Nanophotonics

1. For gold nanoparticles with a radius of 30 nm, find the extinction cross section using

the dipole mode and published values for the dielectric function. Calculate for

particles in air (n=1), water (n=1.33) and glycerol (n=1.473). For Au material

properties see: Johnson and Christy, Phys. Rev. B, 6, 4370 (1972) or Ecthegoin, et al.,

J. Chem. Phys. 125, 164705 (2006).

2. Show size dependence of the extinction cross section as the Au NPs get smaller than

30 nm. Use Au NPs with radii of 5, 10, 15, 20, 25 and 30nm. Use the full Drude

model with the collision damping term using vF = electron Fermi velocity = 1.4 E 6

m/s, A = 5 and γBulk = 1/(9.3 fs). Assume the plasma wavelength is 300 nm and the

NPs are in water. Plot the normalized scattering coefficient for each size.

3. From the Kelly paper (Kelly et al., J. Phys. Chem. B 107, 668 (2003)), find the

expression for the extinction efficiency including both the dipole and quadrapole

terms. Hint #1: use equation 9 in the paper. Hint #2: you have the expression for the

dipole mode only from class.

4. Use the result from problem 3 to graph the extinction efficiency for particles with

radii of 30, 60, 120, 200, and 300 nm. Assume the particles are in water and use the

dielectric function from problem 1.

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