Abstract

The field enhancement in the gap between two Si microdisks is theoretically investigated using the finite difference time domain method. We show that the electric field within this gap increases as the distance between the two disks decreases, and it can be enhanced by as much as two orders of magnitude. By perturbing the Si microdisks to force the field leakage into an ever smaller volume, the field enhancement can reach a value as high as 238 with a deep sub-wavelength mode volume. This behavior is comparable to what can be observed in gap plasmons between metal nanoparticles, but is produced here in purely dielectric structures.

©2007 Optical Society of America

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References

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  1. H. Xu, E. J. Bjerneld, M. Kall, and L. Borjesson, “Spectroscopy of single hemoglobin molecules by surface enhanced Raman scattering” Phys. Rev. Lett. 83, 4357 (1999).
    [Crossref]
  2. J. Jiang, K. Bosnick, M. Maillard, and L. Brus, “Single molecule Raman spectroscopy at the junctions of large Ag nanocrystals,” J. Phys. Chem. B 107, 9964 (2003).
    [Crossref]
  3. Hartschuh, E. J. Sanchez, X. S. Xie, and L. Novotny, “High resolution near field Raman microscopy of single-walled carbon nanotubes,” Phys. Rev. Lett. 90, 095503 (2003).
    [Crossref] [PubMed]
  4. S. A. Maier, “Plasmonic field enhancement and SERS in the effective mode volume picture” Opt. Express 14, 1957 (2006).
    [Crossref] [PubMed]
  5. J. Aizpurua, G. W. Bryant, L. J. Richter, and F. J. Garcia de Abajo, “Optical properties of coupled metallic nanorods for field enhanced spectroscopy,” Phys. Rev. B 71, 235420 (2005).
    [Crossref]
  6. J. T. Robinson, C. Manolatou, L. Chen, and M. Lipson, “Ultrasmall Mode Volumes in Dielectric Optical Microcavities,” Phys. Rev. Lett. 95, 143901 (2005).
    [Crossref] [PubMed]
  7. J. Vahala, “Oprical microcavities,” Nature 424, 839 (2003).
    [Crossref] [PubMed]
  8. V. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081 (2004).
    [Crossref] [PubMed]
  9. M. M. Sigalas, R. S. Williams, D. A. Fattal, S.Y. Wang, and R. G. Beausoleil, “Comparison of field enhancement of scattered waves from dielectric and metallic nanoparticles,” to be submitted.

2006 (1)

2005 (2)

J. Aizpurua, G. W. Bryant, L. J. Richter, and F. J. Garcia de Abajo, “Optical properties of coupled metallic nanorods for field enhanced spectroscopy,” Phys. Rev. B 71, 235420 (2005).
[Crossref]

J. T. Robinson, C. Manolatou, L. Chen, and M. Lipson, “Ultrasmall Mode Volumes in Dielectric Optical Microcavities,” Phys. Rev. Lett. 95, 143901 (2005).
[Crossref] [PubMed]

2004 (1)

V. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081 (2004).
[Crossref] [PubMed]

2003 (3)

J. Vahala, “Oprical microcavities,” Nature 424, 839 (2003).
[Crossref] [PubMed]

J. Jiang, K. Bosnick, M. Maillard, and L. Brus, “Single molecule Raman spectroscopy at the junctions of large Ag nanocrystals,” J. Phys. Chem. B 107, 9964 (2003).
[Crossref]

Hartschuh, E. J. Sanchez, X. S. Xie, and L. Novotny, “High resolution near field Raman microscopy of single-walled carbon nanotubes,” Phys. Rev. Lett. 90, 095503 (2003).
[Crossref] [PubMed]

1999 (1)

H. Xu, E. J. Bjerneld, M. Kall, and L. Borjesson, “Spectroscopy of single hemoglobin molecules by surface enhanced Raman scattering” Phys. Rev. Lett. 83, 4357 (1999).
[Crossref]

Aizpurua, J.

J. Aizpurua, G. W. Bryant, L. J. Richter, and F. J. Garcia de Abajo, “Optical properties of coupled metallic nanorods for field enhanced spectroscopy,” Phys. Rev. B 71, 235420 (2005).
[Crossref]

Almeida, V.

V. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081 (2004).
[Crossref] [PubMed]

Barrios, C. A.

V. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081 (2004).
[Crossref] [PubMed]

Beausoleil, R. G.

M. M. Sigalas, R. S. Williams, D. A. Fattal, S.Y. Wang, and R. G. Beausoleil, “Comparison of field enhancement of scattered waves from dielectric and metallic nanoparticles,” to be submitted.

Bjerneld, E. J.

H. Xu, E. J. Bjerneld, M. Kall, and L. Borjesson, “Spectroscopy of single hemoglobin molecules by surface enhanced Raman scattering” Phys. Rev. Lett. 83, 4357 (1999).
[Crossref]

Borjesson, L.

H. Xu, E. J. Bjerneld, M. Kall, and L. Borjesson, “Spectroscopy of single hemoglobin molecules by surface enhanced Raman scattering” Phys. Rev. Lett. 83, 4357 (1999).
[Crossref]

Bosnick, K.

J. Jiang, K. Bosnick, M. Maillard, and L. Brus, “Single molecule Raman spectroscopy at the junctions of large Ag nanocrystals,” J. Phys. Chem. B 107, 9964 (2003).
[Crossref]

Brus, L.

J. Jiang, K. Bosnick, M. Maillard, and L. Brus, “Single molecule Raman spectroscopy at the junctions of large Ag nanocrystals,” J. Phys. Chem. B 107, 9964 (2003).
[Crossref]

Bryant, G. W.

J. Aizpurua, G. W. Bryant, L. J. Richter, and F. J. Garcia de Abajo, “Optical properties of coupled metallic nanorods for field enhanced spectroscopy,” Phys. Rev. B 71, 235420 (2005).
[Crossref]

Chen, L.

J. T. Robinson, C. Manolatou, L. Chen, and M. Lipson, “Ultrasmall Mode Volumes in Dielectric Optical Microcavities,” Phys. Rev. Lett. 95, 143901 (2005).
[Crossref] [PubMed]

de Abajo, F. J. Garcia

J. Aizpurua, G. W. Bryant, L. J. Richter, and F. J. Garcia de Abajo, “Optical properties of coupled metallic nanorods for field enhanced spectroscopy,” Phys. Rev. B 71, 235420 (2005).
[Crossref]

Fattal, D. A.

M. M. Sigalas, R. S. Williams, D. A. Fattal, S.Y. Wang, and R. G. Beausoleil, “Comparison of field enhancement of scattered waves from dielectric and metallic nanoparticles,” to be submitted.

Hartschuh,

Hartschuh, E. J. Sanchez, X. S. Xie, and L. Novotny, “High resolution near field Raman microscopy of single-walled carbon nanotubes,” Phys. Rev. Lett. 90, 095503 (2003).
[Crossref] [PubMed]

Jiang, J.

J. Jiang, K. Bosnick, M. Maillard, and L. Brus, “Single molecule Raman spectroscopy at the junctions of large Ag nanocrystals,” J. Phys. Chem. B 107, 9964 (2003).
[Crossref]

Kall, M.

H. Xu, E. J. Bjerneld, M. Kall, and L. Borjesson, “Spectroscopy of single hemoglobin molecules by surface enhanced Raman scattering” Phys. Rev. Lett. 83, 4357 (1999).
[Crossref]

Lipson, M.

J. T. Robinson, C. Manolatou, L. Chen, and M. Lipson, “Ultrasmall Mode Volumes in Dielectric Optical Microcavities,” Phys. Rev. Lett. 95, 143901 (2005).
[Crossref] [PubMed]

V. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081 (2004).
[Crossref] [PubMed]

Maier, S. A.

Maillard, M.

J. Jiang, K. Bosnick, M. Maillard, and L. Brus, “Single molecule Raman spectroscopy at the junctions of large Ag nanocrystals,” J. Phys. Chem. B 107, 9964 (2003).
[Crossref]

Manolatou, C.

J. T. Robinson, C. Manolatou, L. Chen, and M. Lipson, “Ultrasmall Mode Volumes in Dielectric Optical Microcavities,” Phys. Rev. Lett. 95, 143901 (2005).
[Crossref] [PubMed]

Novotny, L.

Hartschuh, E. J. Sanchez, X. S. Xie, and L. Novotny, “High resolution near field Raman microscopy of single-walled carbon nanotubes,” Phys. Rev. Lett. 90, 095503 (2003).
[Crossref] [PubMed]

Panepucci, R. R.

V. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081 (2004).
[Crossref] [PubMed]

Richter, L. J.

J. Aizpurua, G. W. Bryant, L. J. Richter, and F. J. Garcia de Abajo, “Optical properties of coupled metallic nanorods for field enhanced spectroscopy,” Phys. Rev. B 71, 235420 (2005).
[Crossref]

Robinson, J. T.

J. T. Robinson, C. Manolatou, L. Chen, and M. Lipson, “Ultrasmall Mode Volumes in Dielectric Optical Microcavities,” Phys. Rev. Lett. 95, 143901 (2005).
[Crossref] [PubMed]

Sanchez, E. J.

Hartschuh, E. J. Sanchez, X. S. Xie, and L. Novotny, “High resolution near field Raman microscopy of single-walled carbon nanotubes,” Phys. Rev. Lett. 90, 095503 (2003).
[Crossref] [PubMed]

Sigalas, M. M.

M. M. Sigalas, R. S. Williams, D. A. Fattal, S.Y. Wang, and R. G. Beausoleil, “Comparison of field enhancement of scattered waves from dielectric and metallic nanoparticles,” to be submitted.

Vahala, J.

J. Vahala, “Oprical microcavities,” Nature 424, 839 (2003).
[Crossref] [PubMed]

Wang, S.Y.

M. M. Sigalas, R. S. Williams, D. A. Fattal, S.Y. Wang, and R. G. Beausoleil, “Comparison of field enhancement of scattered waves from dielectric and metallic nanoparticles,” to be submitted.

Williams, R. S.

M. M. Sigalas, R. S. Williams, D. A. Fattal, S.Y. Wang, and R. G. Beausoleil, “Comparison of field enhancement of scattered waves from dielectric and metallic nanoparticles,” to be submitted.

Xie, X. S.

Hartschuh, E. J. Sanchez, X. S. Xie, and L. Novotny, “High resolution near field Raman microscopy of single-walled carbon nanotubes,” Phys. Rev. Lett. 90, 095503 (2003).
[Crossref] [PubMed]

Xu, H.

H. Xu, E. J. Bjerneld, M. Kall, and L. Borjesson, “Spectroscopy of single hemoglobin molecules by surface enhanced Raman scattering” Phys. Rev. Lett. 83, 4357 (1999).
[Crossref]

J. Phys. Chem. B (1)

J. Jiang, K. Bosnick, M. Maillard, and L. Brus, “Single molecule Raman spectroscopy at the junctions of large Ag nanocrystals,” J. Phys. Chem. B 107, 9964 (2003).
[Crossref]

Nature (2)

J. Vahala, “Oprical microcavities,” Nature 424, 839 (2003).
[Crossref] [PubMed]

V. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081 (2004).
[Crossref] [PubMed]

Opt. Express (1)

Phys. Rev. B (1)

J. Aizpurua, G. W. Bryant, L. J. Richter, and F. J. Garcia de Abajo, “Optical properties of coupled metallic nanorods for field enhanced spectroscopy,” Phys. Rev. B 71, 235420 (2005).
[Crossref]

Phys. Rev. Lett. (3)

J. T. Robinson, C. Manolatou, L. Chen, and M. Lipson, “Ultrasmall Mode Volumes in Dielectric Optical Microcavities,” Phys. Rev. Lett. 95, 143901 (2005).
[Crossref] [PubMed]

Hartschuh, E. J. Sanchez, X. S. Xie, and L. Novotny, “High resolution near field Raman microscopy of single-walled carbon nanotubes,” Phys. Rev. Lett. 90, 095503 (2003).
[Crossref] [PubMed]

H. Xu, E. J. Bjerneld, M. Kall, and L. Borjesson, “Spectroscopy of single hemoglobin molecules by surface enhanced Raman scattering” Phys. Rev. Lett. 83, 4357 (1999).
[Crossref]

Other (1)

M. M. Sigalas, R. S. Williams, D. A. Fattal, S.Y. Wang, and R. G. Beausoleil, “Comparison of field enhancement of scattered waves from dielectric and metallic nanoparticles,” to be submitted.

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Figures (4)

Fig. 1.
Fig. 1. (a) The xz cross section of the structure. (b). The magnitude of the x-component of the electric field in the center of the gap for the structure shown in Fig. 1a. Two Si disks of 2 μm diameter and 200 nm thickness are separated by a 20nm air gap.

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Fig. 2
Fig. 2 (a). The xz cross-section of the magnitude of the electric field distribution at the middle of the disks for the longest wavelength resonance (2.437 μm). A logarithmic scale is used with red color corresponding to the maximum value. The structure consists of two Si disks of 2 μm diameter and 200nm thick separated by a 20nm gap. (b). The xy cross-section of the field distribution at the middle of the structure. A logarithmic scale is used with red color corresponding to the maximum value.

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Fig. 3.
Fig. 3. (a) The xz cross section of the perturbed structure. (b). The magnitude of the x-component of the electric field (normalized to the input field magnitude) in the center of the gap for the structure shown in Fig. 3a. Two Si disks of 2 μm diameter and 200 nm thickness are separated by a 30 nm and 60 nm (green and red lines, respectively) gap and two smaller Si disks of 10nm and 40nm diameter are separated by 20nm air gap. The blue line correspond to the same structure as in Fig. 1b.

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Fig. 4.
Fig. 4. The maximum of the x-component of the electric field normalized to the amplitude of the incoming field, measured at the center of the gap for different values of the gap width. The blue circles correspond to the case of two Si disks, each with a diameter of 2 μm and a thickness of 200 nm (see Fig. 1a). The red crosses correspond to the case of two Si disks separated by d1=30nm and two smaller Si disks separated by a gap of width, d2 (see Fig. 3a).

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