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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 8 — Apr. 11, 2011
  • pp: 7790–7798
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Label-free biosensing with high sensitivity in dual-core microstructured polymer optical fibers

Christos Markos, Wu Yuan, Kyriakos Vlachos, Graham E. Town, and Ole Bang  »View Author Affiliations


Optics Express, Vol. 19, Issue 8, pp. 7790-7798 (2011)
http://dx.doi.org/10.1364/OE.19.007790


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Abstract

We present experimentally feasible designs of a dual-core microstructured polymer optical fiber (mPOF), which can act as a highly sensitive, label-free, and selective biosensor. An immobilized antigen sensing layer on the walls of the holes in the mPOF provides the ability to selectively capture antibody biomolecules. The change of the layer thickness of biomolecules can then be detected as a change in the coupling length between the two cores. We compare mPOF structures with 1, 2, and 3 air-holes between the solid cores and show that the sensitivity increases with increasing distance between the cores. Numerical calculations indicate a record sensitivity up to 20 nm/nm (defined as the shift in the resonance wavelength per nm biolayer) at visible wavelengths, where the mPOF has low loss.

© 2011 OSA

1. Introduction

Microstructured optical fibers (MOFs) based on either silica [1

1. 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(19), 1547–1549 (1996). [CrossRef] [PubMed]

], or polymers, such as poly(methyl methacrylate) (PMMA) [2

2. M. A. van Eijkelenborg, M. Large, A. Argyros, J. Zagari, S. Manos, N. Issa, I. Bassett, S. Fleming, R. McPhedran, C. M. de Sterke, and N. A. Nicorovici, “Microstructured polymer optical fibre,” Opt. Express 9(7), 319–327 (2001). [CrossRef] [PubMed]

] or topas [3

3. G. Emiliyanov, J. B. Jensen, O. Bang, P. E. Hoiby, L. H. Pedersen, E. M. Kjær, and L. Lindvold, “Localized biosensing with Topas microstructured polymer optical fiber,” Opt. Lett. 32(5), 460–462 (2007). [CrossRef] [PubMed]

5

5. K. Nielsen, H. K. Rasmussen, A. J. L. Adam, P. C. M. Planken, O. Bang, and P. U. Jepsen, “Bendable, low-loss Topas fibers for the terahertz frequency range,” Opt. Express 17(10), 8592–8601 (2009). [CrossRef] [PubMed]

], are a class of fibers in which the cladding has an array of holes running along the entire length of the fiber. MOF-based platforms are interesting for biosensing applications, because biological samples can be probed by the guided light inside the holes without removing the coating and cladding of the fiber, maintaining thus the robustness of the sensor [6

6. T. M. Monro, D. J. Richardson, and P. J. Bennet, “Developing holey fibers for evanescent field devices,” Electron. Lett. 35(14), 1188–1189 (1999). [CrossRef]

10

10. X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: A review,” Anal. Chim. Acta 620(1-2), 8–26 (2008). [CrossRef] [PubMed]

]. In addition, the air holes of the MOF may hold a biological sample volume of a few nL per cm of the fiber while still achieving high sensitivity, which is a significant advantage for biosensing applications. Geometrical manipulation of the fiber cross-section gives MOFs an extreme ability to increase the interaction of the guided light with the sample by a number of different configurations and working principles that have already been demonstrated. Typical label-free, fiber-optic biosensors are based on tracking the shift in a resonance (surface plasmon, gratings, Fabry-Pérot, etc.) introduced by the presence of a biological agent [11

11. A. Hassani and M. Skorobogatiy, “Design of the microstructured optical fiber-based surface plasmon resonance sensors with enhanced microfluidics,” Opt. Express 14(24), 11616–11621 (2006). [CrossRef] [PubMed]

22

22. B. Sun, M. Y. Chen, Y. K. Zhang, J. C. Yang, J. Q. Yao, and H. X. Cui, “Microstructured-core photonic-crystal fiber for ultra-sensitive refractive index sensing,” Opt. Express 19(5), 4091–4100 (2011). [CrossRef] [PubMed]

].

Given that a pre-required ability for a label-free biosensor to function is that it is able to work as a sensitive refractive index sensor we will discuss biosensors and refractive index sensors in parallel. The best sensitivities of label-free MOF biosensors to date have been reported in devices in which the sample modifies the phase matching between coupled modes. Rindorf et al. demonstrated experimentally a sensitivity of 1.4 nm/nm, i.e. a 1.4 nm shift in resonance wavelength per nm biolayer of a long-period grating [16

16. L. Rindorf, J. B. Jensen, M. Dufva, L. H. Pedersen, P. E. Høiby, and O. Bang, “Photonic crystal fiber long-period gratings for biochemical sensing,” Opt. Express 14(18), 8224–8231 (2006). [CrossRef] [PubMed]

], and recently Ott et al. predicted a sensitivity of 10.4 nm/nm in a four-wave mixing based label-free biosensor [17

17. J. R. Ott, M. Heuck, C. Agger, P. D. Rasmussen, and O. Bang, “Label-free and selective nonlinear fiber-optical biosensing,” Opt. Express 16(25), 20834–20847 (2008). [CrossRef] [PubMed]

]. In terms of refractive index sensing, Wu et al. recently demonstrated a sensitivity of 30,100 nm per refractive index unit (nm/RIU) in a refractive index guiding dual-core silica MOF operating above cut-off of a selectively filled analyte channel [18

18. D. K. C. Wu, B. T. Kuhlmey, and B. J. Eggleton, “Ultrasensitive photonic crystal fiber refractive index sensor,” Opt. Lett. 34(3), 322–324 (2009). [CrossRef] [PubMed]

]. This device, however, was not suitable for sensing refractive indices less than that of the fiber host. It has now been shown that coating the holes and using fluorinated polymer MOFs will allow to extend the regime of operation to low indices, such as water [19

19. B. T. Kuhlmey, S. Coen, and S. Mahmoodian, “Coated photonic bandgap fibres for low-index sensing applications: cutoff analysis,” Opt. Express 17(18), 16306–16321 (2009). [CrossRef] [PubMed]

]. Yuan et al. demonstrated the design of an all-solid dual-core photonic bandgap fiber, in which a single hole between the cores acts as microfluidic channel for the analyte [20

20. W. Yuan, G. E. Town, and O. Bang, “Refractive Index Sensing in an All-Solid Twin-Core Photonic Bandgap Fiber,” IEEE Sens. J. 10(7), 1767–1770 (2010). [CrossRef]

]. The predicted sensitivity was 70,000 nm/RIU. Town et al. reported a dual-core MOF sensor that could also use simple single-wavelength intensity-based sensing with a sensitivity (change in transmittance per refractive index unit) that could be increased to 169,711%/RIU by selectively filling the two holes between the cores of the coupler [21

21. G. E. Town, W. Yuan, R. McCosker, and O. Bang, “Microstructured optical fiber refractive index sensor,” Opt. Lett. 35(6), 856–858 (2010). [CrossRef] [PubMed]

]. More recently, Sun et al. proposed a refractive index sensor based on a microstructured-core MOF, where coupling changes between the conventional and the microstructured-core depend on the analyte filled into the holes of the core [22

22. B. Sun, M. Y. Chen, Y. K. Zhang, J. C. Yang, J. Q. Yao, and H. X. Cui, “Microstructured-core photonic-crystal fiber for ultra-sensitive refractive index sensing,” Opt. Express 19(5), 4091–4100 (2011). [CrossRef] [PubMed]

]. The authors in [22

22. B. Sun, M. Y. Chen, Y. K. Zhang, J. C. Yang, J. Q. Yao, and H. X. Cui, “Microstructured-core photonic-crystal fiber for ultra-sensitive refractive index sensing,” Opt. Express 19(5), 4091–4100 (2011). [CrossRef] [PubMed]

] demonstrated sensitivity up to 8500 nm/RI, while the detection limit was 2.02x10-6 for an analyte with refractive index of 1.33.

The experimental record sensitivity of 1.4 nm/nm was obtained using a long-period grating and requires therefore post-processing of the fiber, as does any grating or surface-plasmon based sensor. The theoretically predicted record sensitivity of 10.4 nm/nm [17

17. J. R. Ott, M. Heuck, C. Agger, P. D. Rasmussen, and O. Bang, “Label-free and selective nonlinear fiber-optical biosensing,” Opt. Express 16(25), 20834–20847 (2008). [CrossRef] [PubMed]

] uses the inherent nonlinearity of the fiber material for four-wave mixing and thus requires no post-processing. However, it requires a long length of the fiber and high power. The dual-core MOFs have not yet been investigated for label-free biosensing but only for refractive index sensing. The dual-core MOF based refractive index sensors reported so far either require selective filling [18

18. D. K. C. Wu, B. T. Kuhlmey, and B. J. Eggleton, “Ultrasensitive photonic crystal fiber refractive index sensor,” Opt. Lett. 34(3), 322–324 (2009). [CrossRef] [PubMed]

,19

19. B. T. Kuhlmey, S. Coen, and S. Mahmoodian, “Coated photonic bandgap fibres for low-index sensing applications: cutoff analysis,” Opt. Express 17(18), 16306–16321 (2009). [CrossRef] [PubMed]

,21

21. G. E. Town, W. Yuan, R. McCosker, and O. Bang, “Microstructured optical fiber refractive index sensor,” Opt. Lett. 35(6), 856–858 (2010). [CrossRef] [PubMed]

,22

22. B. Sun, M. Y. Chen, Y. K. Zhang, J. C. Yang, J. Q. Yao, and H. X. Cui, “Microstructured-core photonic-crystal fiber for ultra-sensitive refractive index sensing,” Opt. Express 19(5), 4091–4100 (2011). [CrossRef] [PubMed]

], have very small holes [21

21. G. E. Town, W. Yuan, R. McCosker, and O. Bang, “Microstructured optical fiber refractive index sensor,” Opt. Lett. 35(6), 856–858 (2010). [CrossRef] [PubMed]

], or have an all-solid bandgap structure that requires to find two suitable materials that are also compatible for drawing [20

20. W. Yuan, G. E. Town, and O. Bang, “Refractive Index Sensing in an All-Solid Twin-Core Photonic Bandgap Fiber,” IEEE Sens. J. 10(7), 1767–1770 (2010). [CrossRef]

], which can be very difficult [23

23. Y. Gao, N. Guo, B. Gauvreau, M. Rajabian, O. Skorobogata, E. Pone, O. Zabeida, L. Martinu, C. Dubois, and M. Skorobogatiy, “Consecutive solvent evaporation and co-rolling techniques for polymer multilayer hollow fiber preform fabrication,” J. Mater. Res. 21(9), 2246–2254 (2006). [CrossRef]

].

In this work, we have numerically investigated a dual-core mPOF biosensor made of PMMA, in which an antigen sensor layer can selectively capture a thin layer of around 5 nm of antibody biomolecules via the antigen-antibody binding process [7

7. J. B. Jensen, L. H. Pedersen, P. E. Hoiby, L. B. Nielsen, T. P. Hansen, J. R. Folkenberg, J. Riishede, D. Noordegraaf, K. Nielsen, A. Carlsen, and A. Bjarklev, “Photonic crystal fiber based evanescent-wave sensor for detection of biomolecules in aqueous solutions,” Opt. Lett. 29(17), 1974–1976 (2004). [CrossRef] [PubMed]

, 24

24. J. B. Jensen, P. E. Hoiby, G. Emiliyanov, O. Bang, L. Pedersen, and A. Bjarklev, “Selective detection of antibodies in microstructured polymer optical fibers,” Opt. Express 13(15), 5883–5889 (2005). [CrossRef] [PubMed]

]. Dual-core MOFs were first fabricated in silica by Mangan et al. [25

25. B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, and A. H. Greenaway, “Experimental study of dual core photonic crystal fibre,” Electron. Lett. 36(16), 1358–1359 (2000). [CrossRef]

] and in polymer by Padden et al. [26

26. W. E. P. Padden, M. A. van Eijkelenborg, A. Argyros, and N. A. Issa, “Coupling in a twin-core microstructured polymer optical fiber,” Appl. Phys. Lett. 84(10), 1689–1691 (2004). [CrossRef]

], with some of the early modeling work being done by Hansen and Town [27

27. M. Hansen, and G. E. Town, “All-optical switching in dual-core microstructured optical fibres modeled using beam-propagation”, Proceedings, 28th Australian Conference on Optical Fibre Technology (ACOFT2003), Melbourne

, 28

28. M. Hansen, and G. E. Town, “Properties of dual-core couplers in microstructured optical fibres,” Proceeedings, 28th European Conference on Optical Communications (ECOC/IOOC 2003), Vol. 3, p.616–617, Rimini, September, 2003.

]. The main advantage of considering polymer MOFs and PMMA is that biomolecules can be attached directly to the surface of the holes of the fiber [24

24. J. B. Jensen, P. E. Hoiby, G. Emiliyanov, O. Bang, L. Pedersen, and A. Bjarklev, “Selective detection of antibodies in microstructured polymer optical fibers,” Opt. Express 13(15), 5883–5889 (2005). [CrossRef] [PubMed]

], avoiding in this way any further functionalization; combined with the fact that mPOFs can now be routinely fabricated with a wealth of different structures [29

29. M. Large, L. Poladian, G. Barton, and M. A. van Eijkelenborg, Microstructured Polymer Optical Fibres, (Springer, 2008), Chap. 7.

]. In other polymers, such as topas, intermediate layers still have to be used to immobilize the capture layer [3

3. G. Emiliyanov, J. B. Jensen, O. Bang, P. E. Hoiby, L. H. Pedersen, E. M. Kjær, and L. Lindvold, “Localized biosensing with Topas microstructured polymer optical fiber,” Opt. Lett. 32(5), 460–462 (2007). [CrossRef] [PubMed]

, 4

4. G. Emiliyanov, J. B. Jensen, O. Bang, P. E. Hoiby, L. H. Pedersen, E. M. Kjær, and L. Lindvold, “Localized biosensing with Topas microstructured polymer optical fiber: erratum,” Opt. Lett. 32(9), 1059–1059 (2007). [CrossRef]

]. So even though topas mPOF couplers are possible [30

30. K. Nielsen, H. K. Rasmussen, P. U. Jepsen, and O. Bang, “Broadband terahertz fiber directional coupler,” Opt. Lett. 35(17), 2879–2881 (2010). [CrossRef] [PubMed]

], we will focus on PMMA here.

The increment of the layer thickness due to the immobilization of antibody biomolecules will directly affect the coupling coefficient of the dual-core mPOF coupler, and thereby change the transmittance of the coupler. We have compared three dual-core mPOF biosensor structures with different separation distance between the two cores (1, 2 and 3 holes separation). Apriori, the largest separation should result in the largest sensitivity [31

31. G. E. Town, R. F. Copperwhite, R. Kribich, K. O’Dwyer, and B. D. MacCraith, “Comparison of multimode and multichannel couplers for evanescent sensing of refractive index, in Proc. 30th Australian Conf. Optical Fiber Technol., Sydney, Australia, 2005.

] and this is what has been observed. A sensitivity of around 20 nm/nm is achieved for a 15 cm long device at visible wavelengths, where the mPOF exhibits the lowest loss. This is the highest reported sensitivity for a MOF biosensor. The structural parameters of the mPOF biosensor are kept experimentally feasible, both in terms of the pitch and hole diameter of the preform as well as in terms of the device length, when taking into consideration the loss and ease of fabrication and handling.

2. Design parameters of mPOF biosensor

We always consider the holes of the mPOF biosensor filled with water, mainly for two reasons: 1) because water reduces the refractive index contrast between cladding-core, enabling thus single-mode operation of the fiber above 500 nm, and 2) the introduction of samples in aqueous solution into the sensor might leave remnants of water, which from an experimental point of view is difficult to remove. Infiltration techniques have been previously demonstrated both theoretically and experimentally, where water infusion can be achieved either applying capillary forces or with low pressure in pressure chambers, even in holes with diameters of 1 micron [32

32. B. T. Kuhlmey, B. J. Eggleton, and D. K. C. Wu, “Fluid-Filled Solid-Core Photonic Bandgap Fibers,” J. Lightwave Technol. 27(11), 1617–1630 (2009). [CrossRef]

, 33

33. K. Nielsen, D. Noordegraaf, T. Sorensen, A. Bjarklev, and T. Hansen, “Selective filling of photonic crystal fibres,” J. Opt. A, Pure Appl. Opt. 7(8), L13–L20 (2005). [CrossRef]

]. The dispersion of water and PMMA has been included in our calculations based on their Sellmeier equations [34

34. E. Palik, Handbook of Optical Constants of Solids I–III (Academic, 1998).

, 35

35. I. D. Nikolov and C. D. Ivanov, “Optical Plastic Refractive Measurements in the Visible and the Near-Infrared Regions,” Appl. Opt. 39(13), 2067–2070 (2000). [CrossRef]

]. The refractive index and material dispersion of the layer of biomolecules depend on the orientation of the molecules. However, experimental measurements with MOF biosensors have shown that a refractive index of n = 1.45 for α-streptavidin biomolecules is a realistic assumption [16

16. L. Rindorf, J. B. Jensen, M. Dufva, L. H. Pedersen, P. E. Høiby, and O. Bang, “Photonic crystal fiber long-period gratings for biochemical sensing,” Opt. Express 14(18), 8224–8231 (2006). [CrossRef] [PubMed]

]. We therefore use n = 1.45 and neglect dispersion of the thin layer of biomolecules. The numerical investigation of the dual-core mPOF biosensor is done by employing the fully vectorial integrated mode solver of the commercially available Lumerical FDTD solutions software. The effective indices of the fundamental guided modes are computed based on finite difference analysis using Yee’s mesh and the index averaging technique [36

36. Z. Zhu and T. Brown, “Full-vectorial finite-difference analysis of microstructured optical fibers,” Opt. Express 10(17), 853–864 (2002). [PubMed]

].

The proposed structures of the dual-core mPOF biosensor can be fabricated with a two-stage drawing process using a realistic preform of diameter of 6 cm with holes of 2 mm diameter drilled into it. An important parameter of the proposed PMMA-based biosensor is the loss. We have experimentally measured the loss of a single-core PMMA mPOF with a diameter of 130 µm fabricated at DTU Fotonik with the same relative hole size of d/Λ = 0.5 as the proposed dual-core structure (see inset in Fig. 2
Fig. 2 Loss profile of an mPOF with d/Λ = 0.5. Inset: Cross-section of the fiber.
).

We used the cut-back technique and measured the output power of the mPOF at 14 different lengths, starting from 55 cm, using a broadband source (SuperK from NKT photonics). The measurements are performed with great care in order to minimize errors from coupling in/out instabilities, cleaving quality, bending effects, etc. Figure 2 shows the experimentally measured loss of the fiber to be around 5 - 30 dB/m which is significantly higher than the record of 0.1 - 1 dB/m for the range of 500 - 850 nm stated in [29

29. M. Large, L. Poladian, G. Barton, and M. A. van Eijkelenborg, Microstructured Polymer Optical Fibres, (Springer, 2008), Chap. 7.

]. However, the mPOF is made from a cheap low-purity PMMA with non-optimal preform fabrication conditions. Further optimization in terms of cooling liquid used in preform drilling and proper washing and drying in clean atmosphere after drilling, are underway. Given the loss we will use fiber lengths less than 15 cm.

3. Results and discussion

3.1 Sensing mechanism – transmittance

The cores of the mPOF form a balanced linear directional coupler, in which light in the two cores interact due to a weak overlap of their evanescent fields, enabling a periodic transfer of the optical power from one core to the other [27

27. M. Hansen, and G. E. Town, “All-optical switching in dual-core microstructured optical fibres modeled using beam-propagation”, Proceedings, 28th Australian Conference on Optical Fibre Technology (ACOFT2003), Melbourne

,28

28. M. Hansen, and G. E. Town, “Properties of dual-core couplers in microstructured optical fibres,” Proceeedings, 28th European Conference on Optical Communications (ECOC/IOOC 2003), Vol. 3, p.616–617, Rimini, September, 2003.

,38

38. J. Laegsgaard, O. Bang, and A. Bjarklev, “Photonic crystal fiber design for broadband directional coupling,” Opt. Lett. 29(21), 2473–2475 (2004). [CrossRef] [PubMed]

]. This coupling can be understood and analyzed in terms of a pair of supermodes; a symmetric (even) and an asymmetric (odd) supermode. Figures 3(a-b)
Fig. 3 Electric field distribution of the even (a) and odd (b) x-polarized supermode at 1 μm wavelength for the mPOF structure with 3Λ separation between the cores. (c) Effective index difference of the x (solid line) and y (dotted line) polarizations.
shows the even and odd x-polarized intensity distribution of the supermodes of a water-filled dual-core mPOF with 2 holes between the solid cores, while Fig. 3(c) shows the effective index difference between the x- and y-polarization of the supermodes. Although the difference between the effective indices is relative small, the two orthogonal polarizations may yield differences in the coupling length. In any case, the sensing mechanism remains the same and thus only one (x-polarization) is shown here. Experimentally, the elimination of the other polarization can be done via the insertion of a polarizer as proposed by Wu et al. [18

18. D. K. C. Wu, B. T. Kuhlmey, and B. J. Eggleton, “Ultrasensitive photonic crystal fiber refractive index sensor,” Opt. Lett. 34(3), 322–324 (2009). [CrossRef] [PubMed]

].

Given the effective index difference, we can now determine how the capture of a biolayer of a certain thickness t on the walls of the holes of the mPOF affects the coupling length of the biosensor, LC, which is given by:

LC=λ2Δneff(λ,t)
(1)

The coupling length of the dual-core mPOF with 2 holes between the cores decreases monotonically with wavelength as shown in Fig. 4(a)
Fig. 4 (a) Coupling length versus wavelength of the dual-core mPOF biosensor with two holes (3Λ) between the cores, and a 0 nm (solid line), 40nm (dashed), and 45 nm biolayer immobilized onto the walls of the holes. (b) Coupling length of the dual-core mPOF with immobilized 40 nm sensor layer for 2Λ (dotted), 3Λ (dashed), and 4Λ (solid) separation distance between the cores.
. Addition of the antigen sensor layer with 40 nm thickness onto the walls of the holes in the mPOF significantly reduces the coupling length, for all wavelengths. The additional 5 nm thick layer of captured α-streptavidin biomolecules decreases the coupling length even further.

In Fig. 4(b) we compare the coupling length for a dual-core biosensor (i.e., a coupler with 40 nm sensor layer) with 1, 2, and 3 holes between the cores. As expected we see that the coupling length increases with the core-separation because the overlap of the evanescent tails of the core modes becomes weaker. We also see that 3 holes is the maximum separation we can use if we want a fiber length of less than 15 cm below 650 nm.

From the coupling length LC, we can calculate the transmittance of the biosensor using the following expression:
T=cos2(πL/2LC)
(2)
where L is the length of the fiber. Figure 5
Fig. 5 Plot of transmittance Pout/Pin of a 7 cm long dual-core mPOF biosensor versus wavelength (solid line), with an immobilized 40 nm antigen layer (dashed), and with a captured antibody layer of an additional 5 nm thickness (dotted). Separation distance between the cores is 2Λ. (Right) Simple schematic of the coupler with definition of Pout and Pin.
shows the transmittance (output power POUT relative to input power PIN) of a 7 cm long dual-core biosensor in the spectral range 500-800 nm. It clearly demonstrates how the addition of a biolayer changes the transmission by blue-shifting the extrema. Such a transmission spectrum allows for two different sensing schemes: (1) In the perhaps simplest scheme one can use a single-wavelength source and sense the transmitted power, in which case the highest sensitivity would be obtained by biasing the sensor to 50% transmittance [20

20. W. Yuan, G. E. Town, and O. Bang, “Refractive Index Sensing in an All-Solid Twin-Core Photonic Bandgap Fiber,” IEEE Sens. J. 10(7), 1767–1770 (2010). [CrossRef]

,21

21. G. E. Town, W. Yuan, R. McCosker, and O. Bang, “Microstructured optical fiber refractive index sensor,” Opt. Lett. 35(6), 856–858 (2010). [CrossRef] [PubMed]

]. (2) One can also use a broadband source and detector and sense the change in wavelength of an extremum [20

20. W. Yuan, G. E. Town, and O. Bang, “Refractive Index Sensing in an All-Solid Twin-Core Photonic Bandgap Fiber,” IEEE Sens. J. 10(7), 1767–1770 (2010). [CrossRef]

].

Here we focus on the broadband scheme and track the shift of the extrema, as one would when using a long-period grating [16

16. L. Rindorf, J. B. Jensen, M. Dufva, L. H. Pedersen, P. E. Høiby, and O. Bang, “Photonic crystal fiber long-period gratings for biochemical sensing,” Opt. Express 14(18), 8224–8231 (2006). [CrossRef] [PubMed]

] or four-wave mixing for the sensing [17

17. J. R. Ott, M. Heuck, C. Agger, P. D. Rasmussen, and O. Bang, “Label-free and selective nonlinear fiber-optical biosensing,” Opt. Express 16(25), 20834–20847 (2008). [CrossRef] [PubMed]

]. From Fig. 5 we see that the shift is largest for the lowest wavelength extrema. The first extremum will always be a minimum, which is obtained for LC = L, for which T = 0. However, from Fig. 4 we see that LC is always below 7 cm in the 500-800 nm window for a 45 nm biolayer. Thus the capture of the 5nm antibody biolayer should shift this minimum out of the window, which is confirmed in Fig. 5. The first maximum at λ1 = 605 nm blue-shifts by 20 nm when the 5 nm antibody biolayer is captured, which gives a sensitivity of 4 nm/nm. The longer wavelength extrema shift less, e.g., the second minimum at λ2 = 670 nm shifts only Δλ2 = 11 nm.

3.2 Sensitivity

In Fig. 6(b) we show the sensitivity of the dual-core mPOF with two holes (3Λ) between the cores. As expected the sensitivities for the two device lengths of 7 cm and 15 cm lie on the same curve, but the sensitivity is now higher. The maximum sensitivity is now 5.6 nm/nm at 560 nm and again the sensitivity decreases monotonically. However, the slope of the S(λ) curve is much steeper, as shown in Fig. 4(b), and thus there is much to be gained by operating at shorter wavelengths. Thus the maximum sensitivity for a 7 cm device is 4.0 nm/nm at 610 nm, while increasing the length to 15 cm allows to operate at a shorter wavelength of 560 nm and thereby increase the sensitivity to 5.6 nm/nm

By increasing the core separation to 3 holes (4Λ), Fig. 6(c) shows that the sensitivity reaches a level as high as 20 nm/nm at around 630 nm for the 15 cm long device. Importantly, this sensitivity is twice the hitherto record of 10.4 nm/nm using FWM [17

17. J. R. Ott, M. Heuck, C. Agger, P. D. Rasmussen, and O. Bang, “Label-free and selective nonlinear fiber-optical biosensing,” Opt. Express 16(25), 20834–20847 (2008). [CrossRef] [PubMed]

].

4. Conclusion

We have proposed a dual-core mPOF suitable for label-free and selective biosensing. The evanescent wave sensing is carried out inside the holes of the mPOF, which makes the sensor robust, while the dual-core functionality means that no post processing of the fiber is required as e.g., when using grating-based sensors. The basic operation principle relies on tracking the shift of an extremum in the transmittance when the sensor captures a layer of antibody biomolecules.

In our design, we considered a PMMA mPOF with a hexagonal hole structure with a hole diameter of 1 µm and a pitch of Λ = 2 µm. We calculated the coupling lengths for three different dual-core mPOFs with 2Λ, 3Λ and 4Λ core separation and a fixed fiber length of 7 cm and 15 cm. All the design parameters of the dual-core mPOF design are feasible for fabrication and operation and no selective filling is required. In order to verify the appropriate length of the device, we experimentally measured the loss of a single-core mPOF with the same characteristics as the proposed dual-core coupler.

Our results demonstrate that the sensitivity increases with increasing the distance between the solid cores, as also observed by Town et al. for planar structures in a study of refractive index sensing [31

31. G. E. Town, R. F. Copperwhite, R. Kribich, K. O’Dwyer, and B. D. MacCraith, “Comparison of multimode and multichannel couplers for evanescent sensing of refractive index, in Proc. 30th Australian Conf. Optical Fiber Technol., Sydney, Australia, 2005.

]. The distance of course cannot be increased indefinitely, given that the structure has to fit into a preform of a realistic size below 80 mm, where we use 60 mm, and given that hole sizes less than 1.5 mm are impossible to drill sufficiently deep to obtain a long enough preform. A further limitation is in terms of loss, given that the necessary length of the fiber increases with increased core separation.

The sensitivities of the most sensitive dual-core mPOF with 4Λ distance between the cores is for example 20.3 nm/nm at the He-Ne wavelength 633 nm and 8.9 nm/nm at 850 nm, where cheap CMOS technology is available. At these two important wavelengths the loss of our fiber is around 0.15 dB/cm and 0.07 dB/cm, respectively. This is acceptable when considering device lengths less than 15 cm. We note that, the loss can be reduced further, as described in Section 2, to levels less than 1dB/m, as reported by Large et al [29

29. M. Large, L. Poladian, G. Barton, and M. A. van Eijkelenborg, Microstructured Polymer Optical Fibres, (Springer, 2008), Chap. 7.

].

Our record sensitivity of 20.3 nm/nm, i.e., a shift of the resonant peak of transmittance of 20.3 nm per nm thickness of biolayer, is therefore obtained for experimentally very feasible design parameters. The sensitivity is twice the hitherto predicted record of 10.4 nm/nm for a MOF-based biosensor, which required longer fiber lengths and a high-power laser [17

17. J. R. Ott, M. Heuck, C. Agger, P. D. Rasmussen, and O. Bang, “Label-free and selective nonlinear fiber-optical biosensing,” Opt. Express 16(25), 20834–20847 (2008). [CrossRef] [PubMed]

].

Acknowledgments

The authors acknowledge support from IntelliCIS COST Action IC0806. Work of C.M. and K.V. was supported by the Greek NSRF Program with Grant No. 09SYN-24-769. The authors would like also to thank Michael Frosz and Kristian Nielsen for fruitful discussions.

References and links

1.

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(19), 1547–1549 (1996). [CrossRef] [PubMed]

2.

M. A. van Eijkelenborg, M. Large, A. Argyros, J. Zagari, S. Manos, N. Issa, I. Bassett, S. Fleming, R. McPhedran, C. M. de Sterke, and N. A. Nicorovici, “Microstructured polymer optical fibre,” Opt. Express 9(7), 319–327 (2001). [CrossRef] [PubMed]

3.

G. Emiliyanov, J. B. Jensen, O. Bang, P. E. Hoiby, L. H. Pedersen, E. M. Kjær, and L. Lindvold, “Localized biosensing with Topas microstructured polymer optical fiber,” Opt. Lett. 32(5), 460–462 (2007). [CrossRef] [PubMed]

4.

G. Emiliyanov, J. B. Jensen, O. Bang, P. E. Hoiby, L. H. Pedersen, E. M. Kjær, and L. Lindvold, “Localized biosensing with Topas microstructured polymer optical fiber: erratum,” Opt. Lett. 32(9), 1059–1059 (2007). [CrossRef]

5.

K. Nielsen, H. K. Rasmussen, A. J. L. Adam, P. C. M. Planken, O. Bang, and P. U. Jepsen, “Bendable, low-loss Topas fibers for the terahertz frequency range,” Opt. Express 17(10), 8592–8601 (2009). [CrossRef] [PubMed]

6.

T. M. Monro, D. J. Richardson, and P. J. Bennet, “Developing holey fibers for evanescent field devices,” Electron. Lett. 35(14), 1188–1189 (1999). [CrossRef]

7.

J. B. Jensen, L. H. Pedersen, P. E. Hoiby, L. B. Nielsen, T. P. Hansen, J. R. Folkenberg, J. Riishede, D. Noordegraaf, K. Nielsen, A. Carlsen, and A. Bjarklev, “Photonic crystal fiber based evanescent-wave sensor for detection of biomolecules in aqueous solutions,” Opt. Lett. 29(17), 1974–1976 (2004). [CrossRef] [PubMed]

8.

L. Rindorf, P. E. Høiby, J. B. Jensen, L. H. Pedersen, O. Bang, and O. Geschke, “Towards biochips using microstructured optical fiber sensors,” Anal. Bioanal. Chem. 385(8), 1370–1375 (2006). [CrossRef] [PubMed]

9.

M. E. Bosch, A. J. R. Sánchez, F. S. Rojas, and C. B. Ojeda, “Recent development in optical fiber biosensors,” Sensors 7(6), 797–859 (2007). [CrossRef]

10.

X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: A review,” Anal. Chim. Acta 620(1-2), 8–26 (2008). [CrossRef] [PubMed]

11.

A. Hassani and M. Skorobogatiy, “Design of the microstructured optical fiber-based surface plasmon resonance sensors with enhanced microfluidics,” Opt. Express 14(24), 11616–11621 (2006). [CrossRef] [PubMed]

12.

A. Wang, A. Docherty, B. T. Kuhlmey, F. M. Cox, and M. C. J. Large, “Side-hole fiber sensor based on surface plasmon resonance,” Opt. Lett. 34(24), 3890–3892 (2009). [CrossRef] [PubMed]

13.

L. Rindorf and O. Bang, “Highly sensitive refractometer with a photonic-crystal-fiber long-period grating,” Opt. Lett. 33(6), 563–565 (2008). [CrossRef] [PubMed]

14.

J. M. Fini, “Microstructure fibers for optical sensing in gases and liquids,” Meas. Sci. Technol. 15(6), 1120–1128 (2004). [CrossRef]

15.

Y. Zhang, H. Shibru, K. L. Cooper, and A. Wang, “Miniature fiber-optic multicavity Fabry-Perot interferometric biosensor,” Opt. Lett. 30(9), 1021–1023 (2005). [CrossRef] [PubMed]

16.

L. Rindorf, J. B. Jensen, M. Dufva, L. H. Pedersen, P. E. Høiby, and O. Bang, “Photonic crystal fiber long-period gratings for biochemical sensing,” Opt. Express 14(18), 8224–8231 (2006). [CrossRef] [PubMed]

17.

J. R. Ott, M. Heuck, C. Agger, P. D. Rasmussen, and O. Bang, “Label-free and selective nonlinear fiber-optical biosensing,” Opt. Express 16(25), 20834–20847 (2008). [CrossRef] [PubMed]

18.

D. K. C. Wu, B. T. Kuhlmey, and B. J. Eggleton, “Ultrasensitive photonic crystal fiber refractive index sensor,” Opt. Lett. 34(3), 322–324 (2009). [CrossRef] [PubMed]

19.

B. T. Kuhlmey, S. Coen, and S. Mahmoodian, “Coated photonic bandgap fibres for low-index sensing applications: cutoff analysis,” Opt. Express 17(18), 16306–16321 (2009). [CrossRef] [PubMed]

20.

W. Yuan, G. E. Town, and O. Bang, “Refractive Index Sensing in an All-Solid Twin-Core Photonic Bandgap Fiber,” IEEE Sens. J. 10(7), 1767–1770 (2010). [CrossRef]

21.

G. E. Town, W. Yuan, R. McCosker, and O. Bang, “Microstructured optical fiber refractive index sensor,” Opt. Lett. 35(6), 856–858 (2010). [CrossRef] [PubMed]

22.

B. Sun, M. Y. Chen, Y. K. Zhang, J. C. Yang, J. Q. Yao, and H. X. Cui, “Microstructured-core photonic-crystal fiber for ultra-sensitive refractive index sensing,” Opt. Express 19(5), 4091–4100 (2011). [CrossRef] [PubMed]

23.

Y. Gao, N. Guo, B. Gauvreau, M. Rajabian, O. Skorobogata, E. Pone, O. Zabeida, L. Martinu, C. Dubois, and M. Skorobogatiy, “Consecutive solvent evaporation and co-rolling techniques for polymer multilayer hollow fiber preform fabrication,” J. Mater. Res. 21(9), 2246–2254 (2006). [CrossRef]

24.

J. B. Jensen, P. E. Hoiby, G. Emiliyanov, O. Bang, L. Pedersen, and A. Bjarklev, “Selective detection of antibodies in microstructured polymer optical fibers,” Opt. Express 13(15), 5883–5889 (2005). [CrossRef] [PubMed]

25.

B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, and A. H. Greenaway, “Experimental study of dual core photonic crystal fibre,” Electron. Lett. 36(16), 1358–1359 (2000). [CrossRef]

26.

W. E. P. Padden, M. A. van Eijkelenborg, A. Argyros, and N. A. Issa, “Coupling in a twin-core microstructured polymer optical fiber,” Appl. Phys. Lett. 84(10), 1689–1691 (2004). [CrossRef]

27.

M. Hansen, and G. E. Town, “All-optical switching in dual-core microstructured optical fibres modeled using beam-propagation”, Proceedings, 28th Australian Conference on Optical Fibre Technology (ACOFT2003), Melbourne

28.

M. Hansen, and G. E. Town, “Properties of dual-core couplers in microstructured optical fibres,” Proceeedings, 28th European Conference on Optical Communications (ECOC/IOOC 2003), Vol. 3, p.616–617, Rimini, September, 2003.

29.

M. Large, L. Poladian, G. Barton, and M. A. van Eijkelenborg, Microstructured Polymer Optical Fibres, (Springer, 2008), Chap. 7.

30.

K. Nielsen, H. K. Rasmussen, P. U. Jepsen, and O. Bang, “Broadband terahertz fiber directional coupler,” Opt. Lett. 35(17), 2879–2881 (2010). [CrossRef] [PubMed]

31.

G. E. Town, R. F. Copperwhite, R. Kribich, K. O’Dwyer, and B. D. MacCraith, “Comparison of multimode and multichannel couplers for evanescent sensing of refractive index, in Proc. 30th Australian Conf. Optical Fiber Technol., Sydney, Australia, 2005.

32.

B. T. Kuhlmey, B. J. Eggleton, and D. K. C. Wu, “Fluid-Filled Solid-Core Photonic Bandgap Fibers,” J. Lightwave Technol. 27(11), 1617–1630 (2009). [CrossRef]

33.

K. Nielsen, D. Noordegraaf, T. Sorensen, A. Bjarklev, and T. Hansen, “Selective filling of photonic crystal fibres,” J. Opt. A, Pure Appl. Opt. 7(8), L13–L20 (2005). [CrossRef]

34.

E. Palik, Handbook of Optical Constants of Solids I–III (Academic, 1998).

35.

I. D. Nikolov and C. D. Ivanov, “Optical Plastic Refractive Measurements in the Visible and the Near-Infrared Regions,” Appl. Opt. 39(13), 2067–2070 (2000). [CrossRef]

36.

Z. Zhu and T. Brown, “Full-vectorial finite-difference analysis of microstructured optical fibers,” Opt. Express 10(17), 853–864 (2002). [PubMed]

37.

J.-J. Gau, E. H. Lan, B. Dunn, C.-M. Ho, and J. C. S. Woo, “A MEMS based amperometric detector for E. coli bacteria using self-assembled monolayers,” Biosens. Bioelectron. 16(9-12), 745–755 (2001). [CrossRef] [PubMed]

38.

J. Laegsgaard, O. Bang, and A. Bjarklev, “Photonic crystal fiber design for broadband directional coupling,” Opt. Lett. 29(21), 2473–2475 (2004). [CrossRef] [PubMed]

OCIS Codes
(060.2370) Fiber optics and optical communications : Fiber optics sensors
(280.1415) Remote sensing and sensors : Biological sensing and sensors
(060.4005) Fiber optics and optical communications : Microstructured fibers
(130.5460) Integrated optics : Polymer waveguides

ToC Category:
Sensors

History
Original Manuscript: January 20, 2011
Revised Manuscript: March 29, 2011
Manuscript Accepted: March 31, 2011
Published: April 7, 2011

Virtual Issues
Vol. 6, Iss. 5 Virtual Journal for Biomedical Optics

Citation
Christos Markos, Wu Yuan, Kyriakos Vlachos, Graham E. Town, and Ole Bang, "Label-free biosensing with high sensitivity in dual-core microstructured polymer optical fibers," Opt. Express 19, 7790-7798 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-8-7790


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References

  1. 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(19), 1547–1549 (1996). [CrossRef] [PubMed]
  2. M. A. van Eijkelenborg, M. Large, A. Argyros, J. Zagari, S. Manos, N. Issa, I. Bassett, S. Fleming, R. McPhedran, C. M. de Sterke, and N. A. Nicorovici, “Microstructured polymer optical fibre,” Opt. Express 9(7), 319–327 (2001). [CrossRef] [PubMed]
  3. G. Emiliyanov, J. B. Jensen, O. Bang, P. E. Hoiby, L. H. Pedersen, E. M. Kjær, and L. Lindvold, “Localized biosensing with Topas microstructured polymer optical fiber,” Opt. Lett. 32(5), 460–462 (2007). [CrossRef] [PubMed]
  4. G. Emiliyanov, J. B. Jensen, O. Bang, P. E. Hoiby, L. H. Pedersen, E. M. Kjær, and L. Lindvold, “Localized biosensing with Topas microstructured polymer optical fiber: erratum,” Opt. Lett. 32(9), 1059–1059 (2007). [CrossRef]
  5. K. Nielsen, H. K. Rasmussen, A. J. L. Adam, P. C. M. Planken, O. Bang, and P. U. Jepsen, “Bendable, low-loss Topas fibers for the terahertz frequency range,” Opt. Express 17(10), 8592–8601 (2009). [CrossRef] [PubMed]
  6. T. M. Monro, D. J. Richardson, and P. J. Bennet, “Developing holey fibers for evanescent field devices,” Electron. Lett. 35(14), 1188–1189 (1999). [CrossRef]
  7. J. B. Jensen, L. H. Pedersen, P. E. Hoiby, L. B. Nielsen, T. P. Hansen, J. R. Folkenberg, J. Riishede, D. Noordegraaf, K. Nielsen, A. Carlsen, and A. Bjarklev, “Photonic crystal fiber based evanescent-wave sensor for detection of biomolecules in aqueous solutions,” Opt. Lett. 29(17), 1974–1976 (2004). [CrossRef] [PubMed]
  8. L. Rindorf, P. E. Høiby, J. B. Jensen, L. H. Pedersen, O. Bang, and O. Geschke, “Towards biochips using microstructured optical fiber sensors,” Anal. Bioanal. Chem. 385(8), 1370–1375 (2006). [CrossRef] [PubMed]
  9. M. E. Bosch, A. J. R. Sánchez, F. S. Rojas, and C. B. Ojeda, “Recent development in optical fiber biosensors,” Sensors 7(6), 797–859 (2007). [CrossRef]
  10. X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, “Sensitive optical biosensors for unlabeled targets: A review,” Anal. Chim. Acta 620(1-2), 8–26 (2008). [CrossRef] [PubMed]
  11. A. Hassani and M. Skorobogatiy, “Design of the microstructured optical fiber-based surface plasmon resonance sensors with enhanced microfluidics,” Opt. Express 14(24), 11616–11621 (2006). [CrossRef] [PubMed]
  12. A. Wang, A. Docherty, B. T. Kuhlmey, F. M. Cox, and M. C. J. Large, “Side-hole fiber sensor based on surface plasmon resonance,” Opt. Lett. 34(24), 3890–3892 (2009). [CrossRef] [PubMed]
  13. L. Rindorf and O. Bang, “Highly sensitive refractometer with a photonic-crystal-fiber long-period grating,” Opt. Lett. 33(6), 563–565 (2008). [CrossRef] [PubMed]
  14. J. M. Fini, “Microstructure fibers for optical sensing in gases and liquids,” Meas. Sci. Technol. 15(6), 1120–1128 (2004). [CrossRef]
  15. Y. Zhang, H. Shibru, K. L. Cooper, and A. Wang, “Miniature fiber-optic multicavity Fabry-Perot interferometric biosensor,” Opt. Lett. 30(9), 1021–1023 (2005). [CrossRef] [PubMed]
  16. L. Rindorf, J. B. Jensen, M. Dufva, L. H. Pedersen, P. E. Høiby, and O. Bang, “Photonic crystal fiber long-period gratings for biochemical sensing,” Opt. Express 14(18), 8224–8231 (2006). [CrossRef] [PubMed]
  17. J. R. Ott, M. Heuck, C. Agger, P. D. Rasmussen, and O. Bang, “Label-free and selective nonlinear fiber-optical biosensing,” Opt. Express 16(25), 20834–20847 (2008). [CrossRef] [PubMed]
  18. D. K. C. Wu, B. T. Kuhlmey, and B. J. Eggleton, “Ultrasensitive photonic crystal fiber refractive index sensor,” Opt. Lett. 34(3), 322–324 (2009). [CrossRef] [PubMed]
  19. B. T. Kuhlmey, S. Coen, and S. Mahmoodian, “Coated photonic bandgap fibres for low-index sensing applications: cutoff analysis,” Opt. Express 17(18), 16306–16321 (2009). [CrossRef] [PubMed]
  20. W. Yuan, G. E. Town, and O. Bang, “Refractive Index Sensing in an All-Solid Twin-Core Photonic Bandgap Fiber,” IEEE Sens. J. 10(7), 1767–1770 (2010). [CrossRef]
  21. G. E. Town, W. Yuan, R. McCosker, and O. Bang, “Microstructured optical fiber refractive index sensor,” Opt. Lett. 35(6), 856–858 (2010). [CrossRef] [PubMed]
  22. B. Sun, M. Y. Chen, Y. K. Zhang, J. C. Yang, J. Q. Yao, and H. X. Cui, “Microstructured-core photonic-crystal fiber for ultra-sensitive refractive index sensing,” Opt. Express 19(5), 4091–4100 (2011). [CrossRef] [PubMed]
  23. Y. Gao, N. Guo, B. Gauvreau, M. Rajabian, O. Skorobogata, E. Pone, O. Zabeida, L. Martinu, C. Dubois, and M. Skorobogatiy, “Consecutive solvent evaporation and co-rolling techniques for polymer multilayer hollow fiber preform fabrication,” J. Mater. Res. 21(9), 2246–2254 (2006). [CrossRef]
  24. J. B. Jensen, P. E. Hoiby, G. Emiliyanov, O. Bang, L. Pedersen, and A. Bjarklev, “Selective detection of antibodies in microstructured polymer optical fibers,” Opt. Express 13(15), 5883–5889 (2005). [CrossRef] [PubMed]
  25. B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, and A. H. Greenaway, “Experimental study of dual core photonic crystal fibre,” Electron. Lett. 36(16), 1358–1359 (2000). [CrossRef]
  26. W. E. P. Padden, M. A. van Eijkelenborg, A. Argyros, and N. A. Issa, “Coupling in a twin-core microstructured polymer optical fiber,” Appl. Phys. Lett. 84(10), 1689–1691 (2004). [CrossRef]
  27. M. Hansen, and G. E. Town, “All-optical switching in dual-core microstructured optical fibres modeled using beam-propagation”, Proceedings, 28th Australian Conference on Optical Fibre Technology (ACOFT2003), Melbourne
  28. M. Hansen, and G. E. Town, “Properties of dual-core couplers in microstructured optical fibres,” Proceeedings, 28th European Conference on Optical Communications (ECOC/IOOC 2003), Vol. 3, p.616–617, Rimini, September, 2003.
  29. M. Large, L. Poladian, G. Barton, and M. A. van Eijkelenborg, Microstructured Polymer Optical Fibres, (Springer, 2008), Chap. 7.
  30. K. Nielsen, H. K. Rasmussen, P. U. Jepsen, and O. Bang, “Broadband terahertz fiber directional coupler,” Opt. Lett. 35(17), 2879–2881 (2010). [CrossRef] [PubMed]
  31. G. E. Town, R. F. Copperwhite, R. Kribich, K. O’Dwyer, and B. D. MacCraith, “Comparison of multimode and multichannel couplers for evanescent sensing of refractive index,” in Proc. 30th Australian Conf. Optical Fiber Technol., Sydney, Australia, 2005.
  32. B. T. Kuhlmey, B. J. Eggleton, and D. K. C. Wu, “Fluid-Filled Solid-Core Photonic Bandgap Fibers,” J. Lightwave Technol. 27(11), 1617–1630 (2009). [CrossRef]
  33. K. Nielsen, D. Noordegraaf, T. Sorensen, A. Bjarklev, and T. Hansen, “Selective filling of photonic crystal fibres,” J. Opt. A, Pure Appl. Opt. 7(8), L13–L20 (2005). [CrossRef]
  34. E. Palik, Handbook of Optical Constants of Solids I–III (Academic, 1998).
  35. I. D. Nikolov and C. D. Ivanov, “Optical Plastic Refractive Measurements in the Visible and the Near-Infrared Regions,” Appl. Opt. 39(13), 2067–2070 (2000). [CrossRef]
  36. Z. Zhu and T. Brown, “Full-vectorial finite-difference analysis of microstructured optical fibers,” Opt. Express 10(17), 853–864 (2002). [PubMed]
  37. J.-J. Gau, E. H. Lan, B. Dunn, C.-M. Ho, and J. C. S. Woo, “A MEMS based amperometric detector for E. coli bacteria using self-assembled monolayers,” Biosens. Bioelectron. 16(9-12), 745–755 (2001). [CrossRef] [PubMed]
  38. J. Laegsgaard, O. Bang, and A. Bjarklev, “Photonic crystal fiber design for broadband directional coupling,” Opt. Lett. 29(21), 2473–2475 (2004). [CrossRef] [PubMed]

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