Abstract

We report on a possible phase matching between two fundamental modes guided in an appropriately designed photonic crystal fiber. The phase index matching condition can be perfectly fulfilled for second or third harmonic generation and for wavelengths over a large spectral range, simply by tuning the lattice pitch. This can be achieved in such a structure thanks to the coexistence of total internal reflection and photonic bandgap guidance, leading to two different dispersive behaviours for the fundamental and the harmonic waves.

© 2008 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  7. C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Mller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, "Low-loss hollow-core silica/air photonic bandgap fibre," Nature 424, 657-659 (2003).
    [CrossRef] [PubMed]
  8. F. Luan, A. K. George, T. D. Hedley, G. J. Pearce, D.M. Bird, J. C. Knight, and P. St. J. Russell, "All-solid photonic bandgap fiber," Opt. Lett. 29, 2369-2371 (2004).
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    [CrossRef]
  12. W. H. Reeves, J. C. Knight, and P. St. J. Russell, "Demonstration of ultra-flattened dispersion in photonic crystal fibers," Opt. Express 10, 609-613 (2002).
    [PubMed]
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    [CrossRef]
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    [CrossRef]

2007 (3)

2006 (2)

M. Bache, H. Nielsen, J. Lægsgaard, and O. Bang, "Tuning quadratic nonlinear photonic crystal fibers for zero group-velocity mismatch," Opt. Lett. 31, 1612-1614 (2006).
[CrossRef] [PubMed]

J. M. Dudley, G. Genty, and S. Cohen, "Supercontinuum generation in photonic crystal fiber," Rev. Mod. Phys. 78, 1135-1184 (2006).
[CrossRef]

2005 (3)

2004 (3)

F. Luan, A. K. George, T. D. Hedley, G. J. Pearce, D.M. Bird, J. C. Knight, and P. St. J. Russell, "All-solid photonic bandgap fiber," Opt. Lett. 29, 2369-2371 (2004).
[CrossRef] [PubMed]

A. Ortigosa-Blanch, A. Dez, M. Delgado-Pinar, J. L. Cruz, and M. V. Andrs, "Ultrahigh birefringent nonlinear microstructured fiber," IEEE Photon. Technol. Lett. 16, 1667-1669 (2004).
[CrossRef]

J. Lægsgaard and A. Bjarklev, "Photonic crystal fibres with large nonlinear coefficients," J. Opt. A, Pure Appl. Opt. 6, 1-5 (2004).
[CrossRef]

2003 (3)

P. St. J. Russell, "Photonic crystal fibers," Science 299, 358-362 (2003).
[CrossRef] [PubMed]

J. C. Knight, "Photonic crystal fibres," Nature 424, 847-851 (2003).
[CrossRef] [PubMed]

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Mller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, "Low-loss hollow-core silica/air photonic bandgap fibre," Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

2002 (1)

2001 (1)

2000 (1)

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. St. J. Russell, "Anomalous dispersion in photonic crystal fiber," IEEE Photon. Technol. Lett. 12, 807-809 (2000).
[CrossRef]

1999 (2)

1987 (2)

E. Yablonovitch, "Inhibited Spontaneous Emission in Solid-State Physics and Electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987).
[CrossRef] [PubMed]

Allan, D. C.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Mller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, "Low-loss hollow-core silica/air photonic bandgap fibre," Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, "Single-mode photonic band gap guidance of light in air," Science 285, 1537-1539 (1999).
[CrossRef] [PubMed]

Andrs, M. V.

A. Ortigosa-Blanch, A. Dez, M. Delgado-Pinar, J. L. Cruz, and M. V. Andrs, "Ultrahigh birefringent nonlinear microstructured fiber," IEEE Photon. Technol. Lett. 16, 1667-1669 (2004).
[CrossRef]

Arriaga, J.

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. St. J. Russell, "Anomalous dispersion in photonic crystal fiber," IEEE Photon. Technol. Lett. 12, 807-809 (2000).
[CrossRef]

Bache, M.

Bang, O.

Benabid, F.

G. S. Wiederhecker, C. M. B. Cordeiro, F. Couny, F. Benabid, S. A. Maier, J. C. Knight, C. H. B. Cruz, and H. L. Fragnito, "Field enhancement within an optical fibre with a subwavelength air core," Nat. Photonics 1, 115-118 (2007).
[CrossRef]

Bétourné, A.

Bigot, L.

Bird, D.M.

Birks, T. A.

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. St. J. Russell, "Anomalous dispersion in photonic crystal fiber," IEEE Photon. Technol. Lett. 12, 807-809 (2000).
[CrossRef]

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, "Single-mode photonic band gap guidance of light in air," Science 285, 1537-1539 (1999).
[CrossRef] [PubMed]

Bjarklev, A.

J. Lægsgaard and A. Bjarklev, "Photonic crystal fibres with large nonlinear coefficients," J. Opt. A, Pure Appl. Opt. 6, 1-5 (2004).
[CrossRef]

Bonfrate, G.

Borrelli, N. F.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Mller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, "Low-loss hollow-core silica/air photonic bandgap fibre," Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

Bouwmans, G.

Broderick, N. G.

Cohen, S.

J. M. Dudley, G. Genty, and S. Cohen, "Supercontinuum generation in photonic crystal fiber," Rev. Mod. Phys. 78, 1135-1184 (2006).
[CrossRef]

Cordeiro, C. M. B.

G. S. Wiederhecker, C. M. B. Cordeiro, F. Couny, F. Benabid, S. A. Maier, J. C. Knight, C. H. B. Cruz, and H. L. Fragnito, "Field enhancement within an optical fibre with a subwavelength air core," Nat. Photonics 1, 115-118 (2007).
[CrossRef]

Couny, F.

G. S. Wiederhecker, C. M. B. Cordeiro, F. Couny, F. Benabid, S. A. Maier, J. C. Knight, C. H. B. Cruz, and H. L. Fragnito, "Field enhancement within an optical fibre with a subwavelength air core," Nat. Photonics 1, 115-118 (2007).
[CrossRef]

Cregan, R. F.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, "Single-mode photonic band gap guidance of light in air," Science 285, 1537-1539 (1999).
[CrossRef] [PubMed]

Cruz, C. H. B.

G. S. Wiederhecker, C. M. B. Cordeiro, F. Couny, F. Benabid, S. A. Maier, J. C. Knight, C. H. B. Cruz, and H. L. Fragnito, "Field enhancement within an optical fibre with a subwavelength air core," Nat. Photonics 1, 115-118 (2007).
[CrossRef]

Cruz, J. L.

A. Ortigosa-Blanch, A. Dez, M. Delgado-Pinar, J. L. Cruz, and M. V. Andrs, "Ultrahigh birefringent nonlinear microstructured fiber," IEEE Photon. Technol. Lett. 16, 1667-1669 (2004).
[CrossRef]

de Sandro, J. P.

Delgado-Pinar, M.

A. Ortigosa-Blanch, A. Dez, M. Delgado-Pinar, J. L. Cruz, and M. V. Andrs, "Ultrahigh birefringent nonlinear microstructured fiber," IEEE Photon. Technol. Lett. 16, 1667-1669 (2004).
[CrossRef]

Dez, A.

A. Ortigosa-Blanch, A. Dez, M. Delgado-Pinar, J. L. Cruz, and M. V. Andrs, "Ultrahigh birefringent nonlinear microstructured fiber," IEEE Photon. Technol. Lett. 16, 1667-1669 (2004).
[CrossRef]

Douay, M.

Dudley, J. M.

J. M. Dudley, G. Genty, and S. Cohen, "Supercontinuum generation in photonic crystal fiber," Rev. Mod. Phys. 78, 1135-1184 (2006).
[CrossRef]

Fragnito, H. L.

G. S. Wiederhecker, C. M. B. Cordeiro, F. Couny, F. Benabid, S. A. Maier, J. C. Knight, C. H. B. Cruz, and H. L. Fragnito, "Field enhancement within an optical fibre with a subwavelength air core," Nat. Photonics 1, 115-118 (2007).
[CrossRef]

Gallagher, M. T.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Mller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, "Low-loss hollow-core silica/air photonic bandgap fibre," Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

Genty, G.

J. M. Dudley, G. Genty, and S. Cohen, "Supercontinuum generation in photonic crystal fiber," Rev. Mod. Phys. 78, 1135-1184 (2006).
[CrossRef]

George, A. K.

Hedley, T. D.

Joannopoulos, J. D.

John, S.

S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987).
[CrossRef] [PubMed]

Johnson, S. G.

Kazansky, P. G.

Knight, J. C.

G. S. Wiederhecker, C. M. B. Cordeiro, F. Couny, F. Benabid, S. A. Maier, J. C. Knight, C. H. B. Cruz, and H. L. Fragnito, "Field enhancement within an optical fibre with a subwavelength air core," Nat. Photonics 1, 115-118 (2007).
[CrossRef]

F. Luan, A. K. George, T. D. Hedley, G. J. Pearce, D.M. Bird, J. C. Knight, and P. St. J. Russell, "All-solid photonic bandgap fiber," Opt. Lett. 29, 2369-2371 (2004).
[CrossRef] [PubMed]

J. C. Knight, "Photonic crystal fibres," Nature 424, 847-851 (2003).
[CrossRef] [PubMed]

W. H. Reeves, J. C. Knight, and P. St. J. Russell, "Demonstration of ultra-flattened dispersion in photonic crystal fibers," Opt. Express 10, 609-613 (2002).
[PubMed]

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. St. J. Russell, "Anomalous dispersion in photonic crystal fiber," IEEE Photon. Technol. Lett. 12, 807-809 (2000).
[CrossRef]

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, "Single-mode photonic band gap guidance of light in air," Science 285, 1537-1539 (1999).
[CrossRef] [PubMed]

Koch, K. W.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Mller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, "Low-loss hollow-core silica/air photonic bandgap fibre," Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

Lægsgaard, J.

M. Bache, H. Nielsen, J. Lægsgaard, and O. Bang, "Tuning quadratic nonlinear photonic crystal fibers for zero group-velocity mismatch," Opt. Lett. 31, 1612-1614 (2006).
[CrossRef] [PubMed]

J. Lægsgaard and A. Bjarklev, "Photonic crystal fibres with large nonlinear coefficients," J. Opt. A, Pure Appl. Opt. 6, 1-5 (2004).
[CrossRef]

Levenson, J. A.

Lopez, F.

Luan, F.

Maier, S. A.

G. S. Wiederhecker, C. M. B. Cordeiro, F. Couny, F. Benabid, S. A. Maier, J. C. Knight, C. H. B. Cruz, and H. L. Fragnito, "Field enhancement within an optical fibre with a subwavelength air core," Nat. Photonics 1, 115-118 (2007).
[CrossRef]

Mangan, B. J.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, "Single-mode photonic band gap guidance of light in air," Science 285, 1537-1539 (1999).
[CrossRef] [PubMed]

Margulis, W.

Mller, D.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Mller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, "Low-loss hollow-core silica/air photonic bandgap fibre," Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

Myrén, N.

Nielsen, H.

Ortigosa-Blanch, A.

A. Ortigosa-Blanch, A. Dez, M. Delgado-Pinar, J. L. Cruz, and M. V. Andrs, "Ultrahigh birefringent nonlinear microstructured fiber," IEEE Photon. Technol. Lett. 16, 1667-1669 (2004).
[CrossRef]

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. St. J. Russell, "Anomalous dispersion in photonic crystal fiber," IEEE Photon. Technol. Lett. 12, 807-809 (2000).
[CrossRef]

Pearce, G. J.

Perrin, M.

Provino, L.

Pruneri, V.

Pureur, V.

Quiquempois, Y.

Reeves, W. H.

Richardson, D. J.

Roberts, P. J.

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, "Single-mode photonic band gap guidance of light in air," Science 285, 1537-1539 (1999).
[CrossRef] [PubMed]

Russell, P. St. J.

F. Luan, A. K. George, T. D. Hedley, G. J. Pearce, D.M. Bird, J. C. Knight, and P. St. J. Russell, "All-solid photonic bandgap fiber," Opt. Lett. 29, 2369-2371 (2004).
[CrossRef] [PubMed]

P. St. J. Russell, "Photonic crystal fibers," Science 299, 358-362 (2003).
[CrossRef] [PubMed]

W. H. Reeves, J. C. Knight, and P. St. J. Russell, "Demonstration of ultra-flattened dispersion in photonic crystal fibers," Opt. Express 10, 609-613 (2002).
[PubMed]

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. St. J. Russell, "Anomalous dispersion in photonic crystal fiber," IEEE Photon. Technol. Lett. 12, 807-809 (2000).
[CrossRef]

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, "Single-mode photonic band gap guidance of light in air," Science 285, 1537-1539 (1999).
[CrossRef] [PubMed]

Simonneau, C.

Smith, C. M.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Mller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, "Low-loss hollow-core silica/air photonic bandgap fibre," Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

Venkataraman, N.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Mller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, "Low-loss hollow-core silica/air photonic bandgap fibre," Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

Vidakovic, P.

Wadsworth, W. J.

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. St. J. Russell, "Anomalous dispersion in photonic crystal fiber," IEEE Photon. Technol. Lett. 12, 807-809 (2000).
[CrossRef]

West, J. A.

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Mller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, "Low-loss hollow-core silica/air photonic bandgap fibre," Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

Wiederhecker, G. S.

G. S. Wiederhecker, C. M. B. Cordeiro, F. Couny, F. Benabid, S. A. Maier, J. C. Knight, C. H. B. Cruz, and H. L. Fragnito, "Field enhancement within an optical fibre with a subwavelength air core," Nat. Photonics 1, 115-118 (2007).
[CrossRef]

Yablonovitch, E.

E. Yablonovitch, "Inhibited Spontaneous Emission in Solid-State Physics and Electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

IEEE Photon. Technol. Lett. (2)

J. C. Knight, J. Arriaga, T. A. Birks, A. Ortigosa-Blanch, W. J. Wadsworth, and P. St. J. Russell, "Anomalous dispersion in photonic crystal fiber," IEEE Photon. Technol. Lett. 12, 807-809 (2000).
[CrossRef]

A. Ortigosa-Blanch, A. Dez, M. Delgado-Pinar, J. L. Cruz, and M. V. Andrs, "Ultrahigh birefringent nonlinear microstructured fiber," IEEE Photon. Technol. Lett. 16, 1667-1669 (2004).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (1)

J. Lægsgaard and A. Bjarklev, "Photonic crystal fibres with large nonlinear coefficients," J. Opt. A, Pure Appl. Opt. 6, 1-5 (2004).
[CrossRef]

Nat. Photonics (1)

G. S. Wiederhecker, C. M. B. Cordeiro, F. Couny, F. Benabid, S. A. Maier, J. C. Knight, C. H. B. Cruz, and H. L. Fragnito, "Field enhancement within an optical fibre with a subwavelength air core," Nat. Photonics 1, 115-118 (2007).
[CrossRef]

Nature (2)

C. M. Smith, N. Venkataraman, M. T. Gallagher, D. Mller, J. A. West, N. F. Borrelli, D. C. Allan, and K. W. Koch, "Low-loss hollow-core silica/air photonic bandgap fibre," Nature 424, 657-659 (2003).
[CrossRef] [PubMed]

J. C. Knight, "Photonic crystal fibres," Nature 424, 847-851 (2003).
[CrossRef] [PubMed]

Opt. Express (6)

Opt. Lett. (4)

Phys. Rev. Lett. (2)

E. Yablonovitch, "Inhibited Spontaneous Emission in Solid-State Physics and Electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

J. M. Dudley, G. Genty, and S. Cohen, "Supercontinuum generation in photonic crystal fiber," Rev. Mod. Phys. 78, 1135-1184 (2006).
[CrossRef]

Science (2)

R. F. Cregan, B. J. Mangan, J. C. Knight, T. A. Birks, P. St. J. Russell, P. J. Roberts, and D. C. Allan, "Single-mode photonic band gap guidance of light in air," Science 285, 1537-1539 (1999).
[CrossRef] [PubMed]

P. St. J. Russell, "Photonic crystal fibers," Science 299, 358-362 (2003).
[CrossRef] [PubMed]

Other (2)

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: molding the flow of light, (Princeton: Princeton University Press, 1995).

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Figures (6)

Fig. 1.
Fig. 1.

Index difference Δnmaterial in bulk silica glass between a fundamental wavelength λ fund and its second or third harmonic λ harm. Δnmaterial=n(λ fund)-n(λ harm).

Fig. 2.
Fig. 2.

photonic bandgap diagrams of the hybrid structure for different values of r/Λ, calculated without the material dispersion. For each value, the borders of the 3 first bandgaps, as well as the Fundamental Space filling Mode line are plotted. Inset, the cladding unit cell inside the parallelogram.

Fig. 3.
Fig. 3.

Schematic transversal cut and associated band diagram for the hybrid guiding PCF. The three first bandgaps are shaded in light gray. Also shown the fundamental space filling mode index (dashed line). The region where MTIR guidance is possible is shaded in dark gray. The effective index of the fundamental core mode in the 1st bandgap (triangle) and the fundamental MTIR guided core mode (cross) are also plotted. The material dispersion has not been considered here.

Fig. 4.
Fig. 4.

Index difference Δnwaveguide in the hybrid guiding PCF between a fundamental wavelength λ fund, guided by the total reflection effect, and its second or third harmonic λ harm, guided inside the first bandgap. The colored part of both curves indicates that Δnwaveguide is sufficient to compensate Δnmaterial·Δnwaveguide=n(λ fund)-n(λ harm).

Fig. 5.
Fig. 5.

Normalized intensity profiles along the two spatial cross sections defined in Fig. 3, for the fundamental mode at 1500 nm (red line) and its phase index matched second harmonic at 750 nm (green line).

Fig. 6.
Fig. 6.

Tunability of the phase index matching condition for SHG and THG: evolution of Λ as a function of the fundamental wavelength λ fund for various ratio r/Λ.

Tables (1)

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Table 1. Designs fulfiling the phase index matching condition for SHG.

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