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 y.