Computational Nanophotonics

Stephen K. GrayChemistry Division

Argonne National LaboratoryArgonne, IL 60439

gray@tcg.anl.govTel: 630-252-3594

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

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 toGuide Experiment

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)/µo ∂H(x,t)/∂t = -x E(x,t)/µo

∂J(x,t)/∂t = op2 E(x,t)/µo

-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 timesteps

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 :

E and H Leapfrog in time :

More Explicitly : Continuous Equations such as

Get Replaced by Equations Like:

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

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

600 nm

0

Future Work Includes :

• 3D Extensions for arbitrary shapes

• The FD algorithm parallelization

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)