Design conditions in the middle range for implementation of integrated ring resonators in LiNbO₃ by direct laser writing

Abstract

The aim of this work is to design an integrated optical ring resonator to be implemented in LiNbO₃ with a 2.5 mm radius and an operating wavelength of 1550 nm. Considering these ring parameters, a free spectral range of 71.54 pm and a quality factor of ∼ 5 × 10⁵ were calculated. The authors apply results to improve the implementation of femtosecond laser writing in lithium niobate crystals. As it is well-known finite difference time domain method requires large memory and time for processing circuits with large footprint (few square mm), in contrast, the beam propagation method allows to simulate large bends in a simple way. RSoft suite design tools commonly represent circles by closed polygons whose geometrical parameters are not optimised to obtain bending losses as least as possible, as suggested by coherent coupling theory. In this sense, the suitable determination of a splice angle (in this case 1.44°), shape and length for segments are key parameters in the ring design. For this purpose, an <i>ad hoc</i> software was implemented to overcome this drawback. In summary, a 250 sided polygon side showed a suitable coupling performance and established a new layout approach for middle range rings.