Heuristic modelling of laser written mid-infrared LiNbO_3 stressed-cladding waveguides

Mid-infrared lithium niobate cladding waveguides have great potential in low-loss on-chip non-linear optical instruments such as mid-infrared spectrometers and frequency converters, but their three-dimensional femtosecond-laser fabrication is currently not well understood due to the complex interplay between achievable depressed index values and the stress-optic refractive index changes arising as a function of both laser fabrication parameters, and cladding arrangement. Moreover, both the stress-field anisotropy and the asymmetric shape of low-index tracks yield highly birefringent waveguides not useful for most applications where controlling and manipulating the polarization state of a light beam is crucial. To achieve true high performance devices a fundamental understanding on how these waveguides behave and how they can be ultimately optimized is required. In this work we employ a heuristic modelling approach based on the use of standard optical characterization data along with standard computational numerical methods to obtain a satisfactory approximate solution to the problem of designing realistic laser-written circuit building-blocks, such as straight waveguides, bends and evanescent splitters. We infer basic waveguide design parameters such as the complex index of refraction of laser-written tracks at 3.68 µm mid-infrared wavelengths, as well as the cross-sectional stress-optic index maps, obtaining an overall waveguide simulation that closely matches the measured mid-infrared waveguide properties in terms of anisotropy, mode field distributions and propagation losses. We then explore experimentally feasible waveguide designs in the search of a single-mode low-loss behaviour for both ordinary and extraordinary polarizations. We evaluate the overall losses of s-bend components unveiling the expected radiation bend losses of this type of waveguides, and finally showcase a prototype design of a low-loss evanescent splitter. Developing a realistic waveguide model with which robust waveguide designs can be developed will be key for exploiting the potential of the technology.This work was supported by the Spanish MINECO under project MAT2013-47395-C4-4-R, TEC2014-55948-R and FIS2013-44174-P. Catalan Government 2014SGR1358. European Commission (ACP2-GA-2013-314335-JEDI ACE). F. D. acknowledges additional support 2010-ICREA-02 for excellence in research