Path Integral Formulation for Wave Effect in Multilens System

Yamamoto, Kazuhiro

doi:10.4236/ijaa.2017.73018

IJAA

2017

DOI: 10.4236/ijaa.2017.73018

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Path Integral Formulation for Wave Effect in Multilens System

Kazuhiro Yamamoto¹

Abstract: A formula to investigate the wave effect in a multi-lens system is presented on the basis of a path integral formalism by generalizing the work by Nakamura and Deguchi (1999). The wave effect of a system with two lenses is investigated in an analytic way as a simple application to demonstrate usefulness of the formula and variety of wave effect in multi-lens system.

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Cited by 3 publications

References 13 publications

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Multiplane lensing in wave optics

Feldbrugge

2023

Monthly Notices of the Royal Astronomical Society

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Wave effects in lensing form a rich phenomenon at the intersection of classical caustic singularities and quantum interference, yet are notoriously difficult to model. Due to a large number of recently observed pulsars and fast radio bursts in radio astronomy and the prospected increase in sensitivity of gravitational wave detectors, wave effects have already been observed in plasma lensing and will be observed in gravitational lensing in the near future. The interference fringes are sensitive to physical parameters which cannot be inferred from geometric optics. In particular, for multi-plane lensing, the pattern depends on the redshifts of the lens planes. I present a new method to define and efficiently evaluate multi-plane lensing of coherent electromagnetic waves by plasmas and gravitational lenses in polynomial time. This method will allow the use of radio and gravitational wave sources to probe our universe in novel ways.

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Multiplane lensing in wave optics

Feldbrugge

2023

Monthly Notices of the Royal Astronomical Society

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Diffraction of electromagnetic waves by an extended gravitational lens

Turyshev

Toth

2021

Phys. Rev. D

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Multipole decomposition of gravitational lensing

Turyshev

Toth

2022

Phys. Rev. D

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We study gravitational lensing by a generic extended mass distribution. For that, we consider the diffraction of electromagnetic (EM) waves by an extended, weakly aspherical, gravitating object. We account for the static gravitational field of such a lens by representing its exterior potential in the most generic form, expressed via an infinite set of symmetric trace free (STF) tensor multipole mass moments. This yields the most general form of the gravitational phase shift, which allows for a comprehensive description of the optical properties of a generic gravitational lens. We found that at each order of the STF moments, the gravitational phase shift is characterized by only two parameters: a magnitude and a rotation angle that characterize the corresponding caustics, which form in the point spread function (PSF) of the lens. Both of these parameters are uniquely expressed in terms of the transverse-trace free (TT) projections of the multipole moments on the lens plane. Not only does this result simplify the development of physically consistent models of realistic lenses, it also drastically reduces the number of required parameters in the ultimate model. To help with the interpretation of the results, we established the correspondence of the gravitational phase shift expressed via the TT-projected STF multipole mass moments and its representation via spherical harmonics. For axisymmetric mass distributions, the new results are consistent with those that we obtained in previous studies. For arbitrary mass distributions, our results are novel and offer new insight into gravitational lensing by realistic astrophysical systems. These findings are discussed in the context of ongoing astrophysical gravitational lensing investigations as well as observations that are planned with the solar gravitational lens (SGL).

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Path Integral Formulation for Wave Effect in Multilens System

Cited by 3 publications

References 13 publications

Multiplane lensing in wave optics

Multiplane lensing in wave optics

Diffraction of electromagnetic waves by an extended gravitational lens

Multipole decomposition of gravitational lensing

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