Raman scattering is an inelastic scattering of a photon, meaning that scattered photons will have different frequencies from the excitation. When the scattering molecules are on a textured surface, the Raman scattering can be greatly enhanced (thus the term Surface Enhanced Raman scattering (SERS)). Direct simulation of this non-linear Raman scattering is quite challenging (as are most non-linear processes). Most often, FDTD simulations are used to measure the scattering enhancement. This can be done with a linear simulation, making the calculation far easier to setup and analyze. The enhancement factor (EF) is usually defined as (E/E0)^4 where E is the local maximum electric field, and E0 is the amplitude of input source electric field in a linear simulation.
In the following application example, we will measure the local enhancement factor near a Pt nanoparticle on a smooth Ag surface.
Under proper conditions, both the metallic nanoparticle and the plasmonic surface can produce localized surface plasmon and surface plasmon polariton (SPP). When the two geometric objects are very close but not in touch, the constructive interference between their surface plasmons can create huge field intensity in the "hot spot" inside the gap. Typical size of the gap is a few nanometers or even smaller. The fine mesh required to resolve the small gap can lead to large memory requirements and long simulation times. We use a TFSF source, and simulate only a small region of the structure, in order to find the maximally possible EFs.
Simulation setup and results
In this example, the Pt particle has a radius of 40 nm. The particle is located 1 nm above a silver substrate. The interaction between the particle and surface will create a strong local field enhancement where the particle almost touches the surface. To resolve such a tiny gap, we use mesh override named "mesh_gap" with mesh size 0.4 nm in z and 1 nm in xy plane (see tips). We use another coarser override to force a 5nm mesh around the rest of the particle.
A metal boundary condition is used for z min instead of PML to help reduce memory requirements since the fields do not penetrate down to the z min boundary.
The profile monitors "xz" and "yz" are used to record the local field profile at 50 frequency points.
After running this simulation, run the script file sers_pt_ag.lsf to calculate the enhancement factor (E^4). The following figures show E^4 in the XZ plane. The coarse simulation runs in about 10 minutes on a reasonable computer and requires about 550 MB of memory. For the higher accuracy simulation (0.2 nm gap z mesh, 0.5 nm gap x/y mesh), the memory increases to about 2 GB and time increases by about a factor of 5.
Coars and fine mesh results
- Convergence testing: The localized EF may be strongly dependent on the mesh, you may need to perform convergence testing of the mesh.
- Mesh size: We are most interested in making the z mesh small at the gap, to help resolve the very small (1 nm) gap distance). It is less important to force a small mesh in the X/Y directions, since the structure is not changing so rapidly in those directions. However, if the aspect ratio of the mesh (ie. the difference in size between the X/Y and Z mesh) become too large, the simulation can become unstable. In such situation, it may be necessary to force a smaller X/Y mesh. Another possible solution is to slightly reduce the 'dt stability factor' (property can be found in the FDTD region - mesh settings tab).
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 Kwan Kima, Hyang Bong Leea,Kuan Soo Shinb, Surface-enhanced Raman scattering characteristics of nanogaps formed by a flat Ag substrate and spherical Pt nanoparticles, Spectrochimica Acta Part A100(2013) 10-14
 Kwan Kim,Dongha Shin,Hyang Bong Leea and Kuan Soo Shin, Surface-enhanced Raman scattering of 4-aminobenzenethiol on gold: the concept of threshold energy in charge transfer enhancement, Chem. Commun., 2011,47, 2020-2022
 Wen-Di Li, Fei Ding, Jonathan Hu, and Stephen Y. Chou, Three-dimensional cavity nanoantenna coupled plasmonic nanodots for ultrahigh and uniform surface-enhanced Raman scattering over large area, Optics Express, Vol. 19, Issue 5, pp. 3925-3936 (2011)