Coupling between waveguides and microresonators: the local approach

Abstract

Coupling between optical microresonators and waveguides is a critical characteristic of resonant photonic devices that has complex behavior that is not well understood. When the characteristic variation length of the microresonator modes is much larger than the waveguide width, local coupling parameters emerge that are independent of the resonator mode distributions and offer a simplified description of coupling behavior. We develop a robust numerical-fitting-based methodology for experimental determination of the local coupling parameters in all coupling regimes and demonstrate their characterization along a microfiber waveguide coupled to an elongated bottle microresonator.

Simulation and Optimization of SNAP-Taper Coupling System in Displacement Sensing

“…Next, to gain more insight into the effect of the coupling parameter on the transmittance mentioned above, calculations are performed with different parameter D. The effect of the imaginary part of D (Im(D)) on the resonant modes is studied first. With Im(D) changing from 0 to 0.2, the simulation results indicate that Im(D) only describes the shift in the resonant wavelength, which is the same as the discussion in reference [ 32 ]. Since the phase shift has no effect on the Q factor and transmittance of resonant modes, for simplicity’s sake, is set to be zero when we investigate the imaginary part of D (Im(D)).…”

“…With the coupling parameters |C| 2 = 0.015 µm −1 , D = 0.02 + 0.016i µm −1 and S (0) = 0.95 − 0.01i, the results of the calculation when ∆k is set to be 0.024 µm −1 , 0.032 µm −1 and 0.048 µm −1 , respectively, are presented by the surface plot in Figure 4, which depicts the transmission amplitude as a function of the axial position of the SNAP resonator and wavelength. This surface plot quantitatively reproduces the position of the nodes and antinodes of the SNAP mode, and the envelop of the spectral resonances shows close agreement with the parabolic ERV of SNAP profile, which coincides with the rescaling relation between the wavelength variation and the ERV [32]. In addition, it should be pointed out that, as the ∆k increases from 0.024 µm −1 to 0.048 µm −1 , the wavelength between adjacent axial modes gradually augments.…”

SNAP microwave optical filters

“…The optimized positions of MF1 and MF2 are ±𝑧𝑧 𝑜𝑜𝑝𝑝𝑜𝑜 = ±381 µm, and coupling parameter is 𝐷𝐷 = 0.0015 + 0.0017𝑖𝑖 µm -1 . This value of 𝐷𝐷 is an order of magnitude less than those typically observed for the coupling of microfiber and SMR positioned in direct contact [22,23,32]. We suggest that this small coupling can be achieved by placing the microfiber (or a planar waveguide) several hundred nanometers away from the SMR [30].…”

Controlled transportation of light by light at the microscale

“…This can be achieved by appropriate phase-matching microfiber-WGE coupling at frequency ω e and phase unmatching of microfiber-WGS coupling at frequency ω s [40]. In our modeling, we set D s1 = D s2 = 0.005i µm −1 and D e1 = D e2 = 0.05i µm −1 , where the latter correspond to characteristic experimentally observed values [34,41]. We found that the real parts of these coupling parameters with the same order of magnitude do not noticeably modify the WGE (blue curve in Fig.…”