Abstract

We study the second-harmonic (SH) parametric processes in unpoled crystals of Strontium Barium Niobate (SBN) with disordered structures of ferroelectric domains. Such crystals allow for the simultaneous phase matching of several second-order nonlinear processes. We analyze the polarization properties of these parametric processes using two types of generation schemes: quasi-collinear SH generation and transverse SH generation. From our experimental data we determine the ratio of d32 and d33 components of the second order susceptibility tensor and also the statistical properties of the random structure of the SBN crystal.

© 2007 Optical Society of America

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References

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  1. F. Zernike and J. E. Midwinter, Applied Nonlinear Optics (Wiley, New York, 1973).
  2. 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. QE-28, 2631-2654 (1992).
    [CrossRef]
  3. M. Baudrier-Raybaut, R. Haidar, Ph. Kupecek, Ph. Lemasson, and E. Rosencher, "Random quasi-phase-matching in bulk polycrystalline isotropic nonlinear materials," Nature (London) 432, 374-376 (2004).
    [CrossRef]
  4. S. E. Skipetrov, "Disorder is the new order," Nature (London) 432, 285-286 (2004).
    [CrossRef]
  5. E. Yu. Morozov, A. A. Kaminskii, A. S. Chirkin, and D. B. Yusupov, "Second optical harmonic generation in nonlinear crystals with a disordered domain structure," JETP Lett. 73, 647-650 (2001).
    [CrossRef]
  6. X. Vidal and J. Martorell, "Generation of light in media with a random distribution of nonlinear domains," Phys. Rev. Lett. 97, 013902 (2006).
    [CrossRef] [PubMed]
  7. A. R. Tunyagi, M. Ulex, and K. Betzler, "Noncollinear optical frequency doubling in strontium barium niobate," Phys. Rev. Lett. 90, 243901 (2003).
    [CrossRef] [PubMed]
  8. R. Fischer, D. N. Neshev, S. M. Saltiel, W. Krolikowski, and Yu. S. Kivshar, "Broadband femtosecond frequency doubling in random media," Appl. Phys. Lett. 89, 191105(3) (2006).
    [CrossRef]
  9. R. Fischer, D. N. Neshev, S. M. Saltiel, A. A. Sukhorukov,W. Krolikowski, Yu. S. Kivshar, "Monitoring ultrashort pulses by transverse frequency doubling of counterpropagating pulses in random media," Appl. Phys. Lett. 91, 031104(3) (2007).
    [CrossRef]
  10. B. F. Johnston, P. Dekker, M. J. Withford, S. M. Saltiel, and Yu. S. Kivshar, "Simultaneous phase matching and internal interference of two second-order nonlinear parametric processes," Opt. Express 14, 11756-11765 (2006).
    [CrossRef] [PubMed]
  11. J. J. Romero, C. Arago, J. A. Gonzalo, D. Jaque, and J. Garcia Sole, "Spectral and thermal properties of quasiphase-matching second-harmonic generation in Nd3+:Sr0.6Ba0.4(NbO3)2 multi-self-frequency-converter nonlinear crystals," J. Appl. Phys. 93, 3111-3113 (2003).
    [CrossRef]
  12. M. O. Ramirez. D. Jaque, L. Ivleva, and L. E. Bausa, "Evaluation of ytterbium doped strontium barium niobate as a potential tunable laser crystal in the visible," J. Appl. Phys. 95, 6185-6191 (2004).
    [CrossRef]
  13. M. Horowitz, A. Bekker, and B. Fischer, "Broadband second-harmonic generation in SrBaNb2O6 by spread spectrum phase matching with controllable domain gratings," Appl. Phys. Lett. 62, 2619-2621 (1993).
    [CrossRef]
  14. Th. Woike, T. Granzow, U. D¨orfler, Ch. Poetsch, M. W¨ohlecke, and R. Pankrath, "Refractive Indices of Congruently Melting Sr0.61Ba0.39Nb2O6," Phys. Status Solidi A 186, R13-R15 (2001).
    [CrossRef]
  15. E. Yu. Morozov and A. S. Chirkin, "Stochastic quasi-phase matching in nonlinear-optical crystals with an irregular domain structure," Sov. J. Quantum Electron. 34, 227-232 (2004).
    [CrossRef]
  16. Y. Le Grand, D. Rouede, C. Odin, R. Aubry, and S. Mattauch, "Second-harmonic scattering by domains in RbH2PO4 ferroelectric," Opt. Commun. 200, 249-260 (2001).
    [CrossRef]
  17. G. Dolino, "Effects of domain shapes on second harmonic scattering in Triglycine Sulfate," Phys. Rev. B 6, 4025-4035 (1972).
    [CrossRef]
  18. C. R. Jeggo and G. D. Boyd, "Nonlinear optical polarizability of the Niobium-Oxygen bond," J. Appl. Phys. 41, 2741-2743 (1970).
    [CrossRef]

2006 (2)

2004 (4)

M. O. Ramirez. D. Jaque, L. Ivleva, and L. E. Bausa, "Evaluation of ytterbium doped strontium barium niobate as a potential tunable laser crystal in the visible," J. Appl. Phys. 95, 6185-6191 (2004).
[CrossRef]

M. Baudrier-Raybaut, R. Haidar, Ph. Kupecek, Ph. Lemasson, and E. Rosencher, "Random quasi-phase-matching in bulk polycrystalline isotropic nonlinear materials," Nature (London) 432, 374-376 (2004).
[CrossRef]

S. E. Skipetrov, "Disorder is the new order," Nature (London) 432, 285-286 (2004).
[CrossRef]

E. Yu. Morozov and A. S. Chirkin, "Stochastic quasi-phase matching in nonlinear-optical crystals with an irregular domain structure," Sov. J. Quantum Electron. 34, 227-232 (2004).
[CrossRef]

2003 (2)

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

J. J. Romero, C. Arago, J. A. Gonzalo, D. Jaque, and J. Garcia Sole, "Spectral and thermal properties of quasiphase-matching second-harmonic generation in Nd3+:Sr0.6Ba0.4(NbO3)2 multi-self-frequency-converter nonlinear crystals," J. Appl. Phys. 93, 3111-3113 (2003).
[CrossRef]

2001 (3)

E. Yu. Morozov, A. A. Kaminskii, A. S. Chirkin, and D. B. Yusupov, "Second optical harmonic generation in nonlinear crystals with a disordered domain structure," JETP Lett. 73, 647-650 (2001).
[CrossRef]

Y. Le Grand, D. Rouede, C. Odin, R. Aubry, and S. Mattauch, "Second-harmonic scattering by domains in RbH2PO4 ferroelectric," Opt. Commun. 200, 249-260 (2001).
[CrossRef]

Th. Woike, T. Granzow, U. D¨orfler, Ch. Poetsch, M. W¨ohlecke, and R. Pankrath, "Refractive Indices of Congruently Melting Sr0.61Ba0.39Nb2O6," Phys. Status Solidi A 186, R13-R15 (2001).
[CrossRef]

1993 (1)

M. Horowitz, A. Bekker, and B. Fischer, "Broadband second-harmonic generation in SrBaNb2O6 by spread spectrum phase matching with controllable domain gratings," Appl. Phys. Lett. 62, 2619-2621 (1993).
[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. QE-28, 2631-2654 (1992).
[CrossRef]

1972 (1)

G. Dolino, "Effects of domain shapes on second harmonic scattering in Triglycine Sulfate," Phys. Rev. B 6, 4025-4035 (1972).
[CrossRef]

1970 (1)

C. R. Jeggo and G. D. Boyd, "Nonlinear optical polarizability of the Niobium-Oxygen bond," J. Appl. Phys. 41, 2741-2743 (1970).
[CrossRef]

Appl. Phys. Lett. (1)

M. Horowitz, A. Bekker, and B. Fischer, "Broadband second-harmonic generation in SrBaNb2O6 by spread spectrum phase matching with controllable domain gratings," Appl. Phys. Lett. 62, 2619-2621 (1993).
[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. QE-28, 2631-2654 (1992).
[CrossRef]

J. Appl. Phys. (3)

J. J. Romero, C. Arago, J. A. Gonzalo, D. Jaque, and J. Garcia Sole, "Spectral and thermal properties of quasiphase-matching second-harmonic generation in Nd3+:Sr0.6Ba0.4(NbO3)2 multi-self-frequency-converter nonlinear crystals," J. Appl. Phys. 93, 3111-3113 (2003).
[CrossRef]

M. O. Ramirez. D. Jaque, L. Ivleva, and L. E. Bausa, "Evaluation of ytterbium doped strontium barium niobate as a potential tunable laser crystal in the visible," J. Appl. Phys. 95, 6185-6191 (2004).
[CrossRef]

C. R. Jeggo and G. D. Boyd, "Nonlinear optical polarizability of the Niobium-Oxygen bond," J. Appl. Phys. 41, 2741-2743 (1970).
[CrossRef]

JETP Lett. (1)

E. Yu. Morozov, A. A. Kaminskii, A. S. Chirkin, and D. B. Yusupov, "Second optical harmonic generation in nonlinear crystals with a disordered domain structure," JETP Lett. 73, 647-650 (2001).
[CrossRef]

Nature (London) (2)

M. Baudrier-Raybaut, R. Haidar, Ph. Kupecek, Ph. Lemasson, and E. Rosencher, "Random quasi-phase-matching in bulk polycrystalline isotropic nonlinear materials," Nature (London) 432, 374-376 (2004).
[CrossRef]

S. E. Skipetrov, "Disorder is the new order," Nature (London) 432, 285-286 (2004).
[CrossRef]

Opt. Commun. (1)

Y. Le Grand, D. Rouede, C. Odin, R. Aubry, and S. Mattauch, "Second-harmonic scattering by domains in RbH2PO4 ferroelectric," Opt. Commun. 200, 249-260 (2001).
[CrossRef]

Opt. Express (1)

Phys. Rev. B (1)

G. Dolino, "Effects of domain shapes on second harmonic scattering in Triglycine Sulfate," Phys. Rev. B 6, 4025-4035 (1972).
[CrossRef]

Phys. Rev. Lett. (2)

X. Vidal and J. Martorell, "Generation of light in media with a random distribution of nonlinear domains," Phys. Rev. Lett. 97, 013902 (2006).
[CrossRef] [PubMed]

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

Phys. Status Solidi A (1)

Th. Woike, T. Granzow, U. D¨orfler, Ch. Poetsch, M. W¨ohlecke, and R. Pankrath, "Refractive Indices of Congruently Melting Sr0.61Ba0.39Nb2O6," Phys. Status Solidi A 186, R13-R15 (2001).
[CrossRef]

Sov. J. Quantum Electron. (1)

E. Yu. Morozov and A. S. Chirkin, "Stochastic quasi-phase matching in nonlinear-optical crystals with an irregular domain structure," Sov. J. Quantum Electron. 34, 227-232 (2004).
[CrossRef]

Other (3)

R. Fischer, D. N. Neshev, S. M. Saltiel, W. Krolikowski, and Yu. S. Kivshar, "Broadband femtosecond frequency doubling in random media," Appl. Phys. Lett. 89, 191105(3) (2006).
[CrossRef]

R. Fischer, D. N. Neshev, S. M. Saltiel, A. A. Sukhorukov,W. Krolikowski, Yu. S. Kivshar, "Monitoring ultrashort pulses by transverse frequency doubling of counterpropagating pulses in random media," Appl. Phys. Lett. 91, 031104(3) (2007).
[CrossRef]

F. Zernike and J. E. Midwinter, Applied Nonlinear Optics (Wiley, New York, 1973).

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Figures (5)

Fig. 1.
Fig. 1.

Schematic representation of the two experiments: (a) QCSH experiment with the observation of a single SH beam and SH with small noncollinear angle of the fundamental beams; (b) TSH experiment with a single pulse and/or two counter-propagating pulses. In both cases the optical c-axis of the crystal is perpendicular to the plane of drawing.

Fig. 2.
Fig. 2.

(a) SH signal (lines) in the QCSH experiment obtained for different polarization orientations of the fundamental beams A and B. (b) Phase-matching conditions in the QCSH experiment (the case of a single beam); g being the grating vectors that compensate a phase mismatch in a bulk. (c) Image of the SH signal emitted in the TSH experiment with two counter-propagating fundamental beams A and B. Trace in the center is a result of mixing of the beams A and B. In the boxes, it is shown the corresponding phase-matching diagrams of the background single-beam transverse SH scattering AA-S and BB-S as well as of the transverse SH emission by simultaneous interaction of pulses from A and B.

Fig. 3.
Fig. 3.

Function f(Δk). Mean size and dispersion of the domains are a=3 µm and σ=1.15 µm, respectively. Squares indicate experimentally determined values of the ratios f ee-e/f oo-e and f eo-o/f oo-e corresponding to EE-E, OO-E, and OE-O processes.

Fig. 4.
Fig. 4.

Theoretically calculated normalized SH intensity as a function of the polarization of the fundamental beam for single beam SHG. Here the extraordinary SH is induced via simultaneously operating EE-E and OO-E processes. Mutually incoherent interaction is shown by dashed line. Mutually coherent interactions depend also on the sign of the ratio of nonlinear coefficients d 32/d 33 shown in solid (dotted) line when this ratio is positive (negative). Two special cases EE-E and OO-E are marked by arrows. R=0.48 is used.

Fig. 5.
Fig. 5.

Experimentally observed SH signal vs. input polarization angle β for three fixed polarizations of beam A: extraordinary - red full squares; mixed - blue open circles, and ordinary - green open squares. Single beam SH (black full circle); Lines show theoretical results. (a) extraordinary SH; (b) ordinary SH; both (a) and (b) are for SHG in the QCSH experiment. (c) Background TSH and single beam TSH; (d) TSH emission via A and B pulse mixing. Mixed polarizations: α=30°,43.5°,45°,45° for a,b,c,d plot respectively.

Tables (2)

Tables Icon

Table 1. Interaction types and relevant wave vectors responsible for SHG in the QCSH experiment shown in Figs. 2(a,b); 2γ denotes the intersection angle between the fundamental beams measured inside the sample. The bulk phase mismatches (shown for the forward direction only) are calculated with the refraction index taken from Ref. [14].

Tables Icon

Table 2. Effective nonlinear coefficients for separate SHG processes in SBN crystals.

Equations (11)

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k 1 A + k 1 B + g = k 2 ,
I 2 ( o , e ) 2 n 2 ω ε 0 c n 1 ω 2 ( ω c n 2 ω d eff ( o , e ) ) 2 I 1 2 L ,
d eff = e 2 · d ̂ ( 2 ) : e 1 A e 1 B f ( Δ k , a , σ )
f ( Δ k , a , σ ) = 4 Δ k 2 1 exp ( σ 2 Δ k 2 ) 1 + exp ( σ 2 Δ k 2 ) + 2 cos ( a Δ k ) exp ( σ 2 Δ k 2 2 )
f ( Δ k , a , σ ) 1 Δ k 2 .
d eff ( e ) 2 = d 33 2 f ( Δ k ee e ) cos 4 β + d 32 2 f ( Δ k oo e ) sin 4 β
= d 33 2 f ( Δ k ee e ) ( cos 4 β + R sin 4 β ) ,
d eff ( e ) 2 = ( d 33 f ( Δ k ee e ) cos 2 β + d 32 f ( Δ k oo e ) ) 2
= d 33 2 f ( Δ k ee e ) ( cos 2 β ± R sin 2 β ) 2 ,
R = f ( Δ k oo e ) f ( Δ k ee e ) ( d 32 d 33 ) 2 ,
R = f ( Δ k oo e ) f ( Δ k ee e ) ( d 32 d 33 ) 2 = I oo e I ee e ,

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