Extended Data Fig. 2: Minimizing the TE-TM crossing via dispersion engineering.
From: High-efficiency and broadband on-chip electro-optic frequency comb generators
The cut-off of the comb spectrum around 1400 nm originates from the TE-TM polarization crossing. Due to birefringence of lithium niobate, the TE modes that propagate along the y- and z-direction of the thin-film lithium niobate crystal axes have different indices no,TE and \(n_{e,TE}\), respectively, while the indices of TM modes are \(n_{o,TM}\) for both directions. When the TE mode circulates inside the micro-resonator, it experiences different averaged TE indices ranging from ne,TE to \(n_{o,TE}\) at different bending points of the resonator. As a result, in our current geometry (\(w = 1.2\,\mu m\), h = 350 nm, and t = 250 nm), the TM mode has an index that is between the value of no,TE and \(n_{e,TE}\) at wavelengths below ~1450 nm (Left panel), leading to a degeneracy between the TM index and averaged TE indices. This index degeneracy can cause polarization-crossing, which can be pushed toward lower wavelength via dispersion engineering. For example, for a geometry with w = 1.2 μm, h = 350 nm, and t = 150 nm, the range that \(n_{o,TM}\) is in between the \(n_{o,TE}\) and \(n_{e,TE}\) is pushed to ~1250 nm.
