Abstract

The relevance of our definition for sensitivity in refractometric sensing, being the relative change in the transmittance of a certain output channel of an optical device over the change in the refractive index of the probed material, is discussed. It is compared to one based on spectral shift per refractive index unit change. Further, there is discussion on how group delay and sensitivity are interrelated and can be converted into each other and which physical quantities are relevant for high sensitivity. As a by-product of the theory presented, a general expression relating group delay and the ratio of the time-averaged optical energy and the input power is presented.

© 2014 Optical Society of America

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  4. S. V. Pham, M. Dijkstra, A. J. F. Hollink, L. J. Kauppinen, R. M. de Ridder, M. Pollnau, P. V. Lambeck, and H. J. W. M. Hoekstra, “On-chip bulk-index concentration and direct, label-free protein sensing utilizing an optical grated-waveguide cavity,” Sens. Actuators B Chem. 174, 602–608 (2012).
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    [CrossRef]
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    [CrossRef]
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2012 (1)

S. V. Pham, M. Dijkstra, A. J. F. Hollink, L. J. Kauppinen, R. M. de Ridder, M. Pollnau, P. V. Lambeck, and H. J. W. M. Hoekstra, “On-chip bulk-index concentration and direct, label-free protein sensing utilizing an optical grated-waveguide cavity,” Sens. Actuators B Chem. 174, 602–608 (2012).
[CrossRef]

2011 (1)

2010 (3)

2008 (3)

H. J. W. M. Hoekstra, P. V. Lambeck, H. P. Uranus, and T. M. Koster, “Relation between noise and resolution in integrated optical refractometric sensing,” Sens. Actuators B Chem. 134, 702–710 (2008).
[CrossRef]

C. McDonagh, C. S. Burke, and B. D. MacCraith, “Optical chemical sensors,” Chem. Rev. 108, 400–422 (2008).
[CrossRef]

I. M. White and X. Fan, “On the performance quantification of resonant refractive index sensing,” Opt. Express 16, 1022–1028 (2008).

2006 (1)

P. V. Lambeck, “Integrated optical sensors for the chemical domain,” Meas. Sci. Technol. 17, R93–R116 (2006).
[CrossRef]

1999 (1)

P. Pfeifer, U. Aldinger, G. Schwotzer, S. Diekmann, and P. Steinrücke, “Real time sensing of specific molecular binding using surface plasmon resonance spectroscopy,” Sens. Actuators B Chem. 54, 166–175 (1999).
[CrossRef]

1990 (1)

1979 (1)

Aldinger, U.

P. Pfeifer, U. Aldinger, G. Schwotzer, S. Diekmann, and P. Steinrücke, “Real time sensing of specific molecular binding using surface plasmon resonance spectroscopy,” Sens. Actuators B Chem. 54, 166–175 (1999).
[CrossRef]

Bienstman, P.

Bogaerts, W.

Brillouin, L.

L. Brillouin, Wave Propagation and Group Velocity (Academic, 1960).

Burke, C. S.

C. McDonagh, C. S. Burke, and B. D. MacCraith, “Optical chemical sensors,” Chem. Rev. 108, 400–422 (2008).
[CrossRef]

Chadt, K.

M. Vala, K. Chadt, M. Piliarik, and J. Homola, “High-performance compact SPR sensor for multi-analyte sensing,” Sens. Actuators B Chem. 148, 544–549 (2010).
[CrossRef]

Chew, W. C.

W. C. Chew, Waves and Fields in Inhomogeneous Media, IEEE Press Series on Electromagnetic Waves (IEEE, 1995).

Claes, T.

de Ridder, R. M.

S. V. Pham, M. Dijkstra, A. J. F. Hollink, L. J. Kauppinen, R. M. de Ridder, M. Pollnau, P. V. Lambeck, and H. J. W. M. Hoekstra, “On-chip bulk-index concentration and direct, label-free protein sensing utilizing an optical grated-waveguide cavity,” Sens. Actuators B Chem. 174, 602–608 (2012).
[CrossRef]

Diekmann, S.

P. Pfeifer, U. Aldinger, G. Schwotzer, S. Diekmann, and P. Steinrücke, “Real time sensing of specific molecular binding using surface plasmon resonance spectroscopy,” Sens. Actuators B Chem. 54, 166–175 (1999).
[CrossRef]

Dijkstra, M.

S. V. Pham, M. Dijkstra, A. J. F. Hollink, L. J. Kauppinen, R. M. de Ridder, M. Pollnau, P. V. Lambeck, and H. J. W. M. Hoekstra, “On-chip bulk-index concentration and direct, label-free protein sensing utilizing an optical grated-waveguide cavity,” Sens. Actuators B Chem. 174, 602–608 (2012).
[CrossRef]

Fan, X.

I. M. White and X. Fan, “On the performance quantification of resonant refractive index sensing,” Opt. Express 16, 1022–1028 (2008).

Hoekstra, H. J. W. M.

S. V. Pham, M. Dijkstra, A. J. F. Hollink, L. J. Kauppinen, R. M. de Ridder, M. Pollnau, P. V. Lambeck, and H. J. W. M. Hoekstra, “On-chip bulk-index concentration and direct, label-free protein sensing utilizing an optical grated-waveguide cavity,” Sens. Actuators B Chem. 174, 602–608 (2012).
[CrossRef]

H. J. W. M. Hoekstra, P. V. Lambeck, H. P. Uranus, and T. M. Koster, “Relation between noise and resolution in integrated optical refractometric sensing,” Sens. Actuators B Chem. 134, 702–710 (2008).
[CrossRef]

Hollink, A. J. F.

S. V. Pham, M. Dijkstra, A. J. F. Hollink, L. J. Kauppinen, R. M. de Ridder, M. Pollnau, P. V. Lambeck, and H. J. W. M. Hoekstra, “On-chip bulk-index concentration and direct, label-free protein sensing utilizing an optical grated-waveguide cavity,” Sens. Actuators B Chem. 174, 602–608 (2012).
[CrossRef]

Homola, J.

M. Vala, K. Chadt, M. Piliarik, and J. Homola, “High-performance compact SPR sensor for multi-analyte sensing,” Sens. Actuators B Chem. 148, 544–549 (2010).
[CrossRef]

Kauppinen, L. J.

S. V. Pham, M. Dijkstra, A. J. F. Hollink, L. J. Kauppinen, R. M. de Ridder, M. Pollnau, P. V. Lambeck, and H. J. W. M. Hoekstra, “On-chip bulk-index concentration and direct, label-free protein sensing utilizing an optical grated-waveguide cavity,” Sens. Actuators B Chem. 174, 602–608 (2012).
[CrossRef]

Khurgin, J. B.

Koster, T. M.

H. J. W. M. Hoekstra, P. V. Lambeck, H. P. Uranus, and T. M. Koster, “Relation between noise and resolution in integrated optical refractometric sensing,” Sens. Actuators B Chem. 134, 702–710 (2008).
[CrossRef]

Lambeck, P. V.

S. V. Pham, M. Dijkstra, A. J. F. Hollink, L. J. Kauppinen, R. M. de Ridder, M. Pollnau, P. V. Lambeck, and H. J. W. M. Hoekstra, “On-chip bulk-index concentration and direct, label-free protein sensing utilizing an optical grated-waveguide cavity,” Sens. Actuators B Chem. 174, 602–608 (2012).
[CrossRef]

H. J. W. M. Hoekstra, P. V. Lambeck, H. P. Uranus, and T. M. Koster, “Relation between noise and resolution in integrated optical refractometric sensing,” Sens. Actuators B Chem. 134, 702–710 (2008).
[CrossRef]

P. V. Lambeck, “Integrated optical sensors for the chemical domain,” Meas. Sci. Technol. 17, R93–R116 (2006).
[CrossRef]

MacCraith, B. D.

C. McDonagh, C. S. Burke, and B. D. MacCraith, “Optical chemical sensors,” Chem. Rev. 108, 400–422 (2008).
[CrossRef]

McDonagh, C.

C. McDonagh, C. S. Burke, and B. D. MacCraith, “Optical chemical sensors,” Chem. Rev. 108, 400–422 (2008).
[CrossRef]

Mogi, K.

Naganuma, K.

Pfeifer, P.

P. Pfeifer, U. Aldinger, G. Schwotzer, S. Diekmann, and P. Steinrücke, “Real time sensing of specific molecular binding using surface plasmon resonance spectroscopy,” Sens. Actuators B Chem. 54, 166–175 (1999).
[CrossRef]

Pham, S. V.

S. V. Pham, M. Dijkstra, A. J. F. Hollink, L. J. Kauppinen, R. M. de Ridder, M. Pollnau, P. V. Lambeck, and H. J. W. M. Hoekstra, “On-chip bulk-index concentration and direct, label-free protein sensing utilizing an optical grated-waveguide cavity,” Sens. Actuators B Chem. 174, 602–608 (2012).
[CrossRef]

Piliarik, M.

M. Vala, K. Chadt, M. Piliarik, and J. Homola, “High-performance compact SPR sensor for multi-analyte sensing,” Sens. Actuators B Chem. 148, 544–549 (2010).
[CrossRef]

Pollnau, M.

S. V. Pham, M. Dijkstra, A. J. F. Hollink, L. J. Kauppinen, R. M. de Ridder, M. Pollnau, P. V. Lambeck, and H. J. W. M. Hoekstra, “On-chip bulk-index concentration and direct, label-free protein sensing utilizing an optical grated-waveguide cavity,” Sens. Actuators B Chem. 174, 602–608 (2012).
[CrossRef]

Schwotzer, G.

P. Pfeifer, U. Aldinger, G. Schwotzer, S. Diekmann, and P. Steinrücke, “Real time sensing of specific molecular binding using surface plasmon resonance spectroscopy,” Sens. Actuators B Chem. 54, 166–175 (1999).
[CrossRef]

Steinrücke, P.

P. Pfeifer, U. Aldinger, G. Schwotzer, S. Diekmann, and P. Steinrücke, “Real time sensing of specific molecular binding using surface plasmon resonance spectroscopy,” Sens. Actuators B Chem. 54, 166–175 (1999).
[CrossRef]

Uranus, H. P.

H. J. W. M. Hoekstra, P. V. Lambeck, H. P. Uranus, and T. M. Koster, “Relation between noise and resolution in integrated optical refractometric sensing,” Sens. Actuators B Chem. 134, 702–710 (2008).
[CrossRef]

Vala, M.

M. Vala, K. Chadt, M. Piliarik, and J. Homola, “High-performance compact SPR sensor for multi-analyte sensing,” Sens. Actuators B Chem. 148, 544–549 (2010).
[CrossRef]

White, I. M.

I. M. White and X. Fan, “On the performance quantification of resonant refractive index sensing,” Opt. Express 16, 1022–1028 (2008).

Yamada, H.

Yeh, P.

Adv. Opt. Photon. (1)

Chem. Rev. (1)

C. McDonagh, C. S. Burke, and B. D. MacCraith, “Optical chemical sensors,” Chem. Rev. 108, 400–422 (2008).
[CrossRef]

J. Opt. Soc. Am. (1)

Meas. Sci. Technol. (1)

P. V. Lambeck, “Integrated optical sensors for the chemical domain,” Meas. Sci. Technol. 17, R93–R116 (2006).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Sens. Actuators B Chem. (4)

H. J. W. M. Hoekstra, P. V. Lambeck, H. P. Uranus, and T. M. Koster, “Relation between noise and resolution in integrated optical refractometric sensing,” Sens. Actuators B Chem. 134, 702–710 (2008).
[CrossRef]

S. V. Pham, M. Dijkstra, A. J. F. Hollink, L. J. Kauppinen, R. M. de Ridder, M. Pollnau, P. V. Lambeck, and H. J. W. M. Hoekstra, “On-chip bulk-index concentration and direct, label-free protein sensing utilizing an optical grated-waveguide cavity,” Sens. Actuators B Chem. 174, 602–608 (2012).
[CrossRef]

P. Pfeifer, U. Aldinger, G. Schwotzer, S. Diekmann, and P. Steinrücke, “Real time sensing of specific molecular binding using surface plasmon resonance spectroscopy,” Sens. Actuators B Chem. 54, 166–175 (1999).
[CrossRef]

M. Vala, K. Chadt, M. Piliarik, and J. Homola, “High-performance compact SPR sensor for multi-analyte sensing,” Sens. Actuators B Chem. 148, 544–549 (2010).
[CrossRef]

Other (2)

W. C. Chew, Waves and Fields in Inhomogeneous Media, IEEE Press Series on Electromagnetic Waves (IEEE, 1995).

L. Brillouin, Wave Propagation and Group Velocity (Academic, 1960).

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Figures (4)

Fig. 1.
Fig. 1.

Illustration of the huge spectral shifts in a SP setup: (a) schematic of the setup; (b) a typical response curve with T as the reflectance; (c) idealized dispersion curves for the excitation (dotted line), the SP (solid line), and the SP after a small modal index change δN (dashed line).

Fig. 2.
Fig. 2.

Computational results for a simple Fabry–Perot cavity: (a) schematic of the structure and reflectance T2 and transmittance T1; (b) and (c) dispersion curves of the indicated quantities.

Fig. 3.
Fig. 3.

Schematic of a MZI-like setup to convert partial group delay and sensitivity into each other.

Fig. 4.
Fig. 4.

Real and imaginary parts of the quantities (a) S˜1s and (b) S˜+s versus excitation wavelength. The insets show the structural layouts considered.

Equations (40)

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S=|lnT/ns|,
LOD=ασlnT/(SmaxM)
S=|lnTns|λ=|(lnTNSP)λ(NSPns)λ|,
S=|(lnTλ)NSP(λNSP)lnT(NSPns)λ|.
Tm=|tm|2
Pout=Pinm=1Q|tm|2,
τg,m=Im(arg(tm)ω)=Im(lntmω).
df=l=1P(f(nlω))nlωd(nlω),
(fω)n1P=l=1P(f(nlω))nlω((nlω)ω)nl.
((nlω)ω)nl=nl+ω(nlω).
(fnl)ω=(f(nlω))nlω((nlω)nl)ω=ω(f(nlω))nlω,
(fω)n1P=l=1PGl(fnl)ω;Gl1ω((nlω)ω)nl.
τg,m=Im(lntmω)=l=1Pτg,ml,
τg,mlGlIm(lntmnl)
·(E×H*)=iωμ0|H|2+iωε*ε0|E|2,
VRe[·(E×H*)]dτ=Re[surface(E×H*)]·dσ=Vl2nlnlωε0|E|2dτ,
PinPout=Pin(1m=1QTm(nl))=Vlωε0nlnl|E|2dτ.
m=1Q2TmRe(lntmnl)=m=1Q2TmIm(lntmnl)=Vlωε0nl|E|2dτ/Pin,
m=1QTmτg,ml=12(nlω)ωVlε0nl|E|2dτ/Pin,
m=1QTmτg,m=l=1P12(nlω)ωVlε0nl|E|2dτ/Pin=Vε0(ε+(εω)/ω)|E|2dτ/(4Pin).
Imsurface(E×H*)·dσ=0,
Vμ0|H|2dτ=Vεε0|E|2dτ,
m=1QTmτg,m=VDdτ/ASinPoyntingdσ,
DE=ε0[(εω)/ω]|E|2/4
DH=μ0|H|2/4.
vg=unit cellSindτ/unit cellDdτ,
Ey=E0(eik0n1z+t2eik0n1z),z<0,Ey=E0t1(eik0n2(zL)+r21eik0n1(zL))/(1+r21),0<z<L,Ey=E0t1eik0n1(zL),z>L.
Hx=iωμ0Eyz.
r21=n2n1n2+n1,t2=r21(e2ik0n2L1)1r212e2ik0n2L,t1=(1r212)eik0n2L1r212e2ik0n2L,
P2,net/Pin=Re[(1+t2)n1*(1t2*)]/n1=1|t22|2t2n1/n1.
Pin=|E0|2k0n1/(2ωμ0).
S˜mslntmns,
|Re(S˜ms)|=|Re(lntmns)|=12|lnTmns|=12Sms,
t±=(tm±tref)/2,
S˜+slnt+ns=11+tref/tm*lntmns=11+tref/tm*S˜ms,
t1=(τeik0NL)/M;M1τeik0NL,
τg,1=it1*t1/ω=NL(1τ2)/(c|M|2).
vg1=cross sectionDdτ/Pin=N/c,
T1τg,1=NL(1τ2)/(c|M|2)=cavityDdτ/Pin.
S˜1s=0.1ik0L(1τ2)/|M|2.

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