Sawyer D. Campbell

On the use of surrogate models in the analytical decompositions of refractive index gradients obtained through quasiconformal transformation optics

Recent advances in the field of transformation optics (TO) have renewed interest in gradient-index (GRIN) optical systems. By transforming a classically inspired aspherical lens to a flat geometry using TO, one can achieve a design with better field-of-view (FOV) performance than traditional radial GRIN lenses. In order to understand the underlying physics of this performance improvement, TO-derived solutions of various designs are decomposed into a 2D-polynomial basis to analyze their behavior and to determine which terms improve optical performance. A comprehensive study of this sort involves thousands of iterations of numerical TO and ray tracing. By training a surrogate model to approximate the TO calculation, the procedure can be greatly accelerated, dramatically reducing the time of this study from weeks to hours. The accuracy of the surrogate model approximation is verified against the original TO solution, and its usefulness in a system-by-design procedure is tested in a series of single- and multi-objective optimizations.

Size, weight, and power reduction regimes in achromatic gradient-index singlets.

By analyzing the limitations that achromatic gradient-index (GRIN) lens solutions in the radial and axial extremes place on lens thickness and surface curvature, a radial-axial hybrid GRIN theory is developed in order to overcome these restrictions and expose a larger solution space. With the achromatic hybrid GRIN theory, the trade-offs between thickness, curvature, and GRIN type can be directly studied in the context of size, weight, and power (SWaP) reduction. Finally, the achromatic solution space of a silicon-germanium-based material system is explored, and several designs are verified with ray tracing.

Transformation-optics-inspired anti-reflective coating design for gradient index lenses.

Recent developments in transformation optics have led to burgeoning research on gradient index lenses for novel optical systems. Such lenses hold great potential for the advancement of complex optics for a wide range of applications. Despite the plethora of literature on gradient index lenses, previous works have not yet considered the application of anti-reflective coatings to these systems. Reducing system reflections is crucial to the development of this technology for highly sensitive optical applications. Here, we present effective anti-reflective-coating designs for gradient index lens systems. Conventional anti-reflective-design methodologies are leveraged in conjunction with transformation optics to develop coatings that significantly reduce reflections of a flat gradient index lens. Finally, the resulting gradient-index anti-reflective coatings are compared and contrasted with conventional homogeneous anti-reflective coatings.

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.

Multi-objective optimization for GRIN lens design

One of the benefits of using a multi-objective algorithm is that the tradeoffs between objectives for a given design can be easily visualized. In the study of gradient-index optics, this ability can lead to a better understanding of the tradeoffs between the gradient magnitude, Δn, focus quality, and size of the optic. A gradient-index plano-convex lens is proposed to highlight the limitations of a single- objective optimization while the potential of using multi-objective optimization for chromatic- and oblique incidence-corrections are also discussed.

Mitigating Field Enhancement in Metasurfaces and Metamaterials for High-Power Microwave Applications

Metasurfaces and metamaterials have been explored extensively in recent years for their ability to enable a variety of innovative microwave devices. However, because their exotic properties often arise from resonant structures, the large field enhancements under high-power microwave illumination can lead to dielectric breakdown and damage to the device. In order to develop metasurfaces and metamaterials capable of being utilized in high-power microwave applications, this paper investigates techniques for reducing the maximum field enhancement factor (MFEF) in several types of structures from the literature. Starting with a simple Sievenpiper metasurface, this paper evaluates the dependence of MFEF on the structure design parameters. For more complex metasurface geometries, a genetic algorithm is demonstrated that can evolve structures that have minimal MFEF. In addition, negative-index and low-index metamaterials are evaluated for field enhancement. By optimizing for low loss and by operating in the resonance tails, metamaterials with low MFEF can be realized for high-power applications. To illustrate this, a quad-beam focusing metamaterial lens is presented with an MFEF less than 5 over the entire operating band.

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.

Apochromatic singlets enabled by metasurface-augmented GRIN lenses

Chromatic aberrations are a primary limiting factor in thin, high-quality imaging systems. Recent advances in nanoscale manufacturing, however, have enabled the creation of metasurfaces: ultra-thin optical components with sub-wavelength features that can locally manipulate the wavefront phase. Meanwhile, there has been renewed interest in GRadient-INdex (GRIN) lenses due to the extended degrees of design freedom they offer. When combined, these two technologies can provide unparalleled imaging system performance while realizing drastic reductions in size, weight, and power. Through paraxial theory and full ray tracing we produce a lens singlet that can achieve three-color (apochromatic) correction by employing a metasurface-augmented GRIN. This apochromatic singlet has the potential for application in high-quality optical systems.

Color-correcting Gradient-index infrared singlet based on silicon and germanium mixing

Gradient-index (GRIN) lenses are predicted by many to have superior performance compared with lens systems using conventional homogeneous material compositions. Namely, the complexity of classic (i.e. homogeneous) multi-lens sequences required for high performance optical systems can be instead manifested into GRIN profile complexity, allowing for refraction throughout the volume of a lens and not just at the hard surface boundaries. As GRIN material technologies continue to evolve, facilitating more practical GRIN lens implementations, the knowledgebase and design tools to optimize GRIN lens systems must be simultaneously built. In this paper, one of the more unknown, yet crucially important, challenges of GRIN lens design is considered: dispersion. Dispersion and its effects on GRIN lenses are considered and a method to minimize its impact on the performance of GRIN lenses is outlined. Finally, a GRIN focusing lens based on the mixing of Germanium (Ge) and Silicon (Si) is proposed and designed to have minimal focal drift.