Radial GRIN Lenses Based on the Solution of a Regularized Ray Congruence Equation

Paraskevopoulos, Anastasios; Maggiorelli, Francesca; Albani, Matteo; Maci, S.

doi:10.1109/tap.2021.3111315

Cited by 17 publications

(6 citation statements)

References 36 publications

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“…Recently, [30] derived a new equation that is a solution of curved lines in a lens and demonstrated that the lens reduced the phase errors in simulation compared to [10] and [31]. However, the permittivity distributions along the x-axis are almost identical between (3) and the modified equation in [30] since the shortened horn in this paper has a small ratio of t/a. Therefore, we use (3) in this paper.…”

Section: A Design Of Permittivity Profile Of Grin Lensmentioning

confidence: 89%

Low Profile GRIN Lenses With Integrated Matching Using 3-D Printed Ceramic

Kordsmeier

Askari

et al. 2023

IEEE Open J. Antennas Propag.

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In this paper, we investigate a shortened horn antenna with high gain that is enabled by a 3Dprinted gradient index (GRIN) lens composed of high permittivity zirconia (ZrO 2 ). The baseline H-plane sectoral horn antenna is designed with length that is 1/3 of the optimal horn antenna and exhibits a low gain due to the high flaring rate of the horn. Increased gain is achieved by adding a flat GRIN lens at the horn aperture. High permittivity ZrO 2 (ε r = 23) enables lens miniaturization; however, when interfaced with air, reflections at the air interface increase the impedance mismatch. Two different methods for mitigating the reflections are studied. One is a simple λ/4 matching layer that matches the bulk permittivity of ZrO 2 to air. As expected, the λ/4 layers reduce the reflections in part of the 13-18 GHz band but produce high reflection in other parts. The second approach is a GRIN lens with integrated tapered matching layer to match phase and impedance simultaneously. Three tapering methods are studied (exponential, Klopfenstein, linear) for impedance matching. Analytical expressions of the minimum thickness and permittivity distribution are derived. The lens is discretized for print and three types of unit cells are proposed to create a wide range of permittivities ranging from bulk ceramic to air. A ZrO 2 lens prototype printed with an XJet Carmel 1400 is measured and results show good agreement with simulations, including gain performance equivalent to a horn of 2.4x longer length. The measured gain and beamwidth of the lens are 5.4dB higher and 52 • narrower than those of the shortened horn alone at 15 GHz, respectively.

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Section: A Design Of Permittivity Profile Of Grin Lensmentioning

confidence: 89%

Low Profile GRIN Lenses With Integrated Matching Using 3-D Printed Ceramic

Kordsmeier

Askari

et al. 2023

IEEE Open J. Antennas Propag.

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“…Nevertheless, their large and bulky design can be a disadvantage in certain applications. Therefore, innovative flat cylindrical GRIN lenses have been developed using various techniques, including Transformation Optics (TO) [11], [12], ray-tracing optimization [13], and analytical formulas rooted in Geometrical Optics (GO) [14], [15]. All of these methodologies are tailored to specific applications, often constrained by geometric and material limitations, making them less universally applicable.…”

Section: Introductionmentioning

confidence: 99%

GO Analysis of GRIN Lens Antennas by Combining in a Single ODE, Field and Wavefront-Curvature Transport to the Ray Tracing

Gashi,

Paraskevopoulos,

Maci

et al. 2024

IEEE Trans. Antennas Propagat.

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A novel very efficient algorithm based on the Geometrical Optics (GO) is presented for the analysis of graded index (GRIN) lens antennas, namely dielectric inhomogeneous lenses with a three-dimensional arbitrary varying refractive index. A family of curved ray-paths are traced starting from a set of points defined on the lens input interface, which is illuminated by a feed antenna, up to a corresponding set of points on the output interface; i.e., the lens radiating aperture. The ray-tracing is numerically performed in combination with the field transportation along the ray by exploiting an additional wavefront-curvature transport equation, thus providing a single independent vector Ordinary Differential Equation (ODE) for each ray. This scheme allows a complete parallelization of the algorithm by assigning any ray to a different thread. Crossing the lens input/output interfaces at the two end-points of the curved ray is accomplished by augmenting the refraction Snell's law and the Fresnel transmission coefficients with a novel compact closed form dyadic formula for the transmitted wavefront curvature. The ODE output provides the field aperture distribution on the output lens interface, permitting the far field calculation as a radiation integral. To this end, an ad-hoc quadrature rule is exploited, which requires an aperture sampling rate corresponding to the slowly varying part of the integrand, while the rapid phase variation is accounted for analytically; thus resulting in an extremely efficient and frequency independent scheme. The effectiveness and accuracy of the algorithm is shown by resorting to a couple of well-known analytical benchmarks and to two more general examples with real-life antennas: a Spaceborne Weather Radar lens antenna and a feed antenna with a zero-focal lens.

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“…In [33] and [34], an RT model is used to estimate the amplitude and phase distribution needed in an array with a radome on top to avoid grating lobes in a wide scanning range. Geometrical optics (GO) techniques have been widely used for the design of dielectric [35], [36] and parallelplate waveguide (PPW) [37] lens antennas.…”

Section: Introductionmentioning

confidence: 99%

Evaluation of Losses in 3-D-Printed Geodesic Lenses Using a Ray-Tracing Model

Castillo-Tapia,

Rico-Fernández,

Clendinning

et al. 2024

IEEE Trans. Antennas Propagat.

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This paper applies an in-house generalized raytracing model to efficiently compute both the radiation pattern and the efficiency of geodesic lenses with non-rotationally symmetric shapes. Losses due to ohmic effects and surface roughness are included in the model. These losses are very relevant for monolithic geodesic lens antennas as postprocessing techniques cannot be applied to reduce the surface roughness of the internal part of the metallic plates. The model is validated by comparison with full-wave simulations for three different lenses: a circular flat parallel-plate waveguide, an elliptically-compressed geodesic lens, and a water-drop lens. These results show a reduction in computational time by a factor of 600 using the ray-tracing model. A non-rotationally symmetric water drop lens has been manufactured in a monolithic piece using the laser powder-bed fusion technique with successful experimental results.

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Radial GRIN Lenses Based on the Solution of a Regularized Ray Congruence Equation

Cited by 17 publications

References 36 publications

Low Profile GRIN Lenses With Integrated Matching Using 3-D Printed Ceramic

Low Profile GRIN Lenses With Integrated Matching Using 3-D Printed Ceramic

GO Analysis of GRIN Lens Antennas by Combining in a Single ODE, Field and Wavefront-Curvature Transport to the Ray Tracing

Evaluation of Losses in 3-D-Printed Geodesic Lenses Using a Ray-Tracing Model

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