We will calculate the reflectivity of a simple dielectric grating described in Cunningham et al. This grating is designed to create a narrow resonant reflectivity line that can be used in biosensor applications.
The grating is made from a thin layer (120 nm) of Silicon Nitride deposited on a 200 nm thick grating of epoxy. The period of the grating is 550 nm and we will consider a wavelength range of 750 nm to 900 nm. This grating is designed to create a narrow resonant reflectivity line that can be used in biosensor applications.
As a first approach, we will use a dielectric index of 2.05 for the Silicon Nitride and and 1.5 for the epoxy. The grating itself is immersed in water, which can be set by defining the background index for the simulation to be 1.333. We will ignore any material dispersion or loss.
In the setup, we have 3 point time monitors to verify that the field decays by the end of the simulation. We use 2 power monitors with 2000 frequency points to measure the transmission and reflection from 750 to 900 nm. We use a mesh accuracy of 4. However, as with many periodic structures, a mesh override region is required at the grating. This is used only in the x direction to ensure the structures symmetry.
It is also worth noting that the automatic shutoff is set to 10e-9 for this simulation. This structure has a sharp resonance that will last a long time, but contain only a very small fraction of the total energy that was injected into the simulation. The default automatic shutoff setting would terminate the simulation too early, leading to inaccurate power measurements.
Run the simulation. Note that the polarization of the simulation is TE, meaning that the electric field (blue arrows) is normal to the lines of the grating. After running the simulation, look at the reflection time signal in the grating, and zoom in, it should look like the following. We can see that the field has decayed and that the simulation has run long enough, so the data is valid.
Run the script file grating_silicon_nitride.lsf. This file will calculate and plot the transmission (T) and reflection (R) and plot the results as a function of wavelength. It will also plot R+T to verify that R+T=1. The maximum error in R+T=1 is only 0.9% across the entire wavelength range.
The reflection spectrum only is also plotted, as shown below. The figure is nearly identical to the experimental results shown in Figure 3 of Cunningham et al. The small discrepancies are due to any differences in the actual material refractive indices and the values used in the simulation, as well as any manufacturing imperfections in device fabrication.
We can rerun the simulation with TM polarization (electric field tangential to the grating lines) and obtain this result. For this polarization, we don't see the narrow resonance.
Cunningham et al,. "A plastic colorimetric resonant optical biosensor for multiparallel detection of label-free biochemical interactions", Sensors and Actuators, B, 85, 219-226 (2002)