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Gradient Index Optics

Introduction

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..: References :..

[1] Q. Wu, J. P. Turpin, and D. H. Werner, "Integrated Photonic Systems Based on Transformation Optics Enabled Gradient Index Devices" Light: Science and Applications, Vol. 1, No. 38, pp. 1-6, November 2012.

ABSTRACT: Integrated photonics is expected to play an increasingly important role in optical communications, imaging, computing and sensing with the promise for significant reduction in the cost and weight of these systems. Future advancement of this technology is critically dependent on an ability to develop compact and reliable optical components and facilitate their integration on a common substrate. Here we reveal, with the utility of the emerging transformation optics technique, that functional components composed of planar gradient index materials can be designed and readily integrated into photonic circuits. The unprecedented design flexibility of transformation optics allows for the creation of a number of novel devices, such as a light source collimator, waveguide adapters and a waveguide crossing, which have broad applications in integrated photonic chips and are compatible with current fabrication technology. Using the finite-difference time-domain method, we perform full-wave numerical simulations to demonstrate their superior optical performance and efficient integration with other components in an on-chip photonic system. These components only require spatially-varying dielectric materials with no magneticd properties, facilitating low-loss, broadband operation in an integrated photonic environment.
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[2] X. Wang, Q. Wu, J. P. Turpin, and D. H. Werner, "Rigorous Analysis of Axisymmetric Transformation Optics Lenses Embedded in Layered Media Illuminated by Obliquely Incident Plane Waves" Radio Science, Vol. 48, No. 3, pp. 232-247, June 2013.

ABSTRACT: A body of revolution, finite‐difference time‐domain (BOR‐FDTD) method is developed for rigorous analysis of axisymmetric transformation optics (TO) lens devices. For normal incidence, a one dimensional (1‐D) FDTD method based on the total‐field scattered‐field (TFSF) technique was proposed to model the propagation of a plane wave launched from the top of a layered medium in cylindrical coordinates. The 1‐D FDTD solutions were employed to efficiently inject normally incident plane waves into the BOR‐FDTD method. For oblique incidence, analytical formulations were derived and presented by expanding the plane wave into a series of cylindrical modes via Fourier series expansion of the ϕ‐dependent variables, which were then used to introduce obliquely incident plane waves into the TFSF formulas associated with the BOR‐FDTD method. These procedures allowed for accurate simulations of BOR TO lenses embedded in layered media illuminated by obliquely incident waves. The accuracy and efficiency of the proposed method were verified by comparing numerical results with either analytical solutions or a commercial software (COMSOL) package. Thereafter, the developed BOR‐FDTD code was utilized to study the imaging properties of (a) radial gradient‐index (GRIN) lenses with a parabolic index profile, (b) a flat TO GRIN lens, (c) a spherical Luneburg lens, and (d) a cylindrical TO Luneburg lens both in free space and on top of a substrate. Here the TO GRIN lenses were designed by using the quasi‐conformal transformation optics (QCTO) technique. It was found that the flat TO lens was able to provide identical focusing properties as a cemented doublet in both free space and over a dielectric substrate. Moreover, the numerical results demonstrated that the flattened TO Luneburg lens possessed the desired imaging properties under different illuminations for both polarizations.
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[3] D. E. Brocker, J. P. Turpin, P. L. Werner, and D. H. Werner, "Optimization of Gradient Index Lenses using Quasi-Conformal Contour Transformations" IEEE Antennas and Wireless Propagation Letters, Special Cluster on Transformation Electromagnetics, Vol. 13, pp. 1787-1791, November 2014.

ABSTRACT: Transformation electromagnetics (TE) has been used to predict many unconventional and potentially game-changing electromagnetic devices, but they are often left unimplemented due to the complexity of the required material properties. Restricting transformations to quasi-conformal mappings allows all-dielectric gradient-index (GRIN) lens implementations using approaches familiar to optical system designers. We demonstrate spherical-aberration-corrected lenses with spherical surface profiles by mimicking the optical behavior of aspherical lenses using quasi-conformal mappings. Several approaches for mapping aspherical to spherical contours are described and contrasted, including the use of bulk GRIN regions throughout the entire lens as well as layered designs where the GRIN profiles are restricted to thin laminar layers at the surface of the otherwise homogeneous lens. Hence, the proposed methodology provides engineers with a powerfully intuitive means to design, compare, and contrast various equivalently performing GRIN lenses, adding new modeling capabilities to the existing, well-known remedies for optical system optimization. Furthermore, such an approach facilitates straightforward monitoring and manipulation of material gradients and overall change in refractive index.
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[4] K. L. Morgan, D. E. Brocker, S. D. Campbell, D. H. Werner, and P. L. Werner, "Transformation-Optics-Inspired Anti-Reflective Coating Design for Gradient Index Lenses,” Optics Letters, Vol. 40, No. 11, pp. 2521-2524, June, 2015.

ABSTRACT: 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.
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[5] S. D. Campbell, D. E. Brocker, J. Nagar, and D. H. Werner, "SWaP Reduction Regimes in Achromatic GRIN Singlets,” Applied Optics, Vol. 66, No. 13, pp. 3594-3598, April 2016.

ABSTRACT: 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.
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[6] J. A. Easum, S. D. Campbell, J. Nagar, and D. H. Werner, "Analytical Surrogate Model for the Aberrations of an Arbitrary GRIN Lens,” Optics Express, Vol. 24, No. 16, pp. 17805-17818, 2016.

ABSTRACT: 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.
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[7] S. D. Campbell, J. Nagar, and D. H. Werner, "Multi-Element, Multi-Frequency Lens Transformations Enabled by Optical Wavefront Matching,” Optics Express, Vol. 25, No. 15, pp. 17258-17270, July 2017.

ABSTRACT: Transformation optics (TO) has brought forth a renewed interest in gradient-index (GRIN) optics due to its ability to allow arbitrary geometries to electromagnetically mimic the behaviors of more conventional structures via a spatially-inhomogeneous refractive index profile. While quasi-conformal transformation optics (qTO) has seen great success at microwave and RF frequencies, it is inherently limited to single frequency transformations: an immediate shortcoming for designs in the optical regime. Also, achieving desirable solutions from multi-element transformations is difficult for qTO. To overcome these challenges, a multi-component multi-frequency lens transformation procedure based on the wavefront-matching (WFM) design methodology is presented. Finally, the procedure is applied to a number of optical systems to advocate its efficacy as a more general transformation method.
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[8] J. Nagar, S. D. Campbell, and D. H. Werner, "Apochromatic Singlets Enabled by Metasurface-Augmented GRIN Lenses,” Optica, Vol. 5, No. 2, pp. 99-102, February 2018.

ABSTRACT: 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.
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