Abstract

A perturbation theory approach for the analysis of hybrid plasmonic- photonic crystal structures is presented. This theory allows for accurate calculation of the resonance frequency shift and quality factor change when introducing a resonant plasmonic structure into a photonic crystal microcavity. An example calculation is shown, agreeing to within 5% with comprehensive finite difference time domain simulations but taking an order of magnitude less time. This theoretical approach overcomes the challenge of poor scaling in computations with hybrid plasmonic-photonic crystal structures, allowing for rapid design optimization in such hybrid geometries.

© 2012 OSA

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2011

Y. X. Ni, D. L. Gao, Z. F. Sang, L. Gao, and C. W. Qiu, “Influence of spherical anisotropy on the optical properties of plasmon resonant metallic nanoparticles,” Appl. Phys., A Mater. Sci. Process.102(3), 673–679 (2011).
[CrossRef]

I. Mukherjee, G. Hajisalem, and R. Gordon, “One step Integration of metal nanoparticles in photonic crystal nanobeam cavity,” Opt. Express19(23), 22462–22469 (2011).
[CrossRef]

2010

M. Kim, S. H. Lee, M. Choi, B. Ahn, N. Park, Y. H. Lee, and B. Min, “Low-loss surface-plasmonic nanobeam cavities,” Opt. Express18(11), 11089–11096 (2010).
[CrossRef]

M. Barth, S. Schietinger, S. Fischer, J. Becker, N. Nüsse, T. Aichele, B. Löchel, C. Sönnichsen, and O. Benson, “Nanoassembled plasmonic-photonic hybrid cavity for tailored light-matter coupling,” Nano Lett.10(3), 891–895 (2010).
[CrossRef]

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(3), 193–204 (2010).
[CrossRef]

2009

2008

M. W. McCutcheon and M. Loncar, “Design of a silicon nitride photonic crystal cavity with a quality factor of one million for coupling to a diamond nanocrystal,” Opt. Express16(23), 19136–19144 (2008).
[CrossRef]

F. De Angelis, M. Patrini, G. Das, I. Maksymov, M. Galli, L. Businaro, L. C. Andreani, and E. Di Fabrizio, “A hybrid plasmonic photonic nanodevice for label free detection of a few molecules,” Nano Lett.8(8), 2321–2327 (2008).
[CrossRef]

2007

S. Hughes, “Coupled cavity QED using planar photonic crystals,” Phys. Rev. Lett.98(8), 083603 (2007).
[CrossRef]

Y. Liu, Z. Yang, Z. Liang, and L. Qi, “A memory efficient strategy for FDTD implementation applied to photonic crystal problems,” Prog. Electromagn. Res.3, 374–378 (2007).

C. Grillet, C. Monat, C. L. Smith, B. L. Eggleton, D. J. Moss, S. Frédérick, D. Dalacu, P. J. Poole, J. Lapointe, G. Aers, and R. L. Williams, “Nanowire coupling to photonic crystal nanocavities for single photon sources,” Opt. Express15(3), 1267–1276 (2007).
[CrossRef]

L. Lalouat, B. Cluzel, P. Velha, E. Picard, D. Peyrade, J. P. Hugonin, P. Lalanne, E. Hadji, and F. de Fornel, “Near-field interactions between a subwavelength tip and a small-volume photonic-crystal nanocavity,” Phys. Rev. B76(4), 041102 (2007).
[CrossRef]

2006

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science311(5758), 189–193 (2006).
[CrossRef]

S. A. Maier, “Effective mode volume of nanoscale plasmon cavities,” Opt. Quantum Electron.38(1-3), 257–267 (2006).
[CrossRef]

S. A. Maier, “Plasmonics: metal nanostructures for subwavelength photonic devices,” IEEE J. Sel. Top. Quantum Electron.12(6), 1214–1220 (2006).
[CrossRef]

2005

S. A. Maier and H. A. Atwater, “Plasmonics: Localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys.98(1), 011101 (2005).
[CrossRef]

2004

2003

H. Ryu, M. Notomi, and Y. Lee, “High-quality-factor and small-mode-volume hexapole modes in photonic-crystal-slab nanocavities,” Appl. Phys. Lett.83(21), 4294–4296 (2003).
[CrossRef]

K. J. Vahala, “Optical microcavities,” Nature424(6950), 839–846 (2003).
[CrossRef]

2002

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.65(6), 066611 (2002).
[CrossRef]

M. Pelton, C. Santori, J. Vučković, B. Zhang, G. S. Solomon, J. Plant, and Y. Yamamoto, “Efficient sources of single photons: a single quantum dot in a micropost microcavity,” Phys. Rev. Lett.89(23), 233602 (2002).
[CrossRef]

M. Soljačić, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.66(5), 055601 (2002).
[CrossRef]

2001

G. D. Kondylis, F. D. Flaviis, G. J. Pottie, and T. Itoh, “A memory efficient formulation of the finite difference time domain method for the solution of Maxwell’s equations,” IEEE Trans. Microw. Theory Tech.49(7), 1310–1320 (2001).
[CrossRef]

1999

M. Lohmeyer, N. Bahlmann, and P. Hertel, “Geometry tolerance estimation for rectangular dielectric waveguide devices by means of perturbation theory,” Opt. Commun.163(1-3), 86–94 (1999).
[CrossRef]

1997

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and E. F. Schubert, “High extraction efficiency of spontaneous emission from slabs of photonic crystals,” Phys. Rev. Lett.78(17), 3294–3297 (1997).
[CrossRef]

1983

1979

A. Parkash, J. K. Vaid, and A. Mansingh, “Measurement of dielectric parameters at microwave frequencies by cavity-perturbation technique,” IEEE Trans. Microw. Theory Tech.27(9), 791–795 (1979).
[CrossRef]

1972

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6(12), 4370–4379 (1972).
[CrossRef]

Aers, G.

Ahn, B.

Aichele, T.

M. Barth, S. Schietinger, S. Fischer, J. Becker, N. Nüsse, T. Aichele, B. Löchel, C. Sönnichsen, and O. Benson, “Nanoassembled plasmonic-photonic hybrid cavity for tailored light-matter coupling,” Nano Lett.10(3), 891–895 (2010).
[CrossRef]

Andreani, L. C.

F. De Angelis, M. Patrini, G. Das, I. Maksymov, M. Galli, L. Businaro, L. C. Andreani, and E. Di Fabrizio, “A hybrid plasmonic photonic nanodevice for label free detection of a few molecules,” Nano Lett.8(8), 2321–2327 (2008).
[CrossRef]

Atwater, H. A.

S. A. Maier and H. A. Atwater, “Plasmonics: Localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys.98(1), 011101 (2005).
[CrossRef]

Bahlmann, N.

M. Lohmeyer, N. Bahlmann, and P. Hertel, “Geometry tolerance estimation for rectangular dielectric waveguide devices by means of perturbation theory,” Opt. Commun.163(1-3), 86–94 (1999).
[CrossRef]

Barclay, P. E.

Barnard, E. S.

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(3), 193–204 (2010).
[CrossRef]

Barth, M.

M. Barth, S. Schietinger, S. Fischer, J. Becker, N. Nüsse, T. Aichele, B. Löchel, C. Sönnichsen, and O. Benson, “Nanoassembled plasmonic-photonic hybrid cavity for tailored light-matter coupling,” Nano Lett.10(3), 891–895 (2010).
[CrossRef]

Beausoleil, R. G.

Becker, J.

M. Barth, S. Schietinger, S. Fischer, J. Becker, N. Nüsse, T. Aichele, B. Löchel, C. Sönnichsen, and O. Benson, “Nanoassembled plasmonic-photonic hybrid cavity for tailored light-matter coupling,” Nano Lett.10(3), 891–895 (2010).
[CrossRef]

Benech, P.

Benson, O.

M. Barth, S. Schietinger, S. Fischer, J. Becker, N. Nüsse, T. Aichele, B. Löchel, C. Sönnichsen, and O. Benson, “Nanoassembled plasmonic-photonic hybrid cavity for tailored light-matter coupling,” Nano Lett.10(3), 891–895 (2010).
[CrossRef]

Brongersma, M. L.

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(3), 193–204 (2010).
[CrossRef]

Businaro, L.

F. De Angelis, M. Patrini, G. Das, I. Maksymov, M. Galli, L. Businaro, L. C. Andreani, and E. Di Fabrizio, “A hybrid plasmonic photonic nanodevice for label free detection of a few molecules,” Nano Lett.8(8), 2321–2327 (2008).
[CrossRef]

Cai, W.

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(3), 193–204 (2010).
[CrossRef]

Choi, M.

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6(12), 4370–4379 (1972).
[CrossRef]

Cluzel, B.

L. Lalouat, B. Cluzel, P. Velha, E. Picard, D. Peyrade, J. P. Hugonin, P. Lalanne, E. Hadji, and F. de Fornel, “Near-field interactions between a subwavelength tip and a small-volume photonic-crystal nanocavity,” Phys. Rev. B76(4), 041102 (2007).
[CrossRef]

Dalacu, D.

Das, G.

F. De Angelis, M. Patrini, G. Das, I. Maksymov, M. Galli, L. Businaro, L. C. Andreani, and E. Di Fabrizio, “A hybrid plasmonic photonic nanodevice for label free detection of a few molecules,” Nano Lett.8(8), 2321–2327 (2008).
[CrossRef]

De Angelis, F.

F. De Angelis, M. Patrini, G. Das, I. Maksymov, M. Galli, L. Businaro, L. C. Andreani, and E. Di Fabrizio, “A hybrid plasmonic photonic nanodevice for label free detection of a few molecules,” Nano Lett.8(8), 2321–2327 (2008).
[CrossRef]

de Fornel, F.

L. Lalouat, B. Cluzel, P. Velha, E. Picard, D. Peyrade, J. P. Hugonin, P. Lalanne, E. Hadji, and F. de Fornel, “Near-field interactions between a subwavelength tip and a small-volume photonic-crystal nanocavity,” Phys. Rev. B76(4), 041102 (2007).
[CrossRef]

Desieres, Y.

Di Fabrizio, E.

F. De Angelis, M. Patrini, G. Das, I. Maksymov, M. Galli, L. Businaro, L. C. Andreani, and E. Di Fabrizio, “A hybrid plasmonic photonic nanodevice for label free detection of a few molecules,” Nano Lett.8(8), 2321–2327 (2008).
[CrossRef]

Eggleton, B. L.

Fan, S.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and E. F. Schubert, “High extraction efficiency of spontaneous emission from slabs of photonic crystals,” Phys. Rev. Lett.78(17), 3294–3297 (1997).
[CrossRef]

Fink, Y.

M. Soljačić, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.66(5), 055601 (2002).
[CrossRef]

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.65(6), 066611 (2002).
[CrossRef]

Fischer, S.

M. Barth, S. Schietinger, S. Fischer, J. Becker, N. Nüsse, T. Aichele, B. Löchel, C. Sönnichsen, and O. Benson, “Nanoassembled plasmonic-photonic hybrid cavity for tailored light-matter coupling,” Nano Lett.10(3), 891–895 (2010).
[CrossRef]

Flaviis, F. D.

G. D. Kondylis, F. D. Flaviis, G. J. Pottie, and T. Itoh, “A memory efficient formulation of the finite difference time domain method for the solution of Maxwell’s equations,” IEEE Trans. Microw. Theory Tech.49(7), 1310–1320 (2001).
[CrossRef]

Frédérick, S.

Fu, K. M.

Galli, M.

F. De Angelis, M. Patrini, G. Das, I. Maksymov, M. Galli, L. Businaro, L. C. Andreani, and E. Di Fabrizio, “A hybrid plasmonic photonic nanodevice for label free detection of a few molecules,” Nano Lett.8(8), 2321–2327 (2008).
[CrossRef]

Gao, D. L.

Y. X. Ni, D. L. Gao, Z. F. Sang, L. Gao, and C. W. Qiu, “Influence of spherical anisotropy on the optical properties of plasmon resonant metallic nanoparticles,” Appl. Phys., A Mater. Sci. Process.102(3), 673–679 (2011).
[CrossRef]

Gao, L.

Y. X. Ni, D. L. Gao, Z. F. Sang, L. Gao, and C. W. Qiu, “Influence of spherical anisotropy on the optical properties of plasmon resonant metallic nanoparticles,” Appl. Phys., A Mater. Sci. Process.102(3), 673–679 (2011).
[CrossRef]

Ghatak, A. K.

Gordon, R.

Grillet, C.

Hadji, E.

L. Lalouat, B. Cluzel, P. Velha, E. Picard, D. Peyrade, J. P. Hugonin, P. Lalanne, E. Hadji, and F. de Fornel, “Near-field interactions between a subwavelength tip and a small-volume photonic-crystal nanocavity,” Phys. Rev. B76(4), 041102 (2007).
[CrossRef]

Hajisalem, G.

Hertel, P.

M. Lohmeyer, N. Bahlmann, and P. Hertel, “Geometry tolerance estimation for rectangular dielectric waveguide devices by means of perturbation theory,” Opt. Commun.163(1-3), 86–94 (1999).
[CrossRef]

Hughes, S.

Hugonin, J. P.

L. Lalouat, B. Cluzel, P. Velha, E. Picard, D. Peyrade, J. P. Hugonin, P. Lalanne, E. Hadji, and F. de Fornel, “Near-field interactions between a subwavelength tip and a small-volume photonic-crystal nanocavity,” Phys. Rev. B76(4), 041102 (2007).
[CrossRef]

Ibanescu, M.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.65(6), 066611 (2002).
[CrossRef]

M. Soljačić, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.66(5), 055601 (2002).
[CrossRef]

Itoh, T.

G. D. Kondylis, F. D. Flaviis, G. J. Pottie, and T. Itoh, “A memory efficient formulation of the finite difference time domain method for the solution of Maxwell’s equations,” IEEE Trans. Microw. Theory Tech.49(7), 1310–1320 (2001).
[CrossRef]

Joannopoulos, J. D.

M. Soljačić, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.66(5), 055601 (2002).
[CrossRef]

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.65(6), 066611 (2002).
[CrossRef]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and E. F. Schubert, “High extraction efficiency of spontaneous emission from slabs of photonic crystals,” Phys. Rev. Lett.78(17), 3294–3297 (1997).
[CrossRef]

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6(12), 4370–4379 (1972).
[CrossRef]

Johnson, S. G.

M. Soljačić, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.66(5), 055601 (2002).
[CrossRef]

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.65(6), 066611 (2002).
[CrossRef]

Jun, Y. C.

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(3), 193–204 (2010).
[CrossRef]

Kim, M.

Kondylis, G. D.

G. D. Kondylis, F. D. Flaviis, G. J. Pottie, and T. Itoh, “A memory efficient formulation of the finite difference time domain method for the solution of Maxwell’s equations,” IEEE Trans. Microw. Theory Tech.49(7), 1310–1320 (2001).
[CrossRef]

Kumar, A.

Lalanne, P.

L. Lalouat, B. Cluzel, P. Velha, E. Picard, D. Peyrade, J. P. Hugonin, P. Lalanne, E. Hadji, and F. de Fornel, “Near-field interactions between a subwavelength tip and a small-volume photonic-crystal nanocavity,” Phys. Rev. B76(4), 041102 (2007).
[CrossRef]

Lalouat, L.

L. Lalouat, B. Cluzel, P. Velha, E. Picard, D. Peyrade, J. P. Hugonin, P. Lalanne, E. Hadji, and F. de Fornel, “Near-field interactions between a subwavelength tip and a small-volume photonic-crystal nanocavity,” Phys. Rev. B76(4), 041102 (2007).
[CrossRef]

Lapointe, J.

Lee, S. H.

Lee, Y.

H. Ryu, M. Notomi, and Y. Lee, “High-quality-factor and small-mode-volume hexapole modes in photonic-crystal-slab nanocavities,” Appl. Phys. Lett.83(21), 4294–4296 (2003).
[CrossRef]

Lee, Y. H.

Liang, Z.

Y. Liu, Z. Yang, Z. Liang, and L. Qi, “A memory efficient strategy for FDTD implementation applied to photonic crystal problems,” Prog. Electromagn. Res.3, 374–378 (2007).

Liu, Y.

Y. Liu, Z. Yang, Z. Liang, and L. Qi, “A memory efficient strategy for FDTD implementation applied to photonic crystal problems,” Prog. Electromagn. Res.3, 374–378 (2007).

Löchel, B.

M. Barth, S. Schietinger, S. Fischer, J. Becker, N. Nüsse, T. Aichele, B. Löchel, C. Sönnichsen, and O. Benson, “Nanoassembled plasmonic-photonic hybrid cavity for tailored light-matter coupling,” Nano Lett.10(3), 891–895 (2010).
[CrossRef]

Lohmeyer, M.

M. Lohmeyer, N. Bahlmann, and P. Hertel, “Geometry tolerance estimation for rectangular dielectric waveguide devices by means of perturbation theory,” Opt. Commun.163(1-3), 86–94 (1999).
[CrossRef]

Loncar, M.

Maier, S. A.

S. A. Maier, “Plasmonics: metal nanostructures for subwavelength photonic devices,” IEEE J. Sel. Top. Quantum Electron.12(6), 1214–1220 (2006).
[CrossRef]

S. A. Maier, “Effective mode volume of nanoscale plasmon cavities,” Opt. Quantum Electron.38(1-3), 257–267 (2006).
[CrossRef]

S. A. Maier and H. A. Atwater, “Plasmonics: Localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys.98(1), 011101 (2005).
[CrossRef]

Maksymov, I.

F. De Angelis, M. Patrini, G. Das, I. Maksymov, M. Galli, L. Businaro, L. C. Andreani, and E. Di Fabrizio, “A hybrid plasmonic photonic nanodevice for label free detection of a few molecules,” Nano Lett.8(8), 2321–2327 (2008).
[CrossRef]

Mansingh, A.

A. Parkash, J. K. Vaid, and A. Mansingh, “Measurement of dielectric parameters at microwave frequencies by cavity-perturbation technique,” IEEE Trans. Microw. Theory Tech.27(9), 791–795 (1979).
[CrossRef]

McCutcheon, M. W.

Min, B.

Monat, C.

Morand, A.

Moss, D. J.

Mukherjee, I.

Ni, Y. X.

Y. X. Ni, D. L. Gao, Z. F. Sang, L. Gao, and C. W. Qiu, “Influence of spherical anisotropy on the optical properties of plasmon resonant metallic nanoparticles,” Appl. Phys., A Mater. Sci. Process.102(3), 673–679 (2011).
[CrossRef]

Notomi, M.

H. Ryu, M. Notomi, and Y. Lee, “High-quality-factor and small-mode-volume hexapole modes in photonic-crystal-slab nanocavities,” Appl. Phys. Lett.83(21), 4294–4296 (2003).
[CrossRef]

Nüsse, N.

M. Barth, S. Schietinger, S. Fischer, J. Becker, N. Nüsse, T. Aichele, B. Löchel, C. Sönnichsen, and O. Benson, “Nanoassembled plasmonic-photonic hybrid cavity for tailored light-matter coupling,” Nano Lett.10(3), 891–895 (2010).
[CrossRef]

Ozbay, E.

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science311(5758), 189–193 (2006).
[CrossRef]

Park, N.

Parkash, A.

A. Parkash, J. K. Vaid, and A. Mansingh, “Measurement of dielectric parameters at microwave frequencies by cavity-perturbation technique,” IEEE Trans. Microw. Theory Tech.27(9), 791–795 (1979).
[CrossRef]

Patrini, M.

F. De Angelis, M. Patrini, G. Das, I. Maksymov, M. Galli, L. Businaro, L. C. Andreani, and E. Di Fabrizio, “A hybrid plasmonic photonic nanodevice for label free detection of a few molecules,” Nano Lett.8(8), 2321–2327 (2008).
[CrossRef]

Pelton, M.

M. Pelton, C. Santori, J. Vučković, B. Zhang, G. S. Solomon, J. Plant, and Y. Yamamoto, “Efficient sources of single photons: a single quantum dot in a micropost microcavity,” Phys. Rev. Lett.89(23), 233602 (2002).
[CrossRef]

Peyrade, D.

L. Lalouat, B. Cluzel, P. Velha, E. Picard, D. Peyrade, J. P. Hugonin, P. Lalanne, E. Hadji, and F. de Fornel, “Near-field interactions between a subwavelength tip and a small-volume photonic-crystal nanocavity,” Phys. Rev. B76(4), 041102 (2007).
[CrossRef]

Phan-Huy, K.

Picard, E.

L. Lalouat, B. Cluzel, P. Velha, E. Picard, D. Peyrade, J. P. Hugonin, P. Lalanne, E. Hadji, and F. de Fornel, “Near-field interactions between a subwavelength tip and a small-volume photonic-crystal nanocavity,” Phys. Rev. B76(4), 041102 (2007).
[CrossRef]

Plant, J.

M. Pelton, C. Santori, J. Vučković, B. Zhang, G. S. Solomon, J. Plant, and Y. Yamamoto, “Efficient sources of single photons: a single quantum dot in a micropost microcavity,” Phys. Rev. Lett.89(23), 233602 (2002).
[CrossRef]

Poole, P. J.

Pottie, G. J.

G. D. Kondylis, F. D. Flaviis, G. J. Pottie, and T. Itoh, “A memory efficient formulation of the finite difference time domain method for the solution of Maxwell’s equations,” IEEE Trans. Microw. Theory Tech.49(7), 1310–1320 (2001).
[CrossRef]

Qi, L.

Y. Liu, Z. Yang, Z. Liang, and L. Qi, “A memory efficient strategy for FDTD implementation applied to photonic crystal problems,” Prog. Electromagn. Res.3, 374–378 (2007).

Qiu, C. W.

Y. X. Ni, D. L. Gao, Z. F. Sang, L. Gao, and C. W. Qiu, “Influence of spherical anisotropy on the optical properties of plasmon resonant metallic nanoparticles,” Appl. Phys., A Mater. Sci. Process.102(3), 673–679 (2011).
[CrossRef]

Ryu, H.

H. Ryu, M. Notomi, and Y. Lee, “High-quality-factor and small-mode-volume hexapole modes in photonic-crystal-slab nanocavities,” Appl. Phys. Lett.83(21), 4294–4296 (2003).
[CrossRef]

Sang, Z. F.

Y. X. Ni, D. L. Gao, Z. F. Sang, L. Gao, and C. W. Qiu, “Influence of spherical anisotropy on the optical properties of plasmon resonant metallic nanoparticles,” Appl. Phys., A Mater. Sci. Process.102(3), 673–679 (2011).
[CrossRef]

Santori, C.

P. E. Barclay, K. M. Fu, C. Santori, and R. G. Beausoleil, “Hybrid photonic crystal cavity and waveguide for coupling to diamond NV centers,” Opt. Express17(12), 9588–9601 (2009).
[CrossRef]

M. Pelton, C. Santori, J. Vučković, B. Zhang, G. S. Solomon, J. Plant, and Y. Yamamoto, “Efficient sources of single photons: a single quantum dot in a micropost microcavity,” Phys. Rev. Lett.89(23), 233602 (2002).
[CrossRef]

Schietinger, S.

M. Barth, S. Schietinger, S. Fischer, J. Becker, N. Nüsse, T. Aichele, B. Löchel, C. Sönnichsen, and O. Benson, “Nanoassembled plasmonic-photonic hybrid cavity for tailored light-matter coupling,” Nano Lett.10(3), 891–895 (2010).
[CrossRef]

Schubert, E. F.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and E. F. Schubert, “High extraction efficiency of spontaneous emission from slabs of photonic crystals,” Phys. Rev. Lett.78(17), 3294–3297 (1997).
[CrossRef]

Schuller, J. A.

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(3), 193–204 (2010).
[CrossRef]

Skorobogatiy, M. A.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.65(6), 066611 (2002).
[CrossRef]

Smith, C. L.

Soljacic, M.

M. Soljačić, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.66(5), 055601 (2002).
[CrossRef]

Solomon, G. S.

M. Pelton, C. Santori, J. Vučković, B. Zhang, G. S. Solomon, J. Plant, and Y. Yamamoto, “Efficient sources of single photons: a single quantum dot in a micropost microcavity,” Phys. Rev. Lett.89(23), 233602 (2002).
[CrossRef]

Sönnichsen, C.

M. Barth, S. Schietinger, S. Fischer, J. Becker, N. Nüsse, T. Aichele, B. Löchel, C. Sönnichsen, and O. Benson, “Nanoassembled plasmonic-photonic hybrid cavity for tailored light-matter coupling,” Nano Lett.10(3), 891–895 (2010).
[CrossRef]

Thyagarajan, K.

Vahala, K. J.

K. J. Vahala, “Optical microcavities,” Nature424(6950), 839–846 (2003).
[CrossRef]

Vaid, J. K.

A. Parkash, J. K. Vaid, and A. Mansingh, “Measurement of dielectric parameters at microwave frequencies by cavity-perturbation technique,” IEEE Trans. Microw. Theory Tech.27(9), 791–795 (1979).
[CrossRef]

Velha, P.

L. Lalouat, B. Cluzel, P. Velha, E. Picard, D. Peyrade, J. P. Hugonin, P. Lalanne, E. Hadji, and F. de Fornel, “Near-field interactions between a subwavelength tip and a small-volume photonic-crystal nanocavity,” Phys. Rev. B76(4), 041102 (2007).
[CrossRef]

Villeneuve, P. R.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and E. F. Schubert, “High extraction efficiency of spontaneous emission from slabs of photonic crystals,” Phys. Rev. Lett.78(17), 3294–3297 (1997).
[CrossRef]

Vuckovic, J.

M. Pelton, C. Santori, J. Vučković, B. Zhang, G. S. Solomon, J. Plant, and Y. Yamamoto, “Efficient sources of single photons: a single quantum dot in a micropost microcavity,” Phys. Rev. Lett.89(23), 233602 (2002).
[CrossRef]

Weisberg, O.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.65(6), 066611 (2002).
[CrossRef]

White, J. S.

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(3), 193–204 (2010).
[CrossRef]

Williams, R. L.

Yamamoto, Y.

M. Pelton, C. Santori, J. Vučković, B. Zhang, G. S. Solomon, J. Plant, and Y. Yamamoto, “Efficient sources of single photons: a single quantum dot in a micropost microcavity,” Phys. Rev. Lett.89(23), 233602 (2002).
[CrossRef]

Yang, Z.

Y. Liu, Z. Yang, Z. Liang, and L. Qi, “A memory efficient strategy for FDTD implementation applied to photonic crystal problems,” Prog. Electromagn. Res.3, 374–378 (2007).

Yao, P.

Zhang, B.

M. Pelton, C. Santori, J. Vučković, B. Zhang, G. S. Solomon, J. Plant, and Y. Yamamoto, “Efficient sources of single photons: a single quantum dot in a micropost microcavity,” Phys. Rev. Lett.89(23), 233602 (2002).
[CrossRef]

Appl. Phys. Lett.

H. Ryu, M. Notomi, and Y. Lee, “High-quality-factor and small-mode-volume hexapole modes in photonic-crystal-slab nanocavities,” Appl. Phys. Lett.83(21), 4294–4296 (2003).
[CrossRef]

Appl. Phys., A Mater. Sci. Process.

Y. X. Ni, D. L. Gao, Z. F. Sang, L. Gao, and C. W. Qiu, “Influence of spherical anisotropy on the optical properties of plasmon resonant metallic nanoparticles,” Appl. Phys., A Mater. Sci. Process.102(3), 673–679 (2011).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

S. A. Maier, “Plasmonics: metal nanostructures for subwavelength photonic devices,” IEEE J. Sel. Top. Quantum Electron.12(6), 1214–1220 (2006).
[CrossRef]

IEEE Trans. Microw. Theory Tech.

G. D. Kondylis, F. D. Flaviis, G. J. Pottie, and T. Itoh, “A memory efficient formulation of the finite difference time domain method for the solution of Maxwell’s equations,” IEEE Trans. Microw. Theory Tech.49(7), 1310–1320 (2001).
[CrossRef]

A. Parkash, J. K. Vaid, and A. Mansingh, “Measurement of dielectric parameters at microwave frequencies by cavity-perturbation technique,” IEEE Trans. Microw. Theory Tech.27(9), 791–795 (1979).
[CrossRef]

J. Appl. Phys.

S. A. Maier and H. A. Atwater, “Plasmonics: Localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys.98(1), 011101 (2005).
[CrossRef]

J. Lightwave Technol.

Nano Lett.

M. Barth, S. Schietinger, S. Fischer, J. Becker, N. Nüsse, T. Aichele, B. Löchel, C. Sönnichsen, and O. Benson, “Nanoassembled plasmonic-photonic hybrid cavity for tailored light-matter coupling,” Nano Lett.10(3), 891–895 (2010).
[CrossRef]

F. De Angelis, M. Patrini, G. Das, I. Maksymov, M. Galli, L. Businaro, L. C. Andreani, and E. Di Fabrizio, “A hybrid plasmonic photonic nanodevice for label free detection of a few molecules,” Nano Lett.8(8), 2321–2327 (2008).
[CrossRef]

Nat. Mater.

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(3), 193–204 (2010).
[CrossRef]

Nature

K. J. Vahala, “Optical microcavities,” Nature424(6950), 839–846 (2003).
[CrossRef]

Opt. Commun.

M. Lohmeyer, N. Bahlmann, and P. Hertel, “Geometry tolerance estimation for rectangular dielectric waveguide devices by means of perturbation theory,” Opt. Commun.163(1-3), 86–94 (1999).
[CrossRef]

Opt. Express

Opt. Lett.

Opt. Quantum Electron.

S. A. Maier, “Effective mode volume of nanoscale plasmon cavities,” Opt. Quantum Electron.38(1-3), 257–267 (2006).
[CrossRef]

Phys. Rev. B

L. Lalouat, B. Cluzel, P. Velha, E. Picard, D. Peyrade, J. P. Hugonin, P. Lalanne, E. Hadji, and F. de Fornel, “Near-field interactions between a subwavelength tip and a small-volume photonic-crystal nanocavity,” Phys. Rev. B76(4), 041102 (2007).
[CrossRef]

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6(12), 4370–4379 (1972).
[CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys.

M. Soljačić, M. Ibanescu, S. G. Johnson, Y. Fink, and J. D. Joannopoulos, “Optimal bistable switching in nonlinear photonic crystals,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.66(5), 055601 (2002).
[CrossRef]

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisberg, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.65(6), 066611 (2002).
[CrossRef]

Phys. Rev. Lett.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and E. F. Schubert, “High extraction efficiency of spontaneous emission from slabs of photonic crystals,” Phys. Rev. Lett.78(17), 3294–3297 (1997).
[CrossRef]

M. Pelton, C. Santori, J. Vučković, B. Zhang, G. S. Solomon, J. Plant, and Y. Yamamoto, “Efficient sources of single photons: a single quantum dot in a micropost microcavity,” Phys. Rev. Lett.89(23), 233602 (2002).
[CrossRef]

S. Hughes, “Coupled cavity QED using planar photonic crystals,” Phys. Rev. Lett.98(8), 083603 (2007).
[CrossRef]

Prog. Electromagn. Res.

Y. Liu, Z. Yang, Z. Liang, and L. Qi, “A memory efficient strategy for FDTD implementation applied to photonic crystal problems,” Prog. Electromagn. Res.3, 374–378 (2007).

Science

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science311(5758), 189–193 (2006).
[CrossRef]

Other

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons, Inc., 1983).

R. A. Waldron, Theory of Waveguides and Cavities (Maclaren & Sons, 1967).

H. A. Haus, Waves and Fields in Optoelectronics (Prentice Hall Inc., 1984).

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Figures (4)

Fig. 1
Fig. 1

A FIB fabricated photonic crystal nanobeam cavity on silicon nitride [15].

Fig. 2
Fig. 2

(a) 3D schematic showing the photonic crystal nanobeam with a nanoparticle inside the simulation region. The pink arrow shows the direction of the propagation of the mode. The inset is a close-up on the nanoparticle at the center (b) Top view of the nanobeam in the simulation region, forming an unperturbed cavity (c) Zoom-in to the center of the nanobeam after the introduction of the nanoparticle. The shaded area shows the perturbed region considered.

Fig. 3
Fig. 3

(a) The scattering cross section of a 60 × 52 × 10 nm3 silver nanoparticle on a 200 nm thick blank Si3N4 substrate. (b)A transverse cross section through the nanoparticle showing the electric field distribution inside.

Fig. 4
Fig. 4

The shift in the photonic nanobeam cavity frequency and the change in the quality factor with and without (blue) the addition of the nanoparticle from FDTD simulations (black) and perturbation theory (red).

Equations (24)

Equations on this page are rendered with MathJax. Learn more.

E= E 1 e iωt
H= H 1 e iωt
D 1 = ε 0 ε 1 E 1
B 1 = μ 0 μ 1 H 1
E'=( E 1 + E 2 ) e i(ω+δω)t
H'=( H 1 + H 2 ) e i(ω+δω)t
D 2 = ε 0 [ ε 2 ( E 1 + E 2 ) ε 1 E 1 ]
B 2 = μ 0 [ μ 2 ( H 1 + H 2 ) μ 1 H 1 ]
× E 1 =jω B 1
× E 2 =j{ ω B 2 +δω( B 1 + B 2 ) }
× H 1 =jω D 1
× H 2 =j{ ω D 2 +δω( D 1 + D 2 ) }
H 1 .× E 2 + E 1 .× H 2 =jω E 2 . D 1 jω H 2 . B 1 div{ ( H 1 × E 2 )+( E 1 × H 2 ) }
H 1 .× E 2 + E 1 .× H 2 =jω{ E 1 . D 2 H 1 . B 2 }+jδω{ ( E 1 . D 1 H 1 . B 1 )+( E 1 . D 2 H 1 . B 2 ) }
jδω V 1 { ( E 1 . D 1 H 1 . B 1 )+( E 1 . D 2 H 1 . B 2 ) }dV = jω V 1 { ( E 2 . D 1 E 1 . D 2 )( H 2 . B 1 H 1 . B 2 ) }dV V 1 div{ ( H 1 × E 2 )+( E 1 × H 2 ) }dV
jδω V 1 { ( E 1 . D 1 H 1 . B 1 )+( E 1 . D 2 H 1 . B 2 ) }dV = jω V 1 { ( E 2 . D 1 E 1 . D 2 )( H 2 . B 1 H 1 . B 2 ) }dV S 1 { ( H 1 × E 2 )+( E 1 × H 2 ) } .dS
δω ω = V 2 { ( E 2 . D 1 E 1 . D 2 )( H 2 . B 1 H 1 . B 2 ) } dV 1 jω S 1 { ( H 1 × E 2 )+( E 1 × H 2 ) } .dS V 1 ( E 1 . D 1 H 1 . B 1 ) +( E 1 . D 2 H 1 . B 2 )dV
Ω=ω( 1+ i 2 Q 1 )
Ω +δΩ=(ω+δω)( 1+ i 2 Q a ' )
δΩ ω = δω' ω +i{ 1 2 Q a ' 1 2 Q 1 }
Q a , = ω 2( δω''+ ω 2 Q 1 )
τ scat = τ abs ( C abs C scat )
1 τ ' = 1 τ scat + 1 τ abs
λ wg = λ 0 n eff

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