Analytic Sinusoidal Steady-State Electromagnetic Field Expressions for the Ideal Veselago Lens

Keleshteri, Marzieh Eini; Okhmatovski, Vladimir; LoVetri, Joe

doi:10.1109/ojap.2021.3121805

Cited by 5 publications

(18 citation statements)

References 33 publications

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“…Dealing with the cumbersome spectral-domain representation of the GF does not fully reveal the potential of using an ideal VL for quantitative MWI. The recently developed closed-form representation of the VL GF allows us to directly investigate this potential by studying the matrix operators associated with the discretization of the ISP and ISTP integral operators for the VL imaging scenario [30]. We will show that one of the reasons for the less-than-perfect quantitative imaging demonstrated in [33], [34], even with noiseless data, is the use of the non-ideal VL.…”

Section: The Standard Methods Of Microwave Imagingmentioning

confidence: 96%

“…The rays emanate from point B to the second boundary, where they are again re-focused to the outside focus point, C, a distance 2d away from the point source. All of the energy emanating from the point-source towards the lens reaches the focus point C. The GF for both 2D and 3D electromagnetic field cases has been provided in an efficient closed-form representation in [30]. This GF effectively translates the singularity of the free-space GF from the point A to point C with phase change.…”

Section: The Standard Methods Of Microwave Imagingmentioning

confidence: 99%

“…In this research, we prescribe quantitative MWI using an ideal VL and formulate the associated 2D inverse problem. In the mathematical formulation, we use a closed-form definition of the VL Green's function, which was formerly introduced in [30]. We show that, through a direct noniterative inversion method, the contrast sources of an arbitrary OI can be perfectly reconstructed.…”

Section: The Standard Methods Of Microwave Imagingmentioning

confidence: 99%

“…The new GF operator, G V L (r|r 0 ), represents the field at a receiver point due to a point-source located at r0 in the presence of the VL slab. An analytic expression for the VL GF was recently introduced in [30]. For a point source located at r0 = (x 0 , y 0 ) and the VL described as in Subsection (A) the VL GF, G V L , is the solution to the Helmholtz partial differential equation (PDE) boundary value problem (BVP) given as…”

Section: B the Green's Function For The Veselago Lensmentioning

confidence: 99%

“…Notice that the same PDE operator is utilized in each region, because even within the VL slab the wavenumber is k 0 . The effect of the VL is taken into account by the boundary condition on the slab as described in [30]. The solution to the VL GF is given as…”

Section: B the Green's Function For The Veselago Lensmentioning

confidence: 99%

See 4 more Smart Citations

Demonstration of Quantitative Microwave Imaging Using an Ideal Veselago Lens

Keleshteri

Okhmatovski

Jeffrey

et al. 2022

IEEE Open J. Antennas Propag.

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Quantitative microwave imaging employing an ideal Veselago lens is demonstrated using synthetic 2D experiments. Reconstructions of the complex-valued dielectric constant of an arbitrary objectof-interest are obtained from noiseless data using a non-iterative technique. A closed-form Veselago lens Green's function is utilized in the formulation of the problem. The contrast sources corresponding to a single illumination of the object-of-interest is recovered using total-field measurements at several receiver points located in the lens' focusing region. Collecting the field in the presence of the ideal Veselago lens produces well-conditioned matrices for the discretized inverse source problem. The contrast is then directly obtained by first calculating the total-field within the object. Synthetic examples having features as small as λ/25 show that the resolution is only limited by the signal-to-noise ratio of data. Experiments with noisy data reveals that the inversion procedure directly mirrors the noise in the data. Two new filtering processes are introduced based on the truncated Singular Value Decomposition of the data operator and the domain operator involved in the inversion process. These successfully deal with noisy reconstructions. Results show that using the new filtering methods, even with a single illuminating source, outperforms the least-squares method with several illuminating sources.

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Section: The Standard Methods Of Microwave Imagingmentioning

confidence: 96%

Section: The Standard Methods Of Microwave Imagingmentioning

confidence: 99%

Section: The Standard Methods Of Microwave Imagingmentioning

confidence: 99%

Section: B the Green's Function For The Veselago Lensmentioning

confidence: 99%

Section: B the Green's Function For The Veselago Lensmentioning

confidence: 99%

See 3 more Smart Citations

Demonstration of Quantitative Microwave Imaging Using an Ideal Veselago Lens

Keleshteri

Okhmatovski

Jeffrey

et al. 2022

IEEE Open J. Antennas Propag.

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Impact of anomalous surface boundary conditions on the planar negative‐refractive index lens

Eccleston

2022

IET Microwaves Antenna & Prop

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It is shown that anomalous boundary conditions at the surface of a negative‐refractive‐index metamaterial planar lens severely diminishes the resolution of the lens when its relative permittivity and permeability are both −1. Anomalous boundary conditions arise in practical microwave metamaterials that are typically a periodic array of identical unit cells comprising dielectric and conducting elements. For a unit‐cell size much smaller than the wavelength, homogenised permittivity and permeability are the constituent parameters of the average fields. Average fields vary on a scale larger than the unit cell size compared to localised fields associated with the constituent elements. Unlike the tangential components of the localised field, tangential components of the average fields are discontinuous across the surface of such materials. This anomalous boundary condition at the lens surface must be described by generalised sheet transition conditions. This study develops expressions for the negative‐refractive‐index lens optical transfer functions, as a function of spatial frequency, for transverse‐electric waves, that account for anomalous surface boundary conditions. Both the simulations and experimental data are used to verify the expressions at a frequency of 3 GHz.

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Assessing the potential of using a virtual Veselago lens in quantitative microwave imaging

Eini Keleshteri,

Okhmatovski,

Jeffrey

et al. 2024

Inverse Problems

Self Cite

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This study explores the potential of implementing the focusing properties of a virtual ideal Veselago lens within a standard free-space microwave imaging scenario. To achieve this, the virtual lens is introduced as an inhomogeneous numerical background for the inverse source problem. This numerical Vesealgo lens is incorporated into the incident and scattered field decomposition, resulting in a new data equation that involves the Veselago Lens Green's function. In addition to the contrast sources within the object-of-interest, the lens introduces virtual contrast sources along the lens boundaries that depend on the total tangential magnetic field. It is shown that a surface integral contribution that takes into account these surface contrast sources must be added to the collected free-space data before one can invert using the well-conditioned Veselago lens inversion operator. A preliminary investigation of the accuracy to which this surface integral contribution must be computed is performed using additive Gaussian noise. Results show that an error of less than one percent is required to achieve imaging performance similar to utilizing an actual Veselago lens. All results are performed within a 2D simulation environment.

show abstract

Analytic Sinusoidal Steady-State Electromagnetic Field Expressions for the Ideal Veselago Lens

Cited by 5 publications

References 33 publications

Demonstration of Quantitative Microwave Imaging Using an Ideal Veselago Lens

Demonstration of Quantitative Microwave Imaging Using an Ideal Veselago Lens

Impact of anomalous surface boundary conditions on the planar negative‐refractive index lens

Assessing the potential of using a virtual Veselago lens in quantitative microwave imaging

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