Fresnel reflection coefficients in the Fourier domain for a planar surface in uniform motion parallel to its interface

Francisco J. Rodr\'iguez-Fortu\~no; Sebastian Golat; St\'ephane Azar

REVIEW 2 major objections 4 minor 47 references

Fresnel reflection coefficients in the Fourier domain for a planar surface in uniform motion parallel to its interface

T0 review · 2 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read A moving planar surface's reflection matrix is exactly the at-rest Fresnel matrix sandwiched between Lorentz boost matrices, valid for propagating and evanescent waves alike.

desk verdict Useful Fourier-domain reflection matrix for moving planar interfaces; the evanescent extension needs an explicit branch choice for the medium wavevector. read the letter →

arxiv 2506.04417 v1 pith:26MSN4WJ submitted 2025-06-04 physics.optics

Stéphane Azar , Sebastian Golat , Francisco J. Rodríguez-Fortuño This is my paper

classification physics.optics MSC 78A4578A4083A05 PACS 41.20.Jb42.25.Gy73.20.Mf

keywords FresnelreflectionmovingdielectricinterfaceLorentzboostFourier-domainopticsevanescentwavescross-polarizationsurfaceplasmondispersionnon-reciprocity

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper derives a closed-form expression for the reflection matrix of a flat interface between vacuum and a medium moving uniformly parallel to its surface, as a function of incident frequency and transverse wavevector. The construction boosts the incident field into the surface's rest frame, applies the ordinary stationary Fresnel reflection matrix, and boosts the reflected field back, so the result is exact within classical electrodynamics and special relativity rather than an approximation in angle or speed. The same formula works for arbitrary stationary surfaces, including anisotropic or layered ones, and extends to evanescent waves and complex spectral parameters, which is what makes it usable in near-field optics. Applying it to a lossless Drude metal, the paper finds that the surface-plasmon dispersion relation tilts along the direction of motion, producing unidirectional, non-reciprocal plasmon propagation.

What carries the argument

The machinery is the relativistic transformation of plane-wave fields: the 4-wavevector $k^\mu=(\omega/c,k_x,k_y,k_z)$ and the electromagnetic field tensor $F^{\mu\nu}$ are boosted to the surface rest frame, and the $s/p$ polarisation basis is extended to complex wavevectors so evanescent waves remain well defined. The boost acts on the Jones vector through a $2\times2$ matrix whose entries mix $s$ and $p$ amplitudes, and Eq. (14) sandwiches the stationary reflection matrix $\mathbf{R}_0(\omega',k'_x,k'_y)$ between forward and backward versions of that matrix. Leaving $\mathbf{R}_0$ as an arbitrary linear response is what carries the generality to anisotropic, magneto-optical, and slab geometries.

What would settle it

Take a lossless Drude interface at $\beta=0.1c$ and an evanescent incident wave with $k_x=2\omega/c$ and $k_y=0$, compute $r_p$ from Eq. (18), and compare it with a direct numerical solution of Maxwell's equations in the moving medium (equivalently, a stationary medium with moving boundary conditions); any discrepancy in the complex value of $r_p$ would disprove the claimed exactness for evanescent waves.

Watch

Extended reading notes

Core claim

The central result is Eq. (14): in the lab frame the moving-interface reflection matrix is $\mathbf{R}(\omega,k_x,k_y) = \mathbf{M}_+ \mathbf{R}_0(\omega',k'_x,k'_y) \mathbf{M}_-$, where $\mathbf{R}_0$ is the reflection matrix of the same interface at rest and $\mathbf{M}_\pm$ are the $2\times2$ polarisation-boost matrices of Eqs. (9) and (12). The transformed frequency and wavevector satisfy $\omega' = \gamma\omega - \gamma\beta c k_x$, $k'_x = \gamma k_x - \gamma\beta \omega/c$, $k'_y = k_y$, and $k'_z = k_z$. For a stationary isotropic dielectric, the motion introduces cross-polarisation terms proportional to $\beta k_y k_z$, which vanish when the velocity lies in the plane of incidence ($k_y=0$); in that 2D case the coefficients reduce to the stationary Fresnel formulas evaluated at the boosted $(\omega',k'_x)$. The same construction yields the surface-plasmon dispersion relation of a moving Drude metal: a tilted version of the rest-frame dispersion, implying movement-induced unidirectionality and non-reciprocity.

Load-bearing premise

The formula's near-field validity depends on $\mathbf{R}_0$ being well defined when its arguments $\omega',k'_x,k'_y$ become complex under the Lorentz boost of an evanescent lab-frame wave, including a definite square-root branch for the wavevector inside the medium; the paper specifies the vacuum branch but not the medium branch.

Editorial extensions

If this is right

The reflection coefficients are given directly in terms of $(\omega,k_x,k_y)$ with no angles, so angular-spectrum, Green-function, and fluctuational-electrodynamics calculations can use them without further approximation.
A stationary isotropic surface acquires $s$-$p$ cross-polarisation when it moves, proportional to $\beta k_y k_z$; the effect disappears only when the motion lies in the plane of incidence.
For $k_y=0$ the coefficients are just the rest-frame Fresnel formulas evaluated at the Doppler-shifted frequency and wavevector, recovering earlier 2D results and providing a direct reduction test.
For a lossless Drude metal the surface-plasmon dispersion relation tilts along the velocity; at high enough frequency only one propagation direction survives, giving movement-induced surface-plasmon unidirectionality and non-reciprocity.
Because $\mathbf{R}_0$ is left arbitrary, the same sandwich construction applies to moving slabs, moving anisotropic layers, and transmission problems with minimal changes.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The authors list Casimir forces, thermal emission, and local density of states as natural applications but do not compute them; inserting Eq. (14) into fluctuational-electrodynamics kernels would be a direct test of the formula's near-field usefulness.
The linear-in-$\beta$ cross-polarisation could be probed at non-relativistic speeds by using near-field sources with large $k_y k_z$ rather than by accelerating surfaces to relativistic velocities.
The unidirectionality claim suggests a moving plasmonic surface acts as a momentum-space shear filter; a concrete experiment would compare the coupling efficiency of surface plasmons excited from opposite directions on a rotating or translating Drude film.
The analytic-continuation caveat implies that the exactness claim is only as strong as the complex extension of $\mathbf{R}_0$; a direct solver benchmark for evanescent incidence would settle the regime of validity independently of the paper's assumption.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The real contribution here is Eq. (14): a compact expression for the lab-frame reflection matrix of a planar interface moving parallel to its own surface, written directly in frequency/wavevector variables and keeping the rest-frame R0 arbitrary. That Fourier-domain representation is new, and it is exactly the kind of tool that angular-spectrum and Green's-function calculations can pick up and use. The derivation is clean: boost the incident field to the rest frame, apply R0, boost back. The 2D limit reproduces Yeh and the expected Doppler-shifted coefficients, and cross-polarization correctly vanishes when motion lies in the plane of incidence. The appendix on boosting Jones vectors for arbitrary boost direction is solid formalism in its own right. The paper is also honest that the physics is just special relativity plus Maxwell; the packaging is the contribution.

The soft spots are real but not fatal. The paper claims validity for complex ω, kx, ky and for evanescent waves, but the rest-frame R0 is standardly defined for propagating waves. Extending Eq. (14) to evanescent fields requires an analytic continuation, and the paper never specifies the branch of the medium z-wavevector under that continuation. In Eqs. (17)-(18), the radical is left branchless, and the surface-plasmon pole location depends on the Riemann sheet. This is an omission rather than a contradiction; with the standard passive-medium branch choice the formula should work, but the paper should state it and justify the continuation. The s/p basis is also singular at kt=0; normal incidence is not discussed, though that is a minor gap since the limit is well defined. Finally, the unidirectionality claim in Section III is supported by the tilted dispersion plot, but the paper does not crisply define the threshold; that is a presentation issue, not a flaw in the reflection formula.

Who this is for: people working on thermal emission, Casimir forces, or near-field optics near moving surfaces, and anyone who wants a ready-made kernel for scattering calculations. The core result is likely correct, the gaps are fixable, and the paper deserves a serious referee. I'd send it to review and ask the authors to nail down the analytic continuation and the branch choice.

Referee Report

2 major / 4 minor

Summary. The paper derives an exact, Fourier-domain expression for the reflection matrix of a planar surface moving uniformly parallel to its interface. The derivation Lorentz-boosts the incident plane wave to the rest frame of the surface, applies the rest-frame reflection matrix R0, and boosts back. The central result, Eq. (14), expresses the lab-frame matrix as a conjugation of R0 by polarization rotation matrices. For a simple isotropic dielectric, the paper obtains cross-polarization terms linear in the boost parameter. In the 2D limit ky=0, the reflection coefficients reduce to the rest-frame coefficients evaluated at the Doppler-shifted frequency and wavevector. Using a Drude model, the paper computes the surface-plasmon dispersion from the pole of rp and finds a tilted dispersion that leads to motion-induced unidirectionality and non-reciprocity.

Significance. If correct, Eq. (14) is a compact and useful tool for nanophotonics problems involving moving surfaces, since it is expressed directly in the Fourier variables and reduces to known limits at β=0 and ky=0. The derivation is self-contained and avoids ad hoc assumptions; the appendix extends the polarization-boost formalism to arbitrary boost directions. The physical prediction of a tilted SPP dispersion with unidirectional regime is a clean consequence of the boost. However, the advertised validity for evanescent waves and complex arguments requires an analytic continuation of R0 that is not specified, and the displayed diagonal entries of the isotropic-case formula contain a sign error. These issues do not invalidate the main construction but must be corrected and clarified.

major comments (2)

[II.B, Eq. (15)] The expansion of Eq. (14) to the isotropic dielectric case appears to contain a sign error in the diagonal entries. Direct matrix multiplication of the right-hand side of Eq. (14) using the matrices in Eqs. (9) and (12) gives rss = [ (kt^2 kt'^2 - (γβ ky kz)^2) rs0 - (γβ ky kz)^2 rp0 ] / (kt^2 kt'^2) and rpp = [ -(γβ ky kz)^2 rs0 + (kt^2 kt'^2 - (γβ ky kz)^2) rp0 ] / (kt^2 kt'^2). The plus sign in the coefficient (kt^2 kt'^2 + (γβ ky kz)^2) in the manuscript should be a minus. I verified the identity L0,11 M0,11 = kt^2 kt'^2 - (γβ ky kz)^2 using numerical values (e.g., β=0.5, k0=1, kx=0.3, ky=0.4), so the discrepancy is not due to a branch choice. Please correct and verify this equation.
[II.A (after Eq. (14)) and Section III] The claim that Eq. (14) is 'valid for both propagating and evanescent waves, and for complex values in ω, kx and/or ky' is not supported by the derivation. The rest-frame reflection matrix R0(ω', kx', ky') is standardly defined for real propagating waves; for evanescent or complex arguments, an analytic continuation must be specified, including a choice of branch for the medium longitudinal wavevector kz,med. The manuscript fixes the branch of the vacuum kz but never fixes the branch of the radical in Eqs. (17)-(18). The surface-plasmon pole extracted in Section III lies on a specific Riemann sheet of that radical; without an explicit branch convention, the pole location and hence the dispersion relation (20) are not uniquely defined. This gap directly affects the near-field and SPP claims that are central to the abstract. Please specify the analytic continuation of R0 and the branch of kz,med, or restrict the validity claims accordingly.

minor comments (4)

[II.A, Eq. (2) and Eq. (14)] The polarization basis vectors in Eq. (2) and the prefactor in Eq. (14) divide by kt; the case kt=0 (normal incidence) is not discussed. Although the limit is regular (for ky=0 it reduces to Eq. (16)), the manuscript should state how the singular case is handled.
[III, Eq. (20)] Equation (20) is typeset ambiguously; it should read k±spp = [±√εr + β√(εr+1)]/[√(εr+1) ± β√εr] k0. Please format the equation clearly.
[III, Fig. 2 caption] The caption says the dispersion relation corresponds to the maximum of |rp|; for a lossless Drude model the pole is on the real axis and |rp| diverges. Please describe the numerical procedure used to identify the maximum.
[III, after Eq. (19)] Equation (20) is an implicit equation because εr(ω') depends on kx through Eq. (6); it may help the reader to state this explicitly before presenting the plot.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the moving-surface reflection matrix is derived by exact Lorentz conjugation of independent rest-frame Fresnel coefficients.

full rationale

The paper's central result, Eq. (14), is obtained by boosting an incident plane wave into the surface rest frame, multiplying by the rest-frame reflection matrix R0(ω',kx',ky'), and boosting the reflected wave back; R0 is an independent input that is left generic for arbitrary linear materials and, in the dielectric example, is taken from standard Fresnel coefficients. No parameter is fitted to the predicted reflection matrix, and the surface-plasmon dispersion in Eq. (20) is obtained both by setting the denominator of the derived rp to zero and by Lorentz-boosting the known rest-frame SPP relation from Ref. [46]; the two routes agree because both follow from the same exact transformation, not because one route was constructed from the other. The self-citations (Refs. [42] and [47]) are contextual comparisons of cross-polarization and unidirectional propagation, not load-bearing assumptions. The evanescent-regime claim does rely on an unstated analytic continuation of R0 and an unspecified branch of the medium wavevector, but this is a mathematical-rigour concern about the near-field extension, not a circularity: the issue is whether the rest-frame reflection matrix is defined at boosted complex arguments, not whether Eq. (14) reduces to its own inputs. Overall, the derivation is self-contained and no circular step satisfies the requirement of quoting a specific equation that reduces to its own input.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

The central derivation is a conjugation of the rest-frame Fresnel matrix by Lorentz boost matrices, so its axioms are the standard Maxwell/SR machinery plus the existence and analytic-continuability of R0. No free parameters are fitted; the Drude plasma frequency and the velocity v are inputs to the example. No new entities are introduced.

assumptions (4)

standard math Maxwell's equations and the Lorentz transformation of the electromagnetic field tensor apply to the moving interface.
Used throughout Section II.A to transform fields and wavevectors between the lab and rest frames.
domain assumption In the rest frame of the surface, the reflection of incident plane or evanescent waves is described by a known 2x2 Fresnel matrix R0(ω′, k′x, k′y).
Introduced around Eqs. (10) and (11); this is the object that the derivation conjugates. Its analytic continuation to complex arguments is not discussed.
domain assumption The surface at rest is a local, isotropic, non-magnetic dielectric with permittivity εr(ω), taken as lossless Drude for the example.
Used in Sections II.B and III to obtain explicit rss, rsp, rps, rpp and to plot the surface plasmon dispersion.
standard math Square roots of the wavevector components are evaluated on a principal branch (0≤arg kz<π for vacuum); the corresponding branch for the medium wavevector is not explicitly stated.
Stated in Section II.A for kz; the lack of a stated branch for the medium is part of the flagged analytic-continuation gap.

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Cite this review

Pith. "Pith review of Fresnel reflection coefficients in the Fourier domain for a planar surface in uniform motion parallel to its interface." pith.science (2026). https://pith.science/paper/26MSN4WJ

@misc{pith2026250604417,
  author       = {Pith},
  title        = {Pith review of: Fresnel reflection coefficients in the Fourier domain for a planar surface in uniform motion parallel to its interface},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/26MSN4WJ}},
  note         = {Machine review of arXiv:2506.04417}
}

read the original abstract

The optical reflection coefficient of a dielectric medium moving uniformly in the plane spanned by its surface is rigorously calculated using classical electrodynamics and special relativity, and expressed in the Fourier domain, as a function of the incident frequency and wavevector, valid in both the far- and near-field regimes. It is found that cross-polarisation appears as a consequence of the motion, except when it is directed along the plane of incidence. As an example, using a Drude model for the permittivity of the surface at rest, the dispersion relation of its surface modes is calculated. A tilting of the dispersion relation is observed, leading to movement-induced surface plasmon unidirectionality and non-reciprocity.

Figures

Figures reproduced from arXiv: 2506.04417 by the authors.

**Figure 2.** FIG. 2: Plot of the absolute value of the reflection coefficient [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗

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Reference graph

Works this paper leans on

47 extracted references · 46 canonical work pages

[1]

Sommerfield,Optics(Sarat Book Distributors, 1954)

A. Sommerfield,Optics(Sarat Book Distributors, 1954)

work page 1954
[2]

Pauli,Theory of Relativity(Pergamon Press, New York, 1958)

W. Pauli,Theory of Relativity(Pergamon Press, New York, 1958)

work page 1958
[3]

Yeh, Reflection and transmission of electromagnetic waves by a moving dielectric medium, Journal of Applied Physics36, 3513 (1965)

C. Yeh, Reflection and transmission of electromagnetic waves by a moving dielectric medium, Journal of Applied Physics36, 3513 (1965)

work page 1965
[4]

V. P. Pyati, Reflection and refraction of electromagnetic waves by a moving dielectric medium, Journal of Applied Physics38, 652 (1967)

work page 1967
[5]

Shiozawa, K

T. Shiozawa, K. Hazama, and N. Kumagai, Reflection and transmission of electromagnetic waves by a dielectric half-space moving perpendicular to the plane of incidence, Journal of Applied Physics38, 4459 (1967)

work page 1967
[6]

S. W. Lee and Y. T. Lo, Reflection and transmission of electromagnetic waves by a moving uniaxially 13 anisotropic medium, Journal of Applied Physics38, 870 (1967)

work page 1967
[7]

Shiozawa and K

T. Shiozawa and K. Hazama, General solution to the problem of reflection and transmission by a moving dielectric medium, Radio Science3, 569 (1968)

work page 1968
[8]

Huang, Reflection and transmission of electromagnetic waves by a dielectric medium moving in an arbitrary direction, Journal of Applied Physics76, 2575 (1994)

Y.-X. Huang, Reflection and transmission of electromagnetic waves by a dielectric medium moving in an arbitrary direction, Journal of Applied Physics76, 2575 (1994)

work page 1994

Show all 47 references

[9]

C. S. Tsai and B. A. Auld, Wave interactions with moving boundaries, Journal of Applied Physics38, 2106 (1967)

1967
[10]

Idemen and A

M. Idemen and A. Alkumru, Relativistic scattering of a plane-wave by a uniformly moving half-plane, IEEE Transactions on Antennas and Propagation54, 3429 (2006)

2006
[11]

K. S. Kunz, Plane electromagnetic waves in moving media and reflections from moving interfaces, Journal of Applied Physics51, 873 (1980)

1980
[12]

Censor, Scattering of a plane wave at a plane interface separating two moving media, Radio Science4, 1079 (1969)

D. Censor, Scattering of a plane wave at a plane interface separating two moving media, Radio Science4, 1079 (1969)

1969
[13]

Wang and X

H. Wang and X. Zhang, Magnetic response induced by a moving dielectric slab, Journal of Applied Physics 107, 10.1063/1.3427550 (2010)

2010 doi
[14]

Yeh, Reflection and transmission of electromagnetic waves by a moving plasma medium, Journal of Applied Physics37, 3079 (1966)

C. Yeh, Reflection and transmission of electromagnetic waves by a moving plasma medium, Journal of Applied Physics37, 3079 (1966)

1966
[15]

Yeh, Reflection and transmission of electromagnetic waves by a moving plasma medium

C. Yeh, Reflection and transmission of electromagnetic waves by a moving plasma medium. ii. parallel polarizations, Journal of Applied Physics38, 2871 (1967)

1967
[16]

Yeh, Scattering obliquely incident microwaves by a moving plasma column, Journal of Applied Physics 40, 5066 (1969)

C. Yeh, Scattering obliquely incident microwaves by a moving plasma column, Journal of Applied Physics 40, 5066 (1969)

1969
[17]

Chawla and H

B. Chawla and H. Unz, Reflection and transmission of electromagnetic waves normally incident on a plasma slab moving uniformly along a magnetostatic field, IEEE Transactions on Antennas and Propagation17, 771 (1969)

1969
[18]

P. K. Mukherjee and S. P. Talwar, Reflection and transmission of electromagnetic waves at a moving magnetoplasma half-space, Radio Science8, 653 (1973)

1973
[19]

Chakravarti, Nonlinear reflection and transmission of electromagnetic waves by moving plasmas, IEEE Transactions on Antennas and Propagation19, 145 (1971)

A. Chakravarti, Nonlinear reflection and transmission of electromagnetic waves by moving plasmas, IEEE Transactions on Antennas and Propagation19, 145 (1971)

1971
[20]

L. Gan, L. Guo, L. Guo, J. Li, Z. Wang, and X. Luo, Effects of nonuniform moving plasma on the polarization properties of obliquely incident em waves, IEEE Transactions on Plasma Science48, 867 (2020)

2020
[21]

Yeh and K

C. Yeh and K. F. Casey, Reflection and transmission of electromagnetic waves by a moving dielectric slab, Physical Review144, 665 (1966)

1966
[22]

Stolyarov, Reflection and transmission of electromagnetic waves incident on a moving dielectric slab, Radiophysics and Quantum Electronics10, 151 (1967)

S. Stolyarov, Reflection and transmission of electromagnetic waves incident on a moving dielectric slab, Radiophysics and Quantum Electronics10, 151 (1967)

1967
[23]

Yeh, Reflection and transmission of electromagnetic waves by a moving dielectric slab

C. Yeh, Reflection and transmission of electromagnetic waves by a moving dielectric slab. ii. parallel polarization, Physical Review167, 875 (1968)

1968
[24]

Yeh, Propagation along moving dielectric wave guides*, Journal of the Optical Society of America58, 14 767 (1968)

C. Yeh, Propagation along moving dielectric wave guides*, Journal of the Optical Society of America58, 14 767 (1968)

1968
[25]

S. W. Lee and R. Mittra, Scattering of electromagnetic waves by a moving cylinder in free space, Canadian Journal of Physics45, 2999 (1967)

1967
[26]

Censor, Scattering of electromagnetic waves by a cylinder moving along its axis, IEEE Transactions on Microwave Theory and Techniques17, 154 (1969)

D. Censor, Scattering of electromagnetic waves by a cylinder moving along its axis, IEEE Transactions on Microwave Theory and Techniques17, 154 (1969)

1969
[27]

R. C. Restrick, Electromagnetic scattering by a moving conducting sphere, Radio Science3, 1144 (1968)

1968
[28]

R. J. Pogorzelski, Electromagnetic scattering from a radially moving spherical discontinuity, Journal of Applied Physics44, 168 (1973)

1973
[29]

Radpour, A

H. Radpour, A. Pourziad, and K. Sarabandi, Four-dimensional relativistic scattering of electromagnetic waves from an arbitrary collection of moving lossy dielectric spheres, IET Microwaves, Antennas and Propagation15, 180 (2021)

2021
[30]

Chrissoulidis and E

D. Chrissoulidis and E. Kriezis, The scattering behavior of a slightly rough surface moving parallel to its mean plane with uniform velocity, IEEE Transactions on Antennas and Propagation33, 793 (1985)

1985
[31]

Ohkubo, Reflection and transmission of electromagnetic waves by a semi-infinite uniaxial plasma moving perpendicular to the plane of incidence, Radio Science11, 573 (1976)

M. Ohkubo, Reflection and transmission of electromagnetic waves by a semi-infinite uniaxial plasma moving perpendicular to the plane of incidence, Radio Science11, 573 (1976)

1976
[32]

I. M. Besieris, Analysis of electromagnetic radiation in the presence of a uniformly moving, uniaxially anisotropic medium, Journal of Mathematical Physics10, 1156 (1969)

1969
[33]

P. K. Mukherjee and S. P. Talwar, The interaction of an obliquely incident plane electromagnetic wave with an anisotropic moving conducting half-space, Astrophysics and Space Science39, 213 (1976)

1976
[34]

P. K. Mukherjee and S. P. Talwar, Oblique incidence of an electromagnetic wave at a moving ferrite medium, Journal of Applied Physics45, 2521 (1974)

1974
[35]

R. S. Mueller, Reflection of electromagnetic plane waves from a moving ferrite surface, Radio Science22, 461 (1987)

1987
[36]

Tanaka and K

K. Tanaka and K. Hazama, Reflection and transmission of electromagnetic waves by a moving inhomoge- neous medium, Radio Science7, 973 (1972)

1972
[37]

Rattan, G

I. Rattan, G. Gautama, and A. Chakravarti, An investigation of the reflection of electromagnetic pulses from moving plasmas, Journal of Physics D: Applied Physics6, L87 (1973)

1973
[38]

Leonhardt and P

U. Leonhardt and P. Piwnicki, Optics of nonuniformly moving media, Phys. Rev. A60, 4301 (1999)

1999
[39]

Tanaka, Relativistic study of electromagnetic waves in the accelerated dielectric medium, Journal of Applied Physics49, 4311 (1978)

K. Tanaka, Relativistic study of electromagnetic waves in the accelerated dielectric medium, Journal of Applied Physics49, 4311 (1978)

1978
[40]

Tanaka, Reflection and transmission of electromagnetic waves by a linearly accelerated dielectric slab, Physical Review A25, 385 (1982)

K. Tanaka, Reflection and transmission of electromagnetic waves by a linearly accelerated dielectric slab, Physical Review A25, 385 (1982)

1982
[41]

Horsley, M

S. Horsley, M. Artoni, and G. C. La Rocca, Radiation pressure on a moving body: beyond the doppler effect, Journal of the Optical Society of America B29, 3136 (2012)

2012
[42]

J. A. Gir´ on-Sedas, J. J. Kingsley-Smith, and F. J. Rodr ´ ıguez-Fortu˜ no, Lateral optical force on linearly polarized dipoles near a magneto-optical surface based on polarization conversion, Physical Review B100, 10.1103/PhysRevB.100.075419 (2019)

2019 doi
[43]

S. Horsley, Canonical quantization of the electromagnetic field interacting with a moving dielectric medium, 15 Physical Review A—Atomic, Molecular, and Optical Physics86, 023830 (2012)

2012
[44]

D. J. Griffiths,Introduction to Electrodynamics, 4th ed. (Pearson, 2012)

2012
[45]

Novotny and B

L. Novotny and B. Hecht,Principles of nano-optics(Cambridge University Press, 2011)

2011
[46]

S. A. Maier,Plasmonics: Fundamentals and Applications(Springer US, 2007)

2007
[47]

K. Y. Bliokh, F. J. Rodr ´ ıguez-Fortu˜ no, A. Y. Bekshaev, Y. S. Kivshar, and F. Nori, Electric-current-induced unidirectional propagation of surface plasmon-polaritons, Optics Letters43, 963 (2018). 16

2018

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

[1] [1]

Sommerfield,Optics(Sarat Book Distributors, 1954)

A. Sommerfield,Optics(Sarat Book Distributors, 1954)

work page 1954

[2] [2]

Pauli,Theory of Relativity(Pergamon Press, New York, 1958)

W. Pauli,Theory of Relativity(Pergamon Press, New York, 1958)

work page 1958

[3] [3]

Yeh, Reflection and transmission of electromagnetic waves by a moving dielectric medium, Journal of Applied Physics36, 3513 (1965)

C. Yeh, Reflection and transmission of electromagnetic waves by a moving dielectric medium, Journal of Applied Physics36, 3513 (1965)

work page 1965

[4] [4]

V. P. Pyati, Reflection and refraction of electromagnetic waves by a moving dielectric medium, Journal of Applied Physics38, 652 (1967)

work page 1967

[5] [5]

Shiozawa, K

T. Shiozawa, K. Hazama, and N. Kumagai, Reflection and transmission of electromagnetic waves by a dielectric half-space moving perpendicular to the plane of incidence, Journal of Applied Physics38, 4459 (1967)

work page 1967

[6] [6]

S. W. Lee and Y. T. Lo, Reflection and transmission of electromagnetic waves by a moving uniaxially 13 anisotropic medium, Journal of Applied Physics38, 870 (1967)

work page 1967

[7] [7]

Shiozawa and K

T. Shiozawa and K. Hazama, General solution to the problem of reflection and transmission by a moving dielectric medium, Radio Science3, 569 (1968)

work page 1968

[8] [8]

Huang, Reflection and transmission of electromagnetic waves by a dielectric medium moving in an arbitrary direction, Journal of Applied Physics76, 2575 (1994)

Y.-X. Huang, Reflection and transmission of electromagnetic waves by a dielectric medium moving in an arbitrary direction, Journal of Applied Physics76, 2575 (1994)

work page 1994