Abstract

The design and implementation of a phase-sensitive near-field scanning optical microscope incorporating both heterodyne interferometric detection and a phase feedback mechanism are described. Using this microscope we demonstrate a new method for measuring the effective index of the guided mode of a waveguide from the phase images. Two types of LiNbO3 waveguide, defined by titanium diffusion or annealed proton exchange, were studied. Both the profile and the effective index of the mode were measured experimentally. For titanium-diffused waveguides, both agree well with values determined from numerical simulation. In annealed proton-exchanged waveguides that contain periodically poled domains, we find evidence for backreflection from the boundaries between neighboring regions of opposite pole directions, which could result in transmission loss in this type of waveguide.

© 2003 Optical Society of America

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    [CrossRef]
  29. S. K. Korotky, W. J. Minford, L. L. Buhl, M. D. Divino, R. C. Alferness, “Mode size and method for estimating the propagation constant of single-mode Ti:LiNbO3 strip waveguides,” IEEE Trans. Microwave Theory Tech. MTT-30, 1784–1789 (1982).
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    [CrossRef]
  31. M. S. Stern, “Semivectorial polarised finite difference method for optical waveguides with arbitrary index profiles,” Proc. Inst. Electr. Eng. Optoelectron. 135, 56–63 (1988).
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    [CrossRef] [PubMed]
  33. A. L. Campillo, J. W. P. Hsu, C. A. White, C. D. W. Jones, “Direct measurement of the guided modes in LiNbO3 waveguides,” Appl. Phys. Lett. 80, 2239–2241 (2002).
    [CrossRef]

2002 (3)

S. I. Bozhevolnyi, V. S. Volkov, J. Arentoft, A. Boltasseva, T. Søndergaard, M. Kristensen, “Direct mapping of light propagation in photonic crystal waveguides,” Opt. Commun. 212, 51–55 (2002).
[CrossRef]

A. Nesci, R. Dändliker, M. Salt, H. P. Herzig, “Measuring amplitude and phase distribution of fields generated by gratings with sub-wavelength resolution,” Opt. Commun. 205, 229–238 (2002).
[CrossRef]

A. L. Campillo, J. W. P. Hsu, C. A. White, C. D. W. Jones, “Direct measurement of the guided modes in LiNbO3 waveguides,” Appl. Phys. Lett. 80, 2239–2241 (2002).
[CrossRef]

2001 (1)

A. L. Campillo, J. W. P. Hsu, C. A. White, A. Rosenberg, “Mapping the optical intensity distribution in photonic crystals using a near-field scanning optical microscope,” J. Appl. Phys. 89, 2801–2807 (2001).
[CrossRef]

2000 (7)

R. Scarmozzino, A. Gopinath, R. Pregla, S. Helfert, “Numerical techniques for modeling guided-wave photonic devices,” IEEE J. Sel. Top. Quantum Electron. 6, 150–162 (2000).
[CrossRef]

P. L. Phillips, J. C. Knight, J. M. Pottage, G. Kakarantzas, P. St. J. Russell, “Direct measurement of optical phase in the near field,” Appl. Phys. Lett. 76, 541–543 (2000).
[CrossRef]

M. L. M. Balistreri, J. P. Korterik, L. Kuipers, N. F. van Hulst, “Local observations of phase singularities in optical fields in waveguide structures,” Phys. Rev. Lett. 85, 294–297 (2000).
[CrossRef] [PubMed]

T. Miya, “Silica-based planar lightwave circuits: passive and thermally active devices,” IEEE J. Sel. Top. Quantum Electron. 6, 38–45 (2000).
[CrossRef]

K. R. Parameswaran, M. Fujimura, M. H. Chou, M. M. Fejer, “Low-power all-optical gate based on sum frequency mixing in APE waveguides in PPLN,” IEEE Photon. Technol. Lett. 12, 654–656 (2000).
[CrossRef]

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron. 6, 69–82 (2000).
[CrossRef]

G. H. Vander Rhodes, B. B. Goldberg, M. S. Ünlü, S. Chu, B. E. Little, “Internal spatial modes in glass microring resonators,” IEEE J. Sel. Top. Quantum Electron. 6, 46–53 (2000).
[CrossRef]

1999 (1)

R. Stöckle, C. Fokas, V. Deckert, R. Zenobi, “High-quality near-field optical probes by tube etching,” Appl. Phys. Lett. 75, 160–162 (1999).
[CrossRef]

1998 (4)

G. H. Vander Rhodes, M. S. Ünlü, B. B. Goldberg, J. M. Pomeroy, T. F. Krauss, “Characterisation of waveguide microcavities using high-resolution transmission spectroscopy and near-field scanning optical microscopy,” Proc. Inst. Electr. Eng. Optoelectron. 145, 379–383 (1998).
[CrossRef]

R. S. Moyer, R. Grencavich, F. F. Judd, R. C. Kershner, W. J. Minford, R. W. Smith, “Design and qualification of hermetically packaged lithium niobate optical modulator,” IEEE Trans. Components Packag. Manuf. Technol. Part B 21, 130–135 (1998).
[CrossRef]

M. H. Chou, J. Hauden, M. A. Arbore, M. M. Fejer, “1.5-µm-band wavelength conversion based on difference-frequency generation in LiNbO3 waveguides with integrated coupling structures,” Opt. Lett. 23, 1004–1006 (1998).
[CrossRef]

P. Lambelet, A. Sayah, M. Pfeffer, C. Philipona, F. Marquis-Weible, “Chemically etched fiber tips for near-field optical microscopy: a process for smoother tips,” Appl. Opt. 37, 7289–7292 (1998).
[CrossRef]

1996 (2)

K. Kintaka, M. Fujimura, T. Suhara, H. Nishihara, “High-efficiency LiNbO3 waveguide second-harmonic generation devices with ferroelectric-domain-inverted gratings fabricated by applying voltage,” J. Lightwave Technol. 14, 462–468 (1996).
[CrossRef]

M. Lee, E. B. McDaniel, J. W. P. Hsu, “An impedance based non-contact feedback control system for scanning probe microscopes,” Rev. Sci. Instrum. 67, 1468–1471 (1996).
[CrossRef]

1995 (1)

J. W. P. Hsu, M. Lee, B. S. Deaver, “A nonoptical tip-sample distance control method for near-field scanning optical microscopy using impedance changes in an electromechanical system,” Rev. Sci. Instrum. 66, 3177–3181 (1995).
[CrossRef]

1994 (1)

A. G. Choo, H. E. Jackson, U. Thiel, G. N. De Brabander, J. T. Boyd, “Near field measurements of optical channel waveguides and directional couplers,” Appl. Phys. Lett. 65, 947–949 (1994).
[CrossRef]

1992 (1)

1991 (2)

M. L. Bortz, M. M. Fejer, “Annealed proton-exchanged LiNbO3 waveguides,” Opt. Lett. 16, 1844–1846 (1991).
[CrossRef] [PubMed]

F. Roddier, M. Northcott, E. Graves, “A simple low-order adaptive optics system for near-infrared applications,” Publ. Astron. Soc. Pac. 103, 131–149 (1991).
[CrossRef]

1990 (1)

D. P. Tsai, H. E. Jackson, R. C. Reddick, S. H. Sharp, R. J. Warmack, “Photon scanning tunneling microscope study of optical waveguides,” Appl. Phys. Lett. 56, 1515–1517 (1990).
[CrossRef]

1989 (1)

E. J. Lim, M. M. Fejer, R. L. Beyer, “Second-harmonic generation of green light in periodically poled planar lithium niobate waveguide,” Electron. Lett. 25, 174–175 (1989).
[CrossRef]

1988 (2)

P. G. Suchoski, T. K. Findakly, F. J. Leonberger, “Stable low-loss proton-exchanged LiNbO3 waveguide devices with no electro-optic degradation,” Opt. Lett. 13, 1050–1052 (1988).
[CrossRef] [PubMed]

M. S. Stern, “Semivectorial polarised finite difference method for optical waveguides with arbitrary index profiles,” Proc. Inst. Electr. Eng. Optoelectron. 135, 56–63 (1988).

1982 (1)

S. K. Korotky, W. J. Minford, L. L. Buhl, M. D. Divino, R. C. Alferness, “Mode size and method for estimating the propagation constant of single-mode Ti:LiNbO3 strip waveguides,” IEEE Trans. Microwave Theory Tech. MTT-30, 1784–1789 (1982).
[CrossRef]

1981 (1)

K. Fritsch, G. Adamovsky, “Simple circuit for feedback stabilization of a single-mode optical fiber interferometer,” Rev. Sci. Instrum. 52, 996–1000 (1981).
[CrossRef]

1980 (1)

1974 (1)

R. V. Schmidt, I. P. Kaminow, “Metal-diffused optical waveguides in LiNbO3,” Appl. Phys. Lett. 25, 458–460 (1974).
[CrossRef]

Adamovsky, G.

K. Fritsch, G. Adamovsky, “Simple circuit for feedback stabilization of a single-mode optical fiber interferometer,” Rev. Sci. Instrum. 52, 996–1000 (1981).
[CrossRef]

Alferness, R. C.

S. K. Korotky, W. J. Minford, L. L. Buhl, M. D. Divino, R. C. Alferness, “Mode size and method for estimating the propagation constant of single-mode Ti:LiNbO3 strip waveguides,” IEEE Trans. Microwave Theory Tech. MTT-30, 1784–1789 (1982).
[CrossRef]

Arbore, M. A.

Arentoft, J.

S. I. Bozhevolnyi, V. S. Volkov, J. Arentoft, A. Boltasseva, T. Søndergaard, M. Kristensen, “Direct mapping of light propagation in photonic crystal waveguides,” Opt. Commun. 212, 51–55 (2002).
[CrossRef]

Attanasio, D. V.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron. 6, 69–82 (2000).
[CrossRef]

Balistreri, M. L. M.

M. L. M. Balistreri, J. P. Korterik, L. Kuipers, N. F. van Hulst, “Local observations of phase singularities in optical fields in waveguide structures,” Phys. Rev. Lett. 85, 294–297 (2000).
[CrossRef] [PubMed]

Beyer, R. L.

E. J. Lim, M. M. Fejer, R. L. Beyer, “Second-harmonic generation of green light in periodically poled planar lithium niobate waveguide,” Electron. Lett. 25, 174–175 (1989).
[CrossRef]

Boltasseva, A.

S. I. Bozhevolnyi, V. S. Volkov, J. Arentoft, A. Boltasseva, T. Søndergaard, M. Kristensen, “Direct mapping of light propagation in photonic crystal waveguides,” Opt. Commun. 212, 51–55 (2002).
[CrossRef]

Bortz, M. L.

Bossi, D. E.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron. 6, 69–82 (2000).
[CrossRef]

Boyd, J. T.

A. G. Choo, H. E. Jackson, U. Thiel, G. N. De Brabander, J. T. Boyd, “Near field measurements of optical channel waveguides and directional couplers,” Appl. Phys. Lett. 65, 947–949 (1994).
[CrossRef]

Bozhevolnyi, S. I.

S. I. Bozhevolnyi, V. S. Volkov, J. Arentoft, A. Boltasseva, T. Søndergaard, M. Kristensen, “Direct mapping of light propagation in photonic crystal waveguides,” Opt. Commun. 212, 51–55 (2002).
[CrossRef]

Buhl, L. L.

S. K. Korotky, W. J. Minford, L. L. Buhl, M. D. Divino, R. C. Alferness, “Mode size and method for estimating the propagation constant of single-mode Ti:LiNbO3 strip waveguides,” IEEE Trans. Microwave Theory Tech. MTT-30, 1784–1789 (1982).
[CrossRef]

Campillo, A. L.

A. L. Campillo, J. W. P. Hsu, C. A. White, C. D. W. Jones, “Direct measurement of the guided modes in LiNbO3 waveguides,” Appl. Phys. Lett. 80, 2239–2241 (2002).
[CrossRef]

A. L. Campillo, J. W. P. Hsu, C. A. White, A. Rosenberg, “Mapping the optical intensity distribution in photonic crystals using a near-field scanning optical microscope,” J. Appl. Phys. 89, 2801–2807 (2001).
[CrossRef]

Choo, A. G.

A. G. Choo, H. E. Jackson, U. Thiel, G. N. De Brabander, J. T. Boyd, “Near field measurements of optical channel waveguides and directional couplers,” Appl. Phys. Lett. 65, 947–949 (1994).
[CrossRef]

Chou, M. H.

K. R. Parameswaran, M. Fujimura, M. H. Chou, M. M. Fejer, “Low-power all-optical gate based on sum frequency mixing in APE waveguides in PPLN,” IEEE Photon. Technol. Lett. 12, 654–656 (2000).
[CrossRef]

M. H. Chou, J. Hauden, M. A. Arbore, M. M. Fejer, “1.5-µm-band wavelength conversion based on difference-frequency generation in LiNbO3 waveguides with integrated coupling structures,” Opt. Lett. 23, 1004–1006 (1998).
[CrossRef]

Chu, S.

G. H. Vander Rhodes, B. B. Goldberg, M. S. Ünlü, S. Chu, B. E. Little, “Internal spatial modes in glass microring resonators,” IEEE J. Sel. Top. Quantum Electron. 6, 46–53 (2000).
[CrossRef]

Dändliker, R.

A. Nesci, R. Dändliker, M. Salt, H. P. Herzig, “Measuring amplitude and phase distribution of fields generated by gratings with sub-wavelength resolution,” Opt. Commun. 205, 229–238 (2002).
[CrossRef]

Dandridge, A.

De Brabander, G. N.

A. G. Choo, H. E. Jackson, U. Thiel, G. N. De Brabander, J. T. Boyd, “Near field measurements of optical channel waveguides and directional couplers,” Appl. Phys. Lett. 65, 947–949 (1994).
[CrossRef]

Deaver, B. S.

J. W. P. Hsu, M. Lee, B. S. Deaver, “A nonoptical tip-sample distance control method for near-field scanning optical microscopy using impedance changes in an electromechanical system,” Rev. Sci. Instrum. 66, 3177–3181 (1995).
[CrossRef]

Deckert, V.

R. Stöckle, C. Fokas, V. Deckert, R. Zenobi, “High-quality near-field optical probes by tube etching,” Appl. Phys. Lett. 75, 160–162 (1999).
[CrossRef]

Divino, M. D.

S. K. Korotky, W. J. Minford, L. L. Buhl, M. D. Divino, R. C. Alferness, “Mode size and method for estimating the propagation constant of single-mode Ti:LiNbO3 strip waveguides,” IEEE Trans. Microwave Theory Tech. MTT-30, 1784–1789 (1982).
[CrossRef]

Fejer, M. M.

K. R. Parameswaran, M. Fujimura, M. H. Chou, M. M. Fejer, “Low-power all-optical gate based on sum frequency mixing in APE waveguides in PPLN,” IEEE Photon. Technol. Lett. 12, 654–656 (2000).
[CrossRef]

M. H. Chou, J. Hauden, M. A. Arbore, M. M. Fejer, “1.5-µm-band wavelength conversion based on difference-frequency generation in LiNbO3 waveguides with integrated coupling structures,” Opt. Lett. 23, 1004–1006 (1998).
[CrossRef]

M. L. Bortz, M. M. Fejer, “Annealed proton-exchanged LiNbO3 waveguides,” Opt. Lett. 16, 1844–1846 (1991).
[CrossRef] [PubMed]

E. J. Lim, M. M. Fejer, R. L. Beyer, “Second-harmonic generation of green light in periodically poled planar lithium niobate waveguide,” Electron. Lett. 25, 174–175 (1989).
[CrossRef]

Findakly, T. K.

Fokas, C.

R. Stöckle, C. Fokas, V. Deckert, R. Zenobi, “High-quality near-field optical probes by tube etching,” Appl. Phys. Lett. 75, 160–162 (1999).
[CrossRef]

Fritsch, K.

K. Fritsch, G. Adamovsky, “Simple circuit for feedback stabilization of a single-mode optical fiber interferometer,” Rev. Sci. Instrum. 52, 996–1000 (1981).
[CrossRef]

Fritz, D. J.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron. 6, 69–82 (2000).
[CrossRef]

Fujimura, M.

K. R. Parameswaran, M. Fujimura, M. H. Chou, M. M. Fejer, “Low-power all-optical gate based on sum frequency mixing in APE waveguides in PPLN,” IEEE Photon. Technol. Lett. 12, 654–656 (2000).
[CrossRef]

K. Kintaka, M. Fujimura, T. Suhara, H. Nishihara, “High-efficiency LiNbO3 waveguide second-harmonic generation devices with ferroelectric-domain-inverted gratings fabricated by applying voltage,” J. Lightwave Technol. 14, 462–468 (1996).
[CrossRef]

Goldberg, B. B.

G. H. Vander Rhodes, B. B. Goldberg, M. S. Ünlü, S. Chu, B. E. Little, “Internal spatial modes in glass microring resonators,” IEEE J. Sel. Top. Quantum Electron. 6, 46–53 (2000).
[CrossRef]

G. H. Vander Rhodes, M. S. Ünlü, B. B. Goldberg, J. M. Pomeroy, T. F. Krauss, “Characterisation of waveguide microcavities using high-resolution transmission spectroscopy and near-field scanning optical microscopy,” Proc. Inst. Electr. Eng. Optoelectron. 145, 379–383 (1998).
[CrossRef]

Gopinath, A.

R. Scarmozzino, A. Gopinath, R. Pregla, S. Helfert, “Numerical techniques for modeling guided-wave photonic devices,” IEEE J. Sel. Top. Quantum Electron. 6, 150–162 (2000).
[CrossRef]

Graves, E.

F. Roddier, M. Northcott, E. Graves, “A simple low-order adaptive optics system for near-infrared applications,” Publ. Astron. Soc. Pac. 103, 131–149 (1991).
[CrossRef]

Grencavich, R.

R. S. Moyer, R. Grencavich, F. F. Judd, R. C. Kershner, W. J. Minford, R. W. Smith, “Design and qualification of hermetically packaged lithium niobate optical modulator,” IEEE Trans. Components Packag. Manuf. Technol. Part B 21, 130–135 (1998).
[CrossRef]

Hallemeier, P. F.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron. 6, 69–82 (2000).
[CrossRef]

Hauden, J.

Helfert, S.

R. Scarmozzino, A. Gopinath, R. Pregla, S. Helfert, “Numerical techniques for modeling guided-wave photonic devices,” IEEE J. Sel. Top. Quantum Electron. 6, 150–162 (2000).
[CrossRef]

Herzig, H. P.

A. Nesci, R. Dändliker, M. Salt, H. P. Herzig, “Measuring amplitude and phase distribution of fields generated by gratings with sub-wavelength resolution,” Opt. Commun. 205, 229–238 (2002).
[CrossRef]

Hibino, Y.

Hsu, J. W. P.

A. L. Campillo, J. W. P. Hsu, C. A. White, C. D. W. Jones, “Direct measurement of the guided modes in LiNbO3 waveguides,” Appl. Phys. Lett. 80, 2239–2241 (2002).
[CrossRef]

A. L. Campillo, J. W. P. Hsu, C. A. White, A. Rosenberg, “Mapping the optical intensity distribution in photonic crystals using a near-field scanning optical microscope,” J. Appl. Phys. 89, 2801–2807 (2001).
[CrossRef]

M. Lee, E. B. McDaniel, J. W. P. Hsu, “An impedance based non-contact feedback control system for scanning probe microscopes,” Rev. Sci. Instrum. 67, 1468–1471 (1996).
[CrossRef]

J. W. P. Hsu, M. Lee, B. S. Deaver, “A nonoptical tip-sample distance control method for near-field scanning optical microscopy using impedance changes in an electromechanical system,” Rev. Sci. Instrum. 66, 3177–3181 (1995).
[CrossRef]

Jackson, D. A.

Jackson, H. E.

A. G. Choo, H. E. Jackson, U. Thiel, G. N. De Brabander, J. T. Boyd, “Near field measurements of optical channel waveguides and directional couplers,” Appl. Phys. Lett. 65, 947–949 (1994).
[CrossRef]

D. P. Tsai, H. E. Jackson, R. C. Reddick, S. H. Sharp, R. J. Warmack, “Photon scanning tunneling microscope study of optical waveguides,” Appl. Phys. Lett. 56, 1515–1517 (1990).
[CrossRef]

Jones, C. D. W.

A. L. Campillo, J. W. P. Hsu, C. A. White, C. D. W. Jones, “Direct measurement of the guided modes in LiNbO3 waveguides,” Appl. Phys. Lett. 80, 2239–2241 (2002).
[CrossRef]

Judd, F. F.

R. S. Moyer, R. Grencavich, F. F. Judd, R. C. Kershner, W. J. Minford, R. W. Smith, “Design and qualification of hermetically packaged lithium niobate optical modulator,” IEEE Trans. Components Packag. Manuf. Technol. Part B 21, 130–135 (1998).
[CrossRef]

Kakarantzas, G.

P. L. Phillips, J. C. Knight, J. M. Pottage, G. Kakarantzas, P. St. J. Russell, “Direct measurement of optical phase in the near field,” Appl. Phys. Lett. 76, 541–543 (2000).
[CrossRef]

Kaminow, I. P.

R. V. Schmidt, I. P. Kaminow, “Metal-diffused optical waveguides in LiNbO3,” Appl. Phys. Lett. 25, 458–460 (1974).
[CrossRef]

Kershner, R. C.

R. S. Moyer, R. Grencavich, F. F. Judd, R. C. Kershner, W. J. Minford, R. W. Smith, “Design and qualification of hermetically packaged lithium niobate optical modulator,” IEEE Trans. Components Packag. Manuf. Technol. Part B 21, 130–135 (1998).
[CrossRef]

Kintaka, K.

K. Kintaka, M. Fujimura, T. Suhara, H. Nishihara, “High-efficiency LiNbO3 waveguide second-harmonic generation devices with ferroelectric-domain-inverted gratings fabricated by applying voltage,” J. Lightwave Technol. 14, 462–468 (1996).
[CrossRef]

Kissa, K. M.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron. 6, 69–82 (2000).
[CrossRef]

Knight, J. C.

P. L. Phillips, J. C. Knight, J. M. Pottage, G. Kakarantzas, P. St. J. Russell, “Direct measurement of optical phase in the near field,” Appl. Phys. Lett. 76, 541–543 (2000).
[CrossRef]

Korotky, S. K.

S. K. Korotky, W. J. Minford, L. L. Buhl, M. D. Divino, R. C. Alferness, “Mode size and method for estimating the propagation constant of single-mode Ti:LiNbO3 strip waveguides,” IEEE Trans. Microwave Theory Tech. MTT-30, 1784–1789 (1982).
[CrossRef]

Korterik, J. P.

M. L. M. Balistreri, J. P. Korterik, L. Kuipers, N. F. van Hulst, “Local observations of phase singularities in optical fields in waveguide structures,” Phys. Rev. Lett. 85, 294–297 (2000).
[CrossRef] [PubMed]

Krauss, T. F.

G. H. Vander Rhodes, M. S. Ünlü, B. B. Goldberg, J. M. Pomeroy, T. F. Krauss, “Characterisation of waveguide microcavities using high-resolution transmission spectroscopy and near-field scanning optical microscopy,” Proc. Inst. Electr. Eng. Optoelectron. 145, 379–383 (1998).
[CrossRef]

Kristensen, M.

S. I. Bozhevolnyi, V. S. Volkov, J. Arentoft, A. Boltasseva, T. Søndergaard, M. Kristensen, “Direct mapping of light propagation in photonic crystal waveguides,” Opt. Commun. 212, 51–55 (2002).
[CrossRef]

Kuipers, L.

M. L. M. Balistreri, J. P. Korterik, L. Kuipers, N. F. van Hulst, “Local observations of phase singularities in optical fields in waveguide structures,” Phys. Rev. Lett. 85, 294–297 (2000).
[CrossRef] [PubMed]

Lafaw, D. A.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron. 6, 69–82 (2000).
[CrossRef]

Lambelet, P.

Lee, M.

M. Lee, E. B. McDaniel, J. W. P. Hsu, “An impedance based non-contact feedback control system for scanning probe microscopes,” Rev. Sci. Instrum. 67, 1468–1471 (1996).
[CrossRef]

J. W. P. Hsu, M. Lee, B. S. Deaver, “A nonoptical tip-sample distance control method for near-field scanning optical microscopy using impedance changes in an electromechanical system,” Rev. Sci. Instrum. 66, 3177–3181 (1995).
[CrossRef]

Leonberger, F. J.

Lim, E. J.

E. J. Lim, M. M. Fejer, R. L. Beyer, “Second-harmonic generation of green light in periodically poled planar lithium niobate waveguide,” Electron. Lett. 25, 174–175 (1989).
[CrossRef]

Little, B. E.

G. H. Vander Rhodes, B. B. Goldberg, M. S. Ünlü, S. Chu, B. E. Little, “Internal spatial modes in glass microring resonators,” IEEE J. Sel. Top. Quantum Electron. 6, 46–53 (2000).
[CrossRef]

Maack, D.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron. 6, 69–82 (2000).
[CrossRef]

Marquis-Weible, F.

McBrien, G. J.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron. 6, 69–82 (2000).
[CrossRef]

McDaniel, E. B.

M. Lee, E. B. McDaniel, J. W. P. Hsu, “An impedance based non-contact feedback control system for scanning probe microscopes,” Rev. Sci. Instrum. 67, 1468–1471 (1996).
[CrossRef]

Minford, W. J.

R. S. Moyer, R. Grencavich, F. F. Judd, R. C. Kershner, W. J. Minford, R. W. Smith, “Design and qualification of hermetically packaged lithium niobate optical modulator,” IEEE Trans. Components Packag. Manuf. Technol. Part B 21, 130–135 (1998).
[CrossRef]

S. K. Korotky, W. J. Minford, L. L. Buhl, M. D. Divino, R. C. Alferness, “Mode size and method for estimating the propagation constant of single-mode Ti:LiNbO3 strip waveguides,” IEEE Trans. Microwave Theory Tech. MTT-30, 1784–1789 (1982).
[CrossRef]

Miya, T.

T. Miya, “Silica-based planar lightwave circuits: passive and thermally active devices,” IEEE J. Sel. Top. Quantum Electron. 6, 38–45 (2000).
[CrossRef]

Moyer, R. S.

R. S. Moyer, R. Grencavich, F. F. Judd, R. C. Kershner, W. J. Minford, R. W. Smith, “Design and qualification of hermetically packaged lithium niobate optical modulator,” IEEE Trans. Components Packag. Manuf. Technol. Part B 21, 130–135 (1998).
[CrossRef]

Murphy, E. J.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron. 6, 69–82 (2000).
[CrossRef]

Nesci, A.

A. Nesci, R. Dändliker, M. Salt, H. P. Herzig, “Measuring amplitude and phase distribution of fields generated by gratings with sub-wavelength resolution,” Opt. Commun. 205, 229–238 (2002).
[CrossRef]

Nishi, I.

Nishihara, H.

K. Kintaka, M. Fujimura, T. Suhara, H. Nishihara, “High-efficiency LiNbO3 waveguide second-harmonic generation devices with ferroelectric-domain-inverted gratings fabricated by applying voltage,” J. Lightwave Technol. 14, 462–468 (1996).
[CrossRef]

Northcott, M.

F. Roddier, M. Northcott, E. Graves, “A simple low-order adaptive optics system for near-infrared applications,” Publ. Astron. Soc. Pac. 103, 131–149 (1991).
[CrossRef]

Parameswaran, K. R.

K. R. Parameswaran, M. Fujimura, M. H. Chou, M. M. Fejer, “Low-power all-optical gate based on sum frequency mixing in APE waveguides in PPLN,” IEEE Photon. Technol. Lett. 12, 654–656 (2000).
[CrossRef]

Pfeffer, M.

Philipona, C.

Phillips, P. L.

P. L. Phillips, J. C. Knight, J. M. Pottage, G. Kakarantzas, P. St. J. Russell, “Direct measurement of optical phase in the near field,” Appl. Phys. Lett. 76, 541–543 (2000).
[CrossRef]

Pomeroy, J. M.

G. H. Vander Rhodes, M. S. Ünlü, B. B. Goldberg, J. M. Pomeroy, T. F. Krauss, “Characterisation of waveguide microcavities using high-resolution transmission spectroscopy and near-field scanning optical microscopy,” Proc. Inst. Electr. Eng. Optoelectron. 145, 379–383 (1998).
[CrossRef]

Pottage, J. M.

P. L. Phillips, J. C. Knight, J. M. Pottage, G. Kakarantzas, P. St. J. Russell, “Direct measurement of optical phase in the near field,” Appl. Phys. Lett. 76, 541–543 (2000).
[CrossRef]

Pregla, R.

R. Scarmozzino, A. Gopinath, R. Pregla, S. Helfert, “Numerical techniques for modeling guided-wave photonic devices,” IEEE J. Sel. Top. Quantum Electron. 6, 150–162 (2000).
[CrossRef]

Priest, R.

Reddick, R. C.

D. P. Tsai, H. E. Jackson, R. C. Reddick, S. H. Sharp, R. J. Warmack, “Photon scanning tunneling microscope study of optical waveguides,” Appl. Phys. Lett. 56, 1515–1517 (1990).
[CrossRef]

Roddier, F.

F. Roddier, M. Northcott, E. Graves, “A simple low-order adaptive optics system for near-infrared applications,” Publ. Astron. Soc. Pac. 103, 131–149 (1991).
[CrossRef]

Rosenberg, A.

A. L. Campillo, J. W. P. Hsu, C. A. White, A. Rosenberg, “Mapping the optical intensity distribution in photonic crystals using a near-field scanning optical microscope,” J. Appl. Phys. 89, 2801–2807 (2001).
[CrossRef]

Russell, P. St. J.

P. L. Phillips, J. C. Knight, J. M. Pottage, G. Kakarantzas, P. St. J. Russell, “Direct measurement of optical phase in the near field,” Appl. Phys. Lett. 76, 541–543 (2000).
[CrossRef]

Salt, M.

A. Nesci, R. Dändliker, M. Salt, H. P. Herzig, “Measuring amplitude and phase distribution of fields generated by gratings with sub-wavelength resolution,” Opt. Commun. 205, 229–238 (2002).
[CrossRef]

Sayah, A.

Scarmozzino, R.

R. Scarmozzino, A. Gopinath, R. Pregla, S. Helfert, “Numerical techniques for modeling guided-wave photonic devices,” IEEE J. Sel. Top. Quantum Electron. 6, 150–162 (2000).
[CrossRef]

Schmidt, R. V.

R. V. Schmidt, I. P. Kaminow, “Metal-diffused optical waveguides in LiNbO3,” Appl. Phys. Lett. 25, 458–460 (1974).
[CrossRef]

Sharp, S. H.

D. P. Tsai, H. E. Jackson, R. C. Reddick, S. H. Sharp, R. J. Warmack, “Photon scanning tunneling microscope study of optical waveguides,” Appl. Phys. Lett. 56, 1515–1517 (1990).
[CrossRef]

Smith, R. W.

R. S. Moyer, R. Grencavich, F. F. Judd, R. C. Kershner, W. J. Minford, R. W. Smith, “Design and qualification of hermetically packaged lithium niobate optical modulator,” IEEE Trans. Components Packag. Manuf. Technol. Part B 21, 130–135 (1998).
[CrossRef]

Søndergaard, T.

S. I. Bozhevolnyi, V. S. Volkov, J. Arentoft, A. Boltasseva, T. Søndergaard, M. Kristensen, “Direct mapping of light propagation in photonic crystal waveguides,” Opt. Commun. 212, 51–55 (2002).
[CrossRef]

Stern, M. S.

M. S. Stern, “Semivectorial polarised finite difference method for optical waveguides with arbitrary index profiles,” Proc. Inst. Electr. Eng. Optoelectron. 135, 56–63 (1988).

Stöckle, R.

R. Stöckle, C. Fokas, V. Deckert, R. Zenobi, “High-quality near-field optical probes by tube etching,” Appl. Phys. Lett. 75, 160–162 (1999).
[CrossRef]

Suchoski, P. G.

Suhara, T.

K. Kintaka, M. Fujimura, T. Suhara, H. Nishihara, “High-efficiency LiNbO3 waveguide second-harmonic generation devices with ferroelectric-domain-inverted gratings fabricated by applying voltage,” J. Lightwave Technol. 14, 462–468 (1996).
[CrossRef]

Takahashi, H.

Thiel, U.

A. G. Choo, H. E. Jackson, U. Thiel, G. N. De Brabander, J. T. Boyd, “Near field measurements of optical channel waveguides and directional couplers,” Appl. Phys. Lett. 65, 947–949 (1994).
[CrossRef]

Tsai, D. P.

D. P. Tsai, H. E. Jackson, R. C. Reddick, S. H. Sharp, R. J. Warmack, “Photon scanning tunneling microscope study of optical waveguides,” Appl. Phys. Lett. 56, 1515–1517 (1990).
[CrossRef]

Tveten, A. B.

Ünlü, M. S.

G. H. Vander Rhodes, B. B. Goldberg, M. S. Ünlü, S. Chu, B. E. Little, “Internal spatial modes in glass microring resonators,” IEEE J. Sel. Top. Quantum Electron. 6, 46–53 (2000).
[CrossRef]

G. H. Vander Rhodes, M. S. Ünlü, B. B. Goldberg, J. M. Pomeroy, T. F. Krauss, “Characterisation of waveguide microcavities using high-resolution transmission spectroscopy and near-field scanning optical microscopy,” Proc. Inst. Electr. Eng. Optoelectron. 145, 379–383 (1998).
[CrossRef]

van Hulst, N. F.

M. L. M. Balistreri, J. P. Korterik, L. Kuipers, N. F. van Hulst, “Local observations of phase singularities in optical fields in waveguide structures,” Phys. Rev. Lett. 85, 294–297 (2000).
[CrossRef] [PubMed]

Vander Rhodes, G. H.

G. H. Vander Rhodes, B. B. Goldberg, M. S. Ünlü, S. Chu, B. E. Little, “Internal spatial modes in glass microring resonators,” IEEE J. Sel. Top. Quantum Electron. 6, 46–53 (2000).
[CrossRef]

G. H. Vander Rhodes, M. S. Ünlü, B. B. Goldberg, J. M. Pomeroy, T. F. Krauss, “Characterisation of waveguide microcavities using high-resolution transmission spectroscopy and near-field scanning optical microscopy,” Proc. Inst. Electr. Eng. Optoelectron. 145, 379–383 (1998).
[CrossRef]

Volkov, V. S.

S. I. Bozhevolnyi, V. S. Volkov, J. Arentoft, A. Boltasseva, T. Søndergaard, M. Kristensen, “Direct mapping of light propagation in photonic crystal waveguides,” Opt. Commun. 212, 51–55 (2002).
[CrossRef]

Warmack, R. J.

D. P. Tsai, H. E. Jackson, R. C. Reddick, S. H. Sharp, R. J. Warmack, “Photon scanning tunneling microscope study of optical waveguides,” Appl. Phys. Lett. 56, 1515–1517 (1990).
[CrossRef]

White, C. A.

A. L. Campillo, J. W. P. Hsu, C. A. White, C. D. W. Jones, “Direct measurement of the guided modes in LiNbO3 waveguides,” Appl. Phys. Lett. 80, 2239–2241 (2002).
[CrossRef]

A. L. Campillo, J. W. P. Hsu, C. A. White, A. Rosenberg, “Mapping the optical intensity distribution in photonic crystals using a near-field scanning optical microscope,” J. Appl. Phys. 89, 2801–2807 (2001).
[CrossRef]

Wooten, E. L.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron. 6, 69–82 (2000).
[CrossRef]

Yamada, T.

T. Yamada, “LiNbO3 family,” in Landol-Bornstein Numerical Data and Functional Relationships in Science and Technology, New Series, Group III: Crystal and Solid State Physics, K.-H. Hellwege, A. M. Hellwege, eds. (Springer-Verlag, New York, 1981), Vol. 16a, pp. 149–156, 489–499.

Yi-Yan, A.

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron. 6, 69–82 (2000).
[CrossRef]

Zenobi, R.

R. Stöckle, C. Fokas, V. Deckert, R. Zenobi, “High-quality near-field optical probes by tube etching,” Appl. Phys. Lett. 75, 160–162 (1999).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (6)

P. L. Phillips, J. C. Knight, J. M. Pottage, G. Kakarantzas, P. St. J. Russell, “Direct measurement of optical phase in the near field,” Appl. Phys. Lett. 76, 541–543 (2000).
[CrossRef]

A. L. Campillo, J. W. P. Hsu, C. A. White, C. D. W. Jones, “Direct measurement of the guided modes in LiNbO3 waveguides,” Appl. Phys. Lett. 80, 2239–2241 (2002).
[CrossRef]

R. V. Schmidt, I. P. Kaminow, “Metal-diffused optical waveguides in LiNbO3,” Appl. Phys. Lett. 25, 458–460 (1974).
[CrossRef]

D. P. Tsai, H. E. Jackson, R. C. Reddick, S. H. Sharp, R. J. Warmack, “Photon scanning tunneling microscope study of optical waveguides,” Appl. Phys. Lett. 56, 1515–1517 (1990).
[CrossRef]

A. G. Choo, H. E. Jackson, U. Thiel, G. N. De Brabander, J. T. Boyd, “Near field measurements of optical channel waveguides and directional couplers,” Appl. Phys. Lett. 65, 947–949 (1994).
[CrossRef]

R. Stöckle, C. Fokas, V. Deckert, R. Zenobi, “High-quality near-field optical probes by tube etching,” Appl. Phys. Lett. 75, 160–162 (1999).
[CrossRef]

Electron. Lett. (1)

E. J. Lim, M. M. Fejer, R. L. Beyer, “Second-harmonic generation of green light in periodically poled planar lithium niobate waveguide,” Electron. Lett. 25, 174–175 (1989).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (4)

T. Miya, “Silica-based planar lightwave circuits: passive and thermally active devices,” IEEE J. Sel. Top. Quantum Electron. 6, 38–45 (2000).
[CrossRef]

E. L. Wooten, K. M. Kissa, A. Yi-Yan, E. J. Murphy, D. A. Lafaw, P. F. Hallemeier, D. Maack, D. V. Attanasio, D. J. Fritz, G. J. McBrien, D. E. Bossi, “A review of lithium niobate modulators for fiber-optic communications systems,” IEEE J. Sel. Top. Quantum Electron. 6, 69–82 (2000).
[CrossRef]

G. H. Vander Rhodes, B. B. Goldberg, M. S. Ünlü, S. Chu, B. E. Little, “Internal spatial modes in glass microring resonators,” IEEE J. Sel. Top. Quantum Electron. 6, 46–53 (2000).
[CrossRef]

R. Scarmozzino, A. Gopinath, R. Pregla, S. Helfert, “Numerical techniques for modeling guided-wave photonic devices,” IEEE J. Sel. Top. Quantum Electron. 6, 150–162 (2000).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

K. R. Parameswaran, M. Fujimura, M. H. Chou, M. M. Fejer, “Low-power all-optical gate based on sum frequency mixing in APE waveguides in PPLN,” IEEE Photon. Technol. Lett. 12, 654–656 (2000).
[CrossRef]

IEEE Trans. Components Packag. Manuf. Technol. Part B (1)

R. S. Moyer, R. Grencavich, F. F. Judd, R. C. Kershner, W. J. Minford, R. W. Smith, “Design and qualification of hermetically packaged lithium niobate optical modulator,” IEEE Trans. Components Packag. Manuf. Technol. Part B 21, 130–135 (1998).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

S. K. Korotky, W. J. Minford, L. L. Buhl, M. D. Divino, R. C. Alferness, “Mode size and method for estimating the propagation constant of single-mode Ti:LiNbO3 strip waveguides,” IEEE Trans. Microwave Theory Tech. MTT-30, 1784–1789 (1982).
[CrossRef]

J. Appl. Phys. (1)

A. L. Campillo, J. W. P. Hsu, C. A. White, A. Rosenberg, “Mapping the optical intensity distribution in photonic crystals using a near-field scanning optical microscope,” J. Appl. Phys. 89, 2801–2807 (2001).
[CrossRef]

J. Lightwave Technol. (1)

K. Kintaka, M. Fujimura, T. Suhara, H. Nishihara, “High-efficiency LiNbO3 waveguide second-harmonic generation devices with ferroelectric-domain-inverted gratings fabricated by applying voltage,” J. Lightwave Technol. 14, 462–468 (1996).
[CrossRef]

Opt. Commun. (2)

S. I. Bozhevolnyi, V. S. Volkov, J. Arentoft, A. Boltasseva, T. Søndergaard, M. Kristensen, “Direct mapping of light propagation in photonic crystal waveguides,” Opt. Commun. 212, 51–55 (2002).
[CrossRef]

A. Nesci, R. Dändliker, M. Salt, H. P. Herzig, “Measuring amplitude and phase distribution of fields generated by gratings with sub-wavelength resolution,” Opt. Commun. 205, 229–238 (2002).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. Lett. (1)

M. L. M. Balistreri, J. P. Korterik, L. Kuipers, N. F. van Hulst, “Local observations of phase singularities in optical fields in waveguide structures,” Phys. Rev. Lett. 85, 294–297 (2000).
[CrossRef] [PubMed]

Proc. Inst. Electr. Eng. Optoelectron. (2)

M. S. Stern, “Semivectorial polarised finite difference method for optical waveguides with arbitrary index profiles,” Proc. Inst. Electr. Eng. Optoelectron. 135, 56–63 (1988).

G. H. Vander Rhodes, M. S. Ünlü, B. B. Goldberg, J. M. Pomeroy, T. F. Krauss, “Characterisation of waveguide microcavities using high-resolution transmission spectroscopy and near-field scanning optical microscopy,” Proc. Inst. Electr. Eng. Optoelectron. 145, 379–383 (1998).
[CrossRef]

Publ. Astron. Soc. Pac. (1)

F. Roddier, M. Northcott, E. Graves, “A simple low-order adaptive optics system for near-infrared applications,” Publ. Astron. Soc. Pac. 103, 131–149 (1991).
[CrossRef]

Rev. Sci. Instrum. (3)

J. W. P. Hsu, M. Lee, B. S. Deaver, “A nonoptical tip-sample distance control method for near-field scanning optical microscopy using impedance changes in an electromechanical system,” Rev. Sci. Instrum. 66, 3177–3181 (1995).
[CrossRef]

M. Lee, E. B. McDaniel, J. W. P. Hsu, “An impedance based non-contact feedback control system for scanning probe microscopes,” Rev. Sci. Instrum. 67, 1468–1471 (1996).
[CrossRef]

K. Fritsch, G. Adamovsky, “Simple circuit for feedback stabilization of a single-mode optical fiber interferometer,” Rev. Sci. Instrum. 52, 996–1000 (1981).
[CrossRef]

Other (2)

E. Volkl, L. F. Allard, D. C. Joy, eds., Introduction to Electron Holography (Kluwer-Academic, New York, 1999).
[CrossRef]

T. Yamada, “LiNbO3 family,” in Landol-Bornstein Numerical Data and Functional Relationships in Science and Technology, New Series, Group III: Crystal and Solid State Physics, K.-H. Hellwege, A. M. Hellwege, eds. (Springer-Verlag, New York, 1981), Vol. 16a, pp. 149–156, 489–499.

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Figures (7)

Fig. 1
Fig. 1

Orientation of the tip and sample when measuring (a) the cross-sectional mode profile and (b) intensity along the waveguide.

Fig. 2
Fig. 2

Experimental setup used for optical phase detection with a NSOM. The NSOM is incorporated into the signal arm of a fiber-based Mach-Zehnder interferometer. The first coupler is a 99:1 fiber coupler that sends 99% of the light into the waveguide. A 50:50 fiber coupler recombines the two beams. Φ1 and Φ2 are piezoelements used to adjust the phase. The polarization of both arms is controlled by use of fiber paddles. An attenuator is incorporated into the reference arm to equalize approximately the intensity of each arm when recombined.

Fig. 3
Fig. 3

Intensity versus voltage for phase controller calibration. ΔV is the voltage necessary to produce a 2π phase change, which corresponds to a path-length change of λ/n fiber.

Fig. 4
Fig. 4

Cross-sectional 15 µm by 15 µm intensity profiles for the TM modes of the (a) Ti:LiNbO3 and (b) PPLN waveguides. A line cut of the mode profile parallel to the surface through the maxima is shown below each image. The dots represent the experimental data and the solid lines are fits to the Gaussian function.

Fig. 5
Fig. 5

Intensity of light collected by the NSOM tip as a function of the separation between the tip and the Ti:LiNbO3 waveguide in the geometry of Fig. 1(b). A tip position of zero corresponds to an ∼10-nm separation at which point feedback kicks in. The solid line is the exponential fit to the data with a decay length of 72 nm, which corresponds to n eff = 2.0. The dashed line is the expected decay for a mode with n eff = 2.13 at a wavelength of 1550 nm.

Fig. 6
Fig. 6

(a) Topography, (b) intensity, and (c) cos(ϕ) 15 µm × 15 µm images of a Ti-diffused LiNbO3 waveguide for λ = 1550 nm. The change in height is 50 nm (a), the intensity variation is 33 pW (∼13% of the total signal) in (b), and cos(ϕ) varies from 1 (white) to -1 (black).

Fig. 7
Fig. 7

(a) Topography, (b) intensity, and (c) cos(ϕ) 15 µm × 15 µm images for a PPLN waveguide for λ = 1600 nm. The NSOM tip was positioned so that the scanned area contained a boundary. The change in height is 70 nm (a), the intensity variation is 2 pW (∼7% of the total signal) in (b), and cos(ϕ) varies from 1 (white) to -1 (black).

Tables (1)

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Table 1 Effective Index (neff) Determined from Phase Images Taken on Both Types of LiNbO3Waveguidea

Equations (5)

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I = 1/2ENSOM2 + Eref2 + 2ENSOMEref × cosΔϕ + δ0 sinωt,
I12ENSOM2+Eref2+2ENSOMEref cosΔϕJ0δ0-ENSOMEref sinΔϕJ1δ0sinωt+J3δ0sin3ωt++ENSOMEref cosΔϕ×J2δ0sin2ωt+J4δ0sin4ωt+ =Idc+I1f sinωt+I2f sin2ωt+.
Idc=12ENSOM2+Eref2, I1f=-ENSOMErefJ1δ0sinΔϕ.
I=I0 exp-2x2/σ2,
ΔI = Ireflect + 2IreflectIincidentIincident cosδincident-reflect + IrefIincidentcosδref-reflect,

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