Abstract

Using a finite-element, full-wave modeling approach, we present a flexible method of analyzing and simulating dielectric and plasmonic waveguide structures as well as their mode coupling. This method is applied to an integrated plasmonic circuit where a straight dielectric waveguide couples through a straight hybrid long-range plasmon waveguide to a uniformly bent hybrid one. The hybrid waveguide comprises a thin metal core embedded in a two–dimensional dielectric waveguide. The performance of such plasmonic circuits in terms of insertion losses is discussed.

© 2011 OSA

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2010 (1)

2009 (7)

R. Buckley and P. Berini, “Long-range substantially nonradiative metallo-dielectric waveguide,” Opt. Lett. 34, 223–225 (2009).
[CrossRef] [PubMed]

R. Buckley and P. Berini, “Radiation suppressing metallo-dielectric optical waveguides,” J. Lightwave Technol. 27, 2800–2808 (2009).
[CrossRef]

Y.-J. Tsai, A. Degiron, N. M. Jokerst, and D. R. Smith, “Plasmonic multi-mode interference couplers,” Opt. Express 17, 17471–17482 (2009).
[CrossRef] [PubMed]

A. Degiron, S.-Y. Cho, T. Tyler, N. M. Jokerst, and D. R. Smith, “Directional coupling between dielectric and long-range plasmon waveguides,” N. J. Phys. 11, 015002 (2009).
[CrossRef]

P. Berini and R. Buckley, “On the convergence and accuracy of numerical mode computations of surface plasmon waveguides,” J. Comput. Theor. Nanosci. 6, 2040–2053 (2009).
[CrossRef]

T. J. Davis, K. C. Vernon, and D. E. Gomez, “A plasmonic “ac wheatstone bridge” circuit for high-sensitivity phase measurement and single-molecule detection,” J. Appl. Phys. 106, 043502 (2009).
[CrossRef]

G. C. des Francs, J. Grandidier, S. Massenot, A. Bouhelier, J.-C. Weeber, and A. Dereux, “Integrated plasmonic waveguides: A mode solver based on density of states formulation,” Phys. Rev. B 80, 115419 (2009).
[CrossRef]

2008 (6)

M. Mastro, R. Holm, C. E. Jr, and J. Kim, “Electromagnetic propagation in nanostructures,” J. Ceram. Proc. Res. 9, 1–5 (2008).

P. Berini, “Bulk and surface sensitivities of surface plasmon waveguides,” N. J. Phys. 10, 105010 (2008).
[CrossRef]

R. Charbonneau, M. Tencer, N. Lahoud, and P. Berini, “Demonstration of surface sensing using long-range surface plasmon waveguides on silica,” Sens. Actuators B Chem. 134, 455–461 (2008).
[CrossRef]

A. Degiron, S.-Y. Cho, C. Harrison, N. M. Jokerst, C. Dellagiacoma, O. J. F. Martin, and D. R. Smith, “Experimental comparison between conventional and hybrid long-range surface plasmon waveguide bends,” Phys. Rev. A 77, 021804 (2008).
[CrossRef]

J. T. Kim, J. J. Ju, S. Park, M. su Kim, S. K. Park, and M.-H. Lee, “Chip-to-chip optical interconnect using gold long-range surface plasmon polariton waveguides,” Opt. Express 16, 13133–13138 (2008).
[CrossRef] [PubMed]

Y.-C. Lu, L. Yang, W.-P. Huang, and S.-S. Jian, “Improved full-vector finite-difference complex mode solver for optical waveguides of circular symmetry,” J. Lightwave Technol. 26, 1868–1876 (2008).
[CrossRef]

2007 (4)

2006 (6)

2005 (2)

2004 (1)

2003 (2)

T. Nikolajsen, K. Leosson, I. Salakhutdinov, and S. Bozhevolnyi, “Polymer-based surface-plasmon-polariton stripe waveguides at telecommunication wavelengths,” Appl. Phys. Lett. 82, 668–670 (2003).
[CrossRef]

M. Paulus and O. J. F. Martin, “A green’s tensor approach to the modeling of nanostructure replication and characterization,” Radio Sci. 38, 8024 (2003).
[CrossRef]

2002 (3)

P. Bienstman, E. Six, M. Roelens, M. Vanwolleghem, and R. Baets, “Calculation of bending losses in dielectric waveguides using eigenmode expansion and perfectly matched layers,” IEEE Photon. Technol. Lett. 14, 164–166 (2002).
[CrossRef]

Y. Tsuji and M. Koshiba, “Finite element method using port truncation by perfectly matched layer boundary conditions for optical waveguide discontinuity problems,” J. Lightwave Technol. 20, 463–468 (2002).
[CrossRef]

S. Lidgate, P. Sewell, and T. Benson, “Conformal mapping: limitations for waveguide bend analysis,” IEE Proc.: Sci., Meas. Technol. 149, 262–266 (2002).
[CrossRef]

2001 (1)

2000 (1)

M. Paulus, P. Gay-Balmaz, and O. J. F. Martin, “Accurate and efficient computation of the green’s tensor for stratified media,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 62, 5797–5807 (2000).
[CrossRef] [PubMed]

1998 (1)

1997 (3)

W. C. Chew, J. M. Jin, and E. Michielssen, “Complex coordinate stretching as a generalized absorbing boundary condition,” Microw. Opt. Technol. Lett. 17–21 (1997).

F. Teixeira and W. Chew, “Systematic derivation of anisotropic pml absorbing media in cylindrical and spherical coordinates,” IEEE Microw. Guid. Wave Lett. 7, 371–373 (1997).
[CrossRef]

J. Ctyroky, J. Homola, and M. Skalsky, “Modelling of surface plasmon resonance waveguide sensor by complex mode expansion and propagation method,” Opt. Quantum Electron. 29, 301–311 (1997).
[CrossRef]

1993 (1)

T. Yamamoto and M. Koshiba, “Numerical analysis of curvature loss in optical waveguides by the finite-element method,” J. Lightwave Technol. 11, 1579–1583 (1993).
[CrossRef]

1991 (1)

R. J. Deri and E. Kapon, “Low-loss iii–v semiconductor optical waveguides,” IEEE J. Quantum Electron. 27, 626–640 (1991).
[CrossRef]

1975 (1)

M. Heiblum and J. Harris, “Analysis of curved optical waveguides by conformal transformation,” IEEE J. Quantum Electron. QE11, 75–83 (1975).
[CrossRef]

1972 (1)

P. Johnson and R. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Baehr-Jones, T.

Baets, R.

P. Bienstman, E. Six, M. Roelens, M. Vanwolleghem, and R. Baets, “Calculation of bending losses in dielectric waveguides using eigenmode expansion and perfectly matched layers,” IEEE Photon. Technol. Lett. 14, 164–166 (2002).
[CrossRef]

Benson, T.

S. Lidgate, P. Sewell, and T. Benson, “Conformal mapping: limitations for waveguide bend analysis,” IEE Proc.: Sci., Meas. Technol. 149, 262–266 (2002).
[CrossRef]

Berini, P.

Q. Min, C. Chen, P. Berini, and R. Gordon, “Long range surface plasmons on asymmetric suspended thin film structures for biosensing applications,” Opt. Express 18, 19009–19019 (2010).
[CrossRef] [PubMed]

R. Buckley and P. Berini, “Long-range substantially nonradiative metallo-dielectric waveguide,” Opt. Lett. 34, 223–225 (2009).
[CrossRef] [PubMed]

R. Buckley and P. Berini, “Radiation suppressing metallo-dielectric optical waveguides,” J. Lightwave Technol. 27, 2800–2808 (2009).
[CrossRef]

P. Berini and R. Buckley, “On the convergence and accuracy of numerical mode computations of surface plasmon waveguides,” J. Comput. Theor. Nanosci. 6, 2040–2053 (2009).
[CrossRef]

P. Berini, “Bulk and surface sensitivities of surface plasmon waveguides,” N. J. Phys. 10, 105010 (2008).
[CrossRef]

R. Charbonneau, M. Tencer, N. Lahoud, and P. Berini, “Demonstration of surface sensing using long-range surface plasmon waveguides on silica,” Sens. Actuators B Chem. 134, 455–461 (2008).
[CrossRef]

P. Berini, R. Charbonneau, and N. Lahoud, “Long-range surface plasmons on ultrathin membranes,” Nano Lett. 7, 1376–1380 (2007).
[CrossRef] [PubMed]

R. Buckley and P. Berini, “Figures of merit for 2D surface plasmon waveguides and application to metal stripes,” Opt. Express 15, 12174–12182 (2007).
[CrossRef] [PubMed]

R. Charbonneau, C. Scales, I. Breukelaar, S. Fafard, N. Lahoud, G. Mattiussi, and P. Berini, “Passive integrated optics elements based on long-range surface plasmon polaritons,” J. Lightwave Technol. 24, 477–494 (2006).
[CrossRef]

P. Berini and J. Lu, “Curved long-range surface plasmon-polariton waveguides,” Opt. Express 14, 2365–2371 (2006).
[CrossRef] [PubMed]

P. Berini, R. Charbonneau, N. Lahoud, and G. Mattiussi, “Characterization of long–range surface–plasmon–polariton waveguides,” J. Appl. Phys. 98, 043109 (2005).
[CrossRef]

Bienstman, P.

P. Bienstman, E. Six, M. Roelens, M. Vanwolleghem, and R. Baets, “Calculation of bending losses in dielectric waveguides using eigenmode expansion and perfectly matched layers,” IEEE Photon. Technol. Lett. 14, 164–166 (2002).
[CrossRef]

Bolger, P.

A. Krasavin, P. Bolger, A. Zayats, Stær, T. Holmgaard, Z. Chen, S. Bozhevolnyi, L. Markey, and A. Dereux, “Active components for integrated plasmonic circuits,” in “2nd IEEE LEOS Winter Topicals, WTM 2009,” (2009).
[CrossRef]

Bouhelier, A.

G. C. des Francs, J. Grandidier, S. Massenot, A. Bouhelier, J.-C. Weeber, and A. Dereux, “Integrated plasmonic waveguides: A mode solver based on density of states formulation,” Phys. Rev. B 80, 115419 (2009).
[CrossRef]

Bozhevolnyi, S.

T. Nikolajsen, K. Leosson, I. Salakhutdinov, and S. Bozhevolnyi, “Polymer-based surface-plasmon-polariton stripe waveguides at telecommunication wavelengths,” Appl. Phys. Lett. 82, 668–670 (2003).
[CrossRef]

A. Krasavin, P. Bolger, A. Zayats, Stær, T. Holmgaard, Z. Chen, S. Bozhevolnyi, L. Markey, and A. Dereux, “Active components for integrated plasmonic circuits,” in “2nd IEEE LEOS Winter Topicals, WTM 2009,” (2009).
[CrossRef]

Breukelaar, I.

Buckley, R.

Burger, S.

S. Burger, L. Zschiedrich, J. Pomplun, and F. Schmidt, “Jcmsuite: An adaptive fem solver or precise simulations in nano-optics,” in “Integrated Photonics and Nanophotonics Research and Applications,” (Optical Society of America, 2008), paper ITuE4.

Charbonneau, R.

R. Charbonneau, M. Tencer, N. Lahoud, and P. Berini, “Demonstration of surface sensing using long-range surface plasmon waveguides on silica,” Sens. Actuators B Chem. 134, 455–461 (2008).
[CrossRef]

P. Berini, R. Charbonneau, and N. Lahoud, “Long-range surface plasmons on ultrathin membranes,” Nano Lett. 7, 1376–1380 (2007).
[CrossRef] [PubMed]

R. Charbonneau, C. Scales, I. Breukelaar, S. Fafard, N. Lahoud, G. Mattiussi, and P. Berini, “Passive integrated optics elements based on long-range surface plasmon polaritons,” J. Lightwave Technol. 24, 477–494 (2006).
[CrossRef]

P. Berini, R. Charbonneau, N. Lahoud, and G. Mattiussi, “Characterization of long–range surface–plasmon–polariton waveguides,” J. Appl. Phys. 98, 043109 (2005).
[CrossRef]

Chen, C.

Chen, Z.

A. Krasavin, P. Bolger, A. Zayats, Stær, T. Holmgaard, Z. Chen, S. Bozhevolnyi, L. Markey, and A. Dereux, “Active components for integrated plasmonic circuits,” in “2nd IEEE LEOS Winter Topicals, WTM 2009,” (2009).
[CrossRef]

Chew, W.

F. Teixeira and W. Chew, “Systematic derivation of anisotropic pml absorbing media in cylindrical and spherical coordinates,” IEEE Microw. Guid. Wave Lett. 7, 371–373 (1997).
[CrossRef]

Chew, W. C.

W. C. Chew, J. M. Jin, and E. Michielssen, “Complex coordinate stretching as a generalized absorbing boundary condition,” Microw. Opt. Technol. Lett. 17–21 (1997).

Cho, S.-Y.

A. Degiron, S.-Y. Cho, T. Tyler, N. M. Jokerst, and D. R. Smith, “Directional coupling between dielectric and long-range plasmon waveguides,” N. J. Phys. 11, 015002 (2009).
[CrossRef]

A. Degiron, S.-Y. Cho, C. Harrison, N. M. Jokerst, C. Dellagiacoma, O. J. F. Martin, and D. R. Smith, “Experimental comparison between conventional and hybrid long-range surface plasmon waveguide bends,” Phys. Rev. A 77, 021804 (2008).
[CrossRef]

Christy, R.

P. Johnson and R. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Ctyroky, J.

J. Ctyroky, J. Homola, and M. Skalsky, “Modelling of surface plasmon resonance waveguide sensor by complex mode expansion and propagation method,” Opt. Quantum Electron. 29, 301–311 (1997).
[CrossRef]

Cui, X.

Davis, T. J.

T. J. Davis, K. C. Vernon, and D. E. Gomez, “A plasmonic “ac wheatstone bridge” circuit for high-sensitivity phase measurement and single-molecule detection,” J. Appl. Phys. 106, 043502 (2009).
[CrossRef]

Degiron, A.

A. Degiron, S.-Y. Cho, T. Tyler, N. M. Jokerst, and D. R. Smith, “Directional coupling between dielectric and long-range plasmon waveguides,” N. J. Phys. 11, 015002 (2009).
[CrossRef]

Y.-J. Tsai, A. Degiron, N. M. Jokerst, and D. R. Smith, “Plasmonic multi-mode interference couplers,” Opt. Express 17, 17471–17482 (2009).
[CrossRef] [PubMed]

A. Degiron, S.-Y. Cho, C. Harrison, N. M. Jokerst, C. Dellagiacoma, O. J. F. Martin, and D. R. Smith, “Experimental comparison between conventional and hybrid long-range surface plasmon waveguide bends,” Phys. Rev. A 77, 021804 (2008).
[CrossRef]

A. Degiron, C. Dellagiacoma, J. G. McIlhargey, G. Shvets, O. J. F. Martin, and D. R. Smith, “Simulations of hybrid long-range plasmon modes with application to 90 degrees bends,” Opt. Lett. 32, 2354–2356 (2007).
[CrossRef] [PubMed]

A. Degiron and D.R. Smith, “Numerical simulations of long-range plasmons,” Opt. Express 14, 1611–1625 (2006).
[CrossRef] [PubMed]

Dellagiacoma, C.

A. Degiron, S.-Y. Cho, C. Harrison, N. M. Jokerst, C. Dellagiacoma, O. J. F. Martin, and D. R. Smith, “Experimental comparison between conventional and hybrid long-range surface plasmon waveguide bends,” Phys. Rev. A 77, 021804 (2008).
[CrossRef]

A. Degiron, C. Dellagiacoma, J. G. McIlhargey, G. Shvets, O. J. F. Martin, and D. R. Smith, “Simulations of hybrid long-range plasmon modes with application to 90 degrees bends,” Opt. Lett. 32, 2354–2356 (2007).
[CrossRef] [PubMed]

Dereux, A.

G. C. des Francs, J. Grandidier, S. Massenot, A. Bouhelier, J.-C. Weeber, and A. Dereux, “Integrated plasmonic waveguides: A mode solver based on density of states formulation,” Phys. Rev. B 80, 115419 (2009).
[CrossRef]

A. Krasavin, P. Bolger, A. Zayats, Stær, T. Holmgaard, Z. Chen, S. Bozhevolnyi, L. Markey, and A. Dereux, “Active components for integrated plasmonic circuits,” in “2nd IEEE LEOS Winter Topicals, WTM 2009,” (2009).
[CrossRef]

Deri, R. J.

R. J. Deri and E. Kapon, “Low-loss iii–v semiconductor optical waveguides,” IEEE J. Quantum Electron. 27, 626–640 (1991).
[CrossRef]

des Francs, G. C.

G. C. des Francs, J. Grandidier, S. Massenot, A. Bouhelier, J.-C. Weeber, and A. Dereux, “Integrated plasmonic waveguides: A mode solver based on density of states formulation,” Phys. Rev. B 80, 115419 (2009).
[CrossRef]

Fafard, S.

Gay-Balmaz, P.

M. Paulus, P. Gay-Balmaz, and O. J. F. Martin, “Accurate and efficient computation of the green’s tensor for stratified media,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 62, 5797–5807 (2000).
[CrossRef] [PubMed]

Gomez, D. E.

T. J. Davis, K. C. Vernon, and D. E. Gomez, “A plasmonic “ac wheatstone bridge” circuit for high-sensitivity phase measurement and single-molecule detection,” J. Appl. Phys. 106, 043502 (2009).
[CrossRef]

Gordon, R.

Grandidier, J.

G. C. des Francs, J. Grandidier, S. Massenot, A. Bouhelier, J.-C. Weeber, and A. Dereux, “Integrated plasmonic waveguides: A mode solver based on density of states formulation,” Phys. Rev. B 80, 115419 (2009).
[CrossRef]

Harris, J.

M. Heiblum and J. Harris, “Analysis of curved optical waveguides by conformal transformation,” IEEE J. Quantum Electron. QE11, 75–83 (1975).
[CrossRef]

Harrison, C.

A. Degiron, S.-Y. Cho, C. Harrison, N. M. Jokerst, C. Dellagiacoma, O. J. F. Martin, and D. R. Smith, “Experimental comparison between conventional and hybrid long-range surface plasmon waveguide bends,” Phys. Rev. A 77, 021804 (2008).
[CrossRef]

Heiblum, M.

M. Heiblum and J. Harris, “Analysis of curved optical waveguides by conformal transformation,” IEEE J. Quantum Electron. QE11, 75–83 (1975).
[CrossRef]

Heng, X.

Hirono, T.

Hochberg, M.

Holm, R.

M. Mastro, R. Holm, C. E. Jr, and J. Kim, “Electromagnetic propagation in nanostructures,” J. Ceram. Proc. Res. 9, 1–5 (2008).

Holmgaard, T.

A. Krasavin, P. Bolger, A. Zayats, Stær, T. Holmgaard, Z. Chen, S. Bozhevolnyi, L. Markey, and A. Dereux, “Active components for integrated plasmonic circuits,” in “2nd IEEE LEOS Winter Topicals, WTM 2009,” (2009).
[CrossRef]

Homola, J.

J. Ctyroky, J. Homola, and M. Skalsky, “Modelling of surface plasmon resonance waveguide sensor by complex mode expansion and propagation method,” Opt. Quantum Electron. 29, 301–311 (1997).
[CrossRef]

Huang, W.

Huang, W.-P.

Jian, S.-S.

Jin, J.

J. Jin, The Finite Element Method in Electromagnetics, 2nd ed. (John Wiley and Sons, 2002).

Jin, J. M.

W. C. Chew, J. M. Jin, and E. Michielssen, “Complex coordinate stretching as a generalized absorbing boundary condition,” Microw. Opt. Technol. Lett. 17–21 (1997).

Johnson, P.

P. Johnson and R. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Jokerst, N. M.

A. Degiron, S.-Y. Cho, T. Tyler, N. M. Jokerst, and D. R. Smith, “Directional coupling between dielectric and long-range plasmon waveguides,” N. J. Phys. 11, 015002 (2009).
[CrossRef]

Y.-J. Tsai, A. Degiron, N. M. Jokerst, and D. R. Smith, “Plasmonic multi-mode interference couplers,” Opt. Express 17, 17471–17482 (2009).
[CrossRef] [PubMed]

A. Degiron, S.-Y. Cho, C. Harrison, N. M. Jokerst, C. Dellagiacoma, O. J. F. Martin, and D. R. Smith, “Experimental comparison between conventional and hybrid long-range surface plasmon waveguide bends,” Phys. Rev. A 77, 021804 (2008).
[CrossRef]

Jr, C. E.

M. Mastro, R. Holm, C. E. Jr, and J. Kim, “Electromagnetic propagation in nanostructures,” J. Ceram. Proc. Res. 9, 1–5 (2008).

Ju, J. J.

Kakihara, K.

Kapon, E.

R. J. Deri and E. Kapon, “Low-loss iii–v semiconductor optical waveguides,” IEEE J. Quantum Electron. 27, 626–640 (1991).
[CrossRef]

Kim, J.

M. Mastro, R. Holm, C. E. Jr, and J. Kim, “Electromagnetic propagation in nanostructures,” J. Ceram. Proc. Res. 9, 1–5 (2008).

Kim, J. T.

Knapp, D. W.

Kono, N.

Koshiba, M.

Krasavin, A.

A. Krasavin, P. Bolger, A. Zayats, Stær, T. Holmgaard, Z. Chen, S. Bozhevolnyi, L. Markey, and A. Dereux, “Active components for integrated plasmonic circuits,” in “2nd IEEE LEOS Winter Topicals, WTM 2009,” (2009).
[CrossRef]

Lahoud, N.

R. Charbonneau, M. Tencer, N. Lahoud, and P. Berini, “Demonstration of surface sensing using long-range surface plasmon waveguides on silica,” Sens. Actuators B Chem. 134, 455–461 (2008).
[CrossRef]

P. Berini, R. Charbonneau, and N. Lahoud, “Long-range surface plasmons on ultrathin membranes,” Nano Lett. 7, 1376–1380 (2007).
[CrossRef] [PubMed]

R. Charbonneau, C. Scales, I. Breukelaar, S. Fafard, N. Lahoud, G. Mattiussi, and P. Berini, “Passive integrated optics elements based on long-range surface plasmon polaritons,” J. Lightwave Technol. 24, 477–494 (2006).
[CrossRef]

P. Berini, R. Charbonneau, N. Lahoud, and G. Mattiussi, “Characterization of long–range surface–plasmon–polariton waveguides,” J. Appl. Phys. 98, 043109 (2005).
[CrossRef]

Lee, M.-H.

Leosson, K.

T. Nikolajsen, K. Leosson, I. Salakhutdinov, and S. Bozhevolnyi, “Polymer-based surface-plasmon-polariton stripe waveguides at telecommunication wavelengths,” Appl. Phys. Lett. 82, 668–670 (2003).
[CrossRef]

Lidgate, S.

S. Lidgate, P. Sewell, and T. Benson, “Conformal mapping: limitations for waveguide bend analysis,” IEE Proc.: Sci., Meas. Technol. 149, 262–266 (2002).
[CrossRef]

Lin, L.

C. Wang and L. Lin, “Nanoscale waveguiding methods,” Nanoscale Res. Lett. 2, 219–229 (2007).
[CrossRef] [PubMed]

Lu, J.

Lu, Y.-C.

Lui, W.

Marcuse, D.

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic Press, 1974), p. 267.

Markey, L.

A. Krasavin, P. Bolger, A. Zayats, Stær, T. Holmgaard, Z. Chen, S. Bozhevolnyi, L. Markey, and A. Dereux, “Active components for integrated plasmonic circuits,” in “2nd IEEE LEOS Winter Topicals, WTM 2009,” (2009).
[CrossRef]

Martin, O. J. F.

A. Degiron, S.-Y. Cho, C. Harrison, N. M. Jokerst, C. Dellagiacoma, O. J. F. Martin, and D. R. Smith, “Experimental comparison between conventional and hybrid long-range surface plasmon waveguide bends,” Phys. Rev. A 77, 021804 (2008).
[CrossRef]

A. Degiron, C. Dellagiacoma, J. G. McIlhargey, G. Shvets, O. J. F. Martin, and D. R. Smith, “Simulations of hybrid long-range plasmon modes with application to 90 degrees bends,” Opt. Lett. 32, 2354–2356 (2007).
[CrossRef] [PubMed]

M. Paulus and O. J. F. Martin, “A green’s tensor approach to the modeling of nanostructure replication and characterization,” Radio Sci. 38, 8024 (2003).
[CrossRef]

M. Paulus and O. J. F. Martin, “How to tap an innocent waveguide,” Opt. Express 8, 644–648 (2001).
[CrossRef] [PubMed]

M. Paulus, P. Gay-Balmaz, and O. J. F. Martin, “Accurate and efficient computation of the green’s tensor for stratified media,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 62, 5797–5807 (2000).
[CrossRef] [PubMed]

Massenot, S.

G. C. des Francs, J. Grandidier, S. Massenot, A. Bouhelier, J.-C. Weeber, and A. Dereux, “Integrated plasmonic waveguides: A mode solver based on density of states formulation,” Phys. Rev. B 80, 115419 (2009).
[CrossRef]

Mastro, M.

M. Mastro, R. Holm, C. E. Jr, and J. Kim, “Electromagnetic propagation in nanostructures,” J. Ceram. Proc. Res. 9, 1–5 (2008).

Mattiussi, G.

R. Charbonneau, C. Scales, I. Breukelaar, S. Fafard, N. Lahoud, G. Mattiussi, and P. Berini, “Passive integrated optics elements based on long-range surface plasmon polaritons,” J. Lightwave Technol. 24, 477–494 (2006).
[CrossRef]

P. Berini, R. Charbonneau, N. Lahoud, and G. Mattiussi, “Characterization of long–range surface–plasmon–polariton waveguides,” J. Appl. Phys. 98, 043109 (2005).
[CrossRef]

McDowell, E. J.

McIlhargey, J. G.

Michielssen, E.

W. C. Chew, J. M. Jin, and E. Michielssen, “Complex coordinate stretching as a generalized absorbing boundary condition,” Microw. Opt. Technol. Lett. 17–21 (1997).

Min, Q.

Nakano, H.

Nikolajsen, T.

T. Nikolajsen, K. Leosson, I. Salakhutdinov, and S. Bozhevolnyi, “Polymer-based surface-plasmon-polariton stripe waveguides at telecommunication wavelengths,” Appl. Phys. Lett. 82, 668–670 (2003).
[CrossRef]

Park, S.

Park, S. K.

Paulus, M.

M. Paulus and O. J. F. Martin, “A green’s tensor approach to the modeling of nanostructure replication and characterization,” Radio Sci. 38, 8024 (2003).
[CrossRef]

M. Paulus and O. J. F. Martin, “How to tap an innocent waveguide,” Opt. Express 8, 644–648 (2001).
[CrossRef] [PubMed]

M. Paulus, P. Gay-Balmaz, and O. J. F. Martin, “Accurate and efficient computation of the green’s tensor for stratified media,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 62, 5797–5807 (2000).
[CrossRef] [PubMed]

Pomplun, J.

S. Burger, L. Zschiedrich, J. Pomplun, and F. Schmidt, “Jcmsuite: An adaptive fem solver or precise simulations in nano-optics,” in “Integrated Photonics and Nanophotonics Research and Applications,” (Optical Society of America, 2008), paper ITuE4.

Psaltis, D.

Roelens, M.

P. Bienstman, E. Six, M. Roelens, M. Vanwolleghem, and R. Baets, “Calculation of bending losses in dielectric waveguides using eigenmode expansion and perfectly matched layers,” IEEE Photon. Technol. Lett. 14, 164–166 (2002).
[CrossRef]

Saitoh, K.

Salakhutdinov, I.

T. Nikolajsen, K. Leosson, I. Salakhutdinov, and S. Bozhevolnyi, “Polymer-based surface-plasmon-polariton stripe waveguides at telecommunication wavelengths,” Appl. Phys. Lett. 82, 668–670 (2003).
[CrossRef]

Scales, C.

Scherer, A.

Schmidt, F.

S. Burger, L. Zschiedrich, J. Pomplun, and F. Schmidt, “Jcmsuite: An adaptive fem solver or precise simulations in nano-optics,” in “Integrated Photonics and Nanophotonics Research and Applications,” (Optical Society of America, 2008), paper ITuE4.

Sewell, P.

S. Lidgate, P. Sewell, and T. Benson, “Conformal mapping: limitations for waveguide bend analysis,” IEE Proc.: Sci., Meas. Technol. 149, 262–266 (2002).
[CrossRef]

Shibayama, J.

Shvets, G.

Six, E.

P. Bienstman, E. Six, M. Roelens, M. Vanwolleghem, and R. Baets, “Calculation of bending losses in dielectric waveguides using eigenmode expansion and perfectly matched layers,” IEEE Photon. Technol. Lett. 14, 164–166 (2002).
[CrossRef]

Skalsky, M.

J. Ctyroky, J. Homola, and M. Skalsky, “Modelling of surface plasmon resonance waveguide sensor by complex mode expansion and propagation method,” Opt. Quantum Electron. 29, 301–311 (1997).
[CrossRef]

Smith, D. R.

A. Degiron, S.-Y. Cho, T. Tyler, N. M. Jokerst, and D. R. Smith, “Directional coupling between dielectric and long-range plasmon waveguides,” N. J. Phys. 11, 015002 (2009).
[CrossRef]

Y.-J. Tsai, A. Degiron, N. M. Jokerst, and D. R. Smith, “Plasmonic multi-mode interference couplers,” Opt. Express 17, 17471–17482 (2009).
[CrossRef] [PubMed]

A. Degiron, S.-Y. Cho, C. Harrison, N. M. Jokerst, C. Dellagiacoma, O. J. F. Martin, and D. R. Smith, “Experimental comparison between conventional and hybrid long-range surface plasmon waveguide bends,” Phys. Rev. A 77, 021804 (2008).
[CrossRef]

A. Degiron, C. Dellagiacoma, J. G. McIlhargey, G. Shvets, O. J. F. Martin, and D. R. Smith, “Simulations of hybrid long-range plasmon modes with application to 90 degrees bends,” Opt. Lett. 32, 2354–2356 (2007).
[CrossRef] [PubMed]

Smith, D.R.

Soref, R.

R. Soref, “The past, present, and future of silicon photonics,” IEEE J. Sel. Top. Quantum Electron. 12, 1678–1687 (2006).
[CrossRef]

Stær,

A. Krasavin, P. Bolger, A. Zayats, Stær, T. Holmgaard, Z. Chen, S. Bozhevolnyi, L. Markey, and A. Dereux, “Active components for integrated plasmonic circuits,” in “2nd IEEE LEOS Winter Topicals, WTM 2009,” (2009).
[CrossRef]

su Kim, M.

Teixeira, F.

F. Teixeira and W. Chew, “Systematic derivation of anisotropic pml absorbing media in cylindrical and spherical coordinates,” IEEE Microw. Guid. Wave Lett. 7, 371–373 (1997).
[CrossRef]

Tencer, M.

R. Charbonneau, M. Tencer, N. Lahoud, and P. Berini, “Demonstration of surface sensing using long-range surface plasmon waveguides on silica,” Sens. Actuators B Chem. 134, 455–461 (2008).
[CrossRef]

Tsai, Y.-J.

Tsuji, Y.

Tyler, T.

A. Degiron, S.-Y. Cho, T. Tyler, N. M. Jokerst, and D. R. Smith, “Directional coupling between dielectric and long-range plasmon waveguides,” N. J. Phys. 11, 015002 (2009).
[CrossRef]

Vanwolleghem, M.

P. Bienstman, E. Six, M. Roelens, M. Vanwolleghem, and R. Baets, “Calculation of bending losses in dielectric waveguides using eigenmode expansion and perfectly matched layers,” IEEE Photon. Technol. Lett. 14, 164–166 (2002).
[CrossRef]

Vernon, K. C.

T. J. Davis, K. C. Vernon, and D. E. Gomez, “A plasmonic “ac wheatstone bridge” circuit for high-sensitivity phase measurement and single-molecule detection,” J. Appl. Phys. 106, 043502 (2009).
[CrossRef]

Walker, C.

Wang, C.

C. Wang and L. Lin, “Nanoscale waveguiding methods,” Nanoscale Res. Lett. 2, 219–229 (2007).
[CrossRef] [PubMed]

Weeber, J.-C.

G. C. des Francs, J. Grandidier, S. Massenot, A. Bouhelier, J.-C. Weeber, and A. Dereux, “Integrated plasmonic waveguides: A mode solver based on density of states formulation,” Phys. Rev. B 80, 115419 (2009).
[CrossRef]

Wu, J.

Xu, C.

Yamamoto, T.

T. Yamamoto and M. Koshiba, “Numerical analysis of curvature loss in optical waveguides by the finite-element method,” J. Lightwave Technol. 11, 1579–1583 (1993).
[CrossRef]

Yamauchi, J.

Yamazaki, T.

Yang, C.

Yang, L.

Yaqoob, Z.

Yokoyama, K.

Zayats, A.

A. Krasavin, P. Bolger, A. Zayats, Stær, T. Holmgaard, Z. Chen, S. Bozhevolnyi, L. Markey, and A. Dereux, “Active components for integrated plasmonic circuits,” in “2nd IEEE LEOS Winter Topicals, WTM 2009,” (2009).
[CrossRef]

Zschiedrich, L.

S. Burger, L. Zschiedrich, J. Pomplun, and F. Schmidt, “Jcmsuite: An adaptive fem solver or precise simulations in nano-optics,” in “Integrated Photonics and Nanophotonics Research and Applications,” (Optical Society of America, 2008), paper ITuE4.

Appl. Phys. Lett. (1)

T. Nikolajsen, K. Leosson, I. Salakhutdinov, and S. Bozhevolnyi, “Polymer-based surface-plasmon-polariton stripe waveguides at telecommunication wavelengths,” Appl. Phys. Lett. 82, 668–670 (2003).
[CrossRef]

IEE Proc.: Sci., Meas. Technol. (1)

S. Lidgate, P. Sewell, and T. Benson, “Conformal mapping: limitations for waveguide bend analysis,” IEE Proc.: Sci., Meas. Technol. 149, 262–266 (2002).
[CrossRef]

IEEE J. Quantum Electron. (2)

M. Heiblum and J. Harris, “Analysis of curved optical waveguides by conformal transformation,” IEEE J. Quantum Electron. QE11, 75–83 (1975).
[CrossRef]

R. J. Deri and E. Kapon, “Low-loss iii–v semiconductor optical waveguides,” IEEE J. Quantum Electron. 27, 626–640 (1991).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

R. Soref, “The past, present, and future of silicon photonics,” IEEE J. Sel. Top. Quantum Electron. 12, 1678–1687 (2006).
[CrossRef]

IEEE Microw. Guid. Wave Lett. (1)

F. Teixeira and W. Chew, “Systematic derivation of anisotropic pml absorbing media in cylindrical and spherical coordinates,” IEEE Microw. Guid. Wave Lett. 7, 371–373 (1997).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

P. Bienstman, E. Six, M. Roelens, M. Vanwolleghem, and R. Baets, “Calculation of bending losses in dielectric waveguides using eigenmode expansion and perfectly matched layers,” IEEE Photon. Technol. Lett. 14, 164–166 (2002).
[CrossRef]

J. Appl. Phys. (2)

T. J. Davis, K. C. Vernon, and D. E. Gomez, “A plasmonic “ac wheatstone bridge” circuit for high-sensitivity phase measurement and single-molecule detection,” J. Appl. Phys. 106, 043502 (2009).
[CrossRef]

P. Berini, R. Charbonneau, N. Lahoud, and G. Mattiussi, “Characterization of long–range surface–plasmon–polariton waveguides,” J. Appl. Phys. 98, 043109 (2005).
[CrossRef]

J. Ceram. Proc. Res. (1)

M. Mastro, R. Holm, C. E. Jr, and J. Kim, “Electromagnetic propagation in nanostructures,” J. Ceram. Proc. Res. 9, 1–5 (2008).

J. Comput. Theor. Nanosci. (1)

P. Berini and R. Buckley, “On the convergence and accuracy of numerical mode computations of surface plasmon waveguides,” J. Comput. Theor. Nanosci. 6, 2040–2053 (2009).
[CrossRef]

J. Lightwave Technol. (7)

T. Yamamoto and M. Koshiba, “Numerical analysis of curvature loss in optical waveguides by the finite-element method,” J. Lightwave Technol. 11, 1579–1583 (1993).
[CrossRef]

W. Lui, C. Xu, T. Hirono, K. Yokoyama, and W. Huang, “Full-vectorial wave propagation in semiconductor optical bending waveguides and equivalent straight waveguide approximations,” J. Lightwave Technol. 16, 910–914 (1998).
[CrossRef]

Y. Tsuji and M. Koshiba, “Finite element method using port truncation by perfectly matched layer boundary conditions for optical waveguide discontinuity problems,” J. Lightwave Technol. 20, 463–468 (2002).
[CrossRef]

J. Shibayama, T. Yamazaki, J. Yamauchi, and H. Nakano, “Eigenmode analysis of a light-guiding metal line loaded on a dielectric substrate using the imaginary-distance beam-propagation method,” J. Lightwave Technol. 23, 1533–1539 (2005).
[CrossRef]

R. Charbonneau, C. Scales, I. Breukelaar, S. Fafard, N. Lahoud, G. Mattiussi, and P. Berini, “Passive integrated optics elements based on long-range surface plasmon polaritons,” J. Lightwave Technol. 24, 477–494 (2006).
[CrossRef]

Y.-C. Lu, L. Yang, W.-P. Huang, and S.-S. Jian, “Improved full-vector finite-difference complex mode solver for optical waveguides of circular symmetry,” J. Lightwave Technol. 26, 1868–1876 (2008).
[CrossRef]

R. Buckley and P. Berini, “Radiation suppressing metallo-dielectric optical waveguides,” J. Lightwave Technol. 27, 2800–2808 (2009).
[CrossRef]

Microw. Opt. Technol. Lett. (1)

W. C. Chew, J. M. Jin, and E. Michielssen, “Complex coordinate stretching as a generalized absorbing boundary condition,” Microw. Opt. Technol. Lett. 17–21 (1997).

N. J. Phys. (2)

A. Degiron, S.-Y. Cho, T. Tyler, N. M. Jokerst, and D. R. Smith, “Directional coupling between dielectric and long-range plasmon waveguides,” N. J. Phys. 11, 015002 (2009).
[CrossRef]

P. Berini, “Bulk and surface sensitivities of surface plasmon waveguides,” N. J. Phys. 10, 105010 (2008).
[CrossRef]

Nano Lett. (1)

P. Berini, R. Charbonneau, and N. Lahoud, “Long-range surface plasmons on ultrathin membranes,” Nano Lett. 7, 1376–1380 (2007).
[CrossRef] [PubMed]

Nanoscale Res. Lett. (1)

C. Wang and L. Lin, “Nanoscale waveguiding methods,” Nanoscale Res. Lett. 2, 219–229 (2007).
[CrossRef] [PubMed]

Opt. Express (10)

M. Paulus and O. J. F. Martin, “How to tap an innocent waveguide,” Opt. Express 8, 644–648 (2001).
[CrossRef] [PubMed]

P. Berini and J. Lu, “Curved long-range surface plasmon-polariton waveguides,” Opt. Express 14, 2365–2371 (2006).
[CrossRef] [PubMed]

X. Heng, X. Cui, D. W. Knapp, J. Wu, Z. Yaqoob, E. J. McDowell, D. Psaltis, and C. Yang, “Characterization of light collection through a subwavelength aperture from a point source,” Opt. Express 14, 10410–10425 (2006).
[CrossRef] [PubMed]

K. Kakihara, N. Kono, K. Saitoh, and M. Koshiba, “Full-vectorial finite element method in a cylindrical coordinate system for loss analysis of photonic wire bends,” Opt. Express 14, 11128–11141 (2006).
[CrossRef] [PubMed]

A. Degiron and D.R. Smith, “Numerical simulations of long-range plasmons,” Opt. Express 14, 1611–1625 (2006).
[CrossRef] [PubMed]

M. Hochberg, T. Baehr-Jones, C. Walker, and A. Scherer, “Integrated plasmon and dielectric waveguides,” Opt. Express 12, 5481–5486 (2004).
[CrossRef] [PubMed]

Y.-J. Tsai, A. Degiron, N. M. Jokerst, and D. R. Smith, “Plasmonic multi-mode interference couplers,” Opt. Express 17, 17471–17482 (2009).
[CrossRef] [PubMed]

Q. Min, C. Chen, P. Berini, and R. Gordon, “Long range surface plasmons on asymmetric suspended thin film structures for biosensing applications,” Opt. Express 18, 19009–19019 (2010).
[CrossRef] [PubMed]

R. Buckley and P. Berini, “Figures of merit for 2D surface plasmon waveguides and application to metal stripes,” Opt. Express 15, 12174–12182 (2007).
[CrossRef] [PubMed]

J. T. Kim, J. J. Ju, S. Park, M. su Kim, S. K. Park, and M.-H. Lee, “Chip-to-chip optical interconnect using gold long-range surface plasmon polariton waveguides,” Opt. Express 16, 13133–13138 (2008).
[CrossRef] [PubMed]

Opt. Lett. (2)

Opt. Quantum Electron. (1)

J. Ctyroky, J. Homola, and M. Skalsky, “Modelling of surface plasmon resonance waveguide sensor by complex mode expansion and propagation method,” Opt. Quantum Electron. 29, 301–311 (1997).
[CrossRef]

Phys. Rev. A (1)

A. Degiron, S.-Y. Cho, C. Harrison, N. M. Jokerst, C. Dellagiacoma, O. J. F. Martin, and D. R. Smith, “Experimental comparison between conventional and hybrid long-range surface plasmon waveguide bends,” Phys. Rev. A 77, 021804 (2008).
[CrossRef]

Phys. Rev. B (2)

G. C. des Francs, J. Grandidier, S. Massenot, A. Bouhelier, J.-C. Weeber, and A. Dereux, “Integrated plasmonic waveguides: A mode solver based on density of states formulation,” Phys. Rev. B 80, 115419 (2009).
[CrossRef]

P. Johnson and R. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics (1)

M. Paulus, P. Gay-Balmaz, and O. J. F. Martin, “Accurate and efficient computation of the green’s tensor for stratified media,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 62, 5797–5807 (2000).
[CrossRef] [PubMed]

Radio Sci. (1)

M. Paulus and O. J. F. Martin, “A green’s tensor approach to the modeling of nanostructure replication and characterization,” Radio Sci. 38, 8024 (2003).
[CrossRef]

Sens. Actuators B Chem. (1)

R. Charbonneau, M. Tencer, N. Lahoud, and P. Berini, “Demonstration of surface sensing using long-range surface plasmon waveguides on silica,” Sens. Actuators B Chem. 134, 455–461 (2008).
[CrossRef]

Other (5)

A. Krasavin, P. Bolger, A. Zayats, Stær, T. Holmgaard, Z. Chen, S. Bozhevolnyi, L. Markey, and A. Dereux, “Active components for integrated plasmonic circuits,” in “2nd IEEE LEOS Winter Topicals, WTM 2009,” (2009).
[CrossRef]

J. Jin, The Finite Element Method in Electromagnetics, 2nd ed. (John Wiley and Sons, 2002).

COMSOL Multiphysics User Guide, Version 3.3 (COMSOL AB, Stockholm, Sweden, 2006).

S. Burger, L. Zschiedrich, J. Pomplun, and F. Schmidt, “Jcmsuite: An adaptive fem solver or precise simulations in nano-optics,” in “Integrated Photonics and Nanophotonics Research and Applications,” (Optical Society of America, 2008), paper ITuE4.

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic Press, 1974), p. 267.

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Figures (7)

Fig. 1
Fig. 1

Illustration of the considered dielectric and plasmonic waveguide structure. Modes couple from a dielectric waveguide (BCB on SiO2) over a straight to a uniformly bent hybrid plasmonic waveguide (Au core embedded in BCB on SiO2).

Fig. 2
Fig. 2

Coupling from a 6.5μm wide and 1.6μm thick dielectric waveguide to a hybrid plasmonic guide: (a) Coupling efficiency and (b) effective index and absorption of the plasmonic waveguide as a function of the Au strip position within the two–dimensional dielectric waveguide. The center is at y = 0.8μm. The dimensions of the Au strip are 3μm × 20nm. The inset in (a) shows the electric field amplitude distribution for three different y–positions of the plasmonic waveguide.

Fig. 3
Fig. 3

Coupling from a 1.6μm thick dielectric waveguide to a hybrid plasmonic one: coupling efficiency as a function of the dielectric waveguide width for a plasmonic waveguide located at the optimal height. Two different Au strips are investigated, with dimensions 3μm × 20nm and 6μm × 20nm, respectively.

Fig. 4
Fig. 4

Characteristics of bent hybrid plasmonic waveguides: (a) optimal radius and (b) corresponding minimal bending loss as a function of the Au strip width w and thickness (t = 15 . . . 35nm).

Fig. 5
Fig. 5

Minimal bending loss for a 2, 3, 4, 6 and 11μm wide Au strip as a function of the bending radius. The radii correspond to the optimal radii of the respective strip width and thickness as represented in Fig. 4.

Fig. 6
Fig. 6

Lateral and vertical offset between a straight and bent hybrid waveguide: Coupling efficiency as a function (a) of the lateral offset and (b) of the vertical offset. The Au strips of the straight and bent waveguide are 3μm × 20nm and 3μm × 10nm, respectively.

Fig. 7
Fig. 7

Straight and optimally bent waveguide coupling: (a) Au strip thickness and coupling loss as a function of the optimal radius. (b) Optimal lateral offset as a function of the optimal radius. The Au strip is 3μm wide.

Equations (8)

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n t = n exp u r 0 and u = r 0 ln r r 0 ,
× ( E x E y α e z ) e α r 0 θ = ( α ( r 0 r E y + e z y ) α 1 r ( e z + r e z x + r 0 E x ) E y x E x y ) e α r 0 θ ,
[ ɛ ] PML = ɛ [ Λ ]     and     [ μ ] PML = μ [ Λ ] ,
[ Λ ] = [ s θ s y s r 0 0 0 s y s r s θ 0 0 0 s r s θ s y ] .
s r = 1 + j ( r r b L ) 2 δ max ,
{ s ϕ = r ˜ r s y = 1 , with r ˜ = r b r b r s r ( r ) d r ,
C = Ω E y 1 E y 2 * d Ω Ω E y 1 E y 1 * d Ω Ω E y 2 E y 2 * d Ω .
α C = 20 log | C | .

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