Abstract

We demonstrate the presence of strong longitudinal electric fields (Ez) in silicon nanowire waveguides through numerical computation. These waveguide fields can be engineered through choice of waveguide geometry to exhibit amplitudes as high as 97% that of the dominant transverse field component. We show even larger longitudinal fields created in free space by a terminated waveguide can become the dominant electric field component, and demonstrate Ez has a large effect on waveguide nonlinearity. We discuss the possibility of controlling the strength and symmetry of Ez using a dual waveguide design, and show that the resulting longitudinal field is sharply peaked beyond the diffraction limit.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. Dorn, S. Quabis, and G. Leuchs, "Sharper Focus for a Radially Polarized Light Beam," Phys. Rev. Lett. 91, 233901 1-4 (2003).
    [CrossRef]
  2. H. P. Urbach and S. F. Pereira, "Field in Focus with a Maximum Longitudinal Electric Component," Phys. Rev. Lett. 100, 123904 1-4 (2008).
    [CrossRef]
  3. S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, "Focusing light to a tighter spot," Opt. Commun. 179, 1-7 (2000).
    [CrossRef]
  4. Q. Zhan and J. Leger, "Focus shaping using cylindrical vector beams," Opt. Express 10, 324-331 (2000).
  5. L. E. Helseth, "Roles of polarization, phase and amplitude in solid immersion lens systems," Opt. Commun. 191, 161-172 (2001).
    [CrossRef]
  6. J. J. Macklin, J. K. Trautman, T. D. Harris, and L. E. Brus, "Imaging and Time-Resolved Spectroscopy of Single Molecules at an Interface" Science 272, 255-258 (1996).
    [CrossRef]
  7. L. Novotny, E. J. Sanchez, and X. S. Xie, "Near-field optical imaging using metal tips illuminated by higher-order Hermite-Gaussian beams," Ultramicroscopy 71, 21-29 (1998).
    [CrossRef]
  8. A. S. van de Nes, J. J. M. Braat, and S. F. Pereira, "High-density optical data storage," Rep. Prog. Phys. 69, 2323-2363 (2006).
    [CrossRef]
  9. M. O. Scully, "A Simple Laser Linac," Appl. Phys. B. 51, 238-241 (1990).
    [CrossRef]
  10. L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, "Longitudinal Field Modes Probed by Single Molecules," Phys. Rev. Lett. 86, 5251-5254 (2001).
    [CrossRef] [PubMed]
  11. G. Kihara Rurimo, M. Schardt, S. Quabis, S. Malzer, Ch. Dotzler,A. Winkler, G. Leuchs, G. H. Dohler, D. Driscoll, M. Hanson, A. C. Gossard, and S. F. Pereira, "Using a quantum well heterostructure to study the longitudinal and transverse electric field components of a strongly focused laser beam," J. Appl. Phys. 100, 023112 1-6 (2006).
    [CrossRef]
  12. Q. Zhan, "Trapping metallic Rayleigh particles with radial polarization," Opt. Express 12, 3377-3382 (2004)
    [CrossRef] [PubMed]
  13. N. Destouches, B. Sider, A. V. Tishchenko, and O. Parriaux, "Optimization of a Waveguide Grating for Normal TM Mode Coupling," Opt. Quantum Electron. 38,123-131 (2006).
    [CrossRef]
  14. Y. Kozawa and S. Sato, "Observation of the longitudinal field of a focused laser beam by second-harmonic generation," J. Opt. Soc. Am. B 25, 175-179 (2008).
    [CrossRef]
  15. A. Boivin and E. Wolf, "Electromagnetic Field in the Neighborhood of the Focus of a Coherent Beam," Phys. Rev. 138, B1561-B1565 (1965).
    [CrossRef]
  16. M. Lax, W. H. Louisell, and W. B. McKnight, "From Maxwell to paraxial wave optics," Phys. Rev. A 11, 1365-1370 (1975).
    [CrossRef]
  17. V. G. Niziev and A. V. Nesterov, "Longitudinal fields in cylindrical and spherical modes," J. Opt. A: Pure Appl. Opt. 10, 085005 1-7 (2008).
    [CrossRef]
  18. K. Youngworth and T. Brown, "Focusing of high numerical aperture cylindrical-vector beams," Opt. Express 7, 77-87 (2000).
    [CrossRef] [PubMed]
  19. X. Chen, N. C. Panoiu, and R. M. Osgood, Jr., "Theory of Raman-mediated pulsed amplification in silicon-wire waveguides," IEEE J. Quantum Electron. 42, 160-170 (2006).
    [CrossRef]
  20. A. C. Turner, C. Manolatou, B. S. Schmidt, M. Lipson, M. A. Foster, J. E. Sharping, and A. L. Gaeta, "Tailored anomalous group-velocity dispersion in silicon channel waveguides," Opt. Express 14, 4357-4362 (2006).
    [CrossRef] [PubMed]
  21. J. I. Dadap, N. C. Panoiu, X. Chen, I. Hsieh, X. Liu, C. Chou, E. Dulkeith, S. J. McNab, F. Xia, W. M. J. Green, L. Sekaric, Y. A. Vlasov, and R. M. Osgood, Jr., "Nonlinear-optical phase modification in dispersion-engineered Si photonic wires," Opt. Express 16, 1280-1299 (2008).
    [CrossRef] [PubMed]
  22. M. Krause, H. Renner, and E. Brinkmeyer, "Optical isolation in silicon waveguides based on nonreciprocal Raman amplification," Elect. Lett. 44, 691-693 (2008).
    [CrossRef]
  23. C. L. Xu, W. P. Huang, M. S. Stern, and S. K. Chaudhuri, "Full-vectorial mode calculations by finite difference method," IEE Proc. Optoelectron. 141, 281-286 (1994).
    [CrossRef]
  24. L. Tong, J. Lou, and E. Mazur, "Single-mode guiding properties of subwavelength-diameter silica and silicon wire waveguides," Opt. Express 12, 1025-1035 (2004).
    [CrossRef] [PubMed]
  25. G. P. Agrawal, Nonlinear Fiber Optics (Academic, New York, 2001).
  26. V. R. Almeida, Q. Xu, C. A. Barrios, and M. Lipson, "Guiding and confining light in void nanostructure," Opt. Lett. 29, 1209-1211 (2004).
    [CrossRef] [PubMed]
  27. C. Koos, L. Jacome, C. Poulton, J. Leuthold, and W. Freude, "Nonlinear silicon-on-insulator waveguides for all-optical signal processing," Opt. Express 15, 5976-5990 (2007).
    [CrossRef] [PubMed]
  28. M. L. Povinelli, M. Loncar, M. Ibanescu, E. J. Smythe, S. G. Johnson, F. Capasso, and J. D. Joannopoulos, "Evanescent-wave bonding between optical waveguides," Opt. Lett. 30, 3042-3044 (2005).
    [CrossRef] [PubMed]

2008 (3)

2007 (1)

2006 (4)

N. Destouches, B. Sider, A. V. Tishchenko, and O. Parriaux, "Optimization of a Waveguide Grating for Normal TM Mode Coupling," Opt. Quantum Electron. 38,123-131 (2006).
[CrossRef]

X. Chen, N. C. Panoiu, and R. M. Osgood, Jr., "Theory of Raman-mediated pulsed amplification in silicon-wire waveguides," IEEE J. Quantum Electron. 42, 160-170 (2006).
[CrossRef]

A. C. Turner, C. Manolatou, B. S. Schmidt, M. Lipson, M. A. Foster, J. E. Sharping, and A. L. Gaeta, "Tailored anomalous group-velocity dispersion in silicon channel waveguides," Opt. Express 14, 4357-4362 (2006).
[CrossRef] [PubMed]

A. S. van de Nes, J. J. M. Braat, and S. F. Pereira, "High-density optical data storage," Rep. Prog. Phys. 69, 2323-2363 (2006).
[CrossRef]

2005 (1)

2004 (3)

2001 (2)

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, "Longitudinal Field Modes Probed by Single Molecules," Phys. Rev. Lett. 86, 5251-5254 (2001).
[CrossRef] [PubMed]

L. E. Helseth, "Roles of polarization, phase and amplitude in solid immersion lens systems," Opt. Commun. 191, 161-172 (2001).
[CrossRef]

2000 (3)

1998 (1)

L. Novotny, E. J. Sanchez, and X. S. Xie, "Near-field optical imaging using metal tips illuminated by higher-order Hermite-Gaussian beams," Ultramicroscopy 71, 21-29 (1998).
[CrossRef]

1996 (1)

J. J. Macklin, J. K. Trautman, T. D. Harris, and L. E. Brus, "Imaging and Time-Resolved Spectroscopy of Single Molecules at an Interface" Science 272, 255-258 (1996).
[CrossRef]

1994 (1)

C. L. Xu, W. P. Huang, M. S. Stern, and S. K. Chaudhuri, "Full-vectorial mode calculations by finite difference method," IEE Proc. Optoelectron. 141, 281-286 (1994).
[CrossRef]

1990 (1)

M. O. Scully, "A Simple Laser Linac," Appl. Phys. B. 51, 238-241 (1990).
[CrossRef]

1975 (1)

M. Lax, W. H. Louisell, and W. B. McKnight, "From Maxwell to paraxial wave optics," Phys. Rev. A 11, 1365-1370 (1975).
[CrossRef]

1965 (1)

A. Boivin and E. Wolf, "Electromagnetic Field in the Neighborhood of the Focus of a Coherent Beam," Phys. Rev. 138, B1561-B1565 (1965).
[CrossRef]

Almeida, V. R.

Barrios, C. A.

Beversluis, M. R.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, "Longitudinal Field Modes Probed by Single Molecules," Phys. Rev. Lett. 86, 5251-5254 (2001).
[CrossRef] [PubMed]

Boivin, A.

A. Boivin and E. Wolf, "Electromagnetic Field in the Neighborhood of the Focus of a Coherent Beam," Phys. Rev. 138, B1561-B1565 (1965).
[CrossRef]

Braat, J. J. M.

A. S. van de Nes, J. J. M. Braat, and S. F. Pereira, "High-density optical data storage," Rep. Prog. Phys. 69, 2323-2363 (2006).
[CrossRef]

Brinkmeyer, E.

M. Krause, H. Renner, and E. Brinkmeyer, "Optical isolation in silicon waveguides based on nonreciprocal Raman amplification," Elect. Lett. 44, 691-693 (2008).
[CrossRef]

Brown, T.

Brown, T. G.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, "Longitudinal Field Modes Probed by Single Molecules," Phys. Rev. Lett. 86, 5251-5254 (2001).
[CrossRef] [PubMed]

Brus, L. E.

J. J. Macklin, J. K. Trautman, T. D. Harris, and L. E. Brus, "Imaging and Time-Resolved Spectroscopy of Single Molecules at an Interface" Science 272, 255-258 (1996).
[CrossRef]

Capasso, F.

Chaudhuri, S. K.

C. L. Xu, W. P. Huang, M. S. Stern, and S. K. Chaudhuri, "Full-vectorial mode calculations by finite difference method," IEE Proc. Optoelectron. 141, 281-286 (1994).
[CrossRef]

Chen, X.

Chou, C.

Dadap, J. I.

Destouches, N.

N. Destouches, B. Sider, A. V. Tishchenko, and O. Parriaux, "Optimization of a Waveguide Grating for Normal TM Mode Coupling," Opt. Quantum Electron. 38,123-131 (2006).
[CrossRef]

Dorn, R.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, "Focusing light to a tighter spot," Opt. Commun. 179, 1-7 (2000).
[CrossRef]

Dulkeith, E.

Eberler, M.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, "Focusing light to a tighter spot," Opt. Commun. 179, 1-7 (2000).
[CrossRef]

Foster, M. A.

Freude, W.

Gaeta, A. L.

Glöckl, O.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, "Focusing light to a tighter spot," Opt. Commun. 179, 1-7 (2000).
[CrossRef]

Green, W. M. J.

Harris, T. D.

J. J. Macklin, J. K. Trautman, T. D. Harris, and L. E. Brus, "Imaging and Time-Resolved Spectroscopy of Single Molecules at an Interface" Science 272, 255-258 (1996).
[CrossRef]

Helseth, L. E.

L. E. Helseth, "Roles of polarization, phase and amplitude in solid immersion lens systems," Opt. Commun. 191, 161-172 (2001).
[CrossRef]

Hsieh, I.

Huang, W. P.

C. L. Xu, W. P. Huang, M. S. Stern, and S. K. Chaudhuri, "Full-vectorial mode calculations by finite difference method," IEE Proc. Optoelectron. 141, 281-286 (1994).
[CrossRef]

Ibanescu, M.

Jacome, L.

Joannopoulos, J. D.

Johnson, S. G.

Koos, C.

Kozawa, Y.

Krause, M.

M. Krause, H. Renner, and E. Brinkmeyer, "Optical isolation in silicon waveguides based on nonreciprocal Raman amplification," Elect. Lett. 44, 691-693 (2008).
[CrossRef]

Lax, M.

M. Lax, W. H. Louisell, and W. B. McKnight, "From Maxwell to paraxial wave optics," Phys. Rev. A 11, 1365-1370 (1975).
[CrossRef]

Leger, J.

Leuchs, G.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, "Focusing light to a tighter spot," Opt. Commun. 179, 1-7 (2000).
[CrossRef]

Leuthold, J.

Lipson, M.

Liu, X.

Loncar, M.

Lou, J.

Louisell, W. H.

M. Lax, W. H. Louisell, and W. B. McKnight, "From Maxwell to paraxial wave optics," Phys. Rev. A 11, 1365-1370 (1975).
[CrossRef]

Macklin, J. J.

J. J. Macklin, J. K. Trautman, T. D. Harris, and L. E. Brus, "Imaging and Time-Resolved Spectroscopy of Single Molecules at an Interface" Science 272, 255-258 (1996).
[CrossRef]

Manolatou, C.

Mazur, E.

McKnight, W. B.

M. Lax, W. H. Louisell, and W. B. McKnight, "From Maxwell to paraxial wave optics," Phys. Rev. A 11, 1365-1370 (1975).
[CrossRef]

McNab, S. J.

Novotny, L.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, "Longitudinal Field Modes Probed by Single Molecules," Phys. Rev. Lett. 86, 5251-5254 (2001).
[CrossRef] [PubMed]

L. Novotny, E. J. Sanchez, and X. S. Xie, "Near-field optical imaging using metal tips illuminated by higher-order Hermite-Gaussian beams," Ultramicroscopy 71, 21-29 (1998).
[CrossRef]

Osgood, R. M.

Panoiu, N. C.

Parriaux, O.

N. Destouches, B. Sider, A. V. Tishchenko, and O. Parriaux, "Optimization of a Waveguide Grating for Normal TM Mode Coupling," Opt. Quantum Electron. 38,123-131 (2006).
[CrossRef]

Pereira, S. F.

A. S. van de Nes, J. J. M. Braat, and S. F. Pereira, "High-density optical data storage," Rep. Prog. Phys. 69, 2323-2363 (2006).
[CrossRef]

Poulton, C.

Povinelli, M. L.

Quabis, S.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, "Focusing light to a tighter spot," Opt. Commun. 179, 1-7 (2000).
[CrossRef]

Renner, H.

M. Krause, H. Renner, and E. Brinkmeyer, "Optical isolation in silicon waveguides based on nonreciprocal Raman amplification," Elect. Lett. 44, 691-693 (2008).
[CrossRef]

Sanchez, E. J.

L. Novotny, E. J. Sanchez, and X. S. Xie, "Near-field optical imaging using metal tips illuminated by higher-order Hermite-Gaussian beams," Ultramicroscopy 71, 21-29 (1998).
[CrossRef]

Sato, S.

Schmidt, B. S.

Scully, M. O.

M. O. Scully, "A Simple Laser Linac," Appl. Phys. B. 51, 238-241 (1990).
[CrossRef]

Sekaric, L.

Sharping, J. E.

Sider, B.

N. Destouches, B. Sider, A. V. Tishchenko, and O. Parriaux, "Optimization of a Waveguide Grating for Normal TM Mode Coupling," Opt. Quantum Electron. 38,123-131 (2006).
[CrossRef]

Smythe, E. J.

Stern, M. S.

C. L. Xu, W. P. Huang, M. S. Stern, and S. K. Chaudhuri, "Full-vectorial mode calculations by finite difference method," IEE Proc. Optoelectron. 141, 281-286 (1994).
[CrossRef]

Tishchenko, A. V.

N. Destouches, B. Sider, A. V. Tishchenko, and O. Parriaux, "Optimization of a Waveguide Grating for Normal TM Mode Coupling," Opt. Quantum Electron. 38,123-131 (2006).
[CrossRef]

Tong, L.

Trautman, J. K.

J. J. Macklin, J. K. Trautman, T. D. Harris, and L. E. Brus, "Imaging and Time-Resolved Spectroscopy of Single Molecules at an Interface" Science 272, 255-258 (1996).
[CrossRef]

Turner, A. C.

van de Nes, A. S.

A. S. van de Nes, J. J. M. Braat, and S. F. Pereira, "High-density optical data storage," Rep. Prog. Phys. 69, 2323-2363 (2006).
[CrossRef]

Vlasov, Y. A.

Wolf, E.

A. Boivin and E. Wolf, "Electromagnetic Field in the Neighborhood of the Focus of a Coherent Beam," Phys. Rev. 138, B1561-B1565 (1965).
[CrossRef]

Xia, F.

Xie, X. S.

L. Novotny, E. J. Sanchez, and X. S. Xie, "Near-field optical imaging using metal tips illuminated by higher-order Hermite-Gaussian beams," Ultramicroscopy 71, 21-29 (1998).
[CrossRef]

Xu, C. L.

C. L. Xu, W. P. Huang, M. S. Stern, and S. K. Chaudhuri, "Full-vectorial mode calculations by finite difference method," IEE Proc. Optoelectron. 141, 281-286 (1994).
[CrossRef]

Xu, Q.

Youngworth, K.

Youngworth, K. S.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, "Longitudinal Field Modes Probed by Single Molecules," Phys. Rev. Lett. 86, 5251-5254 (2001).
[CrossRef] [PubMed]

Zhan, Q.

Appl. Phys. B. (1)

M. O. Scully, "A Simple Laser Linac," Appl. Phys. B. 51, 238-241 (1990).
[CrossRef]

Elect. Lett. (1)

M. Krause, H. Renner, and E. Brinkmeyer, "Optical isolation in silicon waveguides based on nonreciprocal Raman amplification," Elect. Lett. 44, 691-693 (2008).
[CrossRef]

IEE Proc. Optoelectron. (1)

C. L. Xu, W. P. Huang, M. S. Stern, and S. K. Chaudhuri, "Full-vectorial mode calculations by finite difference method," IEE Proc. Optoelectron. 141, 281-286 (1994).
[CrossRef]

IEEE J. Quantum Electron. (1)

X. Chen, N. C. Panoiu, and R. M. Osgood, Jr., "Theory of Raman-mediated pulsed amplification in silicon-wire waveguides," IEEE J. Quantum Electron. 42, 160-170 (2006).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Commun. (2)

S. Quabis, R. Dorn, M. Eberler, O. Glöckl, and G. Leuchs, "Focusing light to a tighter spot," Opt. Commun. 179, 1-7 (2000).
[CrossRef]

L. E. Helseth, "Roles of polarization, phase and amplitude in solid immersion lens systems," Opt. Commun. 191, 161-172 (2001).
[CrossRef]

Opt. Express (7)

Opt. Lett. (2)

Opt. Quantum Electron. (1)

N. Destouches, B. Sider, A. V. Tishchenko, and O. Parriaux, "Optimization of a Waveguide Grating for Normal TM Mode Coupling," Opt. Quantum Electron. 38,123-131 (2006).
[CrossRef]

Phys. Rev. (1)

A. Boivin and E. Wolf, "Electromagnetic Field in the Neighborhood of the Focus of a Coherent Beam," Phys. Rev. 138, B1561-B1565 (1965).
[CrossRef]

Phys. Rev. A (1)

M. Lax, W. H. Louisell, and W. B. McKnight, "From Maxwell to paraxial wave optics," Phys. Rev. A 11, 1365-1370 (1975).
[CrossRef]

Phys. Rev. Lett. (1)

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, "Longitudinal Field Modes Probed by Single Molecules," Phys. Rev. Lett. 86, 5251-5254 (2001).
[CrossRef] [PubMed]

Rep. Prog. Phys. (1)

A. S. van de Nes, J. J. M. Braat, and S. F. Pereira, "High-density optical data storage," Rep. Prog. Phys. 69, 2323-2363 (2006).
[CrossRef]

Science (1)

J. J. Macklin, J. K. Trautman, T. D. Harris, and L. E. Brus, "Imaging and Time-Resolved Spectroscopy of Single Molecules at an Interface" Science 272, 255-258 (1996).
[CrossRef]

Ultramicroscopy (1)

L. Novotny, E. J. Sanchez, and X. S. Xie, "Near-field optical imaging using metal tips illuminated by higher-order Hermite-Gaussian beams," Ultramicroscopy 71, 21-29 (1998).
[CrossRef]

Other (5)

G. Kihara Rurimo, M. Schardt, S. Quabis, S. Malzer, Ch. Dotzler,A. Winkler, G. Leuchs, G. H. Dohler, D. Driscoll, M. Hanson, A. C. Gossard, and S. F. Pereira, "Using a quantum well heterostructure to study the longitudinal and transverse electric field components of a strongly focused laser beam," J. Appl. Phys. 100, 023112 1-6 (2006).
[CrossRef]

R. Dorn, S. Quabis, and G. Leuchs, "Sharper Focus for a Radially Polarized Light Beam," Phys. Rev. Lett. 91, 233901 1-4 (2003).
[CrossRef]

H. P. Urbach and S. F. Pereira, "Field in Focus with a Maximum Longitudinal Electric Component," Phys. Rev. Lett. 100, 123904 1-4 (2008).
[CrossRef]

V. G. Niziev and A. V. Nesterov, "Longitudinal fields in cylindrical and spherical modes," J. Opt. A: Pure Appl. Opt. 10, 085005 1-7 (2008).
[CrossRef]

G. P. Agrawal, Nonlinear Fiber Optics (Academic, New York, 2001).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1.
Fig. 1.

The Ex (Ey ) and Ez components of the fundamental quasi-TE(-TM) mode supported by a 260 × 4002 nm Si nanowire waveguide surrounded by SiO2 cladding. Graded yellow and blue colors indicate a π-phase difference.

Fig. 2.
Fig. 2.

Ez (max)/E T(max)∣ for the quasi-TE and -TM modes of Si nanowires with variable dimensions, SiO2 substrate, and air (a,b) or SiO2 (c,d) cladding.

Fig. 3.
Fig. 3.

Ez (max)/E T(max)∣ for the HE11 mode in a cylindrical Si nanowire of variable diameter, and air (top blue line) or SiO2 (bottom red line) cladding.

Fig. 4.
Fig. 4.

The (a) Ex and (b) Ez electric field components of a mode propagating in a 260×500 nm2 Si nanowire with SiO2 cladding. (c) ∣Ez /E T(max)2 40 nm from the endface.

Fig. 5.
Fig. 5.

The (a) transverse (Ex ) and (b) longitudinal (Ez ) field components of the fundamental antisymmetric system mode supported by (c) dual waveguides where each waveguide has cross-section dimensions 260 × 500 nm2 separated by a 50 nm gap.

Fig. 6.
Fig. 6.

The(a)Ez and(b)Ex electric field components at the endface of dual 260 × 500 nm2 Si nanowire waveguides with SiO2 cladding, 50 nm gap, terminated into air, and excited by the fundamental antisymmetric system mode. (c) ∣Ez 2 near the edge of the dual waveguide structure. Contour plot (d) and line scan (e) of ∣Ez 2 40 nm from the edge of the waveguide.

Equations (1)

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

E z = λ 0 j 2 π N eff T · E T

Metrics