Abstract

We demonstrate efficient generation of photon pairs at 1316 nm in a fiber-coupled type-II phase-matched Rb-indiffused waveguide in periodically poled KTiOPO4. The integrated waveguide source has a pair production rate of 2×107/s/mW in a 1.08-nm bandwidth, in good agreement with a theoretical model that takes into account the transversal momentum imparted on the phase matching function by the waveguide. We achieve a Hong-Ou-Mandel quantum-interference visibility of 98.2% after subtraction of accidental coincidences, representing the highest reported value for a waveguide-based photon-pair source.

© 2009 Optical Society of America

Full Article  |  PDF Article

Corrections

Tian Zhong, Franco N. C. Wong, Tony D. Roberts, and Philip Battle, "High performance photon-pair source based on a fiber-coupled periodically poled KTiOPO4 waveguide: erratum," Opt. Express 18, 20114-20114 (2010)
https://www.osapublishing.org/oe/abstract.cfm?uri=oe-18-19-20114

References

  • View by:
  • |
  • |
  • |

  1. 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, 1367-1369 (2001).
    [CrossRef]
  2. S. Tanzilli, H. de Riedmatten, W. Tittel, H. Zbinden, P. Baldi, M. De Micheli, D. B. Ostrowsky, and N. Gisin, "Highly efficient photon-pair source using periodically poled lithium niobate waveguide," Electron. Lett. 37, 26-28 (2001).
    [CrossRef]
  3. A. B. U’Ren, C. Silberhorn, K. Banaszek, and I. A. Walmsley, "Efficient conditional preparation of high-fidelity single photon states for fiber-optic quantum networks," Phys. Rev. Lett. 93, 093601 (2004).
    [CrossRef] [PubMed]
  4. T. Suhara, H. Okabe, and M. Fujimura, "Generation of polarization-entangled photons by type-II quasi-phasematched waveguide nonlinear-optic device," IEEE Photon. Technol. Lett. 19, 1093-1095 (2007).
    [CrossRef]
  5. M. Fiorentino, S. M. Spillane, R. G. Beausoleil, T. D. Roberts, P. Battle, and M. W. Munro, "Spontaneous parametric down-conversion in periodically poled KTP waveguides and bulk crystals," Opt. Express 15, 7479-7488 (2007).
    [CrossRef] [PubMed]
  6. A. Martin, V. Cristofori, P. Aboussouan, H. Herrmann, W. Sohler, D. B. Ostrowsky, O. Alibart, and S. Tanzilli, "Integrated optical source of polarization entangled photons at 1310 nm," Opt. Express 17, 1033-1041 (2009).
    [CrossRef] [PubMed]
  7. W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, "Quantum cryptography using entangled photons in energy-time Bell states," Phys. Rev. Lett. 84, 4737-4740 (2000).
    [CrossRef] [PubMed]
  8. T. Honjo, S. W. Nam, H. Takesue, Q. Zhang, H. Kamada, Y. Nishida, O. Tadanaga, M. Asobe, B. Baek, R. Hadfield, S. Miki, M. Fujiwara, M. Sasaki, Z. Wang, K. Inoue, and Y. Yamamoto, "Long-distance entanglementbased quantum key distribution over optical fiber," Opt. Express 16, 19118-19126 (2008).
    [CrossRef]
  9. H. Takesue, E. Diamanti, C. Langrock, M. M. Fejer, and Y. Yamamoto, "10-GHz clock differential phase shift quantum key distribution experiment," Opt. Express 14, 9522-9530 (2006).
    [CrossRef] [PubMed]
  10. C. E. Kuklewicz, M. Fiorentino, G. Messin, F. N. C. Wong, and J. H. Shapiro, "High-flux source of polarizationentangled photons from a periodically poled KTiOPO4 parametric down-converter," Phys. Rev. A 69, 013807 (2004).
    [CrossRef]
  11. C. K. Hong, Z. Y. Ou, and L. Mandel, "Measurement of subpicosecond time intervals between two photons by interference," Phys. Rev. Lett. 59, 2044-2046 (1987).
    [CrossRef] [PubMed]
  12. K. Sanaka, K. Kawahara, and T. Kuga, "New high-efficiency source of photon pairs for engineering quantum entanglement," Phys. Rev. Lett. 86, 5620-5623 (2001).
    [CrossRef] [PubMed]
  13. D. A. Kleinman, "Theory of optical parametric noise" Phys. Rev. 174,1027-1041 (1968).
    [CrossRef]
  14. K. Koch, E. C. Cheung, G. T. Moore, S. H. Chakmakjian, and J. M. Liu, "Hot spots in parametric fluorescence with a pump beam of finite cross section," IEEE J. Quantum Electron. 31, 769-781 (1995).
    [CrossRef]
  15. R. L. Byer and S. E. Harris, "Power and bandwidth of spontaneous parametric emission," Phys. Rev. 168, 1064-1068 (1968).
    [CrossRef]
  16. J. D. Bierlein and H. Vanherzeele, "Potassium titanyl phospate: properties and new applications," J. Opt. Soc. Am. B 6, 622-633 (1989).
    [CrossRef]
  17. M. A. Albota and E. Dauler, "Single photon detection of degenerate photon pairs at 1.55 m from a periodically poled lithium niobate parametric downconverter," J. Mod. Opt. 51, 1417-1432 (2004).
  18. J. Chen, A. J. Pearlman, A. Ling, J. Fan, and A. Migdall, "A versatile waveguide source of photon pairs for chip-scale quantum information processing," Opt. Express 17, 6727-6740 (2009).
    [CrossRef] [PubMed]

2009 (2)

2008 (1)

2007 (2)

T. Suhara, H. Okabe, and M. Fujimura, "Generation of polarization-entangled photons by type-II quasi-phasematched waveguide nonlinear-optic device," IEEE Photon. Technol. Lett. 19, 1093-1095 (2007).
[CrossRef]

M. Fiorentino, S. M. Spillane, R. G. Beausoleil, T. D. Roberts, P. Battle, and M. W. Munro, "Spontaneous parametric down-conversion in periodically poled KTP waveguides and bulk crystals," Opt. Express 15, 7479-7488 (2007).
[CrossRef] [PubMed]

2006 (1)

2004 (3)

C. E. Kuklewicz, M. Fiorentino, G. Messin, F. N. C. Wong, and J. H. Shapiro, "High-flux source of polarizationentangled photons from a periodically poled KTiOPO4 parametric down-converter," Phys. Rev. A 69, 013807 (2004).
[CrossRef]

A. B. U’Ren, C. Silberhorn, K. Banaszek, and I. A. Walmsley, "Efficient conditional preparation of high-fidelity single photon states for fiber-optic quantum networks," Phys. Rev. Lett. 93, 093601 (2004).
[CrossRef] [PubMed]

M. A. Albota and E. Dauler, "Single photon detection of degenerate photon pairs at 1.55 m from a periodically poled lithium niobate parametric downconverter," J. Mod. Opt. 51, 1417-1432 (2004).

2001 (3)

K. Sanaka, K. Kawahara, and T. Kuga, "New high-efficiency source of photon pairs for engineering quantum entanglement," Phys. Rev. Lett. 86, 5620-5623 (2001).
[CrossRef] [PubMed]

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, 1367-1369 (2001).
[CrossRef]

S. Tanzilli, H. de Riedmatten, W. Tittel, H. Zbinden, P. Baldi, M. De Micheli, D. B. Ostrowsky, and N. Gisin, "Highly efficient photon-pair source using periodically poled lithium niobate waveguide," Electron. Lett. 37, 26-28 (2001).
[CrossRef]

2000 (1)

W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, "Quantum cryptography using entangled photons in energy-time Bell states," Phys. Rev. Lett. 84, 4737-4740 (2000).
[CrossRef] [PubMed]

1995 (1)

K. Koch, E. C. Cheung, G. T. Moore, S. H. Chakmakjian, and J. M. Liu, "Hot spots in parametric fluorescence with a pump beam of finite cross section," IEEE J. Quantum Electron. 31, 769-781 (1995).
[CrossRef]

1989 (1)

1987 (1)

C. K. Hong, Z. Y. Ou, and L. Mandel, "Measurement of subpicosecond time intervals between two photons by interference," Phys. Rev. Lett. 59, 2044-2046 (1987).
[CrossRef] [PubMed]

1968 (2)

R. L. Byer and S. E. Harris, "Power and bandwidth of spontaneous parametric emission," Phys. Rev. 168, 1064-1068 (1968).
[CrossRef]

D. A. Kleinman, "Theory of optical parametric noise" Phys. Rev. 174,1027-1041 (1968).
[CrossRef]

Aboussouan, P.

Albota, M. A.

M. A. Albota and E. Dauler, "Single photon detection of degenerate photon pairs at 1.55 m from a periodically poled lithium niobate parametric downconverter," J. Mod. Opt. 51, 1417-1432 (2004).

Alibart, O.

Asobe, M.

Baek, B.

Baldi, P.

S. Tanzilli, H. de Riedmatten, W. Tittel, H. Zbinden, P. Baldi, M. De Micheli, D. B. Ostrowsky, and N. Gisin, "Highly efficient photon-pair source using periodically poled lithium niobate waveguide," Electron. Lett. 37, 26-28 (2001).
[CrossRef]

Banaszek, K.

Battle, P.

Beausoleil, R. G.

Bierlein, J. D.

Brendel, J.

W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, "Quantum cryptography using entangled photons in energy-time Bell states," Phys. Rev. Lett. 84, 4737-4740 (2000).
[CrossRef] [PubMed]

Byer, R. L.

R. L. Byer and S. E. Harris, "Power and bandwidth of spontaneous parametric emission," Phys. Rev. 168, 1064-1068 (1968).
[CrossRef]

Chakmakjian, S. H.

K. Koch, E. C. Cheung, G. T. Moore, S. H. Chakmakjian, and J. M. Liu, "Hot spots in parametric fluorescence with a pump beam of finite cross section," IEEE J. Quantum Electron. 31, 769-781 (1995).
[CrossRef]

Chen, J.

Cheung, E. C.

K. Koch, E. C. Cheung, G. T. Moore, S. H. Chakmakjian, and J. M. Liu, "Hot spots in parametric fluorescence with a pump beam of finite cross section," IEEE J. Quantum Electron. 31, 769-781 (1995).
[CrossRef]

Cristofori, V.

Dauler, E.

M. A. Albota and E. Dauler, "Single photon detection of degenerate photon pairs at 1.55 m from a periodically poled lithium niobate parametric downconverter," J. Mod. Opt. 51, 1417-1432 (2004).

De Micheli, M.

S. Tanzilli, H. de Riedmatten, W. Tittel, H. Zbinden, P. Baldi, M. De Micheli, D. B. Ostrowsky, and N. Gisin, "Highly efficient photon-pair source using periodically poled lithium niobate waveguide," Electron. Lett. 37, 26-28 (2001).
[CrossRef]

de Riedmatten, H.

S. Tanzilli, H. de Riedmatten, W. Tittel, H. Zbinden, P. Baldi, M. De Micheli, D. B. Ostrowsky, and N. Gisin, "Highly efficient photon-pair source using periodically poled lithium niobate waveguide," Electron. Lett. 37, 26-28 (2001).
[CrossRef]

Diamanti, E.

Fan, J.

Fejer, M. M.

Fiorentino, M.

M. Fiorentino, S. M. Spillane, R. G. Beausoleil, T. D. Roberts, P. Battle, and M. W. Munro, "Spontaneous parametric down-conversion in periodically poled KTP waveguides and bulk crystals," Opt. Express 15, 7479-7488 (2007).
[CrossRef] [PubMed]

C. E. Kuklewicz, M. Fiorentino, G. Messin, F. N. C. Wong, and J. H. Shapiro, "High-flux source of polarizationentangled photons from a periodically poled KTiOPO4 parametric down-converter," Phys. Rev. A 69, 013807 (2004).
[CrossRef]

Fujimura, M.

T. Suhara, H. Okabe, and M. Fujimura, "Generation of polarization-entangled photons by type-II quasi-phasematched waveguide nonlinear-optic device," IEEE Photon. Technol. Lett. 19, 1093-1095 (2007).
[CrossRef]

Fujiwara, M.

Gisin, N.

S. Tanzilli, H. de Riedmatten, W. Tittel, H. Zbinden, P. Baldi, M. De Micheli, D. B. Ostrowsky, and N. Gisin, "Highly efficient photon-pair source using periodically poled lithium niobate waveguide," Electron. Lett. 37, 26-28 (2001).
[CrossRef]

W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, "Quantum cryptography using entangled photons in energy-time Bell states," Phys. Rev. Lett. 84, 4737-4740 (2000).
[CrossRef] [PubMed]

Hadfield, R.

Harris, S. E.

R. L. Byer and S. E. Harris, "Power and bandwidth of spontaneous parametric emission," Phys. Rev. 168, 1064-1068 (1968).
[CrossRef]

Herrmann, H.

Hong, C. K.

C. K. Hong, Z. Y. Ou, and L. Mandel, "Measurement of subpicosecond time intervals between two photons by interference," Phys. Rev. Lett. 59, 2044-2046 (1987).
[CrossRef] [PubMed]

Honjo, T.

Inoue, K.

Kamada, H.

Kawahara, K.

K. Sanaka, K. Kawahara, and T. Kuga, "New high-efficiency source of photon pairs for engineering quantum entanglement," Phys. Rev. Lett. 86, 5620-5623 (2001).
[CrossRef] [PubMed]

Kleinman, D. A.

D. A. Kleinman, "Theory of optical parametric noise" Phys. Rev. 174,1027-1041 (1968).
[CrossRef]

Koch, K.

K. Koch, E. C. Cheung, G. T. Moore, S. H. Chakmakjian, and J. M. Liu, "Hot spots in parametric fluorescence with a pump beam of finite cross section," IEEE J. Quantum Electron. 31, 769-781 (1995).
[CrossRef]

Kuga, T.

K. Sanaka, K. Kawahara, and T. Kuga, "New high-efficiency source of photon pairs for engineering quantum entanglement," Phys. Rev. Lett. 86, 5620-5623 (2001).
[CrossRef] [PubMed]

Kuklewicz, C. E.

C. E. Kuklewicz, M. Fiorentino, G. Messin, F. N. C. Wong, and J. H. Shapiro, "High-flux source of polarizationentangled photons from a periodically poled KTiOPO4 parametric down-converter," Phys. Rev. A 69, 013807 (2004).
[CrossRef]

Langrock, C.

Ling, A.

Liu, J. M.

K. Koch, E. C. Cheung, G. T. Moore, S. H. Chakmakjian, and J. M. Liu, "Hot spots in parametric fluorescence with a pump beam of finite cross section," IEEE J. Quantum Electron. 31, 769-781 (1995).
[CrossRef]

Mandel, L.

C. K. Hong, Z. Y. Ou, and L. Mandel, "Measurement of subpicosecond time intervals between two photons by interference," Phys. Rev. Lett. 59, 2044-2046 (1987).
[CrossRef] [PubMed]

Martin, A.

Messin, G.

C. E. Kuklewicz, M. Fiorentino, G. Messin, F. N. C. Wong, and J. H. Shapiro, "High-flux source of polarizationentangled photons from a periodically poled KTiOPO4 parametric down-converter," Phys. Rev. A 69, 013807 (2004).
[CrossRef]

Migdall, A.

Miki, S.

Moore, G. T.

K. Koch, E. C. Cheung, G. T. Moore, S. H. Chakmakjian, and J. M. Liu, "Hot spots in parametric fluorescence with a pump beam of finite cross section," IEEE J. Quantum Electron. 31, 769-781 (1995).
[CrossRef]

Munro, M. W.

Nam, S. W.

Nishida, Y.

Okabe, H.

T. Suhara, H. Okabe, and M. Fujimura, "Generation of polarization-entangled photons by type-II quasi-phasematched waveguide nonlinear-optic device," IEEE Photon. Technol. Lett. 19, 1093-1095 (2007).
[CrossRef]

Ostrowsky, D. B.

A. Martin, V. Cristofori, P. Aboussouan, H. Herrmann, W. Sohler, D. B. Ostrowsky, O. Alibart, and S. Tanzilli, "Integrated optical source of polarization entangled photons at 1310 nm," Opt. Express 17, 1033-1041 (2009).
[CrossRef] [PubMed]

S. Tanzilli, H. de Riedmatten, W. Tittel, H. Zbinden, P. Baldi, M. De Micheli, D. B. Ostrowsky, and N. Gisin, "Highly efficient photon-pair source using periodically poled lithium niobate waveguide," Electron. Lett. 37, 26-28 (2001).
[CrossRef]

Ou, Z. Y.

C. K. Hong, Z. Y. Ou, and L. Mandel, "Measurement of subpicosecond time intervals between two photons by interference," Phys. Rev. Lett. 59, 2044-2046 (1987).
[CrossRef] [PubMed]

Pearlman, A. J.

Roberts, T. D.

Sanaka, K.

K. Sanaka, K. Kawahara, and T. Kuga, "New high-efficiency source of photon pairs for engineering quantum entanglement," Phys. Rev. Lett. 86, 5620-5623 (2001).
[CrossRef] [PubMed]

Sasaki, M.

Shapiro, J. H.

C. E. Kuklewicz, M. Fiorentino, G. Messin, F. N. C. Wong, and J. H. Shapiro, "High-flux source of polarizationentangled photons from a periodically poled KTiOPO4 parametric down-converter," Phys. Rev. A 69, 013807 (2004).
[CrossRef]

Sohler, W.

Spillane, S. M.

Suhara, T.

T. Suhara, H. Okabe, and M. Fujimura, "Generation of polarization-entangled photons by type-II quasi-phasematched waveguide nonlinear-optic device," IEEE Photon. Technol. Lett. 19, 1093-1095 (2007).
[CrossRef]

Tadanaga, O.

Takesue, H.

Tanzilli, S.

A. Martin, V. Cristofori, P. Aboussouan, H. Herrmann, W. Sohler, D. B. Ostrowsky, O. Alibart, and S. Tanzilli, "Integrated optical source of polarization entangled photons at 1310 nm," Opt. Express 17, 1033-1041 (2009).
[CrossRef] [PubMed]

S. Tanzilli, H. de Riedmatten, W. Tittel, H. Zbinden, P. Baldi, M. De Micheli, D. B. Ostrowsky, and N. Gisin, "Highly efficient photon-pair source using periodically poled lithium niobate waveguide," Electron. Lett. 37, 26-28 (2001).
[CrossRef]

Tittel, W.

S. Tanzilli, H. de Riedmatten, W. Tittel, H. Zbinden, P. Baldi, M. De Micheli, D. B. Ostrowsky, and N. Gisin, "Highly efficient photon-pair source using periodically poled lithium niobate waveguide," Electron. Lett. 37, 26-28 (2001).
[CrossRef]

W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, "Quantum cryptography using entangled photons in energy-time Bell states," Phys. Rev. Lett. 84, 4737-4740 (2000).
[CrossRef] [PubMed]

U’Ren, A. B.

Vanherzeele, H.

Walmsley, I. A.

Wang, Z.

Wong, F. N. C.

C. E. Kuklewicz, M. Fiorentino, G. Messin, F. N. C. Wong, and J. H. Shapiro, "High-flux source of polarizationentangled photons from a periodically poled KTiOPO4 parametric down-converter," Phys. Rev. A 69, 013807 (2004).
[CrossRef]

Yamamoto, Y.

Zbinden, H.

S. Tanzilli, H. de Riedmatten, W. Tittel, H. Zbinden, P. Baldi, M. De Micheli, D. B. Ostrowsky, and N. Gisin, "Highly efficient photon-pair source using periodically poled lithium niobate waveguide," Electron. Lett. 37, 26-28 (2001).
[CrossRef]

W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, "Quantum cryptography using entangled photons in energy-time Bell states," Phys. Rev. Lett. 84, 4737-4740 (2000).
[CrossRef] [PubMed]

Zhang, Q.

Electron. Lett. (1)

S. Tanzilli, H. de Riedmatten, W. Tittel, H. Zbinden, P. Baldi, M. De Micheli, D. B. Ostrowsky, and N. Gisin, "Highly efficient photon-pair source using periodically poled lithium niobate waveguide," Electron. Lett. 37, 26-28 (2001).
[CrossRef]

IEEE J. Quantum Electron. (1)

K. Koch, E. C. Cheung, G. T. Moore, S. H. Chakmakjian, and J. M. Liu, "Hot spots in parametric fluorescence with a pump beam of finite cross section," IEEE J. Quantum Electron. 31, 769-781 (1995).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

T. Suhara, H. Okabe, and M. Fujimura, "Generation of polarization-entangled photons by type-II quasi-phasematched waveguide nonlinear-optic device," IEEE Photon. Technol. Lett. 19, 1093-1095 (2007).
[CrossRef]

J. Mod. Opt. (1)

M. A. Albota and E. Dauler, "Single photon detection of degenerate photon pairs at 1.55 m from a periodically poled lithium niobate parametric downconverter," J. Mod. Opt. 51, 1417-1432 (2004).

J. Opt. Soc. Am. B (1)

Opt. Express (5)

Opt. Lett. (1)

Phys. Rev. (2)

D. A. Kleinman, "Theory of optical parametric noise" Phys. Rev. 174,1027-1041 (1968).
[CrossRef]

R. L. Byer and S. E. Harris, "Power and bandwidth of spontaneous parametric emission," Phys. Rev. 168, 1064-1068 (1968).
[CrossRef]

Phys. Rev. A (1)

C. E. Kuklewicz, M. Fiorentino, G. Messin, F. N. C. Wong, and J. H. Shapiro, "High-flux source of polarizationentangled photons from a periodically poled KTiOPO4 parametric down-converter," Phys. Rev. A 69, 013807 (2004).
[CrossRef]

Phys. Rev. Lett. (4)

C. K. Hong, Z. Y. Ou, and L. Mandel, "Measurement of subpicosecond time intervals between two photons by interference," Phys. Rev. Lett. 59, 2044-2046 (1987).
[CrossRef] [PubMed]

K. Sanaka, K. Kawahara, and T. Kuga, "New high-efficiency source of photon pairs for engineering quantum entanglement," Phys. Rev. Lett. 86, 5620-5623 (2001).
[CrossRef] [PubMed]

W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, "Quantum cryptography using entangled photons in energy-time Bell states," Phys. Rev. Lett. 84, 4737-4740 (2000).
[CrossRef] [PubMed]

A. B. U’Ren, C. Silberhorn, K. Banaszek, and I. A. Walmsley, "Efficient conditional preparation of high-fidelity single photon states for fiber-optic quantum networks," Phys. Rev. Lett. 93, 093601 (2004).
[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 (6)

Fig. 1.
Fig. 1.

Geometry of noncollinear propagation of pump k p , signal k s , and idler k i .

Fig. 2.
Fig. 2.

Measured singles counts (dark counts subtracted) for signal, idler, and coincidence counts (accidentals subtracted) versus pump powers. Shaded area is the region of interest in which detector saturation is negligibly small.

Fig. 3.
Fig. 3.

Spectral histogram of signal photons. Theoretical curve is obtained by a convolution of the Gaussian transmission spectrum of the filter and a sinc-squared phase-matching function.

Fig. 4.
Fig. 4.

Experimental setup of HOM quantum interference measurement.

Fig. 5.
Fig. 5.

Measured HOM coincidences and accidentals counts in 300-s time intervals as function of the optical path difference between the signal and idler arms at waveguide temperature of 19.5 °C and with 57 µW pump power. HOM quantum-interference visibility is 98.2% with accidentals subtracted from the raw data.

Fig. 6.
Fig. 6.

Experimental HOM quantum-interference visibilities versus the mean pair number within a coincidence window of 2.5 ns. Solid line represents theoretical calculation of Eq. (14) that considers only double-pair events and first order in α. Dashed curve is the theoretical prediction that includes contributions from all multi-pair events.

Equations (14)

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

dPs=16π3h̄deff2L2cPpε0nsninpλs4λi1AIsinc2(ΔkzL2)dλs,
Δkz=kpzkszkiz2πΛ,
dPs=16π3h̄deff2L2cPpε0nsninpλs4λi12πks2ϕsf(λs,ϕs)dϕsdλs,
Δkt=kstkit,
kjz=kjkjt22kj,j=s,i
Δkz=(kpkski2πΛ)+12(kst2ks+kit2ki).
Δkzkst2ks.
ϕsdiv=πLks.
kst+kit+kgt=0,
Δkz=(kpkski2πΛ)+C2ks,
c=kst2+(kst+kgt)2.
0ϕmax12πks2ϕsdϕs1(2π)2πwxπwxdksxπwyπwydksy=1wxwy.
dPsdλs=16π3h̄deff2L2cPpε0nsninpλs4λi1Awgsinc2(ΔkzL2),
VHOM=14α(1η),

Metrics