Impact Study of Numerical Discretization Accuracy on Parameter Reconstructions and Model Parameter Distributions

In optical nano metrology numerical models are used widely for parameter reconstructions. Using the Bayesian target vector optimization method we fit a finite element numerical model to a Grazing Incidence X-Ray fluorescence data set in order to obtain the geometrical parameters of a nano structured line grating. Gaussian process, stochastic machine learning surrogate models, were trained during the reconstruction and afterwards sampled with a Markov chain Monte Carlo sampler to determine the distribution of the reconstructed model parameters. The numerical discretization parameters of the used finite element model impact the numerical discretization error of the forward model. We investigated the impact of the polynomial order of the finite element ansatz functions on the reconstructed parameters as well as on the model parameter distributions. We showed that such a convergence study allows to determine numerical parameters which allows for efficient and accurate reconstruction results.Comment: Submitted to Metrologia Focus Issue on MATHMET 2023 conferenc

Optimized diamond inverted nanocones for enhanced color center to fiber coupling

Nanostructures can be used for boosting the light outcoupling of color centers in diamond; however, the fiber coupling performance of these nanostructures is rarely investigated. Here, we use a finite element method for computing the emission from color centers in inverted nanocones and the overlap of this emission with the propagation mode in a single-mode fiber. Using different figures of merit, the inverted nanocone parameters are optimized to obtain maximal fiber coupling efficiency, free-space collection efficiency, or rate enhancement. The optimized inverted nanocone designs show promising results with 66% fiber coupling or 83% free-space coupling efficiency at the tin-vacancy center zero-phonon line wavelength of 619 nm. Moreover, when evaluated for broadband performance, the optimized designs show 55% and 76% for fiber coupling and free-space efficiencies respectively, for collecting the full tin-vacancy emission spectrum at room temperature. An analysis of fabrication insensitivity indicates that these nanostructures are robust against imperfections. For maximum emission rate into a fiber mode, a design with a Purcell factor of 2.34 is identified. Finally, possible improvements offered by a hybrid inverted nanocone, formed by patterning into two different materials, are investigated, and increases the achievable fiber coupling efficiency to 71%.Comment: The following article has been accepted by Applied Physics Letters. After it is published, it will be found at https://doi.org/10.1063/5.005033