Abstract

In this article we develop a method to evaluate the poling quality of optical superlattice (OSL) based on two-dimensional (2D) Fourier transform. To demonstrate this method, -Z or +Z face etched OSL samples with desired patterns are fabricated by standard electric field poling technique. By analyzing the processed micrograph of the etched surfaces, the magnitude of the reciprocal vectors of the OSL are calculated directly and rapidly. Second harmonic generation (SHG) experiment is performed to validate the evaluation result.

©2009 Optical Society of America

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References

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  1. Z. D. Gao, S. N. Zhu, S. Y. Tu, and A. H. Kung, “Monolithic red-green-blue laser light source based on cascaded wavelength conversion in periodically-poled stoichiometric lithium tantalate,” Appl. Phys. Lett. 89, 181101 (2006).
    [Crossref]
  2. Q. Chen, Y. Chiu, D. N. Lambeth, T. E. Schlesinger, and D. D. Stancil, “Guided-wave electro-optic beam deflector using domain reversal in LiTaO3,” IEEE J. Lightwave Technol. 12, 1401–1404 (1994).
    [Crossref]
  3. S. Kumar, D. Gurkan, A. E. Willner, K. Parameswaran, and M. Fejer, “All-optical half adder using a PPLN waveguide and an SOA,” OFC 2004 1, 23–27 (2004).
  4. M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum. Electron. 28, 2631–2654 (1992).
    [Crossref]
  5. A. Rosenfeldt and M. Florsheimer, “Nondestructive remote imaging of ferroelectric domain distributions with high three-dimensional resolution,” Appl. Phys. B. 73, 523–529 (2001).
  6. V. Dierolf and C. Sandmann, “Inspection of periodically poled waveguide devices by confocal luminescence microscopy,” Appl. Phys. B. 78, 363–366 (2004).
    [Crossref]
  7. T. J. Yang, V. Gopalan, P. J. Swart, and U. Mohideen, “Direct Observation of Pinning and Bowing of a Single Ferroelectric Domain Wall,” Phys. Rev. Lett. 82, 4106–4109 (1999).
    [Crossref]
  8. K. Pandiyan, Y. S. Kang, H. H. Lim, B. J. Kim, O. Prakash, and M. Cha, “Poling Quality Evaluation of Periodically Poled Lithium Niobate Using Diffraction Method,” J. Opt. Soc. Korea. 12, 205–209 (2008).
    [Crossref]
  9. I. Shoji, T. Kondo, A. Kitamoto, M. Shirane, and R. Ito, “Absolute scale of second-order nonlinear-optical coeffients,” J. Opt. Soc. Am. B 14, 2268–2294 (1997).
    [Crossref]
  10. A. K. Jain, Fundamentals of Digital Image Processing(Prentice-Hall, Englewood Cliffs, 1989).
  11. M. D. Sacchi, T. J. Ulrych, and C. J. Walker, “Interpolation and extrapolation using a high-resolution discrete Fourier transform,” IEEE Trans. Signal Processing. 46, 31–38 (1998).
    [Crossref]
  12. S. N. Zhu, Y. Y. Zhu, Z. Y. Zhang, H. Shu, H. F. Wang, J. F. Hong, C. Z. Ge, and N. B. Ming, “LiTaO3 crystal periodically poled by applying an external pulsed field,” J. Appl. Phys. 77, 5481–5483 (1995).
    [Crossref]
  13. J. Yan, H. W. Li, X. L. Yang, S. W. Xie, and Z. R. Sun, “Second-order nonlinear optical coefficients measurement of LiNbO3 by non-phase-matched second-harmonic generation in uniaxial crystal sphere,” Chinese Laser J. 21, 14–16 (2000).

2008 (1)

K. Pandiyan, Y. S. Kang, H. H. Lim, B. J. Kim, O. Prakash, and M. Cha, “Poling Quality Evaluation of Periodically Poled Lithium Niobate Using Diffraction Method,” J. Opt. Soc. Korea. 12, 205–209 (2008).
[Crossref]

2006 (1)

Z. D. Gao, S. N. Zhu, S. Y. Tu, and A. H. Kung, “Monolithic red-green-blue laser light source based on cascaded wavelength conversion in periodically-poled stoichiometric lithium tantalate,” Appl. Phys. Lett. 89, 181101 (2006).
[Crossref]

2004 (2)

S. Kumar, D. Gurkan, A. E. Willner, K. Parameswaran, and M. Fejer, “All-optical half adder using a PPLN waveguide and an SOA,” OFC 2004 1, 23–27 (2004).

V. Dierolf and C. Sandmann, “Inspection of periodically poled waveguide devices by confocal luminescence microscopy,” Appl. Phys. B. 78, 363–366 (2004).
[Crossref]

2001 (1)

A. Rosenfeldt and M. Florsheimer, “Nondestructive remote imaging of ferroelectric domain distributions with high three-dimensional resolution,” Appl. Phys. B. 73, 523–529 (2001).

2000 (1)

J. Yan, H. W. Li, X. L. Yang, S. W. Xie, and Z. R. Sun, “Second-order nonlinear optical coefficients measurement of LiNbO3 by non-phase-matched second-harmonic generation in uniaxial crystal sphere,” Chinese Laser J. 21, 14–16 (2000).

1999 (1)

T. J. Yang, V. Gopalan, P. J. Swart, and U. Mohideen, “Direct Observation of Pinning and Bowing of a Single Ferroelectric Domain Wall,” Phys. Rev. Lett. 82, 4106–4109 (1999).
[Crossref]

1998 (1)

M. D. Sacchi, T. J. Ulrych, and C. J. Walker, “Interpolation and extrapolation using a high-resolution discrete Fourier transform,” IEEE Trans. Signal Processing. 46, 31–38 (1998).
[Crossref]

1997 (1)

1995 (1)

S. N. Zhu, Y. Y. Zhu, Z. Y. Zhang, H. Shu, H. F. Wang, J. F. Hong, C. Z. Ge, and N. B. Ming, “LiTaO3 crystal periodically poled by applying an external pulsed field,” J. Appl. Phys. 77, 5481–5483 (1995).
[Crossref]

1994 (1)

Q. Chen, Y. Chiu, D. N. Lambeth, T. E. Schlesinger, and D. D. Stancil, “Guided-wave electro-optic beam deflector using domain reversal in LiTaO3,” IEEE J. Lightwave Technol. 12, 1401–1404 (1994).
[Crossref]

1992 (1)

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum. Electron. 28, 2631–2654 (1992).
[Crossref]

Byer, R. L.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum. Electron. 28, 2631–2654 (1992).
[Crossref]

Cha, M.

K. Pandiyan, Y. S. Kang, H. H. Lim, B. J. Kim, O. Prakash, and M. Cha, “Poling Quality Evaluation of Periodically Poled Lithium Niobate Using Diffraction Method,” J. Opt. Soc. Korea. 12, 205–209 (2008).
[Crossref]

Chen, Q.

Q. Chen, Y. Chiu, D. N. Lambeth, T. E. Schlesinger, and D. D. Stancil, “Guided-wave electro-optic beam deflector using domain reversal in LiTaO3,” IEEE J. Lightwave Technol. 12, 1401–1404 (1994).
[Crossref]

Chiu, Y.

Q. Chen, Y. Chiu, D. N. Lambeth, T. E. Schlesinger, and D. D. Stancil, “Guided-wave electro-optic beam deflector using domain reversal in LiTaO3,” IEEE J. Lightwave Technol. 12, 1401–1404 (1994).
[Crossref]

Dierolf, V.

V. Dierolf and C. Sandmann, “Inspection of periodically poled waveguide devices by confocal luminescence microscopy,” Appl. Phys. B. 78, 363–366 (2004).
[Crossref]

Fejer, M.

S. Kumar, D. Gurkan, A. E. Willner, K. Parameswaran, and M. Fejer, “All-optical half adder using a PPLN waveguide and an SOA,” OFC 2004 1, 23–27 (2004).

Fejer, M. M.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum. Electron. 28, 2631–2654 (1992).
[Crossref]

Florsheimer, M.

A. Rosenfeldt and M. Florsheimer, “Nondestructive remote imaging of ferroelectric domain distributions with high three-dimensional resolution,” Appl. Phys. B. 73, 523–529 (2001).

Gao, Z. D.

Z. D. Gao, S. N. Zhu, S. Y. Tu, and A. H. Kung, “Monolithic red-green-blue laser light source based on cascaded wavelength conversion in periodically-poled stoichiometric lithium tantalate,” Appl. Phys. Lett. 89, 181101 (2006).
[Crossref]

Ge, C. Z.

S. N. Zhu, Y. Y. Zhu, Z. Y. Zhang, H. Shu, H. F. Wang, J. F. Hong, C. Z. Ge, and N. B. Ming, “LiTaO3 crystal periodically poled by applying an external pulsed field,” J. Appl. Phys. 77, 5481–5483 (1995).
[Crossref]

Gopalan, V.

T. J. Yang, V. Gopalan, P. J. Swart, and U. Mohideen, “Direct Observation of Pinning and Bowing of a Single Ferroelectric Domain Wall,” Phys. Rev. Lett. 82, 4106–4109 (1999).
[Crossref]

Gurkan, D.

S. Kumar, D. Gurkan, A. E. Willner, K. Parameswaran, and M. Fejer, “All-optical half adder using a PPLN waveguide and an SOA,” OFC 2004 1, 23–27 (2004).

Hong, J. F.

S. N. Zhu, Y. Y. Zhu, Z. Y. Zhang, H. Shu, H. F. Wang, J. F. Hong, C. Z. Ge, and N. B. Ming, “LiTaO3 crystal periodically poled by applying an external pulsed field,” J. Appl. Phys. 77, 5481–5483 (1995).
[Crossref]

Ito, R.

Jain, A. K.

A. K. Jain, Fundamentals of Digital Image Processing(Prentice-Hall, Englewood Cliffs, 1989).

Jundt, D. H.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum. Electron. 28, 2631–2654 (1992).
[Crossref]

Kang, Y. S.

K. Pandiyan, Y. S. Kang, H. H. Lim, B. J. Kim, O. Prakash, and M. Cha, “Poling Quality Evaluation of Periodically Poled Lithium Niobate Using Diffraction Method,” J. Opt. Soc. Korea. 12, 205–209 (2008).
[Crossref]

Kim, B. J.

K. Pandiyan, Y. S. Kang, H. H. Lim, B. J. Kim, O. Prakash, and M. Cha, “Poling Quality Evaluation of Periodically Poled Lithium Niobate Using Diffraction Method,” J. Opt. Soc. Korea. 12, 205–209 (2008).
[Crossref]

Kitamoto, A.

Kondo, T.

Kumar, S.

S. Kumar, D. Gurkan, A. E. Willner, K. Parameswaran, and M. Fejer, “All-optical half adder using a PPLN waveguide and an SOA,” OFC 2004 1, 23–27 (2004).

Kung, A. H.

Z. D. Gao, S. N. Zhu, S. Y. Tu, and A. H. Kung, “Monolithic red-green-blue laser light source based on cascaded wavelength conversion in periodically-poled stoichiometric lithium tantalate,” Appl. Phys. Lett. 89, 181101 (2006).
[Crossref]

Lambeth, D. N.

Q. Chen, Y. Chiu, D. N. Lambeth, T. E. Schlesinger, and D. D. Stancil, “Guided-wave electro-optic beam deflector using domain reversal in LiTaO3,” IEEE J. Lightwave Technol. 12, 1401–1404 (1994).
[Crossref]

Li, H. W.

J. Yan, H. W. Li, X. L. Yang, S. W. Xie, and Z. R. Sun, “Second-order nonlinear optical coefficients measurement of LiNbO3 by non-phase-matched second-harmonic generation in uniaxial crystal sphere,” Chinese Laser J. 21, 14–16 (2000).

Lim, H. H.

K. Pandiyan, Y. S. Kang, H. H. Lim, B. J. Kim, O. Prakash, and M. Cha, “Poling Quality Evaluation of Periodically Poled Lithium Niobate Using Diffraction Method,” J. Opt. Soc. Korea. 12, 205–209 (2008).
[Crossref]

Magel, G. A.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum. Electron. 28, 2631–2654 (1992).
[Crossref]

Ming, N. B.

S. N. Zhu, Y. Y. Zhu, Z. Y. Zhang, H. Shu, H. F. Wang, J. F. Hong, C. Z. Ge, and N. B. Ming, “LiTaO3 crystal periodically poled by applying an external pulsed field,” J. Appl. Phys. 77, 5481–5483 (1995).
[Crossref]

Mohideen, U.

T. J. Yang, V. Gopalan, P. J. Swart, and U. Mohideen, “Direct Observation of Pinning and Bowing of a Single Ferroelectric Domain Wall,” Phys. Rev. Lett. 82, 4106–4109 (1999).
[Crossref]

Pandiyan, K.

K. Pandiyan, Y. S. Kang, H. H. Lim, B. J. Kim, O. Prakash, and M. Cha, “Poling Quality Evaluation of Periodically Poled Lithium Niobate Using Diffraction Method,” J. Opt. Soc. Korea. 12, 205–209 (2008).
[Crossref]

Parameswaran, K.

S. Kumar, D. Gurkan, A. E. Willner, K. Parameswaran, and M. Fejer, “All-optical half adder using a PPLN waveguide and an SOA,” OFC 2004 1, 23–27 (2004).

Prakash, O.

K. Pandiyan, Y. S. Kang, H. H. Lim, B. J. Kim, O. Prakash, and M. Cha, “Poling Quality Evaluation of Periodically Poled Lithium Niobate Using Diffraction Method,” J. Opt. Soc. Korea. 12, 205–209 (2008).
[Crossref]

Rosenfeldt, A.

A. Rosenfeldt and M. Florsheimer, “Nondestructive remote imaging of ferroelectric domain distributions with high three-dimensional resolution,” Appl. Phys. B. 73, 523–529 (2001).

Sacchi, M. D.

M. D. Sacchi, T. J. Ulrych, and C. J. Walker, “Interpolation and extrapolation using a high-resolution discrete Fourier transform,” IEEE Trans. Signal Processing. 46, 31–38 (1998).
[Crossref]

Sandmann, C.

V. Dierolf and C. Sandmann, “Inspection of periodically poled waveguide devices by confocal luminescence microscopy,” Appl. Phys. B. 78, 363–366 (2004).
[Crossref]

Schlesinger, T. E.

Q. Chen, Y. Chiu, D. N. Lambeth, T. E. Schlesinger, and D. D. Stancil, “Guided-wave electro-optic beam deflector using domain reversal in LiTaO3,” IEEE J. Lightwave Technol. 12, 1401–1404 (1994).
[Crossref]

Shirane, M.

Shoji, I.

Shu, H.

S. N. Zhu, Y. Y. Zhu, Z. Y. Zhang, H. Shu, H. F. Wang, J. F. Hong, C. Z. Ge, and N. B. Ming, “LiTaO3 crystal periodically poled by applying an external pulsed field,” J. Appl. Phys. 77, 5481–5483 (1995).
[Crossref]

Stancil, D. D.

Q. Chen, Y. Chiu, D. N. Lambeth, T. E. Schlesinger, and D. D. Stancil, “Guided-wave electro-optic beam deflector using domain reversal in LiTaO3,” IEEE J. Lightwave Technol. 12, 1401–1404 (1994).
[Crossref]

Sun, Z. R.

J. Yan, H. W. Li, X. L. Yang, S. W. Xie, and Z. R. Sun, “Second-order nonlinear optical coefficients measurement of LiNbO3 by non-phase-matched second-harmonic generation in uniaxial crystal sphere,” Chinese Laser J. 21, 14–16 (2000).

Swart, P. J.

T. J. Yang, V. Gopalan, P. J. Swart, and U. Mohideen, “Direct Observation of Pinning and Bowing of a Single Ferroelectric Domain Wall,” Phys. Rev. Lett. 82, 4106–4109 (1999).
[Crossref]

Tu, S. Y.

Z. D. Gao, S. N. Zhu, S. Y. Tu, and A. H. Kung, “Monolithic red-green-blue laser light source based on cascaded wavelength conversion in periodically-poled stoichiometric lithium tantalate,” Appl. Phys. Lett. 89, 181101 (2006).
[Crossref]

Ulrych, T. J.

M. D. Sacchi, T. J. Ulrych, and C. J. Walker, “Interpolation and extrapolation using a high-resolution discrete Fourier transform,” IEEE Trans. Signal Processing. 46, 31–38 (1998).
[Crossref]

Walker, C. J.

M. D. Sacchi, T. J. Ulrych, and C. J. Walker, “Interpolation and extrapolation using a high-resolution discrete Fourier transform,” IEEE Trans. Signal Processing. 46, 31–38 (1998).
[Crossref]

Wang, H. F.

S. N. Zhu, Y. Y. Zhu, Z. Y. Zhang, H. Shu, H. F. Wang, J. F. Hong, C. Z. Ge, and N. B. Ming, “LiTaO3 crystal periodically poled by applying an external pulsed field,” J. Appl. Phys. 77, 5481–5483 (1995).
[Crossref]

Willner, A. E.

S. Kumar, D. Gurkan, A. E. Willner, K. Parameswaran, and M. Fejer, “All-optical half adder using a PPLN waveguide and an SOA,” OFC 2004 1, 23–27 (2004).

Xie, S. W.

J. Yan, H. W. Li, X. L. Yang, S. W. Xie, and Z. R. Sun, “Second-order nonlinear optical coefficients measurement of LiNbO3 by non-phase-matched second-harmonic generation in uniaxial crystal sphere,” Chinese Laser J. 21, 14–16 (2000).

Yan, J.

J. Yan, H. W. Li, X. L. Yang, S. W. Xie, and Z. R. Sun, “Second-order nonlinear optical coefficients measurement of LiNbO3 by non-phase-matched second-harmonic generation in uniaxial crystal sphere,” Chinese Laser J. 21, 14–16 (2000).

Yang, T. J.

T. J. Yang, V. Gopalan, P. J. Swart, and U. Mohideen, “Direct Observation of Pinning and Bowing of a Single Ferroelectric Domain Wall,” Phys. Rev. Lett. 82, 4106–4109 (1999).
[Crossref]

Yang, X. L.

J. Yan, H. W. Li, X. L. Yang, S. W. Xie, and Z. R. Sun, “Second-order nonlinear optical coefficients measurement of LiNbO3 by non-phase-matched second-harmonic generation in uniaxial crystal sphere,” Chinese Laser J. 21, 14–16 (2000).

Zhang, Z. Y.

S. N. Zhu, Y. Y. Zhu, Z. Y. Zhang, H. Shu, H. F. Wang, J. F. Hong, C. Z. Ge, and N. B. Ming, “LiTaO3 crystal periodically poled by applying an external pulsed field,” J. Appl. Phys. 77, 5481–5483 (1995).
[Crossref]

Zhu, S. N.

Z. D. Gao, S. N. Zhu, S. Y. Tu, and A. H. Kung, “Monolithic red-green-blue laser light source based on cascaded wavelength conversion in periodically-poled stoichiometric lithium tantalate,” Appl. Phys. Lett. 89, 181101 (2006).
[Crossref]

S. N. Zhu, Y. Y. Zhu, Z. Y. Zhang, H. Shu, H. F. Wang, J. F. Hong, C. Z. Ge, and N. B. Ming, “LiTaO3 crystal periodically poled by applying an external pulsed field,” J. Appl. Phys. 77, 5481–5483 (1995).
[Crossref]

Zhu, Y. Y.

S. N. Zhu, Y. Y. Zhu, Z. Y. Zhang, H. Shu, H. F. Wang, J. F. Hong, C. Z. Ge, and N. B. Ming, “LiTaO3 crystal periodically poled by applying an external pulsed field,” J. Appl. Phys. 77, 5481–5483 (1995).
[Crossref]

Appl. Phys. B. (2)

A. Rosenfeldt and M. Florsheimer, “Nondestructive remote imaging of ferroelectric domain distributions with high three-dimensional resolution,” Appl. Phys. B. 73, 523–529 (2001).

V. Dierolf and C. Sandmann, “Inspection of periodically poled waveguide devices by confocal luminescence microscopy,” Appl. Phys. B. 78, 363–366 (2004).
[Crossref]

Appl. Phys. Lett. (1)

Z. D. Gao, S. N. Zhu, S. Y. Tu, and A. H. Kung, “Monolithic red-green-blue laser light source based on cascaded wavelength conversion in periodically-poled stoichiometric lithium tantalate,” Appl. Phys. Lett. 89, 181101 (2006).
[Crossref]

Chinese Laser J. (1)

J. Yan, H. W. Li, X. L. Yang, S. W. Xie, and Z. R. Sun, “Second-order nonlinear optical coefficients measurement of LiNbO3 by non-phase-matched second-harmonic generation in uniaxial crystal sphere,” Chinese Laser J. 21, 14–16 (2000).

IEEE J. Lightwave Technol. (1)

Q. Chen, Y. Chiu, D. N. Lambeth, T. E. Schlesinger, and D. D. Stancil, “Guided-wave electro-optic beam deflector using domain reversal in LiTaO3,” IEEE J. Lightwave Technol. 12, 1401–1404 (1994).
[Crossref]

IEEE J. Quantum. Electron. (1)

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum. Electron. 28, 2631–2654 (1992).
[Crossref]

IEEE Trans. Signal Processing. (1)

M. D. Sacchi, T. J. Ulrych, and C. J. Walker, “Interpolation and extrapolation using a high-resolution discrete Fourier transform,” IEEE Trans. Signal Processing. 46, 31–38 (1998).
[Crossref]

J. Appl. Phys. (1)

S. N. Zhu, Y. Y. Zhu, Z. Y. Zhang, H. Shu, H. F. Wang, J. F. Hong, C. Z. Ge, and N. B. Ming, “LiTaO3 crystal periodically poled by applying an external pulsed field,” J. Appl. Phys. 77, 5481–5483 (1995).
[Crossref]

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

J. Opt. Soc. Korea. (1)

K. Pandiyan, Y. S. Kang, H. H. Lim, B. J. Kim, O. Prakash, and M. Cha, “Poling Quality Evaluation of Periodically Poled Lithium Niobate Using Diffraction Method,” J. Opt. Soc. Korea. 12, 205–209 (2008).
[Crossref]

OFC 2004 (1)

S. Kumar, D. Gurkan, A. E. Willner, K. Parameswaran, and M. Fejer, “All-optical half adder using a PPLN waveguide and an SOA,” OFC 2004 1, 23–27 (2004).

Phys. Rev. Lett. (1)

T. J. Yang, V. Gopalan, P. J. Swart, and U. Mohideen, “Direct Observation of Pinning and Bowing of a Single Ferroelectric Domain Wall,” Phys. Rev. Lett. 82, 4106–4109 (1999).
[Crossref]

Other (1)

A. K. Jain, Fundamentals of Digital Image Processing(Prentice-Hall, Englewood Cliffs, 1989).

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Figures (6)

Fig. 1.
Fig. 1. Sample 1: +Z surface (Λ=28.6µm). (a) The original micrograph; (b) The processed image; (c) The final image before analysis.
Fig. 2.
Fig. 2. Fourier transform result of Fig. 1(c). (a) 2D FFT result; (b) 2D FFT result at fy =0; (c) HRFT result is |g 1|=0.625.
Fig. 3.
Fig. 3. Sample 1: -Z surface. (a) The processed micrograph; (b) 2D FFT result at fy =0. The HRFT result is |g 1|=0.592.
Fig. 4.
Fig. 4. Sample 2: -Z surface (Λ=7µm). (a) The original micrograph; (b) 2D FFT result. The HRFT result is |g 1|=0.187.
Fig. 5.
Fig. 5. Sample 3: +Z surface (Squ-PLT, a=9.05µm). (a) The original micrograph; (b) 2D FFT result. The HRFT result is |g01|=0.293.
Fig. 6.
Fig. 6. (a) Evaluated |g 1| at the +Z surface of sample 4 (PPLN, Λ=6.6µm); (b) SHG power and evaluated |g 1|2 at different X-axis position.

Equations (26)

Equations on this page are rendered with MathJax. Learn more.

(P1P2P3)=(d11d12d13d14d15d16d21d22d23d24d25d26d31d32d33d34d35d36)=(E12E22E322E2E32E3E12E1E2).
rect(t)={0,ift>1212,ift=12.1,ift<12
f (x)=Σj=mm[ rect ( j+xΛD ) rect ( jD+xΛ1D ] ,
deff=d33 . g(f) ,
g(f)=1aa2a2f(x)exp(2πifx)dx.
g(fn)=1aa2a2f(x)exp(2πifnx)dx=exp(2πinD)1inπ.
g (fx,fy)=1a·b b2b2a2a2f (x,y) exp [2πi(xfx+yfy) ] dxdy,
deff=d33 . g(fx,fy) ,
U (x,y)=f (x,y) * j=mmk=nn[δ( ja + x ). δ (kb+y) ].
G(fx,fy)=1S (U( x,y) )
=1(2m+1)·(2n+1)·a·b (f( x,y) ) · {j=mmk=nn[δ(ja+x)·δ(kb+y)]}
=g (fx,fy)·1(2m+1)·(2n+1)j=mmk=nnexp[2πi(xfx+yfy )]·δ (ja+x) · δ (kb+y) dxdy
=g (fx,fy) · 1(2m+1)·(2n+1) j=mmk=nnexp[2πi(jafx + kb fy )]
= {g(fx,fy),fx=Maandfy=Nb,Mand Nareintegers0,otherwhenm,n.
g(fx,fy)=1a·b f (x,y)
=1a·b·[u(x,y)·rect (xa) · rect (yb) ]
=[u(x,y)]*[Sinc(afx)·Sinc(bfy)]
=[δ(fy)·m=δ(mΛfx)(1)mδ(mΛfx))i2πm ] * [Sinc(a fx ) · Sinc (bfy)].
E(g(f)Ds)=1a E { a2a2j=mmrect(j+xΛDj)rect(jDj+xΛ1Dj) exp (2πifx)dx}
=1a a2a2j=mm1dd2d2rect(j+xΛDj)rect(jDj+xΛ1Dj)]dpj·exp(2πifx)dx,
E(g(f)Ds)=1ad d2d2a2a2j=mm[rect(j+xΛDj) rect (jDj+xΛ1Dj)].exp(2πifx)dxdp
=1dd2d2exp(2πiDs)1dp=Λexp(2πiD)sin(πdΛ)πdiπ2d .
E(g1) E(g1Ds)={0.0013,D=0.50.0011,D=0.3.
f (x,y)={ 2P (x,y) * [comb (xΛx) comb (yΛy) ] 1 } · rect (xa) · rect (yb) ,
g (fx,fy)={ 2 Λx Λy [P(x,y)] · comb (fxΛy) comb (fxΛy) δ (fx) δ (fy) } * [sinc(a fx )sinc(bfy)] .
I2=2ω12deff2L2I12c3n12n2εοsin2(kL/2)(kL/2)2=C g2 ,

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