Integrated plasmonic waveguides: A mode solver based on density of states formulation

Physical Review B - Condensed Matter and Materials Physics

Volumn 80, Issue 11, 2009, Pages

  Colas Des Francs, Gérard ^a   Grandidier, Jonathan ^a   Massenot, Sébastien ^a,b   Bouhelier, Alexandre ^a   Weeber, Jean Claude ^a   Dereux, Alain ^a  

^a UNIVERSITÉ DE BOURGOGNE   (France)

^b UNIVERSITÉ DE TOULOUSE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 70350578356     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.80.115419     Document Type: Article

References (27)

1. R. G. Hunsperger, Integrated Optics: Theory and Technology (Springer, New York, 2002).
2. B. Steinberger, A. Hohenau, H. Ditlbacher, A. L. Stepanov, A. Drezet, F. R. Aussenegg, A. Leitner, and J. R. Krenn, Appl. Phys. Lett. 88, 094104 (2006). 10.1063/1.2180448
3. T. Holmgaard and S. I. Bozhevolnyi, Phys. Rev. B 75, 245405 (2007). 10.1103/PhysRevB.75.245405
4. A. V. Krasavin and A. V. Zayats, Phys. Rev. B 78, 045425 (2008). 10.1103/PhysRevB.78.045425
5. J. Grandidier, G. Colas des Francs, S. Massenot, A. Bouhelier, L. Markey, J. Weeber, C. Finot, and A. Dereux, Nano Lett. 9, 2935 (2009).
6. V. Ta'eed, Opt. Express 15, 9205 (2007). 10.1364/OE.15.009205
7. S. Massenot, J.-C. Weeber, A. Bouhelier, G. Colas des Francs, J. Grandidier, L. Markey, and A. Dereux, Opt. Express 16, 17599 (2008). 10.1364/OE.16.017599
8. J. Callaway, Quantum Theory of the Solid State (Academic Press, New York, 1976).
9. A. Lagendijk and B. Tiggelen, Phys. Rep. 270, 143 (1996). 10.1016/0370-1573(95)00065-8
10. G. Colas des Francs, C. Girard, J.-C. Weeber, C. Chicane, T. David, A. Dereux, and D. Peyrade, Phys. Rev. Lett. 86, 4950 (2001). 10.1103/PhysRevLett. 86.4950
11. A. Dereux, J. P. Vigneron, P. Lambin, and A. A. Lucas, Phys. Rev. B 38, 5438 (1988). 10.1103/PhysRevB.38.5438
12. O. J. F. Martin, C. Girard, D. R. Smith, and S. Schultz, Phys. Rev. Lett. 82, 315 (1999). 10.1103/PhysRevLett.82.315
13. P. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw Hill, New York, 1953).
14. A. Dereux, Ph.D. thesis, Facultes Universitaires Notre Dame de la Paix, Namur, 1991.
15. A slightly different definition is also possible. Writing δ (ky ′2 - ky2) =1/2 | ky | [δ (ky′ - ky) +δ (ky′ + ky)], we obtain ρ (ky2) =1/2 ky [ρ (ky) +ρ (- ky)] (ky >0). Moreover, ρ (- ky) =ρ (ky) since ± ky simply defines forward and backward propagations. This lead to Δρ (ky; ω) =g/2πΔ ky /2/ (ky - ky0) 2 + (Δ ky /2) 2 instead of Eq. 8 and a degeneracy g/2, excluding forward/backward propagation degeneracy.
16. DOS can also be expressed in the frequency space for fixed momentum ky. Noticing that θ is a function of both ω and v= ky2, we use the identity | θ ω | v | ω v | θ | v θ | ω =-1 that leads to | θ ω | ky =- | v ω | v | θ v | ω =-2 ky / vg πΔ ρ (ky2; ω) =-π/ vg Δρ (ky; ω). A Taylor expansion near the resonance frequency ω0 gives then Δρ (ky; ω) g vg /πΔω/2/ (ω- ω0) 2 + (Δω/2) 2, with Δω=-2ImD (ω0; ky) / [ReD (ω; ky) /ω] (ω= ω0) =1/τ= vg / LSPP, and τ is the mode lifetime. See also M. Kretschmann and A. A. Maradudin, Phys. Rev. B 66, 245408 (2002). 10.1103/PhysRevB.66.245408
17. C. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons, New York, 1983).
18. G. Colas des Francs, C. Girard, and A. Dereux, J. Chem. Phys. 117, 4659 (2002). 10.1063/1.1492795
19. G. Lévêque, G. Colas des Francs, C. Girard, J.-C. Weeber, C. Meier, C. Robilliard, R. Mathevet, and J. Weiner, Phys. Rev. E 65, 036701 (2002). 10.1103/PhysRevE.65.036701
20. M. Paulus and O. J. F. Martin, Phys. Rev. E 63, 066615 (2001). 10.1103/PhysRevE.63.066615
21. A. V. Krasavin and A. V. Zayats, Appl. Phys. Lett. 90, 211101 (2007). 10.1063/1.2740485
22. T. Holmgaard, S. Bozhevolnyi, L. Markey, and A. Dereux, Appl. Phys. Lett. 92, 011124 (2008). 10.1063/1.2825588
23. J. Grandidier, S. Massenot, G. Colas des Francs, A. Bouhelier, J.-C. Weeber, L. Markey, A. Dereux, J. Renger, M. U. González, and R. Quidant, Phys. Rev. B 78, 245419 (2008). 10.1103/PhysRevB.78.245419
24. E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, New York, 1998).
25. A. Drezet, A. Hohenau, D. Koller, A. Stepanov, H. Ditlbacher, B. Steinberger, F. Aussenegg, A. Leitner, and J. Krenn, Mater. Sci. Eng., B 149, 220 (2008). 10.1016/j.mseb.2007.10.010
26. G. Boudebs, S. Cherukulappurath, M. Guignard, J. Troles, F. Smektala, and F. Sanchez, Opt. Commun. 230, 331 (2004). 10.1016/j.optcom.2003.11.021
27. R. Quidant, J.-C. Weeber, A. Dereux, D. Peyrade, G. Colas des Francs, C. Girard, and Y. Chen, Phys. Rev. E 64, 066607 (2001). 10.1103/PhysRevE.64.066607