Sensitization of Rare Earth Ions with Carbon Nanotube Plasmonic Antennas

Complexes containing rare earth ions (REI) and single-walled carbon nanotubes (SWNT) functionalized with single stranded DNA show promise to be utilized for the optical sensing of bio-molecules [1]. However, the electromagnetic interactions between the SWNT and the REI have not been sufficiently studied. In this work, we focus on the plasmonic interaction between the SWNT and a REI such as Terbium or Europium for their use as a biosensing complex.

The SWNT may act as a plasmonic antenna and generate a local field in the vicinity of the REI. We use the transmission line model [2] to model the plasmonic properties of the SWNT antenna.  The incoming light induces a surface current distribution:

I(z)=(V₀/Z_c)sinh[γ_p(l/2-|z|)]

where V₀ is the input voltage into the transmission line model determined by the applied electric field, Z_c is the characteristic impedance of the SWNT which is approximately 12 kΩ, γ_p is the plasmon propogation constant, and l is the length of the tube which we take to be 1 μm.  We estimate a field enhancement factor of approximately 10⁶in the near field given by:

F=ωl(LC/2)^1/2/(k²r²)

where L is the kinetic inductance of the SWNT, C is the total capacitance including both electrostatic and quantum capacitances, r is the radial distance between the SWNT axis and the REI, and k and ω are the wavevector and frequency of the incoming light, respectively.

The electromagnetic fields will be calculated using the electric Hertz potential satisfying the Helmholtz equation with proper boundary conditions.  The conductivity of the SWNT antenna in the transmission line model is given by:

σ=iωL^-1/(ω²+iωL^-1R-C^-1L^-1 γ_p²)

where R is the resistance of the SWNT.

The interaction of these calculated plasmonic fields with the REI will modulate the lifetimes of the REI. The modulated lifetimes of an electric dipole emitter will be calculated to model the allowed optical transitions of the particular REI.  To include the modulations of the optically dark REI transitions, a magnetic dipole emitter will be used.

To conclude, these results will give a better understanding of the near field electromagnetic interactions that take place in complexes containing SWNTs and REIs and allow for more efficient sensors.

Acknowledgement:  This work was supported by:  NSF ECCS-1202398

References:

[1] T. Ignatova, H.Najafov, A. Ryasnyanskiy, I. Biaggio, M. Zheng, and SV. Rotkin, “Significant FRET between SWNT/DNA and Rare Earth Ions: A Signature of Their Spatial Correlations”, ACS Nano 2011 5 (7), 6052-6059

[2] PJ. Burke, S. Li, Z.Yu, "Quantitative theory of nanowire and nanotube antenna performance," IEEE Transactions on  Nanotechnology  2006 5 (4), 314-334.