Abstract

By use of a near-field scanning optical microscope in collection mode, multimode interference was directly measured in an annealed proton-exchanged LiNbO3 waveguide. Periodic transitions from a single-peaked Gaussianlike intensity distribution to a double-peaked intensity distribution were observed. The intensity distribution along the waveguide was calculated, and the results agree well with the experimental observation.

© 2003 Optical Society of America

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  1. L. B. Soldano and E. C. M. Pennings, J. Lightwave Technol. 13, 615 (1995).
    [CrossRef]
  2. G. N. van den Hoven, A. Polman, G. van Dam, J. W. M. van Uffelen, and M. K. Smit, Opt. Lett. 21, 576 (1996).
    [CrossRef] [PubMed]
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    [CrossRef]
  4. D. P. Tsai, H. E. Jackson, R. C. Reddick, S. H. Sharp, and R. J. Warmack, Appl. Phys. Lett. 56, 1515 (1990).
    [CrossRef]
  5. G. H. Vander Rhodes, M. S. Ünlü, B. B. Goldberg, J. M. Pomeroy, and T. F. Krauss, Proc. IEEE Optoelectron. 145, 379 (1998).
    [CrossRef]
  6. A. G. Choo, H. E. Jackson, U. Thiel, G. N. D. Brabander, and J. T. Boyd, Phys. Lett. 65, 947 (1994).
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    [CrossRef]
  8. A. L. Campillo, J. W. P. Hsu, C. A. White, and A. Rosenberg, J. Appl. Phys. 89, 2801 (2001).
    [CrossRef]
  9. P. G. Suchoski, T. K. Findakly, and F. J. Leonberger, Opt. Lett. 13, 1050 (1988).
    [CrossRef] [PubMed]
  10. M. H. Chou, I. Brener, M. M. Fejer, E. E. Chaban, and S. B. Christman, IEEE Photon. Technol. Lett. 11, 653 (1999).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  15. M. Lee, E. B. McDaniel, and J. W. P. Hsu, Rev. Sci. Instrum. 67, 1468 (1996).
    [CrossRef]
  16. A. L. Campillo, “Near field scanning optical microscopy studies of photonic structures and materials,” Ph.D. dissertation (University of Virginia, Charlottesville, Va., 2002).
  17. M. S. Stern, IEEE Proc. Optoelectron. 135, 56 (1988).

2001 (1)

A. L. Campillo, J. W. P. Hsu, C. A. White, and A. Rosenberg, J. Appl. Phys. 89, 2801 (2001).
[CrossRef]

2000 (1)

G. H. Vander Rhodes, B. B. Goldberg, M. S. Ünlü, S. Chu, and B. E. Little, IEEE J. Sel. Top. Quantum Electron. 6, 46 (2000).
[CrossRef]

1999 (2)

M. H. Chou, I. Brener, M. M. Fejer, E. E. Chaban, and S. B. Christman, IEEE Photon. Technol. Lett. 11, 653 (1999).
[CrossRef]

R. Stockle, C. Fokas, V. Deckert, and R. Zenobi, Appl. Phys. Lett. 75, 160 (1999).
[CrossRef]

1998 (2)

P. Lambelet, A. Sayah, M. Pfeffer, C. Philipona, and F. Marquis-Weible, Appl. Opt. 37, 7289 (1998).
[CrossRef]

G. H. Vander Rhodes, M. S. Ünlü, B. B. Goldberg, J. M. Pomeroy, and T. F. Krauss, Proc. IEEE Optoelectron. 145, 379 (1998).
[CrossRef]

1996 (2)

1995 (2)

J. W. P. Hsu, M. Lee, and B. S. Deaver, Rev. Sci. Instrum. 66, 3177 (1995).
[CrossRef]

L. B. Soldano and E. C. M. Pennings, J. Lightwave Technol. 13, 615 (1995).
[CrossRef]

1994 (1)

A. G. Choo, H. E. Jackson, U. Thiel, G. N. D. Brabander, and J. T. Boyd, Phys. Lett. 65, 947 (1994).

1991 (1)

1990 (1)

D. P. Tsai, H. E. Jackson, R. C. Reddick, S. H. Sharp, and R. J. Warmack, Appl. Phys. Lett. 56, 1515 (1990).
[CrossRef]

1989 (1)

R. C. Reddick, R. J. Warmack, and T. L. Ferrell, Phys. Rev. B 39, 767 (1989).
[CrossRef]

1988 (2)

Bortz, M. L.

Boyd, J. T.

A. G. Choo, H. E. Jackson, U. Thiel, G. N. D. Brabander, and J. T. Boyd, Phys. Lett. 65, 947 (1994).

Brabander, G. N. D.

A. G. Choo, H. E. Jackson, U. Thiel, G. N. D. Brabander, and J. T. Boyd, Phys. Lett. 65, 947 (1994).

Brener, I.

M. H. Chou, I. Brener, M. M. Fejer, E. E. Chaban, and S. B. Christman, IEEE Photon. Technol. Lett. 11, 653 (1999).
[CrossRef]

Campillo, A. L.

A. L. Campillo, J. W. P. Hsu, C. A. White, and A. Rosenberg, J. Appl. Phys. 89, 2801 (2001).
[CrossRef]

A. L. Campillo, “Near field scanning optical microscopy studies of photonic structures and materials,” Ph.D. dissertation (University of Virginia, Charlottesville, Va., 2002).

Chaban, E. E.

M. H. Chou, I. Brener, M. M. Fejer, E. E. Chaban, and S. B. Christman, IEEE Photon. Technol. Lett. 11, 653 (1999).
[CrossRef]

Choo, A. G.

A. G. Choo, H. E. Jackson, U. Thiel, G. N. D. Brabander, and J. T. Boyd, Phys. Lett. 65, 947 (1994).

Chou, M. H.

M. H. Chou, I. Brener, M. M. Fejer, E. E. Chaban, and S. B. Christman, IEEE Photon. Technol. Lett. 11, 653 (1999).
[CrossRef]

Christman, S. B.

M. H. Chou, I. Brener, M. M. Fejer, E. E. Chaban, and S. B. Christman, IEEE Photon. Technol. Lett. 11, 653 (1999).
[CrossRef]

Chu, S.

G. H. Vander Rhodes, B. B. Goldberg, M. S. Ünlü, S. Chu, and B. E. Little, IEEE J. Sel. Top. Quantum Electron. 6, 46 (2000).
[CrossRef]

Deaver, B. S.

J. W. P. Hsu, M. Lee, and B. S. Deaver, Rev. Sci. Instrum. 66, 3177 (1995).
[CrossRef]

Deckert, V.

R. Stockle, C. Fokas, V. Deckert, and R. Zenobi, Appl. Phys. Lett. 75, 160 (1999).
[CrossRef]

Fejer, M. M.

M. H. Chou, I. Brener, M. M. Fejer, E. E. Chaban, and S. B. Christman, IEEE Photon. Technol. Lett. 11, 653 (1999).
[CrossRef]

M. L. Bortz and M. M. Fejer, Opt. Lett. 16, 1844 (1991).
[CrossRef] [PubMed]

Ferrell, T. L.

R. C. Reddick, R. J. Warmack, and T. L. Ferrell, Phys. Rev. B 39, 767 (1989).
[CrossRef]

Findakly, T. K.

Fokas, C.

R. Stockle, C. Fokas, V. Deckert, and R. Zenobi, Appl. Phys. Lett. 75, 160 (1999).
[CrossRef]

Goldberg, B. B.

G. H. Vander Rhodes, B. B. Goldberg, M. S. Ünlü, S. Chu, and B. E. Little, IEEE J. Sel. Top. Quantum Electron. 6, 46 (2000).
[CrossRef]

G. H. Vander Rhodes, M. S. Ünlü, B. B. Goldberg, J. M. Pomeroy, and T. F. Krauss, Proc. IEEE Optoelectron. 145, 379 (1998).
[CrossRef]

Hsu, J. W. P.

A. L. Campillo, J. W. P. Hsu, C. A. White, and A. Rosenberg, J. Appl. Phys. 89, 2801 (2001).
[CrossRef]

M. Lee, E. B. McDaniel, and J. W. P. Hsu, Rev. Sci. Instrum. 67, 1468 (1996).
[CrossRef]

J. W. P. Hsu, M. Lee, and B. S. Deaver, Rev. Sci. Instrum. 66, 3177 (1995).
[CrossRef]

Jackson, H. E.

A. G. Choo, H. E. Jackson, U. Thiel, G. N. D. Brabander, and J. T. Boyd, Phys. Lett. 65, 947 (1994).

D. P. Tsai, H. E. Jackson, R. C. Reddick, S. H. Sharp, and R. J. Warmack, Appl. Phys. Lett. 56, 1515 (1990).
[CrossRef]

Krauss, T. F.

G. H. Vander Rhodes, M. S. Ünlü, B. B. Goldberg, J. M. Pomeroy, and T. F. Krauss, Proc. IEEE Optoelectron. 145, 379 (1998).
[CrossRef]

Lambelet, P.

Lee, M.

M. Lee, E. B. McDaniel, and J. W. P. Hsu, Rev. Sci. Instrum. 67, 1468 (1996).
[CrossRef]

J. W. P. Hsu, M. Lee, and B. S. Deaver, Rev. Sci. Instrum. 66, 3177 (1995).
[CrossRef]

Leonberger, F. J.

Little, B. E.

G. H. Vander Rhodes, B. B. Goldberg, M. S. Ünlü, S. Chu, and B. E. Little, IEEE J. Sel. Top. Quantum Electron. 6, 46 (2000).
[CrossRef]

Marquis-Weible, F.

McDaniel, E. B.

M. Lee, E. B. McDaniel, and J. W. P. Hsu, Rev. Sci. Instrum. 67, 1468 (1996).
[CrossRef]

Pennings, E. C. M.

L. B. Soldano and E. C. M. Pennings, J. Lightwave Technol. 13, 615 (1995).
[CrossRef]

Pfeffer, M.

Philipona, C.

Polman, A.

Pomeroy, J. M.

G. H. Vander Rhodes, M. S. Ünlü, B. B. Goldberg, J. M. Pomeroy, and T. F. Krauss, Proc. IEEE Optoelectron. 145, 379 (1998).
[CrossRef]

Reddick, R. C.

D. P. Tsai, H. E. Jackson, R. C. Reddick, S. H. Sharp, and R. J. Warmack, Appl. Phys. Lett. 56, 1515 (1990).
[CrossRef]

R. C. Reddick, R. J. Warmack, and T. L. Ferrell, Phys. Rev. B 39, 767 (1989).
[CrossRef]

Rosenberg, A.

A. L. Campillo, J. W. P. Hsu, C. A. White, and A. Rosenberg, J. Appl. Phys. 89, 2801 (2001).
[CrossRef]

Sayah, A.

Sharp, S. H.

D. P. Tsai, H. E. Jackson, R. C. Reddick, S. H. Sharp, and R. J. Warmack, Appl. Phys. Lett. 56, 1515 (1990).
[CrossRef]

Smit, M. K.

Soldano, L. B.

L. B. Soldano and E. C. M. Pennings, J. Lightwave Technol. 13, 615 (1995).
[CrossRef]

Stern, M. S.

M. S. Stern, IEEE Proc. Optoelectron. 135, 56 (1988).

Stockle, R.

R. Stockle, C. Fokas, V. Deckert, and R. Zenobi, Appl. Phys. Lett. 75, 160 (1999).
[CrossRef]

Suchoski, P. G.

Thiel, U.

A. G. Choo, H. E. Jackson, U. Thiel, G. N. D. Brabander, and J. T. Boyd, Phys. Lett. 65, 947 (1994).

Tsai, D. P.

D. P. Tsai, H. E. Jackson, R. C. Reddick, S. H. Sharp, and R. J. Warmack, Appl. Phys. Lett. 56, 1515 (1990).
[CrossRef]

Ünlü, M. S.

G. H. Vander Rhodes, B. B. Goldberg, M. S. Ünlü, S. Chu, and B. E. Little, IEEE J. Sel. Top. Quantum Electron. 6, 46 (2000).
[CrossRef]

G. H. Vander Rhodes, M. S. Ünlü, B. B. Goldberg, J. M. Pomeroy, and T. F. Krauss, Proc. IEEE Optoelectron. 145, 379 (1998).
[CrossRef]

van Dam, G.

van den Hoven, G. N.

van Uffelen, J. W. M.

Vander Rhodes, G. H.

G. H. Vander Rhodes, B. B. Goldberg, M. S. Ünlü, S. Chu, and B. E. Little, IEEE J. Sel. Top. Quantum Electron. 6, 46 (2000).
[CrossRef]

G. H. Vander Rhodes, M. S. Ünlü, B. B. Goldberg, J. M. Pomeroy, and T. F. Krauss, Proc. IEEE Optoelectron. 145, 379 (1998).
[CrossRef]

Warmack, R. J.

D. P. Tsai, H. E. Jackson, R. C. Reddick, S. H. Sharp, and R. J. Warmack, Appl. Phys. Lett. 56, 1515 (1990).
[CrossRef]

R. C. Reddick, R. J. Warmack, and T. L. Ferrell, Phys. Rev. B 39, 767 (1989).
[CrossRef]

White, C. A.

A. L. Campillo, J. W. P. Hsu, C. A. White, and A. Rosenberg, J. Appl. Phys. 89, 2801 (2001).
[CrossRef]

Zenobi, R.

R. Stockle, C. Fokas, V. Deckert, and R. Zenobi, Appl. Phys. Lett. 75, 160 (1999).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

R. Stockle, C. Fokas, V. Deckert, and R. Zenobi, Appl. Phys. Lett. 75, 160 (1999).
[CrossRef]

D. P. Tsai, H. E. Jackson, R. C. Reddick, S. H. Sharp, and R. J. Warmack, Appl. Phys. Lett. 56, 1515 (1990).
[CrossRef]

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

G. H. Vander Rhodes, B. B. Goldberg, M. S. Ünlü, S. Chu, and B. E. Little, IEEE J. Sel. Top. Quantum Electron. 6, 46 (2000).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

M. H. Chou, I. Brener, M. M. Fejer, E. E. Chaban, and S. B. Christman, IEEE Photon. Technol. Lett. 11, 653 (1999).
[CrossRef]

IEEE Proc. Optoelectron. (1)

M. S. Stern, IEEE Proc. Optoelectron. 135, 56 (1988).

J. Appl. Phys. (1)

A. L. Campillo, J. W. P. Hsu, C. A. White, and A. Rosenberg, J. Appl. Phys. 89, 2801 (2001).
[CrossRef]

J. Lightwave Technol. (1)

L. B. Soldano and E. C. M. Pennings, J. Lightwave Technol. 13, 615 (1995).
[CrossRef]

Opt. Lett. (3)

Phys. Lett. (1)

A. G. Choo, H. E. Jackson, U. Thiel, G. N. D. Brabander, and J. T. Boyd, Phys. Lett. 65, 947 (1994).

Phys. Rev. B (1)

R. C. Reddick, R. J. Warmack, and T. L. Ferrell, Phys. Rev. B 39, 767 (1989).
[CrossRef]

Proc. IEEE Optoelectron. (1)

G. H. Vander Rhodes, M. S. Ünlü, B. B. Goldberg, J. M. Pomeroy, and T. F. Krauss, Proc. IEEE Optoelectron. 145, 379 (1998).
[CrossRef]

Rev. Sci. Instrum. (2)

J. W. P. Hsu, M. Lee, and B. S. Deaver, Rev. Sci. Instrum. 66, 3177 (1995).
[CrossRef]

M. Lee, E. B. McDaniel, and J. W. P. Hsu, Rev. Sci. Instrum. 67, 1468 (1996).
[CrossRef]

Other (1)

A. L. Campillo, “Near field scanning optical microscopy studies of photonic structures and materials,” Ph.D. dissertation (University of Virginia, Charlottesville, Va., 2002).

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Figures (4)

Fig. 1
Fig. 1

Experimental setup: Light from an infrared laser is launched into the LiNbO3 waveguide through a single-mode optical fiber pigtail. A small portion of the light is collected by the NSOM tip and detected by a photodiode. Inset, the geometry of the two-dimensional waveguide used in the calculation W=10 µm.

Fig. 2
Fig. 2

Two nearby 30 µm×30 µm intensity images of λ=1550 nm light propagating in an APE waveguide patterned on a z-cut LiNbO3 substrate. In (a), a single maxima centered on the waveguide is shown. In (b), a transition from a single peak to symmetric double peaks can be seen.

Fig. 3
Fig. 3

(a) Surface electric field variation for the two symmetric width modes [g1x and g3x] supported by this waveguide, calculated with the semivectoral polarized finite-difference method. The two curves are offset for clarity. (b) 60-µm-long section of the intensity E2 evolution along the waveguide [calculated with Eqs. (1) and (2)] for the two symmetric width modes at λ=1.55 µm with a=3.2 µm for the input mode. The transition from a single-peaked Gaussian to a mode with two peaks can be clearly seen.

Fig. 4
Fig. 4

Cross sections of the NSOM images (solid curves) and calculated distributions (dashed curves), each one normalized to its respective maximum intensity. (a) Single-peaked structure. The solid curve is a cross section of the left-hand edge of Fig. 2(a), and the dashed curve is across the left-hand edge of Fig. 3(b). (b) Double-peaked structure. The solid curve is taken across the right-hand edge of Fig. 2(b), and the dashed curve is taken across the right-hand edge of Fig. 3(b). The dotted curve in (b) shows the calculated distribution for the case in which 5% of the power is launched into the lowest-order antisymmetric guided mode.

Equations (2)

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Ex,0=l=1jAlglx,Al=1Nexp-x2/a2glxdx,Nl=exp-x2/a2exp-x2/a2dxglxglxdx,
Ex,z=l=1jAlglxexpiβlz,

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