficult to obtain alternative geometries or hole shapes. In this respect, MPOF has a number of advantages. The much lower processing temperatures of polymers and the controllability of the polymerisation process allow a variety of ways to produce the polymer preforms. In addition to the capillary stacking technique, polymer performs can be made using techniques such as extrusion, polymer casting, polymerization in a mould and injection moulding. With such techniques available, it becomes straightforward to obtain different cross-sections in the preform, with holes of arbitrary shapes and sizes in any desired arrangement.

There are, in fact, many applications for which it is desirable to have holes of specific shapes in the fibre, such as for polarization-maintaining microstructured fibre [10

10. M.J. Steel and R.M. Osgood, “Elliptical-hole photonic crystal fibres,” Opt. Lett. 26, 229–231 (2001). [CrossRef]

,11

11. J. Broeng, D. Mogilevtsev, S.E. Barkou Libori, and A. Bjarklev, “Polarisation-preserving holey fibers,” paper MA1-3, Pacific Rim Conference on Lasers and Electro-Optics, July 2001, Chiba, Japan.

]. Creating holes of specific shapes in a glass microstructured fibre is problematic because the balance between viscosity and surface tension tends to modify the hole structure during the draw process, and often the structure in the fibre is significantly different from that in the preform [12

12. A. Ortigosa-Blanch, J.C. Knight, W.J. Wadsworth, J. Arriaga, B.J. Mangan, T.A. Birks, and P.St.J. Russell, “Highly birefringent photonic crystal fibres,” Opt. Lett. 25, 1325–1327 (2000). [CrossRef]

,13

13. M.A. van Eijkelenborg, J. Canning, T. Ryan, and K. Lyytikainen, “Bending-induced colouring in a photonic crystal fibre,” Optics Express 7, 88–94 (2000). [CrossRef] [PubMed]

]. In addition, the drawing temperature is a crucial parameter when drawing glass microstructured fibre; temperature changes of a few percent can lead to very significant changes in the fibre microstructure. This does not seem to be the case for MPOF, which can be drawn over a large temperature range. For the PMMA example in this paper, the drawing temperature could be varied from 150 °C to 200 °C without significant change to the fibre structure. There seems to be a much closer relationship between the preform structure and the final structure in the fibre. The reason for this is well understood in polymer processing. The drawing process aligns the polymer chains, so that the final material is anisotropic along the fibre direction, and has enhanced strength properties [14

14. C.J. Goh and N. Phan-Thien, “Fibre spinning: an optimal control problem,” in Proceedings of the Institution of Mechanical Engineers, Part E Journal of process mechanical engineering, Vol. 204 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1990), pp. 81–86. [CrossRef]

]. Annealing after the draw can be used to relieve the internal stresses while maintaining the microstructure in the fibre.

In glass fibres, the possibilities for modifying the properties by doping are limited both by the high processing temperatures, which cause many materials to decompose, and the need to avoid phase separation. By contrast, polymers are intrinsically modifiable; it is possible to design and manufacture polymers that include any atomic species, molecular components, dispersed molecules and dispersed phases. For example, the use of techniques such as grafting of functional groups onto the polymer and co-polymerisation make it possible to obtain much higher concentrations of the desired additive than is possible by doping. In addition, by use of surfactant or block co-polymer techniques, it is possible to obtain substantial quantities of inclusions. Examples of the types of materials that could be used in MPOF are: polymers with enhanced non-linearities, electro or magneto-optic effects, metallic or rare-earth inclusions, birefringent materials such as liquid crystals, photorefractive and photochromic materials, dyes, polymers used in the detection of particular compounds and porous materials. The polymers can be specifically designed to allow the fabrication of particular fibre-optic components based on MPOF.

5. Conclusions

Optical guiding in the first polymer microstructured optical fibre (MPOF) has been demonstrated. Experimental evidence has been presented to establish that the MPOF is effectively single moded at optical wavelengths. This is in agreement with our theoretical calculations, which confirm that the MPOF structure effectively guides only a single-mode for two, three and four rings of air holes.

MPOFs have strong potential for applications in telecommunication networks, both as low-cost, low-loss transmission fibre as well as for fibre-optic components. Compared to GI POF, MPOF has important advantages, such as the lifting of a number of the material restrictions. In addition, MPOF can in principle be fabricated at a much lower cost. Compared to glass microstructured fibres, MPOFs effectively have an additional two degrees of freedom: the variety of fibre cross-sections that can be produced is much less restricted, and the choice of available material properties is much greater.

The fabrication of a range of more complex MPOF has been initiated, incorporating the fabrication of single-mode large mode-area MPOF, effective graded-index multi-mode MPOF and polymer photonic band gap fibre. In addition, MPOF will be fabricated with new materials, exploring the possibilities for low-loss transmission and novel functionalities.

6. Acknowledgements

The authors wish to thank Barry Reed, Lional Rajasekera, Thanh Phan, Tom Ryan, John Canning, Leon Poladian, Geoff Henry, Geoff Barton, Mark Sceats, Ian Maxwell, Brian Hawkett and Roger Tanner for technical assistance and advice, and the Australian Key Centre for Microscopy and Microanalysis at the University of Sydney for the electron microscope images. The work was partially funded by the Australian Photonics CRC and Redfern Polymer Optics Pty. Ltd.

References and links

1.

M. Sato, T. Ishigure, and Y. Koike, “Thermally stable high-bandwidth graded-index polymer optical fiber”, J. Lightwave Tech. 18, 952–8 (2000). [CrossRef]

2.

T.A. Birks, J.C. Knight, and P. St. J. Russell, “Endlessly single-mode photonic crystal fibre,” Opt. Lett. 22, 961–963 (1997). [CrossRef] [PubMed]

3.

H. Kubota, K. Suzuki, S. Kawanishi, M. Kakazawa, M. Tanaka, and M. Fujita, “Low-loss, 2 km-long photonic crystal fibre with zero GVD in the near IR suitable for picosecond pulse propagation at the 800 nm band,” Postdeadline paper CPD3, Conference on Lasers and Electro-Optics CLEO2001, Baltimore, MD, USA.

4.

J.C. Knight, T.A. Birks, R.F. Cregan, P.St.J. Russell, and J.-P. de Sandro, “Large mode area photonic crystal fibre,” Electron. Lett. 34, 1347 (1999). [CrossRef]

5.

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

6.

J.C. Knight, T.A. Birks, P.St.J. Russell, and D.M. Atkin, “All-silica single-mode optical fiber with photonic crystal cladding,” Opt. Lett. 21, 1547–1549 (1996). [CrossRef] [PubMed]

7.

J. K. Ranka, R.S. Windeler, and A.J. Stentz, “Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm,” Opt. Lett. 25, 25–27 (2000). [CrossRef]

8.

T.P. White, R.C. McPhedran, C.M. de Sterke, L.C. Botten, and M.J. Steel, “Confinement losses in microstructured optical fibres,” Opt. Lett., in press (2001). [CrossRef]

9.

T.P. White, B.T. Kuhlmey, R.C. McPhedran, D. Maystre, G. Renversez, C. Martijn de Sterke, and L.C. Botten, “Multipole method for microstructured optical fibres I: Formulation,” in preparation (2001).

10.

M.J. Steel and R.M. Osgood, “Elliptical-hole photonic crystal fibres,” Opt. Lett. 26, 229–231 (2001). [CrossRef]

11.

J. Broeng, D. Mogilevtsev, S.E. Barkou Libori, and A. Bjarklev, “Polarisation-preserving holey fibers,” paper MA1-3, Pacific Rim Conference on Lasers and Electro-Optics, July 2001, Chiba, Japan.

12.

A. Ortigosa-Blanch, J.C. Knight, W.J. Wadsworth, J. Arriaga, B.J. Mangan, T.A. Birks, and P.St.J. Russell, “Highly birefringent photonic crystal fibres,” Opt. Lett. 25, 1325–1327 (2000). [CrossRef]

13.

M.A. van Eijkelenborg, J. Canning, T. Ryan, and K. Lyytikainen, “Bending-induced colouring in a photonic crystal fibre,” Optics Express 7, 88–94 (2000). [CrossRef] [PubMed]

14.

C.J. Goh and N. Phan-Thien, “Fibre spinning: an optimal control problem,” in Proceedings of the Institution of Mechanical Engineers, Part E Journal of process mechanical engineering, Vol. 204 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1990), pp. 81–86. [CrossRef]

OCIS Codes
(060.0060) Fiber optics and optical communications : Fiber optics and optical communications
(060.2280) Fiber optics and optical communications : Fiber design and fabrication
(060.2430) Fiber optics and optical communications : Fibers, single-mode
(160.5470) Materials : Polymers
(230.4000) Optical devices : Microstructure fabrication

ToC Category:
Research Papers

History
Original Manuscript: August 23, 2001
Published: September 24, 2001

Citation
Martijn van Eijkelenborg, Maryanne Large, Alexander Argyros, Joseph Zagari, Steven Manos, Nader Issa, Ian Bassett, Simon Fleming, Ross McPhedran, C. Martijn de Sterke, and Nicolae A. Nicorovici, "Microstructured polymer optical fibre," Opt. Express 9, 319-327 (2001)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-9-7-319


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References

  1. M. Sato, T. Ishigure, Y. Koike, "Thermally stable high-bandwidth graded-index polymer optical fiber," J. Lightwave Tech. 18, 952-8 (2000). [CrossRef]
  2. T. A. Birks, J. C. Knight, and P. St. J. Russell, "Endlessly single-mode photonic crystal fibre," Opt. Lett. 22, 961-963 (1997). [CrossRef] [PubMed]
  3. H. Kubota, K. Suzuki, S. Kawanishi, M. Kakazawa, M. Tanaka, M. Fujita, "Low-loss, 2 km-long photonic crystal fibre with zero GVD in the near IR suitable for picosecond pulse propagation at the 800 nm band," Postdeadline paper CPD3, Conference on Lasers and Electro-Optics CLEO 2001, (Optical Society of America, Washington, D.C., 2001).
  4. J. C. Knight, T. A. Birks, R. F. Cregan, P. St. J. Russell, and J.-P. de Sandro, "Large mode area photonic crystal fibre," Electron. Lett. 34, 1347 (1999). [CrossRef]
  5. R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J Russell, P. J. Roberts and D. C. Allen, "Single-mode photonic band gap guidance of light in air," Science 285, 1537-1539 (1999). [CrossRef] [PubMed]
  6. J. C. Knight, T. A. Birks, P. St. J. Russell and D. M. Atkin, "All-silica single-mode optical fiber with photonic crystal cladding," Opt. Lett. 21, 1547-1549 (1996). [CrossRef] [PubMed]
  7. J. K. Ranka, R. S. Windeler, and A. J. Stentz, "Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm," Opt. Lett. 25, 25-27 (2000). [CrossRef]
  8. T. P.White, R. C.McPhedran, C. M. de Sterke, L. C. Botten, and M. J. Steel, "Confinementlosses in microstructured optical fibres," Opt. Lett., in press (2001). [CrossRef]
  9. T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. Martijn de Sterke, L. C. Botten, "Multipole method for microstructured optical fibres I: Formulation," in preparation (2001).
  10. M. J. Steel and R. M. Osgood, "Elliptical-hole photonic crystal fibres," Opt. Lett. 26, 229-231 (2001). [CrossRef]
  11. J. Broeng, D. Mogilevtsev, S. E. Barkou Libori, and A. Bjarklev, "Polarisation-preserving holey fibers," paper MA1-3, Pacific Rim Conference on Lasers and Electro-Optics, July 2001, Chiba, Japan.
  12. A. Ortigosa-Blanch, J. C. Knight, W. J. Wadsworth, J. Arriaga, B. J. Mangan, T. A. Birks, and P. St. J. Russell, "Highly birefringent photonic crystal fibres," Opt. Lett. 25, 1325-1327 (2000). [CrossRef]
  13. M. A. van Eijkelenborg, J. Canning, T. Ryan, and K. Lyytikainen, "Bending-induced colouring in a photonic crystal fibre," Opt. Express 7, 88-94 (2000), http://www.opticsexpress.org/oearchive/source/22842.htm [CrossRef] [PubMed]
  14. C. J. Goh, N. Phan-Thien, "Fibre spinning: an optimal control problem," in Proceedings of the Institution of Mechanical Engineers, Part E Journal of process mechanical engineering, Vol. 204 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1990), pp. 81-86 [CrossRef]

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