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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 17 — Aug. 16, 2010
  • pp: 17950–17957
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An efficient approach for investigating surface plasmon resonance in asymmetric optical fibers based on birefringence analysis

Xia Yu, Shuyan Zhang, Ying Zhang, Ho-Pui Ho, Ping Shum, Hairong Liu, and Deming Liu  »View Author Affiliations


Optics Express, Vol. 18, Issue 17, pp. 17950-17957 (2010)
http://dx.doi.org/10.1364/OE.18.017950


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Abstract

We have analytically investigated the polarization dependence of surface plasmon resonance in fiber structures having strong asymmetry. From our simulation experiments it is found that the resonance wavelength coincides with the zero-birefringence point of two degenerate modes, consequently demonstrating a new approach through which one can accurately locate the resonance peak of the system without having to analyze the loss spectrum. Results obtained using the new technique also reveal better performance in terms of accuracy and computation efficiency. Application of this approach in the analysis of refractive index and pressure sensors based on the single core D-shaped and symmetric multiple air-hole fibers respectively is presented as a demonstration. The proposed technique, which primarily involves the search of zero-birefringence point, may be generalized for the study of other plasmonic waveguide structures.

© 2010 OSA

1. Introduction

For the study of the resonance of SPW excitation in optical fiber waveguides, common analytical models usually simplify the metallic coated waveguide into a multi-layer structure [10

10. H.-Y. Lin, W.-H. Tsai, Y.-C. Tsao, and B.-C. Sheu, “Side-polished multimode fiber biosensor based on surface plasmon resonance with halogen light,” Appl. Opt. 46(5), 800–806 (2007). [CrossRef] [PubMed]

]. In addition, coupled mode theory has also been deployed to investigate the coupling between surface plasmon and confined core modes [11

11. H. Ditlbacher, N. Galler, D. M. Koller, A. Hohenau, A. Leitner, F. R. Aussenegg, and J. R. Krenn, “Coupling dielectric waveguide modes to surface plasmon polaritons,” Opt. Express 16(14), 10455–10464 (2008). [CrossRef] [PubMed]

]. The intersection point of the dispersion curves for the plasmonic mode and core mode, which corresponds to the peak transmission loss of the waveguide, is used for locating the resonance wavelength [12

12. X. Yu, Y. Zhang, S. Pan, P. Shum, M. Yan, Y. Leviatan, and C. Li, “A selectively coated photonic crystal fiber based surface plasmon resonance sensor,” J. Opt. 12(1), 015005 (2010). [CrossRef]

]. However, coupled mode theory is limited especially when the weakly coupled assumption is not satisfied. Moreover, when the fiber structure is strongly asymmetric, two degenerate fundamental modes will further result in more complicated mode coupling conditions in two orthogonal directions. Pone et al. have demonstrated an elliptical holey fiber based pressure sensor by measuring the splitting of resonance wavelengths of the two orthogonal polarizations in the loss spectrum. The splitting value increases with the ellipticity of the air holes [13

13. E. Pone, A. Hassani, S. Lacroix, and M. Skorobogatiy, "A Pressure Sensor Based on the Loss Birefringence of a Microstructured Optical Fiber Containing Metal Coated Elliptical Inclusions," in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest (CD) (Optical Society of America, 2008), paper CMZ3.

]. Lee et al. also investigated the optical properties of asymmetric photonic crystal fibers with a single gold nanowire introduced into the core. Strongly polarization dependent resonance transmission was reported at surface plasmon resonance wavelength [14

14. H. W. Lee, M. A. Schmidt, H. K. Tyagi, L. P. Sempere, and P. S. J. Russell, “Polarization-dependent coupling to plasmon modes on submicron gold wire in photonic crystal fiber,” Appl. Phys. Lett. 93(11), 111102 (2008). [CrossRef]

]. However, when the transmission spectrum is flattened, as in many real cases, it becomes increasingly difficult to obtain sizeable signal change from simply measuring the loss spectrum. On the other hand, until now there exist limited reported studies on polarization dependent SPW excitation in asymmetric optical fibers.

In this paper, we numerically investigate the correlation between resonance coupling and degenerate mode properties. We report a new approach for determining the resonance wavelength when the fiber structure is strongly asymmetric. Two typical asymmetric fiber structures including a D-shaped fiber with gold coating and a photonic crystal fiber with elliptical air holes coated with silver have been demonstrated for the verification of this proposed approach. Polarization- dependent resonance condition is obtained by calculating the birefringence (B) of the fiber with metal inclusions, defined as the difference between the real part of the effective refractive indices of two degenerate modes in the x- and y-polarization direction, respectively. We identify the resonance by looking for the corresponding resonance wavelength when birefringence is zero. The new technique offers several advantages over the conventional approach in terms of the accuracy in determining the resonance wavelength and the efficiency in computational time and memory utilization.

2. Analytical approach

However, the real parts of the effective indices for two orthogonal modes exhibit a crossing point at exactly 637 nm as indicated in Fig. 2(b). Before this specific wavelength, x-polarized mode propagates slower than the y-polarized mode. This abrupt change of phase velocity at the resonance wavelength for the y-polarized mode implies the occurrence of a phase shift that also reflects the nature of the resonance behavior. This zero-birefringence situation also indicates that the x-polarized and y-polarized modes are degenerate and their phase velocities are equivalent. The D-shaped fiber introduced a structural birefringence. However, this birefringence should not have an abrupt change with wavelength, especially in a very narrow range. Therefore, the great phase shift could only be resulted from the metal layer on the polished side. It is corresponding to the phase shift on reflection at the Silica-Gold interface. At the SPR wavelength, where the absorption is the largest, the complex refractive index will contribute to the large variation of phase at this specific wavelength [19

19. A. Vasicek, “The reflection of light from a metal coated with thin films,” J. Phys. 1, 73–77 (1952).

]. It should be noted that the above wavelength range was obtained with a gold layer thickness of 30 nm. The new technique has also been verified with several other thickness values as well. We find excellent agreement on the determination of resonance wavelength using both techniques, thus confirming that the new zero-birefringence approach is indeed valid. In fact, Bienstman et al. have compared both in-house developed and commercial mode solvers, and concluded that generally the calculated imaginary part of the effective index varies much more significantly than the real part for different mode solvers [20

20. P. Bienstman, S. Selleri, L. Rosa, H. P. Uranus, W. C. L. Hopman, R. Costa, A. Melloni, L. C. Andreani, J. P. Hugonin, P. Lalanne, D. Pinto, S. S. A. Obayya, M. Dems, and K. Panajotov, “Modelling leaky photonic wires: A mode solver comparison,” Opt. Quantum Electron. 38(9-11), 731–759 (2007). [CrossRef]

]. Hence we can infer that the new technique would provide more accurate and consistent results than the conventional approach. In addition, a mode solver for only the real part of the propagation constant is sufficient. While the complex value is not a required parameter, it becomes quite clear that the new approach also have the merits of efficient computation as well as memory utilization.

3. Simulation results

Attempts were made to facilitate zero-birefringence point at visible wavelength range by increasing the ambient index on the gold surface from 1.41 to 1.42 as shown in Fig. 3
Fig. 3 Calculated resonance for different ambient refractive indices.
. This zero-birefringence point exhibits a wavelength red-shift from 637 nm to 670 nm. By assuming a 0.01 nm spectral resolution, we can readily obtain a 10−6 refractive index unit measurement sensitivity from this structure. The sensitivity obtained is comparable with other fiber based refractive index sensors reported in the literature [21

21. 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]

] including single-mode polarization maintaining fiber based SPR sensor [22

22. M. Piliarik, J. Homola, and Z. Maníková, “Surface plasmon resonance sensor based on a single-mode polarization-maintaining optical fiber,” Sens. Actuators B Chem. 90(1-3), 236–242 (2003). [CrossRef]

] and tilted Bragg grating based SPR sensor [23

23. Y. Y. Shevchenko and J. Albert, “Plasmon resonances in gold-coated tilted fiber Bragg gratings,” Opt. Lett. 32(3), 211–213 (2007). [CrossRef] [PubMed]

]. Moreover, the steep change at the zero-crossing point should lead to a more accurate measurement of the wavelength shift. Furthermore, devices with such polarization dependent property can be applied as a new kind of in-fiber wavelength dependent notch filter and polarizer [24

24. D. H. Spadoti, B. V. Borges, and M. A. Romero, “Birefringence enhancement by using D-shaped microstructure optical fibers,” J. Opt. A, Pure Appl. Opt. 11(8), 085105 (2009). [CrossRef]

].

4. Extended modeling of photonic crystal fiber

Another typical structure with asymmetric properties is a photonic crystal fiber with elliptical air holes. If the inner surface of these air holes is coated with silver for example, the surface plasmons on the silver layer will be excited by the evanescent field penetrated from the silica/silver interface. The peak loss of the x-polarized coupled mode matches with the zero-birefringence point at ~1030 nm as shown in Fig. 5
Fig. 5 Matching of zero birefringence with peak coupling loss in a photonic crystal fiber (inset) with elliptical air holes: elliptical ratio a/b = 0.82, uniform silver coating (red) thickness is 100 nm, pitch size is 1.5 µm.
. Moreover, the steep birefringence curve should provide more accurate measurement of the resonance wavelength compared to the one based on finding the loss peak from a relatively flat transmission spectrum.

Because of structural asymmetry, two resonances are found for the x- and y-polarized modes respectively. Without loss of generality, we shall only discuss the case involving a shorter resonance wavelength in this paper, i.e. λrs≈1030 nm for the x-polarized mode, while the same arguments can be completely applicable to the long wavelength case. The resonance condition can be calculated using two techniques: (i) our new birefringence approach and (ii) loss spectrum analysis. Firstly, the core-guided confinement mode field distribution before resonance is obtained as shown in Fig. 6(a)
Fig. 6 (a) & (b) Two different x-polarized core confinement mode distribution patterns before and after resonance; (c) & (d) the same core confinement mode (insets) before and after resonance wavelength with their corresponding mode profiles along the horizontal cut at Y = 0.
. At λrs, the sudden jump from the low to high birefringence value corresponds to the SPR point of the x-polarized mode pattern evolving from Fig. 6(a) to (b). After passing the resonance point, the core-guided confinement mode distribution will remain the same as shown in Fig. 6(b). In addition, it is observed that most of the plasmon intensity is concentrated away from the fiber core leading to considerably more field penetration into the cladding holes for Fig. 6(b) than (a) [18

18. A. Hassani and M. Skorobogatiy, “Design criteria for microstructured-optic-fiber based surface-plasmon-resonance sensors,” J. Opt. Soc. Am. B 24(6), 1423–1429 (2007). [CrossRef]

]. Secondly, we can also interpret the resonance process in terms of loss coupling of the core confinement mode. Figure 6(c) & (d) show the intensity distribution of the Poynting vector (along the fiber axis) of the same core confinement mode as it transforms from core-guided mode into the plasmonic regime passing through the resonance wavelength [27

27. J. Hou, D. Bird, A. George, S. Maier, B. Kuhlmey, and J. C. Knight, “Metallic mode confinement in microstructured fibres,” Opt. Express 16(9), 5983–5990 (2008). [CrossRef] [PubMed]

]. As can be seen clearly from the mode intensity profiles, most of the core energy is coupled to the silver/air interface when SPR occurs.

Figure 7
Fig. 7 Calculated birefringence for different hole elliptical ratio with Λ constant, a = 0.8 µm-δ and b = 0.8 µm + δ, where δ is the hole diameter change [13].
shows the change of birefringence value for three cases with different hole ellipticity ratios. The resonance wavelength is blue-shifted as the hole ellipticity ratio decreases. This is expected because a larger hole diameter in the x-direction will lead to a decrease in the resonance wavelength and an enhancement of field confinement [21

21. 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 principle, hole ellipticity can be detected by measuring the resonance wavelength change using the zero-birefringence point technique. The steep change of the birefringence around the zero value in PCF structure is due to the limited calculation points. But it is worth to note that the birefringence value in PCF is two orders of magnitude higher compared with that in D-shaped fiber. This is due to the effective elliptical core can induce a large structural birefringence if the surrounding air-holes are elliptical. While in the case of a D-shaped fiber, the polishing side in the cladding will not vary the core shape at all, therefore, not affecting the structural birefringence significantly.

5. Conclusion

We have analytically investigated the polarization dependence of surface plasmon resonance in two different asymmetric fiber structures. The resonance wavelength is obtained from measuring the zero-birefringence point of the two degenerate core confinement modes. It is applicable for all structures, especially when the asymmetry is large. We have also found excellent agreement between the zero-birefringence approach and the conventional technique based on locating the maximum point of transmission loss spectrum. Two different structures including a metal-coated D-shaped fiber and a photonic crystal fiber with elliptical air holes have also been intensively investigated for verification of this new method. It has been demonstrated that the new approach is more computation efficient as compared to the one based on searching for the peak in spectral transmission loss plot.

Acknowledgement

This work is supported by Singapore A*STAR SERC grant 0921450031, and SIMTech-NTU-CUHK collaborative research project grant U09-P-007SU.

References and links

1.

J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuators B Chem. 54(1-2), 3–15 (1999). [CrossRef]

2.

A. Otto, “Excitation of nonradiative surface plasma waves in silver by the method of frustrated total reflection,” Z. Phys. 216(4), 398–410 (1968). [CrossRef]

3.

E. Kretschmann and H. Raether, “Radiative decay of nonradiative surface plasmons excited by light,” Z. Naturforsch. 23A, 2135–2136 (1968).

4.

S. Arismar Cerqueira Jr., “Recent progress and novel applications of photonic crystal fibers,” Rep. Prog. Phys. 73(2), 024401 (2010). [CrossRef]

5.

A. K. Sharma, R. Jha, and B. D. Gupta, “Fiber-optic sensors based on surface plasmon resonance: a comprehensive review,” IEEE Sens. J. 7(8), 1118–1129 (2007). [CrossRef]

6.

C. Chen, A. Laronche, G. Bouwmans, L. Bigot, Y. Quiquempois, and J. Albert, “Sensitivity of photonic crystal fiber modes to temperature, strain and external refractive index,” Opt. Express 16(13), 9645–9653 (2008). [CrossRef] [PubMed]

7.

F. Du, Y.-Q. Lu, and S.-T. Wu, “Electrically tunable liquid-crystal photonic crystal fiber,” Appl. Phys. Lett. 85(12), 2181–2183 (2004). [CrossRef]

8.

D. Passaro, M. Foroni, F. Poli, A. Cucinotta, S. Selleri, J. Laegsgaard, and A. O. Bjarklev, “All-silica hollow-core microstructured Bragg fibers for biosensor application,” IEEE Sens. J. 8(7), 1280–1286 (2008). [CrossRef]

9.

D. Monzón-Hernández, V. P. Minkovich, J. Villatoro, M. P. Kreuzer, and G. Badenes, “Photonic crystal fiber microtaper supporting two selective higher-order modes with high sensitivity to gas molecules,” Appl. Phys. Lett. 93(8), 081106 (2008). [CrossRef]

10.

H.-Y. Lin, W.-H. Tsai, Y.-C. Tsao, and B.-C. Sheu, “Side-polished multimode fiber biosensor based on surface plasmon resonance with halogen light,” Appl. Opt. 46(5), 800–806 (2007). [CrossRef] [PubMed]

11.

H. Ditlbacher, N. Galler, D. M. Koller, A. Hohenau, A. Leitner, F. R. Aussenegg, and J. R. Krenn, “Coupling dielectric waveguide modes to surface plasmon polaritons,” Opt. Express 16(14), 10455–10464 (2008). [CrossRef] [PubMed]

12.

X. Yu, Y. Zhang, S. Pan, P. Shum, M. Yan, Y. Leviatan, and C. Li, “A selectively coated photonic crystal fiber based surface plasmon resonance sensor,” J. Opt. 12(1), 015005 (2010). [CrossRef]

13.

E. Pone, A. Hassani, S. Lacroix, and M. Skorobogatiy, "A Pressure Sensor Based on the Loss Birefringence of a Microstructured Optical Fiber Containing Metal Coated Elliptical Inclusions," in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest (CD) (Optical Society of America, 2008), paper CMZ3.

14.

H. W. Lee, M. A. Schmidt, H. K. Tyagi, L. P. Sempere, and P. S. J. Russell, “Polarization-dependent coupling to plasmon modes on submicron gold wire in photonic crystal fiber,” Appl. Phys. Lett. 93(11), 111102 (2008). [CrossRef]

15.

J. Homola, “On the sensitivity of surface-plasmon resonance sensors with spectral interrogation,” Sens. Actuators B Chem. 41(1-3), 207–211 (1997). [CrossRef]

16.

B. Lee, S. Roh, and J. Park, “Current status of micro- and nano-structured optical fiber sensors,” Opt. Fiber Technol. 15(3), 209–221 (2009). [CrossRef]

17.

R. Paschotta, (2008, Oct). Encyclopedia of Laser Physics and Technology. [Online]. Available: http://www.rp-photonics.com/encyclopedia.html

18.

A. Hassani and M. Skorobogatiy, “Design criteria for microstructured-optic-fiber based surface-plasmon-resonance sensors,” J. Opt. Soc. Am. B 24(6), 1423–1429 (2007). [CrossRef]

19.

A. Vasicek, “The reflection of light from a metal coated with thin films,” J. Phys. 1, 73–77 (1952).

20.

P. Bienstman, S. Selleri, L. Rosa, H. P. Uranus, W. C. L. Hopman, R. Costa, A. Melloni, L. C. Andreani, J. P. Hugonin, P. Lalanne, D. Pinto, S. S. A. Obayya, M. Dems, and K. Panajotov, “Modelling leaky photonic wires: A mode solver comparison,” Opt. Quantum Electron. 38(9-11), 731–759 (2007). [CrossRef]

21.

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]

22.

M. Piliarik, J. Homola, and Z. Maníková, “Surface plasmon resonance sensor based on a single-mode polarization-maintaining optical fiber,” Sens. Actuators B Chem. 90(1-3), 236–242 (2003). [CrossRef]

23.

Y. Y. Shevchenko and J. Albert, “Plasmon resonances in gold-coated tilted fiber Bragg gratings,” Opt. Lett. 32(3), 211–213 (2007). [CrossRef] [PubMed]

24.

D. H. Spadoti, B. V. Borges, and M. A. Romero, “Birefringence enhancement by using D-shaped microstructure optical fibers,” J. Opt. A, Pure Appl. Opt. 11(8), 085105 (2009). [CrossRef]

25.

M. N. O. Sadiku, Elements of Electromagnetics (Oxford University Press, 2001), pp. 563–565.

26.

A. Kumar, S. Pilevar, and K. Thyagarajan, “Measurements on variation of birefringence with depth of polishing in elliptic core fibers,” Opt. Commun. 72(3-4), 187–189 (1989). [CrossRef]

27.

J. Hou, D. Bird, A. George, S. Maier, B. Kuhlmey, and J. C. Knight, “Metallic mode confinement in microstructured fibres,” Opt. Express 16(9), 5983–5990 (2008). [CrossRef] [PubMed]

OCIS Codes
(060.2310) Fiber optics and optical communications : Fiber optics
(240.6680) Optics at surfaces : Surface plasmons
(260.1440) Physical optics : Birefringence

ToC Category:
Optics at Surfaces

History
Original Manuscript: June 17, 2010
Revised Manuscript: August 2, 2010
Manuscript Accepted: August 2, 2010
Published: August 5, 2010

Citation
Xia Yu, Shuyan Zhang, Ying Zhang, Ho-Pui Ho, Ping Shum, Hairong Liu, and Deming Liu, "An efficient approach for investigating surface plasmon resonance in asymmetric optical fibers based on birefringence analysis," Opt. Express 18, 17950-17957 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-17-17950


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References

  1. J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuators B Chem. 54(1-2), 3–15 (1999). [CrossRef]
  2. A. Otto, “Excitation of nonradiative surface plasma waves in silver by the method of frustrated total reflection,” Z. Phys. 216(4), 398–410 (1968). [CrossRef]
  3. E. Kretschmann and H. Raether, “Radiative decay of nonradiative surface plasmons excited by light,” Z. Naturforsch. 23A, 2135–2136 (1968).
  4. S. Arismar Cerqueira., “Recent progress and novel applications of photonic crystal fibers,” Rep. Prog. Phys. 73(2), 024401 (2010). [CrossRef]
  5. A. K. Sharma, R. Jha, and B. D. Gupta, “Fiber-optic sensors based on surface plasmon resonance: a comprehensive review,” IEEE Sens. J. 7(8), 1118–1129 (2007). [CrossRef]
  6. C. Chen, A. Laronche, G. Bouwmans, L. Bigot, Y. Quiquempois, and J. Albert, “Sensitivity of photonic crystal fiber modes to temperature, strain and external refractive index,” Opt. Express 16(13), 9645–9653 (2008). [CrossRef] [PubMed]
  7. F. Du, Y.-Q. Lu, and S.-T. Wu, “Electrically tunable liquid-crystal photonic crystal fiber,” Appl. Phys. Lett. 85(12), 2181–2183 (2004). [CrossRef]
  8. D. Passaro, M. Foroni, F. Poli, A. Cucinotta, S. Selleri, J. Laegsgaard, and A. O. Bjarklev, “All-silica hollow-core microstructured Bragg fibers for biosensor application,” IEEE Sens. J. 8(7), 1280–1286 (2008). [CrossRef]
  9. D. Monzón-Hernández, V. P. Minkovich, J. Villatoro, M. P. Kreuzer, and G. Badenes, “Photonic crystal fiber microtaper supporting two selective higher-order modes with high sensitivity to gas molecules,” Appl. Phys. Lett. 93(8), 081106 (2008). [CrossRef]
  10. H.-Y. Lin, W.-H. Tsai, Y.-C. Tsao, and B.-C. Sheu, “Side-polished multimode fiber biosensor based on surface plasmon resonance with halogen light,” Appl. Opt. 46(5), 800–806 (2007). [CrossRef] [PubMed]
  11. H. Ditlbacher, N. Galler, D. M. Koller, A. Hohenau, A. Leitner, F. R. Aussenegg, and J. R. Krenn, “Coupling dielectric waveguide modes to surface plasmon polaritons,” Opt. Express 16(14), 10455–10464 (2008). [CrossRef] [PubMed]
  12. X. Yu, Y. Zhang, S. Pan, P. Shum, M. Yan, Y. Leviatan, and C. Li, “A selectively coated photonic crystal fiber based surface plasmon resonance sensor,” J. Opt. 12(1), 015005 (2010). [CrossRef]
  13. E. Pone, A. Hassani, S. Lacroix, and M. Skorobogatiy, "A Pressure Sensor Based on the Loss Birefringence of a Microstructured Optical Fiber Containing Metal Coated Elliptical Inclusions," in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest (CD) (Optical Society of America, 2008), paper CMZ3.
  14. H. W. Lee, M. A. Schmidt, H. K. Tyagi, L. P. Sempere, and P. S. J. Russell, “Polarization-dependent coupling to plasmon modes on submicron gold wire in photonic crystal fiber,” Appl. Phys. Lett. 93(11), 111102 (2008). [CrossRef]
  15. J. Homola, “On the sensitivity of surface-plasmon resonance sensors with spectral interrogation,” Sens. Actuators B Chem. 41(1-3), 207–211 (1997). [CrossRef]
  16. B. Lee, S. Roh, and J. Park, “Current status of micro- and nano-structured optical fiber sensors,” Opt. Fiber Technol. 15(3), 209–221 (2009). [CrossRef]
  17. R. Paschotta, (2008, Oct). Encyclopedia of Laser Physics and Technology. [Online]. Available: http://www.rp-photonics.com/encyclopedia.html
  18. A. Hassani and M. Skorobogatiy, “Design criteria for microstructured-optic-fiber based surface-plasmon-resonance sensors,” J. Opt. Soc. Am. B 24(6), 1423–1429 (2007). [CrossRef]
  19. A. Vasicek, “The reflection of light from a metal coated with thin films,” J. Phys. 1, 73–77 (1952).
  20. P. Bienstman, S. Selleri, L. Rosa, H. P. Uranus, W. C. L. Hopman, R. Costa, A. Melloni, L. C. Andreani, J. P. Hugonin, P. Lalanne, D. Pinto, S. S. A. Obayya, M. Dems, and K. Panajotov, “Modelling leaky photonic wires: A mode solver comparison,” Opt. Quantum Electron. 38(9-11), 731–759 (2007). [CrossRef]
  21. 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]
  22. M. Piliarik, J. Homola, and Z. Maníková, “Surface plasmon resonance sensor based on a single-mode polarization-maintaining optical fiber,” Sens. Actuators B Chem. 90(1-3), 236–242 (2003). [CrossRef]
  23. Y. Y. Shevchenko and J. Albert, “Plasmon resonances in gold-coated tilted fiber Bragg gratings,” Opt. Lett. 32(3), 211–213 (2007). [CrossRef] [PubMed]
  24. D. H. Spadoti, B. V. Borges, and M. A. Romero, “Birefringence enhancement by using D-shaped microstructure optical fibers,” J. Opt. A, Pure Appl. Opt. 11(8), 085105 (2009). [CrossRef]
  25. M. N. O. Sadiku, Elements of Electromagnetics (Oxford University Press, 2001), pp. 563–565.
  26. A. Kumar, S. Pilevar, and K. Thyagarajan, “Measurements on variation of birefringence with depth of polishing in elliptic core fibers,” Opt. Commun. 72(3-4), 187–189 (1989). [CrossRef]
  27. J. Hou, D. Bird, A. George, S. Maier, B. Kuhlmey, and J. C. Knight, “Metallic mode confinement in microstructured fibres,” Opt. Express 16(9), 5983–5990 (2008). [CrossRef] [PubMed]

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