Abstract

We investigate theoretically the performance of photonic crystal fibres with coated holes as refractive index sensors. We show that coating the holes with a high-index material allows to extend the extreme sensitivities analyte-waveguide based geometries offer to the case of low-index analytes, including water-based solutions. As the sensitivity of these sensors is intricately linked to the sensitivity of the cutoff of a single inclusion to the analyte refractive index, our approach relies on the derivation of cutoff equations for coated inclusions. This is performed analytically without approximations, in the fully vectorial case, for modes of all orders. Our analytic approach allows us to rapidly cover the parameter space, and to quickly identify promising geometries. The best results are obtained when considering fluorinated polymer fibres, for which the index of the background material is not too different to that of water, and with thin high-index coatings. Using these results, we propose a sensor based on a directional coupler geometry that would lead to a sensitivity of 2.2×104 nm=RIU for water based solutions with achievable smallest detectable refractive index changes below 10-6.

© 2009 Optical Society of America

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2009 (3)

2008 (3)

2007 (1)

S. Afshar, S. C. Warren-Smith, and T. M. Monro, "Enhancement of fluorescence-based sensing using microstructured optical fibres," Opt. Express 15, 17,891-17,901 (2007).

2006 (6)

A. Hassani and M. Skorobogatiy, "Design of the microstructured optical fiber-based surface plasmon resonance sensors with enhanced microfluidics," Opt. Express 14, 11,616-11,621 (2006).
[CrossRef]

B. T. Kuhlmey, K. Pathmanandavel, and R. C. McPhedran, "Multipole analysis of photonic crystal fibers with coated inclusions," Opt. Express 14, 10,851-10,864 (2006).
[CrossRef]

P. J. A. Sazio, A. Amezcua-Correa, C. E. Finlayson, J. R. Hayes, T. J. Scheidemantel, N. F. Baril, B. R. Jackson, D.-J. Won, F. Zhang, E. R. Margine, V. Gopalan, V. H. Crespi, and J. V. Badding, "Microstructured optical fibers as high-pressure microfluidic reactors," Science 311, 1583-1586 (2006).
[CrossRef] [PubMed]

P. Steinvurzel, E. D. Moore, E. C. M¨agi, and B. J. Eggleton, "Tuning properties of long period gratings in photonic bandgap fibers," Opt. Lett. 31, 2103-2105 (2006).
[CrossRef] [PubMed]

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

D. Pristinski and H. Du, "Solid-core photonic crystal fiber as a Raman spectroscopy platform with a silica core as an internal reference," Opt. Lett. 31, 3246-3248 (2006).
[CrossRef] [PubMed]

2005 (1)

N. M. Litchinitser and E. Poliakov, "Antiresonant guiding microstructured optical fibers for sensing applications," Appl. Phys. B 81, 347-351 (2005).
[CrossRef]

2004 (1)

J. Laegsgaard, "Gap formation and guided modes in photonic bandgap fibres with high-index rods," J. Opt. A— Pure Appl. Opt. 6, 798-804 (2004).
[CrossRef]

2002 (2)

2001 (1)

T. M. Monro, W. Belardi, K. Furusawa, J. C. Baggett, N. G. R. Broderick, and D. J. Richardson, "Sensing with microstructured optical fibres," Meas. Sci. Technol. 12, 854-858 (2001).
[CrossRef]

1985 (1)

1982 (1)

A. C. Boucouvalas and C. D. Papageorgiou, "Cutoff frequencies in optical fibers of arbitrary refractive-index profile using the resonance technique," IEEE J. Quantum Elec. 18, 2027-2031 (1982).
[CrossRef]

1981 (1)

E. Sharma, I. Goyal, and A. Ghatak, "Calculation of cutoff frequencies in optical fibers for arbitrary profiles using the matrix method," IEEE J. Quantum Elec. 17, 2317-2321 (1981).
[CrossRef]

Afshar, S.

S. Afshar, S. C. Warren-Smith, and T. M. Monro, "Enhancement of fluorescence-based sensing using microstructured optical fibres," Opt. Express 15, 17,891-17,901 (2007).

Alkeskjold, T. T.

Amezcua-Correa, A.

P. J. A. Sazio, A. Amezcua-Correa, C. E. Finlayson, J. R. Hayes, T. J. Scheidemantel, N. F. Baril, B. R. Jackson, D.-J. Won, F. Zhang, E. R. Margine, V. Gopalan, V. H. Crespi, and J. V. Badding, "Microstructured optical fibers as high-pressure microfluidic reactors," Science 311, 1583-1586 (2006).
[CrossRef] [PubMed]

Badding, J. V.

P. J. A. Sazio, A. Amezcua-Correa, C. E. Finlayson, J. R. Hayes, T. J. Scheidemantel, N. F. Baril, B. R. Jackson, D.-J. Won, F. Zhang, E. R. Margine, V. Gopalan, V. H. Crespi, and J. V. Badding, "Microstructured optical fibers as high-pressure microfluidic reactors," Science 311, 1583-1586 (2006).
[CrossRef] [PubMed]

Badenes, G.

D. Monzon-Hernandez, 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, 081106/1-3 (2008).
[CrossRef]

Baggett, J. C.

T. M. Monro, W. Belardi, K. Furusawa, J. C. Baggett, N. G. R. Broderick, and D. J. Richardson, "Sensing with microstructured optical fibres," Meas. Sci. Technol. 12, 854-858 (2001).
[CrossRef]

Bang, O.

Baril, N. F.

P. J. A. Sazio, A. Amezcua-Correa, C. E. Finlayson, J. R. Hayes, T. J. Scheidemantel, N. F. Baril, B. R. Jackson, D.-J. Won, F. Zhang, E. R. Margine, V. Gopalan, V. H. Crespi, and J. V. Badding, "Microstructured optical fibers as high-pressure microfluidic reactors," Science 311, 1583-1586 (2006).
[CrossRef] [PubMed]

Bassi, P.

Belardi, W.

T. M. Monro, W. Belardi, K. Furusawa, J. C. Baggett, N. G. R. Broderick, and D. J. Richardson, "Sensing with microstructured optical fibres," Meas. Sci. Technol. 12, 854-858 (2001).
[CrossRef]

Borelli, E.

Botten, L. C.

Boucouvalas, A. C.

A. C. Boucouvalas, "Mode-cutoff frequencies of coaxial optical couplers," Opt. Lett. 10, 95-97 (1985).
[CrossRef] [PubMed]

A. C. Boucouvalas and C. D. Papageorgiou, "Cutoff frequencies in optical fibers of arbitrary refractive-index profile using the resonance technique," IEEE J. Quantum Elec. 18, 2027-2031 (1982).
[CrossRef]

Broderick, N. G. R.

T. M. Monro, W. Belardi, K. Furusawa, J. C. Baggett, N. G. R. Broderick, and D. J. Richardson, "Sensing with microstructured optical fibres," Meas. Sci. Technol. 12, 854-858 (2001).
[CrossRef]

Chen, J. S. Y.

T. G. Euser, J. S. Y. Chen, M. Scharrer, P. St. J. Russell, N. J. Farrer, and P. J. Sadler, "Quantitative broadband chemical sensing in air-suspended solid-core fibers," J. Appl. Phys. 103, 103108/1-7 (2008).
[CrossRef]

Crespi, V. H.

P. J. A. Sazio, A. Amezcua-Correa, C. E. Finlayson, J. R. Hayes, T. J. Scheidemantel, N. F. Baril, B. R. Jackson, D.-J. Won, F. Zhang, E. R. Margine, V. Gopalan, V. H. Crespi, and J. V. Badding, "Microstructured optical fibers as high-pressure microfluidic reactors," Science 311, 1583-1586 (2006).
[CrossRef] [PubMed]

de Sterke, C.

de Sterke, C. M.

Du, H.

Dufva, M.

Eggleton, B. J.

Euser, T. G.

T. G. Euser, J. S. Y. Chen, M. Scharrer, P. St. J. Russell, N. J. Farrer, and P. J. Sadler, "Quantitative broadband chemical sensing in air-suspended solid-core fibers," J. Appl. Phys. 103, 103108/1-7 (2008).
[CrossRef]

Farrer, N. J.

T. G. Euser, J. S. Y. Chen, M. Scharrer, P. St. J. Russell, N. J. Farrer, and P. J. Sadler, "Quantitative broadband chemical sensing in air-suspended solid-core fibers," J. Appl. Phys. 103, 103108/1-7 (2008).
[CrossRef]

Finlayson, C. E.

P. J. A. Sazio, A. Amezcua-Correa, C. E. Finlayson, J. R. Hayes, T. J. Scheidemantel, N. F. Baril, B. R. Jackson, D.-J. Won, F. Zhang, E. R. Margine, V. Gopalan, V. H. Crespi, and J. V. Badding, "Microstructured optical fibers as high-pressure microfluidic reactors," Science 311, 1583-1586 (2006).
[CrossRef] [PubMed]

Furusawa, K.

T. M. Monro, W. Belardi, K. Furusawa, J. C. Baggett, N. G. R. Broderick, and D. J. Richardson, "Sensing with microstructured optical fibres," Meas. Sci. Technol. 12, 854-858 (2001).
[CrossRef]

Ghatak, A.

E. Sharma, I. Goyal, and A. Ghatak, "Calculation of cutoff frequencies in optical fibers for arbitrary profiles using the matrix method," IEEE J. Quantum Elec. 17, 2317-2321 (1981).
[CrossRef]

Gopalan, V.

P. J. A. Sazio, A. Amezcua-Correa, C. E. Finlayson, J. R. Hayes, T. J. Scheidemantel, N. F. Baril, B. R. Jackson, D.-J. Won, F. Zhang, E. R. Margine, V. Gopalan, V. H. Crespi, and J. V. Badding, "Microstructured optical fibers as high-pressure microfluidic reactors," Science 311, 1583-1586 (2006).
[CrossRef] [PubMed]

Goyal, I.

E. Sharma, I. Goyal, and A. Ghatak, "Calculation of cutoff frequencies in optical fibers for arbitrary profiles using the matrix method," IEEE J. Quantum Elec. 17, 2317-2321 (1981).
[CrossRef]

Hassani, A.

A. Hassani and M. Skorobogatiy, "Design of the microstructured optical fiber-based surface plasmon resonance sensors with enhanced microfluidics," Opt. Express 14, 11,616-11,621 (2006).
[CrossRef]

Hayes, J. R.

P. J. A. Sazio, A. Amezcua-Correa, C. E. Finlayson, J. R. Hayes, T. J. Scheidemantel, N. F. Baril, B. R. Jackson, D.-J. Won, F. Zhang, E. R. Margine, V. Gopalan, V. H. Crespi, and J. V. Badding, "Microstructured optical fibers as high-pressure microfluidic reactors," Science 311, 1583-1586 (2006).
[CrossRef] [PubMed]

Hoiby, P. E.

Jackson, B. R.

P. J. A. Sazio, A. Amezcua-Correa, C. E. Finlayson, J. R. Hayes, T. J. Scheidemantel, N. F. Baril, B. R. Jackson, D.-J. Won, F. Zhang, E. R. Margine, V. Gopalan, V. H. Crespi, and J. V. Badding, "Microstructured optical fibers as high-pressure microfluidic reactors," Science 311, 1583-1586 (2006).
[CrossRef] [PubMed]

Jensen, J. B.

Karadeniz, E.

E. Karadeniz and P. Kornreich, "Optical fibers with high-index-contrast dielectric thin films," Opt. Eng. 45, 105,006 (2006).
[CrossRef]

Kornreich, P.

E. Karadeniz and P. Kornreich, "Optical fibers with high-index-contrast dielectric thin films," Opt. Eng. 45, 105,006 (2006).
[CrossRef]

Kreuzer, M. P.

D. Monzon-Hernandez, 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, 081106/1-3 (2008).
[CrossRef]

Kuhlmey, B.

Kuhlmey, B. T.

Laegsgaard, J.

Li, J.

Litchinitser, N. M.

N. M. Litchinitser and E. Poliakov, "Antiresonant guiding microstructured optical fibers for sensing applications," Appl. Phys. B 81, 347-351 (2005).
[CrossRef]

T. P. White, R. C. McPhedran, C. M. de Sterke, N. M. Litchinitser, and B. J. Eggleton, "Resonance and scattering in microstructured optical fibers," Opt. Lett. 27, 1977-1979 (2002).
[CrossRef]

M¨agi, E. C.

Margine, E. R.

P. J. A. Sazio, A. Amezcua-Correa, C. E. Finlayson, J. R. Hayes, T. J. Scheidemantel, N. F. Baril, B. R. Jackson, D.-J. Won, F. Zhang, E. R. Margine, V. Gopalan, V. H. Crespi, and J. V. Badding, "Microstructured optical fibers as high-pressure microfluidic reactors," Science 311, 1583-1586 (2006).
[CrossRef] [PubMed]

Maystre, D.

McPhedran, R.

McPhedran, R. C.

B. T. Kuhlmey, K. Pathmanandavel, and R. C. McPhedran, "Multipole analysis of photonic crystal fibers with coated inclusions," Opt. Express 14, 10,851-10,864 (2006).
[CrossRef]

T. P. White, R. C. McPhedran, C. M. de Sterke, N. M. Litchinitser, and B. J. Eggleton, "Resonance and scattering in microstructured optical fibers," Opt. Lett. 27, 1977-1979 (2002).
[CrossRef]

Minkovich, V. P.

D. Monzon-Hernandez, 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, 081106/1-3 (2008).
[CrossRef]

Monro, T. M.

S. Afshar, S. C. Warren-Smith, and T. M. Monro, "Enhancement of fluorescence-based sensing using microstructured optical fibres," Opt. Express 15, 17,891-17,901 (2007).

T. M. Monro, W. Belardi, K. Furusawa, J. C. Baggett, N. G. R. Broderick, and D. J. Richardson, "Sensing with microstructured optical fibres," Meas. Sci. Technol. 12, 854-858 (2001).
[CrossRef]

Monzon-Hernandez, D.

D. Monzon-Hernandez, 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, 081106/1-3 (2008).
[CrossRef]

Moore, E. D.

Noordegraaf, D.

Papageorgiou, C. D.

A. C. Boucouvalas and C. D. Papageorgiou, "Cutoff frequencies in optical fibers of arbitrary refractive-index profile using the resonance technique," IEEE J. Quantum Elec. 18, 2027-2031 (1982).
[CrossRef]

Pathmanandavel, K.

B. T. Kuhlmey, K. Pathmanandavel, and R. C. McPhedran, "Multipole analysis of photonic crystal fibers with coated inclusions," Opt. Express 14, 10,851-10,864 (2006).
[CrossRef]

Pedersen, L. H.

Poliakov, E.

N. M. Litchinitser and E. Poliakov, "Antiresonant guiding microstructured optical fibers for sensing applications," Appl. Phys. B 81, 347-351 (2005).
[CrossRef]

Pristinski, D.

Renversez, G.

Richardson, D. J.

T. M. Monro, W. Belardi, K. Furusawa, J. C. Baggett, N. G. R. Broderick, and D. J. Richardson, "Sensing with microstructured optical fibres," Meas. Sci. Technol. 12, 854-858 (2001).
[CrossRef]

Rindorf, L.

Russell, P. St. J.

T. G. Euser, J. S. Y. Chen, M. Scharrer, P. St. J. Russell, N. J. Farrer, and P. J. Sadler, "Quantitative broadband chemical sensing in air-suspended solid-core fibers," J. Appl. Phys. 103, 103108/1-7 (2008).
[CrossRef]

Sadler, P. J.

T. G. Euser, J. S. Y. Chen, M. Scharrer, P. St. J. Russell, N. J. Farrer, and P. J. Sadler, "Quantitative broadband chemical sensing in air-suspended solid-core fibers," J. Appl. Phys. 103, 103108/1-7 (2008).
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[CrossRef] [PubMed]

Scharrer, M.

T. G. Euser, J. S. Y. Chen, M. Scharrer, P. St. J. Russell, N. J. Farrer, and P. J. Sadler, "Quantitative broadband chemical sensing in air-suspended solid-core fibers," J. Appl. Phys. 103, 103108/1-7 (2008).
[CrossRef]

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P. J. A. Sazio, A. Amezcua-Correa, C. E. Finlayson, J. R. Hayes, T. J. Scheidemantel, N. F. Baril, B. R. Jackson, D.-J. Won, F. Zhang, E. R. Margine, V. Gopalan, V. H. Crespi, and J. V. Badding, "Microstructured optical fibers as high-pressure microfluidic reactors," Science 311, 1583-1586 (2006).
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P. J. A. Sazio, A. Amezcua-Correa, C. E. Finlayson, J. R. Hayes, T. J. Scheidemantel, N. F. Baril, B. R. Jackson, D.-J. Won, F. Zhang, E. R. Margine, V. Gopalan, V. H. Crespi, and J. V. Badding, "Microstructured optical fibers as high-pressure microfluidic reactors," Science 311, 1583-1586 (2006).
[CrossRef] [PubMed]

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Wu, S.-T.

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P. J. A. Sazio, A. Amezcua-Correa, C. E. Finlayson, J. R. Hayes, T. J. Scheidemantel, N. F. Baril, B. R. Jackson, D.-J. Won, F. Zhang, E. R. Margine, V. Gopalan, V. H. Crespi, and J. V. Badding, "Microstructured optical fibers as high-pressure microfluidic reactors," Science 311, 1583-1586 (2006).
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[CrossRef]

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Meas. Sci. Technol. (1)

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T. G. Euser, J. S. Y. Chen, M. Scharrer, P. St. J. Russell, N. J. Farrer, and P. J. Sadler, "Quantitative broadband chemical sensing in air-suspended solid-core fibers," J. Appl. Phys. 103, 103108/1-7 (2008).
[CrossRef]

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Figures (8)

Fig. 1.
Fig. 1.

Left: Schematic of a solid core photonic bandgap fibre for refractive index sensing and, right, its transmission properties as a function of normalised frequency V. The holes of a PCF are filled with a high-index analyte. Guidance in the core then occurs in the bandgaps of the high index photonic crystal cladding, which are delimited by the cutoffs of the modes of single analyte-filled holes.

Fig. 2.
Fig. 2.

Left: Schematic of an index-sensor based on a directional coupler in a selectively filled PCF. Right: Effective index of core (n eff,core) and analyte waveguide (n eff,wg) modes: phase matching between the two modes occurs near the cutoff λc of the modes of the analyte waveguide. The coupling of light from the core to the waveguide results in a narrow transmission notch near λc that can be used to measure the analyte’s refractive index. For details, see Refs. [14, 17].

Fig. 3.
Fig. 3.

Index profile of the coated inclusion.

Fig. 4.
Fig. 4.

Effective index of selected modes near their cutoffs. Here n a=1.0, n b=1.6, n c=1.45, r a/r b=0.8. The cutoff frequencies are given at the top.

Fig. 5.
Fig. 5.

Scaled sensitivity (left) and cutoff frequency (right) for the first (top) and second (bottom) m=0 modes.

Fig. 6.
Fig. 6.

Scaled sensitivity (left) and cutoff frequency (right) for the first (top) and second (bottom) m=1 modes.

Fig. 7.
Fig. 7.

Scaled sensitivity (left) and cutoff wavelength (right) for a variety of modes with n c=1.383, n a=1.35, r a=0.99r b. Numbers indicate m, solid and dotted curves are for the first and second mode of each m value respectively. For m=0 modes, the first (second) modes are the TE (TM) modes respectively.

Fig. 8.
Fig. 8.

a) Effective index of core and analyte waveguide modes of a selectively filled directional coupler refractive index sensor. Black solid curve: core mode of the PCF (n eff;core); Blue solid curves: TM and HE11 waveguide modes when the analyte channel has a refractive index of n a=1.35; red dashed curves: TM and HE11 waveguide modes when the analyte channel has n a=1.351. Black horizontal dotted line: background index n c. Red and blue crosses indicate the cutoffs of the isolated coated cylinder. b) and c) Power distribution of HE and TM modes of the coated inclusion at the phase- matching wavelength respectively.

Equations (35)

Equations on this page are rendered with MathJax. Learn more.

S = λrna .
δn0 ΔλS 1SNR0.25 ,
σ = Sλr
Vc = 2πρλ na2nbg2
σ = nana2nbg2 .
𝓔 (r,θ,z,t)=E(r,θ)exp[i(βzωt)]
𝓗 (r,θ,z,t)=1Z0K(r,θ)exp[i(βzωt)],
ψ + (nj2k02β2)ψ=0,
ψ (r,θ)=m(Amψ,jJm(kjr)+Bmψ,jHm(1)(kjr))eimθ,j{a,b,c}
V = k0 rb nb2nc2,
Amj = (AmE,jAmK,j) and Bmj = (BmE,jBmK,j)
Am = S+ Am+ + S Bm
Bm+ + S++ Am+ + S+ Bm ,
Amb = Sbc Bmb
Bmb = Sab++ Amb .
(ISbcSab++)Amb=0
det (ISbcSab++)=0,
det [(Sab++)1Sbc] = 0 .
limkc0 Sbc = [H0(1)J000H0(1)J0]
limkc Sbc = [H1(1)J11πrb2k02nc(nb2nc2)J12log[rbkc2]nb2πrb2k02nc(nb2nc2)J12log[rbkc2]H1(1)J1]
limkc0 Sbc =
(EE)1δm[(m1)rbk0(nb2JmHm(1)+nc2Hm(1)Jm)nb2nc2+τmJmHm(1)]
(EK) 2(m1)ncπδm
(KE) nb2 (limkc0Sbc,EK)
(KK)1δm[(m1)rbk0(nb2Hm(1)Jm+nc2JmHm(1))nb2nc2+τmJmHm(1)]
δm = (m1)rbk0JmJm(nb2+nc2)nb2nc2+τmJm2
τm = m (m1)(nb2+nc2)(rbnck0)2(nb2nc2)
neff (V)nc[1+2(rbk0nc)2exp(αVVc)]
LD rb exp (α2(VVc))
(Sab++)1 = (EE) 1δ [(αJJ++αJ+J)(n2αJH++n+2αH+J)m2J2J+H+τ2]
(EK)1δ[2mJ2τπrak0kk+]
(KE) n+2 [Sab++]1(EK)
(KK)1δ[(αJH++αH+J)(n2αJJ++n+2αJ+J)m2J2J+H+τ2]
δ = (αJ+JαJJ++) (n2αJJ++n+2αJ+J)+(mJ+Jτ)2
τ = βrakk+ (n2n+2)

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