Gap effects on whispering-gallery mode microresonances

Photon tunneling between an optical resonator and a light-delivery coupler is strongly dependent on the gap dimension which can vary from zero to size of an optical wavelength involved. In this systematic report, we investigate the gap effects of whispering-gallery modes in two modeling systems: a waveguide-coupling resonator of 2μm and l0μm in diameter, respectively. Maxwell's equations which govern the EM wave propagation and photon tunneling in the microsystems are solved using the finite element method. The simulation accuracy and sensitivity is examined. It is found that when the maximum element size in the computationally sensitive regions is below 1/8 of the wavelength involved, the calculations are accurate. An optimal gap exists for maximum energy coupling and is a strong function of the wavelength of the resonant mode. The Q factor increases exponentially with increasing gap and saturates as the gap approaches the optical wavelength. An optimum gap can be defined at the half maximum energy coupling where both the Q factor and coupling efficiency are high. We also calculate the effects of gap width on the resonance shift. We find that the resonance wavelength is increased (decreased) with decreasing gap width for the 10μm (2μm) diameter resonator with narrow gap widths.