Study of Surface Plasmon Resonance (SPR) In a Nano-Structured Material

 

Jagmeet Singh Sekhon* and S.S. Verma

Department of Physics, Sant Longowal Institute of Engineering and Technology Longowal (Deemed to be University), Distt.-Sangrur, (Punjab) ―148-106, India.

*Corresponding Author E-mail: jagmeetsekhon@ymail.com

ABSTRACT:

In the present analysis, absorption spectrum of gold nanorod is modeled by Gans theory with the introduction of inter-band transition contribution to the dielectric function of the gold material. A linear relationship is found between the absorption maxima of longitudinal plasmon resonance and aspect ratio. Since the absorption maxima of the longitudinal plasmon resonance also depend on the refractive index value of the surrounding medium therefore, the surrounding medium in present analysis was taken as water with its refractive index value of 1.33. It is observed that with the increase in aspect ratio of gold nanorod the absorption intensity increases and the resonance wavelength shifts towards red regime of visible spectrum and further increase in the aspect ratio (~4) results a resonance wavelength in the near infrared regime. Further, a comparison with the results obtained for gold nanorods by the different theoretical models, like LC circuit model, discrete dipole approximation (DDA), experimental data, as well as the linear fit equation of experimental data was done to authenticate the parametric effect in present analysis on plasmon resonance in nano-structured materials (nanorod here). Our analytical results show a close agreement with linear curve fit equation of experimental data in comparison to the other models.

 

KEYWORDS: Surface Plasmon, Resonance, Aspect ratio, Nanorod

 

INTRODUCTION:

Metal nanostructures exhibit strong absorption spectra in the visible region of the spectrum. The origin of this absorption is attributed to the collective conduction band electron oscillation, called plasmons, in the response to the electrical field of the electromagnetic radiation of light¹. This plasmon resonance results to enhance electric field inside and around the metal nanoparticles. Such an effect leads to potential applications like cancer diagnosis and therapy², and plasmonic waveguides³. Kooij and Poelsema⁴ describe the phenomena of plasmon resonance for spherical gold nano-particles by using Mie theory for novel materials like gold and silver. Further extension of Mie theory, called Gans theory, which is useful to study the optical phenomena related to the ellipsoidal shaped nanoparticles. The optical properties of arbitrarily shaped particles can be found only in approximate way because of complex shape motifs of nanoparticles.

 

In literature, nanorods^4,5 are considered as ellipsoidal shaped and shows two resonance frequency peaks in its spectrum. One is called transverse resonance peak, which shows blue-shift with increase in aspect ratio as well as dielectric function value of surrounding medium, whereas the second peak called longitudinal resonance peak which shows red-shifts with increase in aspect ratio and dielectric function value of the surrounding medium.

 

Discrete dipole approximation (DDA) has been extensively developed in the past few years and is an efficiently computational method capable of treating arbitrarily shaped particles. Brioude et al.⁶ used DDA and reported that the increase in aspect ratio leads the red-shift of absorption peak and shows a linear relationship between resonance wavelength and  aspect ratio. Similarly, Kooij and Poelsema⁴ treated nanorods as different shaped like cylindrical, ellipsoidal and rectangular and reported that DDA can provide much better results if any other targeted geometry was used instead of above mention three.  Recently, Huang et al.⁷ had proposed a new scheme (LC model) to study the optical behavior of nanorods without solving the Maxwell’s equations. The non-linear behavior of the plasmon resonance was shown by introducing both the radius and aspect ratio separately in the resonance wavelength expression and author (Huang) says that this overcomes the deficiency of Gans theory in which resonance wavelength depends only upon the aspect ratio.

 

We have used the Gans theory⁵ with the introduction of inter-band contributions to the dielectric function and modeled the optical absorption spectra of gold nanorod samples with varying aspect ratio for a fixed value of the dielectric constant of the surrounding medium. We were able to drive a simple relation between resonance wavelength (absorption maxima) and the aspect ratio. Comparison of present results for Gans theory calculations (with the introduction of inter-band contributions to the dielectric function) was made with other theoretical models like LC model, Gans theory⁵ (excluding the inter-band transition effect in the dielectric function), and DDA as well as with some experimental results and for linear fit equation of experimental data.

 

Theoretical Model:

The particles having size much smaller in comparison to the wavelength of incident light i.e., the nanoparticles, feel a field, which is spatially constant, but having a time dependent phase are known to be in quasi-static limit. In this limit, the displacement of charge in a particle is homogeneous leading to a dipolar charge distribution on the surface of nanoparticle. In quasi-static limit, the absorption and scattering cross-sections⁴ are given by:

 

 

CONCLUSION:

In this paper, we studied the plasmon absorption peak of gold nanorods for longitudinal dipolar mode governed by the aspect ratio of nanorods. The calculations are found to be close to the experimental linear fit calculations and to DDA simulation. A linear relationship was derived between absorption maxima and aspect ratio for a fixed value of dielectric function of the surrounding medium (water here). Hence, Gans theory with the introduction of inter-band contributions in the dielectric functions described in the present paper provides a useful calculation methodology to study the resonance spectra for the nanorod. The nanorod with same aspect ratio but size greater than the skin depth will result for the inclusion of retardation effect and multipolar excitation (both excluded in the present analysis) may wider the absorption peak, and change in absorption maxima position and hence, should be taken care in further studies.

 

ACKNOWLEDGEMENTS:

Jagmeet Singh would like to thank SLIET, Longowal authorities for financial support in the form of Institute fellowship towards his Ph. D.

 

REFERENCES:

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Received on 04.05.2011        Accepted on 09.06.2011        

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