In this example, we determine the resonant frequencies plot the first and second order whispering gallery modes supported by a GaN microrod.
Whispering gallery modes occur when light is trapped in a sphere or disk by total internal reflection. These modes can have high Q and low mode volume. Applications of these structures include microlasers and optical switches.In this example we are interested in finding the first and second order whispering gallery modes of a GaN cylinder, reproducing the resulting field profile from the reference paper by Tamboli et al. (see the References section above). Here, the resonances of the structure are expected at 418 and 428 nm wavelengths.
To start with, we can locate the resonant frequencies of the structure by running an initial simulation using a dipole source and time monitors. We set the wavelength range injected by the dipole source to be between 400 and 450 nm to excite the resonant frequencies in this range. We have also placed the source near the edge of the structure since this is where we expect the modal fields to be strong.
To find the resonant frequencies of the structure, we can take the Fourier transform of the field over time from a time monitor, however, for high Q devices, using a frequency domain monitor with end apodization is preferable since the fields do not decay fully by the end of the simulation. More information can be found on the apodization page. In the simulation file, a point monitor is used and is also placed close to the edge of the structure.
After finding the location of the resonant frequencies, we can set the frequency domain profile monitors to record the field profile at the resonant frequencies by editing the General tab.
The following plot shows the field spectrum from the frequency domain power monitor. Using the findpeaks script shows that the resonant frequencies are x and y which corresponds to wavelengths of approximately 418.2 nm and 428.6 nm. Using a finer mesh can give more accurate results.
The resulting plots of the magnetic field profile at 418 and 428 nm agree with figure 4 from the reference.
A. C. Tamboli, E.D. Haberer, R. Sharma, K. H. Lee, S. Nakamura and E. L. Hu, Room-temperature continuous-wave lasing in GaN/InGaN microdisks, Nature Photonics, v1, pp. 61–64 (2007)