Nanometric Rulers Based on Plasmon Coupling in Pairs of Gold Nanoparticles

Using a generalized multiparticle Mie theory, we calculated the optical properties of gold nanoparticle (Au NP) pairs of 8-80 nm in diameter (D) and 0.1-120 nm in interparticle gap (s) under typical experimental conditions: an unpolarized incident light and random orientation of the pairs in space. By analyzing the extinction spectra of coupled spheres, three ranges of interparticle separations (long, middle and short) with different plasmon coupling regimes were distinguished. For long interparticle distances, a single plasmon peak in the spectrum at wavelength Delta lambda red-shifts exponentially relative to that of an isolated particle at wavelength lambda(0) as a function of x = s/D: Delta lambda/lambda(0) = (Delta lambda - lambda(0))/lambda(0) = a exp(-x/t), with a decay constant (t = 0.19) being nearly independent of nanoparticle diameters at D < 50 nm. Stronger shifts (0.04 < a < 0.08) are observed for 30-60 nm Au NPs. In the middle distance range (0.02 < s/D < (s/D)(split)), the extinction spectra of dimers have two plasmon peaks: transverse and longitudinal. The shift of long-wavelength peak can be reasonably approximated by the equation Delta lambda/lambda(0) = a(0) + a(1) exp(-x/t(1)), where the parameters a(1) (= 0.352) and t(1) (= 0.032) do not depend on the nanoparticle sizes, and a(0) increases with particle size. The boundary between the long and middle interparticle distance ranges, (s/D)(split), strongly varies with the Au NP diameter. At s/D < 0.02, the birth and evolution of third plasmon peak that is located between the transverse and longitudinal peaks has a strong effect upon the spectral properties of closely coupled NPs. Now the fractional shift of the longitudinal peak obeys the equation Delta lambda/lambda(0) = a(0) + a(1) exp(-x/t(1)) + a(2) exp(-x/t(2)), where t(2) = 0.004 and a(2) = 0.643. The constancy of coefficients a(i) and t(i) for Au NPs of different sizes means that the fractional shifts of plasmon resonances of coupled pairs corrected by parameter a(0) have to fall on a common curve. The obtained results clearly point that the Au NPs pairs can be used as the highly sensitive instruments to measure both absolute distances and their changes in the nanometric range of lengths.