Waveguide-based photonic microcavities and their associated high quality factor resonances are of increasing importance for a number of technological applications, including filtering and sensing. An example of these types of photonic microcavities is a six air-slot microcavity, with the central semiconductor tooth intentionally widened to introduce a transmission resonance within the stop band of the underlying Bragg structure. This particular photonic microcavity is designed to be supported by a high index substrate, unlike the alternative air membrane photonic microcavities.
The built-in mode solver is used to calculate and launch a waveguide mode into the microcavity. The microcavity is excited by launching a TE-polarized guided mode of the input optical waveguide. The MODE mode solver, which is integrated within the FDTD simulation environment, allows the end user to easily select the desired waveguide mode for launch from the complete set of guided modes. This waveguide mode is incident upon the photonic microcavity, and the frequency response of the microcavity is measured using field profile simulation monitors.
Although we use the mode source in this example, its also possible to determine the resonant frequency and quality factor (Q) using a different type of source such as dipole sources which are used in the Q analysis group. More information on the Q analysis group can be found at Quality factor calculations.
Use a broadband excitation to locate the cavity resonance. By placing a time monitor at the output of the waveguide microcavity, we can measure how long it takes for the radiation to resonate within the structure and radiate away. By looking at the data to the left, we can see that the majority of the optical energy has radiated away 1000 fs after the start of the simulation. However, because we want to accurately measure the Q of these modes, we wait for 2000 fs to ensure we do not terminate the simulation before all of the energy has passed through the monitors and into the PML.
Fast Fourier transform (FFT) of the time-domain signal shows that the Bragg structure has a large stop band which extends from 185 to 215 THz, with a defect transmission peak within the stop band.
- to find the resonance, use broadband excitation and measure the time response
- via the built-in FFT, look at the frequency content of the measured time signal through simple mouse actions. You will have to zoom into the desired frequency range.
- note the resonance occurs at a frequency of 196.1 THz
Measure the Q-factor of the waveguide resonance.Closer examination of the microcavity transmission resonance, as shown on the left, allows one to measure the quality (Q) factor of the transmission peak defined as the ratio of the peak center frequency to its full-width half-maximum (FWHM). The resonance shown has a quality factor of about 200. As the cavity quality factor represents the ratio of the energy storage to the energy loss, achieving higher quality requires minimizing radiation loss.
Measure the CW field enhancement on (top figure) and off (bottom figure) resonance. To measure the field enhancement within the microcavity, frequency-domain (CW) measurement monitors can be used to measure the steady-state field distribution. Furthermore, our frequency-domain monitors provide this data at multiple frequency points within a single simulation, offering tremendous advantage over non-FDTD frequency-domain simulation tools.
- on resonance, a six-fold intensity enhancement is observed
- off resonance, it is seen that negligible radiation propagates through the cavity, and most is reflected from the Bragg stack
Kleckner, T.C. and Modotto, D. and Locatelli, A. and Mondia, J.P. and Linden, S. and Morandotti, R. and De Angelis, C. and Stanley, C.R. and van Driel, H.M. and Aitchison, J.S, "Design, fabrication, and characterization of deep-etched waveguide gratings," Lightwave Technology 23(11) pp. 3832-3842 (2005)