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Wave propagation in complex coordinates
Classical Physics · Submitted 17 Jul 2015
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Extending this property to all angles of incidence leads us to a generalized form of the Poschl Teller potentials.
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The abstract, sentence by sentence
We investigate the analytic continuation of wave equations into the complex position plane. For the particular case of electromagnetic waves we provide a physical meaning for such an analytic continuation in terms of a family of closely related inhomogeneous media. For bounded permittivity profiles we find the phenomenon of reflection can be related to branch cuts in the wave that originate from poles of the permittivity at complex positions. Demanding that these branch cuts disappear, we derive a large family of inhomogeneous media that are reflectionless for a single angle of incidence. Extending this property to all angles of incidence leads us to a generalized form of the Poschl Teller potentials. We conclude by analyzing our findings within the phase integral (WKB) method.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We investigate the analytic continuation of wave equations into the complex position plane. | contribution 0.98 | 0.92 | 0.04 | asserted 0.86 |
| s1 | For the particular case of electromagnetic waves we provide a physical meaning for such an analytic continuation in terms of a family of closely related inhomogeneous media. | interpretation 0.70 | 0.92 | 0.08 | asserted 1.00 |
| s2 | For bounded permittivity profiles we find the phenomenon of reflection can be related to branch cuts in the wave that originate from poles of the permittivity at complex positions. | result 0.96 | 0.92 | 0.10 | asserted 1.00 |
| s3 | Demanding that these branch cuts disappear, we derive a large family of inhomogeneous media that are reflectionless for a single angle of incidence. | result 0.77 | 0.94 | 0.17 | asserted 1.00 |
| s4 | Extending this property to all angles of incidence leads us to a generalized form of the Poschl Teller potentials. | result 0.93 | 0.91 | 0.37 | asserted 1.00 |
| s5 | We conclude by analyzing our findings within the phase integral (WKB) method. | method 0.55 | 0.90 | 0.26 | asserted 0.68 |
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The paper
Original abstract
We investigate the analytic continuation of wave equations into the complex position plane. For the particular case of electromagnetic waves we provide a physical meaning for such an analytic continuation in terms of a family of closely related inhomogeneous media. For bounded permittivity profiles we find the phenomenon of reflection can be related to branch cuts in the wave that originate from poles of the permittivity at complex positions. Demanding that these branch cuts disappear, we derive a large family of inhomogeneous media that are reflectionless for a single angle of incidence. Extending this property to all angles of incidence leads us to a generalized form of the Poschl Teller potentials. We conclude by analyzing our findings within the phase integral (WKB) method.
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How the literature uses it
3 arXiv papers cite this in 11 sentences
Papers citing it · 6 sentences without a confident label
Uses its method or tool 2 papers
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The generalized reflection and transmission coefficients are then given by [equation] Integrating formally both sides of Eq.(19) from $-∞$ to $∞$ and using Eqs.(20) and (22), one can write [equation] Note that, as compared to more conventional WKB analysis of Ref. [ref] , following Ref. [ref] we use for the asymptotic states the expression (9) , which offers the advantage of avoiding branch cuts arising form square root of the potential and simplifies the analysis when extending the equations into the complex plane.
Wave reflection in dielectric media obeying spatial Kramers-Kronig relations · 3. One-way reflectionless property of Kramers-Kronig dielectric media · 0.82
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For perpendicular incidence we do not need to distinguish between two independent polarizations of the wave and we can consider the scalar Helmholtz equation [equation] A simple method of generating materials that do not reflect from one side (utilized in [ref] , for example) is to write down an expression for $E(x,ω)$ that for $x→±∞$ becomes a plane wave moving to the right (or left).
All-frequency reflectionlessness · Introduction · 0.86
Cites it as background 3 papers
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In a recent work, Horsley et al. introduced the idea of spatial KK relations in planar inhomogeneous dielectric media [ref] (see also Ref. [ref] ).
Wave reflection in dielectric media obeying spatial Kramers-Kronig relations · 1. Introduction · 0.96
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Recent work [ref] has shown that complex inhomogenous media satisfying the spatial Kramers–Kronig relations have curious scattering properties, being generally reflectionless from one side and in many cases having unit transmission.
The KdV hierarchy in optics · Kramers–Kronig media · 0.86
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The question of what governs reflection is subtle and a completely general answer is still elusive [ref] .
All-frequency reflectionlessness · Introduction · 0.92
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