Abstract

Degenerate four-wave mixing is considered in large mode area hybrid photonic crystal fibers, combining photonic bandgap guidance and index guidance. Co- and orthogonally polarized pump, signal and idler fields are considered numerically by calculating the parametric gain and experimentally by spontaneous degenerate four-wave mixing. Intermodal and birefringence assisted intramodal phase matching is observed. Good agreement between calculations and experimental observations is obtained. Intermodal four-wave mixing is achieved experimentally with a conversion efficiency of 17%.

© 2015 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Degenerate four wave mixing in large mode area hybrid photonic crystal fibers

Sidsel R. Petersen, Thomas T. Alkeskjold, and Jesper Lægsgaard
Opt. Express 21(15) 18111-18124 (2013)

Polarization switch of four-wave mixing in large mode area hybrid photonic crystal fibers

Sidsel R. Petersen, Thomas T. Alkeskjold, Christina B. Olausson, and Jesper Lægsgaard
Opt. Lett. 40(4) 487-490 (2015)

Supercontinuum generation, four-wave mixing, and fission of higher-order solitons in photonic-crystal fibers

Anton V. Husakou and Joachim Herrmann
J. Opt. Soc. Am. B 19(9) 2171-2182 (2002)

References

  • View by:
  • |
  • |
  • |

  1. J. D. Harvey, R. Leonhardt, S. Coen, G. K. L. Wong, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “Scalar modulation instability in the normal dispersion regime by use of a photonic crystal fiber,” Opt. Lett. 28(22), 2225–2227 (2003).
    [Crossref] [PubMed]
  2. S. R. Petersen, T. T. Alkeskjold, and J. Lægsgaard, “Degenerate four wave mixing in large mode area hybrid photonic crystal fibers,” Opt. Express 21(15), 18111–18124 (2013).
    [Crossref] [PubMed]
  3. S. R. Petersen, T. T. Alkeskjold, C. B. Olausson, and J. Lægsgaard, “Extended parametric gain range in photonic crystal fibers with strongly frequency-dependent field distributions,” Opt. Lett. 39(16), 4891–4894 (2014).
    [Crossref] [PubMed]
  4. P. D. Rasmussen, J. Lægsgaard, and O. Bang, “Degenerate four wave mixing in solid core photonic bandgap fibers,” Opt. Express 16(6), 4059–4068 (2008).
    [Crossref] [PubMed]
  5. A. Cerqueira S, J. M. Chavez Boggio, H. E. Hernandez-Figueroa, H. L. Fragnito, and J. C. Knight, “Highly efficient generation of cascaded Four-Wave Mixing products in a Hybrid Photonic Crystal Fiber,” in Proc. of European Conference on Optical Communication (ECOC)2007.
  6. J. Zhao, P. Yan, J. Shu, C. Du, S. Ruan, H. Wei, and J. Luo, “Efficient anti-stokes signal generation through degenerate four wave mixing in an all solid photonic bandgap fiber,” Opt. Commun. 284(21), 5208–5211 (2011).
    [Crossref]
  7. R. T. Murray, E. J. R. Kelleher, S. V. Popov, A. Mussot, A. Kudlinski, and J. R. Taylor, “Widely tunable polarization maintaining photonic crystal fiber based parametric wavelength conversion,” Opt. Express 21(13), 15826–15833 (2013).
    [Crossref] [PubMed]
  8. E. A. Zlobina, S. I. Kablukov, and S. A. Babi, “Phase matching for parametric generation in polarization maintaining photonic crystal fiber pumped by tunable Yb-doped fiber laser,” J. Opt. Soc. Am. B 29(8), 1959–1967 (2012).
    [Crossref]
  9. J. Yuan, G. Zhou, H. Liu, C. Xia, X. Sang, Q. Wu, C. Yu, K. Wang, B. Yan, Y. Han, G. Farrell, and L. Hou, “Coherent anti-stokes raman scattering microscopy by dispersive wave generations in a polarization maintaining photonic crystal fiber,” Pr. Electromagn. Res. 141, 659–670 (2013).
    [Crossref]
  10. S. R. Petersen, T. T. Alkeskjold, C. B. Olausson, and J. Lægsgaard, “Polarization switch of four-wave mixing in large mode area hybrid photonic crystal fibers,” Opt. Lett. 40(4), 487–490 (2015).
    [Crossref] [PubMed]
  11. R. H. Stolen, J. E. Bjorkholm, and A. Ashkin, “Phase-matched three-wave mixing in silica fiber optical waveguides,” Appl. Phys. Lett. 24(7), 308–310 (1974).
    [Crossref]
  12. R. H. Stolen, “Phase-matched-stimulated four-photon mixing in silica-fiber waveguides,” IEEE J. Quantum Elect. 11(3), 100–103 (1975).
    [Crossref]
  13. P. Steinvurzel, J. Demas, B. Tai, Y. Chen, L. Yan, and S. Ramachandran, “Broadband parametric wavelength conversion at 1 μm with large mode area fibers,” Opt. Lett. 39(4), 743–746 (2014).
    [Crossref] [PubMed]
  14. E. Coscelli, F. Poli, T. T. Alkeskjold, D. Passaro, A. Cucinotta, L. Leick, J. Broeng, and S. Selleri, “Single-mode analysis of Yb-doped double-cladding distributed spectral filtering photonic crystal fibers,” Opt. Express 18(26), 27197–27204 (2010).
    [Crossref]
  15. S. R. Petersen, T. T. Alkeskjold, F. Poli, E. Coscelli, M. M. Jørgensen, M. Laurila, J. Lægsgaard, and J. Broeng, “Hybrid Ytterbium-doped large-mode-area photonic crystal fiber amplifier for long wavelengths,” Opt. Express 20(6), 6010–6020 (2012).
    [Crossref] [PubMed]
  16. T. T. Alkeskjold, “Large-mode-area ytterbium-doped fiber amplifier with distributed narrow spectral filtering and reduced bend sensitivity,” Opt. Express 17(19), 16394–16405 (2009).
    [Crossref] [PubMed]
  17. A. Argyros, T. A. Birks, S. G. Leon-Saval, C. M. B. Cordeiro, and P. St. J. Russell, “Guidance properties of low-contrast photonic bandgap fibres,” Opt. Express 13(7), 2503–2511 (2005).
    [Crossref] [PubMed]
  18. S. C. Rashleigh, “Measurement of fiber birefringence by wavelength scanning: effect of dispersion,” Opt. Lett. 8(6), 336–338 (1983).
    [Crossref] [PubMed]
  19. COMSOL Multiphysics, version 4.4, www.comsol.com .
  20. J. K. Lyngsø, B. J. Mangan, C. B. Olausson, and P. J. Roberts, “Stress induced birefringence in hybrid TIR/PBG guiding solid photonic crystal fibers,” Opt. Express 18(13), 14031–14040 (2010).
    [Crossref] [PubMed]
  21. G. P. Agrawal, Nonlinear Fiber Optics, 4, (Elsevier, 2007).
  22. M. E. Marhic, K. K. Y. Wong, and L. G. Kazovsky, “Fiber optical parametric amplifiers with linearly or circularly polarized waves,” J. Opt. Soc. Am. B 20(12), 2425–2433 (2003).
    [Crossref]
  23. D. Milam, “Review and assessment of measured values of the nonlinear refractive-index coefficient of fused silica,” App. Opt. 37(3), 546–550 (1998).
    [Crossref]

2015 (1)

2014 (2)

2013 (3)

2012 (2)

2011 (1)

J. Zhao, P. Yan, J. Shu, C. Du, S. Ruan, H. Wei, and J. Luo, “Efficient anti-stokes signal generation through degenerate four wave mixing in an all solid photonic bandgap fiber,” Opt. Commun. 284(21), 5208–5211 (2011).
[Crossref]

2010 (2)

2009 (1)

2008 (1)

2005 (1)

2003 (2)

1998 (1)

D. Milam, “Review and assessment of measured values of the nonlinear refractive-index coefficient of fused silica,” App. Opt. 37(3), 546–550 (1998).
[Crossref]

1983 (1)

1975 (1)

R. H. Stolen, “Phase-matched-stimulated four-photon mixing in silica-fiber waveguides,” IEEE J. Quantum Elect. 11(3), 100–103 (1975).
[Crossref]

1974 (1)

R. H. Stolen, J. E. Bjorkholm, and A. Ashkin, “Phase-matched three-wave mixing in silica fiber optical waveguides,” Appl. Phys. Lett. 24(7), 308–310 (1974).
[Crossref]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 4, (Elsevier, 2007).

Alkeskjold, T. T.

Argyros, A.

Ashkin, A.

R. H. Stolen, J. E. Bjorkholm, and A. Ashkin, “Phase-matched three-wave mixing in silica fiber optical waveguides,” Appl. Phys. Lett. 24(7), 308–310 (1974).
[Crossref]

Babi, S. A.

Bang, O.

Birks, T. A.

Bjorkholm, J. E.

R. H. Stolen, J. E. Bjorkholm, and A. Ashkin, “Phase-matched three-wave mixing in silica fiber optical waveguides,” Appl. Phys. Lett. 24(7), 308–310 (1974).
[Crossref]

Broeng, J.

Cerqueira S, A.

A. Cerqueira S, J. M. Chavez Boggio, H. E. Hernandez-Figueroa, H. L. Fragnito, and J. C. Knight, “Highly efficient generation of cascaded Four-Wave Mixing products in a Hybrid Photonic Crystal Fiber,” in Proc. of European Conference on Optical Communication (ECOC)2007.

Chavez Boggio, J. M.

A. Cerqueira S, J. M. Chavez Boggio, H. E. Hernandez-Figueroa, H. L. Fragnito, and J. C. Knight, “Highly efficient generation of cascaded Four-Wave Mixing products in a Hybrid Photonic Crystal Fiber,” in Proc. of European Conference on Optical Communication (ECOC)2007.

Chen, Y.

Coen, S.

Cordeiro, C. M. B.

Coscelli, E.

Cucinotta, A.

Demas, J.

Du, C.

J. Zhao, P. Yan, J. Shu, C. Du, S. Ruan, H. Wei, and J. Luo, “Efficient anti-stokes signal generation through degenerate four wave mixing in an all solid photonic bandgap fiber,” Opt. Commun. 284(21), 5208–5211 (2011).
[Crossref]

Farrell, G.

J. Yuan, G. Zhou, H. Liu, C. Xia, X. Sang, Q. Wu, C. Yu, K. Wang, B. Yan, Y. Han, G. Farrell, and L. Hou, “Coherent anti-stokes raman scattering microscopy by dispersive wave generations in a polarization maintaining photonic crystal fiber,” Pr. Electromagn. Res. 141, 659–670 (2013).
[Crossref]

Fragnito, H. L.

A. Cerqueira S, J. M. Chavez Boggio, H. E. Hernandez-Figueroa, H. L. Fragnito, and J. C. Knight, “Highly efficient generation of cascaded Four-Wave Mixing products in a Hybrid Photonic Crystal Fiber,” in Proc. of European Conference on Optical Communication (ECOC)2007.

Han, Y.

J. Yuan, G. Zhou, H. Liu, C. Xia, X. Sang, Q. Wu, C. Yu, K. Wang, B. Yan, Y. Han, G. Farrell, and L. Hou, “Coherent anti-stokes raman scattering microscopy by dispersive wave generations in a polarization maintaining photonic crystal fiber,” Pr. Electromagn. Res. 141, 659–670 (2013).
[Crossref]

Harvey, J. D.

Hernandez-Figueroa, H. E.

A. Cerqueira S, J. M. Chavez Boggio, H. E. Hernandez-Figueroa, H. L. Fragnito, and J. C. Knight, “Highly efficient generation of cascaded Four-Wave Mixing products in a Hybrid Photonic Crystal Fiber,” in Proc. of European Conference on Optical Communication (ECOC)2007.

Hou, L.

J. Yuan, G. Zhou, H. Liu, C. Xia, X. Sang, Q. Wu, C. Yu, K. Wang, B. Yan, Y. Han, G. Farrell, and L. Hou, “Coherent anti-stokes raman scattering microscopy by dispersive wave generations in a polarization maintaining photonic crystal fiber,” Pr. Electromagn. Res. 141, 659–670 (2013).
[Crossref]

Jørgensen, M. M.

Kablukov, S. I.

Kazovsky, L. G.

Kelleher, E. J. R.

Knight, J. C.

J. D. Harvey, R. Leonhardt, S. Coen, G. K. L. Wong, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “Scalar modulation instability in the normal dispersion regime by use of a photonic crystal fiber,” Opt. Lett. 28(22), 2225–2227 (2003).
[Crossref] [PubMed]

A. Cerqueira S, J. M. Chavez Boggio, H. E. Hernandez-Figueroa, H. L. Fragnito, and J. C. Knight, “Highly efficient generation of cascaded Four-Wave Mixing products in a Hybrid Photonic Crystal Fiber,” in Proc. of European Conference on Optical Communication (ECOC)2007.

Kudlinski, A.

Lægsgaard, J.

Laurila, M.

Leick, L.

Leonhardt, R.

Leon-Saval, S. G.

Liu, H.

J. Yuan, G. Zhou, H. Liu, C. Xia, X. Sang, Q. Wu, C. Yu, K. Wang, B. Yan, Y. Han, G. Farrell, and L. Hou, “Coherent anti-stokes raman scattering microscopy by dispersive wave generations in a polarization maintaining photonic crystal fiber,” Pr. Electromagn. Res. 141, 659–670 (2013).
[Crossref]

Luo, J.

J. Zhao, P. Yan, J. Shu, C. Du, S. Ruan, H. Wei, and J. Luo, “Efficient anti-stokes signal generation through degenerate four wave mixing in an all solid photonic bandgap fiber,” Opt. Commun. 284(21), 5208–5211 (2011).
[Crossref]

Lyngsø, J. K.

Mangan, B. J.

Marhic, M. E.

Milam, D.

D. Milam, “Review and assessment of measured values of the nonlinear refractive-index coefficient of fused silica,” App. Opt. 37(3), 546–550 (1998).
[Crossref]

Murray, R. T.

Mussot, A.

Olausson, C. B.

Passaro, D.

Petersen, S. R.

Poli, F.

Popov, S. V.

Ramachandran, S.

Rashleigh, S. C.

Rasmussen, P. D.

Roberts, P. J.

Ruan, S.

J. Zhao, P. Yan, J. Shu, C. Du, S. Ruan, H. Wei, and J. Luo, “Efficient anti-stokes signal generation through degenerate four wave mixing in an all solid photonic bandgap fiber,” Opt. Commun. 284(21), 5208–5211 (2011).
[Crossref]

Russell, P. St. J.

Sang, X.

J. Yuan, G. Zhou, H. Liu, C. Xia, X. Sang, Q. Wu, C. Yu, K. Wang, B. Yan, Y. Han, G. Farrell, and L. Hou, “Coherent anti-stokes raman scattering microscopy by dispersive wave generations in a polarization maintaining photonic crystal fiber,” Pr. Electromagn. Res. 141, 659–670 (2013).
[Crossref]

Selleri, S.

Shu, J.

J. Zhao, P. Yan, J. Shu, C. Du, S. Ruan, H. Wei, and J. Luo, “Efficient anti-stokes signal generation through degenerate four wave mixing in an all solid photonic bandgap fiber,” Opt. Commun. 284(21), 5208–5211 (2011).
[Crossref]

Steinvurzel, P.

Stolen, R. H.

R. H. Stolen, “Phase-matched-stimulated four-photon mixing in silica-fiber waveguides,” IEEE J. Quantum Elect. 11(3), 100–103 (1975).
[Crossref]

R. H. Stolen, J. E. Bjorkholm, and A. Ashkin, “Phase-matched three-wave mixing in silica fiber optical waveguides,” Appl. Phys. Lett. 24(7), 308–310 (1974).
[Crossref]

Tai, B.

Taylor, J. R.

Wadsworth, W. J.

Wang, K.

J. Yuan, G. Zhou, H. Liu, C. Xia, X. Sang, Q. Wu, C. Yu, K. Wang, B. Yan, Y. Han, G. Farrell, and L. Hou, “Coherent anti-stokes raman scattering microscopy by dispersive wave generations in a polarization maintaining photonic crystal fiber,” Pr. Electromagn. Res. 141, 659–670 (2013).
[Crossref]

Wei, H.

J. Zhao, P. Yan, J. Shu, C. Du, S. Ruan, H. Wei, and J. Luo, “Efficient anti-stokes signal generation through degenerate four wave mixing in an all solid photonic bandgap fiber,” Opt. Commun. 284(21), 5208–5211 (2011).
[Crossref]

Wong, G. K. L.

Wong, K. K. Y.

Wu, Q.

J. Yuan, G. Zhou, H. Liu, C. Xia, X. Sang, Q. Wu, C. Yu, K. Wang, B. Yan, Y. Han, G. Farrell, and L. Hou, “Coherent anti-stokes raman scattering microscopy by dispersive wave generations in a polarization maintaining photonic crystal fiber,” Pr. Electromagn. Res. 141, 659–670 (2013).
[Crossref]

Xia, C.

J. Yuan, G. Zhou, H. Liu, C. Xia, X. Sang, Q. Wu, C. Yu, K. Wang, B. Yan, Y. Han, G. Farrell, and L. Hou, “Coherent anti-stokes raman scattering microscopy by dispersive wave generations in a polarization maintaining photonic crystal fiber,” Pr. Electromagn. Res. 141, 659–670 (2013).
[Crossref]

Yan, B.

J. Yuan, G. Zhou, H. Liu, C. Xia, X. Sang, Q. Wu, C. Yu, K. Wang, B. Yan, Y. Han, G. Farrell, and L. Hou, “Coherent anti-stokes raman scattering microscopy by dispersive wave generations in a polarization maintaining photonic crystal fiber,” Pr. Electromagn. Res. 141, 659–670 (2013).
[Crossref]

Yan, L.

Yan, P.

J. Zhao, P. Yan, J. Shu, C. Du, S. Ruan, H. Wei, and J. Luo, “Efficient anti-stokes signal generation through degenerate four wave mixing in an all solid photonic bandgap fiber,” Opt. Commun. 284(21), 5208–5211 (2011).
[Crossref]

Yu, C.

J. Yuan, G. Zhou, H. Liu, C. Xia, X. Sang, Q. Wu, C. Yu, K. Wang, B. Yan, Y. Han, G. Farrell, and L. Hou, “Coherent anti-stokes raman scattering microscopy by dispersive wave generations in a polarization maintaining photonic crystal fiber,” Pr. Electromagn. Res. 141, 659–670 (2013).
[Crossref]

Yuan, J.

J. Yuan, G. Zhou, H. Liu, C. Xia, X. Sang, Q. Wu, C. Yu, K. Wang, B. Yan, Y. Han, G. Farrell, and L. Hou, “Coherent anti-stokes raman scattering microscopy by dispersive wave generations in a polarization maintaining photonic crystal fiber,” Pr. Electromagn. Res. 141, 659–670 (2013).
[Crossref]

Zhao, J.

J. Zhao, P. Yan, J. Shu, C. Du, S. Ruan, H. Wei, and J. Luo, “Efficient anti-stokes signal generation through degenerate four wave mixing in an all solid photonic bandgap fiber,” Opt. Commun. 284(21), 5208–5211 (2011).
[Crossref]

Zhou, G.

J. Yuan, G. Zhou, H. Liu, C. Xia, X. Sang, Q. Wu, C. Yu, K. Wang, B. Yan, Y. Han, G. Farrell, and L. Hou, “Coherent anti-stokes raman scattering microscopy by dispersive wave generations in a polarization maintaining photonic crystal fiber,” Pr. Electromagn. Res. 141, 659–670 (2013).
[Crossref]

Zlobina, E. A.

App. Opt. (1)

D. Milam, “Review and assessment of measured values of the nonlinear refractive-index coefficient of fused silica,” App. Opt. 37(3), 546–550 (1998).
[Crossref]

Appl. Phys. Lett. (1)

R. H. Stolen, J. E. Bjorkholm, and A. Ashkin, “Phase-matched three-wave mixing in silica fiber optical waveguides,” Appl. Phys. Lett. 24(7), 308–310 (1974).
[Crossref]

IEEE J. Quantum Elect. (1)

R. H. Stolen, “Phase-matched-stimulated four-photon mixing in silica-fiber waveguides,” IEEE J. Quantum Elect. 11(3), 100–103 (1975).
[Crossref]

J. Opt. Soc. Am. B (2)

Opt. Commun. (1)

J. Zhao, P. Yan, J. Shu, C. Du, S. Ruan, H. Wei, and J. Luo, “Efficient anti-stokes signal generation through degenerate four wave mixing in an all solid photonic bandgap fiber,” Opt. Commun. 284(21), 5208–5211 (2011).
[Crossref]

Opt. Express (8)

R. T. Murray, E. J. R. Kelleher, S. V. Popov, A. Mussot, A. Kudlinski, and J. R. Taylor, “Widely tunable polarization maintaining photonic crystal fiber based parametric wavelength conversion,” Opt. Express 21(13), 15826–15833 (2013).
[Crossref] [PubMed]

S. R. Petersen, T. T. Alkeskjold, and J. Lægsgaard, “Degenerate four wave mixing in large mode area hybrid photonic crystal fibers,” Opt. Express 21(15), 18111–18124 (2013).
[Crossref] [PubMed]

P. D. Rasmussen, J. Lægsgaard, and O. Bang, “Degenerate four wave mixing in solid core photonic bandgap fibers,” Opt. Express 16(6), 4059–4068 (2008).
[Crossref] [PubMed]

E. Coscelli, F. Poli, T. T. Alkeskjold, D. Passaro, A. Cucinotta, L. Leick, J. Broeng, and S. Selleri, “Single-mode analysis of Yb-doped double-cladding distributed spectral filtering photonic crystal fibers,” Opt. Express 18(26), 27197–27204 (2010).
[Crossref]

S. R. Petersen, T. T. Alkeskjold, F. Poli, E. Coscelli, M. M. Jørgensen, M. Laurila, J. Lægsgaard, and J. Broeng, “Hybrid Ytterbium-doped large-mode-area photonic crystal fiber amplifier for long wavelengths,” Opt. Express 20(6), 6010–6020 (2012).
[Crossref] [PubMed]

T. T. Alkeskjold, “Large-mode-area ytterbium-doped fiber amplifier with distributed narrow spectral filtering and reduced bend sensitivity,” Opt. Express 17(19), 16394–16405 (2009).
[Crossref] [PubMed]

A. Argyros, T. A. Birks, S. G. Leon-Saval, C. M. B. Cordeiro, and P. St. J. Russell, “Guidance properties of low-contrast photonic bandgap fibres,” Opt. Express 13(7), 2503–2511 (2005).
[Crossref] [PubMed]

J. K. Lyngsø, B. J. Mangan, C. B. Olausson, and P. J. Roberts, “Stress induced birefringence in hybrid TIR/PBG guiding solid photonic crystal fibers,” Opt. Express 18(13), 14031–14040 (2010).
[Crossref] [PubMed]

Opt. Lett. (5)

Pr. Electromagn. Res. (1)

J. Yuan, G. Zhou, H. Liu, C. Xia, X. Sang, Q. Wu, C. Yu, K. Wang, B. Yan, Y. Han, G. Farrell, and L. Hou, “Coherent anti-stokes raman scattering microscopy by dispersive wave generations in a polarization maintaining photonic crystal fiber,” Pr. Electromagn. Res. 141, 659–670 (2013).
[Crossref]

Other (3)

A. Cerqueira S, J. M. Chavez Boggio, H. E. Hernandez-Figueroa, H. L. Fragnito, and J. C. Knight, “Highly efficient generation of cascaded Four-Wave Mixing products in a Hybrid Photonic Crystal Fiber,” in Proc. of European Conference on Optical Communication (ECOC)2007.

COMSOL Multiphysics, version 4.4, www.comsol.com .

G. P. Agrawal, Nonlinear Fiber Optics, 4, (Elsevier, 2007).

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 (11)

Fig. 1
Fig. 1 (a) Microscope image of the hybrid photonic crystal fiber. The small dark features indicate the location of the airholes, while the larger dark features indicate the location of the Germanium-doped silica rods. (b) White light transmission spectrum through a 6 m length of hybrid photonic crystal fiber. The 2nd, 3rd, and 4th bandgaps are observed. The inset shows an image of the output of 1064 nm launched in the core of the hybrid photonic crystal fiber.
Fig. 2
Fig. 2 (a) Measurement of the group birefringence in a 1.5 m length of hybrid photonic crystal fiber using the scanning wavelength method. (b) White light transmission measurement of light polarized along the slow and the fast axis in a 6 m length of hybrid PCF.
Fig. 3
Fig. 3 Calculated field distributions of the fundamental mode (FM) and the two orientations of the LP11 mode for the modes polarized along the slow axis at 1064 nm.
Fig. 4
Fig. 4 (a) Calculated overlap integral of the fundamental mode and two orientations of the LP11 modes with the core region. The polarization along the slow and fast axis are considered. The LP11 modes are labeled according to Fig. 3. The legend in Fig. 4(b) also applies to Fig. 4(a). (b) Calculated group velocity dispersion (GVD) of the fundamental mode and two orientations of the LP11 modes. The polarization along the slow and fast axis are considered. (c) Calculated birefringence, neff,s − neff,f, of the fundamental mode and two orientations of the LP11 modes. (d) Calculated group birefringence, ngs − ngf, and overlap integral with the core region of the fundamental mode polarized along the slow and fast axis.
Fig. 5
Fig. 5 Calculated parametric gain for co- and orthogonally polarized pump, signal and idler fields. The FM polarized along the slow and fast axis are considered as the pump mode, indicated with the arrow in the ”Input” microscope image inset. A pump wavelength and power of respectively 1064 nm and 25 kW is used. The parametric gain for signal and idler generated in the FM, HOM11, and HOM12 is calculated, the polarization states of the FWM components are indicated with the arrow in the ”Output” microscope image inset. The legend in the bottom right graph applies to all the graphs.
Fig. 6
Fig. 6 (a) Calculated parametric gain in the hybrid photonic crystal fiber (PCF) for orthogonally polarized pump, signal, and idler fields, all in the fundamental mode. The pump is polarized along the slow axis, and the signal and idler are polarized along the fast axis. The parametric gain of a simulated large mode area (LMA) polarization maintaining (PM) fiber with a core diameter of 28 μm and birefringence of 2.21 × 10−5 is also shown for orthogonally polarized pump, signal and idler. A pump wavelength and power of 1064 nm and 25 kW, respectively, are used in both cases. (b) Calculated maximum parametric gain in a simulated LMA PM fiber with a mode field diameter of 28 μm for a pump wavelength of 1064 nm and a pump power of 25 kW. The gain values lies in the range 1.9 m−1 and 2.2 m−1. The mode refractive indices are calculated by the Sellmeier equation, a constant offset corresponding to the birefringence is used in the fast axis.
Fig. 7
Fig. 7 Schematic illustration of the measurement setup. A linearly polarized Ytterbium-doped 40 ps 1064 nm fiber laser with repetition rate of 1 MHz is launched in the hybrid photonic crystal fiber through two half-wave plates, λ/2, a polarizing beam splitter, and a 1064 nm laser line filter. The fiber output is collected in an integrating sphere through a polarizer.
Fig. 8
Fig. 8 Output spectra of the hybrid photonic crystal fiber for different pump peak powers. The pump polarization state is indicated with the arrow in the ”Input” microscope image inset. The output polarization state is indicated with the arrow in the ”Output” microscope image inset. The pump peak powers are stated in the legends, the legends shown in the bottom graphs also applies to the graphs of same polarization input state.
Fig. 9
Fig. 9 Output from the 2 m long hybrid PCF with an input peak power of 210 kW. The wavelengths of the imaged modes are stated in the figures. In (a) the output is divided spatially through a prism, the components are imaged onto an IR-card. In (b) and (c) the output is imaged onto a black and white CCD camera through a narrow spectral filter.
Fig. 10
Fig. 10 Average output power with respect to the average input power of the hybrid photonic crystal fiber. The total output power and the power in each of the principal fiber axes, the slow and fast axis, are shown. The fiber length and pump polarization are stated under each graph.
Fig. 11
Fig. 11 Conversion efficiency of the 848 nm component given by average output power at 848 nm with respect to the average input power of the pump laser. Cascaded four-wave mixing is observed for pump peak powers beyound 165 kW giving rise to light generation at 705 nm. An image of the mode at 705 nm is shown in the inset.

Tables (1)

Tables Icon

Table 1 Physical values used in the calculation of the stress birefringence.

Equations (25)

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

2 E n 2 c 2 E t = μ 0 2 P N L t 2 ,
E = 1 2 j = 1 3 [ E j e i ω j t + E j * e i ω j t ] ,
P NL = 1 2 j = 1 3 [ P j e i ω j t + P j * e i ω j t ] .
P NL = ε 0 χ x x x x ( 3 ) ( E · E ) E .
P 1 = 1 4 ε 0 χ x x x x ( 3 ) ( ( E 1 · E 1 ) E 1 * + 2 ( E 1 * · E 1 ) E 1 + 2 ( E 2 * · E 2 ) E 1 + 2 ( E 3 * · E 3 ) E 1 + 2 ( E 2 * · E 1 ) E 2 + 2 ( E 3 * · E 1 ) E 3 + 2 ( E 2 · E 1 ) E 2 * + 2 ( E 3 · E 1 ) E 3 * + 2 ( E 3 · E 1 * ) E 2 + 2 ( E 2 · E 1 * ) E 3 + 2 ( E 2 · E 3 ) E 1 * ) ,
P 2 = 1 4 ε 0 χ x x x x ( 3 ) ( ( E 2 · E 2 ) E 2 * + 2 ( E 2 * · E 2 ) E 2 + 2 ( E 1 * · E 1 ) E 2 + 2 ( E 3 * · E 3 ) E 2 + 2 ( E 1 * · E 2 ) E 1 + 2 ( E 3 * · E 2 ) E 3 + 2 ( E 1 · E 2 ) E 1 * + 2 ( E 3 · E 2 ) E 3 * + 2 ( E 1 · E 3 * ) E 1 + ( E 1 · E 1 ) E 3 * ) ,
P 3 = 1 4 ε 0 χ x x x x ( 3 ) ( ( E 3 · E 3 ) E 3 * + 2 ( E 3 * · E 3 ) E 3 + 2 ( E 1 * · E 1 ) E 3 + 2 ( E 2 * · E 2 ) E 3 + 2 ( E 1 * · E 3 ) E 1 + 2 ( E 2 * · E 3 ) E 2 + 2 ( E 1 · E 3 ) E 1 * + 2 ( E 2 · E 3 ) E 2 * + 2 ( E 1 · E 2 * ) E 1 + ( E 1 · E 1 ) E 2 * ) .
P 1 = 1 4 ε 0 χ x x x x ( 3 ) ( ( E 1 · E 1 ) E 1 * + 2 ( E 1 * · E 1 ) E 1 ) ,
P 2 = 1 2 ε 0 χ x x x x ( 3 ) ( ( E 1 * · E 1 ) E 2 + ( E 1 * · E 2 ) E 1 + ( E 1 · E 2 ) E 1 * + ( E 1 · E 3 * ) E 1 + 1 2 ( E 1 · E 1 ) E 3 * ) ,
P 3 = 1 2 ε 0 χ x x x x ( 3 ) ( ( E 1 * · E 1 ) E 3 + ( E 1 * · E 3 ) E 1 + ( E 1 · E 3 ) E 1 * + ( E 1 · E 2 * ) E 1 + 1 2 ( E 1 · E 1 ) E 2 * ) .
E j = F j ( x , y ) A j ( z ) e i β j z F j ( x , y ) A j e i β j z ,
A 1 2 x 2 F 1 ( x , y ) + A 1 2 y 2 F 1 ( x , y ) F 1 ( x , y ) β 1 2 A 1 + n 2 ω 1 2 c 2 F 1 ( x , y ) A 1 + F 1 ( x , y ) 2 z 2 A 1 + 2 i β 1 F 1 ( x , y ) z A 1 = ω 1 2 4 c 2 χ x x x x ( 3 ) F 1 2 ( x , y ) F 1 * ( x , y ) ( ( A 1 · A 1 ) A 1 * + 2 ( A 1 * · A 1 ) A 1 ) ,
F 1 ( x , y ) 2 x 2 A 1 + 2 i β 1 F 1 ( x , y ) z A 1 = ω 1 2 4 c 2 χ x x x x ( 3 ) F 1 2 ( x , y ) F 1 * ( x , y ) ( ( A 1 · A 1 ) A 1 * + 2 ( A 1 * · A 1 ) A 1 ) .
z A 1 = i ω 1 n 2 3 c F 1 2 ( x , y ) F 1 * 2 ( x , y ) d x d y F 1 ( x , y ) F 1 * ( x , y ) d x d y ( ( A 1 · A 1 ) A 1 * + 2 ( A 1 * · A 1 ) A 1 ) .
z A 1 = i ω 1 n 2 3 c F 1 2 ( x , y ) F 1 * 2 ( x , y ) d x d y ( F 1 ( x , y ) F 1 * ( x , y ) d x d y ) 2 ( ( A 1 · A 1 ) A 1 * + 2 ( A 1 * · A 1 ) A 1 ) .
z A 2 = 2 i ω 2 n 2 3 c [ f 12 ( ( A 1 * · A 1 ) A 2 + ( A 1 * · A 2 ) A 1 + ( A 1 · A 2 ) A 1 * ) + f 1132 ( ( A 3 * · A 1 ) A 1 + 1 2 ( A 1 · A 1 ) A 3 * ) e i Δ β z ] ,
z A 3 = 2 i ω 2 n 2 3 c [ f 13 ( ( A 1 * · A 1 ) A 3 + ( A 1 * · A 3 ) A 1 + ( A 1 · A 3 ) A 1 * ) + f 1123 ( ( A 2 * · A 1 ) A 1 + 1 2 ( A 1 · A 1 ) A 2 * ) e i Δ β z ] ,
f j k = F j * F j F k * F k d x d y F j F j * d x d y F k F k * d x d y ,
f i j k l = F i F j F k * F l * d x d y F i F i * d x d y F j F j * d x d y F k F k * d x d y F l F l * d x d y .
A j = A j ( e ^ x 0 ) ,
κ = Δ β + 2 n 2 ω 1 c P p ( f 12 + f 13 f 11 ) ,
g = ( n 2 ω 1 c P p f 1123 ) 2 ( κ 2 ) 2 ,
A 1 = A 1 ( e ^ x 0 ) , A j = A j ( 0 e ^ y ) , j = 2 , 3.
κ = Δ β + 2 n 2 ω 1 c P p ( 1 3 f 12 + 1 3 f 13 f 11 ) ,
g = ( n 2 ω 1 3 c P p f 1123 ) 2 ( κ 2 ) 2 ,

Metrics