Abstract

We demonstrate a new technique for high resolution imaging of near field profiles in highly confining photonic structures. This technique, Transmission-based Near-field Scanning Optical Microscopy (TraNSOM), measures changes in transmission through a waveguide resulting from near field perturbation by a scanning metallic probe. Using this technique we compare different mode polarizations and measure a transverse optical decay length of λ/15 in sub-micron Silicon On Insulator (SOI) waveguides. These measurements compare well to theoretical results.

© 2006 Optical Society of America

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References

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  1. B. Jalali, et al., “Advances in silicon-on-insulator optoelectronics,” IEEE J. Sel. Top. Quantum Electron. 4, 938947 (1998).
  2. V.R. Almeida, C.A. Barrios, R.R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
    [Crossref] [PubMed]
  3. Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435, 325–327 (2005).
    [Crossref] [PubMed]
  4. A. Liu, et al., “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427, 615–618 (2004).
    [Crossref] [PubMed]
  5. T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, and E. Kuramochi, “Fast bistable all-optical switch and memory on a silicon photonic crystal on-chip,” Opt. Lett. 30, 2575–2577 (2005).
    [Crossref] [PubMed]
  6. Y.A. Vlasov, M. O’Boyle, H.F. Hamann, and S.J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438, 65–69 (2005).
    [Crossref] [PubMed]
  7. Y. Okawachi, et al., “All-optical slow-light on a photonic chip,” Opt. Express 14, 2317–2322 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-6-2317.
    [Crossref] [PubMed]
  8. H. Rong, et al., “Raman gain and nonlinear optical absorption measurements in a low-loss silicon waveguide,” App. Phys. Lett. 85, 2196–2198 (2004).
    [Crossref]
  9. Q. Xu, V.R. Almeida, and M. Lipson, “Time-resolved study of raman gain in highly confined silicon-on-insulator waveguides,” Opt. Express 12, 4437 (2004), http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-19-4437.
    [Crossref] [PubMed]
  10. R.L. Espinola, J.I. Dadap, R.M. Osgood, S.J. McNab, and Y.A. Vlasov, “Raman amplification in ultrasmall silicon-on-insulator wire waveguides,” Opt. Express 12, 3713 (2004), http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-16-3713.
    [Crossref] [PubMed]
  11. R. Naisheng, et al., “A continuous-wave raman silicon laser,” Nature 433, 725–728 (2005).
    [Crossref]
  12. O. Boyraz and B. Jalali, “Demonstration of directly modulated silicon raman laser,” Opt. Express 13, 796 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-3-796.
    [Crossref] [PubMed]
  13. M.A. Foster, et al., “Broad-band optical parametric gain on a silicon photonic chip,” Nature 441, 960–963 (2006).
    [Crossref] [PubMed]
  14. S. Bourzeix, et al., “Near-field optical imaging of light propagation in semiconductor waveguide structures,” App. Phys. Lett. 73, 1035–1037 (1998).
    [Crossref]
  15. B. Hecht, et al., “Scanning near-field optical microscopy with aperture probes: Fundamentals and applications,” J. Chem. Phys. 112, 7761–7774 (2000).
    [Crossref]
  16. C.D. Poweleit, D.H. Naghski, S.M. Lindsay, J.T. Boyd, and H.E. Jackson, “Near field scanning optical microscopy measurements of optical intensity distributions in semiconductor channel waveguides,” App. Phys. Lett. 69, 3471–3473 (1996).
    [Crossref]
  17. G.H. Rhodes Vander, et al., “Measurement of internal spatial modes and local propagation properties in optical waveguides,” App. Phys. Lett. 75, 2368–2370 (1999).
    [Crossref]
  18. H.A. Bethe, “Theory of diffraction by small holes,” Phys. Rev. 66, 163 (1944).
    [Crossref]
  19. R. Bachelot, P. Gleyzes, and A.C. Boccara, “Near-field optical microscope based on local perturbation of a diffraction spot,” Opt. Lett. 20, 1924–1926 (1995).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  21. R. Bachelot, et al., “Probing photonic and optoelectronic structures by apertureless scanning near-field optical microscopy,” Microsc. Res. Tech. 64, 441–452 (2004).
    [Crossref]
  22. L. Gomez, et al., “Apertureless scanning near-field optical microscopy: A comparison between homodyne and heterodyne approaches,” J. Opt. Soc. Am. B 23, 823–833 (2006).
    [Crossref]
  23. I. Stefanon, et al., “Heterodyne detection of guided waves using a scattering-type scanning near-field optical microscope,” Opt. Express 13, (2005).
    [Crossref] [PubMed]
  24. M.L.M. Balistreri, H. Gersen, J.P. Korterik, L. Kuipers, and N.F. van Hulst, “Tracking femtosecond laser pulses in space and time,” Science 294, 1080–1082 (2001).
    [Crossref] [PubMed]
  25. W.C.L. Hopman, et al., “Nano-mechanical tuning and imaging of a photonic crystal micro-cavity resonance,” Opt. Express 14, 8745–8752 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-19-8745.
    [Crossref] [PubMed]
  26. V.R. Almeida, R.R. Panepucci, and M. Lipson, “Nanotaper for compact mode conversion,” Opt. Lett. 28, 1302–1304 (2003).
    [Crossref] [PubMed]
  27. S.J. McNab, N. Moll, and Y.A. Vlasov, “Ultra-low loss photonic integrated circuit with membrane-type photonic crystal waveguides,” Opt. Express 11, 2927 (2003), http://www.opticsinfobase.org/abstract.cfm?URI=oe-11-22-2927.
    [Crossref] [PubMed]
  28. J.D. Jackson, Classical electrodynamics. 3rd ed (John Wiley & Sons, Inc., Hoboken, NJ,1999).
  29. H.C. Van de Hulst, Light scattering by small particles (Dover Publications. Inc., New York, NY,1981).
  30. A.F. Koenderink, M. Kafesaki, B.C. Buchler, and V. Sandoghdar, “Controlling the resonance of a photonic crystal microcavity by a near-field probe,” Phys. Rev. Lett. 95, 153904–153901 (2005).
    [Crossref] [PubMed]
  31. L. Aigony, et al., “Polarization effects in apertureless scanning near-field optical microscopy: An experimental study,” Opt. Lett. 24, 187–189 (1999).
    [Crossref]
  32. M. Labardi, et al., “Highly efficient second-harmonic nanosource for near-field optics and microscopy,” Opt. Lett. 29, 62–64 (2004).
    [Crossref] [PubMed]

2006 (4)

2005 (7)

O. Boyraz and B. Jalali, “Demonstration of directly modulated silicon raman laser,” Opt. Express 13, 796 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-3-796.
[Crossref] [PubMed]

T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, and E. Kuramochi, “Fast bistable all-optical switch and memory on a silicon photonic crystal on-chip,” Opt. Lett. 30, 2575–2577 (2005).
[Crossref] [PubMed]

A.F. Koenderink, M. Kafesaki, B.C. Buchler, and V. Sandoghdar, “Controlling the resonance of a photonic crystal microcavity by a near-field probe,” Phys. Rev. Lett. 95, 153904–153901 (2005).
[Crossref] [PubMed]

Y.A. Vlasov, M. O’Boyle, H.F. Hamann, and S.J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438, 65–69 (2005).
[Crossref] [PubMed]

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435, 325–327 (2005).
[Crossref] [PubMed]

R. Naisheng, et al., “A continuous-wave raman silicon laser,” Nature 433, 725–728 (2005).
[Crossref]

I. Stefanon, et al., “Heterodyne detection of guided waves using a scattering-type scanning near-field optical microscope,” Opt. Express 13, (2005).
[Crossref] [PubMed]

2004 (7)

R. Bachelot, et al., “Probing photonic and optoelectronic structures by apertureless scanning near-field optical microscopy,” Microsc. Res. Tech. 64, 441–452 (2004).
[Crossref]

A. Liu, et al., “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427, 615–618 (2004).
[Crossref] [PubMed]

V.R. Almeida, C.A. Barrios, R.R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
[Crossref] [PubMed]

H. Rong, et al., “Raman gain and nonlinear optical absorption measurements in a low-loss silicon waveguide,” App. Phys. Lett. 85, 2196–2198 (2004).
[Crossref]

M. Labardi, et al., “Highly efficient second-harmonic nanosource for near-field optics and microscopy,” Opt. Lett. 29, 62–64 (2004).
[Crossref] [PubMed]

R.L. Espinola, J.I. Dadap, R.M. Osgood, S.J. McNab, and Y.A. Vlasov, “Raman amplification in ultrasmall silicon-on-insulator wire waveguides,” Opt. Express 12, 3713 (2004), http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-16-3713.
[Crossref] [PubMed]

Q. Xu, V.R. Almeida, and M. Lipson, “Time-resolved study of raman gain in highly confined silicon-on-insulator waveguides,” Opt. Express 12, 4437 (2004), http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-19-4437.
[Crossref] [PubMed]

2003 (2)

2001 (1)

M.L.M. Balistreri, H. Gersen, J.P. Korterik, L. Kuipers, and N.F. van Hulst, “Tracking femtosecond laser pulses in space and time,” Science 294, 1080–1082 (2001).
[Crossref] [PubMed]

2000 (1)

B. Hecht, et al., “Scanning near-field optical microscopy with aperture probes: Fundamentals and applications,” J. Chem. Phys. 112, 7761–7774 (2000).
[Crossref]

1999 (2)

G.H. Rhodes Vander, et al., “Measurement of internal spatial modes and local propagation properties in optical waveguides,” App. Phys. Lett. 75, 2368–2370 (1999).
[Crossref]

L. Aigony, et al., “Polarization effects in apertureless scanning near-field optical microscopy: An experimental study,” Opt. Lett. 24, 187–189 (1999).
[Crossref]

1998 (2)

S. Bourzeix, et al., “Near-field optical imaging of light propagation in semiconductor waveguide structures,” App. Phys. Lett. 73, 1035–1037 (1998).
[Crossref]

B. Jalali, et al., “Advances in silicon-on-insulator optoelectronics,” IEEE J. Sel. Top. Quantum Electron. 4, 938947 (1998).

1996 (1)

C.D. Poweleit, D.H. Naghski, S.M. Lindsay, J.T. Boyd, and H.E. Jackson, “Near field scanning optical microscopy measurements of optical intensity distributions in semiconductor channel waveguides,” App. Phys. Lett. 69, 3471–3473 (1996).
[Crossref]

1995 (1)

1994 (1)

1944 (1)

H.A. Bethe, “Theory of diffraction by small holes,” Phys. Rev. 66, 163 (1944).
[Crossref]

Aigony, L.

Almeida, V.R.

Bachelot, R.

R. Bachelot, et al., “Probing photonic and optoelectronic structures by apertureless scanning near-field optical microscopy,” Microsc. Res. Tech. 64, 441–452 (2004).
[Crossref]

R. Bachelot, P. Gleyzes, and A.C. Boccara, “Near-field optical microscope based on local perturbation of a diffraction spot,” Opt. Lett. 20, 1924–1926 (1995).
[Crossref] [PubMed]

Balistreri, M.L.M.

M.L.M. Balistreri, H. Gersen, J.P. Korterik, L. Kuipers, and N.F. van Hulst, “Tracking femtosecond laser pulses in space and time,” Science 294, 1080–1082 (2001).
[Crossref] [PubMed]

Barrios, C.A.

V.R. Almeida, C.A. Barrios, R.R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
[Crossref] [PubMed]

Bethe, H.A.

H.A. Bethe, “Theory of diffraction by small holes,” Phys. Rev. 66, 163 (1944).
[Crossref]

Boccara, A.C.

Bourzeix, S.

S. Bourzeix, et al., “Near-field optical imaging of light propagation in semiconductor waveguide structures,” App. Phys. Lett. 73, 1035–1037 (1998).
[Crossref]

Boyd, J.T.

C.D. Poweleit, D.H. Naghski, S.M. Lindsay, J.T. Boyd, and H.E. Jackson, “Near field scanning optical microscopy measurements of optical intensity distributions in semiconductor channel waveguides,” App. Phys. Lett. 69, 3471–3473 (1996).
[Crossref]

Boyraz, O.

Buchler, B.C.

A.F. Koenderink, M. Kafesaki, B.C. Buchler, and V. Sandoghdar, “Controlling the resonance of a photonic crystal microcavity by a near-field probe,” Phys. Rev. Lett. 95, 153904–153901 (2005).
[Crossref] [PubMed]

Dadap, J.I.

Espinola, R.L.

Foster, M.A.

M.A. Foster, et al., “Broad-band optical parametric gain on a silicon photonic chip,” Nature 441, 960–963 (2006).
[Crossref] [PubMed]

Gersen, H.

M.L.M. Balistreri, H. Gersen, J.P. Korterik, L. Kuipers, and N.F. van Hulst, “Tracking femtosecond laser pulses in space and time,” Science 294, 1080–1082 (2001).
[Crossref] [PubMed]

Gleyzes, P.

Gomez, L.

Hamann, H.F.

Y.A. Vlasov, M. O’Boyle, H.F. Hamann, and S.J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438, 65–69 (2005).
[Crossref] [PubMed]

Hecht, B.

B. Hecht, et al., “Scanning near-field optical microscopy with aperture probes: Fundamentals and applications,” J. Chem. Phys. 112, 7761–7774 (2000).
[Crossref]

Hopman, W.C.L.

Hulst, H.C. Van de

H.C. Van de Hulst, Light scattering by small particles (Dover Publications. Inc., New York, NY,1981).

Hulst, N.F. van

M.L.M. Balistreri, H. Gersen, J.P. Korterik, L. Kuipers, and N.F. van Hulst, “Tracking femtosecond laser pulses in space and time,” Science 294, 1080–1082 (2001).
[Crossref] [PubMed]

Inouye, Y.

Jackson, H.E.

C.D. Poweleit, D.H. Naghski, S.M. Lindsay, J.T. Boyd, and H.E. Jackson, “Near field scanning optical microscopy measurements of optical intensity distributions in semiconductor channel waveguides,” App. Phys. Lett. 69, 3471–3473 (1996).
[Crossref]

Jackson, J.D.

J.D. Jackson, Classical electrodynamics. 3rd ed (John Wiley & Sons, Inc., Hoboken, NJ,1999).

Jalali, B.

O. Boyraz and B. Jalali, “Demonstration of directly modulated silicon raman laser,” Opt. Express 13, 796 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-3-796.
[Crossref] [PubMed]

B. Jalali, et al., “Advances in silicon-on-insulator optoelectronics,” IEEE J. Sel. Top. Quantum Electron. 4, 938947 (1998).

Kafesaki, M.

A.F. Koenderink, M. Kafesaki, B.C. Buchler, and V. Sandoghdar, “Controlling the resonance of a photonic crystal microcavity by a near-field probe,” Phys. Rev. Lett. 95, 153904–153901 (2005).
[Crossref] [PubMed]

Kawata, S.

Koenderink, A.F.

A.F. Koenderink, M. Kafesaki, B.C. Buchler, and V. Sandoghdar, “Controlling the resonance of a photonic crystal microcavity by a near-field probe,” Phys. Rev. Lett. 95, 153904–153901 (2005).
[Crossref] [PubMed]

Korterik, J.P.

M.L.M. Balistreri, H. Gersen, J.P. Korterik, L. Kuipers, and N.F. van Hulst, “Tracking femtosecond laser pulses in space and time,” Science 294, 1080–1082 (2001).
[Crossref] [PubMed]

Kuipers, L.

M.L.M. Balistreri, H. Gersen, J.P. Korterik, L. Kuipers, and N.F. van Hulst, “Tracking femtosecond laser pulses in space and time,” Science 294, 1080–1082 (2001).
[Crossref] [PubMed]

Kuramochi, E.

Labardi, M.

Lindsay, S.M.

C.D. Poweleit, D.H. Naghski, S.M. Lindsay, J.T. Boyd, and H.E. Jackson, “Near field scanning optical microscopy measurements of optical intensity distributions in semiconductor channel waveguides,” App. Phys. Lett. 69, 3471–3473 (1996).
[Crossref]

Lipson, M.

Liu, A.

A. Liu, et al., “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427, 615–618 (2004).
[Crossref] [PubMed]

McNab, S.J.

Mitsugi, S.

Moll, N.

Naghski, D.H.

C.D. Poweleit, D.H. Naghski, S.M. Lindsay, J.T. Boyd, and H.E. Jackson, “Near field scanning optical microscopy measurements of optical intensity distributions in semiconductor channel waveguides,” App. Phys. Lett. 69, 3471–3473 (1996).
[Crossref]

Naisheng, R.

R. Naisheng, et al., “A continuous-wave raman silicon laser,” Nature 433, 725–728 (2005).
[Crossref]

Notomi, M.

O’Boyle, M.

Y.A. Vlasov, M. O’Boyle, H.F. Hamann, and S.J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438, 65–69 (2005).
[Crossref] [PubMed]

Okawachi, Y.

Osgood, R.M.

Panepucci, R.R.

V.R. Almeida, C.A. Barrios, R.R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
[Crossref] [PubMed]

V.R. Almeida, R.R. Panepucci, and M. Lipson, “Nanotaper for compact mode conversion,” Opt. Lett. 28, 1302–1304 (2003).
[Crossref] [PubMed]

Poweleit, C.D.

C.D. Poweleit, D.H. Naghski, S.M. Lindsay, J.T. Boyd, and H.E. Jackson, “Near field scanning optical microscopy measurements of optical intensity distributions in semiconductor channel waveguides,” App. Phys. Lett. 69, 3471–3473 (1996).
[Crossref]

Pradhan, S.

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435, 325–327 (2005).
[Crossref] [PubMed]

Rhodes Vander, G.H.

G.H. Rhodes Vander, et al., “Measurement of internal spatial modes and local propagation properties in optical waveguides,” App. Phys. Lett. 75, 2368–2370 (1999).
[Crossref]

Rong, H.

H. Rong, et al., “Raman gain and nonlinear optical absorption measurements in a low-loss silicon waveguide,” App. Phys. Lett. 85, 2196–2198 (2004).
[Crossref]

Sandoghdar, V.

A.F. Koenderink, M. Kafesaki, B.C. Buchler, and V. Sandoghdar, “Controlling the resonance of a photonic crystal microcavity by a near-field probe,” Phys. Rev. Lett. 95, 153904–153901 (2005).
[Crossref] [PubMed]

Schmidt, B.

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435, 325–327 (2005).
[Crossref] [PubMed]

Shinya, A.

Stefanon, I.

I. Stefanon, et al., “Heterodyne detection of guided waves using a scattering-type scanning near-field optical microscope,” Opt. Express 13, (2005).
[Crossref] [PubMed]

Tanabe, T.

Vlasov, Y.A.

Xu, Q.

App. Phys. Lett. (4)

H. Rong, et al., “Raman gain and nonlinear optical absorption measurements in a low-loss silicon waveguide,” App. Phys. Lett. 85, 2196–2198 (2004).
[Crossref]

S. Bourzeix, et al., “Near-field optical imaging of light propagation in semiconductor waveguide structures,” App. Phys. Lett. 73, 1035–1037 (1998).
[Crossref]

C.D. Poweleit, D.H. Naghski, S.M. Lindsay, J.T. Boyd, and H.E. Jackson, “Near field scanning optical microscopy measurements of optical intensity distributions in semiconductor channel waveguides,” App. Phys. Lett. 69, 3471–3473 (1996).
[Crossref]

G.H. Rhodes Vander, et al., “Measurement of internal spatial modes and local propagation properties in optical waveguides,” App. Phys. Lett. 75, 2368–2370 (1999).
[Crossref]

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

B. Jalali, et al., “Advances in silicon-on-insulator optoelectronics,” IEEE J. Sel. Top. Quantum Electron. 4, 938947 (1998).

J. Chem. Phys. (1)

B. Hecht, et al., “Scanning near-field optical microscopy with aperture probes: Fundamentals and applications,” J. Chem. Phys. 112, 7761–7774 (2000).
[Crossref]

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

Microsc. Res. Tech. (1)

R. Bachelot, et al., “Probing photonic and optoelectronic structures by apertureless scanning near-field optical microscopy,” Microsc. Res. Tech. 64, 441–452 (2004).
[Crossref]

Nature (6)

R. Naisheng, et al., “A continuous-wave raman silicon laser,” Nature 433, 725–728 (2005).
[Crossref]

M.A. Foster, et al., “Broad-band optical parametric gain on a silicon photonic chip,” Nature 441, 960–963 (2006).
[Crossref] [PubMed]

V.R. Almeida, C.A. Barrios, R.R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004).
[Crossref] [PubMed]

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435, 325–327 (2005).
[Crossref] [PubMed]

A. Liu, et al., “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427, 615–618 (2004).
[Crossref] [PubMed]

Y.A. Vlasov, M. O’Boyle, H.F. Hamann, and S.J. McNab, “Active control of slow light on a chip with photonic crystal waveguides,” Nature 438, 65–69 (2005).
[Crossref] [PubMed]

Opt. Express (7)

I. Stefanon, et al., “Heterodyne detection of guided waves using a scattering-type scanning near-field optical microscope,” Opt. Express 13, (2005).
[Crossref] [PubMed]

W.C.L. Hopman, et al., “Nano-mechanical tuning and imaging of a photonic crystal micro-cavity resonance,” Opt. Express 14, 8745–8752 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-19-8745.
[Crossref] [PubMed]

S.J. McNab, N. Moll, and Y.A. Vlasov, “Ultra-low loss photonic integrated circuit with membrane-type photonic crystal waveguides,” Opt. Express 11, 2927 (2003), http://www.opticsinfobase.org/abstract.cfm?URI=oe-11-22-2927.
[Crossref] [PubMed]

Y. Okawachi, et al., “All-optical slow-light on a photonic chip,” Opt. Express 14, 2317–2322 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-6-2317.
[Crossref] [PubMed]

R.L. Espinola, J.I. Dadap, R.M. Osgood, S.J. McNab, and Y.A. Vlasov, “Raman amplification in ultrasmall silicon-on-insulator wire waveguides,” Opt. Express 12, 3713 (2004), http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-16-3713.
[Crossref] [PubMed]

Q. Xu, V.R. Almeida, and M. Lipson, “Time-resolved study of raman gain in highly confined silicon-on-insulator waveguides,” Opt. Express 12, 4437 (2004), http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-19-4437.
[Crossref] [PubMed]

O. Boyraz and B. Jalali, “Demonstration of directly modulated silicon raman laser,” Opt. Express 13, 796 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-3-796.
[Crossref] [PubMed]

Opt. Lett. (6)

Phys. Rev. (1)

H.A. Bethe, “Theory of diffraction by small holes,” Phys. Rev. 66, 163 (1944).
[Crossref]

Phys. Rev. Lett. (1)

A.F. Koenderink, M. Kafesaki, B.C. Buchler, and V. Sandoghdar, “Controlling the resonance of a photonic crystal microcavity by a near-field probe,” Phys. Rev. Lett. 95, 153904–153901 (2005).
[Crossref] [PubMed]

Science (1)

M.L.M. Balistreri, H. Gersen, J.P. Korterik, L. Kuipers, and N.F. van Hulst, “Tracking femtosecond laser pulses in space and time,” Science 294, 1080–1082 (2001).
[Crossref] [PubMed]

Other (2)

J.D. Jackson, Classical electrodynamics. 3rd ed (John Wiley & Sons, Inc., Hoboken, NJ,1999).

H.C. Van de Hulst, Light scattering by small particles (Dover Publications. Inc., New York, NY,1981).

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Figures (4)

Fig. 1.
Fig. 1.

Experimental setup for TraNSOM measurements.

Fig. 2.
Fig. 2.

Model of the TraNSOM measurement where Pin is the power input from the source, T 1 is the transmittivity between the source and the probe, Pabs is the power absorbed by the probe, Psca is the power scattered by the probe, T 2 is the transmittivity between the probe and the detector, and Pout is the power detected at the output.

Fig. 3.
Fig. 3.

(a) AFM image of the SOI waveguide (b) simultaneously recorded TraNSOM image of the fundamental quasi-TM mode (c) simulated major component (|Ey |2) of the fundamental quasi-TM mode. Dashed lines show the outline of the probe at three positions. Bold arrows show the path of the probe convolution. (d) Solid line shows the measured TraNSOM signal taken along the solid line in (b). Dashed line shows the simultaneously measured topography. Dotted line shows the probe-field convolution for all three polarization components according to (1) with Q ext = 6.4 and Q ext = 0.08.

Fig. 4.
Fig. 4.

(a) AFM image of the SOI waveguide (b) simultaneously recorded TraNSOM image of the fundamental quasi-TE mode (c) Simulated minor component (|Ey |2) of the fundamental quasi-TE mode. Dashed lines show the outline of the probe at three positions. Bold arrows show the path of the probe convolution. (d) Solid line shows the measured TraNSOM signal taken along the solid line in (b). Dashed line shows the simultaneously measured topography. Dotted line shows the probe-field convolution for all three polarization components according to (1) with Q ext = 6.4 and Q ext = 0.08.

Equations (5)

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P ext = P abs + P sca = Q ext 1 2 μ 0 ε 0 A E x 2 da + Q ext 1 2 μ 0 ε 0 A E y 2 da + Q ext 1 2 μ 0 ε 0 A E z 2 da ,
P ext Q ext 1 2 μ 0 ε 0 A E y 2 da .
P out = T 1 T 2 P in ( 1 P ext P 1 ) ,
P out 0 = T 1 T 2 P in .
Δ T 1 P out P out 0 = P ext P 1 Q ext μ ε A E y 2 da ( E × H ) · z ̂ da .

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