John A. Easum

Modularization of gradient-index optical design using wavefront matching enabled optimization.

This paper proposes a new design paradigm which allows for a modular approach to replacing a homogeneous optical lens system with a higher-performance GRadient-INdex (GRIN) lens system using a WaveFront Matching (WFM) method. In multi-lens GRIN systems, a full-system-optimization approach can be challenging due to the large number of design variables. The proposed WFM design paradigm enables optimization of each component independently by explicitly matching the WaveFront Error (WFE) of the original homogeneous component at the exit pupil, resulting in an efficient design procedure for complex multi-lens systems.

Analytical surrogate model for the aberrations of an arbitrary GRIN lens.

Current analytical expressions between Gradient-Index (GRIN) lens parameters and optical aberrations are limited to paraxial approximations, which are not suitable for realizing GRIN lenses with wide fields of view or small f-numbers. Here, an analytical surrogate model of an arbitrary GRIN lens ray-trace evaluation is formulated using multivariate polynomial regressions to correlate input GRIN lens parameters with output Zernike coefficients, without the need for approximations. The time needed to compute the resulting surrogate model is over one order-of-magnitude faster than traditional ray trace simulations with very little losses in accuracy, which can enable previously infeasible design studies to be completed.

Advancements in transformation optics-enabled gradient-index lens design

Transformation Optics (TO) provides the mathematical framework for representing the behavior of electromagnetic radiation in a given geometry by “transforming” it to an alternative, usually more desirable, geometry through an appropriate mapping of the constituent material parameters. Using a quasi-conformal mapping, the restrictions on the required material parameters can be relaxed allowing isotropic inhomogeneous all-dielectric materials to be employed. This approach has led to the development of a new and powerful design tool for gradient-index (GRIN) optical systems. Using TO, aspherical lenses can be transformed to simpler spherical and flat geometries or even rotationally-asymmetric shapes which result in true 3D GRIN profiles. TO can also potentially be extended to collapse an entire lens system into a representative GRIN profile thus reducing its physical dimensions while retaining the optical performance of the original system. However, dispersion effects of the constituent materials often limit the bandwidth of metamaterial and TO structures thus restricting their potential applicability. Nonetheless, with the proper pairing of GRIN profile and lens geometry to a given material system, chromatic aberrations can be minimized. To aid in the GRIN construction, we employ advanced multi-objective optimization algorithms which allow the designer to explicitly view the trade-offs between all design objectives such as RMS spot size, field-of-view (FOV), lens thickness, 𝛥𝑛, and focal drift due to chromatic aberrations. We present an overview of our TO-enabled GRIN lens design process and analysis techniques while demonstrating designs which minimize the presence of mono- and poly-chromatic aberrations and discuss their requisite material systems.

A Low Cost and Highly Efficient Metamaterial Reflector Antenna

The design of an efficient, metamaterial-based reflector antenna capable of operation at high power is presented. Metamaterial unit cells are comprised of end-loaded dipoles (ELDs) with capacitive lumped elements at their center. Enhanced power handling is realized by mitigating field enhancement through rounded edges and using appropriate high voltage capacitors as loads. The metamaterial is designed to have discrete, configurable reflection phase through choice of capacitor on the ELDs. Unit cells are fabricated and patterned to a square, flat reflector surface and configured for broadside reflection with an offset-fed horn antenna. Simulated and measured radiation patterns of the complete antenna system are presented with excellent agreement. High-power testing verifies the ability of the metasurface to withstand extreme incident electric field strengths.

Multi-objective surrogate-assisted optimization applied to patch antenna design

In this paper, we present a multi-objective optimization technique for designing a patch antenna on a finite ground plane by employing a surrogate model which is formulated by utilizing various regression and model selection techniques. The method presented enables simultaneous training and optimization of the surrogate model with few initial samples required. The techniques used enable faster convergence of the Pareto set when compared to a traditional multi-objective optimization scheme.

High Power Metasurface Reflectarray Antennas Using Switched Shorted Circular Elements

A metamaterial design that can rapidly reconfigure its reflection phase angle and safely operate under high incident field strengths is presented for use in a high power microwave (HPM) reflectarray system. The design offers switching between reflection phase angles to allow for beam control with a stationary reflector and feed horn. Two variations of the design are presented which offer (a) fixed (but selectable) reflection phases with high-power operation and (b) on-the-fly reconfigurable reflection phases with low-power operation. For design (b), reconfiguration is easily and quickly accomplished though simple relay-style switching operation. The designs are developmental steps towards a fully on-the-fly reconfigurable reflectarray which can operate with several megawatts of peak input power. Fabrication and testing of the prototype antennas and metasurfaces were carried out and presented.

Surrogate-assisted transformation optics inspired GRIN lens design and optimization

It has been shown that Transformation Optics (TO)-derived gradient-index (GRIN) lenses often outperform more traditional GRIN designs. In order to better understand the origins of this performance improvement, such TO-derived solutions have previously been decomposed into a 2D-polynomial basis, which unveiled the presence of large radial-axial “cross-term” contributions to the index profile. While these terms are crucial in maximizing the performance of GRIN lenses, finding the optimal index profile becomes a more challenging problem due to the expanded number of input variables. However, this optimization process can be considerably accelerated through the introduction of surrogate models at several stages of the design process.

Multiobjective Optimization-Aided Metamaterials-by-Design With Application to Highly Directive Nanodevices

A formal inverse design procedure which combines the advantageous aspects of both multiobjective optimization and system-by-design is proposed. The solution technique provides a systematic method to discover the various tradeoffs inherent in engineering design. To showcase the robustness and flexibility of the proposed approach, two unique highly directive nanodevices are explored. First, the problem of achieving highly directive scattering from core–shell nanoparticles is investigated. Then, a Yagi–Uda nanoloop array is designed with the goal of producing highly directive radiation patterns. The results of these studies reveal the underlying physics of these devices while also providing the engineer with a wide variety of candidate designs to choose from, showcasing the utility of the proposed metamaterials-by-design approach based on multiobjective optimization.

GRIN lens design through the use of surrogate models based on Zernike aberrations

In this paper, we present a computational method for rapidly designing GRadient-INdex (GRIN) lenses by employing a surrogate model that relates input lens parameters to output Zernike aberrations. This approach also provides a path forward for the designer to identify which lens parameters have the largest impact on specific aberrations. Through the use of orthogonal Latin Hypercube Sampling (LHS) and multivariate polynomial regressions, a surrogate model is trained to approximate the ray trace evaluations. Finally, a plano-convex GRIN lens based on Silicon-Germanium mixing is optimized using both full ray trace and surrogate model evaluations. A ~40× speed improvement is realized with the surrogate-assisted optimization while achieving similar optical performance.

A new GRIN lens design paradigm based on wavefront matching

GRadient INdex (GRIN) optics has revolutionized the field of lens design by providing an unparalleled amount of design freedom, resulting in high-performance optical systems. Unfortunately, this design freedom leads to a large number of parameters in multi-element systems, since the GRIN distributions need to be described in addition to the lens geometries. This can lead to slow convergence and stagnation for even the most robust numerical optimizers. This paper proposes a modular, black-box design paradigm which allows for the optimization of each element in the system independently. This leads to an efficient strategy to design all-GRIN systems from scratch, or to replace existing homogeneous doublets and triplets in a system with GRIN singlets.