In this example, light is incident upon an interface beyond the critical angle. In most situations, such an interface will have 100% reflection. However, if another high index layer is nearby, light will evanescently couple through the low index gap into the upper layer.
Simulation setup
The above figure shows a plane wave propagating at 33 degrees through a material with an index of 2. There is a 0.5um air gap between the two high index layers. The source wavelength is 1um.
The built in parameter sweep is used to change the source angle and run one simulation per source angle. As in the plane wave R and T calculations, the source angle is set in the model. The model then changes both the source angle and the minimum number of PML layers to match the source angle. For more details, see the section entitled PML on the Planewave technique page (go to the R and T calculations link directly above).
Analysis
A quick calculation with Snell's law would lead you to believe that nothing will propagate beyond the first interface, since 33 degrees is past the critical angle of this interface.
$$ \begin{array}{l}{n_{1} \sin \theta_{1}=n_{2} \sin \theta_{2}} \\ {2 \sin \theta_{1}=1 \sin (90)} \\ {\theta_{1}=30}\end{array} $$
However, the evanescent fields extend some distance through the air and can couple into the third layer.
Result
This figure shows a cross-section of the Ez2 in the y-direction. The source is located at y=-0.9um. The air gap is from 0-0.5um. The constant value of 0.9 shows the reflected wave behind the source. The sinusoidal region is caused by interference between the incident wave and the reflected wave. The exponentially decaying line from 0-0.5 shows the evanescent wave extending through the air. Past y=0.5, the wave couples into a propagating mode in the third layer. To reproduce this image run evanescent.fsp and plot the Ez intensity vs y from the field monitor.
The transmission and reflection curves with a 2 layer stack n=2:1. The critical angle is clearly visible at 30 degrees. To reproduce this plot
- edit the multilayer stack in the simulation: set the num_layers variable in the to 2
- run the evanescent.lsf script file (the sweep will be run automatically
Transmission and reflection curves with a 3 layer stack n=2:1:2, when the middle layer is 0.5 um thick. The third layer allows the light to evanescently couple across the air gap. To reproduce this plot
- edit the multilayer stack in the simulation: set the num_layers variable in the to 3
- run the evanescent.lsf script file (the sweep will be run automatically)