Journal ArticleDOI
Generalization of Bateman-Hillion progressive wave and Bessel-Gauss pulse solutions of the wave equation via a separation of variables
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In this paper, the Bessel-Gauss pulses and Bateman-Hillion relatively undistorted progressive waves are presented, and simple solutions describing localized wave propagation are found based on a kind of separation of variables.Abstract:
Tw on ew families of exact solutions of the wave equation uxx + uyy + uzz − c −2 utt = 0g eneralizing Bessel–Gauss pulses and Bateman–Hillion relatively undistorted progressive waves, respectively are presented. In each of these families new simple solutions describing localized wave propagation are found. The approach is based on a kind of separation of variables.read more
Citations
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Localized Light Waves: Paraxial and Exact Solutions of the Wave Equation (a Review)
TL;DR: In this article, simple explicit localized solutions are systematized over the whole space of a linear wave equation, which models the propagation of optical radiation in a linear approximation, and a similarity between these exact solutions and harmonic in time fields obtained in the paraxial approximation based on the Leontovich-Fock parabolic equation has been studied.
Journal ArticleDOI
Beams of electromagnetic radiation carrying angular momentum : The Riemann-Silberstein vector and the classical-quantum correspondence
TL;DR: In this article, it is shown that the relationship between the classical properties of the beam and the quantum characteristics of the photons that make a particular beam is best expressed in terms of the Riemann-Silberstein vector, a complex combination of the electric and magnetic field vectors.
Journal ArticleDOI
New Structures in Paraxial Gaussian Beams
TL;DR: Within the classical parabolic equation approach, two new families of localized paraxial beams are constructed in the entire space as mentioned in this paper, and the solutions are different from the well-known solutions of the Hermite-Gauss or LaguerreGauss types.
Journal ArticleDOI
Photon localization barrier can be overcome
Peeter Saari,M. Menert,H. Valtna +2 more
TL;DR: For cylindrical one-photon states, this paper showed that the falloff in the waist cross-section plane is quadratically exponential (Gaussian) and such strong localization persists in the course of propagation.
Journal ArticleDOI
Localized electromagnetic pulses with azimuthal dependence
TL;DR: In this article, a family of solutions of the wave equation which are localized in space-time and have azimuthal dependence was presented, thus enlarging the previously known set of solutions.
References
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Journal ArticleDOI
Methods of Theoretical Physics. By P.M. Morse and H. Feschbach. 2vols., Pp.xxii, 1978. 120s. each vol. 1953.(McGraw-Hill)
Book
Methods of Mathematical Physics
Richard Courant,David Hilbert +1 more
TL;DR: In this paper, the authors present an algebraic extension of LINEAR TRANSFORMATIONS and QUADRATIC FORMS, and apply it to EIGEN-VARIATIONS.
Journal ArticleDOI
Methods of Mathematical Physics
TL;DR: In this paper, the authors present an algebraic extension of LINEAR TRANSFORMATIONS and QUADRATIC FORMS, and apply it to EIGEN-VARIATIONS.
Journal ArticleDOI
Bessel-Gauss beams
TL;DR: In this paper, a new type of solution of the paraxial wave equation is presented, which encompasses as limiting cases both the diffraction-free beam and the gaussian beam.