In this example, we construct a complete three-dimensional model of the interaction of a focused optical beam and a perfectly reflecting surface with a nanoparticle (post). The goal is to determine the minimum feature size of the nanoparticle that results in a strong scattered signal.
Simulation Setup
Open the nanoparticle_dgtd.ldev project file in DGTD. The "materials" folder contains a dielectric material named "Glass" with an index of 1.55 that is used to fill the simulation volume (using the "background material" option in the simulation region). The "geometry" folder contains three geometries. The "surface" models the reflective surface, the "post" models the nanoparticle, and the "source_plane" inserts a plane in the simulated volume to be used as the source injection plane. The material for all the geometries are set to "Glass". PEC boundary conditions are assigned to the bottom surface of the simulation region and to the "post" to model perfectly reflecting surfaces. PML boundary conditions are used at all other simulation boundaries. A Gaussian source is used to inject a Gaussian beam from the "source_plane" with a waist radius of 0.3 um. The center of focus of the beam is set to the bottom surface (z min) of the simulation region. An EM field monitor "R" is assigned to the z max boundary of the simulation region to record the reflected optical signal.
Results and Discussion
Open the attached script file nanoparticle_dgdtd.lsf along with the project file and run the script. The script runs two simulations with and without the nanoparticle (post). Once the simulations finish the script plots the electric field profile of the reflected optical signal at the z max boundary of the simulation region.
 |
 |
| Reflected electric field profile without the nanoparticle | Reflected electric field profile with the nanoparticle |
Without the nanoparticle present, the reflected beam looks almost identical to the incident beam. However, once it moves under the beam, the reflected beam contains a lot of structure. From the near-field profile plotted, we can see that only the central part of the beam interacts with the nanoparticle strongly.
Next, the script plots the far field radiation pattern for the same two simulations. Without the nanoparticle, the majority of the reflected power is would be collected with an objective with the same divergence angle as the Gaussian source. With the nanoparticle present, there is significant scattered field in the y direction, greatly reducing the amount of power that would be collected by the objective.
 |
 |
| Far field intensity profile without the nanoparticle | Far field intensity profile with the nanoparticle |
The visualizer in DGTD also provides the option to create a polar radiation plot of the far field projection data. To draw a polar radiation plot of the far field projections simply go to the plot editor using the "show/hide chart settings" button
and select "Radiation plot" in the pull-down menu option for "surface" plot type. The resulting radiation plot clearly shows that the reflected light gets scattered at a large angle when the nanoparticle is present.
 |
 |
| Far field radiation plot without the nanoparticle | Far field radiation plot with the nanoparticle |
To quantify this, we can use the near2far script command in DGTD to project the reflected electric field intensity profile (E^2) from the "R" monitor to far field. Using the createsphericalsurface script command we can create a spherical surface in the far field that covers the divergence angle of the Gaussian source and project the reflected near field intensity on the surface (using the near2far script command). We can also project the near field intensity on a hemisphere in the far field (which will capture the total reflected light). By using the quadtri script command we can then integrate the power on each surface and the ratio will give us the portion of the reflected power that can be collected using a lens with the same divergence angle as the Gaussian source.
This can be done using the signal_power.lsf script file. The project file has a parameter sweep set up that varies the dimension (y span) of the nanoparticle in order to determine when the minimum signal is returned (maximum scattering). Once the sweep is run, use the script file signal_power.lsf to load the near field result from each of the sweep files, projects the near field intensity to far field and calculate the portion of the reflected power that can be collected using a lens with the same divergence angle as the Gaussian source as described above.
