Abstract

We propose a new method for the directional excitation of surface plasmon polaritons by a metal nanoparticle antenna, based on the elliptical polarization of the normal modes of the antenna when it is in close proximity to a metallic substrate. The proposed theoretical model allows for the full characterization of the modes, giving the dipole configuration, frequency and lifetime. As a proof of principle, we have performed calculations for a dimer antenna and we report that surface plasmon polaritons can be excited in a given direction with an intensity of more than two orders of magnitude larger than in the opposite direction. Furthermore, using the fact that the response to any excitation can be written as a superposition of the normal modes, we show that this directionality can easily be accessed by exciting the system with a local source or a plane wave. Lastly, exploiting the interference between the normal modes, the directionality can be switched for a specific excitation. We envision the proposed mechanism to be a very useful tool for the design of antennas in layered media.

© 2016 Optical Society of America

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2015 (6)

Z. Dong, H.-S. Chu, D. Zhu, W. Du, Y. A. Akimov, W. P. Goh, T. Wang, K. E. J. Goh, C. Troadec, C. A. Nijhuis, and J. K. W. Yang, “Electrically-excited surface plasmon polaritons with directionality control,” ACS Photonics 2, 385 (2015).
[Crossref]

W. Yao, S. Liu, H. Liao, Z. Li, C. Sun, J. Chen, and Q. Gong, “Efficient directional excitation of surface plasmons by a single-element nanoantenna,” Nano Lett. 15, 3115 (2015).
[Crossref] [PubMed]

B. le Feber, N. Rotenburg, and K. Kuipers, “Nanophotonic control of circular dipole emission,” Nat. Commun. 6, 6695 (2015)
[Crossref] [PubMed]

K. Y. Bliokh, D. Smirnova, and F. Nori, “Quantum spin Hall effect of light,” Science 348, 1448 (2015).
[Crossref] [PubMed]

K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Nori, and A. V. Zayats, “Spin-orbit interactions of light,” Nat. Photonics 9, 796 (2015)
[Crossref]

P. J. Compaijen, V. A. Malyshev, and J. Knoester, “Engineering plasmon dispersion relations: hybrid nanoparticle chain-substrate plasmon polaritons,” Opt. Express 23, 2280 (2015).
[Crossref] [PubMed]

2014 (8)

R. Mitsch, C. Sayrin, B. Albrecht, P. Schneeweiss, and A. Rauschenbeutel, “Quantum state-controlled directional spontaneous emission of photons into a nanophotonic waveguide,” Nat. Comm. 5, 5713 (2014)
[Crossref]

J. Petersen, J. Volz, and A. Rauschenbeutel, “Chiral nanophotonic waveguide interface based on spin-orbit interaction of light,” Science 346, 67 (2014).
[Crossref] [PubMed]

A. Pors, M. G. Nielsen, T. Bernardin, J.-C. Weeber, and S. I. Bozhevolnyi, “Efficient unidirectional polarization-controlled excitation of surface plasmon polaritons,” Light: Sci. Appl. 3, e197 (2014).
[Crossref]

J. Yang, X. Xiao, C. Hu, W. Zhang, S. Zhou, and J. Zhang, “Broadband surface plasmon polariton directional coupling via asymmetric optical slot nanoantenna pair,” Nano Lett. 14, 704 (2014).
[Crossref] [PubMed]

D. Zhu, Z. Dong, H.-S. Chu, Y. A. Akimov, and J. K. W. Yang, “Image dipole method for the beaming of plasmons from point sources,” ACS Photonics 1, 1307 (2014).
[Crossref]

T. Coenen, F. Bernal Arango, A. F. Koenderink, and A. Polman, “Directional emission from a single plasmonic scatterer,” Nat. Commun. 5, 3250 (2014).
[Crossref] [PubMed]

M. Neugebauer, T. Bauer, P. Banzer, and G. Leuchs, “Polarization tailored light driven directional optical nanobeacon,” Nano Lett. 14, 2546 (2014)
[Crossref] [PubMed]

C. Lemke, T. Leissner, A. Evlyukhin, J. W. Radke, A. Klick, J. Fiutowski, J. Kjelstrup-Hansen, H.-G. Rubahn, B. N. Chichkov, C. Reinhardt, and M. Bauer, “The interplay between localized and propagating plasmonic excitations tracked in space and time,” Nano Lett. 14, 2431 (2014).
[Crossref] [PubMed]

2013 (6)

J. Munárriz, A. V. Malyshev, V. A. Malyshev, and J. Knoester, “Optical nanoantennas with tunable radiation patterns,” Nano Lett. 13, 444 (2013).
[Crossref] [PubMed]

J. Lin, J. P. B. Mueller, Q. Wang, G. Yuan, N. Antoniou, X.-C. Yuan, and F. Capasso, “Polarization-controlled tunable directional coupling of surface plasmon polaritons,” Science 340, 331 (2013).
[Crossref] [PubMed]

M. S. Tame, K. R. McEnery, K. Özdemir, J. Lee, S. A. Maier, and M. S. Kim, “Quantum plasmonics,” Nat. Phys. 9, 329 (2013).
[Crossref]

F. J. Rodríguez-Fortuño, G. Marino, P. Ginzburg, D. O’Connor, A. Martínez, G. A. Wurtz, and A. V. Zayats, “Near-field interference for the unidirectional excitation of electromagnetic guided modes,” Science 340, 328 (2013).
[Crossref] [PubMed]

J. P. B. Mueller and F. Capasso, “Asymmetric surface plasmon polariton emission by a dipole emitter near a metal surface,” Phys. Rev. B 88, 121410(R) (2013).
[Crossref]

P. J. Compaijen, V. A. Malyshev, and J. Knoester, “Surface-mediated light transmission in metal nanoparticle chains,” Phys. Rev. B 87, 205437 (2013).
[Crossref]

2012 (6)

K. Y. Bliokh and F. Nori, “Transverse spin of a surface polariton,” Phys. Rev. A 85, 061801(R) (2012)
[Crossref]

A. Farhang, S. A. Ramakrishna, and O. J. F. Martin, “Compound resonance-induced coupling effects in composite plasmonic metamaterials,” Opt. Express 20, 29447 (2012).
[Crossref]

N. Hartmann, G. Piredda, J. Berthelot, G. Colas Des Francs, A. Bouhelier, and A. Hartschuh, “Launching propagating surface plasmon polaritons by a single carbon nanotube dipolar emitter,” Nano Lett. 12, 177 (2012).
[Crossref]

R. S. Pavlov, A. G. Curto, and N. F. van Hulst, “Log-periodic optical antennas with broadband directivity,” Opt. Commun. 285, 3334 (2012).
[Crossref]

S.-Y. Lee, I.-M. Lee, J. Park, S. Oh, W. Lee, K.-Y. Kim, and B. Lee, “Role of magnetic currents in nanoslit excitation of surface plasmon polaritons,” Phys. Rev. Lett. 108, 213907 (2012).
[Crossref]

F. Bernal Arango, A. Kwadrin, and A. F. Koenderink, “Plasmonic antennas hybridized with dielectric waveguides,” ACS Nano 6, 10156 (2012).
[Crossref] [PubMed]

2011 (5)

L. Novotny and N. van Hulst, “Antennas for light,” Nat. Photonics 5, 83 (2011).
[Crossref]

T. Coenen, E. J. R. Vesseur, A. Polman, and A. F. Koenderink, “Directional emission from plasmonic Yagi-Uda antennas probed by angle-resolved cathodoluminescence spectroscopy,” Nano Lett. 11, 3779 (2011).
[Crossref] [PubMed]

N. J. Halas, S. Lal, W.-S. Chang, S. Link, and P. Nordlander, “Plasmons in strongly coupled metallic nanostructures,” Chem. Rev. 111, 3913 (2011).
[Crossref] [PubMed]

S. Campione, S. Steshenko, and F. Capolino, “Complex bound and leaky modes in chains of plasmonic nanospheres,” Opt. Express 19, 18345 (2011).
[Crossref] [PubMed]

A. L. Koh, A. I. Fernández-Domínguez, D. W. McComb, S. A. Maier, and J. K. W. Yang, “High-resolution mapping of electron-beam-excited plasmon modes in lithographically defined gold nanostructures,” Nano Lett. 11, 1323 (2011).
[Crossref] [PubMed]

2010 (2)

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9, 193 (2010).
[Crossref] [PubMed]

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4, 83 (2010).
[Crossref]

2009 (5)

A. F. Koenderink, “Plasmon nanoparticle array waveguides for single photon and single plasmon sources,” Nano Lett. 9, 4228 (2009).
[Crossref] [PubMed]

A. L. Falk, F. H. L. Koppens, C. L. Yu, K. Kang, N. de Leon Snapp, A. V. Akimov, M.-H. Jo, M. D. Lukin, and H. Park, “Near-field electrical detection of optical plasmons and single-plasmon sources,” Nat. Phys. 5, 475 (2009).
[Crossref]

M. W. Knight, Y. Wu, J. B. Lassiter, P. Nordlander, and N. J. Halas, “Substrates matter: influence of an adjacent dielectric on an individual plasmonic nanoparticle,” Nano Lett. 9, 2188 (2009).
[Crossref] [PubMed]

P. Bharadwaj, B. Deutsch, and L. Novotny, “Optical antennas,” Advances in Optics and Photonics 1, 438 (2009).
[Crossref]

D. Brunazzo, E. Descrovi, and O. J. F. Martin, “Narrowband optical interactions in a plasmonic nanoparticle chain coupled to a metallic film,” Opt. Lett. 34, 1405 (2009).
[Crossref] [PubMed]

2008 (2)

A. V. Malyshev, V. A. Malyshev, and J. Knoester, “Frequency-controlled localization of optical signals in graded plasmonic chains,” Nano Lett. 8, 2369 (2008).
[Crossref] [PubMed]

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for sub-wavelength confinement and long-range propagation,” Nat. Photonics 2, 496 (2008).
[Crossref]

2007 (6)

D. E. Chang, A. S. Sorensen, P. R. Hemmer, and M. D. Lukin, “Strong coupling of single emitters to surface plasmons,” Phys. Rev. B 76, 035420 (2007).
[Crossref]

R. de Waele, A. F. Koenderink, and A. Polman, “Tunable nanoscale localization of energy on plasmon particle arrays,” Nano Lett. 7, 2004 (2007).
[Crossref]

K. B. Crozier, E. Togan, E. Simsek, and T. Yang, “Experimental measurement of the dispersion relations of the surface plasmon modes of metal nanoparticle chains,” Opt. Express 15, 17482 (2007).
[Crossref] [PubMed]

A. F. Koenderink, R. de Waele, J. C. Prangsma, and A. Polman, “Experimental evidence for large dynamic effects on the plasmon dispersion of subwavelength metal nanoparticle waveguides,” Phys. Rev. B 76, 201403 (2007).
[Crossref]

M. Aeschlimann, M. Bauer, D. Bayer, T. Brixner, F. J. G. De Abajo, W. Pfeiffer, M. Rohmer, C. Spindler, and F. Steeb, “Adaptive sub-wavelength control of nanoscopic fields,” Nature 446, 301 (2007).
[Crossref] [PubMed]

V. A. Markel and A. K. Sarychev, “Propagation of surface plasmons in ordered and disordered chains of metal nanospheres,” Phys. Rev. B 75, 085426 (2007).
[Crossref]

2006 (6)

A. Alù and N. Engheta, “Theory of linear chains of metamaterial/plasmonic particles as subdiffraction optical nanotransmission lines,” Phys. Rev. B 74, 205436 (2006).
[Crossref]

A. F. Koenderink and A. Polman, “Complex response and polariton-like dispersion splitting in periodic metal nanoparticle chains,” Phys. Rev. B 74, 033402 (2006).
[Crossref]

G. Lévêque and O. J. F. Martin, “Optical interactions in a plasmonic particle coupled to a metallic film,” Opt. Express 14, 9971 (2006).
[Crossref] [PubMed]

A. B. Evlyukhin and S. I. Bozhevolnyi, “Surface plasmon polariton guiding by chains of nanoparticles,” Laser Phys. Lett. 3, 396 (2006).
[Crossref]

R. Zia, J. A. Schuller, A. Chandran, and M. L. Brongersma, “Plasmonics: the next chip-scale technology,” Mater. Today 9, 20 (2006).
[Crossref]

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189 (2006).
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N. Hartmann, G. Piredda, J. Berthelot, G. Colas Des Francs, A. Bouhelier, and A. Hartschuh, “Launching propagating surface plasmon polaritons by a single carbon nanotube dipolar emitter,” Nano Lett. 12, 177 (2012).
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R. de Waele, A. F. Koenderink, and A. Polman, “Tunable nanoscale localization of energy on plasmon particle arrays,” Nano Lett. 7, 2004 (2007).
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A. F. Koenderink, R. de Waele, J. C. Prangsma, and A. Polman, “Experimental evidence for large dynamic effects on the plasmon dispersion of subwavelength metal nanoparticle waveguides,” Phys. Rev. B 76, 201403 (2007).
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W. Yao, S. Liu, H. Liao, Z. Li, C. Sun, J. Chen, and Q. Gong, “Efficient directional excitation of surface plasmons by a single-element nanoantenna,” Nano Lett. 15, 3115 (2015).
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Tame, M. S.

M. S. Tame, K. R. McEnery, K. Özdemir, J. Lee, S. A. Maier, and M. S. Kim, “Quantum plasmonics,” Nat. Phys. 9, 329 (2013).
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Togan, E.

Troadec, C.

Z. Dong, H.-S. Chu, D. Zhu, W. Du, Y. A. Akimov, W. P. Goh, T. Wang, K. E. J. Goh, C. Troadec, C. A. Nijhuis, and J. K. W. Yang, “Electrically-excited surface plasmon polaritons with directionality control,” ACS Photonics 2, 385 (2015).
[Crossref]

van Hulst, N.

L. Novotny and N. van Hulst, “Antennas for light,” Nat. Photonics 5, 83 (2011).
[Crossref]

van Hulst, N. F.

R. S. Pavlov, A. G. Curto, and N. F. van Hulst, “Log-periodic optical antennas with broadband directivity,” Opt. Commun. 285, 3334 (2012).
[Crossref]

Vesseur, E. J. R.

T. Coenen, E. J. R. Vesseur, A. Polman, and A. F. Koenderink, “Directional emission from plasmonic Yagi-Uda antennas probed by angle-resolved cathodoluminescence spectroscopy,” Nano Lett. 11, 3779 (2011).
[Crossref] [PubMed]

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J. Petersen, J. Volz, and A. Rauschenbeutel, “Chiral nanophotonic waveguide interface based on spin-orbit interaction of light,” Science 346, 67 (2014).
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J. Lin, J. P. B. Mueller, Q. Wang, G. Yuan, N. Antoniou, X.-C. Yuan, and F. Capasso, “Polarization-controlled tunable directional coupling of surface plasmon polaritons,” Science 340, 331 (2013).
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Wang, T.

Z. Dong, H.-S. Chu, D. Zhu, W. Du, Y. A. Akimov, W. P. Goh, T. Wang, K. E. J. Goh, C. Troadec, C. A. Nijhuis, and J. K. W. Yang, “Electrically-excited surface plasmon polaritons with directionality control,” ACS Photonics 2, 385 (2015).
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W. H. Weber and G. W. Ford, “Propagation of optical excitations by dipolar interactions in metal nanoparticle chains,” Phys. Rev. B 70, 125429 (2004).
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A. Pors, M. G. Nielsen, T. Bernardin, J.-C. Weeber, and S. I. Bozhevolnyi, “Efficient unidirectional polarization-controlled excitation of surface plasmon polaritons,” Light: Sci. Appl. 3, e197 (2014).
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J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9, 193 (2010).
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F. J. Rodríguez-Fortuño, G. Marino, P. Ginzburg, D. O’Connor, A. Martínez, G. A. Wurtz, and A. V. Zayats, “Near-field interference for the unidirectional excitation of electromagnetic guided modes,” Science 340, 328 (2013).
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J. Yang, X. Xiao, C. Hu, W. Zhang, S. Zhou, and J. Zhang, “Broadband surface plasmon polariton directional coupling via asymmetric optical slot nanoantenna pair,” Nano Lett. 14, 704 (2014).
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Z. Dong, H.-S. Chu, D. Zhu, W. Du, Y. A. Akimov, W. P. Goh, T. Wang, K. E. J. Goh, C. Troadec, C. A. Nijhuis, and J. K. W. Yang, “Electrically-excited surface plasmon polaritons with directionality control,” ACS Photonics 2, 385 (2015).
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J. Lin, J. P. B. Mueller, Q. Wang, G. Yuan, N. Antoniou, X.-C. Yuan, and F. Capasso, “Polarization-controlled tunable directional coupling of surface plasmon polaritons,” Science 340, 331 (2013).
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J. Yang, X. Xiao, C. Hu, W. Zhang, S. Zhou, and J. Zhang, “Broadband surface plasmon polariton directional coupling via asymmetric optical slot nanoantenna pair,” Nano Lett. 14, 704 (2014).
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J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9, 193 (2010).
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L. Novotny and N. van Hulst, “Antennas for light,” Nat. Photonics 5, 83 (2011).
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Figures (7)

Fig. 1
Fig. 1 A schematic illustration of the considered system: a dimer of silver nanospheres with different sizes, embedded in medium 1, located above and parallel to a metallic substrate (medium 2). a1 and a2 are the radii of particle 1 and 2, respectively, d is the center-to-center spacing between the MNPs and h is the distance from the dimer to the substrate. Throughout this work, we will consider the metallic substrate to be silver and the embedding medium to be glass.
Fig. 2
Fig. 2 (a) SPP dispersion on the interface between silver and glass. Also indicated are: (i) the resonance frequency ωMNP of a silver MNP with a radius of a = 25 nm, (ii) the frequency of the surface plasmon resonance ωsp, (iii) the lightline in glass. (b) The modulus squared of the dipole moment of a silver MNP located in glass at h = 50 nm above the glass-silver interface, induced by a stationary z-polarized electric field of angular frequency ω. (c) Logarithmic plot of the square of the real part of the z-component of the electric field that is produced by the MNP is plotted in the xz-plane (y = 0) for an excitation frequency of ω = 4 rad/fs (highest peak in panel (b)). The system’s geometry is the same as in panel (b).
Fig. 3
Fig. 3 The modes of a dimer comprising two equal-size silver MNPs embedded in glass are shown, with (right) and without (left) the presence of a silver substrate, using a = 25, d = 90 and h = 50 nm. The black arrow indicates the dipole moment, while the dashed line represents the contour traced out by the dipole as a function of time. For each mode the complex normal mode frequency ω in units of rad/fs is also given.
Fig. 4
Fig. 4 (a) As in the right panel of Fig. 3, but now for an asymmetric dimer, with particle sizes a1 = 15 and a2 = 25 nm, respectively. The asymmetry and ellipticity of the modes are clearly seen from the arrows representing the dipole moments. (b) The intensity of the electric field generated as a function of x along the line y = 0, z = 5 nm by each of the modes depicted in (a). The modes are normalized and the intensity is scaled in such a way that the highest peak in mode 4 equals 1. All modes radiate more in the −x direction and this effect is the strongest for mode 4.
Fig. 5
Fig. 5 The radiation profiles of the asymmetric dimer are plotted. In both cases, the field produced by mode 4 of Fig. 4 is shown. (a) The square of the real part of the z-component of the electric field in the xz-plane. (b) The normalized electric field intensity profile on a plane parallel to the xy-plane, at a height of z = 5 nm above the substrate. Both pictures show a strong asymmetry along the x-axis, with an intensity contrast of a factor of 140 between x = +500 and x = −500 nm along the line y = 0 nm.
Fig. 6
Fig. 6 The normalized intensity of the field radiated by the asymmetric dimer as a response to two different excitations. 1 − z-polarized excitation on the smaller MNP only, with ω = 4.50 rad/fs; 2 - both particles excited by an equal z-polarized electric field at both particles, with ω = 4.85 rad/fs. The intensity is calculated along a line parallel to and at a height of 5 nm above the substrate, and with y = 0 nm.
Fig. 7
Fig. 7 A typical form of the integration path. The dotted lines represent the branch cuts corresponding to the glass medium and the silver substrate. The circle indicates the position of the singularity of rp, i.e. the SPP. The frequency considered here is ω = 4 − 0.6i.

Equations (9)

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1 α ( ω ) = ε M N P ( ω ) + 2 ε 1 ε M N P ( ω ) + ε 1 1 a 3 k 1 2 a 2 i 3 k 1 3 .
E ( r ) = k 1 2 ε 1 G ^ ( ω , r , r ) p ,
1 ε 1 ( 1 α 1 ( ω ) I ^ k 1 2 G ^ ( ω , r 1 , r 2 ) k 1 2 G ^ ( ω , r 2 , r 1 ) 1 α 2 ( ω ) I ^ ) ( p 1 p 2 ) = ( E 1 ext E 2 ext ) ,
G ^ H ( ω ; r , r ) = [ I ^ + k 1 2 ] exp ( i k 1 | r r | ) | r r | .
ε MNP = ε 2 = ε ( ω ) = 5.45 0.73 ω p 2 ( ω 2 + i ω γ ) ,
p = a 1 v 1 + a 2 v 2 ,
e i k 1 R R = i 0 d k ρ k ρ k 1 , z J 0 ( k ρ ρ ) e i k 1 , z | z | , k 1 , z = k 1 2 k ρ 2 .
r s = μ 2 k 1 , z μ 1 k 2 , z μ 2 k 1 , z μ 1 k 2 , z , r p = ε 2 k 1 , z ε 1 k 2 , z ε 2 k 1 , z ε 1 k 2 , z , k i , z = k i 2 k ρ 2 ,
G z z ref = i 0 k ρ 3 k 1 2 k 1 , z ( ε 2 k 1 , z ε 1 k 2 , z ε 2 k 1 , z ε 1 k 2 , z ) e i k 1 , z ( z + h ) d k ρ

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