2. Computational Nanophotonics Stephen K. Gray Chemistry Division Argonne National Laboratory Argonne, IL 60439 gray@tcg.anl.gov Tel: 630-252-3594 gray@tcg.anl.gov

3. Motivation Wish to control light or electromagnetic energy in nano- sized optical devices Problem: optical light has wavelength >> 1nm Possible Solution - use near-field coupling of light with surface plasmons of metal nanoparticles => arrays of metal nanoparticles become photonic devices => steady or pulsed modes of illumination surface-plasmon resonance in Au nanoparticles

4. Excitation Transfer in Nanophotonics arrays of metal nanoparticles + substrate represented by spatially varying dielectric constant discretized fields E and H on 3D grids finite difference solution to Maxwell’s (curl) equations for time and spatial dependence of E and H fields Want Simulations to Guide Experiment

5. Finite Difference Time Domain (FDTD) Method Maxwell’s PDEs, outside nanoparticle: inside nanoparticle ∂E(x,t)/∂t =  x H(x,t)/  (x) ∂E(x,t)/∂t = [  x H(x,t) - J(x,t)]/  ∞ ∂H(x,t)/∂t = -  x E(x,t)/µ o ∂J(x,t)/∂t =  o  p 2 E(x,t)/µ o - J(x,t) are discretized in space and time : in general, 6 or more components are represented on a 3D spatial grid and propagated in discrete time steps

6. FDTD Basics : Yee Algorithm based on staggered space and time grids Each E component surrounded by 4 H components Each H component surrounded by 4 E components Space :

7. E and H Leapfrog in time :

8. More Explicitly : Continuous Equations such as

9. Get Replaced by Equations Like:

10. Current ANL Calculations 2D uniform grids (2000 x 2000) over 10000 time steps Silver “nanowire” (nanoscale radius infinite cylinder) arrays considered Variety of array configurations examined

11. Example: pulse of vertically polarized, 400 nm light shows 100 nm scale localization when passing (left to right) through a funnel configuration of 30 nm diameter silver nanowires [S. K. Gray and T. Kupka, Phys. Rev. B, submitted (2003).] 0 600 nm 0

12. Future Work Includes : 3D Extensions for arbitrary shapes The FD algorithm parallelization

13. Some Useful References : Quinten et al., Optics Letters 23, 1331 (1998) Maier et al., Advanced Materials 13, 1501 (2001) Maier et al., Appl. Phys. Lett. 81, 1714 (2002) Krenn et al., Europhys. Lett. 60, 663 (2002) Kottmann and Martin, Optics Express 12, 655 (2001 )