Nanoparticle Scattering

Nanoparticle plasmons: scattering, absorption, and extinction cross section measurement with FDTD Solutions

For light incident on metallic nanoparticles, resonant interactions with the electronic charge density near the surface, called surface plasmon polaritons, play an important role in determining the efficiency with which incident light is absorbed and scattered.

In this example we determine, for a silver nanowire with a diameter of 50 nm, the freqeuncy dependence of the surface plasmon polariton resonance and calculate the scattering, extinction and absorption cross sections as a function of wavelength near this resonance.  The amount of field enhancement achieved near the surface when excited on resonance is also determined.

University of Maryland"Our experience using parallel FDTD Solutions on a dual quad core Xeon Processor workstation has been fantastic! It greatly helped us in decreasing processing time for our plasmon-enhanced fluorescence calculations and hence greatly increased our computational throughput. We are extremely satisfied with the parallel version of FDTD Solutions and would recommend it to the scientific community at large.
- M. Chowdhury, University of Maryland

Step 1: Construct the nanoparticle project in the layout editor and simulate

The layout editor shows the position of the simulation objects. Different classes of objects (physical primitives, radiation sources, monitors) are color coded for easy identification. Objects can be moved and resized easily with the mouse.  Using the total-field scattered-field source to excite the nanoparticle with a broadband optical signal makes it easy to determine the extinction, absorption and scattered field spectrum all from a single simulation.

schematic of silver nanoparticle and total-field scattered-field source
Two-dimensional model of nanoparticle in FDTD Solutions.  More complicated three-dimensional models are easily built using one or more of the dozens of simulation primitives available in the simulation object library as shown.

Step 2: Gain understanding - watch the movie

Movies showing the simulation dynamics are easily created, and provide information that facilitates understanding of device behavior.  Here, the movie shows how a broadband optical pulse interacts in the near field with a silver nanoparticle.

The movie shows how the total-field scattered-field source works; the inner region contains the total field (incident+scattered) while the outer region contains only the scattered field.

Step 3: Measure the time response

Integrated analysis routines facilitate data analysis and visualization. Choose from drop-down menus which monitor you wish to analyze, and the field component of interest.  For example, by selecting the time monitor and the magnetic field component in the z-direction from pull-down menus, a plot of the time signal is easily produced.

time response of nanoparticle to incoming total field scattered field source
Note the strong scattering that occurs during the optical pulse.  Capturing the scattered signals at all times allows us to reconstruct the frequency response of the nanoparticle.

Step 4: Measuring the scattering, absorption, and extinction cross sections

The built-in parameter sweep and optimization environment can be used to perform parameter sweeps, distribute jobs across a number of computers, and speed simulation and analysis.  Here, we used customized analysis routines available in the FDTD Solutions Knowledge Base to compute the scattering, absorption and extinction cross sections of the nanoparticle and compare them against the analytic response.

nanoparticle plasmon scattering and absorption cross sections
Comparison of the extinction, scattering and absorption cross sections of the silver nanoparticle with theory.  Excellent agreement is obtained quickly after a single broadband simulation is performed.

Step 5: Determining the field profiles on and off resonance

Use frequency-domain monitors to record the steady-state / continuous-wave response of interest. Multiple steady- state responses can be determined in a single simulation, saving time over frequency-based solution techniques that require a simulation is performed at each frequency point of interest.

nanoparticle plasmon field profile on resonance
Off resonance, little field enhancement is obtained.  Here, the field enhancement is simulated to be just above 1.3X.
nanoparticle plasmon field profile off resonance
On resonance, the field enhancement is much greater.  Here, the field enhancement is measured to be larger than 20X.