Abstract

We study the coupling between photonic molecules and waveguides in photonic crystal slab structures using finite-difference time-domain method and coupled mode theory. In a photonic molecule with two cavities, the coupling of cavity modes results in two super-modes with symmetric and anti-symmetric field distributions. When two super-modes are excited simultaneously, the energy of electric field oscillates between the two cavities. To excite and probe the energy oscillation, we integrate photonic molecule with two photonic crystal waveguides. In coupled structure, we find that the quality factors of two super-modes might be different because of different field distributions of super-modes. After optimizing the radii of air holes between two cavities of photonic molecule, nearly equal quality factors of two super-modes are achieved, and coupling strengths between the waveguide modes and two super-modes are almost the same. In this case, complete energy oscillations between two cavities can be obtained with a pumping source in one waveguide, which can be read out by another waveguide. Finally, we demonstrate that the designed structure can be used for ultrafast optical switching with a time scale of a few picoseconds.

© 2015 Optical Society of America

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References

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2013 (2)

2012 (2)

K. Mnaymneh, S. Frédérick, D. Dalacu, J. Lapointe, P. J. Poole, and R. L. Williams, “Enhanced photonic crystal cavity-waveguide coupling using local slow-light engineering,” Opt. Lett. 37(2), 280–282 (2012).
[Crossref] [PubMed]

Y. Sato, Y. Tanaka, J. Upham, Y. Takahashi, T. Asano, and S. Noda, “Strong coupling between distant photonic nanocavities and its dynamic control,” Nat. Photonics 6(1), 56–61 (2012).
[Crossref]

2010 (3)

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[Crossref]

X. Xu, H. Baker, and D. A. Williams, “Highly Sensitive, Photon Number Resolving Detectors Mediated by Phonons Using δ-doped GaAs Transistors,” Nano Lett. 10(4), 1364–1368 (2010).
[Crossref] [PubMed]

X. Yang, X. Xu, X. Wang, H. Ni, Q. Han, Z. Niu, and D. A. Williams, “Optically controlled quantum dot gated transistors with high on/off ratio,” Appl. Phys. Lett. 96(8), 083503 (2010).
[Crossref]

2009 (1)

R. H. Hadfield, “Single-photon detectors for optical quantum information applications,” Nat. Photonics 3(12), 696–705 (2009).
[Crossref]

2008 (4)

X. Xu, F. Brossard, K. Hammura, D. A. Williams, B. Alloing, L. Li, and A. Fiore, ““Plug and Play” single photons at 1.3 μm approaching gigahertz operation,” Appl. Phys. Lett. 93(2), 021124 (2008).
[Crossref]

H. J. Kimble, “The quantum internet,” Nature 453(7198), 1023–1030 (2008).
[Crossref] [PubMed]

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320(5876), 646–649 (2008).
[Crossref] [PubMed]

K. A. Atlasov, K. F. Karlsson, A. Rudra, B. Dwir, and E. Kapon, “Wavelength and loss splitting in directly coupled photonic-crystal defect microcavities,” Opt. Express 16(20), 16255–16264 (2008).
[Crossref] [PubMed]

2007 (5)

A. Faraon, E. Waks, D. Englund, I. Fushman, and J. Vučković, “Efficient photonic crystal cavity-waveguide couplers,” Appl. Phys. Lett. 90(7), 073102 (2007).
[Crossref]

D. Englund, A. Faraon, B. Zhang, Y. Yamamoto, and J. Vucković, “Generation and transfer of single photons on a photonic crystal chip,” Opt. Express 15(9), 5550–5558 (2007).
[Crossref] [PubMed]

J. Topolancik, B. Ilic, and F. Vollmer, “Experimental Observation of Strong Photon Localization in Disordered Photonic Crystal Waveguides,” Phys. Rev. Lett. 99(25), 253901 (2007).
[Crossref] [PubMed]

X. Xu, I. Toft, R. T. Phillips, J. Mar, K. Hammura, and D. A. Williams, ““Plug and play” single-photon sources,” Appl. Phys. Lett. 90(6), 061103 (2007).
[Crossref]

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445(7130), 896–899 (2007).
[Crossref] [PubMed]

2005 (1)

2004 (3)

W. Bogaerts, D. Taillaert, B. Luyssaert, P. Dumon, J. Van Campenhout, P. Bienstman, D. Van Thourhout, R. Baets, V. Wiaux, and S. Beckx, “Basic structures for photonic integrated circuits in silicon-on-insulator,” Opt. Express 12(8), 1583–1591 (2004).
[Crossref] [PubMed]

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432(7014), 200–203 (2004).
[Crossref] [PubMed]

X. Xu, D. Williams, and J. Cleaver, “Electrically pumped single-photon sources in lateral pin junctions,” Appl. Phys. Lett. 85(15), 3238–3240 (2004).
[Crossref]

2003 (5)

X. Li, Y. Wu, D. Steel, D. Gammon, T. H. Stievater, D. S. Katzer, D. Park, C. Piermarocchi, and L. J. Sham, “An all-optical quantum gate in a semiconductor quantum dot,” Science 301(5634), 809–811 (2003).
[Crossref] [PubMed]

K. J. Vahala, “Optical microcavities,” Nature 424(6950), 839–846 (2003).
[Crossref] [PubMed]

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003).
[Crossref] [PubMed]

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “Investigation of high-Q channel drop filters using donor-type defects in two-dimensional photonic crystal slabs,” Appl. Phys. Lett. 83(8), 1512–1514 (2003).
[Crossref]

S. McNab, N. Moll, and Y. Vlasov, “Ultra-low loss photonic integrated circuit with membrane-type photonic crystal waveguides,” Opt. Express 11(22), 2927–2939 (2003).
[Crossref] [PubMed]

1999 (1)

A. Imamoğlu, D. D. Awschalom, G. Burkard, D. P. DiVincenzo, D. Loss, M. Sherwin, and A. Small, “Quantum information processing using quantum dot spins and cavity QED,” Phys. Rev. Lett. 83(20), 4204–4207 (1999).
[Crossref]

1998 (2)

S. Fan, P. Villeneuve, J. Joannopoulos, and H. Haus, “Channel drop filters in photonic crystals,” Opt. Express 3(1), 4–11 (1998).
[Crossref] [PubMed]

M. Bayer, T. Gutbrod, J. Reithmaier, A. Forchel, T. Reinecke, P. Knipp, A. Dremin, and V. Kulakovskii, “Optical modes in photonic molecules,” Phys. Rev. Lett. 81(12), 2582–2585 (1998).
[Crossref]

1997 (1)

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature 386(6621), 143–149 (1997).
[Crossref]

1996 (1)

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77(18), 3787–3790 (1996).
[Crossref] [PubMed]

1994 (1)

R. D. Meade, A. Devenyi, J. Joannopoulos, O. Alerhand, D. Smith, and K. Kash, “Novel applications of photonic band gap materials: Low‐loss bends and high Q cavities,” J. Appl. Phys. 75(9), 4753–4755 (1994).
[Crossref]

1991 (1)

H. Haus and W. Huang, “Coupled-mode theory,” Proc. IEEE 79(10), 1505–1518 (1991).
[Crossref]

Akahane, Y.

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003).
[Crossref] [PubMed]

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “Investigation of high-Q channel drop filters using donor-type defects in two-dimensional photonic crystal slabs,” Appl. Phys. Lett. 83(8), 1512–1514 (2003).
[Crossref]

Alerhand, O.

R. D. Meade, A. Devenyi, J. Joannopoulos, O. Alerhand, D. Smith, and K. Kash, “Novel applications of photonic band gap materials: Low‐loss bends and high Q cavities,” J. Appl. Phys. 75(9), 4753–4755 (1994).
[Crossref]

Alloing, B.

X. Xu, F. Brossard, K. Hammura, D. A. Williams, B. Alloing, L. Li, and A. Fiore, ““Plug and Play” single photons at 1.3 μm approaching gigahertz operation,” Appl. Phys. Lett. 93(2), 021124 (2008).
[Crossref]

Asano, T.

Y. Sato, Y. Tanaka, J. Upham, Y. Takahashi, T. Asano, and S. Noda, “Strong coupling between distant photonic nanocavities and its dynamic control,” Nat. Photonics 6(1), 56–61 (2012).
[Crossref]

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “Investigation of high-Q channel drop filters using donor-type defects in two-dimensional photonic crystal slabs,” Appl. Phys. Lett. 83(8), 1512–1514 (2003).
[Crossref]

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003).
[Crossref] [PubMed]

Atatüre, M.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445(7130), 896–899 (2007).
[Crossref] [PubMed]

Atlasov, K. A.

Awschalom, D. D.

A. Imamoğlu, D. D. Awschalom, G. Burkard, D. P. DiVincenzo, D. Loss, M. Sherwin, and A. Small, “Quantum information processing using quantum dot spins and cavity QED,” Phys. Rev. Lett. 83(20), 4204–4207 (1999).
[Crossref]

Badolato, A.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445(7130), 896–899 (2007).
[Crossref] [PubMed]

Baets, R.

Baker, H.

X. Xu, H. Baker, and D. A. Williams, “Highly Sensitive, Photon Number Resolving Detectors Mediated by Phonons Using δ-doped GaAs Transistors,” Nano Lett. 10(4), 1364–1368 (2010).
[Crossref] [PubMed]

Bayer, M.

M. Bayer, T. Gutbrod, J. Reithmaier, A. Forchel, T. Reinecke, P. Knipp, A. Dremin, and V. Kulakovskii, “Optical modes in photonic molecules,” Phys. Rev. Lett. 81(12), 2582–2585 (1998).
[Crossref]

Beckx, S.

Bermel, P.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[Crossref]

Bienstman, P.

Bogaerts, W.

Brossard, F.

X. Xu, F. Brossard, K. Hammura, D. A. Williams, B. Alloing, L. Li, and A. Fiore, ““Plug and Play” single photons at 1.3 μm approaching gigahertz operation,” Appl. Phys. Lett. 93(2), 021124 (2008).
[Crossref]

Brossard, F. S.

Burkard, G.

A. Imamoğlu, D. D. Awschalom, G. Burkard, D. P. DiVincenzo, D. Loss, M. Sherwin, and A. Small, “Quantum information processing using quantum dot spins and cavity QED,” Phys. Rev. Lett. 83(20), 4204–4207 (1999).
[Crossref]

Chan, C. C.

Chen, J. C.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77(18), 3787–3790 (1996).
[Crossref] [PubMed]

Cleaver, J.

X. Xu, D. Williams, and J. Cleaver, “Electrically pumped single-photon sources in lateral pin junctions,” Appl. Phys. Lett. 85(15), 3238–3240 (2004).
[Crossref]

Cryan, M. J.

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320(5876), 646–649 (2008).
[Crossref] [PubMed]

Dalacu, D.

Deppe, D. G.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432(7014), 200–203 (2004).
[Crossref] [PubMed]

Devenyi, A.

R. D. Meade, A. Devenyi, J. Joannopoulos, O. Alerhand, D. Smith, and K. Kash, “Novel applications of photonic band gap materials: Low‐loss bends and high Q cavities,” J. Appl. Phys. 75(9), 4753–4755 (1994).
[Crossref]

DiVincenzo, D. P.

A. Imamoğlu, D. D. Awschalom, G. Burkard, D. P. DiVincenzo, D. Loss, M. Sherwin, and A. Small, “Quantum information processing using quantum dot spins and cavity QED,” Phys. Rev. Lett. 83(20), 4204–4207 (1999).
[Crossref]

Dremin, A.

M. Bayer, T. Gutbrod, J. Reithmaier, A. Forchel, T. Reinecke, P. Knipp, A. Dremin, and V. Kulakovskii, “Optical modes in photonic molecules,” Phys. Rev. Lett. 81(12), 2582–2585 (1998).
[Crossref]

Dumon, P.

Dwir, B.

Ell, C.

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, “Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity,” Nature 432(7014), 200–203 (2004).
[Crossref] [PubMed]

Englund, D.

D. Englund, A. Faraon, B. Zhang, Y. Yamamoto, and J. Vucković, “Generation and transfer of single photons on a photonic crystal chip,” Opt. Express 15(9), 5550–5558 (2007).
[Crossref] [PubMed]

A. Faraon, E. Waks, D. Englund, I. Fushman, and J. Vučković, “Efficient photonic crystal cavity-waveguide couplers,” Appl. Phys. Lett. 90(7), 073102 (2007).
[Crossref]

Fält, S.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445(7130), 896–899 (2007).
[Crossref] [PubMed]

Fan, S.

S. Fan, P. Villeneuve, J. Joannopoulos, and H. Haus, “Channel drop filters in photonic crystals,” Opt. Express 3(1), 4–11 (1998).
[Crossref] [PubMed]

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: putting a new twist on light,” Nature 386(6621), 143–149 (1997).
[Crossref]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77(18), 3787–3790 (1996).
[Crossref] [PubMed]

Faraon, A.

A. Faraon, E. Waks, D. Englund, I. Fushman, and J. Vučković, “Efficient photonic crystal cavity-waveguide couplers,” Appl. Phys. Lett. 90(7), 073102 (2007).
[Crossref]

D. Englund, A. Faraon, B. Zhang, Y. Yamamoto, and J. Vucković, “Generation and transfer of single photons on a photonic crystal chip,” Opt. Express 15(9), 5550–5558 (2007).
[Crossref] [PubMed]

Fiore, A.

X. Xu, F. Brossard, K. Hammura, D. A. Williams, B. Alloing, L. Li, and A. Fiore, ““Plug and Play” single photons at 1.3 μm approaching gigahertz operation,” Appl. Phys. Lett. 93(2), 021124 (2008).
[Crossref]

Forchel, A.

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Appl. Phys. Lett. (6)

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X. Xu, F. Brossard, K. Hammura, D. A. Williams, B. Alloing, L. Li, and A. Fiore, ““Plug and Play” single photons at 1.3 μm approaching gigahertz operation,” Appl. Phys. Lett. 93(2), 021124 (2008).
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X. Yang, X. Xu, X. Wang, H. Ni, Q. Han, Z. Niu, and D. A. Williams, “Optically controlled quantum dot gated transistors with high on/off ratio,” Appl. Phys. Lett. 96(8), 083503 (2010).
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Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “Investigation of high-Q channel drop filters using donor-type defects in two-dimensional photonic crystal slabs,” Appl. Phys. Lett. 83(8), 1512–1514 (2003).
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A. Faraon, E. Waks, D. Englund, I. Fushman, and J. Vučković, “Efficient photonic crystal cavity-waveguide couplers,” Appl. Phys. Lett. 90(7), 073102 (2007).
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Comput. Phys. Commun. (1)

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
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J. Appl. Phys. (1)

R. D. Meade, A. Devenyi, J. Joannopoulos, O. Alerhand, D. Smith, and K. Kash, “Novel applications of photonic band gap materials: Low‐loss bends and high Q cavities,” J. Appl. Phys. 75(9), 4753–4755 (1994).
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Nano Lett. (1)

X. Xu, H. Baker, and D. A. Williams, “Highly Sensitive, Photon Number Resolving Detectors Mediated by Phonons Using δ-doped GaAs Transistors,” Nano Lett. 10(4), 1364–1368 (2010).
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Nat. Photonics (2)

R. H. Hadfield, “Single-photon detectors for optical quantum information applications,” Nat. Photonics 3(12), 696–705 (2009).
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Y. Sato, Y. Tanaka, J. Upham, Y. Takahashi, T. Asano, and S. Noda, “Strong coupling between distant photonic nanocavities and its dynamic control,” Nat. Photonics 6(1), 56–61 (2012).
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Nature (6)

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Opt. Express (8)

D. Englund, A. Faraon, B. Zhang, Y. Yamamoto, and J. Vucković, “Generation and transfer of single photons on a photonic crystal chip,” Opt. Express 15(9), 5550–5558 (2007).
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Figures (6)

Fig. 1
Fig. 1 A PM formed of two coupled PhC L3 cavities. (a) Two L3 cavities are aligned in line along the x-axis and separated by two air holes. The lattice constant is a, air hole radius is 0.3a and slab thickness is a. The dielectric constant of slab is 12.96. (b) Resonant spectrum of coupled system. AS and S modes correspond to odd and even parities of the field distributions, respectively. (c) Hz field distribution of AS mode of PM. (d) Hz field distribution of S mode of PM. The air holes enclosed by green dashed circles with radius rm are used to optimize the coupled structure.
Fig. 2
Fig. 2 Energy oscillations between two cavities of a PM. (a) Time evolution of field intensities in a coupled system within cavity 1 and cavity 2 in the case of coupled mode theory, indicating an incomplete energy oscillation between two coupled cavities. (b) FDTD simulation of time evolution of electric field energy in a PM having structure parameters in Fig. 1(a). The energy oscillations between two cavities are not complete as well, which is in a good agreement with the results in (a).
Fig. 3
Fig. 3 Structure optimization for complete energy oscillations in a PM. (a) Eigen frequencies and (b) quality factors of AS and S modes as a function of rm. (c) Energy oscillations between two cavities by coupled mode theory when the quality factors of AS and S modes are equalized at rm = 0.382a. (d) FDTD simulation results with same parameters as used in the coupled mode theory.
Fig. 4
Fig. 4 Photonic crystal waveguide and the photonic band diagram. (a) A W1 waveguide structure formed by removing one array of air holes in PhC structure. (b) Band diagram of W1 waveguide. The red and blue solid lines show the zeroth-order and the first-order waveguide modes.
Fig. 5
Fig. 5 Coupling between a PM and waveguides. (a) Coupled structure between a PM and two waveguides. PM is aligned along the x-axis and two waveguides are tilted with respect to the x-axis by 60° angle. The PM and the waveguides are separated by three air holes. Waveguide In and waveguide Out are used as signal input and output respectively. (b) Transmission spectrum of the coupled structure. A Gaussian source is set in waveguide In and energy flux is detected at waveguide Out. Two peaks correspond to the split AS and S modes. (c) and (d) show Hz field distributions of AS and S modes, respectively.
Fig. 6
Fig. 6 Structure optimization for complete energy oscillations in a coupled PM-waveguide structure. Eigen frequencies (a) and quality factors (b) of AS and S modes as a function of rm. (c) The energy oscillations between two cavities when the PM is excited by waveguide modes. (d) The energy oscillations can be read out by another waveguide.

Equations (5)

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d a 1 dt =i ω 1 a 1 γ 1 2 a 1 iκ a 2 d a 2 dt =i ω 2 a 2 γ 2 2 a 2 iκ a 1
ω ± = 1 2 [ ω 1 + ω 2 i γ 1 + γ 2 2 ]± 1 2 [ ( ω 1 ω 2 ) i 2 ( γ 1 γ 2 ) ] 2 +4 κ 2
a 1 ( t )= 1 2i e i ω + t [ 1+ e i( ω + ω )t ] a 2 ( t )= 1 2 e i ω + t [ 1 e i( ω + ω )t ]
| a 1 ( t ) | 2 = 1 4 e 2 γ S t | 1+ e i( ω S ω AS )t e ( γ AS γ S )t | 2 | a 2 ( t ) | 2 = 1 4 e 2 γ S t | 1 e i( ω S ω AS )t e ( γ AS γ S )t | 2
d a 1 dt =i ω 0 a 1 γ c + γ wg 2 a 1 iκ a 2 γ wg a In d a 2 dt =i ω 0 a 2 γ c + γ wg 2 a 2 iκ a 1 a Out = γ wg a 2

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