The biaxial nonlinear crystal BiB_{3}O_{6} as a polarization entangled photon source using non-collinear type-II parametric down-conversion |
Optics Express, Vol. 19, Issue 21, pp. 20420-20434 (2011)
http://dx.doi.org/10.1364/OE.19.020420
Acrobat PDF (1893 KB)
Abstract
We describe the full characterization of the biaxial nonlinear crystal BiB_{3}O_{6} (BiBO) as a polarization entangled photon source using non-collinear type-II parametric down-conversion. We consider the relevant parameters for crystal design, such as cutting angles, polarization of the photons, effective nonlinearity, spatial and temporal walk-offs, crystal thickness and the effect of the pump laser bandwidth. Experimental results showing entanglement generation with high rates and a comparison to the well investigated β-BaB_{2}O_{4} (BBO) crystal are presented as well. Changing the down-conversion crystal of a polarization entangled photon source from BBO to BiBO enhances the generation rate as if the pump power was increased by 2.5 times. Such an improvement is currently required for the generation of multiphoton entangled states.
© 2011 OSA
1. Introduction
1. R. Ghosh and L. Mandel, “Observation of nonclassical effects in the interference of two photons,” Phys. Rev. Lett. 59, 1903–1905 (1987). [CrossRef] [PubMed]
3. 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, 4337–4341 (1995). [CrossRef] [PubMed]
4. P. Becker, “Borate materials in nonlinear optics,” Adv. Mater. 10, 979–992 (1998). [CrossRef]
5. R. C. Eckardt, H. Masuda, Y. X. Fan, and R. L. Byer, “Absolute and relative nonlinear optical coefficients of KDP, KD^{*}P, BaB_{2}O_{4}, LiIO_{3}, MgO:LiNbO_{3} and KTP measured by phase-matched second-harmonic generation,” IEEE J. Quantum Electron. 26, 922–933 (1990). [CrossRef]
6. D. Bouwmeester, J. -W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature (London) 390, 575–579 (1997). [CrossRef]
8. J. -W. Pan, M. Daniell, S. Gasparoni, G. Weihs, and A. Zeilinger, “Experimental demonstration of four-photon entanglement and high-fidelity teleportation,” Phys. Rev. Lett. 86, 4435–4438 (2001). [CrossRef] [PubMed]
9. D. Bouwmeester, J. -W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, “Observation of three-photon Greenberger-Horne-Zeilinger entanglement,” Phys. Rev. Lett. 82, 1345–1349 (1999). [CrossRef]
11. A. Halevy, E. Megidish, T. Shacahm, L. Dovrat, and H. S. Eisenberg, “Projection of two biphoton qutrits onto a maximally entangled state,” Phys. Rev. Lett. 106, 130502 (2011). [CrossRef] [PubMed]
12. C. -Y. Lu, X. -Q. Zhou, O. Gühne, W. -B. Gao, J. Zhang, Z. -S. Yuan, A. Goebel, T. Yang, and J. -W. Pan, “Experimental entanglement of six photons in graph states,” Nature Physics 3, 91–95 (2007). [CrossRef]
15. S. Barz, G. Cronenberg, A. Zeilinger, and P. Walther, “Heralded generation of entangled photon pairs,” Nature Photonics 4, 553–556 (2010). [CrossRef]
6. D. Bouwmeester, J. -W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature (London) 390, 575–579 (1997). [CrossRef]
12. C. -Y. Lu, X. -Q. Zhou, O. Gühne, W. -B. Gao, J. Zhang, Z. -S. Yuan, A. Goebel, T. Yang, and J. -W. Pan, “Experimental entanglement of six photons in graph states,” Nature Physics 3, 91–95 (2007). [CrossRef]
17. R. Krischek, W. Wieczorek, A. Ozawa, N. Kiesel, P. Michelberger, T. Udem, and H. Weinfurter, “Ultraviolet enhancement cavity for ultrafast nonlinear optics and high-rate multiphoton entanglement experiments,” Nature Photonics 4, 170–173 (2010). [CrossRef]
18. H. Hellwig, J. Liebertz, and L. Bohatý, “Exceptional large nonlinear coefficients in the monoclinic Bismuth Borate BiB_{3}O_{6},” Solid State Commun. 109, 249–251 (1999). [CrossRef]
19. H. Hellwig, J. Liebertz, and L. Bohatý, “Linear optical properties of the monoclinic bismuth BiB_{3}O_{6},” Appl. Phys. 88, 240–244 (2000). [CrossRef]
20. V. Petrov, M. Ghotbi, O. Kokabee, A. Esteban-Martin, F. Noack, A. Gaydardzhiev, I. Nikolov, P. Tzankov, I. Buchvarov, K. Miyata, A. Majchrowski, I. V. Kityk, F. Rotermund, E. Michalski, and M. Ebrahim-Zadeh, “Femtosecond nonlinear frequency conversion based on BiB_{3}O_{6},” Laser & Photon. Rev. 4, 1–46 (2009). [PubMed]
21. B. L. Higgins, D. W. Berry, S. D. Bartlett, H. M. Wiseman, and G. J. Pryde, “Entanglement-free Heisenberg-limited phase estimation,” Nature 450, 393–396 (2007). [CrossRef] [PubMed]
22. R. Rangarajan, M. Goggin, and P. Kwiat, “Optimizing type-I polarization-entangled photons,” Opt. Express 77, 18920–18933 (2009). [CrossRef]
18. H. Hellwig, J. Liebertz, and L. Bohatý, “Exceptional large nonlinear coefficients in the monoclinic Bismuth Borate BiB_{3}O_{6},” Solid State Commun. 109, 249–251 (1999). [CrossRef]
2. Investigation of PDC parameters in BiBO
2.1. Crystal design
2.2. Phase-matching calculation
19. H. Hellwig, J. Liebertz, and L. Bohatý, “Linear optical properties of the monoclinic bismuth BiB_{3}O_{6},” Appl. Phys. 88, 240–244 (2000). [CrossRef]
26. M. V. Hobden, “Phase-matched second-harmonic generation in biaxial crystals,” J. Appl. Phys. 38, 4365–4372 (1967). [CrossRef]
27. N. Boeuf, D. Branning, I. Chaperot, E. Dauler, S. Guérin, G. Jaeger, A. Muller, and A. Migdall, “Calculating characteristics of noncollinear phase matching in uniaxial and biaxial crystals,” Opt. Eng. 39, 1016–1024 (2000). [CrossRef]
26. M. V. Hobden, “Phase-matched second-harmonic generation in biaxial crystals,” J. Appl. Phys. 38, 4365–4372 (1967). [CrossRef]
2.3. The photons’ polarization
19. H. Hellwig, J. Liebertz, and L. Bohatý, “Linear optical properties of the monoclinic bismuth BiB_{3}O_{6},” Appl. Phys. 88, 240–244 (2000). [CrossRef]
27. N. Boeuf, D. Branning, I. Chaperot, E. Dauler, S. Guérin, G. Jaeger, A. Muller, and A. Migdall, “Calculating characteristics of noncollinear phase matching in uniaxial and biaxial crystals,” Opt. Eng. 39, 1016–1024 (2000). [CrossRef]
2.4. The effective second order nonlinearity
5. R. C. Eckardt, H. Masuda, Y. X. Fan, and R. L. Byer, “Absolute and relative nonlinear optical coefficients of KDP, KD^{*}P, BaB_{2}O_{4}, LiIO_{3}, MgO:LiNbO_{3} and KTP measured by phase-matched second-harmonic generation,” IEEE J. Quantum Electron. 26, 922–933 (1990). [CrossRef]
30. P. Tzankov and V. Petrov, “Effective second-order nonlinearity in acentric optical crystals with low symmetry,” Appl. Opt. 44, 6971–6985 (2005). [CrossRef] [PubMed]
30. P. Tzankov and V. Petrov, “Effective second-order nonlinearity in acentric optical crystals with low symmetry,” Appl. Opt. 44, 6971–6985 (2005). [CrossRef] [PubMed]
30. P. Tzankov and V. Petrov, “Effective second-order nonlinearity in acentric optical crystals with low symmetry,” Appl. Opt. 44, 6971–6985 (2005). [CrossRef] [PubMed]
31. M. Ghotbi and M. Ebrahim-Zadeh, “Optical second harmonic generation properties of BiB_{3}O_{6},” Opt. Express 12, 6002–6019 (2004). [CrossRef] [PubMed]
2.5. The spatial walk-off angle
3. 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, 4337–4341 (1995). [CrossRef] [PubMed]
2.6. The temporal walk-off
2.7. Pump bandwidth and the entanglement quality
35. W. P. Grice and I. A. Walmsley, “Spectral information and distinguishability in type-II down-conversion with a broadband pump,” Phys. Rev. A 56, 1627–1634 (1997). [CrossRef]
34. Y. -H. Kim, S. P. Kulik, M. V. Chekhova, W. P. Grice, and Y. Shih, “Experimental entanglement concentration and universal Bell-state synthesizer,” Phys. Rev. A 67, 010301(R) (2003). [CrossRef]
3. Entanglement measurements
3.1. The experimental setup
36. C. Kurtsiefer, M. Oberparleiter, and H. Weinfurter, “High-efficiency entangled photon pair collection in type-II parametric fluorescence,” Phys. Rev. A 62, 023802 (2001). [CrossRef]
3.2. Experimental results
3. 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, 4337–4341 (1995). [CrossRef] [PubMed]
34. Y. -H. Kim, S. P. Kulik, M. V. Chekhova, W. P. Grice, and Y. Shih, “Experimental entanglement concentration and universal Bell-state synthesizer,” Phys. Rev. A 67, 010301(R) (2003). [CrossRef]
3. 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, 4337–4341 (1995). [CrossRef] [PubMed]
37. D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A 64, 052312 (2001). [CrossRef]
34. Y. -H. Kim, S. P. Kulik, M. V. Chekhova, W. P. Grice, and Y. Shih, “Experimental entanglement concentration and universal Bell-state synthesizer,” Phys. Rev. A 67, 010301(R) (2003). [CrossRef]
4. Conclusions
Acknowledgments
References and links
1. | R. Ghosh and L. Mandel, “Observation of nonclassical effects in the interference of two photons,” Phys. Rev. Lett. 59, 1903–1905 (1987). [CrossRef] [PubMed] |
2. | R. W. Boyd, Nonlinear Optics, 2nd edition (Academic Press, 2003). |
3. | 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, 4337–4341 (1995). [CrossRef] [PubMed] |
4. | P. Becker, “Borate materials in nonlinear optics,” Adv. Mater. 10, 979–992 (1998). [CrossRef] |
5. | R. C. Eckardt, H. Masuda, Y. X. Fan, and R. L. Byer, “Absolute and relative nonlinear optical coefficients of KDP, KD^{*}P, BaB_{2}O_{4}, LiIO_{3}, MgO:LiNbO_{3} and KTP measured by phase-matched second-harmonic generation,” IEEE J. Quantum Electron. 26, 922–933 (1990). [CrossRef] |
6. | D. Bouwmeester, J. -W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature (London) 390, 575–579 (1997). [CrossRef] |
7. | J. -W. Pan, D. Bouwmeester, H. Weinfurter, and A. Zeilinger, “Experimental entanglement swapping: entangling photons that never interacted,” Phys. Rev. Lett. 80, 3891–3894 (1998). [CrossRef] |
8. | J. -W. Pan, M. Daniell, S. Gasparoni, G. Weihs, and A. Zeilinger, “Experimental demonstration of four-photon entanglement and high-fidelity teleportation,” Phys. Rev. Lett. 86, 4435–4438 (2001). [CrossRef] [PubMed] |
9. | D. Bouwmeester, J. -W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, “Observation of three-photon Greenberger-Horne-Zeilinger entanglement,” Phys. Rev. Lett. 82, 1345–1349 (1999). [CrossRef] |
10. | A. Lamas-Linares, J. C. Howell, and D. Bouwmeester, “Stimulated emission of polarization-entangled photons,” Nature (London) 412, 887–890 (2001). [CrossRef] |
11. | A. Halevy, E. Megidish, T. Shacahm, L. Dovrat, and H. S. Eisenberg, “Projection of two biphoton qutrits onto a maximally entangled state,” Phys. Rev. Lett. 106, 130502 (2011). [CrossRef] [PubMed] |
12. | C. -Y. Lu, X. -Q. Zhou, O. Gühne, W. -B. Gao, J. Zhang, Z. -S. Yuan, A. Goebel, T. Yang, and J. -W. Pan, “Experimental entanglement of six photons in graph states,” Nature Physics 3, 91–95 (2007). [CrossRef] |
13. | M. Rådmark, M. Wieśniak, M. Żukowski, and M. Bourennane, “Experimental filtering of two-, four-, and six-photon singlets from a single parametric down-conversion source,” Phys. Rev. A 80, 040302(R) (2009). [CrossRef] |
14. | C. Wagenknecht, C. -M. Li, A. Reingruber, X. -H. Bao, A. Goebe, Y. -A. Chen, Q. Zhang, K. Chen, and J. -W. Pan, “Experimental demonstration of a heralded entanglement source,” Nature Photonics 4, 549–552 (2010). [CrossRef] |
15. | S. Barz, G. Cronenberg, A. Zeilinger, and P. Walther, “Heralded generation of entangled photon pairs,” Nature Photonics 4, 553–556 (2010). [CrossRef] |
16. | X. -C. Yao, T. -X. Wang, P. Xu, H. Lu, G. -S. Pan, X. -H. Bao, C. -Z. Peng, C. -Y. Lu, Y. -A. Chen, and J. -W. Pan, “Observation of eight-photon entanglement,” arXiv:1105.6318 (2011). |
17. | R. Krischek, W. Wieczorek, A. Ozawa, N. Kiesel, P. Michelberger, T. Udem, and H. Weinfurter, “Ultraviolet enhancement cavity for ultrafast nonlinear optics and high-rate multiphoton entanglement experiments,” Nature Photonics 4, 170–173 (2010). [CrossRef] |
18. | H. Hellwig, J. Liebertz, and L. Bohatý, “Exceptional large nonlinear coefficients in the monoclinic Bismuth Borate BiB_{3}O_{6},” Solid State Commun. 109, 249–251 (1999). [CrossRef] |
19. | H. Hellwig, J. Liebertz, and L. Bohatý, “Linear optical properties of the monoclinic bismuth BiB_{3}O_{6},” Appl. Phys. 88, 240–244 (2000). [CrossRef] |
20. | V. Petrov, M. Ghotbi, O. Kokabee, A. Esteban-Martin, F. Noack, A. Gaydardzhiev, I. Nikolov, P. Tzankov, I. Buchvarov, K. Miyata, A. Majchrowski, I. V. Kityk, F. Rotermund, E. Michalski, and M. Ebrahim-Zadeh, “Femtosecond nonlinear frequency conversion based on BiB_{3}O_{6},” Laser & Photon. Rev. 4, 1–46 (2009). [PubMed] |
21. | B. L. Higgins, D. W. Berry, S. D. Bartlett, H. M. Wiseman, and G. J. Pryde, “Entanglement-free Heisenberg-limited phase estimation,” Nature 450, 393–396 (2007). [CrossRef] [PubMed] |
22. | R. Rangarajan, M. Goggin, and P. Kwiat, “Optimizing type-I polarization-entangled photons,” Opt. Express 77, 18920–18933 (2009). [CrossRef] |
23. | R. Fröhlich, L. Bohatý, and J. Liebertz, “Die Kristallstruktur von Wismutborat, BiB_{3}O_{6},” Acta Crystallogr. Sec. C 40, 343–344 (1985). [CrossRef] |
24. | IEEE Standard Boards and American National Standard Institute, IEEE Standard on Piezoelectricity 176-1987, (American National Standard Institute, 1987). |
25. | S. Haussühl, L. Bohatý, and P. Becker, “Piezoelectric and elastic properties of the nonlinear optical material bismuth triborate, BiB_{3}O_{6},” Appl. Phys. A 82, 495–502 (2006). [CrossRef] |
26. | M. V. Hobden, “Phase-matched second-harmonic generation in biaxial crystals,” J. Appl. Phys. 38, 4365–4372 (1967). [CrossRef] |
27. | N. Boeuf, D. Branning, I. Chaperot, E. Dauler, S. Guérin, G. Jaeger, A. Muller, and A. Migdall, “Calculating characteristics of noncollinear phase matching in uniaxial and biaxial crystals,” Opt. Eng. 39, 1016–1024 (2000). [CrossRef] |
28. | A. Yariv and P. Yeh, Optical Waves in Crystals (John Wiley & Sons, 2003). |
29. | F. Zernike and J. E. Midwinter, Applied Nonlinear Optics (John Wiley & Sons, 1973). |
30. | P. Tzankov and V. Petrov, “Effective second-order nonlinearity in acentric optical crystals with low symmetry,” Appl. Opt. 44, 6971–6985 (2005). [CrossRef] [PubMed] |
31. | M. Ghotbi and M. Ebrahim-Zadeh, “Optical second harmonic generation properties of BiB_{3}O_{6},” Opt. Express 12, 6002–6019 (2004). [CrossRef] [PubMed] |
32. | M. Born and E. Wolf, Principles of Optics, 6th edition (Pergamon Press, 1993). |
33. | P. Butcher and D. Cotter, The Elements of Nonlinear Optics (Cambridge University Press, 1990). |
34. | Y. -H. Kim, S. P. Kulik, M. V. Chekhova, W. P. Grice, and Y. Shih, “Experimental entanglement concentration and universal Bell-state synthesizer,” Phys. Rev. A 67, 010301(R) (2003). [CrossRef] |
35. | W. P. Grice and I. A. Walmsley, “Spectral information and distinguishability in type-II down-conversion with a broadband pump,” Phys. Rev. A 56, 1627–1634 (1997). [CrossRef] |
36. | C. Kurtsiefer, M. Oberparleiter, and H. Weinfurter, “High-efficiency entangled photon pair collection in type-II parametric fluorescence,” Phys. Rev. A 62, 023802 (2001). [CrossRef] |
37. | D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A 64, 052312 (2001). [CrossRef] |
38. | J. B. Altepeter, E. R. Jeffrey, and P. G. Kwiat, “Photonic state tomography,” Adv. At. Mol. Opt. Phys. 52, 105–159 (2005). |
OCIS Codes
(190.4400) Nonlinear optics : Nonlinear optics, materials
(190.4410) Nonlinear optics : Nonlinear optics, parametric processes
(260.1180) Physical optics : Crystal optics
(270.0270) Quantum optics : Quantum optics
(270.5585) Quantum optics : Quantum information and processing
ToC Category:
Nonlinear Optics
History
Original Manuscript: June 28, 2011
Revised Manuscript: September 11, 2011
Manuscript Accepted: September 12, 2011
Published: October 3, 2011
Citation
A. Halevy, E. Megidish, L. Dovrat, H.S. Eisenberg, P. Becker, and L. Bohatý, "The biaxial nonlinear crystal BiB_{3}O_{6} as a polarization entangled photon source using non-collinear type-II parametric down-conversion," Opt. Express 19, 20420-20434 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-21-20420
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References
- R. Ghosh and L. Mandel, “Observation of nonclassical effects in the interference of two photons,” Phys. Rev. Lett.59, 1903–1905 (1987). [CrossRef] [PubMed]
- R. W. Boyd, Nonlinear Optics, 2nd edition (Academic Press, 2003).
- 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, 4337–4341 (1995). [CrossRef] [PubMed]
- P. Becker, “Borate materials in nonlinear optics,” Adv. Mater.10, 979–992 (1998). [CrossRef]
- R. C. Eckardt, H. Masuda, Y. X. Fan, and R. L. Byer, “Absolute and relative nonlinear optical coefficients of KDP, KD*P, BaB2O4, LiIO3, MgO:LiNbO3 and KTP measured by phase-matched second-harmonic generation,” IEEE J. Quantum Electron.26, 922–933 (1990). [CrossRef]
- D. Bouwmeester, J. -W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature (London)390, 575–579 (1997). [CrossRef]
- J. -W. Pan, D. Bouwmeester, H. Weinfurter, and A. Zeilinger, “Experimental entanglement swapping: entangling photons that never interacted,” Phys. Rev. Lett.80, 3891–3894 (1998). [CrossRef]
- J. -W. Pan, M. Daniell, S. Gasparoni, G. Weihs, and A. Zeilinger, “Experimental demonstration of four-photon entanglement and high-fidelity teleportation,” Phys. Rev. Lett.86, 4435–4438 (2001). [CrossRef] [PubMed]
- D. Bouwmeester, J. -W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, “Observation of three-photon Greenberger-Horne-Zeilinger entanglement,” Phys. Rev. Lett.82, 1345–1349 (1999). [CrossRef]
- A. Lamas-Linares, J. C. Howell, and D. Bouwmeester, “Stimulated emission of polarization-entangled photons,” Nature (London)412, 887–890 (2001). [CrossRef]
- A. Halevy, E. Megidish, T. Shacahm, L. Dovrat, and H. S. Eisenberg, “Projection of two biphoton qutrits onto a maximally entangled state,” Phys. Rev. Lett.106, 130502 (2011). [CrossRef] [PubMed]
- C. -Y. Lu, X. -Q. Zhou, O. Gühne, W. -B. Gao, J. Zhang, Z. -S. Yuan, A. Goebel, T. Yang, and J. -W. Pan, “Experimental entanglement of six photons in graph states,” Nature Physics3, 91–95 (2007). [CrossRef]
- M. Rådmark, M. Wieśniak, M. Żukowski, and M. Bourennane, “Experimental filtering of two-, four-, and six-photon singlets from a single parametric down-conversion source,” Phys. Rev. A80, 040302(R) (2009). [CrossRef]
- C. Wagenknecht, C. -M. Li, A. Reingruber, X. -H. Bao, A. Goebe, Y. -A. Chen, Q. Zhang, K. Chen, and J. -W. Pan, “Experimental demonstration of a heralded entanglement source,” Nature Photonics4, 549–552 (2010). [CrossRef]
- S. Barz, G. Cronenberg, A. Zeilinger, and P. Walther, “Heralded generation of entangled photon pairs,” Nature Photonics4, 553–556 (2010). [CrossRef]
- X. -C. Yao, T. -X. Wang, P. Xu, H. Lu, G. -S. Pan, X. -H. Bao, C. -Z. Peng, C. -Y. Lu, Y. -A. Chen, and J. -W. Pan, “Observation of eight-photon entanglement,” arXiv:1105.6318 (2011).
- R. Krischek, W. Wieczorek, A. Ozawa, N. Kiesel, P. Michelberger, T. Udem, and H. Weinfurter, “Ultraviolet enhancement cavity for ultrafast nonlinear optics and high-rate multiphoton entanglement experiments,” Nature Photonics4, 170–173 (2010). [CrossRef]
- H. Hellwig, J. Liebertz, and L. Bohatý, “Exceptional large nonlinear coefficients in the monoclinic Bismuth Borate BiB3O6,” Solid State Commun.109, 249–251 (1999). [CrossRef]
- H. Hellwig, J. Liebertz, and L. Bohatý, “Linear optical properties of the monoclinic bismuth BiB3O6,” Appl. Phys.88, 240–244 (2000). [CrossRef]
- V. Petrov, M. Ghotbi, O. Kokabee, A. Esteban-Martin, F. Noack, A. Gaydardzhiev, I. Nikolov, P. Tzankov, I. Buchvarov, K. Miyata, A. Majchrowski, I. V. Kityk, F. Rotermund, E. Michalski, and M. Ebrahim-Zadeh, “Femtosecond nonlinear frequency conversion based on BiB3O6,” Laser & Photon. Rev.4, 1–46 (2009). [PubMed]
- B. L. Higgins, D. W. Berry, S. D. Bartlett, H. M. Wiseman, and G. J. Pryde, “Entanglement-free Heisenberg-limited phase estimation,” Nature450, 393–396 (2007). [CrossRef] [PubMed]
- R. Rangarajan, M. Goggin, and P. Kwiat, “Optimizing type-I polarization-entangled photons,” Opt. Express77, 18920–18933 (2009). [CrossRef]
- R. Fröhlich, L. Bohatý, and J. Liebertz, “Die Kristallstruktur von Wismutborat, BiB3O6,” Acta Crystallogr. Sec. C40, 343–344 (1985). [CrossRef]
- IEEE Standard Boards and American National Standard Institute, IEEE Standard on Piezoelectricity 176-1987, (American National Standard Institute, 1987).
- S. Haussühl, L. Bohatý, and P. Becker, “Piezoelectric and elastic properties of the nonlinear optical material bismuth triborate, BiB3O6,” Appl. Phys. A82, 495–502 (2006). [CrossRef]
- M. V. Hobden, “Phase-matched second-harmonic generation in biaxial crystals,” J. Appl. Phys.38, 4365–4372 (1967). [CrossRef]
- N. Boeuf, D. Branning, I. Chaperot, E. Dauler, S. Guérin, G. Jaeger, A. Muller, and A. Migdall, “Calculating characteristics of noncollinear phase matching in uniaxial and biaxial crystals,” Opt. Eng.39, 1016–1024 (2000). [CrossRef]
- A. Yariv and P. Yeh, Optical Waves in Crystals (John Wiley & Sons, 2003).
- F. Zernike and J. E. Midwinter, Applied Nonlinear Optics (John Wiley & Sons, 1973).
- P. Tzankov and V. Petrov, “Effective second-order nonlinearity in acentric optical crystals with low symmetry,” Appl. Opt.44, 6971–6985 (2005). [CrossRef] [PubMed]
- M. Ghotbi and M. Ebrahim-Zadeh, “Optical second harmonic generation properties of BiB3O6,” Opt. Express12, 6002–6019 (2004). [CrossRef] [PubMed]
- M. Born and E. Wolf, Principles of Optics, 6th edition (Pergamon Press, 1993).
- P. Butcher and D. Cotter, The Elements of Nonlinear Optics (Cambridge University Press, 1990).
- Y. -H. Kim, S. P. Kulik, M. V. Chekhova, W. P. Grice, and Y. Shih, “Experimental entanglement concentration and universal Bell-state synthesizer,” Phys. Rev. A67, 010301(R) (2003). [CrossRef]
- W. P. Grice and I. A. Walmsley, “Spectral information and distinguishability in type-II down-conversion with a broadband pump,” Phys. Rev. A56, 1627–1634 (1997). [CrossRef]
- C. Kurtsiefer, M. Oberparleiter, and H. Weinfurter, “High-efficiency entangled photon pair collection in type-II parametric fluorescence,” Phys. Rev. A62, 023802 (2001). [CrossRef]
- D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Phys. Rev. A64, 052312 (2001). [CrossRef]
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