## Sensitive label-free biosensing using critical modes in aperiodic photonic structures

Optics Express, Vol. 16, Issue 17, pp. 12511-12522 (2008)

http://dx.doi.org/10.1364/OE.16.012511

Acrobat PDF (821 KB)

### Abstract

In this paper, we introduce a novel approach for optical sensing based on the excitation of critically localized modes in two-dimensional deterministic aperiodic structures generated by a Rudin-Shapiro (RS) sequence. Based on a rigorous computational analysis, we demonstrate that RS photonic structures provide a large number of resonant modes better suited for sensing applications compared to traditional band-edge and defect-localized modes in periodic photonic structures. Finally, we show that enhanced sensitivity to refractive index variations as low as Δ*n*=0.002 in RS structures results from the extended nature of critical modes and can enable the fabrication of novel label-free optical biosensors.

© 2008 Optical Society of America

## 1. Introduction

1. S. Chan, P. M. Fauchet, Y. Li, L. J. Rothberg, and B. L. Miller, “Porous silicon microcavities for biosensing applications,” Phys. Status Solidi A , **182**, 541–546 (2000). [CrossRef]

2. B. Schmidt, V. Almeida, C. Manolatou, S. Preble, and M. Lipson, “Nanocavity in a silicon waveguide for ultrasensitive nanoparticle detection,” Appl. Phys. Lett. **85**, 4854–4856 (2004). [CrossRef]

3. S. Xiao and N. A. Mortensen, “Highly dispersive photonic band-gap-edge optofluidic biosensors,” J. Eur. Opt. Soc. **1**, 06026 (2006). [CrossRef]

9. E. Krioukov, D. J. W. Klunder, A. Driessen, J. Greve, and C. Otto, “Sensor based on an integrated optical microcavity,” Opt. Lett. **27**, 512–514 (2002). [CrossRef]

17. A. D. McFarland and R. P. Van Duyne, “Single silver nanoparticles as real-time optical sensors with zeptomole sensitivity,” Nano Lett. **3**, 1057–1062 (2003). [CrossRef]

20. I. M. White and X. Fan, “On the performance quantification of resonant refractive index sensors,” Opt. Express **16**, 1020–1028 (2008). [CrossRef] [PubMed]

20. I. M. White and X. Fan, “On the performance quantification of resonant refractive index sensors,” Opt. Express **16**, 1020–1028 (2008). [CrossRef] [PubMed]

36. S. V. Boriskina, A. Gopinath, and L. Dal Negro, “Optical gaps, mode patterns and dipole radiation in two-dimensional aperiodic photonic structures,” Physica E (in the press); preprint at http://arxiv.org/abs/0807.4131

37. L. Dal Negro, N.-N. Feng, and A. Gopinath, “Electromagnetic coupling and plasmon localization in deterministic aperiodic arrays,” J. Opt. A: Pure Appl. Opt. **10**064013 (2008). [CrossRef]

26. M. Dulea, M. Johansson, and R. Riklund, “Localization of electrons and electromagnetic waves in a deterministic aperiodic system,” Phys. Rev. B , **45**, 105–114 (1992). [CrossRef]

38. L. Kroon, E. Lennholm, and R. Riklund, “Localization-delocalization in aperiodic systems,” Phys. Rev. B **66**, 094204 (2002). [CrossRef]

38. L. Kroon, E. Lennholm, and R. Riklund, “Localization-delocalization in aperiodic systems,” Phys. Rev. B **66**, 094204 (2002). [CrossRef]

39. L. Kroon and R. Riklund, “Absence of localization in a model with correlation measure as a random lattice,” Phys. Rev. B , **69**, 094204 (2004). [CrossRef]

37. L. Dal Negro, N.-N. Feng, and A. Gopinath, “Electromagnetic coupling and plasmon localization in deterministic aperiodic arrays,” J. Opt. A: Pure Appl. Opt. **10**064013 (2008). [CrossRef]

## 2. Computational method

40. G. Tayeb and D. Maystre, “Rigorous theoretical study of finite-size two-dimensional photonic crystals doped by microcavities,” J. Opt. Soc. Am. A **14**, 3323–3332 (1997). [CrossRef]

*N*cylindrical scatterers can be constructed as a superposition of partial fields scattered from each cylinder. These partial fields are expanded in infinite Fourier-Bessel series in the coordinate systems with the origins at the centers of individual cylinders. Using the addition theorem for Bessel functions, the interacting partial fields can be transformed into series expansions in the same coordinate system. Imposing the field continuity conditions at the boundary of each cylinder and truncating the infinite series at the maximum multipole order

_{c}*N*, the final inhomogeneous matrix equation for the Lorenz/Mie multipole scattering coefficients can be obtained:

*r*is the center-to-center distance between

_{pl}*p*-th and

*l*-th cylinders;

*θ*is the argument of the vector

_{pl}*r⃗*=

_{pl}*r⃗*-

_{l}*r⃗*;

_{p}*ε*=

_{h}*n*

^{2}

*is the permittivity of the host medium;*

_{h}*S*are the polarization-dependent elements of the scattering matrix of each cylinder, which are obtained by applying the field boundary conditions at the cylinder cross-section contour; and

^{p}_{m}*Q*are the Fourier expansion coefficients of the field illuminated by a line source in the host medium (see e.g. [41

^{p}_{m}41. A. A. Asatryan, K. Busch, R. C. McPhedran, L. C. Botten, C. Martijn de Sterke, and N. A. Nicorovici, “Two-dimensional Green’s function and local density of states in photonic crystals consisting of a finite number of cylinders of infinite length,” Phys. Rev. E , **63**, 046612 (2001). [CrossRef]

42. S. V. Pishko, P. Sewell, T. M. Benson, and S. V. Boriskina, “Efficient analysis and design of low-loss WG-mode coupled resonator optical waveguide bends,” J. Lightwave Technol. **25**, 2487–2494 (2007). [CrossRef]

^{-5}.

## 3. Results and discussion

*r*/

*a*=0.2 (

*a*is the nearest-neighbor center-to-center separation) and dielectric permittivity

*ε*=10.5. The material and structural parameters have been chosen to be the same as in Ref. 3

3. S. Xiao and N. A. Mortensen, “Highly dispersive photonic band-gap-edge optofluidic biosensors,” J. Eur. Opt. Soc. **1**, 06026 (2006). [CrossRef]

*L*surrounding the structure [34

34. Y. Lai, Z.-Q. Zhang, C.-H. Chan, and L. Tsang, “Anomalous properties of the band-edge states in large two-dimensional photonic quasicrystals,” Phys. Rev. B **76**, 165132 (2007). [CrossRef]

42. S. V. Pishko, P. Sewell, T. M. Benson, and S. V. Boriskina, “Efficient analysis and design of low-loss WG-mode coupled resonator optical waveguide bends,” J. Lightwave Technol. **25**, 2487–2494 (2007). [CrossRef]

43. Y. Wang, X. Hu, X. Xu, B. Cheng, and D. Zhang, “Localized modes in defect-free dodecagonal quasiperiodic photonic crystals,” Phys. Rev. B **68**, 165106 (2003). [CrossRef]

**S**is the Poynting vector and

**n**is a unit vector normal to the contour enclosing the structure. Existence of photonic bandgaps and spectral locations of resonant modes in photonic structures can be revealed by inspecting the frequency dependence of the total radiated energy flow. For finite-size photonic structures, bandgaps are manifested as regions of the reduced radiated power in their frequency spectra [34

34. Y. Lai, Z.-Q. Zhang, C.-H. Chan, and L. Tsang, “Anomalous properties of the band-edge states in large two-dimensional photonic quasicrystals,” Phys. Rev. B **76**, 165132 (2007). [CrossRef]

42. S. V. Pishko, P. Sewell, T. M. Benson, and S. V. Boriskina, “Efficient analysis and design of low-loss WG-mode coupled resonator optical waveguide bends,” J. Lightwave Technol. **25**, 2487–2494 (2007). [CrossRef]

43. Y. Wang, X. Hu, X. Xu, B. Cheng, and D. Zhang, “Localized modes in defect-free dodecagonal quasiperiodic photonic crystals,” Phys. Rev. B **68**, 165106 (2003). [CrossRef]

30. C. Rockstuhl, U. Peschel, and F. Lederer, “Correlation between single-cylinder properties and bandgap formation in photonic structures,” Opt. Lett. **31**, 1741–1743 (2006). [CrossRef] [PubMed]

*N*~30, red lines) and larger structures (

_{c}*N*~100, blue lines). The total power radiated by the source embedded in a photonic structure is normalized by dividing it by the power radiated from the source in the free space. A clear difference can be observed in the behavior of the optical spectra of the two structure types with the increase of the sample size. For a periodic lattice, the size increase causes further reduction of the radiation power in the bandgap and also the shift of the band-edge modes, in accordance with previous studies [34

_{c}34. Y. Lai, Z.-Q. Zhang, C.-H. Chan, and L. Tsang, “Anomalous properties of the band-edge states in large two-dimensional photonic quasicrystals,” Phys. Rev. B **76**, 165132 (2007). [CrossRef]

*a*/

*λ*=0.289 and

*a*/

*λ*=0.467.

*λ*=

*λ*(

*n*+Δ

_{h}*n*)-

*λ*(

*n*),nm) experienced by the optical modes of the larger-size (

_{h}*N*~100) square lattice periodic PhC (red bars) and the aperiodic RS structure (blue bars) scaled to operate at

_{c}*λ*~1.55 µm if the ambient refractive index is increased by Δ

*n*=0.002. Figure 4(b) shows the quality factors of the corresponding modes. The chosen value of Δ

*n*represents the smallest increment that can be typically obtained in commercially available optical fluids and thus is often used to measure the sensitivity of PhC biosensors [3

3. S. Xiao and N. A. Mortensen, “Highly dispersive photonic band-gap-edge optofluidic biosensors,” J. Eur. Opt. Soc. **1**, 06026 (2006). [CrossRef]

7. E. Chow, A. Grot, L. W. Mirkarimi, M. Sigalas, and G. Girolami, “Ultracompact biochemical sensor built with two-dimensional photonic crystal microcavity,” Opt. Lett. **29**, 1093–1095 (2004). [CrossRef] [PubMed]

*S*=Δ

*λ*Δ

*n*(measured in nm/RIU).

_{h}**1**, 06026 (2006). [CrossRef]

4. N. A. Mortensen, S. Xiao, and J. Pedersen, “Liquid-infiltrated photonic crystals: enhanced light-matter interactions for lab-on-a-chip applications,” Microfluidics and Nanofluidics **4**, 117–127 (2008). [CrossRef]

*λ*=0.29 nm,

*S*=147 nm/RIU), while the resonant frequencies of its high-frequency band-edge mode (an air(liquid) band [3

**1**, 06026 (2006). [CrossRef]

4. N. A. Mortensen, S. Xiao, and J. Pedersen, “Liquid-infiltrated photonic crystals: enhanced light-matter interactions for lab-on-a-chip applications,” Microfluidics and Nanofluidics **4**, 117–127 (2008). [CrossRef]

*λ*=1.8 nm,

*S*=902 nm/RIU and Δ

*λ*=1.82 nm,

*S*=913 nm/RIU, respectively). This observation is in a perfect agreement with previous studies [3

**1**, 06026 (2006). [CrossRef]

16. S. V. Boriskina, “Spectrally-engineered photonic molecules as optical sensors with enhanced sensitivity: a proposal and numerical analysis,” J. Opt. Soc. Am. B **23**, 1565–1573 (2006). [CrossRef]

20. I. M. White and X. Fan, “On the performance quantification of resonant refractive index sensors,” Opt. Express **16**, 1020–1028 (2008). [CrossRef] [PubMed]

*λ*=0.28 nm (

*S*=138 nm/RIU), while the resonant frequency of the high-frequency band-edge mode is more sensitive to the ambient refractive index change (Δ

*λ*=1.44 nm,

*S*=718 nm/RIU).

*λ*~0.5 nm) caused by the change of the ambient refractive index (as seen in Fig. 4(a)). However, all the high-Q modes appearing in and just above the bandgap show enhanced sensitivity to the presence of the analyte over the modes of the periodic PhC (1.98 nm≤Δ

*λ*≤2.56 nm and 988 nm/RIU≤

*S*≤1282 nm/RIU).

4. N. A. Mortensen, S. Xiao, and J. Pedersen, “Liquid-infiltrated photonic crystals: enhanced light-matter interactions for lab-on-a-chip applications,” Microfluidics and Nanofluidics **4**, 117–127 (2008). [CrossRef]

15. H. Zhu, I. M. White, J. D. Suter, P. S. Dale, and X. Fan, “Analysis of biomolecule detection with optofluidic ring resonator sensors,” Opt. Express **15**, 9139–9146 (2007). [CrossRef] [PubMed]

**16**, 1020–1028 (2008). [CrossRef] [PubMed]

*f*=1-

_{d}*f*[4

_{h}**4**, 117–127 (2008). [CrossRef]

*V*and the normalized adimensional effective mode volume

_{eff}*Ṽ*(see, e.g., [45

_{eff}45. J. Vučković, M. Lončar, H. Mabuchi, and A. Scherer, “Design of photonic crystal microcavities for cavity QED,” Phys. Rev. E **65**, 016608 (2001). [CrossRef]

**r**

_{max}is the position of the maximum field intensity.

**4**, 117–127 (2008). [CrossRef]

15. H. Zhu, I. M. White, J. D. Suter, P. S. Dale, and X. Fan, “Analysis of biomolecule detection with optofluidic ring resonator sensors,” Opt. Express **15**, 9139–9146 (2007). [CrossRef] [PubMed]

**16**, 1020–1028 (2008). [CrossRef] [PubMed]

45. J. Vučković, M. Lončar, H. Mabuchi, and A. Scherer, “Design of photonic crystal microcavities for cavity QED,” Phys. Rev. E **65**, 016608 (2001). [CrossRef]

*Ṽ*as compared to those of the modes with the high field intensity concentrated in the high-index dielectric material. However, no clear dependence of the mode sensitivity on the effective volume can be observed. We conclude that the normalized effective modal volume is not a useful parameter for estimating the sensitivity of the optical refractive index sensors. Nevertheless, it can still be considered a useful figure-of-merit for quantifying performance of optical biosensors based on other detection schemes, such as fluorescence enhancement [46

_{eff}46. S. Blair and Y. Chen, “Resonant-enhanced evanescent-wave fluorescence biosensing with cylindrical optical cavities,” Appl. Opt. **40**, 570–582 (2001). [CrossRef]

14. 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**, 783–787 (2007). [CrossRef] [PubMed]

**16**, 1020–1028 (2008). [CrossRef] [PubMed]

*Q*

_{‖}=5.1·10

^{4}), its overall Q-factor in a 3D realization (1/

*Q*=1/

*Q*

_{‖}+1/

*Q*) will be severely limited by vertical out-of-plane loss (radiative Q-factor

_{R}*Q*). This out-of-plane radiative loss results from the strong in-plane localization of the modal field, and one possible way of decreasing it is controllable delocalization of the in-plane modal field distribution, which in turn increases in-plane energy leakage [44]. Our investigation of localization properties of critical modes in aperiodic structures revealed the fact that the vertical and lateral leakage of their fields can be optimally balanced, which results in the optimization of the overall mode Q-factor. (Note that a similar effect has previously been observed in periodic photonic lattices with various degrees of structural and material disorder [47

_{R}47. A. Yamilov, X. Wu, X. Liu, R. P. H. Chang, and H. Cao, “Self-optimization of optical confinement in an ultraviolet photonic crystal slab laser,” Phys. Rev. Lett. **96**, 083905 (2006). [CrossRef] [PubMed]

48. S. V. Zhukovsky, D. N. Chigrin, and J. Kroha, “Low-loss resonant modes in deterministically aperiodic nanopillar waveguides,” J. Opt. Soc. Am. B **23**, 2265–2272 (2006). [CrossRef]

*N*~30, red lines and

_{c}*N*~100, blue lines) are plotted in Fig. 6. No spectral gaps open for the TE-polarized waves [30

_{c}30. C. Rockstuhl, U. Peschel, and F. Lederer, “Correlation between single-cylinder properties and bandgap formation in photonic structures,” Opt. Lett. **31**, 1741–1743 (2006). [CrossRef] [PubMed]

32. A. Della Villa, S. Enoch, G. Tayeb, F. Capolino, V. Pierro, and V. Galdi, “Localized modes in photonic quasicrystals with Penrose-type lattice,” Opt. Express **14**, 10021–10027 (2006). [CrossRef] [PubMed]

*n*=0.002, and summarized the results in Fig. 7. As in the case of the TM polarization, the corresponding data for the Bloch-type mode of a periodic structure are shown for comparison (red bars). The results presented in Fig. 7 clearly demonstrate that even in the absence of the TE bandgap aperiodic photonic structures sustain many quasi-localized critical modes that can be useful for sensing applications (wavelength shifts range from 1.34 nm (

*S*=670 nm/RIU) to 2.29 nm (

*S*=1145 nm/RIU)). Magnetic field distributions of the Bloch-type mode of the periodic structure and two critical modes of the Rudin-Shapiro structure are shown in Fig. 8.

*λ*~600 nm range from 0.76 nm to 0.99 nm (for Δ

*n*=0.002), yielding refractive index sensitivity of 382–496 nm/RIU. Experimentally reported typical sensitivity values of surfaceplasmon (SP) biosensors based on individual Ag nanoparticles and Ag nanoparticle arrays range from 150 to 235 nm/RIU for the same working frequency [17

17. A. D. McFarland and R. P. Van Duyne, “Single silver nanoparticles as real-time optical sensors with zeptomole sensitivity,” Nano Lett. **3**, 1057–1062 (2003). [CrossRef]

18. M. D. Malinsky, K. L. Kelly, G. C. Schatz, and R. P. Van Duyne, “Chain length dependence and sensing capabilities of the localized surface plasmon resonance of silver nanoparticles chemically modified with alkanethiol selfassembled monolayers,” J. Am. Chem. Soc. **123**, 1471–1482 (2001). [CrossRef]

*S*=250 nm/RIU) have recently been reported for organic vapor SP resonance sensors based on the arrays of gold nanoshells [19

19. C.-S. Cheng, Y.-Q. Chen, and C.-J. Lu, “Organic vapour sensing using localized surface plasmon resonance spectrum of metallic nanoparticles self assemble monolayer,” Talanta **73**, 358–365 (2007). [CrossRef] [PubMed]

*S*=22.89 nm/RIU, Q=4900), microrings (

*S*=70 nm/RIU, Q=20,000) and point-defect microcavities in periodic photonic crystals (

*S*=200 nm/RIU, Q=400) operating at

*λ*~1.55 µm.

## 4. Conclusion

*n*=0.002 and a working wavelength around 1.55 µm, which translates to the refractive index sensitivity of 1282 nm/RIU. For comparison, the high-frequency band-edge mode and the single-defect mode of a square-lattice periodic PhC with the same material properties and nearest-neighbor separations shift by 1.8 (

*S*=902 nm/RIU) and 1.82 nm (

*S*=913 nm/RIU), respectively (see also [3

**1**, 06026 (2006). [CrossRef]

49. A. Sharkawy, D. Pustai, S. Shi, D. Prather, S. McBride, and P. Zanzucchi, “Modulating dispersion properties of low index photonic crystal structures using microfluidics,” Opt. Express **13**, 2814–2827 (2005). [CrossRef] [PubMed]

50. D. Erickson, T. Rockwood, T. Emery, A. Scherer, and D. Psaltis, “Nanofluidic tuning of photonic crystal circuits,” Opt. Lett. **31**, 59–61 (2006). [CrossRef] [PubMed]

46. S. Blair and Y. Chen, “Resonant-enhanced evanescent-wave fluorescence biosensing with cylindrical optical cavities,” Appl. Opt. **40**, 570–582 (2001). [CrossRef]

51. R. W. Boyd and J. E. Heebner, “Sensitive disk resonator photonic biosensor,” Appl. Opt. **40**, 5742–5747 (2001). [CrossRef]

52. J. R. Lakowicz, J. Malicka, I. Gryczynski, Z. Gryczynski, and C. D. Geddes, “Radiative decay engineering: the role of photonic mode density in biotechnology,” J. Phys. D: Appl. Phys. **36**, R240–R249 (2003). [CrossRef]

## Acknowledgment

*Development of novel SERS substrates via rationally designed nanofabrication strategies*, the DARPA project:

*Chemical Communication*, and the NATO Collaborative Linkage Grant CBP.NUKR.CLG 982430:

*Micro- and nano-cavity structures for imaging, biosensing and novel materials*.

## References and links

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37. | L. Dal Negro, N.-N. Feng, and A. Gopinath, “Electromagnetic coupling and plasmon localization in deterministic aperiodic arrays,” J. Opt. A: Pure Appl. Opt. |

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41. | A. A. Asatryan, K. Busch, R. C. McPhedran, L. C. Botten, C. Martijn de Sterke, and N. A. Nicorovici, “Two-dimensional Green’s function and local density of states in photonic crystals consisting of a finite number of cylinders of infinite length,” Phys. Rev. E , |

42. | S. V. Pishko, P. Sewell, T. M. Benson, and S. V. Boriskina, “Efficient analysis and design of low-loss WG-mode coupled resonator optical waveguide bends,” J. Lightwave Technol. |

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45. | J. Vučković, M. Lončar, H. Mabuchi, and A. Scherer, “Design of photonic crystal microcavities for cavity QED,” Phys. Rev. E |

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47. | A. Yamilov, X. Wu, X. Liu, R. P. H. Chang, and H. Cao, “Self-optimization of optical confinement in an ultraviolet photonic crystal slab laser,” Phys. Rev. Lett. |

48. | S. V. Zhukovsky, D. N. Chigrin, and J. Kroha, “Low-loss resonant modes in deterministically aperiodic nanopillar waveguides,” J. Opt. Soc. Am. B |

49. | A. Sharkawy, D. Pustai, S. Shi, D. Prather, S. McBride, and P. Zanzucchi, “Modulating dispersion properties of low index photonic crystal structures using microfluidics,” Opt. Express |

50. | D. Erickson, T. Rockwood, T. Emery, A. Scherer, and D. Psaltis, “Nanofluidic tuning of photonic crystal circuits,” Opt. Lett. |

51. | R. W. Boyd and J. E. Heebner, “Sensitive disk resonator photonic biosensor,” Appl. Opt. |

52. | J. R. Lakowicz, J. Malicka, I. Gryczynski, Z. Gryczynski, and C. D. Geddes, “Radiative decay engineering: the role of photonic mode density in biotechnology,” J. Phys. D: Appl. Phys. |

**OCIS Codes**

(130.6010) Integrated optics : Sensors

(170.4520) Medical optics and biotechnology : Optical confinement and manipulation

(170.4580) Medical optics and biotechnology : Optical diagnostics for medicine

(230.5750) Optical devices : Resonators

(290.4210) Scattering : Multiple scattering

(160.5298) Materials : Photonic crystals

**ToC Category:**

Medical Optics and Biotechnology

**History**

Original Manuscript: June 18, 2008

Revised Manuscript: July 28, 2008

Manuscript Accepted: July 30, 2008

Published: August 4, 2008

**Virtual Issues**

Vol. 3, Iss. 10 *Virtual Journal for Biomedical Optics*

**Citation**

Svetlana V. Boriskina and Luca Dal Negro, "Sensitive label-free biosensing using critical modes in aperiodic photonic structures," Opt. Express **16**, 12511-12522 (2008)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-17-12511

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