Abstract

Molecular emitters located in an optical cavity are known to experience a dramatic modification of the energy and dynamics of their light emission, establishing novel routes for the generation of non-classical states of light. Under monochromatic illumination, spectral asymmetries in cavity-enhanced molecular fluorescence often emerge due to the formation of hybrid polaritonic states (upper and lower polaritons). By applying the theory of open-quantum systems, we show that under strong-coupling conditions, it is essential to account for the interaction of the molecular electronic states with their vibrational environment (dephasing reservoir) to address the complex dynamics of light emission. The interaction with the dephasing reservoir yields a transfer of energy between the polariton states, favoring the transition toward the lower polariton. As a result, we show that the inelastic light emission originates mainly from the lower polariton state regardless of the pumping laser frequency, thus producing asymmetric light emission spectra. Furthermore, we show that, when several molecules are considered, intermolecular coupling can break the symmetry of the system, enabling originally dark polaritons to emit light, as revealed in the fluorescence spectrum by the emergence of new emission peaks. These results stress that accounting for the interaction with dephasing reservoirs is key to interpret molecular light emission in cavities, consistent with experimental observations.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (7)

D. G. Baranov, M. Wersäll, J. Cuadra, T. J. Antosiewicz, and T. Shegai, “Novel nanostructures and materials for strong light–matter interactions,” ACS Photon. 5, 24–42 (2018).
[Crossref]

F. Herrera and F. C. Spano, “Theory of nanoscale organic cavities: the essential role of vibration-photon dressed states,” ACS Photon. 5, 65–79 (2018).
[Crossref]

M. A. Zeb, P. G. Kirton, and J. Keeling, “Exact states and spectra of vibrationally dressed polaritons,” ACS Photon. 5, 249–257 (2018).
[Crossref]

J.-J. Greffet, P. Bouchon, G. Brucoli, and F. Marquier, “Light emission by nonequilibrium bodies: local Kirchhoff law,” Phys. Rev. X 8, 021008 (2018).
[Crossref]

R. Sáez-Blázquez, J. Feist, A. I. Fernández-Domnguez, and F. J. Garca-Vidal, “Organic polaritons enable local vibrations to drive long-range energy transfer,” Phys. Rev. B 97, 241407 (2018).
[Crossref]

R. F. Ribeiro, L. A. Martínez-Martínez, M. Du, J. Campos-Gonzalez-Angulo, and J. Yuen-Zhou, “Polariton chemistry: controlling molecular dynamics with optical cavities,” Chem. Sci. 9, 6325–6339 (2018).
[Crossref]

M. Du, L. A. Martínez-Martínez, R. F. Ribeiro, Z. Hu, V. M. Menon, and J. Yuen-Zhou, “Theory for polariton-assisted remote energy transfer,” Chem. Sci. 9, 6659–6669 (2018).
[Crossref]

2017 (12)

J. Flick, C. Schäfer, M. Ruggenthaler, H. Appel, and A. Rubio, “Ab-initio optimized effective potentials for real molecules in optical cavities: photon contributions to the molecular ground state,” ACS Photon. 5, 992–1005 (2017).

Y. Sun, P. Wen, Y. Yoon, G. Liu, M. Steger, L. N. Pfeiffer, K. West, D. W. Snoke, and K. A. Nelson, “Bose–Einstein condensation of long-lifetime polaritons in thermal equilibrium,” Phys. Rev. Lett. 118, 016602 (2017).
[Crossref]

X. Zhong, T. Chervy, L. Zhang, A. Thomas, J. George, C. Genet, J. A. Hutchison, and T. W. Ebbesen, “Energy transfer between spatially separated entangled molecules,” Angew. Chem. (Int. Ed.) 56, 9034–9038 (2017).
[Crossref]

M. Wersäll, J. Cuadra, T. J. Antosiewicz, S. Balci, and T. Shegai, “Observation of mode splitting in photoluminescence of individual plasmonic nanoparticles strongly coupled to molecular excitons,” Nano Lett. 17, 551–558 (2017).
[Crossref]

T. Itoh, Y. S. Yamamoto, and Y. Ozaki, “Plasmon-enhanced spectroscopy of absorption and spontaneous emissions explained using cavity quantum optics,” Chem. Soc. Rev. 46, 3904–3921 (2017).
[Crossref]

B. Doppagne, M. C. Chong, E. Lorchat, S. Berciaud, M. Romeo, H. Bulou, A. Boeglin, F. Scheurer, and G. Schull, “Vibronic spectroscopy with submolecular resolution from STM-induced electroluminescence,” Phys. Rev. Lett. 118, 127401 (2017).
[Crossref]

L. Zhang, Y.-J. Yu, L.-G. Chen, Y. Luo, B. Yang, F.-F. Kong, G. Chen, Y. Zhang, Q. Zhang, Y. Luo, J. L. Yang, Z.-C. Dong, and J. G. Hou, “Electrically driven single-photon emission from an isolated single molecule,” Nat. Commun. 8, 580 (2017).
[Crossref]

Y. Zhang, Q.-S. Meng, L. Zhang, Y. Luo, Y.-J. Yu, B. Yang, Y. Zhang, R. Esteban, J. Aizpurua, Y. Luo, J. L. Yang, Z.-C. Dong, and J. G. Hou, “Sub-nanometre control of the coherent interaction between a single molecule and a plasmonic nanocavity,” Nat. Commun. 8, 15225 (2017).
[Crossref]

H. Imada, K. Miwa, M. Imai-Imada, S. Kawahara, K. Kimura, and Y. Kim, “Single-molecule investigation of energy dynamics in a coupled plasmon–exciton system,” Phys. Rev. Lett. 119, 013901 (2017).
[Crossref]

F. Herrera and F. C. Spano, “Absorption and photoluminescence in organic cavity QED,” Phys. Rev. A 95, 053867 (2017).
[Crossref]

R. Sáez-Blázquez, J. Feist, A. I. Fernández-Domínguez, and F. J. García-Vidal, “Enhancing photon correlations through plasmonic strong coupling,” Optica 4, 1363–1367 (2017).
[Crossref]

F. Herrera and F. C. Spano, “Dark vibronic polaritons and the spectroscopy of organic microcavities,” Phys. Rev. Lett. 118, 223601 (2017).
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2016 (10)

J. Galego, F. J. Garcia-Vidal, and J. Feist, “Suppressing photochemical reactions with quantized light fields,” Nat. Commun. 7, 13841 (2016).
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R. Chikkaraddy, B. de Nijs, F. Benz, S. J. Barrow, O. A. Scherman, E. Rosta, A. Demetriadou, P. Fox, O. Hess, and J. J. Baumberg, “Single-molecule strong coupling at room temperature in plasmonic nanocavities,” Nature 535, 127–130 (2016).
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2015 (7)

A. Canaguier-Durand, C. Genet, A. Lambrecht, T. W. Ebbesen, and S. Reynaud, “Non-Markovian polariton dynamics in organic strong coupling,” Eur. Phys. J. D 69, 24 (2015).
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K. Roy-Choudhury and S. Hughes, “Spontaneous emission from a quantum dot in a structured photonic reservoir: phonon-mediated breakdown of Fermi’s golden rule,” Optica 2, 434–437 (2015).
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J. del Pino, J. Feist, and F. J. Garcia-Vidal, “Quantum theory of collective strong coupling of molecular vibrations with a microcavity mode,” New J. Phys. 17, 053040 (2015).
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G. Zengin, M. Wersäll, S. Nilsson, T. J. Antosiewicz, M. Käll, and T. Shegai, “Realizing strong light–matter interactions between single-nanoparticle plasmons and molecular excitons at ambient conditions,” Phys. Rev. Lett. 114, 157401 (2015).
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P. Törmä and W. L. Barnes, “Strong coupling between surface plasmon polaritons and emitters: a review,” Rep. Prog. Phys. 78, 013901 (2015).
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J. George, S. Wang, T. Chervy, A. Canaguier-Durand, G. Schaeffer, J.-M. Lehn, J. A. Hutchison, C. Genet, and T. W. Ebbesen, “Ultra-strong coupling of molecular materials: spectroscopy and dynamics,” Faraday Discuss. 178, 281–294 (2015).
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J. Galego, F. J. Garcia-Vidal, and J. Feist, “Cavity-induced modifications of molecular structure in the strong-coupling regime,” Phys. Rev. X 5, 041022 (2015).
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2014 (8)

A. Delga, J. Feist, J. Bravo-Abad, and F. J. Garcia-Vidal, “Quantum emitters near a metal nanoparticle: strong coupling and quenching,” Phys. Rev. Lett. 112, 253601 (2014).
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T. J. Antosiewicz, S. P. Apell, and T. Shegai, “Plasmon–exciton interactions in a core–shell geometry: from enhanced absorption to strong coupling,” ACS Photon. 1, 454–463 (2014).
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G. M. Akselrod, C. Argyropoulos, T. B. Hoang, C. Ciracì, C. Fang, J. Huang, D. R. Smith, and M. H. Mikkelsen, “Probing the mechanisms of large Purcell enhancement in plasmonic nanoantennas,” Nat. Photonics 8, 835–840 (2014).
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J. D. Plumhof, T. Stöferle, L. Mai, U. Scherf, and R. F. Mahrt, “Room-temperature Bose–Einstein condensation of cavity exciton–polaritons in a polymer,” Nat. Mater. 13, 247–252 (2014).
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2013 (9)

T. Schwartz, J. A. Hutchison, J. Léonard, C. Genet, S. Haacke, and T. W. Ebbesen, “Polariton dynamics under strong light–molecule coupling,” Chem. Phys. Chem. 14, 125–131 (2013).
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A. Kell, X. Feng, M. Reppert, and R. Jankowiak, “On the shape of the phonon spectral density in photosynthetic complexes,” J. Phys. Chem. B 117, 7317–7323 (2013).
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A. Canaguier-Durand, E. Devaux, J. George, Y. Pang, J. A. Hutchison, T. Schwartz, C. Genet, N. Wilhelms, J.-M. Lehn, and T. W. Ebbesen, “Thermodynamics of molecules strongly coupled to the vacuum field,” Angew. Chem. (Int. Ed.) 52, 10533–10536 (2013).
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N. Christogiannis, N. Somaschi, P. Michetti, D. M. Coles, P. G. Savvidis, P. G. Lagoudakis, and D. G. Lidzey, “Characterizing the electroluminescence emission from a strongly coupled organic semiconductor microcavity led,” Adv. Opt. Mater. 1, 503–509 (2013).
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S. Kéa-Cohen, S. A. Maier, and D. D. C. Bradley, “Ultrastrongly coupled exciton–polaritons in metal-clad organic semiconductor microcavities,” Adv. Opt. Mater. 1, 827–833 (2013).
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P. Vasa, W. Wang, R. Pomraenke, M. Lammers, M. Maiuri, C. Manzoni, G. Cerullo, and C. Lienau, “Real-time observation of ultrafast Rabi oscillations between excitons and plasmons in metal nanostructures with J-aggregates,” Nat. Photonics 7, 128–132 (2013).
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G. Zengin, G. Johansson, P. Johansson, T. J. Antosiewicz, M. Käll, and T. Shegai, “Approaching the strong coupling limit in single plasmonic nanorods interacting with J-aggregates,” Sci. Rep. 3, 3074 (2013).
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2012 (5)

A. Salomon, R. J. Gordon, Y. Prior, T. Seideman, and M. Sukharev, “Strong coupling between molecular excited states and surface plasmon modes of a slit array in a thin metal film,” Phys. Rev. Lett. 109, 073002 (2012).
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J. Roden, W. T. Strunz, K. B. Whaley, and A. Eisfeld, “Accounting for intra-molecular vibrational modes in open quantum system description of molecular systems,” J. Chem. Phys. 137, 204110 (2012).
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C. Kreisbeck and T. Kramer, “Long-lived electronic coherence in dissipative exciton dynamics of light-harvesting complexes,” J. Phys. Chem. Lett. 3, 2828–2833 (2012).
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G. Tosi, G. Christmann, N. Berloff, P. Tsotsis, T. Gao, Z. Hatzopoulos, P. Savvidis, and J. Baumberg, “Sculpting oscillators with light within a nonlinear quantum fluid,” Nat. Phys. 8, 190–194 (2012).
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J. A. Hutchison, T. Schwartz, C. Genet, E. Devaux, and T. W. Ebbesen, “Modifying chemical landscapes by coupling to vacuum fields,” Angew. Chem. (Int. Ed.) 51, 1592–1596 (2012).
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2011 (5)

C. Roy and S. Hughes, “Influence of electron–acoustic-phonon scattering on intensity power broadening in a coherently driven quantum-dot–cavity system,” Phys. Rev. X 1, 021009 (2011).

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2008 (2)

A. Trügler and U. Hohenester, “Strong coupling between a metallic nanoparticle and a single molecule,” Phys. Rev. B 77, 115403 (2008).
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2007 (1)

R. Balili, V. Hartwell, D. Snoke, L. Pfeiffer, and K. West, “Bose–Einstein condensation of microcavity polaritons in a trap,” Science 316, 1007–1010 (2007).
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2006 (2)

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szymańska, R. André, J. L. Staehli, V. Savona, P. B. Littlewood, B. Deveaud, and L. S. Dang, “Bose–Einstein condensation of exciton polaritons,” Nature 443, 409–414 (2006).
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2005 (3)

J. Dintinger, S. Klein, F. Bustos, W. L. Barnes, and T. W. Ebbesen, “Strong coupling between surface plasmon–polaritons and organic molecules in subwavelength hole arrays,” Phys. Rev. B 71, 035424 (2005).
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P. Michetti and G. C. La Rocca, “Polariton states in disordered organic microcavities,” Phys. Rev. B 71, 115320 (2005).
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J. Bellessa, C. Bonnand, J. C. Plenet, and J. Mugnier, “Strong coupling between surface plasmons and excitons in an organic semiconductor,” Phys. Rev. Lett. 93, 036404 (2004).
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2003 (1)

V. M. Agranovich, M. Litinskaia, and D. G. Lidzey, “Cavity polaritons in microcavities containing disordered organic semiconductors,” Phys. Rev. B 67, 085311 (2003).
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2002 (3)

P. A. Hobson, W. L. Barnes, D. G. Lidzey, G. A. Gehring, D. M. Whittaker, M. S. Skolnick, and S. Walker, “Strong exciton–photon coupling in a low-Q all-metal mirror microcavity,” Appl. Phys. Lett. 81, 3519–3521 (2002).
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1999 (1)

D. G. Lidzey, D. D. C. Bradley, T. Virgili, A. Armitage, M. S. Skolnick, and S. Walker, “Room temperature polariton emission from strongly coupled organic semiconductor microcavities,” Phys. Rev. Lett. 82, 3316–3319 (1999).
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1998 (1)

D. G. Lidzey, D. Bradley, M. Skolnick, T. Virgili, S. Walker, and D. Whittaker, “Strong exciton–photon coupling in an organic semiconductor microcavity,” Nature 395, 53–55 (1998).
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Supplementary Material (1)

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» Supplement 1       Supplementary material completing information of the main text

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Figures (4)

Fig. 1.
Fig. 1. Effect of dephasing processes on the light emission from a cavity mode strongly coupled with a single exciton. (a) Schematic representation of a molecule interacting with its dephasing bath containing internal molecular vibrations but also environmental degrees of freedom such as fluctuating polarization of the solvent molecules. The bath modes are represented by bosonic annihilation operators Bi. (b) Schematic-level diagrams of an exciton in a cavity that is decoupled (left) and after the coupling is turned on (right) within the MBM. The cavity–exciton coupling gives rise to new polariton states, |+ and |, and opens new incoherent decay paths between |+ and | with respective rates of γσ+>γσ+. (c) Level diagram indicating the incoherent population transfer between the polariton states as in panel (b) but for the JCM where the rates γσ+ and γσ+ are equal (γσ+=γσ+=sin2θcos2θγϕ). (d) The bath spectral density J(ω) is given by Eq. (22) for the parameters γR=400  meV, ΩR=400  meV, and dR=0.173 [for which J(0)20  meV]. Calculations of selected emission and absorption spectra for smaller values of ΩR are shown in Supplement 1. The vertical lines indicate the positions where the spectral density is evaluated to obtain the values of the Markovian decay rates γσ+, γσ+, and γϕ.
Fig. 2.
Fig. 2. Photon emission spectra normalized to the incident laser intensity |E|2 as a function of excitation frequency ωL within (a) the explicit-bath model, (b) the Markovian-bath model, and (c) the Jaynes–Cummings model. In all the calculations, we have considered the parameters ω0=ωc=2  eV, γa=150  meV, γσ=2×102  meV, and g=100  meV. The pure dephasing constant for JCM is γϕ=J(0). The parameters of the bath are γB=400  meV, ΩR=400  meV, and dR=0.173.
Fig. 3.
Fig. 3. (a) Schematic representation of the polariton incoherent dynamics obtained from the full model. The strong coupling leads to formation of bright upper, |+, and lower, |, polaritons that are decoupled from the dark states, |Di. The coupling of the polariton and the dark states with the dephasing reservoir gives rise to the incoherent transfer of populations from the higher energy states to the lower energy states. The bare cavity incoherently decays with rate γa, the excitons of the bare molecules incoherently decay with rates γσi=γσ. The bright polariton states |+ and | then experience the incoherent decay into the ground state |0 with rates γS+ and γS, respectively. The dark polaritons decay to the ground state with equal rates γSD=γσ. Finally, population transfer among the polariton branches occurs with rates γSDS+, γSSD, and γSS+, as marked in the schematic. The population transfer is accompanied by dephasing processes (not shown). (b) Emission (black line) and absorption (blue dashed line) spectra of four molecular excitons (N=4) coupled to the cavity mode. The emission from | prevails over the |+ emission due to the incoherent population transfer caused by the dephasing reservoir. The absorption spectrum, on the other hand, contains both |+ and | peaks of similar intensity. Last, the emission and absorption spectra each contain a peak appearing close to the frequency of the decoupled molecules that arises from the dark polariton states |Di that are now coupled to the bright polaritons |+ and |. [(c)–(f)] Emission spectra as a function of excitation energy ωL for N=2,3,4,5  molecules, respectively. In all the cases, (b)–(f) show that the molecular excitons of equal energies ω0=2  eV are perfectly tuned to the cavity resonance ωc=2  eV and interact with the cavity mode via gi=g=100  meV. The system is pumped by a laser of amplitude E=0.1  meV. Additional parameters are γa=150  meV, γB=400  meV, γσ=2×102  meV, d=0.173, and ΩR=400  meV.
Fig. 4.
Fig. 4. Decay of polariton populations, n+ (upper polariton—black), n (lower polariton—red), and nD (dark polariton—blue), on a logarithmic scale as a function of time assuming that initially n+=1 and n=nD=0. (a) The full calculation (EBM—dashed lines) is compared with the REM (full lines) for N=4 molecules and g=100  meV. (b) The populations calculated from the REM for N=1000 molecules, using Ng=200  meV. The remaining parameters are γa=150  meV, γB=400  meV, γσ=2×102  meV, d=0.173, and ΩR=400  meV.

Equations (32)

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He,i=ω0σiσi,
Hres,i=ΩRBiBi,
Heres,i=dRΩRσiσi(Bi+Bi).
Hee=ijGijσiσj+H.c.,
Hc=ωcaa,
Hec,i=giσia+H.c.,
Htot=Hc+Hee+i(He,i+Hres,i+Heres,i+Hec,i).
ρ˙=1i[Htot,ρ]+iLOi(ρ),
|+=cosθ|e,0+sinθ|g,1,|=sinθ|e,0+cosθ|g,1,
tan(2θ)=2gω0ωcand0<2θ<π.
σσ|22|=cos2θ|++|+sin2θ||sinθcosθ(|+|+|+|).
Heres=dRΩRσσ(B+B)=σσF=[cos2θσ+++sin2θσsinθcosθ(σ++σ+)]F,
σ+=σ+(0)ei(ω+ω)t,
σ+=σ+(0)ei(ωω+)t,
σ++=σ++(0),
σ=σ(0),
ω±=ω0+ωc2±g2+(ω0ωc)24
γσ+=cos2θsin2θJ(ω+ω),
γσ+=cos2θsin2θJ(ωω+),
γϕ=J(0).
J(ω)=2R{0dseiωsF(t+s)F(t)},
J(ω)=2γBdR2ΩR2(ΩRω)2+γB2.
γσ+=γasin2θ,
γσ=γacos2θ,
asinθσ++cosθσ,
La(ρ)Lσ+(ρ)+Lσ(ρ).
Lσσ(ρ)=γϕ2(2σσρσσ{σσ,ρ}).
Hpump=E(aeiωLt+aeiωLt),
sA(ω)=2R0a(τ)a(0)sseiωτdτ,
sE(ω;ωL)=2R0a(τ)a(0)sseiωτdτ,
Gij=G0|ij|3for  ijandGij=0for  i=j,
G0=p024πϵ0r03,