OSA's Digital Library

Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editor: Gregory W. Faris
  • Vol. 5, Iss. 2 — Jan. 21, 2010
« Show journal navigation

Whispering gallery mode bio-sensor 
for label-free detection of single molecules: thermo-optic vs. reactive mechanism

S. Arnold, S. I. Shopova, and S. Holler  »View Author Affiliations


Optics Express, Vol. 18, Issue 1, pp. 281-287 (2010)
http://dx.doi.org/10.1364/OE.18.000281


View Full Text Article

Acrobat PDF (448 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Thermo-optic and reactive mechanisms for label-free sensing of bio-particles are compared theoretically for Whispering Gallery Mode (WGM) resonators (sphere, toroid) formed from silica and stimulated into a first order equatorial mode. Although it has been expected that a thermo-optic mechanism should “greatly enhance” wavelength shift signals [A.M. Armani et al, Science 317, 783-787 (2007)] accompanying protein binding on a silica WGM cavity having high Q (108), for a combination of wavelength (680 nm), drive power (1 mW), and cavity size (43 μm radius), our calculations find no such enhancement. The possible reasons for this disparity are discussed.

© 2009 OSA

1. Introduction

2. Theory

Antigens are detected by a WGM sensor when antibodies immobilized on the sensor surface capture them, and interact with the resonant microcavity both reactively [3

3. S. Arnold, M. Khoshsima, I. Teraoka, S. Holler, and F. Vollmer, “Shift of whispering-gallery modes in microspheres by protein adsorption,” Opt. Lett. 28(4), 272–274 (2003). [CrossRef] [PubMed]

] and thermo-optically [4

4. A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317(5839), 783–787 (2007). [CrossRef] [PubMed]

]. Comparison of the two interaction mechanisms is aided by carefully examining the WGM biosensor system.

Energy is injected into the WGM of a microsphere or toroid by evanescently coupling power P from an optical fiber. In the reactive mechanism a tiny change in phase occurs in the light orbit as the wave polarizes an antigen that has entered the evanescent field of the WGM. This interaction involves the real part of the polarizability of the antigen, Re[α]. Since the interaction simply changes the local refractive index (RI), the phase shift and the resultant frequency shift of the resonant state are independent of the circulating power in the cavity. The thermo-optic mechanism as described in Ref. 4 is in stark contrast since its frequency shift is proportional to P. The latter mechanism works by heating the antigen through linear absorption and transferring some of this heat to the resonator. Local heating of the resonator is thereby proportional to the imaginary part of the polarizability, Im[α], and causes an additional change in RI with temperature T as characterized by the thermo-optic coefficient dn/dT. Our goal is to estimate the relative magnitude of the thermo-optic vs. reactive frequency shift for an antigen binding to an antibody immobilized on the equator of a silica microcavity driven into its equatorial mode, while in an aqueous environment.

We first choose a spherical WGM resonator since its high symmetry allows for analytical solutions. In fact, the first-order reactive perturbation has already been worked out [3

3. S. Arnold, M. Khoshsima, I. Teraoka, S. Holler, and F. Vollmer, “Shift of whispering-gallery modes in microspheres by protein adsorption,” Opt. Lett. 28(4), 272–274 (2003). [CrossRef] [PubMed]

,7

7. I. Teraoka and S. Arnold, “Theory of resonance shifts in TE and TM whispering gallery modes by nonradial perturbations for sensing applications,” J. Opt. Soc. Am. B 23(7), 1381–1389 (2006). [CrossRef]

] and shown to agree with experimental data [8

8. F. Vollmer, S. Arnold, and D. Keng, “Single virus detection from the reactive shift of a whispering-gallery mode,” Proc. Natl. Acad. Sci. U.S.A. 105(52), 20701–20704 (2008). [CrossRef] [PubMed]

,9

9. S. Arnold, D. Keng, S. I. Shopova, S. Holler, W. Zurawsky, and F. Vollmer, “Whispering Gallery Mode Carousel-a photonic mechanism for enhanced nanoparticle detection in biosensing,” Opt. Express 17(8), 6230–6238 (2009). [CrossRef] [PubMed]

]. As for the thermo-optic mechanism, it has only been described for a micro-torus for which an explicit solution has not been presented [4

4. A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317(5839), 783–787 (2007). [CrossRef] [PubMed]

]. After arriving at generalized results for the micro-sphere we will return to a discussion of numerical results for the micro-torus.

We start by estimating the strength of the heat source h generated by absorption of energy from the WGM by the antigen molecule at position r a. This heat is produced when the electric field at the antigen at frequency ω, E(ra,t)=E0(ra)exp(iωt), drives the out-of-phase component of the induced dipole moment p; h=E(ra,t)·p/t, where is the time average over one cycle. Since p=αE(ra,t), we find
h=12ωIm[α]|E0(ra)|2.
(1)
Here we assume as in Ref. [4

4. A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317(5839), 783–787 (2007). [CrossRef] [PubMed]

] that the “quantum efficiency” for generating heat is one (i.e. scattering is minimal). The imaginary component of the polarizability is proportional to the absorption cross-section σ of a given molecule [Im[α] = (ε 0 n m/k) σ, where n m is the environmental refractive index and k the free-space wave-vector] and can be estimated from the attenuation of light through a cuvette filled with the associated solution.

|E0(ra)|24|Yll(x^)|2exp(2Γa)ε0(ns2nm2)R3Wm.
(7)

The delta-function heat plume will be conducted both into the silica and the surrounding medium. Bio-sensing experiments are carried out over seconds. By contrast thermal relaxation takes microseconds. So all we need to calculate is the steady state temperature distribution T(r). This is most easily arrived at from the solution to
κ2T=hδ(rra),
(9)
where κ is the thermal conductivity (κ s and κ m within the sphere and in the surroundings, respectively). Since a << R, a simple “flat earth” hypothesis is reasonable. By analogy with electrostatics the heat source may be treated as a point charge near a dielectric interface for which the solution appears in Ref.[10

10. J. D. Jackson, Classical Electrodynamics, (3rd ed., John Wiley & Sons Inc., Hoboken, NJ, 1998), pp.154–156.

]. The “thermal charge” h and its image are used to satisfy the boundary conditions at the interface for the temperature and its normal derivative [11

11. J. V. Beck, K. D. Cole, A. Haji-Sheikh, and B. Litkouhi, Heat conduction using Green’s functions, (Hemisphere Publishing Corp., Washington, DC, 1992).

].

The temperature elevation within the microsphere δT is simply a function of the distance ξ from the heat source, and is given as
δT=h2πξ(κs+κm).
(10)
where

ξ[r2+(R+a)22r(R+a)sinθcosϕ]1/2.
(11)

The temperature increase in Eq. (10) causes a change in RI within the microsphere through the thermo-optic effect, δn=(dn/dT)δT. Altogether the RI change is
δn=dn/dTπξ(κs+κm)Im[α/ε0]PQ(ns2nm2)R3cin[jl(nskR)]2|E0(ra)|2.
(12)
where Eqs. (4), 5, 8 and 10 were used. This complicated equation provides all of the essential dependences. The distance ξ can be no smaller than a (~1 nm). We can use Eq. (12) to estimate the frequency shift δω. Based on the formalism developed for the reactive effect [7

7. I. Teraoka and S. Arnold, “Theory of resonance shifts in TE and TM whispering gallery modes by nonradial perturbations for sensing applications,” J. Opt. Soc. Am. B 23(7), 1381–1389 (2006). [CrossRef]

,12

12. S. Arnold, R. Ramjit, D. Keng, V. Kolchenko, and I. Teraoka, “MicroParticle PhotoPhysics illuminates viral bio-sensing,” Faraday Discuss. 137, 65–83, discussion 99–113 (2007). [CrossRef] [PubMed]

]:
δωω=δ([n(r)]2)E(r)·E0*(r)dV2[n(r)]2|E0(r)|2dV.
(13)
where [n(r)]2 is the relative permittivity at r which changes by δ ([n(r)]2), and E(r) is the field after the RI change. Equation (13) applies to both the thermo-optic and reactive cases. Since the perturbation in refractive index is in the numerator, and the denominators are identical for both cases, a comparison of the frequency shifts simply involves finding the ratio of the numerator for the thermo-optic case to the numerator for the reactive case. In what follows we will evaluate the numerator for each in turn, and label them N t and N r, respectively.

For the thermo-optic case it is convenient to write δ(n2)=2nδn. For the TE mode, E is just E 0 in the silica, and the numerator is

Nt=2nsδn(r)|E0(r)|2dV.
(14)

For the reactive case the antigen bound to the equator represents a local change in the polarization δP=ε0δ(n2)E equivalent to its induced dipole moment per unit volume Re[α]E0/Va. Consequently δ(n2)E=Re[α/ε0]E0/Va, and integration over the antigen’s volume Va in the numerator of Eq. (13) gives

Nr=Re[α/ε0]|E0(ra)|2.
(18)

All we have left to do is to compare the thermo-optic frequency shift (δω)t to the reactive frequency shift (δω)r through the ratio N t /N r,

(δω)t(δω)r=NtNr=ηIlRIm[α/ε0]Re[α/ε0]PQ.
(19)

Equation (19) is surprisingly simple and ripe for evaluation. First let’s deal with the factor η. For silica in water n s = 1.454, n m = 1.329, κ s + κ m = 1.88 Wm–1K–1, dn/dT = 1.3 × 10−5 K–1, and therefore η = 1.84 × 10−5 m/W. We will take R, P, and Q to be 43 µm, 1 mW, and 108 respectively as our standard parameters, close to the parameters used in the paper by A. M. Armani et al [4

4. A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317(5839), 783–787 (2007). [CrossRef] [PubMed]

]. For an antigen bound to the equator the dimensionless Il factor is found to be 0.14. All that we require now is to find the “loss-tangent” (Im[α/ε0]/Re[α/ε0])for a characteristic protein [e.g. Streptavidin, Bovine Serum Albumin (BSA)]. The real part Re[α/ε0]is typically determined from the change in refractive index upon adding protein to solution, whereas the imaginary part Im[α/ε0]is determined from the solution’s optical absorption. BSA is a good choice for calculating the frequency shift ratio in Eq. (19) since refractive index data allow us to determine that Re[α/ε0]=4.8×10-20cm3 [3

3. S. Arnold, M. Khoshsima, I. Teraoka, S. Holler, and F. Vollmer, “Shift of whispering-gallery modes in microspheres by protein adsorption,” Opt. Lett. 28(4), 272–274 (2003). [CrossRef] [PubMed]

], and we have determined Im[α/ε0] at 680 nm from our measurements of absorbance in solution to be 1.3 × 10−24 cm3 [13

13. S. A. Wise, and R. A. Watters, “Bovine serum albumin (7% Solution) (SRM 927d),” NIST Gaithersburg, MD (2006).

]. We find the ratio of the thermo-optic to reactive frequency shift to be 0.16. Surprisingly, the thermo-optic effect is smaller than the reactive effect in the presence of 100W of circulating power! A similar result is found for Streptavidin, a protein used in Ref. 4

4. A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317(5839), 783–787 (2007). [CrossRef] [PubMed]

.

This small thermo-optic effect in relation to the reactive effect for BSA for the standard parameters is particularly surprising considering the anticipated enhancement in Ref. 4

4. A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317(5839), 783–787 (2007). [CrossRef] [PubMed]

. It should be pointed out that by taking the ratio in Eq. (19) we have eliminated the explicit dependence on mode volume; both the thermo-optic and reactive effects are inversely proportional to mode volume. In this way we have reduced the dependence on the type of WGM resonator. However there will be a small dependence in the integral Il. This integral represents the surface normalized overlap between the thermal plume and the WGM ring of intensity. One can construct a similar integral for the toroidal case for which the wavefunctions are obtained from FEM (e.g., Comsol) numerical solutions to the vector Helmholtz equation. The value for Il obtained for the toroidal mode in Ref. [4

4. A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317(5839), 783–787 (2007). [CrossRef] [PubMed]

], for our standard parameters (the overall radius of the toroidal resonator is 43 μm), is only slightly different than that for the equatorial mode of a micro-spheroid having the same overall size (i.e. 0.17 vs. 0.14). So the ratio of the thermo-optic to reactive shift for the toroid is 0.19. By using FEM we also calculated the ratio of the reactive shift for the toroid to that of the sphere to be 2.0. By putting all of these ratios together we find that the thermo-optic shift of the toroid to the reactive shift of the microspherical resonator for BSA should be 0.38. However the thermo-optic shifts calculated for the toroidal resonator in Ref. 4 are extraordinarily large in comparison to the corresponding reactive shifts that we calculate for a microspherical resonator having the same overall size [3

3. S. Arnold, M. Khoshsima, I. Teraoka, S. Holler, and F. Vollmer, “Shift of whispering-gallery modes in microspheres by protein adsorption,” Opt. Lett. 28(4), 272–274 (2003). [CrossRef] [PubMed]

]. For example, for Streptavidin this ratio is ~5000. A large part of the explanation for this disparity lies in the reported molecular absorption cross-sections in Ref. 4

4. A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317(5839), 783–787 (2007). [CrossRef] [PubMed]

.

For a Rayleigh sized particle the imaginary part of the polarizability Im[α] may be expressed in terms of an absorption cross section σ as we have pointed out earlier, and the thermo-optic shift would be proportional to σ. Although this is explicitly stated by Armani et al [4

4. A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317(5839), 783–787 (2007). [CrossRef] [PubMed]

], we believe that the cross sections used in Ref. 4 to support the thermo-optic mechanism are “massively” inflated!

As an example we return to the case of the protein Streptavidin. The authors of Ref. 4 report a spectroscopic measured absorption cross-section for Streptavidin at 680 nm of 2×10−16 cm2. Our own absorbance measurements on a 0.1 mM solution of Streptavidin (Invitrogen 43-4302) find this cross-section to be 1.5×10−19 cm2, a factor of 1300 times smaller than that in Ref. [4

4. A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317(5839), 783–787 (2007). [CrossRef] [PubMed]

]. This relatively small cross-section is not uncommon for protein in the red portion of the spectrum. The NIST standard for protein is BSA (Bovine Serum Albumin, SRM 927d) [13

13. S. A. Wise, and R. A. Watters, “Bovine serum albumin (7% Solution) (SRM 927d),” NIST Gaithersburg, MD (2006).

]. BSA has a molecular weight comparable to Streptavidin and from the NIST absorbance data at 600 nm, BSA’s absorption cross-section is 0.7×10−19 cm2. Measurements on 7% BSA (mass) in PBS (Phosphate Buffered Saline) agreed with NIST’s measurements and were used to validate our measurement procedure. Our Streptavidin cross section plugged into Armani’s theoretical equation would yield a wavelength shift less than one thousandth of what is calculated and measured in Ref. [4

4. A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317(5839), 783–787 (2007). [CrossRef] [PubMed]

].

How about the non-protein cross sections? The Cy5-antigen used in Ref. 4 is reported to have a spectroscopic measured absorption cross section of 4×10−14 cm2 at 680 nm. Such a cross-section for a dye molecule with oscillator strength ~1 and having Cy5′s fluorescence decay rate and spectral width (in solution at room temperature) is unprecedented and unphysical [14

14. W. E. Moerner and D. P. Fromm, “Methods of single-molecule fluorescence spectroscopy and microscopy,” Rev. Sci. Instrum. 74(8), 3597–3619 (2003). [CrossRef]

]. Indeed, there is supporting data for a much smaller cross section. An absorption cross section at 680 nm for Cy5 molecule attached to DNA of ~0.7×10−16 cm2 can be extracted from data in Ref. [15

15. 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]

]. Finally from Invitrogen molar extinction data taken on the Cy5-antigen we have found the cross section at 680 nm to be 10−16 cm2. This Cy5-antigen cross section plugged into Armani’s theoretical equation would yield a wavelength shift about 1/400 of what is calculated and measured in Ref. [4

4. A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317(5839), 783–787 (2007). [CrossRef] [PubMed]

]. This effect is expected to be further lowered due to excited state saturation as well as emission; saturation reduces the effective absorption cross section [14

14. W. E. Moerner and D. P. Fromm, “Methods of single-molecule fluorescence spectroscopy and microscopy,” Rev. Sci. Instrum. 74(8), 3597–3619 (2003). [CrossRef]

] and emission reduces the amount of absorbed energy converted to heating the surroundings.

3. Conclusion

We have provided theory that directly compares the thermo-optic to the reactive mechanisms for label-free biosensing with WGM resonators. We arrive at an expression that compares these two mechanisms for a given WGM resonator independent of mode volume. The application of this theory produces surprising conclusions with respect to Ref. 4

4. A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317(5839), 783–787 (2007). [CrossRef] [PubMed]

.

For the conditions presented in Ref. 4 (i.e. standard parameters) our calculations show that the thermo-optic mechanism associated with linear absorption is smaller than its reactive counterpart, and cannot account for even one thousandth of the reported frequency shifts attributed to single protein binding.

Acknowledgments

The authors acknowledge a National Science Foundation grant CBET 0933531 for financial support.

References and links

1.

F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5(7), 591–596 (2008). [CrossRef] [PubMed]

2.

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]

3.

S. Arnold, M. Khoshsima, I. Teraoka, S. Holler, and F. Vollmer, “Shift of whispering-gallery modes in microspheres by protein adsorption,” Opt. Lett. 28(4), 272–274 (2003). [CrossRef] [PubMed]

4.

A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317(5839), 783–787 (2007). [CrossRef] [PubMed]

5.

M. Loncar, “Molecular sensors: Cavities lead the way,” Nat. Photonics 1(10), 565–567 (2007). [CrossRef]

6.

D. Evanko, “Incredible shrinking optics,” Nat. Methods 4(9), 683 (2007). [CrossRef]

7.

I. Teraoka and S. Arnold, “Theory of resonance shifts in TE and TM whispering gallery modes by nonradial perturbations for sensing applications,” J. Opt. Soc. Am. B 23(7), 1381–1389 (2006). [CrossRef]

8.

F. Vollmer, S. Arnold, and D. Keng, “Single virus detection from the reactive shift of a whispering-gallery mode,” Proc. Natl. Acad. Sci. U.S.A. 105(52), 20701–20704 (2008). [CrossRef] [PubMed]

9.

S. Arnold, D. Keng, S. I. Shopova, S. Holler, W. Zurawsky, and F. Vollmer, “Whispering Gallery Mode Carousel-a photonic mechanism for enhanced nanoparticle detection in biosensing,” Opt. Express 17(8), 6230–6238 (2009). [CrossRef] [PubMed]

10.

J. D. Jackson, Classical Electrodynamics, (3rd ed., John Wiley & Sons Inc., Hoboken, NJ, 1998), pp.154–156.

11.

J. V. Beck, K. D. Cole, A. Haji-Sheikh, and B. Litkouhi, Heat conduction using Green’s functions, (Hemisphere Publishing Corp., Washington, DC, 1992).

12.

S. Arnold, R. Ramjit, D. Keng, V. Kolchenko, and I. Teraoka, “MicroParticle PhotoPhysics illuminates viral bio-sensing,” Faraday Discuss. 137, 65–83, discussion 99–113 (2007). [CrossRef] [PubMed]

13.

S. A. Wise, and R. A. Watters, “Bovine serum albumin (7% Solution) (SRM 927d),” NIST Gaithersburg, MD (2006).

14.

W. E. Moerner and D. P. Fromm, “Methods of single-molecule fluorescence spectroscopy and microscopy,” Rev. Sci. Instrum. 74(8), 3597–3619 (2003). [CrossRef]

15.

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]

OCIS Codes
(040.1880) Detectors : Detection
(170.0170) Medical optics and biotechnology : Medical optics and biotechnology
(230.3990) Optical devices : Micro-optical devices

ToC Category:
Sensors

History
Original Manuscript: November 6, 2009
Revised Manuscript: December 14, 2009
Manuscript Accepted: December 15, 2009
Published: December 23, 2009

Virtual Issues
Vol. 5, Iss. 2 Virtual Journal for Biomedical Optics

Citation
S. Arnold, S. I. Shopova, and S. Holler, "Whispering gallery mode bio-sensor 
for label-free detection of single molecules: thermo-optic vs. reactive mechanism," Opt. Express 18, 281-287 (2010)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-18-1-281


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5(7), 591–596 (2008). [CrossRef] [PubMed]
  2. 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]
  3. S. Arnold, M. Khoshsima, I. Teraoka, S. Holler, and F. Vollmer, “Shift of whispering-gallery modes in microspheres by protein adsorption,” Opt. Lett. 28(4), 272–274 (2003). [CrossRef] [PubMed]
  4. A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317(5839), 783–787 (2007). [CrossRef] [PubMed]
  5. M. Loncar, “Molecular sensors: Cavities lead the way,” Nat. Photonics 1(10), 565–567 (2007). [CrossRef]
  6. D. Evanko, “Incredible shrinking optics,” Nat. Methods 4(9), 683 (2007). [CrossRef]
  7. I. Teraoka and S. Arnold, “Theory of resonance shifts in TE and TM whispering gallery modes by nonradial perturbations for sensing applications,” J. Opt. Soc. Am. B 23(7), 1381–1389 (2006). [CrossRef]
  8. F. Vollmer, S. Arnold, and D. Keng, “Single virus detection from the reactive shift of a whispering-gallery mode,” Proc. Natl. Acad. Sci. U.S.A. 105(52), 20701–20704 (2008). [CrossRef] [PubMed]
  9. S. Arnold, D. Keng, S. I. Shopova, S. Holler, W. Zurawsky, and F. Vollmer, “Whispering Gallery Mode Carousel-a photonic mechanism for enhanced nanoparticle detection in biosensing,” Opt. Express 17(8), 6230–6238 (2009). [CrossRef] [PubMed]
  10. J. D. Jackson, Classical Electrodynamics, (3rd ed., John Wiley & Sons Inc., Hoboken, NJ, 1998), pp.154–156.
  11. J. V. Beck, K. D. Cole, A. Haji-Sheikh, and B. Litkouhi, Heat conduction using Green’s functions, (Hemisphere Publishing Corp., Washington, DC, 1992).
  12. S. Arnold, R. Ramjit, D. Keng, V. Kolchenko, and I. Teraoka, “MicroParticle PhotoPhysics illuminates viral bio-sensing,” Faraday Discuss. 137, 65–83, discussion 99–113 (2007). [CrossRef] [PubMed]
  13. S. A. Wise, and R. A. Watters, “Bovine serum albumin (7% Solution) (SRM 927d),” NIST Gaithersburg, MD (2006).
  14. W. E. Moerner and D. P. Fromm, “Methods of single-molecule fluorescence spectroscopy and microscopy,” Rev. Sci. Instrum. 74(8), 3597–3619 (2003). [CrossRef]
  15. 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]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Figures

Fig. 1
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited