## High-flux photon-pair source from electrically induced parametric down conversion after second-harmonic generation in single optical superlattice

Optics Express, Vol. 15, Issue 13, pp. 8275-8283 (2007)

http://dx.doi.org/10.1364/OE.15.008275

Acrobat PDF (186 KB)

### Abstract

We present here a possible high-flux photon-pair source constructed by single lithium niobate optical superlattice (OSL) with a combined quasi-periodically and periodically poled structure, which is from the principle of electrically induced parametric down conversion (PDC) after second-harmonic generation (SHG), predicted by the united theory developed in this paper, in which SHG, PDC and electro-optic (EO) effect are comparably treated as two-order nonlinear effects. In the OSL, the e-polarized fundamental frequency photons are first converted to double frequency ones with the same polarization; then the PDC process is triggered by EO effect when the fundamental frequency photons are almost exhausted; finally, the double frequency photons are converted again to a series of two-photon pair of fundamental wave. It is demonstrated that at 100 °C, in a 20.2*mm* long OSL with a 30*V* / *mm* applied electric field, a 100MW/cm^{2}, 1080 nm laser beam can be translated to a flux of high-purity two-photon pairs with a conversion efficiency close to 100%; and for a longer OSL the pump intensity can be further lowered. The device can also act as an ultra-low field electro-optic switch.

© 2007 Optical Society of America

## 1. Introduction

1. A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. **67**, 661 (1991). [CrossRef] [PubMed]

2. C. H. Bennett and S. J. Wiesner, “Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states,” Phys. Rev. Lett. **69**, 2881 (1992). [CrossRef] [PubMed]

3. C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. **70**, 1895 (1993). [CrossRef] [PubMed]

4. M. Zukowski, A. Zeilinger, M. A. Horne, and A. K. Ekert, “Event-ready-detectors Bell experiment via entanglement swapping,” Phys. Rev. Lett. **71**, 4287 (1993). [CrossRef] [PubMed]

5. A. Barenco, D. Deutsch, A. Ekert, and R. Jozsa, “Conditional quantum dynamics and logic gates,” Phys. Rev. Lett. **74**, 4083 (1995). [CrossRef] [PubMed]

6. Y. H. Shih and C. O. Alley, “New type of Einstein-Podolsky-Rosen-Bohm experiment using pairs of light quanta produced by optical parametric down conversion,” Phys. Rev. Lett. **61**, 2921 (1988). [CrossRef] [PubMed]

9. F. De Martini, “Amplification of quantum entanglement,” Phys. Rev. Lett. **81**, 2842 (1998). [CrossRef]

10. X. Li, Q. Pan, J. Jing, J. Zhang, C. Xie, and K. Peng, “Quantum dense coding exploiting a bright Einstein-Podolsky-Rosen beam,” Phys. Rev. Lett. **88**, 047904 (2002). [CrossRef] [PubMed]

11. P. G. Kwiat, E. Waks, A. G. White, I. Appelbaum, and P. H. Eberhard, “Ultrabright source of polarization-entangled photons,” Phys. Rev. A **60**, R773 (1999). [CrossRef]

12. P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. **75**, 4337 (1995). [CrossRef] [PubMed]

13. C. E. Kuklewicz, M. Fiorentino, G. Messin, F. N. C. Wong, and J. H. Shapiro, “High-flux source of polarization-entangled photons from a periodically poled KTiOPO_{4} parametric down-converter,” Phys. Rev. A **69**, 013807 (2004). [CrossRef]

14. M. Pelton, P. Marsden, D. Ljunggren, M. Tengner, A. Karlsson, A. Fragemann, C. Canalias, and F. Laurell, “Bright, single-spatial-mode source of frequency non-degenerate, polarization-entangled photon pairs using periodically poled KTP,” Opt. Exp. **12**, 3573 (2004). [CrossRef]

13. C. E. Kuklewicz, M. Fiorentino, G. Messin, F. N. C. Wong, and J. H. Shapiro, “High-flux source of polarization-entangled photons from a periodically poled KTiOPO_{4} parametric down-converter,” Phys. Rev. A **69**, 013807 (2004). [CrossRef]

16. K. Banaszek, A. B. U’Ren, and I. A. Walmsley, “Generation of correlated photons in controlled spatial modes by downconversion in nonlinear waveguides,” Opt. Lett. **26**, 1367(2001). [CrossRef]

17. J. Jing, J. Zhang, Y. Yan, F. Zhao, C. Xie, and K. Peng, “Experimental demonstration of tripartite entanglement and controlled dense coding for continuous variables,” Phys. Rev. Lett. **90**, 167903 (2003). [CrossRef] [PubMed]

18. A. Arie, G. Rosenman, V. Mahal, A. Skliar, M. Oron, M. Katz, and D. Eger, “Green and ultraviolet quasi-phase-matched second harmonic generation in bulk periodically-poled KTiOPO_{4},” Opt. Commun. **142**, 265 (1997). [CrossRef]

21. I. Yokohama, M. Asobe, A. Yokoo, H. Itoh, and T. Kaino, “All-optical switching by use of cascading of phase-matched sum-frequency generation and difference-frequency generation processes,” J. Opt. Soc. Am. B **14**, 3368 (1997). [CrossRef]

22. L. E. Myers and W. R. Bosenberg, “Periodically poled lithium niobate and quasi-phase-matched optical parametric oscillators,” IEEE J. Quantum Electron. **33**, 1663 (1997). [CrossRef]

23. K. El Hadi, M. Sundheimer, P. Aschieri, P. Baldi, M. P. De Micheli, D. B. Ostrowsky, and F. Laurell, “Quasi-phase-matched parametric interactions in proton-exchanged lithium niobate waveguides,” J. Opt. Soc. Am. B **14**, 3197 (1997). [CrossRef]

24. M. Fujimura, T. Suhara, and H. Nishihara, “Periodically domain-inverted LiNbO_{3} for waveguide auasi-phase-matched nonlinear optic wavelength conversion devices,” Bull. Mater. Sci. **22**, 413 (1999). [CrossRef]

27. C. J. K. Virmani ,Plasma Phys.15, 1039 (1973). [CrossRef]

30. K. Chang, A. Chiang, T. Lin, B. Wong, Y. Chen, and Y. Huang, “Simultaneous wavelength conversion and amplitude modulation in a monolithic periodically-poled lithium niobate,” Opt. Commun. **203**, 163 (2002). [CrossRef]

31. Y. Chen, F. Fan, Y. Lin, Y. Huang, J. Shy, Y. Lan, and Y. Chen, “Simultaneous amplitude modulation and wavelength conversion in an asymmetric-duty-cycle periodically poled lithium niobate,” Opt. Commun. **223**, 417 (2003). [CrossRef]

30. K. Chang, A. Chiang, T. Lin, B. Wong, Y. Chen, and Y. Huang, “Simultaneous wavelength conversion and amplitude modulation in a monolithic periodically-poled lithium niobate,” Opt. Commun. **203**, 163 (2002). [CrossRef]

31. Y. Chen, F. Fan, Y. Lin, Y. Huang, J. Shy, Y. Lan, and Y. Chen, “Simultaneous amplitude modulation and wavelength conversion in an asymmetric-duty-cycle periodically poled lithium niobate,” Opt. Commun. **223**, 417 (2003). [CrossRef]

34. C. Huang, Q. Wang, and Y. Zhu, “Cascaded frequency doubling and electro-optic coupling in a single optical superlattice,” Appl. Phys. B **80**, 741 (2005). [CrossRef]

13. C. E. Kuklewicz, M. Fiorentino, G. Messin, F. N. C. Wong, and J. H. Shapiro, “High-flux source of polarization-entangled photons from a periodically poled KTiOPO_{4} parametric down-converter,” Phys. Rev. A **69**, 013807 (2004). [CrossRef]

16. K. Banaszek, A. B. U’Ren, and I. A. Walmsley, “Generation of correlated photons in controlled spatial modes by downconversion in nonlinear waveguides,” Opt. Lett. **26**, 1367(2001). [CrossRef]

35. S. Tanzilli, H. De Riedmatten, W. Tittel, H. Zbinden, P. Baldi, M. De Micheli, D. B. Ostrowski, and N. Gisin, “Highly efficient photo-pair source using periodically poled lithium niobate waveguide,” Electron. Lett. **37**, 26 (2001). [CrossRef]

35. S. Tanzilli, H. De Riedmatten, W. Tittel, H. Zbinden, P. Baldi, M. De Micheli, D. B. Ostrowski, and N. Gisin, “Highly efficient photo-pair source using periodically poled lithium niobate waveguide,” Electron. Lett. **37**, 26 (2001). [CrossRef]

## 2. The united theory of SHG, PDC and EO effect

36. W. She and W. Lee, “Wave coupling theory of linear electrooptic effect,” Opt. Commun. **195**, 303 (2001). [CrossRef]

37. G. Zheng, H. Wang, and W. She, “Wave coupling theory of quasi-phase-matched linear electro-optic effect,” Opt. Exp. **14**, 5535 (2006). [CrossRef]

34. C. Huang, Q. Wang, and Y. Zhu, “Cascaded frequency doubling and electro-optic coupling in a single optical superlattice,” Appl. Phys. B **80**, 741 (2005). [CrossRef]

*x*-axis and

*z*-axis of the OSL, respectively. And the applied dc electric field

*E*

_{0}is along the

*y*-axis of Section 1 of the OSL; F is a filter, only allowing e-polarized fundamental wave to pass. Section 1 and 2 represent QPPLN and PPLN, respectively.

38. Y. Lu, Z. Wan, Q. Wang, Y. Xi, and N. Ming, “Electro-optic effect of periodically poled optical superlattice LiNbO_{3} and its applications,” Appl. Phys. Lett. **77**, 3719 (2000). [CrossRef]

39. C. Huang, Y. Wang, and Y. Zhu, “Effect of electro-optic modulation on coupled quasi-phase-matched frequency conversion,” Appl. Opt. **44**, 4980 (2005). [CrossRef] [PubMed]

36. W. She and W. Lee, “Wave coupling theory of linear electrooptic effect,” Opt. Commun. **195**, 303 (2001). [CrossRef]

37. G. Zheng, H. Wang, and W. She, “Wave coupling theory of quasi-phase-matched linear electro-optic effect,” Opt. Exp. **14**, 5535 (2006). [CrossRef]

*ω*(

_{i}*i*= 1,2), the total second-order polarization should involve a part describing the EO effect such as

**P**

^{(2)}

_{EO(ωi)}= 2

*ε*

_{0}

*χ*

^{(2)}(

*ω*,0):

_{i}**E**

*(*

_{iy}*x*)

**E**

_{0}exp(

*ik*

_{iy}*x*) + 2

*ε*

_{0}

*χ*

^{(2)}(

*ω*,0):

_{i}**E**

*(*

_{iz}*x*)E

_{0}exp(

*ik*

_{iz}*x*) [36

36. W. She and W. Lee, “Wave coupling theory of linear electrooptic effect,” Opt. Commun. **195**, 303 (2001). [CrossRef]

**P**

^{(2)}

_{SHG}and

**P**

^{(2)}

_{PDC}relative to SHG and PDC[40], where

**E**

_{iy}(

*x*) and

**E**

_{iz}(

*x*) denote two independent amplitude components of the monochromatic light field corresponding to wave vectors

**k**

_{iy}and

**k**

_{iz}(

*y*,

*z*represent the polarizations relative to o-ray and e-ray), respectively. By treating the total second-order polarization as a perturbation, following the way presented by Ref. [36

**195**, 303 (2001). [CrossRef]

37. G. Zheng, H. Wang, and W. She, “Wave coupling theory of quasi-phase-matched linear electro-optic effect,” Opt. Exp. **14**, 5535 (2006). [CrossRef]

*r*

_{32}= 0 and

*d*

_{23},

*d*

_{34}= 0 for LN, the coupling equations for present case (EO effect:

*ω*1

_{z}↔

*ω*1

_{y},

*ω*2

_{z}↔

*ω*2

_{y}; SHG and/or PDC:

*ω*1

_{y}+

*ω*1

_{y}↔

*ω*2

_{y},

*ω*1

_{y}+

*ω*1

_{z}↔

*ω*2

_{y},

*ω*1

_{z}+

*ω*1

_{z}↔

*ω*2

_{y},

*ω*1

_{y}+

*ω*1

_{y}↔

*ω*2

_{z},

*ω*1

_{y}+

*ω*1

_{z}↔

*ω*2

_{z},

*ω*1

_{z}+

*ω*1

_{z}↔

*ω*2

_{z}) can be deduced from Maxwell’s equations as follows:

*E*,

_{jμ}*ω*,

_{jμ}*k*and

_{jμ}*n*(

_{jμ}*j*= 1,2 , referring to the fundamental wave and the second harmonic, respectively;

*μ*=

*y*,

*z*) are the electric fields, the angular frequencies, the wave numbers and the refractive indices, respectively;

*k*

_{0}is the wave number of the fundamental wave in vacuum;

*d*

_{22},

*d*

_{24},

*d*

_{32},

*d*

_{33};

*r*

_{22},

*r*

_{32}and

*r*

_{42}are the double frequency and EO coefficients, respectively;

*c*is the speed of light in vacuum; the asterisk denotes complex conjugation; and

*f*(

*x*) is the structure function that is +1 or -1 for the positive or negative domains of the OSL, respectively. The right side of each equation includes two parts: the bracketed stands for SHG and PDC; and the others refer to EO effect. When the external electric field is absent, the coupling equations (1)–(4) reduce to the familiar wave coupling equations describing SHG or PDC.

## 3. High-flux photon-pair source from electrically induced parametric down conversion after second harmonic generation in single OSL

41. G. Luo, S. Zhu, J. He, Y. Zhu, H. Wang, Z. Liu, C. Zhang, and N. Ming, “Simultaneously efficient blue and red light generations in a periodically poled LiTaO_{3},” Appl. Phys. Lett. **78**, 3006 (2001). [CrossRef]

25. S. Zhu, Y. Zhu, and N. Ming, “Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice,” Science **278**, 843 (1997). [CrossRef]

26. C. Zhang, H. Wei, Y. Zhu, H. Wang, S. Zhu, and N. Ming, “Third-harmonic generation in a general two-component quasi-periodic optical superlattice,” Opt. Lett. **26**, 899 (2001). [CrossRef]

*k*(EO effect) and Δ

_{a}*k*(SHG) in the first section of OSL and one compensation for Δ

_{f}*k*(PDC) in the second section of OSL, respectively. So we can choose a hybrid OSL consisting of a two-component QPPLN (section 1) and a one-component PPLN (section 2). Suppose that a 1080

_{f}*nm*extraordinary wave is used as a pump one and the temperature is at 100°

*c*, then Δ

*k*= 0.4262

_{a}*μm*

^{-1}and |Δ

*k*| = 0.8977

_{f}*μm*

^{-1}. According to Ref. [42

42. Keren Fradkin-Kashi and Ady Arie, “Multiple-wavelength quasi-phase-matched nonlinear interactions,” IEEE J. Quantum Electron. **35**, 1649 (1999). [CrossRef]

*D*' =τ' ∙

*l*+

_{A}*l*;

_{B}*l*and

_{A}*l*are the lengths of the fundamental blocks A and B, respectively. By choosing

_{B}*m*= 1,

*n*= 0 ,

*m*' =1 and

*n*' =1, the parameters τ' and

*D*' can be determined immediately. They are τ' =1.1061 and

*D*' =14.74

*μm*, respectively. Therefore the structure of QPPLN can be determined [42

42. Keren Fradkin-Kashi and Ady Arie, “Multiple-wavelength quasi-phase-matched nonlinear interactions,” IEEE J. Quantum Electron. **35**, 1649 (1999). [CrossRef]

*l*=

_{A}*l*

_{A}^{ +}+

*l*

_{A}^{-}and

*l*=

_{B}*l*

_{B}^{ +}+

*l*

_{B}^{-}. We further choose

*l*=6.00

_{A}*μm*and

*l*

_{A}^{ +}=

*l*

_{B}^{ +}=

*l*= 3.00

*μm*, then

*l*=

_{B}*D*' -τ' ∙

*l*=8.10

_{A}*μm*. Two Fourier coefficients corresponding to

*k*

_{10}and

*k*

_{11}can be determined [39

39. C. Huang, Y. Wang, and Y. Zhu, “Effect of electro-optic modulation on coupled quasi-phase-matched frequency conversion,” Appl. Opt. **44**, 4980 (2005). [CrossRef] [PubMed]

*f*

_{10}=0.1288,

*f*

_{11}= 0.5324, respectively. For the PPLN, the fundamental block A’ is further composed of one positive and one negative ferroelectric domain, whose length is

*D*=

*l*

_{A'}^{ +}+

*l*

_{A'}^{ -}. Then we expand

*f*(

*x*) as a Fourier series such as

*f*(

*x*) = Σ

_{m}

*f*exp(-

_{m}*iG*) +

_{m}x*const*. (

*m*= ±1,±2,±3,⋯), in which the

*f*

_{m}=(2/

*mπ*)sin(

*mπl*

_{A'}

^{ +}/

*D*) ;

*G*=2

_{m}*πm*/

*D*. We choose

*D*= 2

*π*/(-Δ

*k*) , then

_{f}*G*

_{1}=-Δ

*k*and Δ

_{f}*k*can be compensated by

_{f}*G*

_{1}in section 2. Under these conditions,

*D*= 2

*π*/(-Δ

*k*) = 6.99

_{f}*μm*. We further choose

*l*

_{A'}

^{ +}=3.50

*μm*. Then the Fourier coefficient concerned is

*f*

_{1}=0.6366 . Therefore, by ignoring those terms with nonzero mismatches of wave vectors, Eqs. (1)–(4) can be simplified as

*MW*/cm

^{2}for calculation. It is found that a 3.4

*mm*long QPPLN is more suitable. The numerical results reflecting the dependences of normalized intensities of e-polarized pump fundamental wave, e-polarized second harmonic and o-polarized fundamental wave respectively on the length of the crystal and electric field are shown in Fig. 2, in which (A)-(C) corresponds to electric fields 0, 30 and 100V/mm, respectively. In the calculations the Sellmeier equation [43

43. G. J. Edwards and M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. and Quant. Electron. **16**, 373 (1984). [CrossRef]

*d*

_{22}=3.0 ,

*d*

_{24}=-5.0 ,

*d*

_{32}=-5.0 ,

*d*

_{33}= -33 ;

*r*

_{22}= 3.0 ,

*r*

_{32}=0 ,

*r*

_{42}= 28 (in 10

^{-12}

*m*/

*V*) are used.

*k*and Δ

_{a}*k*two processes including SHG and EO effect take place synchronously in the first section of OSL and the PDC process occurs in the second section of OSL after SHG and EO effect [Fig. 2(B)]. In the first section of OSL a large portion of e-polarized fundamental frequency photons are converted to double frequency ones with the same polarization and a very small portion of them are turned into o-polarized fundamental frequency photons by EO effect. At 10.4

_{f}*mm*almost all the e-polarized fundamental frequency photons are converted to the double frequency ones and the remnant ratio is about 1.0987×10

^{-8}; while the o-polarized fundamental wave from EO effect is with a normalized intensity of 3.1692×10

^{-5}. In the first section of OSL there also exists another process: the o-polarized fundamental frequency photons are partially turned, again by EO effect, into a part of the seeds of e-polarized fundamental frequency photons for PDC, which is the key turning

*dE*

_{1z}(

*x*)/

*dx*from <0 to >0 therefore triggering PDC in the second section of OSL. At 20.2

*mm*the double frequency photons are almost fully converted to a series of fundamental two-photon pairs still with e-polarization through PDC. Actually, in the OSL the second harmonic only plays a role of intermedium. When further increasing the electric field, for example,

*E*

_{0}=100

*V*/

*mm*, the EO effect becomes stronger, which might obstruct the generation of pure two-photon pairs of e-polarized fundamental wave, because the e-polarized fundamental seeds for PDC is much more than that at lower electric field. For the process of degenerate PDC described above, the Heisenberg equations of motion are [44]

*d*

*n*̑

_{ω}/

*dt*= 0-2

*dn*ˆ

_{2ω}/

*dt*, or

*d*<

*n*̑

_{ω}>/

*dt*= -2

*d*<

*n*ˆ

_{2ω}>/

*dt*therefore

*n*ˆ

_{2ω}=

*A*ˆ

^{+}

_{2ω}

*A*ˆ

_{2ω},

*n*ˆ

_{ω}=

*A*ˆ

^{+}

_{ω}

*A*ˆ

_{ω}, are the photon number operators of double frequency and fundamental lights, respectively. Besides, we have the frequency relation

*ω*

_{1z}+

*ω*

_{1z}=

*ω*

_{2z}and further the energy relation of photons

35. S. Tanzilli, H. De Riedmatten, W. Tittel, H. Zbinden, P. Baldi, M. De Micheli, D. B. Ostrowski, and N. Gisin, “Highly efficient photo-pair source using periodically poled lithium niobate waveguide,” Electron. Lett. **37**, 26 (2001). [CrossRef]

_{2}cooled germanium avalanche photodiodes (Ge-APDs) operating in Geiger mode for detecting [35

**37**, 26 (2001). [CrossRef]

45. W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, “Violation of Bell inequalities by photons more than 10 km apart, ” Phys. Rev. Lett. **81**, 3563 (1998). [CrossRef]

*mm*OSL, the intensity of pump can be as low as 20

*MW*/cm

^{2}with an external electric field of 30

*V*/

*mm*. One can see in fact that the device can also act as an ultra-low field electro-optic switch, which requires much lower field (~10

*V*/

*mm*) than that of traditional one with half-wave field (~10

^{2}-10

^{3}

*V*/

*mm*). The second harmonic also only plays a role of intermedium in the device.

## 4. Conclusion

*mm*long OSL with appropriate structure and a 30

*V*/

*mm*applied electric field, a 100MW/cm

^{2}, 1080 nm laser beam can be translated to a flux of high-purity two-photon pairs with a conversion efficiency close to 100% ; and for a longer OSL the pump intensity can be further lowered. The device can also act as an ultra-low field electro-optic switch, which requires much lower field (~10

*V*/

*mm*) than that of traditional one with half-wave field (~10

^{2}-10

^{3}

*V*/

*mm*) [38

38. Y. Lu, Z. Wan, Q. Wang, Y. Xi, and N. Ming, “Electro-optic effect of periodically poled optical superlattice LiNbO_{3} and its applications,” Appl. Phys. Lett. **77**, 3719 (2000). [CrossRef]

46. Y. H. Chen and Y. C. Huang, “Actively Q-switched Nd:YVO_{4} laser using an electro-optic periodically poled lithium niobate crystal as a laser Q-switch,” Opt. Lett. **28**, 1460 (2003). [CrossRef] [PubMed]

47. K. S. Abedin, T. Tsuritani, M. Sato, H. Ito, K. Shimamura, and T. Fukuda, “Integrated electro-optic Q switching in a domain-inverted Nd:LiTaO_{3},” Opt. Lett. **20**, 1985 (1995). [CrossRef] [PubMed]

## Acknowledgments

## References and links

1. | A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. |

2. | C. H. Bennett and S. J. Wiesner, “Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states,” Phys. Rev. Lett. |

3. | C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. |

4. | M. Zukowski, A. Zeilinger, M. A. Horne, and A. K. Ekert, “Event-ready-detectors Bell experiment via entanglement swapping,” Phys. Rev. Lett. |

5. | A. Barenco, D. Deutsch, A. Ekert, and R. Jozsa, “Conditional quantum dynamics and logic gates,” Phys. Rev. Lett. |

6. | Y. H. Shih and C. O. Alley, “New type of Einstein-Podolsky-Rosen-Bohm experiment using pairs of light quanta produced by optical parametric down conversion,” Phys. Rev. Lett. |

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14. | M. Pelton, P. Marsden, D. Ljunggren, M. Tengner, A. Karlsson, A. Fragemann, C. Canalias, and F. Laurell, “Bright, single-spatial-mode source of frequency non-degenerate, polarization-entangled photon pairs using periodically poled KTP,” Opt. Exp. |

15. | M. Fiorentino, G. Messin, C. E. Kuklewicz, F. N. C. Wong, and J. H. Shapiro, “Generation of ultrabright tunable polarization entanglement without spatial, spectral, or temporal constraints,” Phys. Rev. A |

16. | K. Banaszek, A. B. U’Ren, and I. A. Walmsley, “Generation of correlated photons in controlled spatial modes by downconversion in nonlinear waveguides,” Opt. Lett. |

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18. | A. Arie, G. Rosenman, V. Mahal, A. Skliar, M. Oron, M. Katz, and D. Eger, “Green and ultraviolet quasi-phase-matched second harmonic generation in bulk periodically-poled KTiOPO |

19. | G. D. Miller, R. G. Batchko, W. M. Tulloch, D. R. Weise, M. M. Fejer, and R. L. Byer, “42%-efficient single-pass cw second-harmonic generation in periodically poled lithium niobate,” Opt. Lett. |

20. | S. Wang, V. Pasiskevicius, F. Laurell, and H. Karlsson, “Ultraviolet generation by first-order frequency doubling in periodically poled KTiOPO |

21. | I. Yokohama, M. Asobe, A. Yokoo, H. Itoh, and T. Kaino, “All-optical switching by use of cascading of phase-matched sum-frequency generation and difference-frequency generation processes,” J. Opt. Soc. Am. B |

22. | L. E. Myers and W. R. Bosenberg, “Periodically poled lithium niobate and quasi-phase-matched optical parametric oscillators,” IEEE J. Quantum Electron. |

23. | K. El Hadi, M. Sundheimer, P. Aschieri, P. Baldi, M. P. De Micheli, D. B. Ostrowsky, and F. Laurell, “Quasi-phase-matched parametric interactions in proton-exchanged lithium niobate waveguides,” J. Opt. Soc. Am. B |

24. | M. Fujimura, T. Suhara, and H. Nishihara, “Periodically domain-inverted LiNbO |

25. | S. Zhu, Y. Zhu, and N. Ming, “Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice,” Science |

26. | C. Zhang, H. Wei, Y. Zhu, H. Wang, S. Zhu, and N. Ming, “Third-harmonic generation in a general two-component quasi-periodic optical superlattice,” Opt. Lett. |

27. | C. J. K. Virmani ,Plasma Phys.15, 1039 (1973). [CrossRef] |

28. | G. Blau, M. Cairone, P. A. Chollet, and F. Kajzar, “Electro-optic modulation and second-harmonic generation through grating-induced resonant excitation of guided modes,” Proc. SPIE |

29. | N. O’Brien, M. Missey, P. Powers, V. ominic, and K. L. Schepler, “Electro-optical spectral tuning in a continuous-wave, asymmetric-duty-cycle, periodically poled LiNbO |

30. | K. Chang, A. Chiang, T. Lin, B. Wong, Y. Chen, and Y. Huang, “Simultaneous wavelength conversion and amplitude modulation in a monolithic periodically-poled lithium niobate,” Opt. Commun. |

31. | Y. Chen, F. Fan, Y. Lin, Y. Huang, J. Shy, Y. Lan, and Y. Chen, “Simultaneous amplitude modulation and wavelength conversion in an asymmetric-duty-cycle periodically poled lithium niobate,” Opt. Commun. |

32. | F. Xu, J. Liao, X. Zhang, J. He, H. Wang, and N. Ming, “Complete conversion of sum-frequency generation enhanced by controllable linear gratings induced by an electro-optic effect in a periodic optical superlattice,” Phys. Rev. A |

33. | F. Xu, J. Liao, C. Guo, J. He, H. Wang, S. Zhu, Z. Wang, Y. Zhu, and N. Ming, “Highly efficient direct third-harmonic generation based on control of the electro-optic effect in quasi-periodic optical superlattices,” Opt. Lett. |

34. | C. Huang, Q. Wang, and Y. Zhu, “Cascaded frequency doubling and electro-optic coupling in a single optical superlattice,” Appl. Phys. B |

35. | S. Tanzilli, H. De Riedmatten, W. Tittel, H. Zbinden, P. Baldi, M. De Micheli, D. B. Ostrowski, and N. Gisin, “Highly efficient photo-pair source using periodically poled lithium niobate waveguide,” Electron. Lett. |

36. | W. She and W. Lee, “Wave coupling theory of linear electrooptic effect,” Opt. Commun. |

37. | G. Zheng, H. Wang, and W. She, “Wave coupling theory of quasi-phase-matched linear electro-optic effect,” Opt. Exp. |

38. | Y. Lu, Z. Wan, Q. Wang, Y. Xi, and N. Ming, “Electro-optic effect of periodically poled optical superlattice LiNbO |

39. | C. Huang, Y. Wang, and Y. Zhu, “Effect of electro-optic modulation on coupled quasi-phase-matched frequency conversion,” Appl. Opt. |

40. | A. Yariv, |

41. | G. Luo, S. Zhu, J. He, Y. Zhu, H. Wang, Z. Liu, C. Zhang, and N. Ming, “Simultaneously efficient blue and red light generations in a periodically poled LiTaO |

42. | Keren Fradkin-Kashi and Ady Arie, “Multiple-wavelength quasi-phase-matched nonlinear interactions,” IEEE J. Quantum Electron. |

43. | G. J. Edwards and M. Lawrence, “A temperature-dependent dispersion equation for congruently grown lithium niobate,” Opt. and Quant. Electron. |

44. | L. Mandel and E. Wolf, |

45. | W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, “Violation of Bell inequalities by photons more than 10 km apart, ” Phys. Rev. Lett. |

46. | Y. H. Chen and Y. C. Huang, “Actively Q-switched Nd:YVO |

47. | K. S. Abedin, T. Tsuritani, M. Sato, H. Ito, K. Shimamura, and T. Fukuda, “Integrated electro-optic Q switching in a domain-inverted Nd:LiTaO |

**OCIS Codes**

(190.2620) Nonlinear optics : Harmonic generation and mixing

(190.4410) Nonlinear optics : Nonlinear optics, parametric processes

(270.0270) Quantum optics : Quantum optics

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: April 19, 2007

Revised Manuscript: June 1, 2007

Manuscript Accepted: June 1, 2007

Published: June 18, 2007

**Citation**

Dong Huang and Weilong She, "High-flux photon-pair source from electrically induced parametric down conversion after second-harmonic generation in single optical superlattice," Opt. Express **15**, 8275-8283 (2007)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-13-8275

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