## Second-harmonic parametric scattering in ferroelectric crystals with disordered nonlinear domain structures

Optics Express, Vol. 15, Issue 24, pp. 15868-15877 (2007)

http://dx.doi.org/10.1364/OE.15.015868

Acrobat PDF (1448 KB)

### 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 d_{32} and d_{33} 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

## 1. Introduction

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]

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]

*µ*m. Recently, we have shown that this ultra-broad parametric generation can be used to map complex infrared spectra into visible [8

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, and 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]

## 2. Experimental setups and results

**Q**uasi

**C**ollinear

**S**econd

**H**armonic experiment. In the second case, the generated SH wave propagates transversely to the fundamental beam, and we refer to this setup as the TSH experiment:

**T**ransverse

**S**econd

**H**armonic experiment.

*τ*=8 ns, repetition rate 10 Hz) is arranged to deliver two beams (which we refer to as beams

**A**and

**B**) with total energy of 3 mJ each and diameter of 5 mm (FWHM). The beams intersect at the external angle 4° inside an unpoled SBN crystal.

*τ*=150 fs, repetition rate 76 MHz) is arranged to deliver two counter-propagating beams with power 300 mW and diameter 1 mm. The two beams are loosely focused in the crystal. The beam paths are chosen in such a way that the counter-propagating pulses meet in the central part of the SBN crystal. The use of femtosecond pulses is essential for this geometry as the pulse length is shorter than the crystal length, allowing to distinguish between the single beam contribution to the SH signal and SH due to

**A**and

**B**mixing.

**A**and

**B**is controlled by

*λ*/2 wave plates. The geometries of the two experimental setups are shown schematically in Figs. 1(a,b), respectively.

*d*̂

^{(2)}. Since the direction of the fundamental beams is close or coincides with the crystallographic x-axis, the relevant components are d

_{33}and d

_{32}=d

_{24}. The unpoled SBN crystal is composed of random needle-like anti-parallel ferroelectric domains which are oriented along z-axis with an average domain size between 2 and 3

*µ*m [11

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 Nd^{3+}:Sr_{0.6}Ba_{0.4}(NbO_{3})_{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]

**A**- extraordinary;

**B**- ordinary), and (III) two ordinary polarized fundamental beams. The SH signal is emitted in the form of three well-resolved vertical lines. The side lines (numbered 1, 3, 4, 6, 7, and 9) represent the SH signal emitted separately by each of the fundamental beams. The middle lines (numbered 2, 5, and 8) appear only when both the beams

**A**and

**B**are present

*simultaneously*and hence represent the non-collinear SH generation by two fundamental beams. The polarization state of each SH lines is marked as “e” (extraordinary) or “o” (ordinary). We notice that all but one outputs (line #5) are extraordinary polarized. The presence of this particular ordinary polarized signal defies the previous claims that in SBN crystals only extraordinary SH signal could be generated [13

13. M. Horowitz, A. Bekker, and B. Fischer, “Broadband second-harmonic generation in SrBaNb_{2}O_{6} by spread spectrum phase matching with controllable domain gratings,” Appl. Phys. Lett. **62**, 2619–2621 (1993). [CrossRef]

*E*

_{1A}

*O*

_{1B}-

*O*

_{2}that is governed by the same component

*d*

_{32}also responsible for the process

*O*

_{1A}

*O*

_{1B}-

*E*

_{2}. However, since the phase mismatch for the former interaction is larger, the emitted SH signal is weaker than that in the latter process.

**k**

_{1A}and

**k**

_{1B}represent the fundamental waves,

**k**

_{2}is for the SH wave, and

**g**is one of the grating vectors supplied by a random structure of the nonlinear quadratic medium. As is seen

**g**have different sizes and orientation, but they always lie in the xy-plane. This is in contrast to the SHG with single uniform QPM structures with only a fixed set of the grating vectors available. Due to the randomness of the unpoled SBN crystal, a set of grating vectors with different magnitudes and orientations is available for phase matching. This enables phase matching in an extremely broad range of wavelengths and the SH emission in a broad angular range, as is seen in the images shown in Fig. 2(a). The angular distance between the maxima is of the order of 10 degrees. Moreover, as is demonstrated below, this continuum of grating vectors allows for simultaneous phase matching of several nonlinear parametric processes.

**k**

_{1A},

**k**

_{1B}, and

**k**

_{2}correspond to different wave vectors of the fundamental waves listed in Table 1, where we show only the interactions for which both input beams are purely ordinary or purely extraordinary. For arbitrary polarization of the fundamental beams, the SH signal contains contributions of several processes.

**AA**-

**S**and

**BB**-

**S**. The central bright peak is a result of the

**AB**-

**S**interaction in the position where two counter-propagating femtosecond pulses overlap, and it represents the autocorrelation signal of the pulses [9

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

*x*-axis only, two

*χ*

^{(2)}components can be involved in the interactions:

*d*=

_{zzz}*d*

_{33}and

*d*=

_{zyy}*d*

_{32}, so the medium polarization at the doubled frequency can have only

*z*and

*y*components. As the camera “looks” in the y direction, it can only “see”

*z*(extraordinary) polarized signal. Therefore, only signals originating from the processes

*E*

_{1}

*E*

_{1}-

*E*

_{2}or

*O*

_{1}

*O*

_{1}-

*E*

_{2}can be observed, as has been confirmed by this experiment. In the insets of Fig. 2(c), the phase-matching conditions for single-beam SH processes (

**AA**-

**S**and

**BB**-

**S**) and the SH process with counter-propagating fundamental beams (

**AB**-

**S**) are shown. The corresponding bulk phase mismatches depend on which particular situation is realized. For a single-beam transverse SHG the phase mismatches are

*Δk*

_{oo-e}=

*Δk*

_{ee-e}=

*k*

_{2e}=36.3

*µ*m

^{-1}.

## 3. Theoretical model

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]

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]

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 RbH_{2}PO_{4} 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]

*et al.*[16

16. Y. Le Grand, D. Rouede, C. Odin, R. Aubry, and S. Mattauch, “Second-harmonic scattering by domains in RbH_{2}PO_{4} ferroelectric,” Opt. Commun. **200**, 249–260 (2001). [CrossRef]

16. Y. Le Grand, D. Rouede, C. Odin, R. Aubry, and S. Mattauch, “Second-harmonic scattering by domains in RbH_{2}PO_{4} ferroelectric,” Opt. Commun. **200**, 249–260 (2001). [CrossRef]

**A**and

**B**(expressed by unit vectors

**e**

_{1A}and

**e**

_{1B}) and

*a*and

*σ*denote the mean value and dispersion (standard deviation) of the domain size distribution [16

_{2}PO_{4} ferroelectric,” Opt. Commun. **200**, 249–260 (2001). [CrossRef]

*Δk*,

*d*

_{eff}on the polarization of the interacting beams is the possibility two different processes to contribute simultaneously to the strength of the generated SH signal for a given polarization. For example, an extraordinary polarized SH signal is generated simultaneously by the following two parametric processes:

*O*

_{1}

*O*

_{1}-

*E*

_{2}and

*E*

_{1}

*E*

_{1}-

*E*

_{2}. On the other hand, an ordinary SH signal builds up from contributions created via

*E*

_{1A}

*O*

_{1B}-

*O*

_{2}and

*O*

_{1A}

*E*

_{1B}-

*O*

_{2}interactions. Had these processes been taking place in the perfect QPM structures they would naturally have contributed coherently to the total SH signal. In fact, this has been demonstrated in the recent experiment with a QPM grating in LiNbO

_{3}crystal that supported simultaneously

*E*

_{1}

*E*

_{1}-

*E*

_{2}and

*O*

_{1}

*O*

_{1}-

*E*

_{2}interactions [10

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]

*R*is defined as

**B**(expressed by its azimuthal angle

*β*). The polarization angle is measured counterclockwise from zero which corresponds to the extraordinary polarization. Since, in general, the extraordinary SH signal consists of two contributions,

*EE*-

*E*and

*OO*-

*E*, the intensity of the SH signal will depend on whether contributions from both of these processes add coherently or not. It also appears that in the former case the total generated signal depends on the sign of the ratio of the nonlinear coefficients

*d*

_{33}/

*d*

_{32}. Interestingly enough, there is no data available in the literature regarding the signs of those two nonlinear components of the

*χ*

^{(2)}tensor. Therefore, the plots in Fig. 4(a) describe all possible scenarios. The dashed line refers to the mutually incoherent contributions. The solid and dotted plots represent the mutually coherent case but differ in sign of

*d*

_{32}/

*d*

_{33}(positive in the former and negative in the latter cases). It is clear that the character of those plots change significantly depending on whether contributions from different processes add coherently or incoherently. In particular, for the mutually coherent processes and opposite signs of nonlinear coefficients the SH signal vanishes for a particular polarization of the input beam. This behavior is analogous to the one reported recently in the case of the QPM grating in lithium niobate [10

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]

## 4. Results and discussion

**B**is varied (via its azimuthal angle

*β*) while the polarization of the beam

**A**is set to one of the following three states: extraordinary,

*α*=0 (filled squares); mixed, 0°<

*α*<90° (open circles), and ordinary,

*α*=90° (open squares). Figures 5(a–b) and 5(c–d) show the results of both QCSH and TSH experiments, respectively. The lines show the theoretical results in the absence of interference between different contributions to the SH signal. We compare, e.g., the data shown in Fig. 5(a) by filled circles with the data shown in Fig. 4 by a dashed line, which depicts the SH signal emitted by a single beam. We note a very good agreement between theory and experiment; this confirms that disorder in the domain distribution in our crystal causes simultaneous processes to contribute incoherently into the overall signal.

*E*

_{1A}

*O*

_{1B}-

*O*

_{2}or

*O*

_{1A}

*E*

_{1B}-

*O*

_{2}interaction. Ordinary SH can also be observed with a single beam SH generation. The signal reaches its maximum when the input polarization is at 45° with respect to the YZ axes, and vanishes for ordinary or extraordinary polarization [see Fig. 5(b)]. From the definition of the

*R*in Eq. (8) we obtain

*I*

_{ee-e}is the SH signal at

*β*=0°(180°), and

*I*

_{oo-e}is the SH signal at

*β*=90°(270°) for the experiments with a single beam [see Fig. 5(a) and Fig. 5(c)]. Therefore, one can directly find the value of

*R*as a ratio of the intensities of the SH signal taken in two different polarization arrangements. In the QCSH experiment, the best theoretical fit is obtained for

*R*=0.48 [Fig. 5(a,b)], while in the case of TSH experiment the best fit is obtained for

*R*=0.19 [Fig. 5(c,d)]. The value

*R*=0.48 is also used in our theoretical plots in Fig. 4. As we pointed out above, for the TSH experiment with counter-propagating fundamentals

*Δk*

_{oo-e}~

*Δk*

_{ee-e}and, consequently,

*f*(

*Δk*

_{oo-e})/

*f*(

*Δk*

_{ee-e})≈1. Subsequently, we obtain |

*d*

_{32}/

*d*

_{33}|=0.44. This is close to the value of 0.5 obtained in Ref. [13

13. M. Horowitz, A. Bekker, and B. Fischer, “Broadband second-harmonic generation in SrBaNb_{2}O_{6} by spread spectrum phase matching with controllable domain gratings,” Appl. Phys. Lett. **62**, 2619–2621 (1993). [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]

*d*

_{32}/

*d*

_{33}|, one can estimate the mean value

*a*and dispersion

*σ*of the domain distribution. To this end we measure the intensity of the emitted SH in the central part of the emission lines #5 (

*OE*-

*O*process), #8 (

*OO*-

*E*process) and #2 (

*EE*-

*E*process) seen in Fig. 2. From these measurements, we evaluate the ratios:

*f*(

*Δk*

_{oe-o})/

*f*(

*Δk*

_{oo-e})=0.12 and

*f*(

*Δk*

_{ee-e})/

*f*(

*Δk*

_{oo-e})=0.3, and then from Eq. (4) we find

*a*=3.25

*µ*m and

*σ*=1.15

*µ*m. These values are consistent with Refs. [11

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 Nd^{3+}:Sr_{0.6}Ba_{0.4}(NbO_{3})_{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]

## 5. Conclusions

*d*

_{32}/

*d*

_{33}. We have demonstrated that, by measuring the power of the second harmonics in a few different processes, we can determine the statistical properties of the disordered domain distribution such as an average size of the domains and their dispersion.

## Acknowledgments

## References and links

1. | F. Zernike and J. E. Midwinter, |

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 . |

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) |

4. | S. E. Skipetrov, “Disorder is the new order,” Nature (London) |

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. |

6. | X. Vidal and J. Martorell, “Generation of light in media with a random distribution of nonlinear domains,” Phys. Rev. Lett. |

7. | A. R. Tunyagi, M. Ulex, and K. Betzler, “Noncollinear optical frequency doubling in strontium barium niobate,” Phys. Rev. Lett. |

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. |

9. | R. Fischer, D. N. Neshev, S. M. Saltiel, A. A. Sukhorukov, W. Krolikowski, and Yu. S. Kivshar, “Monitoring ultrashort pulses by transverse frequency doubling of counterpropagating pulses in random media,” Appl. Phys. Lett. |

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 |

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 Nd |

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. |

13. | M. Horowitz, A. Bekker, and B. Fischer, “Broadband second-harmonic generation in SrBaNb |

14. | Th. Woike, T. Granzow, U. Dörfler, Ch. Poetsch, M. Wöhlecke, and R. Pankrath, “Refractive Indices of Congruently Melting Sr |

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 . |

16. | Y. Le Grand, D. Rouede, C. Odin, R. Aubry, and S. Mattauch, “Second-harmonic scattering by domains in RbH |

17. | G. Dolino, “Effects of domain shapes on second harmonic scattering in Triglycine Sulfate,” Phys. Rev. B |

18. | C. R. Jeggo and G. D. Boyd, “Nonlinear optical polarizability of the Niobium-Oxygen bond,” J. Appl. Phys. |

**OCIS Codes**

(190.0190) Nonlinear optics : Nonlinear optics

(190.2620) Nonlinear optics : Harmonic generation and mixing

(190.4420) Nonlinear optics : Nonlinear optics, transverse effects in

(190.4720) Nonlinear optics : Optical nonlinearities of condensed matter

(290.0290) Scattering : Scattering

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: October 4, 2007

Revised Manuscript: November 10, 2007

Manuscript Accepted: November 11, 2007

Published: November 15, 2007

**Citation**

Jose Trull, Crina Cojocaru, Robert Fischer, Solomon M. Saltiel, Kestutis Staliunas, Ramon Herrero, Ramon Vilaseca, Dragomir N. Neshev, Wieslaw Krolikowski, and Yuri S. Kivshar, "Second-harmonic parametric scattering in ferroelectric crystals with disordered nonlinear domain structures," Opt. Express **15**, 15868-15877 (2007)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-24-15868

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### References

- F. Zernike and J. E. Midwinter, Applied Nonlinear Optics (Wiley, New York, 1973).
- 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]
- 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, 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- G. Dolino, "Effects of domain shapes on second harmonic scattering in Triglycine Sulfate," Phys. Rev. B 6, 4025-4035 (1972). [CrossRef]
- C. R. Jeggo and G. D. Boyd, "Nonlinear optical polarizability of the Niobium-Oxygen bond," J. Appl. Phys. 41, 2741-2743 (1970). [CrossRef]

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