Jogender Nagar

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.

Closed-Form Expressions for the Radiation Properties of Nanoloops in the Terahertz, Infrared and Optical Regimes

Since the pioneering work of Heinrich Hertz, perfect-electric conductor (PEC) loop antennas for RF applications have been studied extensively. Meanwhile, nanoloops are promising in the optical regime for their applications in a wide range of emerging technologies. Unfortunately, analytical expressions for the radiation properties of conducting loops have not been extended to the optical regime. This paper presents closed-form expressions for the electric fields, total radiated power, directivity, and gain for thin-wire nanoloops operating in the terahertz, infrared and optical regimes. This is accomplished by extending the formulation for PEC loops to include the effects of dispersion and loss. The expressions derived for a gold nanoloop are implemented and the results agree well with full-wave computational simulations, but with a speed increase of more than 300×. This allows the scientist or engineer to quickly prototype designs and gain a deeper understanding of the underlying physics. Moreover, through rapid numerical experimentation, these closed-form expressions made possible the discovery that broadband super-directivity occurs naturally for nanoloops of a specific size and material composition. This is an unexpected and potentially transformative result that does not occur for PEC loops. Additionally, the Appendices give useful guidelines on how to efficiently compute the required integrals.

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.

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.

Theoretical derivation of the radiation parameters for thin-wire nanoloop antennas

Conducting loops have been rigorously analyzed in the microwave/RF regime due to their simplicity and versatility. In the terahertz, infrared and optical regimes nanoloops are extremely promising for a variety of applications, including as solar cells or optical sensors. However, due to the complex behavior of metals, a complete theoretical derivation of the radiation parameters of a nanoloop at these frequencies has not yet been performed. This paper will extend the formulation of thin-wire Perfect-Electric Conductor (PEC) loops to include the effects of loss and dispersion. Closed form expressions for the radiated fields, directivity and gain will be presented. The expressions involve integrals of Bessel and Lommel-Weber functions as well as Q-type integrals. Various series representations for these integrals will be presented along with guidelines on which are the most efficient. Validation of the equations will be provided through a comparison with full-wave solvers. While these simulations take on the order of hours, the analytical expressions can be evaluated on the order of seconds.

Advanced multi-objective and surrogate-assisted optimization of topologically diverse metasurface architectures

Advancements in micro-and nano-fabrication techniques are enabling the realization of high-performance metasurfaces which exploit the generalized Snell’s law of refraction to achieve disruptive optical functionalities. Moreover, metasurfaces can be used in conjunction with conventional optical elements to achieve massive size, weight, and power (SWaP) reduction. However, no commercial tools exist which can efficiently model optical systems whose geometrical features span many orders-of-magnitude in spatial scale. Therefore, new forward solvers must be developed in order to make such multiscale problems tractable. Furthermore, optimization of multiscale optical systems is crucially-important in order to maximize system performance and minimize SWaP. While how one achieves a specific set of desired performances with conventional optical elements is generally well understood and thoroughly presented in design textbooks, it is not always clear how to design a nanoscale optical device to best achieve a desired set of performances. Therefore, a small subset of well-understood and/or canonical structures such as split-ring resonators are typically employed to achieve the targeted functionality. However, relaxing the device’s topological constraints may lead to improved performance albeit at the expense of a larger solution space to explore. To mitigate this issue, we employ custom state-of-the art multi-objective and surrogate-assisted optimization algorithms to explore the solution space afforded by emerging manufacturing techniques in order to design metasurface topologies that achieve an arbitrary number of user-specified performance criteria.