Abstract

A two-dimensional (2-D) model for photon-scanning tunneling microscopy (PSTM) of integrated optical devices is evaluated. The simulations refer to a setup where the optical field in the vicinity of the sample is probed by detecting the optical power that is transferred via evanescent or radiative coupling to the tapered tip of an optical fiber close to the sample surface. Scanning the tip across the surface leads to a map of the local optical field in the sample. As a step beyond the mere analysis of the sample device, simulations are considered that include the sample as well as the probe tip. An efficient semianalytical simulation technique based on quadridirectional eigenmode expansions is applied. Results for a series of configurations, where slab waveguides with different types of corrugations serve as samples, allow assessment of the relation between the PSTM signal and the local field distribution in the sample. A reasonable qualitative agreement was observed between these computations and a previous experimental PSTM investigation of a waveguide Bragg grating.

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  1. M. L. M. Balistreri, J. P. Korterik, G. J. Veldhuis, L. Kuipers and N. F. van Hulst, "Quantitative photon tunneling and shear-force microscopy of planar waveguide splitters and mixers", J. Appl. Phys., vol. 89, no. 6, pp. 3307-3314, 2001.
  2. D. P. Tsai, H. E. Jackson, R. C. Reddick, S. H. Sharp and R. J. Warmack, "Photon scanning tunneling microscope study of optical waveguides", Appl. Phys. Lett., vol. 56, no. 16, pp. 1515-1517, 1990.
  3. 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", Appl. Phys. Lett., vol. 69, no. 23, pp. 3471-3473, 1996.
  4. G. H. Vander Rhodes, B. B. Goldberg, M. S. Ünl, S. T. Chu, W. Pan, T. Kaneko, Y. Kokobun and B. E. Little, "Measurement of internal spatial modes and local propagation properties in optical waveguides", Appl. Phys. Lett., vol. 75, no. 16, pp. 2368-2370, 1999.
  5. M. L. M. Balistreri, J. P. Korterik, L. Kuipers and N. F. van Hulst, "Photon scanning tunneling microscopy with a three-dimensional multiheight imaging mode", Appl. Phys. Lett., vol. 77, no. 25, pp. 4092-4094, 2000.
  6. M. L. M. Balistreri, J. P. Korterik, L. Kuipers and N. F. van Hulst, "Phase mapping of optical fields in integrated optical waveguide structures", J. Lightw. Technol., vol. 19, no. 8, pp. 1169-1176, Aug. 2001.
  7. M. L. M. Balistreri, J. P. Korterik, L. Kuipers and N. F. van Hulst, "Visualization of mode transformation in a planar waveguide splitter by near-field optical phase imaging", Appl. Phys. Lett., vol. 79, no. 7, pp. 910-912, 2001.
  8. C. Peeters, E. Flck, A. M. Otter, M. L. M. Balistreri, J. P. Korterik, L. Kuipers and N. F. van Hulst, "Photon scanning tunneling microscopy of tailor-made photonic structures", Appl. Phys. Lett., vol. 77, no. 1, pp. 142-144, 2000.
  9. E. Flck, M. Hammer, A. M. Otter, J. P. Korterijk, L. Kuipers and N. F. van Hulst, "Amplitude and phase evolution of optical fields inside periodic photonic structures", J. Lightw. Technol., vol. 21, no. 5, pp. 1384-1393, May 2003.
  10. A. L. Campillo, J. W. P. Hsu, C. A. White and A. Rosenberg, "Mapping the optical intensity distribution in photonic crystals using a near-field scanning optical microscope", J. Appl. Phys., vol. 89, no. 5, pp. 2801-2807, 2001 .
  11. P. Kramper, A. Birner, M. Agio, C. M. Soukoulis, F. Mller, U. Gsele, J. Mlynek and V. Sandoghdar, "Direct spectroscopy of a deep two-dimensional photonic crystal microresonator", Phys. Rev. B, Condens. Matter, vol. 64, p. 233 102, 2001.
  12. K. Okamoto, M. Loncar, T. Yoshie, A. Scherer, Y. Qui and P. Gogna, "Near-field scanning optical microscopy of photonic crystal nanocavities", Appl. Phys. Lett. , vol. 82, no. 11, pp. 1676-1678, 2003.
  13. D. J. W. Klunder, M. L. M. Balistreri, F. C. Blom, H. J. W. M. Hoekstra, A. Driessen, L. Kuipers and N. F. van Hulst, "High-resolution photon-scanning tunneling microscope measurements of the whispering gallery modes in a cylindrical microresonator", IEEE Photon. Technol. Lett., vol. 12, no. 11, pp. 1531-1533, Nov. 2000.
  14. M. L. M. Balistreri, D. J. W. Klunder, F. C. Blom, A. Driessen, J. P. Korterik, L. Kuipers and N. F. van Hulst, "Experimental analysis of the whispering-gallery modes in a cylindrical optical microcavity", J. Opt. Soc. Amer. B, Opt. Phys., vol. 18, no. 4, pp. 465-471, 2001.
  15. D. J. W. Klunder, M. L. M. Balistreri, F. C. Blom, H. J. W. M. Hoekstra, A. Driessen, L. Kuipers and N. F. van Hulst, "Detailed analysis of the intracavity phenomena inside a cylindrical microresonator", J. Lightw. Technol., vol. 20, no. 3, pp. 519-529, Mar. 2002.
  16. L. Novotny, D. W. Pohl and P. Regli, "Light propagation through nanometer-sized structures: the two-dimensional-aperture scanning near-field optical microscope", J. Opt. Soc. Amer. A, Opt. Image Sci., vol. 11, no. 6, pp. 1768-1779, 1994.
  17. L. Novotny, D. W. Pohl and P. Regli, "Near-field, far-field and imaging properties of the 2-D aperture SNOM", Ultramicroscopy, vol. 57, pp. 180-188, 1995.
  18. B. Hecht, D. W. Pohl, H. Heinzelmann and L. Novotny, "Tunnel near-filed optical microscopy: TNOM-2", Ultramicroscopy, vol. 61, pp. 99-104, 1995.
  19. A. Castiaux, A. Dereux, J.-P. Vigneron, C. Girard and O. J. F. Martin, "Electromagnetic fields in two-dimensional models of near-field optical microscope tips", Ultramicroscopy, vol. 60, pp. 1-9, 1995 .
  20. R. X. Bian, R. C. Dunn and X. S. Xie, "Single molecule emission characteristics in near-field microscopy", Phys. Rev. Lett., vol. 75, no. 26, pp. 4772-4775, 1995 .
  21. L. Novotny, D. W. Pohl and B. Hecht, "Scanning near-field optical probe with ultrasmall spot size", Opt. Lett., vol. 20, no. 9, pp. 970-972, 1995.
  22. L. Novotny, R. X. Brian and X. S. Xie, "Theory of nanometric optical tweezers", Phys. Rev. Lett., vol. 79, no. 4, pp. 645-648, 1997.
  23. G. von Freymann, T. Schimmel, M. Wegener, B. Hanewinkel, A. Knorr and S. W. Koch, "Computer simulations on near-field optical microscopy: Can subwavelength resolution be obtained using uncoated optical fiber probes?", Appl. Phys. Lett., vol. 73, no. 9, pp. 1170-1172, 1998.
  24. C. Hafner, The Generalized Multipole Technique for Computational Electromagnetics, Boston, MA: Artech House, 1990.
  25. O. J. F. Martin, A. Dereux and C. Girard, "Iterative scheme for computing exactly the total field propagating in dielectric structures of arbitrary shape", J. Opt. Soc. Amer. A, Opt. Image Sci., vol. 11, no. 3, pp. 1073-1080, 1994.
  26. O. J. F. Martin, C. Girard and A. Dereux, "Generalized field propagator for electromagnetic scattering and light confinement", Phys. Rev. Lett., vol. 74, no. 4, pp. 526-529, 1995.
  27. K. S. Yee, "Numerical solution of boundary value problems involving Maxwell's equations in isotropic media", IEEE Trans. Antennas Propagat., vol. 14, no. 3, pp. 302-307, May 1966.
  28. A. Taflove, Computational Electrodynamis: The Finite Difference Time Domain Method, Norwood, MA: Artech House, 1995.
  29. S. Fan, I. Appelbaum and J. D. Joannopoulos, "Near-field scanning optical microscopy as a simultaneous probe of fields and band structure of photonic crystals: A computational study", Appl. Phys. Lett., vol. 75, no. 22, pp. 3461-3463, 1999.
  30. M. Hammer, "Quadridirectional eigenmode expansion scheme for 2-D modeling of wave propagation in integrated optics", Opt. Commun. , vol. 235, no. 4-6, pp. 285-303, 2004.
  31. C. Vassallo, Optical Waveguide Concepts, Amsterdam: The Netherlands: Elsevier, 1991.
  32. G. Sztefka and H. P. Nolting, "Bidirectional eigenmode propagation for large refractive index steps", IEEE Photon. Technol. Lett., vol. 5, no. 5, pp. 554-557, May 1993.
  33. J. Willems, J. Haes and R. Baets, "The bidirectional mode expansion method for two-dimensional waveguides: the TM case", Opt. Quantum Electron., vol. 27, pp. 995-1007, 1995.
  34. M. Lohmeyer and R. Stoffer, "Integrated optical cross strip polarizer concept", Opt. Quantum Electron., vol. 33, no. 4/5, pp. 413-431, 2001 .
  35. M. Lohmeyer, "Mode expansion modeling of rectangular integrated optical microresonators", Opt. Quantum Electron., vol. 34, no. 5, pp. 541-557, 2002.
  36. A. L. Campillo and J. W. P. Hsu, "Intensity and phase mapping of guided light in LiNbO3 waveguides with an interferometric near-field scanning optical microscope", Appl. Opt., vol. 42, no. 36, pp. 7149-7156, 2003.
  37. R. Stoffer, H. J. W. M. Hoekstra, R. M. de Ridder, E. van Groesen and F. P. H. van Beckum, "Numerical studies of 2-D photonic crystals: waveguides, coupling between waveguides and filters", Opt. Quantum Electron., vol. 32, pp. 947-961, 2000.
  38. A. Suryanto, E. van Groesen, M. Hammer and H. J. W. M. Hoekstra, "A finite element scheme to study the nonlinear optical response of a finite grating without and with defect", Opt. Quantum Electron., vol. 35, no. 4, pp. 313-332, 2003.
  39. N. F. van Hulst, J.-A. Veerman, M. F. Garca-Parajó and L. Kuipers, "Analysis of individual (macro)molecules and proteins using near-field optics", J. Chem. Phys., vol. 112, no. 18, pp. 7799-7810, 2000.
  40. E. Flck, N. F. van Hulst, W. L. Vos and L. Kuipers, "Near-field investigation of three-dimensional photonic crystals", Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top., vol. 68, p. 015 601(R), 2003.
  41. M. L. M. Balistreri, J. P. Korterik, L. Kuipers and N. F. van Hulst, "Local observations of phase singularities in optical fields in waveguide structures", Phys. Rev. Lett., vol. 85, no. 2, pp. 294-297, 2000.

Other (41)

M. L. M. Balistreri, J. P. Korterik, G. J. Veldhuis, L. Kuipers and N. F. van Hulst, "Quantitative photon tunneling and shear-force microscopy of planar waveguide splitters and mixers", J. Appl. Phys., vol. 89, no. 6, pp. 3307-3314, 2001.

D. P. Tsai, H. E. Jackson, R. C. Reddick, S. H. Sharp and R. J. Warmack, "Photon scanning tunneling microscope study of optical waveguides", Appl. Phys. Lett., vol. 56, no. 16, pp. 1515-1517, 1990.

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", Appl. Phys. Lett., vol. 69, no. 23, pp. 3471-3473, 1996.

G. H. Vander Rhodes, B. B. Goldberg, M. S. Ünl, S. T. Chu, W. Pan, T. Kaneko, Y. Kokobun and B. E. Little, "Measurement of internal spatial modes and local propagation properties in optical waveguides", Appl. Phys. Lett., vol. 75, no. 16, pp. 2368-2370, 1999.

M. L. M. Balistreri, J. P. Korterik, L. Kuipers and N. F. van Hulst, "Photon scanning tunneling microscopy with a three-dimensional multiheight imaging mode", Appl. Phys. Lett., vol. 77, no. 25, pp. 4092-4094, 2000.

M. L. M. Balistreri, J. P. Korterik, L. Kuipers and N. F. van Hulst, "Phase mapping of optical fields in integrated optical waveguide structures", J. Lightw. Technol., vol. 19, no. 8, pp. 1169-1176, Aug. 2001.

M. L. M. Balistreri, J. P. Korterik, L. Kuipers and N. F. van Hulst, "Visualization of mode transformation in a planar waveguide splitter by near-field optical phase imaging", Appl. Phys. Lett., vol. 79, no. 7, pp. 910-912, 2001.

C. Peeters, E. Flck, A. M. Otter, M. L. M. Balistreri, J. P. Korterik, L. Kuipers and N. F. van Hulst, "Photon scanning tunneling microscopy of tailor-made photonic structures", Appl. Phys. Lett., vol. 77, no. 1, pp. 142-144, 2000.

E. Flck, M. Hammer, A. M. Otter, J. P. Korterijk, L. Kuipers and N. F. van Hulst, "Amplitude and phase evolution of optical fields inside periodic photonic structures", J. Lightw. Technol., vol. 21, no. 5, pp. 1384-1393, May 2003.

A. L. Campillo, J. W. P. Hsu, C. A. White and A. Rosenberg, "Mapping the optical intensity distribution in photonic crystals using a near-field scanning optical microscope", J. Appl. Phys., vol. 89, no. 5, pp. 2801-2807, 2001 .

P. Kramper, A. Birner, M. Agio, C. M. Soukoulis, F. Mller, U. Gsele, J. Mlynek and V. Sandoghdar, "Direct spectroscopy of a deep two-dimensional photonic crystal microresonator", Phys. Rev. B, Condens. Matter, vol. 64, p. 233 102, 2001.

K. Okamoto, M. Loncar, T. Yoshie, A. Scherer, Y. Qui and P. Gogna, "Near-field scanning optical microscopy of photonic crystal nanocavities", Appl. Phys. Lett. , vol. 82, no. 11, pp. 1676-1678, 2003.

D. J. W. Klunder, M. L. M. Balistreri, F. C. Blom, H. J. W. M. Hoekstra, A. Driessen, L. Kuipers and N. F. van Hulst, "High-resolution photon-scanning tunneling microscope measurements of the whispering gallery modes in a cylindrical microresonator", IEEE Photon. Technol. Lett., vol. 12, no. 11, pp. 1531-1533, Nov. 2000.

M. L. M. Balistreri, D. J. W. Klunder, F. C. Blom, A. Driessen, J. P. Korterik, L. Kuipers and N. F. van Hulst, "Experimental analysis of the whispering-gallery modes in a cylindrical optical microcavity", J. Opt. Soc. Amer. B, Opt. Phys., vol. 18, no. 4, pp. 465-471, 2001.

D. J. W. Klunder, M. L. M. Balistreri, F. C. Blom, H. J. W. M. Hoekstra, A. Driessen, L. Kuipers and N. F. van Hulst, "Detailed analysis of the intracavity phenomena inside a cylindrical microresonator", J. Lightw. Technol., vol. 20, no. 3, pp. 519-529, Mar. 2002.

L. Novotny, D. W. Pohl and P. Regli, "Light propagation through nanometer-sized structures: the two-dimensional-aperture scanning near-field optical microscope", J. Opt. Soc. Amer. A, Opt. Image Sci., vol. 11, no. 6, pp. 1768-1779, 1994.

L. Novotny, D. W. Pohl and P. Regli, "Near-field, far-field and imaging properties of the 2-D aperture SNOM", Ultramicroscopy, vol. 57, pp. 180-188, 1995.

B. Hecht, D. W. Pohl, H. Heinzelmann and L. Novotny, "Tunnel near-filed optical microscopy: TNOM-2", Ultramicroscopy, vol. 61, pp. 99-104, 1995.

A. Castiaux, A. Dereux, J.-P. Vigneron, C. Girard and O. J. F. Martin, "Electromagnetic fields in two-dimensional models of near-field optical microscope tips", Ultramicroscopy, vol. 60, pp. 1-9, 1995 .

R. X. Bian, R. C. Dunn and X. S. Xie, "Single molecule emission characteristics in near-field microscopy", Phys. Rev. Lett., vol. 75, no. 26, pp. 4772-4775, 1995 .

L. Novotny, D. W. Pohl and B. Hecht, "Scanning near-field optical probe with ultrasmall spot size", Opt. Lett., vol. 20, no. 9, pp. 970-972, 1995.

L. Novotny, R. X. Brian and X. S. Xie, "Theory of nanometric optical tweezers", Phys. Rev. Lett., vol. 79, no. 4, pp. 645-648, 1997.

G. von Freymann, T. Schimmel, M. Wegener, B. Hanewinkel, A. Knorr and S. W. Koch, "Computer simulations on near-field optical microscopy: Can subwavelength resolution be obtained using uncoated optical fiber probes?", Appl. Phys. Lett., vol. 73, no. 9, pp. 1170-1172, 1998.

C. Hafner, The Generalized Multipole Technique for Computational Electromagnetics, Boston, MA: Artech House, 1990.

O. J. F. Martin, A. Dereux and C. Girard, "Iterative scheme for computing exactly the total field propagating in dielectric structures of arbitrary shape", J. Opt. Soc. Amer. A, Opt. Image Sci., vol. 11, no. 3, pp. 1073-1080, 1994.

O. J. F. Martin, C. Girard and A. Dereux, "Generalized field propagator for electromagnetic scattering and light confinement", Phys. Rev. Lett., vol. 74, no. 4, pp. 526-529, 1995.

K. S. Yee, "Numerical solution of boundary value problems involving Maxwell's equations in isotropic media", IEEE Trans. Antennas Propagat., vol. 14, no. 3, pp. 302-307, May 1966.

A. Taflove, Computational Electrodynamis: The Finite Difference Time Domain Method, Norwood, MA: Artech House, 1995.

S. Fan, I. Appelbaum and J. D. Joannopoulos, "Near-field scanning optical microscopy as a simultaneous probe of fields and band structure of photonic crystals: A computational study", Appl. Phys. Lett., vol. 75, no. 22, pp. 3461-3463, 1999.

M. Hammer, "Quadridirectional eigenmode expansion scheme for 2-D modeling of wave propagation in integrated optics", Opt. Commun. , vol. 235, no. 4-6, pp. 285-303, 2004.

C. Vassallo, Optical Waveguide Concepts, Amsterdam: The Netherlands: Elsevier, 1991.

G. Sztefka and H. P. Nolting, "Bidirectional eigenmode propagation for large refractive index steps", IEEE Photon. Technol. Lett., vol. 5, no. 5, pp. 554-557, May 1993.

J. Willems, J. Haes and R. Baets, "The bidirectional mode expansion method for two-dimensional waveguides: the TM case", Opt. Quantum Electron., vol. 27, pp. 995-1007, 1995.

M. Lohmeyer and R. Stoffer, "Integrated optical cross strip polarizer concept", Opt. Quantum Electron., vol. 33, no. 4/5, pp. 413-431, 2001 .

M. Lohmeyer, "Mode expansion modeling of rectangular integrated optical microresonators", Opt. Quantum Electron., vol. 34, no. 5, pp. 541-557, 2002.

A. L. Campillo and J. W. P. Hsu, "Intensity and phase mapping of guided light in LiNbO3 waveguides with an interferometric near-field scanning optical microscope", Appl. Opt., vol. 42, no. 36, pp. 7149-7156, 2003.

R. Stoffer, H. J. W. M. Hoekstra, R. M. de Ridder, E. van Groesen and F. P. H. van Beckum, "Numerical studies of 2-D photonic crystals: waveguides, coupling between waveguides and filters", Opt. Quantum Electron., vol. 32, pp. 947-961, 2000.

A. Suryanto, E. van Groesen, M. Hammer and H. J. W. M. Hoekstra, "A finite element scheme to study the nonlinear optical response of a finite grating without and with defect", Opt. Quantum Electron., vol. 35, no. 4, pp. 313-332, 2003.

N. F. van Hulst, J.-A. Veerman, M. F. Garca-Parajó and L. Kuipers, "Analysis of individual (macro)molecules and proteins using near-field optics", J. Chem. Phys., vol. 112, no. 18, pp. 7799-7810, 2000.

E. Flck, N. F. van Hulst, W. L. Vos and L. Kuipers, "Near-field investigation of three-dimensional photonic crystals", Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top., vol. 68, p. 015 601(R), 2003.

M. L. M. Balistreri, J. P. Korterik, L. Kuipers and N. F. van Hulst, "Local observations of phase singularities in optical fields in waveguide structures", Phys. Rev. Lett., vol. 85, no. 2, pp. 294-297, 2000.

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