We present a procedure for the design of multilevel metalenses and their fabrication with multiphoton-based direct laser writing. This work pushes this fast and versatile fabrication technique to its limits in terms of achievable feature size dimensions for the creation of compact high-numerical aperture metalenses on flat substrates and optical fiber tips. We demonstrate the design of metalenses with various numerical apertures up to 0.96, and optimize the fabrication process towards nanostructure shape reproducibility. We perform optical characterization of the metalenses towards spot size, focusing efficiency, and optical functionality with a fiber beam collimation design, and compare their performance with refractive and diffractive counterparts fabricated with the same technology.

Most microwave filters are currently designed using direct electromagnetic (EM) optimization. This method holds several disadvantages regarding the provided physical insight to designers and duration of the optimization process. To circumvent these drawbacks, we propose a filter design based on scalable circuit models. This model-driven design competes with EM optimization by maintaining the accuracy of the optimization results while providing a very significant speedup and gaining physical insight on the EM working mechanism of the filter of interest. This paper discusses the advantages of using the proposed model-driven design by the illustration on a defected ground structure filter. A scalable equivalent circuit model is used in the design procedure to provide physical insight to the designer and to speed up the design process enormously.

In this paper, we propose a novel parameterized model order reduction technique for circuits described by the delayed partial element equivalent circuit method. The moment vectors associated with frequency are excluded while forming the moments’ subspace. This leads to obtaining very compact parameterized reduced order models. An implicit multiparameter moment matching algorithm is used for the moments related to the design parameters. Numerical results validate the accuracy and efficiency of the proposed technique in both frequency- and time-domain. The time-domain response of the reduced order models is obtained using the numerical inversion of Laplace transform, which avoids stability issues as well as the computationally expensive repeated interpolation steps associated with conventional time-stepping integration method for delayed differential equations.

Full-wave time-domain computational electromagnetic (CEM) solvers, which are integral equation (IE)-based, may suffer from what is called “late-time instability” problems. This unstable behavior occurs for CEM solvers for very fast rise-time input signals. A multitude of techniques has been devised by researchers over the years to solve the problem. In this article, we pursue an approach for the stable solution of full-wave partial element equivalent circuit (PEEC) models for fast-rising input waveforms. In particular, step and impulse response will be considered that are the most challenging from a stability point of view. For the solver part, a conventional full-wave PEEC code is used that requires one to use retarded partial elements. Unfortunately, a PEEC, as well as impedance Z-(method of moment) solvers using suitable numerical time-stepping methods have stability problems, especially for fast rising impulse or step inputs. An important step forward is achieved in this work by providing a larger class of stable solutions well above the stability achieved for time-stepping methods in the last 50 years. The time-domain stability is achieved by replacing the stepping integration methods with a numerical inversion of Laplace transform (NILT) technique. The NILT transform starts out by applying it to a frequency-domain PEEC solution. The surprising result is that the NILT-based method has a variable time-dependent bandwidth that is advantageous for the full-wave IE solution stability. In this article, we give several examples that show that a PEEC-NILT solution provides accurate and stable results for impulse, step- and piece-wise linear input waveforms.

Performing simulations with electromagnetic (EM) solvers can be a computationally complex task that is time consuming and resource demanding. Adaptive frequency sampling (AFS) techniques are very effective in reducing the computational complexity of frequency-domain simulations performed by EM solvers. In this work, we propose a novel AFS technique based on local rational models. This brings multiple advantages, such as accurate and efficient model uncertainty estimation, the local refinement of subintervals of the full frequency range of interest, and suitability toward parallel computing. Multiple numerical examples thoroughly validate the proposed technique. The local rational models can also be used as an accurate frequency-domain macromodeling technique after the AFS process is completed.