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Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editor: Gregory W. Faris
  • Vol. 1, Iss. 6 — Jun. 13, 2006
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Design optimization of nano-grating surface plasmon resonance sensors

Kyung Hun Yoon, Michael L. Shuler, and Sung June Kim  »View Author Affiliations


Optics Express, Vol. 14, Issue 11, pp. 4842-4849 (2006)
http://dx.doi.org/10.1364/OE.14.004842


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Abstract

In this study, we propose nano-grating surface plasmon resonance (NGSPR) sensors and show the design optimization process. NGSPR sensors with line width less than 50 nm show narrow reflection peaks from the excitation of localized surface plasmon polaritons. The wavelength of resonance reflection can be customized by adjusting the grating period. We predict that a refractive index sensitivity of more than 400 nm/RIU can be obtained using an optimized structure. Sharp reflection resonance peaks with FWHM of 0.03 eV will further enhance the sensitivity of the sensors. The simple optical configuration of normal incidence and high refractive index sensitivity make it possible for NGSPR sensors to be used as portable biosensors for high-throughput screening applications.

© 2006 Optical Society of America

1. Introduction

Surface plasmon polariton (SPP) is an oscillation of free electrons inside a metal surface. When the frequency of the SPP is coincident with the external electromagnetic waves, there is a strong absorption of the electromagnetic waves. This resonance condition is very sensitive to the refractive index change of the surrounding material of the metal film. These properties of SPP can be used as a sensor for surface chemistry [1

1. J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuators B 54, 3–15 (1999) [CrossRef]

]. For a few decades surface plasmon resonance (SPR) sensors have been important in detecting the interaction of biomolecules. SPR sensors do not need any optical, electrical, or radioactive labels for detection. In proteomics, label-free detection is a very attractive characteristic and SPR sensors are major candidates for high-throughput screening solutions in the field of proteomics [2

2. Jin-Mi Jung, Yong-Beom Shin, Min-Gon Kim, Hyeon-Su Ro, Hee-Tae Jung, and Bong Hyun Chung, “A fusion protein expression analysis using surface plasmon resonance imaging,” Anal. Biochem. 330, 251–256 (2004) [CrossRef] [PubMed]

].

Conventional SPR sensors use the attenuation total internal refraction (ATIR) method to excite the SPP. The Kretschmann configuration is usually adopted. This angle incident configuration prohibits these SPR sensors from being used to measure large sample arrays. In an SPR imaging system the sensitivity increases with longer wavelength, but surface plasmon propagation length is proportional to the wavelength, which sets the limit for the unit cell size in an array [3

3. Jennifer M. Brockman, Bryce P. Nelson, and Robert M. Corn, “Surface plasmon resonance imaging measurements of ultrathin organic films,” Annu. Rev. Phys. Chem. 51, 41–63 (2000). [CrossRef] [PubMed]

]. In the Kretschmann configuration angle dependence of sensitivity is so great that a portable application is difficult to achieve.

Nobel metals such as gold or silver show extraordinary optical characteristics when the size is order of subwavelength (or sub 100 nanometer size) [4

4. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998). [CrossRef]

]. Optical absorption and scattering characteristics of nanosize metal varies with the size, shape, array type and the dielectric constant of surrounding materials [5

5. K. Lance Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: The influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107, 668–677 (2003). [CrossRef]

]. This phenomenon is called localized surface plasmon resonance (LSPR). Metallic nanoparticles have been used as labels to detect biochemical reactions in colloidal status using scattering spectrum analysis methods [6

6. N. Nath and A. Chilkoti, “A colorimetric gold nanoparticle sensor to interrogate Biomolecular interactions in real time on a surface,” Anal. Chem. 74, 504–509 (2002). [CrossRef] [PubMed]

]. A Northwestern University group developed a nano-sphere lithography (NSL) method for mass production of nano-triangular silver on a substrate. This NSL method produces sensors with a limited uniform area of a few tens of micrometers due to defects during the self-assembling process. LSPR sensors with a simple configuration can be made at low cost compared to conventional SPR sensors. Such a simple optical configuration is also attractive for portable applications.

Absorption or scattering spectrum analysis has been used for nanoparticle based LSPR sensors. In LSPR sensors, the resonance wavelength shift due to a change in the refractive index of surrounding materials is smaller than that of conventional SPR sensors. Additionally, full-width at half-maximum (FWHM) values of resonance peaks is broader which leads to sensitivity degradation. However, 1-D or 2-D arrays of silver nanoparticles are expected to have a narrow resonance peak [7

7. S. Zou and G. C. Schatz, “Narrow plasmonic/photonic extinction and scattering line shapes for one and two dimensional silver nanoparticle arrays,” J. Chem. Phys. 121, 12606–12612 (2004). [CrossRef] [PubMed]

]. When the target samples are turbid or opaque, the absorption or scattering spectrum can be affected by the samples themselves.

In this study, we propose a new approach to LSPR sensors that would be easily implemented into a portable system with high sensitivity. In this approach a nanosize grating is incorporated into the surface propagating type SPR sensors. Nano-grating surface plasmon (NGSPR) sensors use vertical illumination to excite localized surface plasmon polarition (LSPP). The use of nano-grating can enhance the refractive index sensitivity of LSPR sensors by large resonance wavelength shifts with the surrounding materials and sharp reflection resonance peaks. The influence of structural factors of nano-gratings on the sensitivity of NGSPR sensors was investigated using the rigorous coupled waveguide analysis (RCWA) method. The RCWA method is widely used for the calculation of optical properties of nanostructures [8

8. K. M. Byun, S. J. Kim, and D. Kim, “Design study of highly sensitive nanowire- enhanced surface plasmon resonance biosensors using rigorous coupled wave analysis,” Opt. Express 13, 3737–3742 (2005). [CrossRef] [PubMed]

]. The purpose of this computational study is to predict the optimal design of such a device.

2. Sensor structure and simulation parameters

A schematic diagram of the proposed NGSPR sensor is shown in Fig. 1. The sensor chip is composed of a thin metal film on a transparent substrate with nano-grating on it. Nano-grating can be made by either etching the substrate or molding the substrate. The structural parameters of the NGSPR sensors are shown in Fig. 1. Where Λ is the period of grating, u is the width of the upper region of the grating, d is the depth of the grating, and t is the depth of metal layer.

The transparent substrate is assumed to be SF10 glass and optical properties were obtained from manufactures. A thin gold film is deposited on top of the nano-grating carved substrate. Optical properties of the gold at the incident wavelength were taken from [9

9. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972). [CrossRef]

]. Sample materials on the thin gold film were assumed to have a refractive index range from 1.2 to 1.5. Biochemical reactions take place in the liquid solutions with typical refractive index values in this range. A TM-polarized light source is assumed. The range of wavelengths in the simulation was set from 500 nm to 850 nm. Below 500 nm the gold film absorbs the incident light and reflectance is very low. Above 850 nm silicon photodiodes or imaging devices such as CCD or CMOS sensors have little sensitivity. The reflection spectra were obtained using the RCWA method with normal incidence of light from the substrate side.

Fig. 1. Schematic diagram of a nano-grating based reflection type SPR sensor

3. Results and discussion

For a sensor with a period of 400 nm, the expected resonance wavelength due to the substrate-gold interaction is about 680 nm. Peak 2 in Fig. 2 is 710 nm, which is almost the same wavelength expected value from the simple estimation. Peak 2 is not influenced by the change of the refractive index of sample materials on the gold film, and can be identified as the substrate peak. Peak 1 is dependent on the change of refractive index of sample materials on the gold film, and can be identified as the sample peak. Due to the absorption of light by the gold film, the sample peak is not sharp enough to be distinguishable below 550 nm.

Fig. 2. Calculated reflectance spectra of a NGSPR sensor in various refractive index conditions (Λ=400 nm, u=50 nm, d=40 nm, t=40 nm)

In Fig. 3, the calculated reflectance spectra of the NGSPR sensor with a grating period of 500 nm are shown. The substrate peaks shifted into more than 850 nm. The sample peaks are in the simulated wavelength range. FWHM of the resonance peak is less than 10 nm and the refractive index sensitivity is about 440 nm/RIU. Calculated reflectance spectra of a NGSPR sensor with a period of 600 nm are shown in Fig. 4. The refractive index sensitivity is more than 500 nm/RIU but the FWHM is wider than that of the 500 nm period sensor and the resonance dips are shallower. Previously published values of refractive index sensitivities are 400 nm/RIU for gold nanohole arrays [11

11. A. G. Brolo, R. Gordon, B. Leatherm, and K. L. Kavanagh, “Surface plasmon sensor based on the enhanced light transmission through arrays of nanoholes in gold films,” Langmuir 20, 4813–4815 (2004). [CrossRef]

], 328.5 nm/RIU for gold nanoshells [12

12. Y. G. Sun and Y. N. Xia, “Gold and silver nanoparticles: A class of chromophores with colors tunable in the range from 400 to 750 nm,” Analyst 128, 686–691 (2003). [CrossRef] [PubMed]

], and 150 nm/RIU for NSL fabricated LSPR sensors [13

13. M. Duval Malinsky, K. Lance 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 self-assembled monolayers,” J. Am. Chem. Soc. 123, 1471–1482 (2001). [CrossRef]

].

A “figure of merit” (FOM) was defined in [14

14. L. J. Sherry, S.-H. Chang, G. C. Schatz, R. P. Van Duyne, B. J. Wiley, and Y. Xia, “Localized surface Plasmon Resonance Spectroscopy of single silver nanocubes,” Nano Lett. 5, 2034–2038 (2005). [CrossRef] [PubMed]

] to compare the overall performance of optical sensors as

FOM=m(eVRIU)FWHM(eV),
(1)

where m is the slope of wavelength over the refractive index. Overall the refractive index sensitivity of optical sensors is affected by the FWHM. A wide FWHM makes it difficult to distinguish small changes in the peak value. The deeper and narrower the resonance reflection peak is, the more accurate the determination of minimum reflection wavelength. NGSPR sensors have a very narrow resonance reflection peak with FWHM of 0.03 eV. The calculated FOM value is about 60 for a grating period of 500 nm. Usual nanoparticle based refractive index sensors have a FOM value of less than 10 due to a wide FWHM of absorption or scattering spectrum.

Fig. 3. Calculated reflectance spectra of a NGSPR sensor in various refractive index conditions (Λ=500 nm, u=50 nm, d=40 nm, t=40 nm)
Fig. 4. Calculated reflectance spectra of a NGSPR sensor in various refractive index conditions (Λ=600 nm, u=50 nm, d=40 nm, t=40 nm)

The effects of grating feature size on reflectance spectra of NGSPR sensors with a grating period of 500 nm are shown in Fig. 5. There are sharp resonance peaks when u, the width of the upper region of the grating, is 25 nm or 50 nm. When u is larger than 50 nm, the resonance peaks are broad. We also found that the NGSPR sensors with grating period of 500 nm have similar sharp resonance reflection peaks when u is wider than 450 nm. That is, there should be a region whose feature size is less than 50 nm to have a sharp resonance reflection peak. Some conventional grating coupled SPR (GC-SPR) sensors have similar structure with the NGSPR sensors. In GC-SPR sensors, u is usually 50 % of the grating period, which means u is more than a hundred nanometers. A conventional GC-SPR sensor doesn’t have sharp reflection peak when light is incident upon it vertically.

Fig. 5. Calculated reflectance spectra of NGSPR sensors (Λ=500 nm, d=40 nm, t=40 nm) with a feature size of 25 nm (a), 50 nm (b), 100 nm (c), and 250 nm (d)
Fig. 6. Calculated reflectance spectra of NGSPR sensors with various profiles and widths (Λ=500 nm, d=50 nm, t=50 nm, sample material is water)

Grating geometry effects were simulated with different u values. As shown in Fig. 6 when u=70 nm, grating geometry has a great effect on the resonance peak shape. No sharp resonance reflection peak can be found when the feature geometry is rectangle or rounded. In the case of u=50 nm, the peaks are always sharp, though the peak wavelength is slightly different. These simulation results indicate that a grating feature size of less than 50 nm should result in a sharp resonance reflection peak for any grating geometry. Geometrical deformations during the fabrication process will not degrade the sensitivity of the sensors if the minimum feature size of the grating is less than 50 nm.

To investigate the impact of grating depth, this parameter was varied from 30 nm to 60 nm, while the thickness of metal layer was set to 50 nm, period to 500 nm, and upper layer width to 50 nm. When the grating depth is shallow, the resonance peak is not deep [Figs. 7(a), 7(b)]. The reflection spectra are almost identical when the depth of the grating is equal to or greater than the thickness of the metal layer [Figs. 7(c), 7(d)].

Fig. 7. Calculated reflectance spectra of NGSPR sensors (Λ=500 nm, u=50 nm, t=50 nm) with a grating depth of 30 nm (a), 40 nm (b), 50 nm (c), and 60 nm (d)

A comparison of reflectance spectra obtained with different metal layer thickness is shown in Fig. 8. The metal layer thickness was varied from 30 nm to 60 nm. The depth of the grating was equal to the thickness of the metal layer. An NGSPR sensor with 30 nm metal layer thickness shows shallow resonance reflection peak in the short wavelength region. When the thickness of the metal layer is between 40 nm and 50 nm, the resonance peaks are sharp and deep. When the thickness of the metal layer becomes more than 60 nm, the depth of the resonance reflection peaks become shallow and have large FWHM values. The resonance reflection peak comes from the interaction between the metal film and the sample materials. The thicker the metal layer is, the less the amount of light coupled into the sample materials, which reduces the coupling effects. When the metal film is too thin, radiation damping from the metal film increases, which also reduces the coupling effects [15

15. J. Davies and I. Faulkner, Surface Analytical Techniques for Probing Biomaterial Processes (CRC Press, 1996), Chap. 3.

]. Optimum thickness for NGSPR sensors from this simulation study is between 40 nm and 50 nm.

This work has shown different effects of structural factors on the reflectance spectra from the work by Hick et. al [16

16. E. M. Hicks, X. Zhang, S. Zou, O. Lyandres, K. G. Spears, G. C. Schatz, and R. P. Van Duyne, “Plasmonic properties of film over Nanowell surfaces fabricated by Nanosphere Lithographpy,” J. Phys. Chem. B 109, 22351–22358 (2005). [CrossRef]

], which used the NSL method to make nanowell structure with the light source from the sample side. The NGSPR sensor with optical illumination from the substrate side is less effected by a buffer solution that is turbid or opaque to the wavelength of the light used for a measurement. Resonance reflection peaks are deeper when the light comes from the substrate side. Additionally, the optical setup can remain stationary when one changes the samples. In [16

16. E. M. Hicks, X. Zhang, S. Zou, O. Lyandres, K. G. Spears, G. C. Schatz, and R. P. Van Duyne, “Plasmonic properties of film over Nanowell surfaces fabricated by Nanosphere Lithographpy,” J. Phys. Chem. B 109, 22351–22358 (2005). [CrossRef]

], the authors found that resonance reflection peak wavelength changes with the etching depth. In comparison, NGSPR sensors are predicted to be not sensitive to the grating depth, if the grating depth is deeper than the metal layer thickness as shown in Fig. 7.

Fig. 8. Calculated reflectance spectra of NGSPR sensors (Λ=500 nm, u=50 nm) with a metal layer thickness of 30 nm (a), 40 nm (b), 50 nm (c), and 60 nm (d)

4. Conclusion

Here we estimate the optimal design of a novel type of sensor. NGSPR sensors with a minimum grating feature size less than 50 nm and a period of 500 nm produce relatively sharp resonance reflection peaks. The resonance wavelength of the sample peak varies with the refractive index of the sample materials. NGSPR sensors have a simple structure for mass fabrication and less sensitive to the grating geometry. The predicted refractive index sensitivity of NGSPR sensors is larger than 400 nm/RIU and the FOM value is expected to be more than 60 due to the narrow FWHM, which is much better than alternative methods.

NGSPR sensors can be made into robust equipment using visible wavelength spectroscopy in reflection geometry. This simple vertical illumination reflection spectroscopic configuration can be easily implemented in small size systems without any moving parts and refractive index matching mechanisms. Recent developments in nanolithography and nanofabrication methods can make it possible to fabricate NGSPR sensor chips at low cost in mass manufacture. The size of unit cells in NGSPR sensors can be made smaller compared to conventional SPR imaging sensors in which the unit cell size is limited by the surface plasmon propagation length. NGSPR sensors can be used as an economic tools for highthroughput screening (HTS) application.

Acknowledgments

References and links

1.

J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuators B 54, 3–15 (1999) [CrossRef]

2.

Jin-Mi Jung, Yong-Beom Shin, Min-Gon Kim, Hyeon-Su Ro, Hee-Tae Jung, and Bong Hyun Chung, “A fusion protein expression analysis using surface plasmon resonance imaging,” Anal. Biochem. 330, 251–256 (2004) [CrossRef] [PubMed]

3.

Jennifer M. Brockman, Bryce P. Nelson, and Robert M. Corn, “Surface plasmon resonance imaging measurements of ultrathin organic films,” Annu. Rev. Phys. Chem. 51, 41–63 (2000). [CrossRef] [PubMed]

4.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998). [CrossRef]

5.

K. Lance Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: The influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107, 668–677 (2003). [CrossRef]

6.

N. Nath and A. Chilkoti, “A colorimetric gold nanoparticle sensor to interrogate Biomolecular interactions in real time on a surface,” Anal. Chem. 74, 504–509 (2002). [CrossRef] [PubMed]

7.

S. Zou and G. C. Schatz, “Narrow plasmonic/photonic extinction and scattering line shapes for one and two dimensional silver nanoparticle arrays,” J. Chem. Phys. 121, 12606–12612 (2004). [CrossRef] [PubMed]

8.

K. M. Byun, S. J. Kim, and D. Kim, “Design study of highly sensitive nanowire- enhanced surface plasmon resonance biosensors using rigorous coupled wave analysis,” Opt. Express 13, 3737–3742 (2005). [CrossRef] [PubMed]

9.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972). [CrossRef]

10.

S. Zou, N. Janel, and G. C. Schatz, “Silver nanoparticle array structures that produce remarkably narrow plasmon lineshapes,” J. Chem. Phys. 120, 10871–10875 (2004). [CrossRef] [PubMed]

11.

A. G. Brolo, R. Gordon, B. Leatherm, and K. L. Kavanagh, “Surface plasmon sensor based on the enhanced light transmission through arrays of nanoholes in gold films,” Langmuir 20, 4813–4815 (2004). [CrossRef]

12.

Y. G. Sun and Y. N. Xia, “Gold and silver nanoparticles: A class of chromophores with colors tunable in the range from 400 to 750 nm,” Analyst 128, 686–691 (2003). [CrossRef] [PubMed]

13.

M. Duval Malinsky, K. Lance 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 self-assembled monolayers,” J. Am. Chem. Soc. 123, 1471–1482 (2001). [CrossRef]

14.

L. J. Sherry, S.-H. Chang, G. C. Schatz, R. P. Van Duyne, B. J. Wiley, and Y. Xia, “Localized surface Plasmon Resonance Spectroscopy of single silver nanocubes,” Nano Lett. 5, 2034–2038 (2005). [CrossRef] [PubMed]

15.

J. Davies and I. Faulkner, Surface Analytical Techniques for Probing Biomaterial Processes (CRC Press, 1996), Chap. 3.

16.

E. M. Hicks, X. Zhang, S. Zou, O. Lyandres, K. G. Spears, G. C. Schatz, and R. P. Van Duyne, “Plasmonic properties of film over Nanowell surfaces fabricated by Nanosphere Lithographpy,” J. Phys. Chem. B 109, 22351–22358 (2005). [CrossRef]

OCIS Codes
(050.2770) Diffraction and gratings : Gratings
(130.6010) Integrated optics : Sensors
(240.6680) Optics at surfaces : Surface plasmons

ToC Category:
Optics at Surfaces

History
Original Manuscript: March 31, 2006
Revised Manuscript: May 12, 2006
Manuscript Accepted: May 16, 2006
Published: May 29, 2006

Virtual Issues
Vol. 1, Iss. 6 Virtual Journal for Biomedical Optics

Citation
Kyung Hun Yoon, Michael L. Shuler, and Sung June Kim, "Design optimization of nano-grating surface plasmon resonance sensors," Opt. Express 14, 4842-4849 (2006)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-14-11-4842


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References

  1. J. Homola, S. S. Yee, and G. Gauglitz, "Surface plasmon resonance sensors: review," Sens. Actuators B 54, 3-15 (1999). [CrossRef]
  2. J.-M. Jung, Y.-B. Shin, M.-G. Kim, H.-S. Ro, H.-T. Jung, and B. H. Chung, "A fusion protein expression analysis using surface plasmon resonance imaging," Anal. Biochem. 330, 251-256 (2004). [CrossRef] [PubMed]
  3. J. M. Brockman, B. P. Nelson, and R. M. Corn, "Surface plasmon resonance imaging measurements of ultrathin organic films," Annu. Rev. Phys. Chem. 51, 41-63 (2000). [CrossRef] [PubMed]
  4. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391,667-669 (1998). [CrossRef]
  5. K. Lance Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, "The optical properties of metal nanoparticles: The influence of size, shape, and dielectric environment," J. Phys. Chem. B 107, 668-677 (2003). [CrossRef]
  6. N. Nath and A. Chilkoti, "A colorimetric gold nanoparticle sensor to interrogate Biomolecular interactions in real time on a surface," Anal. Chem. 74, 504-509 (2002). [CrossRef] [PubMed]
  7. S. Zou and G. C. Schatz, "Narrow plasmonic/photonic extinction and scattering line shapes for one and two dimensional silver nanoparticle arrays," J. Chem. Phys. 121, 12606-12612 (2004). [CrossRef] [PubMed]
  8. K. M. Byun, S. J. Kim, and D. Kim, "Design study of highly sensitive nanowire- enhanced surface plasmon resonance biosensors using rigorous coupled wave analysis," Opt. Express 13, 3737-3742 (2005). [CrossRef] [PubMed]
  9. P. B. Johnson and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370-4379 (1972). [CrossRef]
  10. S. Zou, N. Janel, and G. C. Schatz, "Silver nanoparticle array structures that produce remarkably narrow plasmon lineshapes," J. Chem. Phys. 120, 10871-10875 (2004). [CrossRef] [PubMed]
  11. A. G. Brolo, R. Gordon, B. Leatherm, and K. L. Kavanagh, "Surface plasmon sensor based on the enhanced light transmission through arrays of nanoholes in gold films," Langmuir 20, 4813-4815 (2004). [CrossRef]
  12. Y. G. Sun, and Y. N. Xia, "Gold and silver nanoparticles: A class of chromophores with colors tunable in the range from 400 to 750 nm," Analyst 128, 686-691 (2003). [CrossRef] [PubMed]
  13. M. Duval Malinsky, K. Lance 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 self-assembled monolayers," J. Am. Chem. Soc. 123, 1471-1482 (2001). [CrossRef]
  14. L. J. Sherry, S.-H. Chang, G. C. Schatz, R. P. Van Duyne, B. J. Wiley, and Y. Xia, "Localized surface Plasmon Resonance Spectroscopy of single silver nanocubes," Nano Lett. 5, 2034-2038 (2005). [CrossRef] [PubMed]
  15. J. Davies and I. Faulkner, Surface Analytical Techniques for Probing Biomaterial Processes (CRC Press, 1996), Chap. 3.
  16. E. M. Hicks, X. Zhang, S. Zou, O. Lyandres, K. G. Spears, G. C. Schatz, and R. P. Van Duyne, "Plasmonic properties of film over Nanowell surfaces fabricated by Nanosphere Lithographpy," J. Phys. Chem. B 109, 22351-22358 (2005). [CrossRef]

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