Ring resonator gap determination design rule and parameter extraction
method for sub-GHz resolution whole C-band Si3N4 integrated spectrometer
Abstract
A panoramic ultra-high resolution photonic integrated circuit
spectrometer is under development by the authors. The architecture
comprises a tunable ring resonator stage and an AWG stage. The
resolution defines the bandwidth of the ring resonator determined by the
cross-coupled power and hence the gap between the access and ring
waveguides. The AWG channel frequency spacing determines the required
free-spectral range (FSR) and hence the perimeter of the ring resonator.
The specified < 1GHz resolution combined with a FSR of 50 GHz
render accurate simulation difficult obstructing the design process. In
this report, a simplified design rule to determine the minimum gap
between straight access waveguides and a circular ring waveguide is
proposed. Realistic assumptions such as existence of local bisymmetry
and adiabatic mode evolution throughout the coupling region permit a
simple mode solver to determine the relationship between the
cross-coupled power and the minimum gap size. A parameter extraction
method is also formulated for add-drop rings equipped with two nominally
identical couplers that disentangles the loss and coupling ring
parameters from intensity-only transmission measurements. The proposed
rule is applied to the design of ring resonators fabricated on a
Si3N4 platform. The parameter extraction
method is used to analyze the measured characterization data of the ring
resonators. The results show good agreement between the design rule and
parameters extracted from the measured data (measurement shows maximum
deviation of ~43 nm from the design rule estimation) and
provide experimental confirmation of the technological viability of the
ring resonators required by the spectrometer.