Abstract

A novel technique for characterizing thin-film second-order nonlinearities with submicrometer resolution for the film’s depth is proposed. This method is substantially a variation of the classic one-beam Maker’s fringe technique and uses the second harmonic generated by two noncollinear fundamental beams. Compared with that for the one-beam case, this configuration reduces the coherence length of the process, thus increasing the resolution for the nonlinear depth measurements. The technique has been implemented on thermally poled silica samples, revealing the initial growth of the nonlinear region.

© 2000 Optical Society of America

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  1. P. D. Maker, R. W. Terhune, M. Nisenhoff, and C. M. Savage, Phys. Rev. Lett. 8, 21 (1962).
    [CrossRef]
  2. J. Jerphagnon and K. Kurtz, J. Appl. Phys. 41, 1667 (1970).
    [CrossRef]
  3. R. A. Myers, N. Mukherjee, and S. R. J. Brueck, Opt. Lett. 16, 1732 (1991).
    [CrossRef] [PubMed]
  4. V. Pruneri, F. Somoggia, G. Bonfrate, P. G. Kazansky, and G. M. Yang, Appl. Phys. Lett. 74, 2423 (1993).
    [CrossRef]
  5. D. Pureur, A. C. Liu, M. J. F. Digonnet, and G. S. Kino, Opt. Lett. 23, 588 (1998).
    [CrossRef]
  6. Y. Quiquempois, G. Martinelli, F. Valentin, P. Bernage, P. Niay, and M. Douay, in Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides, E. J. Friedele, R. Kashyap, and T. Erdogan, eds., Vol. 33 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), paper ThE21, pp. 106–108.
  7. N. Bloembergen and P. S. Pershan, Phys. Rev. 128, 606 (1962).
    [CrossRef]
  8. P. G. Kazansky and P. St. J. Russell, Opt. Commun. 110, 611 (1994).
    [CrossRef]
  9. T. G. Alley and S. R. J. Brueck, Opt. Lett. 23, 1170 (1998).
    [CrossRef]
  10. A. Triques, C. Cordiero, V. Balestrieri, B. Lesche, W. Margulis, and I. Carvalho, Appl. Phys. Lett. 76, 2496 (2000).
    [CrossRef]

2000 (1)

A. Triques, C. Cordiero, V. Balestrieri, B. Lesche, W. Margulis, and I. Carvalho, Appl. Phys. Lett. 76, 2496 (2000).
[CrossRef]

1998 (2)

1994 (1)

P. G. Kazansky and P. St. J. Russell, Opt. Commun. 110, 611 (1994).
[CrossRef]

1993 (1)

V. Pruneri, F. Somoggia, G. Bonfrate, P. G. Kazansky, and G. M. Yang, Appl. Phys. Lett. 74, 2423 (1993).
[CrossRef]

1991 (1)

1970 (1)

J. Jerphagnon and K. Kurtz, J. Appl. Phys. 41, 1667 (1970).
[CrossRef]

1962 (2)

P. D. Maker, R. W. Terhune, M. Nisenhoff, and C. M. Savage, Phys. Rev. Lett. 8, 21 (1962).
[CrossRef]

N. Bloembergen and P. S. Pershan, Phys. Rev. 128, 606 (1962).
[CrossRef]

Alley, T. G.

Balestrieri, V.

A. Triques, C. Cordiero, V. Balestrieri, B. Lesche, W. Margulis, and I. Carvalho, Appl. Phys. Lett. 76, 2496 (2000).
[CrossRef]

Bernage, P.

Y. Quiquempois, G. Martinelli, F. Valentin, P. Bernage, P. Niay, and M. Douay, in Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides, E. J. Friedele, R. Kashyap, and T. Erdogan, eds., Vol. 33 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), paper ThE21, pp. 106–108.

Bloembergen, N.

N. Bloembergen and P. S. Pershan, Phys. Rev. 128, 606 (1962).
[CrossRef]

Bonfrate, G.

V. Pruneri, F. Somoggia, G. Bonfrate, P. G. Kazansky, and G. M. Yang, Appl. Phys. Lett. 74, 2423 (1993).
[CrossRef]

Brueck, S. R. J.

Carvalho, I.

A. Triques, C. Cordiero, V. Balestrieri, B. Lesche, W. Margulis, and I. Carvalho, Appl. Phys. Lett. 76, 2496 (2000).
[CrossRef]

Cordiero, C.

A. Triques, C. Cordiero, V. Balestrieri, B. Lesche, W. Margulis, and I. Carvalho, Appl. Phys. Lett. 76, 2496 (2000).
[CrossRef]

Digonnet, M. J. F.

Douay, M.

Y. Quiquempois, G. Martinelli, F. Valentin, P. Bernage, P. Niay, and M. Douay, in Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides, E. J. Friedele, R. Kashyap, and T. Erdogan, eds., Vol. 33 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), paper ThE21, pp. 106–108.

Jerphagnon, J.

J. Jerphagnon and K. Kurtz, J. Appl. Phys. 41, 1667 (1970).
[CrossRef]

Kazansky, P. G.

P. G. Kazansky and P. St. J. Russell, Opt. Commun. 110, 611 (1994).
[CrossRef]

V. Pruneri, F. Somoggia, G. Bonfrate, P. G. Kazansky, and G. M. Yang, Appl. Phys. Lett. 74, 2423 (1993).
[CrossRef]

Kino, G. S.

Kurtz, K.

J. Jerphagnon and K. Kurtz, J. Appl. Phys. 41, 1667 (1970).
[CrossRef]

Lesche, B.

A. Triques, C. Cordiero, V. Balestrieri, B. Lesche, W. Margulis, and I. Carvalho, Appl. Phys. Lett. 76, 2496 (2000).
[CrossRef]

Liu, A. C.

Maker, P. D.

P. D. Maker, R. W. Terhune, M. Nisenhoff, and C. M. Savage, Phys. Rev. Lett. 8, 21 (1962).
[CrossRef]

Margulis, W.

A. Triques, C. Cordiero, V. Balestrieri, B. Lesche, W. Margulis, and I. Carvalho, Appl. Phys. Lett. 76, 2496 (2000).
[CrossRef]

Martinelli, G.

Y. Quiquempois, G. Martinelli, F. Valentin, P. Bernage, P. Niay, and M. Douay, in Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides, E. J. Friedele, R. Kashyap, and T. Erdogan, eds., Vol. 33 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), paper ThE21, pp. 106–108.

Mukherjee, N.

Myers, R. A.

Niay, P.

Y. Quiquempois, G. Martinelli, F. Valentin, P. Bernage, P. Niay, and M. Douay, in Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides, E. J. Friedele, R. Kashyap, and T. Erdogan, eds., Vol. 33 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), paper ThE21, pp. 106–108.

Nisenhoff, M.

P. D. Maker, R. W. Terhune, M. Nisenhoff, and C. M. Savage, Phys. Rev. Lett. 8, 21 (1962).
[CrossRef]

Pershan, P. S.

N. Bloembergen and P. S. Pershan, Phys. Rev. 128, 606 (1962).
[CrossRef]

Pruneri, V.

V. Pruneri, F. Somoggia, G. Bonfrate, P. G. Kazansky, and G. M. Yang, Appl. Phys. Lett. 74, 2423 (1993).
[CrossRef]

Pureur, D.

Quiquempois, Y.

Y. Quiquempois, G. Martinelli, F. Valentin, P. Bernage, P. Niay, and M. Douay, in Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides, E. J. Friedele, R. Kashyap, and T. Erdogan, eds., Vol. 33 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), paper ThE21, pp. 106–108.

Russell, P. St. J.

P. G. Kazansky and P. St. J. Russell, Opt. Commun. 110, 611 (1994).
[CrossRef]

Savage, C. M.

P. D. Maker, R. W. Terhune, M. Nisenhoff, and C. M. Savage, Phys. Rev. Lett. 8, 21 (1962).
[CrossRef]

Somoggia, F.

V. Pruneri, F. Somoggia, G. Bonfrate, P. G. Kazansky, and G. M. Yang, Appl. Phys. Lett. 74, 2423 (1993).
[CrossRef]

Terhune, R. W.

P. D. Maker, R. W. Terhune, M. Nisenhoff, and C. M. Savage, Phys. Rev. Lett. 8, 21 (1962).
[CrossRef]

Triques, A.

A. Triques, C. Cordiero, V. Balestrieri, B. Lesche, W. Margulis, and I. Carvalho, Appl. Phys. Lett. 76, 2496 (2000).
[CrossRef]

Valentin, F.

Y. Quiquempois, G. Martinelli, F. Valentin, P. Bernage, P. Niay, and M. Douay, in Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides, E. J. Friedele, R. Kashyap, and T. Erdogan, eds., Vol. 33 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), paper ThE21, pp. 106–108.

Yang, G. M.

V. Pruneri, F. Somoggia, G. Bonfrate, P. G. Kazansky, and G. M. Yang, Appl. Phys. Lett. 74, 2423 (1993).
[CrossRef]

Appl. Phys. Lett. (2)

V. Pruneri, F. Somoggia, G. Bonfrate, P. G. Kazansky, and G. M. Yang, Appl. Phys. Lett. 74, 2423 (1993).
[CrossRef]

A. Triques, C. Cordiero, V. Balestrieri, B. Lesche, W. Margulis, and I. Carvalho, Appl. Phys. Lett. 76, 2496 (2000).
[CrossRef]

J. Appl. Phys. (1)

J. Jerphagnon and K. Kurtz, J. Appl. Phys. 41, 1667 (1970).
[CrossRef]

Opt. Commun. (1)

P. G. Kazansky and P. St. J. Russell, Opt. Commun. 110, 611 (1994).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. (1)

N. Bloembergen and P. S. Pershan, Phys. Rev. 128, 606 (1962).
[CrossRef]

Phys. Rev. Lett. (1)

P. D. Maker, R. W. Terhune, M. Nisenhoff, and C. M. Savage, Phys. Rev. Lett. 8, 21 (1962).
[CrossRef]

Other (1)

Y. Quiquempois, G. Martinelli, F. Valentin, P. Bernage, P. Niay, and M. Douay, in Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides, E. J. Friedele, R. Kashyap, and T. Erdogan, eds., Vol. 33 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), paper ThE21, pp. 106–108.

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Figures (4)

Fig. 1
Fig. 1

Geometrical layout of the noncollinear Maker’s fringe technique: The plane xzˆ is defined as the lab reference system (taken so that zˆ is the symmetry axis of the two incident beams). θ1, θ2, and γ are the two fundamental (fund.) beam and SH internal propagation angles, respectively. α is the sample tilt angle, and Θ is the relative angle between the two input fundamental beams.

Fig. 2
Fig. 2

Comparison of (a) a one-beam or collinear MFT Θ=0° and (b) a two-noncollinear-beam MFT Θ=90°. Solid curve and dotted curves, values of L. Note the different scale for the angle axis.

Fig. 3
Fig. 3

Experimental results: normalized SH conversion efficiency ηSH as a function of the external tilt angle α for noncollinear fundamental beams with Θ=90°. Filled circles, experimental values obtained for two samples from Table 1. Solid curves, best calculated fits.

Fig. 4
Fig. 4

Experimental results: measured nonlinear depth as a function of poling time for the five measured samples of Table 1.

Tables (1)

Tables Icon

Table 1 Summary of Measured Valuesa

Equations (3)

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lc=πΔk=πk2ω-kω,1-kω,2,
ΔkΘ,α=4πλnλ2-nλ2cosθ1Θ,α-γΘ,α+cosθ2Θ,α-γΘ,α,
ηSHΘ,α=2ω2ε0c03nω2n2ωuΘ,απw02T2ωTω,1Tω,2deffΘ,α×--dxdy0Lcos γΘ,αE1E2 expiΔkΘ,αzdz2,

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