Eigenmode decomposition method for full-wave modeling of microring resonators

We develop a theoretical predictive model for an all-pass ring resonator that enables the most complete description of linear coupling regimes. The model is based on eigenmode decomposition of Maxwell's equations with a full account of the confined and leaky modes, as opposed to the existing phenomenological methods restricted to the confined modes only. This model enables a quantitative description of all-pass ring resonators and provides insights into the physics underlying microring-waveguide coupling. We experimentally validate the model using transmission measurements in the linear regime of aluminum nitride resonators. The developed model is then used to explore the field enhancement in microrings crucial for nonlinear photonic applications.

Figure 1

An optical microscope image of the fabricated AlN resonator with the radius of 50 µm. The inset shows cross-sectional TEM image of the fabricated AlN waveguide.

Figure 2

Sketch of the model system marked with the notations used. Insets give the cross-sectional dimensions (a) and the field distribution in the waveguide (b) and the ring (c).

Figure 3

The coupling loss rates of the microrings eigenmodes around the 1.3 µm wavelength predicted by the theoretical model.

Figure 4

The intrinsic loss rates of the microrings eigenmodes around the 1.3 µm wavelength obtained in numerical modeling.

Figure 5

Theoretical and experimental quality factors of optical resonances around the 1.3 µm wavelength in the AlN resonators with different radii and waveguide-ring gaps.

Figure 6

Electric field enhancement ${\eta }_m\left(k_n\right)$ as a function of gap $a$ between the ring and the waveguide for different ring radii $R$.

Figure 7

Experimentally measured waveguide transmittance minima around the 1.3 µm wavelength as a function of ring-waveguide gap for different microring radii. The arrows show the minima with the highest microring-induced extinction.

Figure 8

Maximum field enhancement ${\eta }_m^{cr}\left(k_n\right)$ achieved at critical gap $a_{cr}$ as a function of $R.$ The experimentally measured $a_{cr}$ are shown by the scatterers.

Figure 9

Sketch of a pulley-type microring resonator.

Figure 10

Experimental setup used for transmission measurement.

Figure 11

Experimental output coupled power as a function of waveguide length.