In this example, we construct a two-dimensional model of a photonic crystal cavity, and excite it with a dipole
source. Using broadband excitation and via fast Fourier transform of the resulting time signal, we can determine
where the cavity resonance occurs. The decay of the time signal provides valuable information about the Q-factor
of the cavity. Using these design techniques, we determine how to resize the holes forming the cavity to either
tune the cavity resonance to the center of the telecommunications c-band at 193.1THz, or to optimize the Q-factor
of the resonance.
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"FDTD Solutions is essential for my research on optical microcavities. It dramatically outperforms
the rival software in terms of speed, the transparent user environment, the analysis tools, and the
support. It is not just the staggeringly efficient parallel engine, which allows rapid iteration
through a design problem. It is the complete package: an elegant interface, a powerful scripting
language which has essentially replaced matlab for my data processing, an accurate treatment of metals
and loss, an invaluable database of example simulations and scripts, and same-day support from
physicists with a deep understanding of my research questions.
M. McCutcheon, Harvard
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Step 1: Construct the photonic crystal cavity in the layout editor, and simulate
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The layout editor shows the positioning of all of the simulation objects. Different classes of objects (physical
primitives, radiation sources, monitors) are color coded for easy identification. Objects can be moved and resized with simple mouse movements.
- blue regions denote 'etch' regions, such that material is removed from the background
- orange region is the computation area with symmetric and absorbing (PML) boundary conditions
- yellow lines and symbols show measurement monitors
- window at the bottom shows the script window, where customized commands and analysis can be performed
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Step 2: Use broadband excitation to locate the cavity resonance
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FDTD Solutions' broadband source allows for very wideband excitation, and can
be used to extract the response across a very wide frequency range in a single simulation.
- to find the resonance, use broadband excitation and measure the time response
- via the built-in fast Fourier transform, look at the frequency content of the measured time signal through
simple mouse actions
- note the resonance occurs at a frequency of 203THz
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Step 3: Measure the Q-factor and examine the cavity mode profile
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Integrated analysis routines facilitate data analysis and visualization. Choose from drop-down menus which
monitor you wish to analyze, and the field component of interest.
- using narrowband excitation, excite only the 203THz mode and plot the time respone on a logarithmic scale
- the slope of the line can be used to determine that the Q-factor is 1130
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Curious why the Q-factor is not higher? Use frequency-domain monitors to extract the steady-state or continuous-wave
response at a specified frequency to extract the cavity mode.
- set a frequency domain monitor to record the steady-state response at 203THz, and extract the mode profile
- note that for the size of cavity simulated, there is a non-negligible field amplitude (plotted on a log scale)
at the edge of the cavity
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Step 4: Automate simulation and analysis to tune the cavity resonance
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Use the integrated scripting environment to construct and run a series of simulations to perform parameter sweeps
and optimize performance.
- ten simulations performed in sequence allow us to map out the resonant frequency of the cavity as a function
of hole radius
- note a hole radius of 57nm results in a resonance center at 193.1THZ, the center of the telecommunications c-band
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Step 5: By varying only the hole radius, what is the maximum Q achievable?
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- write a script to automate analysis of the time signal and calculate the Q-factor for each simulation
- find out that a maximum Q of 1212 is possible at a hole radius of 69nm
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