Abstract

The effect of birefringence in 2-fold-symmetric microstructured optical fibers on the phase matching conditions for four-wave mixing is analyzed. The three general types of four-wave mixing are considered. General features are obtained through analytic expansions of phase-matching formulas. Three commonly used designs of fibers are analyzed numerically. Particular designs allow the generation of specified wavelengths, supercontinuum or entangled photons.

© 2010 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |

  1. A. Ortigosa-Blanch, J. C. Knight, W. J. Wadsworth, J. Arriaga, B. Mangan, T. Birks, and P. S. Russell, “Highly birefringent photonic crystal fibers,” Opt. Lett. 25(18), 1325 (2000), URL http://www.opticsinfobase.org/abstract.cfm?URI=ol-25-18-1325.
    [CrossRef]
  2. M. Steel, and R. Osgood, “Polarization and dispersive properties of elliptical-hole photonic crystal fibers,” J. Lightwave Technol. 19(4), 495–503 (2001), URL http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=920847.
    [CrossRef]
  3. R. Stolen, M. Bösch, and C. Lin, “Phase matching in birefringent fibers,” Opt. Lett. 6(5), 213 (1981), URL http://ol.osa.org/abstract.cfm?URI=ol-6-5-213.
    [CrossRef] [PubMed]
  4. G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic Press, Boston, 2006).
  5. S. Murdoch, R. Leonhardt, and J. D. Harvey, “Polarization modulation instability in weakly birefringent fibers,” Opt. Lett. 20(8), 866 (1995), URL http://ol.osa.org/abstract.cfm?URI=ol-20-8-866.
    [CrossRef] [PubMed]
  6. R. Kruhlak, G. K. L. Wong, J. Chen, S. Murdoch, R. Leonhardt, J. D. Harvey, N. Joly, and J. C. Knight, “Polarization modulation instability in photonic crystal fibers,” Opt. Lett. 31(10), 1379 (2006), URL http://ol.osa.org/abstract.cfm?URI=ol-31-10-1379.
    [CrossRef] [PubMed]
  7. J. D. Harvey, R. Leonhardt, S. Coen, G. K. L. Wong, J. C. Knight, W. J. Wadsworth, and P. S. Russell, “Scalar modulation instability in the normal dispersion regime by use of a photonic crystal fiber,” Opt. Lett. 28(22), 2225 (2003), URL http://ol.osa.org/abstract.cfm?URI=ol-28-22-2225.
    [CrossRef] [PubMed]
  8. F. Biancalana, and D. Skryabin, “Vector modulational instabilities in ultra-small core optical fibres,” J. Opt. A: Pure Appl. Opt. 6(4), 301–306 (2004), URL http://stacks.iop.org/1464-4258/6/i=4/a=002?key=crossref.048f95044d026e6efb96f637f8ad2229.
    [CrossRef]
  9. G. K. L. Wong, A. Chen, S. Murdoch, R. Leonhardt, J. D. Harvey, N. Joly, J. C. Knight, W. J. Wadsworth, and P. S. Russell, “Continuous-wave tunable optical parametric generation in a photonic-crystal fiber,” J. Opt. Soc. Am. B 22(11), 2505 (2005), URL http://josab.osa.org/abstract.cfm?URI=josab-22-11-2505.
    [CrossRef]
  10. M. Halder, J. Fulconis, B. Cemlyn, A. Clark, C. Xiong, W. J. Wadsworth, and J. Rarity, “Nonclassical 2-photon interference with separate intrinsically narrowband fibre sources,” Opt. Express 17(6), 4670–4676 (2009), URL http://www.ncbi.nlm.nih.gov/pubmed/19293896.
    [CrossRef] [PubMed]
  11. J. Rothenberg, “Modulational instability for normal dispersion,” Phys. Rev. A 42(1), 682–685 (1990), URL http://pra.aps.org/abstract/PRA/v42/i1/p682_1.
    [CrossRef] [PubMed]
  12. P. Drummond, T. Kennedy, J. M. Dudley, R. Leonhardt, and J. D. Harvey, “Cross-phase modulational instability in high-birefringence fibers,” Opt. Commun. 78(2), 137–142 (1990), URL http://linkinghub.elsevier.com/retrieve/pii/003040189090110F.
    [CrossRef]
  13. J. Chen, G. K. L. Wong, S. Murdoch, R. Kruhlak, R. Leonhardt, J. D. Harvey, N. Joly, and J. C. Knight, “Crossphase modulation instability in photonic crystal fibers,” Opt. Lett. 31(7), 873 (2006), URL http://ol.osa.org/abstract.cfm?URI=ol-31-7-873.
    [CrossRef] [PubMed]
  14. A. Nguyen, K. Phan Huy, E. Brainis, P. Mergo, J. Wojcik, T. Nasilowski, J. Van Erps, H. Thienpont, and S. Massar, “Enhanced cross phase modulation instability in birefringent photonic crystal fibers in the anomalous dispersion regime,” Opt. Express 14(18), 8290 (2006), URL http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-18-8290.
    [CrossRef] [PubMed]
  15. R. Stolen, and J. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum Electron. 18(7), 1062–1072 (1982), URL http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1071660.
    [CrossRef]
  16. C. Lesvigne, V. Couderc, A. Tonello, P. Leproux, A. Barthélémy, S. Lacroix, F. Druon, P. Blandin, M. Hanna, and P. Georges, “Visible supercontinuum generation controlled by intermodal four-wave mixing in microstructured fiber,” Opt. Lett. 32(15), 2173 (2007), URL http://www.opticsinfobase.org/abstract.cfm?URI=ol-32-15-2173.
    [CrossRef] [PubMed]
  17. A. Tonello, S. Pitois, S. Wabnitz, G. Millot, T. Martynkien, W. Urbanczyk, J. Wojcik, A. Locatelli, M. Conforti, and C. De Angelis, “Frequency tunable polarization and intermodal modulation instability in high birefringence holey fiber,” Opt. Express 14(1), 397 (2006), URL http://www.opticsexpress.org/abstract.cfm?URI=oe-14-1-397.
    [CrossRef] [PubMed]
  18. L. Labonté, D. Pagnoux, P. Roy, F. Bahloul, and M. Zghal, “Numerical and experimental analysis of the birefringence of large air fraction slightly unsymmetrical holey fibres,” Opt. Commun. 262(2), 180–187 (2006), URL http://linkinghub.elsevier.com/retrieve/pii/S0030401805014008.
    [CrossRef]
  19. L. Labonté, E. Pone, M. Skorobogatiy, N. Godbout, S. Lacroix, and D. Pagnoux, “Analysis of the birefringence of solid-core air-silica microstructured fibers,” Proc. SPIE pp. 73,570N–73,570N–11 (2009), URL http://link.aip.org/link/PSISDG/v7357/i1/p73570N/s1\&Agg=doi.
  20. P. S. Russell, “Photonic-Crystal Fibers,” J. Lightwave Technol. 24(12), 4729–4749 (2006), URL http://www.opticsinfobase.org/JLT/abstract.cfm?URI=JLT-24-12-4729.
    [CrossRef]
  21. E. Pone, A. Hassani, S. Lacroix, A. Kabashin, and M. Skorobogatiy, “Boundary integral method for the challenging problems in bandgap guiding, plasmonics and sensing,” Opt. Express 15(16), 10231 (2007), URL http://www.opticsexpress.org/abstract.cfm?URI=oe-15-16-10231.
    [CrossRef] [PubMed]
  22. M. Hirano, T. Nakanishi, T. Okuno, and M. Onishi, “Silica-Based Highly Nonlinear Fibers and Their Application,” IEEE J. Sel. Top. Quantum Electron. 15(1), 103–113 (2009), URL http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=4773307.
    [CrossRef]
  23. Y. Deng, Q. Lin, F. Lu, G. P. Agrawal, and W. Knox, “Broadly tunable femtosecond parametric oscillator using a photonic crystal fiber,” Opt. Lett. 30(10), 1234 (2005), URL http://ol.osa.org/abstract.cfm?URI=ol-30-10-1234.
    [CrossRef] [PubMed]
  24. J. Sharping, “Microstructure fiber based optical parametric oscillators,” J. Lightwave Technol. 26(14), 2184–2191 (2008), URL http://www.opticsinfobase.org/JLT/abstract.cfm?uri=JLT-26-14-2184.
    [CrossRef]
  25. M. Lehtonen, G. Genty, H. Ludvigsen, and M. Kaivola, “Supercontinuum generation in a highly birefringent microstructured fiber,” Appl. Phys. Lett. 82(14), 2197 (2003), URL http://apl.aip.org/applab/v82/i14/p2197_s1.
    [CrossRef]
  26. Z. Zhu, and T. G. Brown, “Polarization properties of supercontinuum spectra generated in birefringent photonic crystal fibers,” J. Opt. Soc. Am. B 21(2), 249 (2004), URL http://josab.osa.org/abstract.cfm?URI=josab-21-2-249.
    [CrossRef]
  27. J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Opt. 78(4), 1135–1184 (2006), URL http://link.aps.org/doi/10.1103/RevModPhys.78.1135.
    [CrossRef]
  28. K. Garay-Palmett, H. McGuinness, O. Cohen, J. Lundeen, and R. Rangel-Rojo, A. U’ren, M. Raymer, C. McKinstrie, S. Radic, and I. Walmsley, “Photon pair-state preparation with tailored spectral properties by spontaneous four-wave mixing in photonic-crystal fiber,” Opt. Express 15(22), 14870 (2007), URL http://www.opticsexpress.org/abstract.cfm?URI=oe-15-22-14870.
    [CrossRef] [PubMed]
  29. J. Sharping, J. Chen, X. Li, P. Kumar, and R. Windeler, “Quantum-correlated twin photons from microstructure fiber,” Opt. Express 12(14), 3086 (2004), URL http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-14-3086.
    [CrossRef] [PubMed]
  30. J. Rarity, J. Fulconis, J. Duligall, W. J. Wadsworth, and P. S. Russell, “Photonic crystal fiber source of correlated photon pairs,” Opt. Express 13(2), 534 (2005), URL http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-2-534.
    [CrossRef] [PubMed]
  31. J. Slater, J.-S. Corbeil, S. Virally, F. Bussières, A. Kudlinski, G. Bouwmans, S. Lacroix, N. Godbout, and W. Tittel, “Microstructured fiber source of photon pairs at widely separated wavelengths,” Opt. Lett. 35(4), 499–501 (2010), URL http://www.ncbi.nlm.nih.gov/pubmed/20160797.
    [CrossRef] [PubMed]
  32. C. Söller, B. Brecht, P. Mosley, L. Zang, A. Podlipensky, N. Joly, P. S. Russell, and C. Silberhorn, “Bridging Visible and Telecom Wavelengths with a Single-Mode Broadband Photon Pair Source,” ArXiv (2009), URL http://arxiv.org/abs/0908.2932.
  33. E. Brainis, “Four-photon scattering in birefringent fibers,” Phys. Rev. A 79(2), 023840 (2009), URL http: //link.aps.org/doi/10.1103/PhysRevA.79.023840.
    [CrossRef]
  34. O. Cohen, J. Lundeen, B. Smith, G. Puentes, P. Mosley, and I. Walmsley, “Tailored Photon-Pair Generation in Optical Fibers,” Phys. Rev. Lett. 102(12), 123603 (2009), URL http://prl.aps.org/abstract/PRL/ v102/i12/e123603.
    [CrossRef] [PubMed]
  35. J. Fan, and A. Migdall, “Generation of cross-polarized photon pairs in a microstructure fiber with frequency conjugate laser pump pulses,” Opt. Express 13(15), 5777 (2005), URL http://www.opticsexpress.org/abstract.cfm?URI=oe-13-15-5777.
    [CrossRef] [PubMed]
  36. B. Smith, P. Mahou, O. Cohen, J. Lundeen, and I. Walmsley, “Photon pair generation in birefringent optical fibers,” Opt. Express 17(26), 23589 (2009), URL http://www.opticsexpress.org/abstract.cfm?URI=oe-17-26-23589.
    [CrossRef]
  37. A. McMillan, J. Fulconis, M. Halder, C. Xiong, J. Rarity, and W. J. Wadsworth, “Narrowband high-fidelity all-fibre source of heralded single photons at 1570 nm,” Opt. Express 17(8), 6156 (2009), URL http://www.opticsinfobase.org/abstract.cfm?URI=oe-17-8-6156.
    [CrossRef] [PubMed]

Other (37)

A. Ortigosa-Blanch, J. C. Knight, W. J. Wadsworth, J. Arriaga, B. Mangan, T. Birks, and P. S. Russell, “Highly birefringent photonic crystal fibers,” Opt. Lett. 25(18), 1325 (2000), URL http://www.opticsinfobase.org/abstract.cfm?URI=ol-25-18-1325.
[CrossRef]

M. Steel, and R. Osgood, “Polarization and dispersive properties of elliptical-hole photonic crystal fibers,” J. Lightwave Technol. 19(4), 495–503 (2001), URL http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=920847.
[CrossRef]

R. Stolen, M. Bösch, and C. Lin, “Phase matching in birefringent fibers,” Opt. Lett. 6(5), 213 (1981), URL http://ol.osa.org/abstract.cfm?URI=ol-6-5-213.
[CrossRef] [PubMed]

G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic Press, Boston, 2006).

S. Murdoch, R. Leonhardt, and J. D. Harvey, “Polarization modulation instability in weakly birefringent fibers,” Opt. Lett. 20(8), 866 (1995), URL http://ol.osa.org/abstract.cfm?URI=ol-20-8-866.
[CrossRef] [PubMed]

R. Kruhlak, G. K. L. Wong, J. Chen, S. Murdoch, R. Leonhardt, J. D. Harvey, N. Joly, and J. C. Knight, “Polarization modulation instability in photonic crystal fibers,” Opt. Lett. 31(10), 1379 (2006), URL http://ol.osa.org/abstract.cfm?URI=ol-31-10-1379.
[CrossRef] [PubMed]

J. D. Harvey, R. Leonhardt, S. Coen, G. K. L. Wong, J. C. Knight, W. J. Wadsworth, and P. S. Russell, “Scalar modulation instability in the normal dispersion regime by use of a photonic crystal fiber,” Opt. Lett. 28(22), 2225 (2003), URL http://ol.osa.org/abstract.cfm?URI=ol-28-22-2225.
[CrossRef] [PubMed]

F. Biancalana, and D. Skryabin, “Vector modulational instabilities in ultra-small core optical fibres,” J. Opt. A: Pure Appl. Opt. 6(4), 301–306 (2004), URL http://stacks.iop.org/1464-4258/6/i=4/a=002?key=crossref.048f95044d026e6efb96f637f8ad2229.
[CrossRef]

G. K. L. Wong, A. Chen, S. Murdoch, R. Leonhardt, J. D. Harvey, N. Joly, J. C. Knight, W. J. Wadsworth, and P. S. Russell, “Continuous-wave tunable optical parametric generation in a photonic-crystal fiber,” J. Opt. Soc. Am. B 22(11), 2505 (2005), URL http://josab.osa.org/abstract.cfm?URI=josab-22-11-2505.
[CrossRef]

M. Halder, J. Fulconis, B. Cemlyn, A. Clark, C. Xiong, W. J. Wadsworth, and J. Rarity, “Nonclassical 2-photon interference with separate intrinsically narrowband fibre sources,” Opt. Express 17(6), 4670–4676 (2009), URL http://www.ncbi.nlm.nih.gov/pubmed/19293896.
[CrossRef] [PubMed]

J. Rothenberg, “Modulational instability for normal dispersion,” Phys. Rev. A 42(1), 682–685 (1990), URL http://pra.aps.org/abstract/PRA/v42/i1/p682_1.
[CrossRef] [PubMed]

P. Drummond, T. Kennedy, J. M. Dudley, R. Leonhardt, and J. D. Harvey, “Cross-phase modulational instability in high-birefringence fibers,” Opt. Commun. 78(2), 137–142 (1990), URL http://linkinghub.elsevier.com/retrieve/pii/003040189090110F.
[CrossRef]

J. Chen, G. K. L. Wong, S. Murdoch, R. Kruhlak, R. Leonhardt, J. D. Harvey, N. Joly, and J. C. Knight, “Crossphase modulation instability in photonic crystal fibers,” Opt. Lett. 31(7), 873 (2006), URL http://ol.osa.org/abstract.cfm?URI=ol-31-7-873.
[CrossRef] [PubMed]

A. Nguyen, K. Phan Huy, E. Brainis, P. Mergo, J. Wojcik, T. Nasilowski, J. Van Erps, H. Thienpont, and S. Massar, “Enhanced cross phase modulation instability in birefringent photonic crystal fibers in the anomalous dispersion regime,” Opt. Express 14(18), 8290 (2006), URL http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-18-8290.
[CrossRef] [PubMed]

R. Stolen, and J. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum Electron. 18(7), 1062–1072 (1982), URL http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1071660.
[CrossRef]

C. Lesvigne, V. Couderc, A. Tonello, P. Leproux, A. Barthélémy, S. Lacroix, F. Druon, P. Blandin, M. Hanna, and P. Georges, “Visible supercontinuum generation controlled by intermodal four-wave mixing in microstructured fiber,” Opt. Lett. 32(15), 2173 (2007), URL http://www.opticsinfobase.org/abstract.cfm?URI=ol-32-15-2173.
[CrossRef] [PubMed]

A. Tonello, S. Pitois, S. Wabnitz, G. Millot, T. Martynkien, W. Urbanczyk, J. Wojcik, A. Locatelli, M. Conforti, and C. De Angelis, “Frequency tunable polarization and intermodal modulation instability in high birefringence holey fiber,” Opt. Express 14(1), 397 (2006), URL http://www.opticsexpress.org/abstract.cfm?URI=oe-14-1-397.
[CrossRef] [PubMed]

L. Labonté, D. Pagnoux, P. Roy, F. Bahloul, and M. Zghal, “Numerical and experimental analysis of the birefringence of large air fraction slightly unsymmetrical holey fibres,” Opt. Commun. 262(2), 180–187 (2006), URL http://linkinghub.elsevier.com/retrieve/pii/S0030401805014008.
[CrossRef]

L. Labonté, E. Pone, M. Skorobogatiy, N. Godbout, S. Lacroix, and D. Pagnoux, “Analysis of the birefringence of solid-core air-silica microstructured fibers,” Proc. SPIE pp. 73,570N–73,570N–11 (2009), URL http://link.aip.org/link/PSISDG/v7357/i1/p73570N/s1\&Agg=doi.

P. S. Russell, “Photonic-Crystal Fibers,” J. Lightwave Technol. 24(12), 4729–4749 (2006), URL http://www.opticsinfobase.org/JLT/abstract.cfm?URI=JLT-24-12-4729.
[CrossRef]

E. Pone, A. Hassani, S. Lacroix, A. Kabashin, and M. Skorobogatiy, “Boundary integral method for the challenging problems in bandgap guiding, plasmonics and sensing,” Opt. Express 15(16), 10231 (2007), URL http://www.opticsexpress.org/abstract.cfm?URI=oe-15-16-10231.
[CrossRef] [PubMed]

M. Hirano, T. Nakanishi, T. Okuno, and M. Onishi, “Silica-Based Highly Nonlinear Fibers and Their Application,” IEEE J. Sel. Top. Quantum Electron. 15(1), 103–113 (2009), URL http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=4773307.
[CrossRef]

Y. Deng, Q. Lin, F. Lu, G. P. Agrawal, and W. Knox, “Broadly tunable femtosecond parametric oscillator using a photonic crystal fiber,” Opt. Lett. 30(10), 1234 (2005), URL http://ol.osa.org/abstract.cfm?URI=ol-30-10-1234.
[CrossRef] [PubMed]

J. Sharping, “Microstructure fiber based optical parametric oscillators,” J. Lightwave Technol. 26(14), 2184–2191 (2008), URL http://www.opticsinfobase.org/JLT/abstract.cfm?uri=JLT-26-14-2184.
[CrossRef]

M. Lehtonen, G. Genty, H. Ludvigsen, and M. Kaivola, “Supercontinuum generation in a highly birefringent microstructured fiber,” Appl. Phys. Lett. 82(14), 2197 (2003), URL http://apl.aip.org/applab/v82/i14/p2197_s1.
[CrossRef]

Z. Zhu, and T. G. Brown, “Polarization properties of supercontinuum spectra generated in birefringent photonic crystal fibers,” J. Opt. Soc. Am. B 21(2), 249 (2004), URL http://josab.osa.org/abstract.cfm?URI=josab-21-2-249.
[CrossRef]

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Opt. 78(4), 1135–1184 (2006), URL http://link.aps.org/doi/10.1103/RevModPhys.78.1135.
[CrossRef]

K. Garay-Palmett, H. McGuinness, O. Cohen, J. Lundeen, and R. Rangel-Rojo, A. U’ren, M. Raymer, C. McKinstrie, S. Radic, and I. Walmsley, “Photon pair-state preparation with tailored spectral properties by spontaneous four-wave mixing in photonic-crystal fiber,” Opt. Express 15(22), 14870 (2007), URL http://www.opticsexpress.org/abstract.cfm?URI=oe-15-22-14870.
[CrossRef] [PubMed]

J. Sharping, J. Chen, X. Li, P. Kumar, and R. Windeler, “Quantum-correlated twin photons from microstructure fiber,” Opt. Express 12(14), 3086 (2004), URL http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-14-3086.
[CrossRef] [PubMed]

J. Rarity, J. Fulconis, J. Duligall, W. J. Wadsworth, and P. S. Russell, “Photonic crystal fiber source of correlated photon pairs,” Opt. Express 13(2), 534 (2005), URL http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-2-534.
[CrossRef] [PubMed]

J. Slater, J.-S. Corbeil, S. Virally, F. Bussières, A. Kudlinski, G. Bouwmans, S. Lacroix, N. Godbout, and W. Tittel, “Microstructured fiber source of photon pairs at widely separated wavelengths,” Opt. Lett. 35(4), 499–501 (2010), URL http://www.ncbi.nlm.nih.gov/pubmed/20160797.
[CrossRef] [PubMed]

C. Söller, B. Brecht, P. Mosley, L. Zang, A. Podlipensky, N. Joly, P. S. Russell, and C. Silberhorn, “Bridging Visible and Telecom Wavelengths with a Single-Mode Broadband Photon Pair Source,” ArXiv (2009), URL http://arxiv.org/abs/0908.2932.

E. Brainis, “Four-photon scattering in birefringent fibers,” Phys. Rev. A 79(2), 023840 (2009), URL http: //link.aps.org/doi/10.1103/PhysRevA.79.023840.
[CrossRef]

O. Cohen, J. Lundeen, B. Smith, G. Puentes, P. Mosley, and I. Walmsley, “Tailored Photon-Pair Generation in Optical Fibers,” Phys. Rev. Lett. 102(12), 123603 (2009), URL http://prl.aps.org/abstract/PRL/ v102/i12/e123603.
[CrossRef] [PubMed]

J. Fan, and A. Migdall, “Generation of cross-polarized photon pairs in a microstructure fiber with frequency conjugate laser pump pulses,” Opt. Express 13(15), 5777 (2005), URL http://www.opticsexpress.org/abstract.cfm?URI=oe-13-15-5777.
[CrossRef] [PubMed]

B. Smith, P. Mahou, O. Cohen, J. Lundeen, and I. Walmsley, “Photon pair generation in birefringent optical fibers,” Opt. Express 17(26), 23589 (2009), URL http://www.opticsexpress.org/abstract.cfm?URI=oe-17-26-23589.
[CrossRef]

A. McMillan, J. Fulconis, M. Halder, C. Xiong, J. Rarity, and W. J. Wadsworth, “Narrowband high-fidelity all-fibre source of heralded single photons at 1570 nm,” Opt. Express 17(8), 6156 (2009), URL http://www.opticsinfobase.org/abstract.cfm?URI=oe-17-8-6156.
[CrossRef] [PubMed]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1.
Fig. 1.

Usual types of birefringent solid core air-silica MSFs under study: (A) two larger holes limit the core dimension; (B) the core consists of two missing holes; (C) the core consists of three missing holes. While in the former case, the birefringence is induced by a reduction in the core vertical y-dimension, in these two latter cases, the birefringence is induced by an increase in the core horizontal x-dimension. Symmetry x- and y-axes thus correspond to the largest and smallest dimension of the core, respectively. In the Fiber A case, the two different holes can be smaller than the others, thus making the y-dimension larger than the x one, as in Ref. 10.

Fig. 2.
Fig. 2.

Spectral dependence of (a) the phase birefringence Bϕ, and (b) the average modal dispersion D = (Dx +Dy)/2. The various curves are calculated for the fundamental mode of Fiber B (see Fig. 1), and correspond to various fractions of air d/Λ. For a step Λ=2μm, the values of this parameter, indicated for each curve, represent the holes radius expressed in μm. Note that the silica dispersion was taken into account for these calculations.

Fig. 3.
Fig. 3.

Spectral dependence of the second order β2 and fourth order β4 dispersion coefficients (βn = dnβ/dωnωp). The curves are calculated for the fundamental mode of Fiber B (see Fig. 1), and correspond to various fractions of air d/Λ. For a step Λ = 2μm, the values of this parameter, indicated for each curve, represent the holes radius expressed in μm. Note that the silica dispersion was taken into account for these calculations.

Fig. 4.
Fig. 4.

C, O, and M phase matching curves for Fiber B as per Fig. 1. Those figures show daughter wavelengths (λout) plotted vs. pump wavelengths (λin). In both cases, the step is Λ=2 μm, but the diameter of the holes is different: d1 = 0.8 and d2 = 1.6 μm, respectively. All these phase matching curves are calculated for γP = 0.

Fig. 5.
Fig. 5.

O-type phase matching curves for the three form birefringent MSFs as per Fig. 1. For all fibers, the step is Λ = 2 μm and the diameter of the small holes is d = 1.4 μm. For fiber A, the diameter of the large holes is D = 2.2 μm. The geometry of the associated fiber structures is shown in inset. All these phase matching curves are calculated for γP = 0. Vertical lines represents ZDWs.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

ω++ω=2ωpandn+ω++nω=(np1+np2) ωp ,
Ω2=6β2β4 (1±123β4β22γP).
γ=kn2Aeff.
Aeff=Aψ+2dAAψ2dAAψP12dAAψP22dAANLψ+ψψP1ψP2dA
Aeff(Aψ2dA)2ANLψ4dA.
Ω2=6β2β4 (1±123β4β22[k(nn)γP3])
β4Ω4±4Δβ3Ω3+12β2Ω2±12Δβ1Ω+12γP=0
Bϕ=α·λm

Metrics