Tuning and enhancing Q-factors of photonic crystal cavities with FDTD Solutions
High Q photonic crystal cavities are of interest for applications including very low threshold lasers, high finesse filters, sensing and detection applications, as well as for ongoing important experiments into cavity quantum electrodynamics.
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 envelope of the time signal provides valuable information and a means by which one can very accurately measure the Q-factor of the specific cavity modes. Using these design techniques, we determine how to resize the holes forming the cavity to optimize the Q-factor of the resonance to realize a Q of approximately 700. It is possible to use the same approach to study cavities with much higher Q's on the order of tens to hundreds of thousands.
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 "FDTD Solutions is essential for my research on optical microcavities ... 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 schematic of the photonic crystal cavity, showing the location of the source and the measurement monitors
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. Complicated structures like the photonic crystal cavity can be easily constructed using sophisticated simulation objects within the Object Library, which contains various photonic crystal elements, including the photonic crystal cavity used here, together with the dispersive material models contained within the material database.
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Three-dimensional model of the photonic crystal cavity built within FDTD Solutions. Dispersive materials can be assigned to each simulation primitive to ease construction of a complete device model.
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Step 2: Use the predefined Qualify Factor analysis object to locate the cavity resonances and measure the Q-factors of the cavity modes
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. A built in Quality Factor analysis object allows the end user to identify the resonant frequencies and associated quality factors for all the modes in a multimode cavity.
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For the cavity geometry specified, two resonant modes are identified.
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The Quality Factor analysis object calculates the decay of the time signal envelope for each mode to determine the Q-factors of the modes to be approximately 200 and 320.
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Step 3: Obtain the cavity mode profiles using a frequency-domain profile monitor
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. Here, we show two-dimensional spatial field data of one of the two cavity mode profiles.
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Cavity mode electric field intensity profile obtained from the frequency domain profile monitor.
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Step 4: By varying only the hole radius, what is the maximum Q achievable?
Use the optimization and parameter sweep framework within FDTD Solutions to optimize your designs. Here, we use the particle swarm optimization algorithm to find the hole radius that maximizes the cavity Q factor.
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After 20 generations of the particle swarm optimization algorithm, an optimal hole radius of 166nm is found, corresponding to a Q factor of 670.
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