The intensity transmission of a micro-ring resonator connected to a single bus
waveguide is given by the following equation:
T² (2) =
r² + y²2ry cos (KLT)
1+ (ry)² - 2ry cos(kLr)
Where k=neff2/2 is the wave vector, r is the self-coupling field coefficient, y is the
single-pass field amplitude transmission given by y² = e-ar, a are the waveguide
losses, L₁=27*R is the cavity round trip and R is the cavity radius.
a) Calculate the Free-Spectral Range (FSR) of a resonator operating at a
wavelength 1-1550 nm with radius R=10 μm, losses a-3 cm³¹, a self-coupling
field coefficient r=0.9, and effective index neff-3.5. (Assume ng=neff).
b) Using the resonator parameters defined in section a) and a self-coupling field
coefficient r=0.9, plot the intensity transmission as a function of the
wavelength over a few spectral ranges. Consider a centre wavelength 1550
nm for your plot.
c) Using the resonator parameters defined in section a), plot the intensity
transmission at resonance over the range of self-coupling field coefficients
r=0.98 -0.995 with increments Ar= 0.001.
d) Calculate the single-pass field amplitude transmission y and discuss the results
of section c) for r
Fig: 1
