Abstract

We study the role of the individual ferroelectric domain shape on the second-harmonic emission in strontium barium niobate featuring a random quadratic nonlinearity. The noncollinearly emitted second-harmonic signal is scanned in the far-field at different incident angles for different domain size distributions. This offers the possibility to retrieve the Fourier spectrum, corresponding to the spatial domain distribution and domain shape. Based on images of the domain structures retrieved by Čerenkov-type second-harmonic microscopy, domain patterns are simulated, the second-harmonic intensities are calculated, and finally compared with the measurements.

© 2013 Optical Society of America

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  1. A. R. Tunyagi, M. Ulex, and K. Betzler, “Noncollinear optical frequency doubling in strontium barium niobate,” Phys. Rev. Lett.90, 243901 (2003).
    [CrossRef] [PubMed]
  2. R. Fischer, D. N. Neshev, S. M. Saltiel, A. A. Sukhorukov, W. Krolikowski, and Y. S. Kivshar, “Monitoring ultrashort pulses by transverse frequency doubling of counterpropagating pulses in random media,” Appl. Phys. Lett.91, 031104 (2007).
    [CrossRef]
  3. V. Roppo, D. Dumay, J. Trull, C. Cojocaru, S. M. Saltiel, K. Staliunas, R. Vilaseca, D. N. Neshev, W. Krolikowski, and Y. S. Kivshar, “Planar second-harmonic generation with noncollinear pumps in disordered media,” Opt. Express16, 14192–14199 (2008).
    [CrossRef] [PubMed]
  4. J. Trull, C. Cojocaru, R. Fischer, S. M. Saltiel, K. Staliunas, R. Herrero, R. Vilaseca, D. N. Neshev, W. Krolikowski, and Y. S. Kivshar, “Second-harmonic parametric scattering in ferroelectric crystals with disordered nonlinear domain structures,” Opt. Express15, 15868–15877 (2007).
    [CrossRef] [PubMed]
  5. V. Roppo, W. Wang, K. Kalinowski, Y. Kong, C. Cojocaru, J. Trull, R. Vilaseca, M. Scalora, W. Krolikowski, and Y. Kivshar, “The role of ferroelectric domain structure in second harmonic generation in random quadratic media,” Opt. Express18, 4012–4022 (2010).
    [CrossRef] [PubMed]
  6. M. Ayoub, J. Imbrock, and C. Denz, “Second harmonic generation in multi-domain χ2media: from disorder to order,” Opt. Express19, 11340–11354 (2011).
    [CrossRef] [PubMed]
  7. L. Tian, D. A. Scrymgeour, and V. Gopalan, “Real-time study of domain dynamics in ferroelectric Sr0.61Ba0.39Nb2O6,” J. Appl. Phys.97, 114111 (2005).
    [CrossRef]
  8. K. Terabe, S. Takekawa, M. Nakamura, K. Kitamura, S. Higuchi, Y. Gotoh, and A. Gruverman, “Imaging and engineering the nanoscale-domain structure of a Sr0.61Ba0.39Nb2O6crystal using a scanning force microscope,” Appl. Phys. Lett.81, 2044–2046 (2002).
    [CrossRef]
  9. M. Ayoub, P. Roedig, J. Imbrock, and C. Denz, “Domain-shape-based modulation of Čerenkov second-harmonic generation in multidomain strontium barium niobate,” Opt. Lett.36, 4371–4373 (2011).
    [CrossRef] [PubMed]
  10. J. Bravo-Abad, X. Vidal, J. L. D. Juárez, and J. Martorell, “Optical second-harmonic scattering from a non-diffusive random distribution of nonlinear domains,” Opt. Express18, 14202–14211 (2010).
    [CrossRef] [PubMed]
  11. M. Ayoub, P. Roedig, K. Koynov, J. Imbrock, and C. Denz, “Čerenkov-type second-harmonic spectroscopy in random nonlinear photonic structures,” Opt. Express21, 8220–8230 (2013).
    [CrossRef] [PubMed]
  12. Y. Sheng, A. Best, H.-J. Butt, W. Krolikowski, A. Arie, and K. Koynov, “Three-dimensional ferroelectric domain visualization by Čerenkov-type second harmonic generation,” Opt. Express18, 16539–16545 (2010).
    [CrossRef] [PubMed]
  13. S. M. Russell, P. E. Powers, M. J. Missey, and K. L. Schepler, “Broadband mid-infrared generation with two-dimensional quasi-phase-matched structures,” J. Quantum Electronics37, 877–887 (2001).
    [CrossRef]
  14. A. Arie and N. Voloch, “Periodic, quasi-periodic, and random quadratic nonlinear photonic crystals,” Laser and Photon. Rev.4, 355–373 (2010).
    [CrossRef]
  15. K. Kalinowski, P. Roedig, Y. Sheng, M. Ayoub, J. Imbrock, C. Denz, and W. Krolikowski, “Enhanced Čerenkov second-harmonic emission in nonlinear photonic structures,” Opt. Lett.37, 1832–1834 (2012).
    [CrossRef] [PubMed]

2013 (1)

2012 (1)

2011 (2)

2010 (4)

2008 (1)

2007 (2)

J. Trull, C. Cojocaru, R. Fischer, S. M. Saltiel, K. Staliunas, R. Herrero, R. Vilaseca, D. N. Neshev, W. Krolikowski, and Y. S. Kivshar, “Second-harmonic parametric scattering in ferroelectric crystals with disordered nonlinear domain structures,” Opt. Express15, 15868–15877 (2007).
[CrossRef] [PubMed]

R. Fischer, D. N. Neshev, S. M. Saltiel, A. A. Sukhorukov, W. Krolikowski, and Y. S. Kivshar, “Monitoring ultrashort pulses by transverse frequency doubling of counterpropagating pulses in random media,” Appl. Phys. Lett.91, 031104 (2007).
[CrossRef]

2005 (1)

L. Tian, D. A. Scrymgeour, and V. Gopalan, “Real-time study of domain dynamics in ferroelectric Sr0.61Ba0.39Nb2O6,” J. Appl. Phys.97, 114111 (2005).
[CrossRef]

2003 (1)

A. R. Tunyagi, M. Ulex, and K. Betzler, “Noncollinear optical frequency doubling in strontium barium niobate,” Phys. Rev. Lett.90, 243901 (2003).
[CrossRef] [PubMed]

2002 (1)

K. Terabe, S. Takekawa, M. Nakamura, K. Kitamura, S. Higuchi, Y. Gotoh, and A. Gruverman, “Imaging and engineering the nanoscale-domain structure of a Sr0.61Ba0.39Nb2O6crystal using a scanning force microscope,” Appl. Phys. Lett.81, 2044–2046 (2002).
[CrossRef]

2001 (1)

S. M. Russell, P. E. Powers, M. J. Missey, and K. L. Schepler, “Broadband mid-infrared generation with two-dimensional quasi-phase-matched structures,” J. Quantum Electronics37, 877–887 (2001).
[CrossRef]

Arie, A.

Ayoub, M.

Best, A.

Betzler, K.

A. R. Tunyagi, M. Ulex, and K. Betzler, “Noncollinear optical frequency doubling in strontium barium niobate,” Phys. Rev. Lett.90, 243901 (2003).
[CrossRef] [PubMed]

Bravo-Abad, J.

Butt, H.-J.

Cojocaru, C.

Denz, C.

Dumay, D.

Fischer, R.

J. Trull, C. Cojocaru, R. Fischer, S. M. Saltiel, K. Staliunas, R. Herrero, R. Vilaseca, D. N. Neshev, W. Krolikowski, and Y. S. Kivshar, “Second-harmonic parametric scattering in ferroelectric crystals with disordered nonlinear domain structures,” Opt. Express15, 15868–15877 (2007).
[CrossRef] [PubMed]

R. Fischer, D. N. Neshev, S. M. Saltiel, A. A. Sukhorukov, W. Krolikowski, and Y. S. Kivshar, “Monitoring ultrashort pulses by transverse frequency doubling of counterpropagating pulses in random media,” Appl. Phys. Lett.91, 031104 (2007).
[CrossRef]

Gopalan, V.

L. Tian, D. A. Scrymgeour, and V. Gopalan, “Real-time study of domain dynamics in ferroelectric Sr0.61Ba0.39Nb2O6,” J. Appl. Phys.97, 114111 (2005).
[CrossRef]

Gotoh, Y.

K. Terabe, S. Takekawa, M. Nakamura, K. Kitamura, S. Higuchi, Y. Gotoh, and A. Gruverman, “Imaging and engineering the nanoscale-domain structure of a Sr0.61Ba0.39Nb2O6crystal using a scanning force microscope,” Appl. Phys. Lett.81, 2044–2046 (2002).
[CrossRef]

Gruverman, A.

K. Terabe, S. Takekawa, M. Nakamura, K. Kitamura, S. Higuchi, Y. Gotoh, and A. Gruverman, “Imaging and engineering the nanoscale-domain structure of a Sr0.61Ba0.39Nb2O6crystal using a scanning force microscope,” Appl. Phys. Lett.81, 2044–2046 (2002).
[CrossRef]

Herrero, R.

Higuchi, S.

K. Terabe, S. Takekawa, M. Nakamura, K. Kitamura, S. Higuchi, Y. Gotoh, and A. Gruverman, “Imaging and engineering the nanoscale-domain structure of a Sr0.61Ba0.39Nb2O6crystal using a scanning force microscope,” Appl. Phys. Lett.81, 2044–2046 (2002).
[CrossRef]

Imbrock, J.

Juárez, J. L. D.

Kalinowski, K.

Kitamura, K.

K. Terabe, S. Takekawa, M. Nakamura, K. Kitamura, S. Higuchi, Y. Gotoh, and A. Gruverman, “Imaging and engineering the nanoscale-domain structure of a Sr0.61Ba0.39Nb2O6crystal using a scanning force microscope,” Appl. Phys. Lett.81, 2044–2046 (2002).
[CrossRef]

Kivshar, Y.

Kivshar, Y. S.

Kong, Y.

Koynov, K.

Krolikowski, W.

K. Kalinowski, P. Roedig, Y. Sheng, M. Ayoub, J. Imbrock, C. Denz, and W. Krolikowski, “Enhanced Čerenkov second-harmonic emission in nonlinear photonic structures,” Opt. Lett.37, 1832–1834 (2012).
[CrossRef] [PubMed]

Y. Sheng, A. Best, H.-J. Butt, W. Krolikowski, A. Arie, and K. Koynov, “Three-dimensional ferroelectric domain visualization by Čerenkov-type second harmonic generation,” Opt. Express18, 16539–16545 (2010).
[CrossRef] [PubMed]

V. Roppo, W. Wang, K. Kalinowski, Y. Kong, C. Cojocaru, J. Trull, R. Vilaseca, M. Scalora, W. Krolikowski, and Y. Kivshar, “The role of ferroelectric domain structure in second harmonic generation in random quadratic media,” Opt. Express18, 4012–4022 (2010).
[CrossRef] [PubMed]

V. Roppo, D. Dumay, J. Trull, C. Cojocaru, S. M. Saltiel, K. Staliunas, R. Vilaseca, D. N. Neshev, W. Krolikowski, and Y. S. Kivshar, “Planar second-harmonic generation with noncollinear pumps in disordered media,” Opt. Express16, 14192–14199 (2008).
[CrossRef] [PubMed]

J. Trull, C. Cojocaru, R. Fischer, S. M. Saltiel, K. Staliunas, R. Herrero, R. Vilaseca, D. N. Neshev, W. Krolikowski, and Y. S. Kivshar, “Second-harmonic parametric scattering in ferroelectric crystals with disordered nonlinear domain structures,” Opt. Express15, 15868–15877 (2007).
[CrossRef] [PubMed]

R. Fischer, D. N. Neshev, S. M. Saltiel, A. A. Sukhorukov, W. Krolikowski, and Y. S. Kivshar, “Monitoring ultrashort pulses by transverse frequency doubling of counterpropagating pulses in random media,” Appl. Phys. Lett.91, 031104 (2007).
[CrossRef]

Martorell, J.

Missey, M. J.

S. M. Russell, P. E. Powers, M. J. Missey, and K. L. Schepler, “Broadband mid-infrared generation with two-dimensional quasi-phase-matched structures,” J. Quantum Electronics37, 877–887 (2001).
[CrossRef]

Nakamura, M.

K. Terabe, S. Takekawa, M. Nakamura, K. Kitamura, S. Higuchi, Y. Gotoh, and A. Gruverman, “Imaging and engineering the nanoscale-domain structure of a Sr0.61Ba0.39Nb2O6crystal using a scanning force microscope,” Appl. Phys. Lett.81, 2044–2046 (2002).
[CrossRef]

Neshev, D. N.

Powers, P. E.

S. M. Russell, P. E. Powers, M. J. Missey, and K. L. Schepler, “Broadband mid-infrared generation with two-dimensional quasi-phase-matched structures,” J. Quantum Electronics37, 877–887 (2001).
[CrossRef]

Roedig, P.

Roppo, V.

Russell, S. M.

S. M. Russell, P. E. Powers, M. J. Missey, and K. L. Schepler, “Broadband mid-infrared generation with two-dimensional quasi-phase-matched structures,” J. Quantum Electronics37, 877–887 (2001).
[CrossRef]

Saltiel, S. M.

Scalora, M.

Schepler, K. L.

S. M. Russell, P. E. Powers, M. J. Missey, and K. L. Schepler, “Broadband mid-infrared generation with two-dimensional quasi-phase-matched structures,” J. Quantum Electronics37, 877–887 (2001).
[CrossRef]

Scrymgeour, D. A.

L. Tian, D. A. Scrymgeour, and V. Gopalan, “Real-time study of domain dynamics in ferroelectric Sr0.61Ba0.39Nb2O6,” J. Appl. Phys.97, 114111 (2005).
[CrossRef]

Sheng, Y.

Staliunas, K.

Sukhorukov, A. A.

R. Fischer, D. N. Neshev, S. M. Saltiel, A. A. Sukhorukov, W. Krolikowski, and Y. S. Kivshar, “Monitoring ultrashort pulses by transverse frequency doubling of counterpropagating pulses in random media,” Appl. Phys. Lett.91, 031104 (2007).
[CrossRef]

Takekawa, S.

K. Terabe, S. Takekawa, M. Nakamura, K. Kitamura, S. Higuchi, Y. Gotoh, and A. Gruverman, “Imaging and engineering the nanoscale-domain structure of a Sr0.61Ba0.39Nb2O6crystal using a scanning force microscope,” Appl. Phys. Lett.81, 2044–2046 (2002).
[CrossRef]

Terabe, K.

K. Terabe, S. Takekawa, M. Nakamura, K. Kitamura, S. Higuchi, Y. Gotoh, and A. Gruverman, “Imaging and engineering the nanoscale-domain structure of a Sr0.61Ba0.39Nb2O6crystal using a scanning force microscope,” Appl. Phys. Lett.81, 2044–2046 (2002).
[CrossRef]

Tian, L.

L. Tian, D. A. Scrymgeour, and V. Gopalan, “Real-time study of domain dynamics in ferroelectric Sr0.61Ba0.39Nb2O6,” J. Appl. Phys.97, 114111 (2005).
[CrossRef]

Trull, J.

Tunyagi, A. R.

A. R. Tunyagi, M. Ulex, and K. Betzler, “Noncollinear optical frequency doubling in strontium barium niobate,” Phys. Rev. Lett.90, 243901 (2003).
[CrossRef] [PubMed]

Ulex, M.

A. R. Tunyagi, M. Ulex, and K. Betzler, “Noncollinear optical frequency doubling in strontium barium niobate,” Phys. Rev. Lett.90, 243901 (2003).
[CrossRef] [PubMed]

Vidal, X.

Vilaseca, R.

Voloch, N.

A. Arie and N. Voloch, “Periodic, quasi-periodic, and random quadratic nonlinear photonic crystals,” Laser and Photon. Rev.4, 355–373 (2010).
[CrossRef]

Wang, W.

Appl. Phys. Lett. (2)

K. Terabe, S. Takekawa, M. Nakamura, K. Kitamura, S. Higuchi, Y. Gotoh, and A. Gruverman, “Imaging and engineering the nanoscale-domain structure of a Sr0.61Ba0.39Nb2O6crystal using a scanning force microscope,” Appl. Phys. Lett.81, 2044–2046 (2002).
[CrossRef]

R. Fischer, D. N. Neshev, S. M. Saltiel, A. A. Sukhorukov, W. Krolikowski, and Y. S. Kivshar, “Monitoring ultrashort pulses by transverse frequency doubling of counterpropagating pulses in random media,” Appl. Phys. Lett.91, 031104 (2007).
[CrossRef]

J. Appl. Phys. (1)

L. Tian, D. A. Scrymgeour, and V. Gopalan, “Real-time study of domain dynamics in ferroelectric Sr0.61Ba0.39Nb2O6,” J. Appl. Phys.97, 114111 (2005).
[CrossRef]

J. Quantum Electronics (1)

S. M. Russell, P. E. Powers, M. J. Missey, and K. L. Schepler, “Broadband mid-infrared generation with two-dimensional quasi-phase-matched structures,” J. Quantum Electronics37, 877–887 (2001).
[CrossRef]

Laser and Photon. Rev. (1)

A. Arie and N. Voloch, “Periodic, quasi-periodic, and random quadratic nonlinear photonic crystals,” Laser and Photon. Rev.4, 355–373 (2010).
[CrossRef]

Opt. Express (7)

J. Trull, C. Cojocaru, R. Fischer, S. M. Saltiel, K. Staliunas, R. Herrero, R. Vilaseca, D. N. Neshev, W. Krolikowski, and Y. S. Kivshar, “Second-harmonic parametric scattering in ferroelectric crystals with disordered nonlinear domain structures,” Opt. Express15, 15868–15877 (2007).
[CrossRef] [PubMed]

V. Roppo, D. Dumay, J. Trull, C. Cojocaru, S. M. Saltiel, K. Staliunas, R. Vilaseca, D. N. Neshev, W. Krolikowski, and Y. S. Kivshar, “Planar second-harmonic generation with noncollinear pumps in disordered media,” Opt. Express16, 14192–14199 (2008).
[CrossRef] [PubMed]

V. Roppo, W. Wang, K. Kalinowski, Y. Kong, C. Cojocaru, J. Trull, R. Vilaseca, M. Scalora, W. Krolikowski, and Y. Kivshar, “The role of ferroelectric domain structure in second harmonic generation in random quadratic media,” Opt. Express18, 4012–4022 (2010).
[CrossRef] [PubMed]

J. Bravo-Abad, X. Vidal, J. L. D. Juárez, and J. Martorell, “Optical second-harmonic scattering from a non-diffusive random distribution of nonlinear domains,” Opt. Express18, 14202–14211 (2010).
[CrossRef] [PubMed]

Y. Sheng, A. Best, H.-J. Butt, W. Krolikowski, A. Arie, and K. Koynov, “Three-dimensional ferroelectric domain visualization by Čerenkov-type second harmonic generation,” Opt. Express18, 16539–16545 (2010).
[CrossRef] [PubMed]

M. Ayoub, J. Imbrock, and C. Denz, “Second harmonic generation in multi-domain χ2media: from disorder to order,” Opt. Express19, 11340–11354 (2011).
[CrossRef] [PubMed]

M. Ayoub, P. Roedig, K. Koynov, J. Imbrock, and C. Denz, “Čerenkov-type second-harmonic spectroscopy in random nonlinear photonic structures,” Opt. Express21, 8220–8230 (2013).
[CrossRef] [PubMed]

Opt. Lett. (2)

Phys. Rev. Lett. (1)

A. R. Tunyagi, M. Ulex, and K. Betzler, “Noncollinear optical frequency doubling in strontium barium niobate,” Phys. Rev. Lett.90, 243901 (2003).
[CrossRef] [PubMed]

Supplementary Material (2)

» Media 1: MP4 (538 KB)     
» Media 2: MP4 (443 KB)     

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Figures (4)

Fig. 1
Fig. 1

Disordered ferroelectric domain patterns in as-grown (a) and repoled (b) strontium barium niobate imaged by scanning Čerenkov-type SHG microscopy; (c) An experimental photograph of planar SH at 400 nm for a repoled sample, corresponding to an averaged domain size shown in (b); (d) Phase-matching condition diagram; (e) Schematic illustration of the experimental setup.

Fig. 2
Fig. 2

(a, d) Modeled real space of random up- and down-domain structure for the two averaged domain sizes of 0.25 μm and 3.5 μm, respectively; (b, e) The corresponding Fourier spectra. The strongest Fourier coefficients are marked with dashed white circles; (c, f) Calculated SH angular intensity for the two domain distributions for a fundamental wavelength of 800 nm.

Fig. 3
Fig. 3

(a) Experimentally measured SH signal at 400 nm while rotating the unpoled SBN sample; (b) Simulated SH intensity as a function of the incident and emission angles ( Media 1). The fundamental beam direction is marked with a dashed line.

Fig. 4
Fig. 4

(a) Experimentally measured SH signal at 400 nm while rotating the repoled SBN sample ( Media 2); (b, c, d) Simulated SH intensity as a function of the incident and emission angles for the squareness degrees s = 0.4, 0.6, 0.8, respectively. The insets show the corresponding modeled domain shape. The fundamental beam direction is marked by a dashed line.

Equations (2)

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s 2 x 2 y 2 r D 4 ( x 2 r D 2 + y 2 r D 2 ) + 1 = 0 .
I SH d eff 2 I FW 2 L z 2 | S ( Δ k x , Δ k y ) | 2 sinc 2 ( Δ k z L z 2 ) ,

Metrics