## Periodic plasmonic enhancing epitopes on a whispering gallery mode biosensor |

Optics Express, Vol. 20, Issue 24, pp. 26147-26159 (2012)

http://dx.doi.org/10.1364/OE.20.026147

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### Abstract

We propose the attachment of a periodic array of gold nanoparticles (epitopes) to the equator of a Whispering Gallery Mode Biosensor for the purpose of plasmonically enhancing nanoparticle sensing in a self-referencing manner while increasing the capture rate of analyte to antibodies attached to these plasmonic epitopes. Our approach can be applied to a variety of whispering gallery mode resonators from silicon/silica rings and disks to capillaries. The interpretation of the signals is particularly simple since the optical phase difference between the epitopes is designed to be an integer multiple of π, allowing the wavelength shift from each binding event to add independently.

© 2012 OSA

## 1. Introduction

*e.g.,*oblate spheroid in Fig. 1 ), thereby substantially increasing the available surface for analyte binding while still retaining the frequency shift boost. Beyond increasing the number of possible events and reducing the time between events the periodic configuration changes our measurement approach from “spectral step-sensing” [4] to “self-referencing” [11]. Self-referencing can be understood in the following way. On a bare cavity a WGM circulating in a given direction or in the opposite direction will have the same frequency. A particle on the equator couples these modes and splits this degeneracy into two resonances. This splitting is apparent when the reactive shift exceeds the modal linewidth. For a single nanoparticle the splitting is twice the average shift, which enables the interaction to be measured from the frequency separation between the split modes. A large number of periodic epitopes are assured to produce mode splitting even if one epitope does not [12]. The advantage of the “self-referencing” approach to measurement is that it is differential and can therefore eliminate common mode noise. A key advantage of the periodic epitopes is that this design builds a quasi-1D photonic band structure. Near the band edge where the inter-epitope optical phase difference is π, adsorption on any of the plasmonic epitopes produces additional splitting that is simply additive. In what follows we will discuss the enhancement by possible local plasmonic epitopes. Following this we will describe our theoretical approach, apply it to nonperiodic mode splitting problems in the past, and finally to periodic plasmonic epitope sensing of dielectric bio-nanoparticles.

## 2. Possible plasmonic epitopes

*etc*.) [16–19]. Specific detection can be achieved by functionalizing each epitope’s hot spot regions,

*i.e*., with antibodies that exclusively allow binding of distinctive target analytes suspended in aqueous media.

## 3. Theory of one, two and N plasmonic epitopes

*et al.*[11] before moving on to the necklace. We concentrate theoretically on the equatorial mode of an oblate axisymmetric microcavity. Without the plasmonic epitope or significant roughness we have a bare cavity in which two counterpropagating equatorial WGMs have identical resonance frequencies; they are degenerate. Since the microcavity is a high

*Q*system, the modes of this system can be considered to be quasi-normal modes [21]. This allows for quantum analogs such as photonic atoms [22]. Such analogs compel one to borrow the theoretical machinery of quantum mechanics in order to describe high

*Q*optical systems. For bound nanoplasmonic epitope perturbing a WGM, degenerate perturbation theory can be used to predict the eigenvalues and eigenstates of the system.

*s,*angular momentum quantum number

*r*is radial variable (~radius of the ring),

*k*is the wave vector and

*m*guarantees that

*m*=

*kr*. Bare WGM microcavities typically support both clockwise (

*cw*) and counterclockwise (

*ccw*) equitorial modes, which for the same

*m*are degenerate in frequency. Using Eqs. (2) and (3), orthogonal basis vectors for these

*ccw*and

*cw*equatorial traveling waves arerespectively, where

*g*[11,24]. Equation (5) is in a conveniently simple form by keeping Planck’s constant in place. However, because of our single photon approach

_{p}photons

*g*would not change since the intensities in the numerator and denominator scale together with N

_{p}. In what follows we will stick with the form in Eq. (5) by including

*ccw*and

*cw*states through degenerate perturbation theory. For a two state system one has to solve an eigenvalue equation involving a 2x2 matrix

*a*and

_{ccw}*a*are amplitudes for being in a superposition stateIn the absence of an off-diagonal term we return to Eq. (5) as expected. Unique solutions are guaranteed by setting the determinant of the secular equations represented by Eq. (7) equal to zero.

_{cw}*et al*. [11]. The epitope clearly splits the degeneracy, and the magnitude of the splitting 2|

*g*| depends only on the value of

*g*. If

*g*is a negative number, as it would be for an epitope having a polarizability which is positive,

*i.e*., the location of the nodes and anti-nodes in the relation to the epitopes), we need to determine the eigenvectors in Eq. (10). The solution of the following equation provides the required eigenvectors,For simplicity, the epitope is assumed to be on the

*X*-axis (i.e.,

*i.e.*,

*g*. It should be noted that the amplitude squared of the SSW state is twice that of either travelling wave state consistent with the factor of 2 increase in frequency shift. The other state

*i.e.,*relative positions). If the second epitope is identical to the first epitope (

*g*

_{1}=

*g*

_{2}=

*g*), then the total magnitude of the splitting is 4|

*g*|

*g*|

*et al*. [26].

*g*|. This means, when the optical phase difference between consecutive epitopes is π, then frequency shift due to each epitope adds independently. In the presence of 10 epitopes, variation in the frequency shift as a function of ΔФ is shown in Fig. 4 . It can be seen that maximum frequency shift is 20g at ΔФ = π due to the superposition of the travelling waves, and the average shift for all possible phase differences is 10g; this is exactly the shift produced by a travelling wave. The peak that appears at π is known as the first order peak and higher order peaks appear at integer multiples of π. The peak width is inversely proportional to

*N*; in order to observe a significant splitting experimentally, the inter-epitopes phase difference must have an error of less than half of the peak width. If the position of each epitope is Gaussian-distributed around the correct position with standard deviation σ, the mode splitting will be reduced. For example, for an operating wavelength of 800 nm in silica, if σ/

*r*= 0.025 μm/40 μm, the mode splitting becomes 90% of the full splitting. For a smaller σ of 0.015 μm, the fraction rises to 96%. If one epitope is missing, then the model fails. In practice, both issues can be dealt with by quality control and post-fabrication examination. We can also view the proposed periodic epitope system as a diffraction grating, with each epitope being the grating groove. It is well known that the grating sensitivity (resolution) depends upon the total number of grooves illuminated on the surface of the grating (

*N*) and diffraction order (

*n*). Although the sensitivity (magnitude of splitting) of the proposed epitope system is dependent on

*N*like a diffraction grating, it is independent of

*n*. In other words, the magnitude of the splitting is the same for all orders.

*N*-periodic epitope system are given by the following Equation by assuming

*N*particles, the observation of mode splitting requireswhere

*N*increases the possibility of observing the splitting.

*e.g.,*bio-nanoparticle) detection, if a dielectric analyte is adsorbed to any one of the epitopes then (

*N-*1) epitopes have the same interaction with the microcavity (

*g*) and one epitope which adsorbs the analyte particle has the different interaction (

*i.e.,*position T or B in Fig. 2), then the splitting becomes

*i.e*., a protein molecule) is attached to a spherical plasmonic epitope, then

*e.g.,*solid gold sphere or gold shell structure as in Fig. 2),

*Q*= 4x10

^{5}). If 8 copies of the virus adsorbed randomly on the equator of this resonator the mean splitting for a statistical number of trials would be

^{6}(line width = 195 fm), a value easily within reach of such a microcavity [27], the splitting due to these 8 viruses would still not be seen. It is to be noted that the mode splitting due to the imperfections (Rayleigh scattering) will be present when the ring resonator has an extremely high Q-factor (~10

^{8}). With a low Q-factor, such a splitting does not occur. In our case, because of the lossy metallic nanoparticles, our Q-factor is much lower (~10

^{6}).

*g*| and linewidth change

^{6}; 2|g| = 350 fm does not exceed the overall linewidth of 425 fm (195 fm from the original linewidth plus 230 fm caused by the deposition of a nanoparticle). Splitting would be seen for two epitopes separated by an optical phase of

*n*π since the magnitude of the splitting is 700 fm compared with an overall linewidth of 635 fm. With 4 optimally placed epitopes the splitting magnitude would be 2x4x175 = 1400 fm, well in excess of the overall linewidth. The key question now is: how much additional splitting will be produced by the binding of viruses onto the functionalized hotspots of these epitopes? From Ref.6, which only used one epitope, the maximum shift for a virus was 17 fm, which would have produced an unseen increase in splitting of 34 fm. With 8 viruses adsorbing on our 4 epitopes for which a splitting should be apparent, an increase in splitting of ~280 fm is calculated (upper trace in Fig. 6). So we have gone from an invisible splitting of 3.5 fm by random adsorption on silica to a visible increase of 280 fm for adsorption onto a phased array of 4 epitopes.

## 4. Discussion

^{6}in the near infrared [28–30], where modes of plasmonic epitopes are easily excited, and single virus and protein detection can be anticipated. By using an array of ring resonators with each carrying different selective receptors, a lab on a chip multiplexed to the same laser can be anticipated.

## Acknowledgments

## References and links

1. | M. S. Luchansky and R. C. Bailey, “High-Q Optical Sensors for Chemical and Biological Analysis,” Anal. Chem. |

2. | Y. Sun and X. Fan, “Optical ring resonators for biochemical and chemical sensing,” Anal. Bioanal. Chem. |

3. | S. Arnold, M. Khoshsima, I. Teraoka, S. Holler, and F. Vollmer, “Shift of whispering-gallery modes in microspheres by protein adsorption,” Opt. Lett. |

4. | 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. |

5. | S. Arnold, R. Ramjit, D. Keng, V. Kolchenko, and I. Teraoka, “MicroParticle PhotoPhysics illuminates viral biosensing,” Faraday Discuss. 137, 65–83 (2007) (discussion pp. 99–113). |

6. | V. R. Dantham, S. Holler, V. Kolchenko, Z. Wan, and S. Arnold, “Taking whispering gallery-mode single virus detection and sizing to the limit,” Appl. Phys. Lett. |

7. | S. I. Shopova, R. Rajmangal, S. Holler, and S. Arnold, “Plasmonic enhancement of a whispering-gallery-mode biosensor for single nanoparticle detection,” Appl. Phys. Lett. |

8. | M. A. Santiago-Cordoba, S. V. Boriskina, F. Vollmer, and M. C. Demirel, “Nanoparticle-based protein detection by optical shift of a resonant microcavity,” Appl. Phys. Lett. |

9. | L. Novotny, R. X. Bian, and X. S. Xie, “Theory of nanometric optical tweezers,” Phys. Rev. Lett. |

10. | 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 |

11. | J. Zhu, Ş. K. Ozdemir, Y. F. Xiao, L. Li, L. He, D. R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics |

12. | W. Kim, Ş. K. Ozdemir, J. Zhu, L. He, and L. Yang, “Demonstration of mode splitting in an optical microcavity in aqueous environment,” Appl. Phys. Lett. |

13. | R. D. Averitt, S. L. Westcott, and N. J. Halas, “Linear optical properties of gold nanoshells,” J. Opt. Soc. Am. B |

14. | J. D. Swaim, J. Knittel, and W. P. Bowen, “Detection limits in whispering gallery biosensors with plasmonic enhancement,” Appl. Phys. Lett. |

15. | P. Zijlstra, P. M. R. Paulo, and M. Orrit, “Optical detection of single non-absorbing molecules using the surface plasmon resonance of a gold nanorod,” Nat. Nanotechnol. |

16. | W. Ahn, S. V. Boriskina, Y. Hong, and B. M. Reinhard, “Photonic-plasmonic mode coupling in on-chip integrated optoplasmonic molecules,” ACS Nano |

17. | M. Chamanzar and A. Adibi, “Hybrid nanoplasmonic-photonic resonators for efficient coupling of light to single plasmonic nanoresonators,” Opt. Express |

18. | M. Chamanzar, E. S. Hosseini, S. Yegnanarayanan, and A. Adibi, “Hybrid Plasmonic-photonic Resonators for Sensing and Spectroscopy,” CLEO/QELS San Francisco, CA. 2011, Paper QTuE4. |

19. | I. M. White, J. Gohring, and X. Fan, “SERS-based detection in an optofluidic ring resonator platform,” Opt. Express |

20. | D. Sarid and W. Challener, |

21. | E. S. C. Ching, P. T. Leung, and K. Young, “The role of quasinormal modes,” in |

22. | S. Arnold, “Microspheres, photonic atoms, and the physics of nothing,” Am. Sci. |

23. | I. Teraoka and S. Arnold, “Resonance shifts of counterpropagating whispering-gallery modes: degenerate perturbation theory and application to resonator sensors with axial symmetry,” J. Opt. Soc. Am. B |

24. | A. Mazzei, S. Götzinger, L. S. Menezes, G. Zumofen, O. Benson, and V. Sandoghdar, “Controlled Coupling of Counterpropagating Whispering-Gallery Modes by a Single Rayleigh Scatterer: A Classical Problem in a Quantum Optical Light,” Phys. Rev. Lett. |

25. | J. Zhu, Ş. K. Özdemir, L. He, and L. Yang, “Controlled manipulation of mode splitting in an optical microcavity by two Rayleigh scatterers,” Opt. Express |

26. | L. Chantada, N. I. Nikolaev, A. L. Ivanov, P. Borri, and W. Langbein, “Optical resonances in microcylinders: response to perturbations for biosensing,” J. Opt. Soc. Am. B |

27. | W. Kim, Ş. K. Özdemir, J. Zhu, and L. Yang, “Observation and characterization of mode splitting in microsphere resonators in aquatic environment,” Appl. Phys. Lett. |

28. | E. S. Hosseini, S. Yegnanarayanan, M. Soltani, and A. Adibi, “Ultra-high quality factor microdisk resonators for chip-scale visible integrated photonics,” in |

29. | A. Gondarenko, J. S. Levy, and M. Lipson, “High confinement micron-scale silicon nitride high Q ring resonator,” Opt. Express |

30. | M.-C. Tien, J. F. Bauters, M. J. R. Heck, D. T. Spencer, D. J. Blumenthal, and J. E. Bowers, “Ultra-high quality factor planar Si |

**OCIS Codes**

(230.5750) Optical devices : Resonators

(240.6680) Optics at surfaces : Surface plasmons

(260.5740) Physical optics : Resonance

(280.1415) Remote sensing and sensors : Biological sensing and sensors

(140.3945) Lasers and laser optics : Microcavities

**ToC Category:**

Sensors

**History**

Original Manuscript: August 31, 2012

Revised Manuscript: October 25, 2012

Manuscript Accepted: October 31, 2012

Published: November 5, 2012

**Virtual Issues**

Vol. 7, Iss. 12 *Virtual Journal for Biomedical Optics*

**Citation**

Stephen Arnold, Venkata Ramanaiah Dantham, Curtis Barbre, Bruce A. Garetz, and Xudong Fan, "Periodic plasmonic enhancing epitopes on a whispering gallery mode biosensor," Opt. Express **20**, 26147-26159 (2012)

http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-20-24-26147

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### References

- M. S. Luchansky and R. C. Bailey, “High-Q Optical Sensors for Chemical and Biological Analysis,” Anal. Chem. 84(2), 793–821 (2012).
- Y. Sun and X. Fan, “Optical ring resonators for biochemical and chemical sensing,” Anal. Bioanal. Chem. 399(1), 205–211 (2011).
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- M.-C. Tien, J. F. Bauters, M. J. R. Heck, D. T. Spencer, D. J. Blumenthal, and J. E. Bowers, “Ultra-high quality factor planar Si3N4 ring resonators on Si substrates,” Opt. Express 19(14), 13551–13556 (2011).

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