In this example, we will simulate material gain in a long-range dielectric-loaded surface plasmon-polariton (SPP) waveguide.
We will base this example on the waveguide design purposed in reference . The dimensions of the waveguide have been parameterized and can be set in the user properties section of the model analysis group. We will start with the refractive index of the buffer set to 2.05 (with the imaginary part set to 0). The resultant modal profile is shown in the figure below. We can use the Visualizer to plot the cross section of this mode profile along x=0.
The motivation for introducing gain into this waveguide is to compensate for the high propagation loss that is typical of SPP waveguides, and to achieve lossless propagation of plasmonic modes. To introduce gain into the buffer layer, we will add a negative imaginary part to the refractive index of the buffer layer as shown below:
One can see that the imaginary part of the resulting effective index is now negative, corresponding to a gain of 58.9 dB/cm.
For this device, the optical power confinement in the gain region is an important quantity of interest since it can be used to determine how effective the material gain is in compensating for the propagation loss. The optical power confinement in an arbitrary region can be easily determined using the Power and intensity integration feature. This can be done through the GUI (under Modal analysis - "Power and intensity integration" option), or through the scripting environment to work out the confinement factor. For example, to find the % power confined in the buffer region:
# set the power integration region to the buffer region
setanalysis('x1',getnamed('buffer','x min')); setanalysis('x2',getnamed('buffer','x max')); setanalysis('y1',getnamed('buffer','y min')); setanalysis('y2',getnamed('buffer','y max')); # calculate fraction of power buffer region ?fraction_integrated = getanalysis('fraction integrated'); result: 0.278539
- S. Garcia-Blanco, M. Pollnau and S. Bozhevolnyi, Loss compensation in long-range dielectric-loaded surface plasmon-polariton waveguides, optics Express, Vol. 19, No. 25, pp. 25298-253100 (2011)