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REVIEW 3 major objections 6 minor 102 references

Quantum optical scattering by macroscopic lossy objects: A general approach

T0 review · 3 major / 6 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read The paper claims that the full quantum transformation of light scattered by an arbitrary linear lossy object is given by one unitary input-output relation built from classical transmission, emission, and absorption dyadics; if correct…

desk verdict A serious input-output framework for lossy continuum scattering, but the unitarity hinges on an unproved completeness relation imported from prior work. read the letter →

arxiv 2411.18543 v1 pith:FCSGVKAZ submitted 2024-11-27 quant-ph

Alessandro Ciattoni This is my paper · ORCID
classification quant-ph MSC 81V8078A4581P40 PACS 42.50.Ct42.25.Bs
keywords quantumopticalscatteringmacroscopicelectrodynamicsmodifiedLangevinnoiseformalisminput-outputrelationslossymediapolaritonsdecoherencedyadicGreen'sfunction
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

This paper attempts to supply the missing general theory of quantum radiation scattering by an arbitrary macroscopic object that absorbs and disperses light. Its central claim is that one unitary input-output relation, whose entries are the classical transmission, emission, and absorption dyadics, completely determines how ingoing polaritons become outgoing polaritons, and hence how any quantum state of light is transformed. The payoff is practical: once a classical dyadic Green's function is known, all quantum scattering predictions follow, including the decoherence and entanglement that losses force on the scattered radiation. The paper works out one- and two-polariton scattering, showing that losses force the scattered field into a statistical mixture and that entanglement among ingoing photons can shape that mixture.

What carries the argument

The load-bearing object is the input-output matrix of Eq. (38), a unitary operator on the direct sum of the Hilbert spaces of scattering, electric, and magnetic polaritons. Its kernel entries are the classical dyadics--transmission $T_{\omega ss}(\mathbf n|\mathbf m)$, emission $E_{\omega se}$, $E_{\omega sm}$, absorption $A_{\omega es}$, $A_{\omega ms}$, and $Q_{\omega\nu\nu'}$--so the matrix converts the classical description of the object's electrodynamics directly into quantum transition amplitudes. Unitarity is proven in Appendix E from the fundamental integral relation Eq. (5) for the dyadic Green's function $G_\omega$, and it guarantees that ingoing and outgoing polariton operators generate equivalent Fock-space representations. The change-of-basis matrix between these representations is a permanent of one-particle amplitudes $Z_{\tau\mu}$, which is why bosonic symmetry appears automatically in the outgoing state.

What would settle it

Numerically evaluate Eq. (5) and the seven operator relations in Eq. (31) for a solvable lossy object, such as a homogeneous lossy sphere with known dyadic Green's functions; any violation invalidates the central claim, and a complementary experiment is to check that a single-photon input produces the exact mixed-state form $P_s|\Phi_{1s}\rangle\langle\Phi_{1s}|+(P_e+P_m)|0\rangle\langle 0|$ with no residual coherence between the one-photon and vacuum sectors.

Watch

Extended reading notes

Core claim

The main result is the ingoing-outgoing quantum state relation in Eq. (53), together with the input-output unitary relation in Eq. (38). Eq. (38) states that the annihilation operators of outgoing s-, e-, and m-polaritons are a unitary matrix applied to the ingoing polariton operators; the matrix blocks are the classical transmission dyadic $T_{\omega ss}$, emission dyadics $E_{\omega se}$ and $E_{\omega sm}$, absorption dyadics $A_{\omega es}$ and $A_{\omega ms}$, and internal-energy redistribution dyadics $Q_{\omega\nu\nu'}$. Eq. (53) then expresses the outgoing many-polariton wavefunction as a symmetrized product of one-particle amplitudes, each amplitude being a matrix element of one of these classical dyadics. Thus every quantum scattering amplitude is fixed by the object's classical electromagnetic response. In the standard case of an initially unexcited object, radiation scattering is governed by $T_{\omega ss}$ while radiation absorption creates outgoing e- and m-polaritons; tracing out the object yields a reduced density operator for the scattered light that is generally mixed, so lossy scattering causes quantum decoherence and unavoidable radiation-object entanglement.

Load-bearing premise

The entire construction rests on Eq. (5), an integral identity for the classical electromagnetic Green's function that the paper states as a fundamental property and uses to prove unitarity but does not itself prove; if it fails for a physically realizable lossy object, the input-output relation and all derived state transformations collapse.

Editorial extensions

If this is right

  • All quantum predictions for scattering by any linear lossy object can be computed from the classical dyadic Green's function; separate quantization of the object is not needed.
  • Total polariton number is conserved and each single-polariton transition keeps its frequency, so the scattering process is fully elastic at the level of the enlarged radiation-object system.
  • For an initially inert object, absorption of an ingoing photon necessarily creates e- or m-polaritons, and when these are unmeasured the scattered light is a mixed state; lossy scattering therefore always induces decoherence.
  • One-polariton scattering produces a Schmidt rank-2 state, meaning a single photon is never decoupled from the object after lossy scattering; the reduced state is an incoherent mixture of the elastically scattered photon and vacuum.
  • In two-polariton scattering, entanglement between the two ingoing photons controls the eigenstates of the one-photon part of the scattered mixture, so input entanglement can be used to manipulate the statistical mixture of the output light.

Reading between the lines

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

  • I infer that the formalism enables inverse design: because all quantum amplitudes are classical dyadics, one could search over permittivity and permeability profiles for an object that realizes a desired quantum transformation, such as a specified entangled-state generator.
  • I infer a conditional-measurement scheme: if the object's e/m polaritons are measured rather than traced out, the scattered s-polariton state becomes a heralded state, and the paper's Eqs. (38) and (53) supply the amplitudes needed to compute its purity.
  • I infer that the purity of scattered light as a function of frequency should map the frequency-dependent absorption dyadics, because the decoherence factor in Eq. (70) is built entirely from the electric and magnetic absorption factors $J_e$ and $J_m$.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 6 minor

Summary. This paper develops a formal framework for quantum optical scattering by a finite-size, lossy, inhomogeneous magnetodielectric object in vacuum, based on the modified Langevin noise formalism (MLNF). The electric field is expressed in terms of scattering (s), electric (e), and magnetic (m) polariton operators, and the authors identify ingoing and outgoing field operators in the far-field limits. Their central results are the input-output unitary relation Eq. (38), which connects outgoing (G, F_e, F_m) to ingoing (g, f_e, f_m) polaritons through the classical transmission, emission, absorption, and redistribution dyadics, and the ingoing-outgoing quantum state relation Eq. (53), which expresses the outgoing wavefunction as a permanent of matrix elements of these dyadics. The paper also derives the reduced density operator of scattered s-polaritons for an initially inert object and works out one- and two-polariton examples, emphasizing loss-induced decoherence and the effect of input entanglement.

Significance. If correct, this is a useful and quite general framework: it extends LNF-based input-output theory from finite-port devices to a continuum of scattering channels and gives explicit quantum transition amplitudes in terms of classical dyadic Green's function quantities. A notable strength is that the paper contains no fitted parameters and the algebraic derivations are carried out in detail in Appendices D-K; the final formulas are falsifiable once the classical dyadics are computed. The two-polariton example provides a concrete mechanism by which input entanglement can be converted into a manipulation of the mixed state of scattered radiation. The main caveat is that the entire construction rests on one unproved identity imported from the author's earlier work.

major comments (3)
  1. [Section II, Eq. (5)] The 'fundamental integral relation' in Eq. (5) is the single non-algebraic input from which Appendix E derives the seven operator relations in Eq. (31), the unitarity of the input-output matrix Eq. (35), and hence the input-output relation Eq. (38). It is stated in Sec. II as a property of the dyadic Green's function and attributed to the prior MLNF paper [86]; it is not proved or independently checked in this manuscript. Because Eq. (5) mixes a surface integral over the far-field amplitude W with volume integrals over e/m modes, a missing term or additional regularity condition on epsilon_omega and mu_omega would invalidate Eq. (30) and the probability-conservation identity Eq. (65), and with them the central state relation Eq. (53). I request either a self-contained derivation of Eq. (5) under explicitly stated hypotheses, or a direct numerical verification for a nontrivial lossy scatterer (for example, a lossy sphere) confirming the operator relation Eq. (31).
  2. [Abstract and Section I] The abstract and Sec. I state that the formalism applies 'with no restrictions' to the object's optical response and inhomogeneous composition. However, the derivation assumes a scalar, local, isotropic magnetodielectric response epsilon_omega(r), mu_omega(r) (Eq. (1)); anisotropic and nonlocal media are not covered, and the boundary conditions in Eq. (2) are those of an isotropic object. This overstatement of scope should be corrected in the abstract and introduction, or the formalism should be extended to tensor-valued epsilon and mu.
  3. [Section VI] The one- and two-polariton examples in Section VI only manipulate the formal wavefunctions of Sec. V; they do not compute the classical dyadics T_omega_ss, E_omega_s_nu, A_omega_nu_s, Q_omega_nu_nu' for any physical object, nor do they verify that the seven operator relations of Eqs. (E13) and (E25) hold. As a result, the paper demonstrates the logical structure of the input-output theory but not that the required unitary operator matrix can actually be constructed for a finite lossy object. A worked example with explicit Green's functions (e.g., a homogeneous lossy sphere or a planar slab) would substantially strengthen the central claim, or the paper should explicitly state that numerical evaluation is beyond its scope.
minor comments (6)
  1. [Throughout] There are numerous typos and misspellings ('radidly', 'Converserly', 'entaglement', 'statisfies', 'outgoning', 'proability', 'eigevectors', 'revelas', 'beavior', 'litterature'); the manuscript needs a careful proofreading pass.
  2. [Eq. (87) and Appendix K, Eq. (K7)] The two-polariton entangled state is written as 1/sqrt(2)[phi_1(xi_1_s) phi_2(xi_2_s) + phi_1(xi_1_s) phi_2(xi_2_s)], with the two terms identical. From the following derivation, the second term should be phi_2(xi_1_s) phi_1(xi_2_s); please fix this typo.
  3. [Appendix K] The 'Schwartz inequalities' should be 'Schwarz inequalities'.
  4. [Conclusion] The final paragraph states as a conclusion that for 'any number of ingoing polaritons' the statistical mixture depends on input entanglement, but only the two-polariton case was analyzed. Please either soften this to a conjecture or provide the general argument.
  5. [Eqs. (3) and (10)] The relation F_omega_s(r|m) = sqrt(hbar k_omega^3 / (pi epsilon_0)) W_omega^T(-m|r) is central but the direction argument -m may be confusing because W_omega is defined with n as the observation direction. A brief remark connecting Eqs. (3) and (10) would improve readability.
  6. [Section IV] The spaces L2_e and L2_m are described as 'two identical copies' of L2_l, but the physical source variables r lie in all space; since the kernels G_omega_nu and Q_omega_nu_nu' vanish outside the object, the distinction is harmless. A sentence explaining the support of the relevant kernels would avoid confusion.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the quantum input-output and state relations are derived from classical dyadic identities plus bosonization; the imported completeness relation Eq. (5) is a dependency and a correctness risk, but not a circular reduction.

full rationale

The derivation chain is a bosonization of classical scattering: MLNF supplies the field operator Eq. (13); far-field asymptotics identifies ingoing and outgoing polariton operators; imposing bosonic commutation relations yields the unitarity constraint Eq. (28). The paper then solves Eq. (28) by deriving the classical transmission-emission-absorption identities Eqs. (31) and (35) from the dyadic Green's function completeness relation Eq. (5). No fitted parameter appears anywhere: the input-output matrix entries are the classical transmission, emission, and absorption dyadics, and the central state relation Eq. (53) is the change-of-basis overlap computed from those dyadics via permanents, with the lossless limit reducing to the known textbook photon scattering relation Eq. (57). The only load-bearing imported premise is Eq. (5), which is presented as a fundamental property and is not proved in this paper; it is inherited from the author's prior MLNF work (Ref. [86]). This is a verification and correctness dependency rather than circularity: Eq. (5) is a parameter-free identity about classical dyadic Green's functions, it is not identical to the target result, and it can in principle be checked independently of the quantum predictions. The paper therefore does not reduce its predictions to its inputs by construction, and no self-definitional, fitted-input, or renaming pattern is present.

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

No new entities and no fitted parameters are introduced. The formalism leans on the author's earlier MLNF, whose fundamental completeness relation Eq (5) is the principal imported axiom; without it the unitarity and all subsequent quantum predictions do not follow.

assumptions (4)
  • domain assumption Completeness of MLNF modes: Eq (5), connecting the scattering-mode surface integral and e/m medium-mode volume integrals to Im G / k.
    Primary input from the author's prior MLNF formalism [86]; it is assumed as a fundamental property of the dyadic Green's function and underpins the unitarity of the input-output relation.
  • domain assumption Canonical bosonic commutation relations for s-, e-, and m-polaritons, Eqs (12)-(15).
    Defines the quantum Hilbert space and ensures mode operators satisfy boson statistics; inherited from MLNF.
  • domain assumption Object response is local, linear, isotropic and causal: εω(r) and μω(r) are holomorphic in the upper half-plane, with vacuum outside the object.
    Used in the boundary value problems Eq (2) and (7); excludes anisotropic and nonlocal media despite the abstract's 'no restrictions' wording.
  • standard math Sommerfeld radiation condition and scattering boundary condition, Eq (2) and (7).
    Needed for the far-field identification of ingoing and outgoing modes.

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Cite this review

Pith. "Pith review of Quantum optical scattering by macroscopic lossy objects: A general approach." pith.science (2026). https://pith.science/paper/FCSGVKAZ

@misc{pith2026241118543,
  author       = {Pith},
  title        = {Pith review of: Quantum optical scattering by macroscopic lossy objects: A general approach},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FCSGVKAZ}},
  note         = {Machine review of arXiv:2411.18543}
}
read the original abstract

We develop a general approach to describe the scattering of quantum light by a lossy macroscopic object placed in vacuum with no restrictions on both its dispersive optical response and its spatially inhomogeneous composition. Our analysis is based on the modified Langevin noise formalism, a recently introduced version of macroscopic quantum electrodynamics where scattering (s) modes are explicitly separated from electric (e) and magnetic (m) medium excitations; accordingly the formalism involves three kinds of non-interacting boson polaritons such that, in the lossless limit, s-polaritons reduce to standard photons whereas e- and m-polaritons disappear. We analytically derive the input-output unitary relation joining the boson operators of the ingoing and outgoing polaritons, a nontrivial result hinging upon original relations which comprehensively describe the transmission-emission-absorption interplay pertaining the classical radiation scattering, relations we here deduce by resorting to the dyadic Green's function properties. Besides we exploit the input-output relation to connect the output state of the field to the input one, this unveiling the role played by various classical electromagnetic dyadics in quantum optical scattering. We specialize the discussion to the most common situation where the object is initially not electromagnetically excited, with the ingoing electromagnetic state only containing s-polaritons, and we analyze the impact of the classical transmission and absorption dyadics on the transitions from ingoing to outgoing s-polariton and on the creation of outgoing e- and m-polaritons, respectively. Since the scattered radiation is collected in the far-field and the object is usually left unmeasured, we analytically derive the reduced density operator of the outgoing s-polaritons.

Figures

Figures reproduced from arXiv: 2411.18543 by the authors.

Figure 1
Figure 1. FIG. 1. Pictorial scketch of the MLNF portrayal of a macro [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Quantum optical scattering in the Heisenberg pic [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Role played by the classical dyadics in the quantum [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Basic scattering process [PITH_FULL_IMAGE:figures/full_fig_p012_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Ingoing [PITH_FULL_IMAGE:figures/full_fig_p015_5.png]

Discussion (0). Continue with ORCID to comment.

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Works this paper leans on

102 extracted references · 77 canonical work pages

  1. [86]

    Ciattoni, Quantum electrodynamics of lossy mag- netodielectric samples in vacuum: Modified Langevin noise formalism, Phys

    A. Ciattoni, Quantum electrodynamics of lossy mag- netodielectric samples in vacuum: Modified Langevin noise formalism, Phys. Rev. A 110, 013707 (2024)

    work page 2024

  2. [1]

    M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press (2010)

    2010

  3. [2]

    C. M. Caves, Quantum-mechanical noise in an interfer- ometer, Phys. Rev. D 23, 1693-1708 (1981)

    1981

  4. [3]

    C. M. Caves, Quantum limits on noise in linear ampli- fiers, Phys. Rev. D 26, 1817-1839 (1982)

    1982

  5. [4]

    Loudon, Quantum theory of combined first or- der/second order optical interference experiments, Opt

    R. Loudon, Quantum theory of combined first or- der/second order optical interference experiments, Opt. Commun. 45, 361-366 (1983)

    1983

  6. [5]

    Mandel, The problem of non-locality and simulta- neous photon detection behind a beam splitter, Phys

    L. Mandel, The problem of non-locality and simulta- neous photon detection behind a beam splitter, Phys. Lett. 103A, 416-418 (1984)

    1984

  7. [6]

    Ley and R

    M. Ley and R. Loudon, Optical amplification and inter- ference, Opt. Commun. 54, 317-322 (1985)

    1985

  8. [7]

    Ley and R

    M. Ley and R. Loudon, Theory of single-photon inter- ference experiments Opt. Acta 33, 371-380 (1986)

    1986

Show all 102 references
  1. [8]

    Prasad, M

    S. Prasad, M. O. Scully and W. Martienssen, A quan- tum description of the beam splitter, Opt. Commun. 62, 139-145 (1987)

    1987

  2. [9]

    Z. Y. Ou, C. K. Hong and L. Mandel, Relation between input and output states for a beam splitter, Opt. Com- mun. 63, 118-122 (1987)

    1987

  3. [10]

    Fearn and R

    H. Fearn and R. Loudon, Quantum theory of the lossless beam splitter, Opt. Commun. 64, 485-490 (1987)

    1987

  4. [11]

    Luis and L

    A. Luis and L. Sanchez-Soto, A quantum description of the beam splitter, Quantum Semiclass. Opt. 7, 153-160 (1995)

    1995

  5. [12]

    Makarov Theory for the Beam Splitter in Quantum Optics: Quantum Entanglement of Photons and Their Statistics, HOM Effect, Mathematics 10, 4794 (2022)

    D. Makarov Theory for the Beam Splitter in Quantum Optics: Quantum Entanglement of Photons and Their Statistics, HOM Effect, Mathematics 10, 4794 (2022)

    2022

  6. [13]

    Huttner and Y

    B. Huttner and Y. Ben-Aryeh, Influence of a beam splitter on photon statistics Phys. Rev. A 38, 204-211 (1988)

    1988

  7. [14]

    R. A. Campos, B. E. A. Saleh and M. C. Teich, Quantum-mechanical lossless beam splitter: SU(2) sym- metry and photon statistics, Phys. Rev. A 40, 1371- 1384 (1989)

    1989

  8. [15]

    C. K. Hong, Z. Y. Ou and L. Mandel, Measurement of subpicosecond time intervals between two photons by interference, Phys. Rev. Lett. 59, 2044-2046 (1987)

    1987

  9. [16]

    Fearn and R

    H. Fearn and R. Loudon, Theory of two-photon inter- ference, J. Opt. Soc. Am. B 6, No, 917-927 (1989)

    1989

  10. [17]

    Bouchard, A

    F. Bouchard, A. Sit, Y. Zhang, R. Fickler, F. M. Mi- atto, Y. Yao, F. Sciarrino and E. Karimi, Two-photon interference: the Hong–Ou–Mandel effect, Rep. Prog. Phys. 84, 012402 (2021)

    2021

  11. [18]

    M. S. Kim, W. Son, V. Buzek and P. L. Knight, Entan- glement by a beam splitter: Nonclassicality as a pre- requisite for entanglement, Phys. Rev. A 65, 032323 (2002)

    2002

  12. [19]

    Xiang-bin, Theorem for the beam-splitter entangler, Phys

    W. Xiang-bin, Theorem for the beam-splitter entangler, Phys. Rev. A 66, 024303 (2002)

    2002

  13. [20]

    Kn¨ oll, W

    L. Kn¨ oll, W. Vogel and D. G. Welsch, Action of passive, lossless optical systems in quantum optics, Phys. Rev. A 36, 3803-3818 (1987)

    1987

  14. [21]

    Ley and R

    M. Ley and R. Loudon, Quantum theory of high- resolution length measurement with a Fabry-Perot in- terferometer, J. Mod. Opt. 34, 227-255 (1987)

    1987

  15. [22]

    Savasta, O

    S. Savasta, O. Di Stefano and R. Girlanda, Three- dimensional quantum-optical input–output relations for arbitrary planar dielectrics J. Opt. Soc. Am. B 19 (2002)

    2002

  16. [23]

    Khanbekyan, L

    M. Khanbekyan, L. Kn¨ oll and D. G. Welsch, Input- output relations at dispersing and absorbing planar mul- tilayers for the quantized electromagnetic field contain- 38 ing evanescent components, Phys. Rev. A 67, 063812 (2003)

    2003

  17. [24]

    Atamana, The quantum optical description of a Fabry-Perot interferometer and the prediction of an an- tibunching effect, Eur

    S. Atamana, The quantum optical description of a Fabry-Perot interferometer and the prediction of an an- tibunching effect, Eur. Phys. J. D 69, 187 (2015)

    2015

  18. [25]

    D. N. Klyshko, Nonunitary transformations in quantum optics, Phys. Lett. A 137, 334-338 (1989)

    1989

  19. [26]

    Tischler, C

    N. Tischler, C. Rockstuhl and K. S lowik, Quantum Op- tical Realization of Arbitrary Linear Transformations Allowing for Loss and Gain, Phys. Rev. X 8, 021017 (2018)

    2018

  20. [27]

    S. M. Barnett, C. R. Gilson, B. Huttner and N. Imoto, Field Commutation Relations in Optical Cavities, Phys. Rev. Lett. 77, 1739-1742 (1996)

    1996

  21. [28]

    Gruner and D.-G

    T. Gruner and D.-G. Welsch, Quantum-optical input- output relations for dispersive and lossy multilayer di- electric plates Phys. Rev. A 54, 1661-1677 (1996)

    1996

  22. [29]

    S. M. Barnett, J. Jeffers and A. Gatti, Quantum op- tics of lossy beam splitters Phys. Rev. A 57, 2134-2145 (1998)

    1998

  23. [30]

    Kn¨ oll, S

    L. Kn¨ oll, S. Scheel, E. Schmidt, D. G. Welsch and A. V. Chizhov, Quantum-state transformation by dispersive and absorbing four-port devices, Phys. Rev. A 59, 4716- 4726 (1999)

    1999

  24. [31]

    Jeffers, Interference and the lossless lossy beam split- ter, J

    J. Jeffers, Interference and the lossless lossy beam split- ter, J. Mod. Opt. 47, 1819-1824 (2000)

    2000

  25. [32]

    Scheel, L

    S. Scheel, L. Kn¨ oll, T. Opatrny and D. G. Welsch, En- tanglement transformation at absorbing and amplifying four-port devices, Phys. Rev. A 62, 043803 (2000)

    2000

  26. [33]

    Scheel, T

    S. Scheel, T. Opatrny and D. G. Welsch, Entanglement Degradation of a Two-Mode Squeezed Vacuum in Ab- sorbing and Amplifying Optical Fibers, Opt. Spectrosc. 91, 411–417 (2001)

    2001

  27. [34]

    A. V. Chizhov, E. Schmidt, L. Kn¨ oll and D. G. Welsch, Propagation of entangled light pulses through dispersing and absorbing channels, J. Opt. B: Quantum Semiclass. Opt. 3, 77–83 (2001)

    2001

  28. [35]

    B. Vest, M. C. Dheur, E. Devaux, A. Baron, E. Rousseau, J. P. Hugonin, J. J. Greffet, G. Messin and F. Marquier, Anti-coalescence of bosons on a lossy beam splitter, Science 356, 1373–1376 (2017)

    2017

  29. [36]

    A. ¨U. C. Hardal and M. Wubs, Quantum coherent ab- sorption of squeezed light, Optica 6, 181-189 (2019)

    2019

  30. [37]

    P. K. Jha, N. Shitrit, J. Kim, X. Ren, Y. Wang and X. Zhang, Metasurface-Mediated Quantum Entanglement, ACS Photonics 5, 971-976 (2018)

    2018

  31. [38]

    K. Wang, J. G. Titchener, S. S. Kruk, L. Xu, H. P. Chung, M. Parry, I. I. Kravchenko, Y. H. Chen, A. S. Solntsev, Y. S. Kivshar, D. N. Neshev and A. A. Sukho- rukov, Quantum metasurface for multiphoton interfer- ence and state reconstruction, Science 361, 1104–1108 (2018)

    2018

  32. [39]

    Georgi, M

    P. Georgi, M. Massaro, K. H. Luo, B. Sain, N. Montaut, H. Herrmann, T. Weiss, G. Li, C. Silberhorn and T. Zentgraf, Metasurface interferometry toward quantum sensors, Light sci. appl. 8, 70 (2019)

    2019

  33. [40]

    Q. Li, W. Bao, Z. Nie, Y. Xia, Y. Xue, Y. Wang, S. Yang and X. Zhang, A non-unitary metasurface enables con- tinuous control of quantum photon–photon interactions from bosonic to fermionic, Nat. Photon 15, 267–271 (2021)

    2021

  34. [41]

    Santiago-Cruz1, S

    T. Santiago-Cruz1, S. D. Gennaro, O. Mitrofanov, S. Addamane, J. Reno, I. Brener and M. V. Chekhova, Resonant metasurfaces for generating complex quantum states, Science 377, 991–995 (2022)

    2022

  35. [42]

    A. S. Solntsev, G. S. Agarwal and Y. Kivshar, Metasur- faces for quantum photonics, Nat. Photon. 15, 327–336 (2021)

    2021

  36. [43]

    F. Ding, S. I. Bozhevolnyi Advances in quantum meta- optics

  37. [44]

    Zhang and Y

    J. Zhang and Y. Kivshar, Quantum metaphotonics: Recent advances and perspective, APL Quantum 1, 020902 (2024)

    2024

  38. [45]

    R. J. Glauber and M. Lewenstein, Quantum optics of dielectric media, Phys. Rev. A 43, 467-491 (1991)

    1991

  39. [46]

    B. J. Dalton, E. S. Guerra and P. L. Knight, Field quan- tization in dielectric media and the generalized multi- polar Hamiltonian, Phys. Rev. A 54, 2292-2313 (1996)

    1996

  40. [47]

    Fano, Atomic Theory of Electromagnetic Interac- tions in Dense Materials, Phys

    U. Fano, Atomic Theory of Electromagnetic Interac- tions in Dense Materials, Phys. Rev. 103, 1202-1218 (1956)

    1956

  41. [48]

    J. J. Hopfield, Theory of the Contribution of Excitons to the Complex Dielectric Constant of Crystals, Phys. Rev. 112, 1555-1567 (1958)

    1958

  42. [49]

    Huttner and S

    B. Huttner and S. M. Barnett, Dispersion and Loss in a Hopfield Dielectric, Europhys. Lett. 18, 487-492 (1992)

    1992

  43. [50]

    Huttner and S

    B. Huttner and S. M. Barnett, Quantization of the elec- tromagnetic field in dielectrics, Phys. Rev. A 46, 4306- 4322 (1992)

    1992

  44. [51]

    L. G. Suttorp and M. Wubs, Field quantization in in- homogeneous absorptive dielectrics, Phys. Rev. A 70, 013816 (2004)

    2004

  45. [52]

    L. G. Suttorp and A. J. van Wonderen, Fano diagonal- ization of a polariton model for an inhomogeneous ab- sorptive dielectric, Europhys. Lett. 67, 766–772 (2004)

    2004

  46. [53]

    Kheirandish and M

    F. Kheirandish and M. Soltani, Extension of the Huttner-Barnett model to a magnetodielectric medium, Phys. Rev. A 78, 012102 (2008)

    2008

  47. [54]

    Matloob, Electromagnetic field quantization in a lin- ear isotropic dielectric, Phys

    R. Matloob, Electromagnetic field quantization in a lin- ear isotropic dielectric, Phys. Rev. A 69, 052110 (2004)

    2004

  48. [55]

    Kheirandish and M

    F. Kheirandish and M. Amooshahi, Electromagnetic field quantization in a linear polarizable and magnetiz- able medium, Phys. Rev. A 74, 042102 (2006)

    2006

  49. [56]

    N. A. R. Bhat and J. E. Sipe, Hamiltonian treatment of the electromagnetic field in dispersive and absorptive structured media, Phys. Rev. A 73, 063808 (2006)

    2006

  50. [57]

    Amooshahi and F

    M. Amooshahi and F. Kheirandish, Electromagnetic field quantization in a magnetodielectric medium with external charges, Phys. Rev. A 76, 062103 (2007)

    2007

  51. [58]

    L. G. Suttorp, Field quantization in inhomogeneous anisotropic dielectrics with spatio-temporal dispersion, J. Phys. A: Math. Theor. 40, 3697–3719 (2007)

    2007

  52. [59]

    Amooshahia, Canonical quantization of electromag- netic field in an anisotropic polarizable and magnetiz- able medium, J

    M. Amooshahia, Canonical quantization of electromag- netic field in an anisotropic polarizable and magnetiz- able medium, J. Math. Phys. 50, 062301 (2009)

    2009

  53. [60]

    Gruner and D

    T. Gruner and D. G. Welsch, Green-function approach to the radiation-field quantization for homogeneous and inhomogeneous Kramers-Kronig dielectrics, Phys. Rev. A 53, 1818-1829 (1996)

    1996

  54. [61]

    Scheel, L

    S. Scheel, L. Kn¨ oll, and D. G. Welsch QED commu- tation relations for inhomogeneous Kramers-Kronig di- electrics, Phys. Rev. A 58, 700-706 (1998)

    1998

  55. [62]

    H. T. Dung, L. Kn¨ oll, and D. G. Welsch, Three- dimensional quantization of the electromagnetic field in dispersive and absorbing inhomogeneous dielectrics, Phys. Rev. A 57, 3931-3942 (1998)

    1998

  56. [63]

    Scheel and S

    S. Scheel and S. Y. Buhmann, Macroscopic quantum 39 electrodynamics - concepts and applications, Acta Phys. Slovaca 58, 675-809 (2008)

    2008

  57. [64]

    S. Y. Buhmann, D. T. Butcher and S. Scheel, Macro- scopic quantum electrodynamics in nonlocal and nonre- ciprocal media, New J. Phys. 14, 083034 (2012)

    2012

  58. [65]

    T. G. Philbin, Canonical quantization of macroscopic electromagnetism, New J. Phys. 12, 123008 (2010)

    2010

  59. [66]

    S. Y. Buhmann and D. G. Welsch, Casimir-Polder forces on excited atoms in the strong atom-field cou- pling regime, Phys. Rev. A 77, 012110 (2008)

    2008

  60. [67]

    S. Y. Buhmann, Dispersion Forces I: Macroscopic Quantum Electrodynamics and Ground-State Casimir, Casimir Polder and van der Waals Forces, Springer- Verlag, Berlin, Heidelberg (2012)

    2012

  61. [68]

    S. Y. Buhmann, Dispersion Forces II: Many-Body Ef- fects, Excited Atoms, Finite Temperature and Quantum Friction, Springer-Verlag, Berlin, Heidelberg (2012)

    2012

  62. [69]

    Scheel, L

    S. Scheel, L. Kn¨ oll, and D. G. Welsch and S. M. Barnett, Quantum local-field corrections and spontaneous decay, Phys. Rev. A 69, 1590-1597 (1999)

    1999

  63. [70]

    H. T. Dung, L. Kn¨ oll, and D. G. Welsch, Spontaneous decay in the presence of dispersing and absorbing bod- ies: General theory and application to a spherical cavity, Phys. Rev. A 62, 053804 (2000)

    2000

  64. [71]

    Rivera, I

    N. Rivera, I. Kaminer, B. Zhen, J. D. Joannopoulos and M. Soljaˇ ci´ c, Shrinking light to allow forbidden transi- tions on the atomic scale, Science 353, 263-269 (2016)

    2016

  65. [72]

    J. L. Hemmerich, R. Bennett, and S. Y. Buhmann, The influence of retardation and dielectric environments on interatomic Coulombic decay, Nat. Commun. 9, 2934 (2018)

    2018

  66. [73]

    Khanbekyan, L

    M. Khanbekyan, L. Kn¨ oll, D. G. Welsch, A. A. Semenov and W. Vogel, QED of lossy cavities: Operator and quantum-state input-output relations, Phys. Rev. A 72, 053813 (2005)

    2005

  67. [74]

    Khanbekyan, D

    M. Khanbekyan, D. G. Welsch, C. Di Fidio and W. Vogel, Cavity-assisted spontaneous emission as a single- photon source: Pulse shape and efficiency of one-photon Fock-state preparation, Phys. Rev. A78, 013822 (2008)

    2008

  68. [75]

    Dzsotjan, B

    D. Dzsotjan, B. Rousseaux, H. R. Jauslin, G. Colas des Francs, C. Couteau and S. Guerin, Mode-selective quan- tization and multimodal effective models for spherically layered systems, Phys. Rev. A 94, 023818 (2016)

    2016

  69. [76]

    Hakami, L

    J. Hakami, L. Wang and M. S. Zubairy, Spectral properties of a strongly coupled quantum-dot–metal- nanoparticle system, Phys. Rev. A 89, 053835 (2014)

    2014

  70. [77]

    Kurman and I

    Y. Kurman and I. Kaminer, Tunable bandgap renormal- ization by nonlocal ultra-strong coupling in nanopho- tonics, Nat. Phys. 16 , 868–874 (2020)

    2020

  71. [78]

    Feist, A

    J. Feist, A. I. Fern´ andez-Dom ´ ınguez and F. J. Garc ´ ıa- Vidal, Macroscopic QED for quantum nanophotonics: emitter-centered modes as a minimal basis for multi- emitter problems, Nanophotonics 10, 477–489 (2021)

    2021

  72. [79]

    Di Giulio, O

    V. Di Giulio, O. Kfir, C. Ropers and F. Javier Garc ´ ıa de Abajo, Modulation of Cathodoluminescence Emission by Interference with External Light, ACS Nano 2021 15, 7290-7304 (2021)

    2021

  73. [80]

    A. B. Hayun, O. Reinhardt, J. Nemirovsky, A. Karnieli, N. Rivera and I. Kaminer, Shaping quantum photonic states using free electrons, Sci. Adv. 7, eabe4270 (2021)

    2021

  74. [81]

    O. Kfir, V. Di Giulio, F. Javier Garc ´ ıa de Abajo and C. Ropers, Optical coherence transfer mediated by free electrons, Sci. Adv. 7, eabf6380 (2021)

    2021

  75. [82]

    Ciattoni, Fast Electrons Interacting with Chiral Mat- ter: Mirror-Symmetry Breaking of Quantum Decoher- ence and Lateral Momentum Transfer, Phys

    A. Ciattoni, Fast Electrons Interacting with Chiral Mat- ter: Mirror-Symmetry Breaking of Quantum Decoher- ence and Lateral Momentum Transfer, Phys. Rev. Appl. 19, 034086 (2023)

    2023

  76. [83]

    Ciattoni, Quantum interaction of subrelativistic aloof electrons with mesoscopic samples, Phys

    A. Ciattoni, Quantum interaction of subrelativistic aloof electrons with mesoscopic samples, Phys. Rev. B 107, 125403 (2023)

    2023

  77. [84]

    G. W. Hanson, F. Lindel, S. Y. Buhmann, The Langevin Noise Approach for Lossy Media and the Lossless Limit, J. Opt. Soc. Am. B 38, 758-768 (2021)

    2021

  78. [85]

    D. Y. Na, T. E. Roth , J. Zhu, W. C. Chew and C. J. Ryu, Numerical framework for modeling quantum elec- tromagnetic systems involving finite-sized lossy dielec- tric objects in free space, Phys. Rev. A 107, 063702 (2023)

    2023

  79. [87]

    Garrison and R

    J. Garrison and R. Chiao, Quantum Optics, Oxford Uni- versity Press (2008)

    2008

  80. [88]

    C. T. Tai, Dyadic Green Functions in Electromagnetic Theory IEEE Press (1994)

    1994

  81. [89]

    W. C. Chew, Waves and Fields in Inhomogenous Media, IEEE Press (1995)

    1995

  82. [90]

    Drezet, Equivalence between the Hamiltonian and Langevin noise descriptions of plasmon polaritons in a dispersive and lossy inhomogeneous medium, Phys

    A. Drezet, Equivalence between the Hamiltonian and Langevin noise descriptions of plasmon polaritons in a dispersive and lossy inhomogeneous medium, Phys. Rev. A 96, 033849 (2017)

    2017

  83. [91]

    Kristenssen, Scattering of Electromagnetic Waves by Obstacles, Scitech Publishing (2016)

    G. Kristenssen, Scattering of Electromagnetic Waves by Obstacles, Scitech Publishing (2016)

    2016

  84. [92]

    In that paper the expo- sition has been based on the scattering modes them- self Fωmλ (r) and the modal dyadics Fωs ( r| m) has not been introduced

    We wish to note that in the present paper the discussion of the classical scattering modes slightly departs from the one appearing in Ref.[86]. In that paper the expo- sition has been based on the scattering modes them- self Fωmλ (r) and the modal dyadics Fωs ( r| m) has not b...

  85. [93]

    Saxon, Tensor Scattering Matrix for the Electromag- netic Field, Phys

    D. Saxon, Tensor Scattering Matrix for the Electromag- netic Field, Phys. Rev. 100, 1771-1775 (1955)

    1955

  86. [94]

    Rother, Self-consistent Green’s function formalism for acoustic and light scattering

    T. Rother, Self-consistent Green’s function formalism for acoustic and light scattering. Part 3: Unitarity and symmetry, Opt. Commun. 266, 380–389 (2006)

    2006

  87. [95]

    Z domTωss ( n| m) · TT ∗ ωss ( n′| m) + X α=e,m Z d3sEωsα ( n| s) · ET ∗ ωsα ( n′| s) # , h ˆFων (r) , ˆF† ω′ν′ (r′) i = δ (ω − ω′)

    readily provides the relation Z d3r V· (∇ ×U) = Z d3r (∇ ×V) · U − Z S∞ dS ur · (V × U) (A7) where ur = r/r is the radial unit vectors and the surface integral is performed over the sphere S∞ of infinite radius by means of the limiting prescription R S∞ dS f= lim R→∞ R SR dS f...

  88. [96]

    R. P. Kanwal, Generalized Functions: Theory and Ap- plications 3rd ed., Birkh¨ auser, Boston (2004)

    2004

  89. [97]

    Born and E

    M. Born and E. Wolf, Principle of Optics, Cambridge University Press (2019)

    2019

  90. [98]

    Colton and R

    D. Colton and R. Kress, Eigenvalues of the Far Field Operator and Inverse Scattering Theory, SIAM J. Math. Anal. 26, 601-615 (1995)

    1995

  91. [99]

    Kirsch, Factorization of the far-field operator for the inhomogeneous medium case and an application in inverse scattering theory, Inverse Probl

    A. Kirsch, Factorization of the far-field operator for the inhomogeneous medium case and an application in inverse scattering theory, Inverse Probl. 15, 413–429 (1999)

    1999

  92. [100]

    Kirsch, The factorization method for Maxwell’s equa- tions, Inverse Probl

    A. Kirsch, The factorization method for Maxwell’s equa- tions, Inverse Probl. 20, S117–S134 (2004)

    2004

  93. [101]

    Colton and R

    D. Colton and R. Kress, Inverse Acoustic and Electro- magnetic Scattering Theory, Springer (2014)

    2014

  94. [102]

    Cohen-Tannoudji, B

    C. Cohen-Tannoudji, B. Diu and F. Lalo¨ e, Quantum Mechanics Volume III, Wiley-VCH (2020)

    2020

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