Computed imaging for the near-field

Carney, P. Scott; Frazin, R. A.; Rutherford, Joseph M.; Bozhevolnyi, Sergey I.; Volkov, Valentyn S.; Boltasseva, Alexandra; Schotland, John C.

doi:10.1364/fio.2003.wo2

Cited by 3 publications

(3 citation statements)

References 9 publications

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“…Nevertheless, insight into the structure of the ISP has been obtained. In particular, the inverse series is well suited to the study of waves which do not propagate over large scales such as diffuse waves in random media and evanescent electromagnetic waves in nanoscale systems [2,3]. In the latter case, the inverse scattering series has also been shown to be computationally effective [15].…”

Section: Discussionmentioning

confidence: 99%

Convergence and stability of the inverse scattering series for diffuse waves

2008

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Section: Discussionmentioning

confidence: 99%

Convergence and stability of the inverse scattering series for diffuse waves

2008

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“…By bringing the scanning device close to the samples, the non-radiative components, which does not propagate to the farfield detector, are captured, and sub-wavelength features can be obtained by exploiting these evanescent waves. This super-resolving capability makes near-field optics particularly attractive [19].…”

Section: Introductionmentioning

confidence: 99%

Periodic surface identification with phase or phaseless near-field data

Zheng¹,

Cheng²,

Li³

et al. 2017

Inverse Problems

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We investigate the inverse diffraction grating problem which is to reconstruct the periodic surface from the diffracted field. The surface is assumed to be a sufficiently smooth and small perturbation of the flat surface. A novel computational method is developed to solve the inverse problem with superresolution by using phase or phaseless near-field data. The method utilizes Rayleigh's coefficients of the near field data and updates iteratively the approximated surface function by solving a truncated linearized system. Monotonicity of the error estimate is proved under the small perturbation assumption of the surface. Numerical examples are shown to verify the theoretical findings and illustrate the effectiveness of the proposed method.

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“…Therefore, the illuminating field could consist of high spatial frequency evanescent plane waves. They may be generated at the interface of two media by total internal reflection [10,13], which has been in practical use for decades and primarily been used in near-field optics [4,5]. A recent review on the near-field microscopy and near-field optics may be found in [9].…”

Section: Introductionmentioning

confidence: 99%

Inverse medium scattering for the Helmholtz equation at fixed frequency

Bao¹,

Li²

2005

Inverse Problems

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Consider a time-harmonic electromagnetic plane wave incident on a medium enclosed by a bounded domain in R 2. In this paper, existence and uniqueness of the variational problem for the direct scattering are established. An energy estimate for the scattered field is obtained on which the Born approximation is based. The Fréchet differentiability of the scattering map is examined. A new continuation method for the inverse medium scattering, which reconstructs the scatterer of an inhomogeneous medium from the boundary measurements of the scattered waves, is developed. The algorithm requires only single-frequency scattering data. Using an initial guess from the Born approximation, each update is obtained via recursive linearization on the spatial frequency of a one-parameter family of plane waves by solving one forward and one adjoint problem of the Helmholtz equation.

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Computed imaging for the near-field

Cited by 3 publications

References 9 publications

Convergence and stability of the inverse scattering series for diffuse waves

Convergence and stability of the inverse scattering series for diffuse waves

Periodic surface identification with phase or phaseless near-field data

Inverse medium scattering for the Helmholtz equation at fixed frequency

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