Abstract

Degenerate four wave mixing in solid core photonic bandgap fibers is studied theoretically. We demonstrate the possibility of generating parametric gain across bandgaps, and propose a specific design suited for degenerate four wave mixing when pumping at 532nm. The possibility of tuning the efficiency of the parametric gain by varying the temperature is also considered. The results are verified by numerical simulations of pulse propagation.

© 2008 Optical Society of America

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  1. P. St. J. Russell, "Photonic-Crystal Fibers," J. Lightwave Technol. 24, 4729-4749 (2006).
    [CrossRef]
  2. J. M. Dudley, G. Genty, and S. Coen, "Supercontinuum generation in photonic crystal fiber," Rev. Mod. Phys.  78, 1135 (2006).
    [CrossRef]
  3. R. T. Bise, R. S. Windeler, K. S. Kranz, C. Kerbage, B. J. Eggleton, and D. J. Trevor, "Tunable photonic bandgap fiber," in Optical Fiber Communications Conference, Post Conference vol. 70 of OSA Trends in Optics and Photonics Series Technical Digest (Optical Society of America, Washington, D.C., 2002), 466-468.
  4. T. Larsen, A. Bjarklev, D. Hermann, and J. Broeng, "Optical devices based on liquid crystal photonic bandgap fibres," Opt. Express 11, 2589-2596 (2003). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-11-20-2589.
    [CrossRef] [PubMed]
  5. 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]
  6. A. Argyros, T. Birks, S. Leon-Saval, C. M. Cordeiro, F. Luan, and P. St. J. Russell, "Photonic bandgap with an index step of one percent," Opt. Express 13, 309-314 (2005). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-13-1-309.
    [CrossRef] [PubMed]
  7. N. M. Litchinitser, A. K. Abeeluck, C. Headley, and B. J. Eggleton, "Antiresonant reflecting photonic crystal optical waveguides," Opt. Lett. 27, 1592-1594 (2002).
    [CrossRef]
  8. K. Saitoh, N. Florous, and M. Koshiba, "Ultra-flattened chromatic dispersion controllability using a defectedcore photonic crystal fiber with low confinement losses," Opt. Express 13, 8365-8371 (2005). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-13-21-8365.
    [CrossRef] [PubMed]
  9. K. S. Abedin, J. T. Gopinath, E. P. Ippen, C. E. Kerbage, R. S. Windeler, and B. J. Eggleton, "Highly nondegenerate femtosecond four-wave mixing in tapered microstructure fiber," Appl. Phys. Lett. 81, 1384-1386 (2002).
    [CrossRef]
  10. D. A. Akimov, E. E. Serebryannikov, A. M. Zheltikov, M. Schmitt, R. Maksimenka, W. Kiefer, K. V. Dukel’skii, V. S. Shevandin, and Y. N. Kondrat’ev, "Efficient anti-Stokes generation through phase-matched four-wave mixing in higher-order modes of a microstructure fiber," Opt. Lett. 28, 1948-1950 (2003).
    [CrossRef] [PubMed]
  11. A. Fuerbach, P. Steinvurzel, J. A. Bolger, A. Nulsen, and B. J. Eggleton, "Nonlinear propagation effects in antiresonant high-index inclusion photonic crystal fibers," Opt. Lett. 30, 830-832 (2005).
    [CrossRef] [PubMed]
  12. A. Fuerbach, P. Steinvurzel, J. A. Bolger, and B. J. Eggleton, "Nonlinear pulse propagation at zero dispersion wavelength in anti-resonant photonic crystal fibers," Opt. Express 13, 2977-2987 (2005). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-13-8-2977.
    [CrossRef] [PubMed]
  13. A. V. Husakou and J. Herrmann, "Supercontinuum Generation of Higher-Order Solitons by Fission in Photonic Crystal Fibers," Phys. Rev. Lett. 87, 203,901 (2001).
  14. I. Cristiani, R. Tediosi, L. Tartara, and V. Degiorgio, "Dispersive wave generation by solitons in microstructured optical fibers," Opt. Express 12, 124-135 (2004). URL >http://www.opticsexpress.org/abstract.cfm?URI=oe-12-1-124.
    [CrossRef] [PubMed]
  15. S. Lebrun, P. Delaye, R. Frey, and G. Roosen, "High-efficiency single-mode Raman generation in a liquid-filled photonic bandgap fiber," Opt. Lett. 32, 337-339 (2007).
    [CrossRef] [PubMed]
  16. G. P. Agrawal, Nonlinear Fiber Optics, third edition (Academic Press, San Diego, 2001).
  17. Comsol Multiphysics 3.3a (2007) URLwww.comsol.com.
  18. Cargille Laboratories, Specifications of Cargille Optical Liquids URL www.cargille.com.
  19. P. Steinvurzel, C. M. de Sterke, B. J. Eggleton, B. T. Kuhlmey, and M. J. Steel, "Mode field distributions in solid core photonic bandgap fibers," Opt. Commun. 263, 207-213 (2006).
    [CrossRef]
  20. T. Birks, D. Bird, T. Hedley, J. Pottage, and P. St. J. Russell, "Scaling laws and vector effects in bandgap-guiding fibres," Opt. Express 12, 69-74 (2004). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-12-1-69.
    [CrossRef] [PubMed]
  21. T. A. Birks, F. Luan, G. J. Pearce, A. Wang, J. C. Knight, and D. M. Bird, "Bend loss in all-solid bandgap fibres," Opt. Express 14, 5688-5698 (2006). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-14-12-5688.
    [CrossRef] [PubMed]
  22. W. H. Reeves, J. C. Knight, P. St. J. Russell, and P. J. Roberts, "Demonstration of ultra-flattened dispersion in photonic crystal fibers," Opt. Express 10, 609-613 (2002). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-10-14-609.
    [PubMed]
  23. T. Toyoda and M. Yabe, "The temperature dependence of the refractive indices of fused silica and crystal quartz," J. Phys. D 16, L97 (1983).
    [CrossRef]
  24. R. W. Boyd, Nonlinear Optics, second edition (Academic Press, San Diego, 2003).
  25. P. V. Mamyshev and S. V. Chernikov, "Ultrashort-pulse propagation in optical fibers," Opt. Lett. 15, 1076 (1990).
    [CrossRef] [PubMed]
  26. J. Laegsgaard, "Mode profile dispersion in the generalised nonlinear Schr¨odinger equation," Opt. Express 15, 16,110-16,123 (2007). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-15-24-16110.
    [CrossRef]
  27. S. Coen, D. A. Wardle, and J. D. Harvey, "Observation of Non-Phase-Matched Parametric Amplification in Resonant Nonlinear Optics," Phys. Rev. Lett. 89, 273901 (2002).
    [CrossRef]

2007 (1)

2006 (2)

P. St. J. Russell, "Photonic-Crystal Fibers," J. Lightwave Technol. 24, 4729-4749 (2006).
[CrossRef]

P. Steinvurzel, C. M. de Sterke, B. J. Eggleton, B. T. Kuhlmey, and M. J. Steel, "Mode field distributions in solid core photonic bandgap fibers," Opt. Commun. 263, 207-213 (2006).
[CrossRef]

2005 (1)

2004 (1)

2003 (1)

2002 (3)

N. M. Litchinitser, A. K. Abeeluck, C. Headley, and B. J. Eggleton, "Antiresonant reflecting photonic crystal optical waveguides," Opt. Lett. 27, 1592-1594 (2002).
[CrossRef]

S. Coen, D. A. Wardle, and J. D. Harvey, "Observation of Non-Phase-Matched Parametric Amplification in Resonant Nonlinear Optics," Phys. Rev. Lett. 89, 273901 (2002).
[CrossRef]

K. S. Abedin, J. T. Gopinath, E. P. Ippen, C. E. Kerbage, R. S. Windeler, and B. J. Eggleton, "Highly nondegenerate femtosecond four-wave mixing in tapered microstructure fiber," Appl. Phys. Lett. 81, 1384-1386 (2002).
[CrossRef]

2001 (1)

A. V. Husakou and J. Herrmann, "Supercontinuum Generation of Higher-Order Solitons by Fission in Photonic Crystal Fibers," Phys. Rev. Lett. 87, 203,901 (2001).

1990 (1)

1983 (1)

T. Toyoda and M. Yabe, "The temperature dependence of the refractive indices of fused silica and crystal quartz," J. Phys. D 16, L97 (1983).
[CrossRef]

Abedin, K. S.

K. S. Abedin, J. T. Gopinath, E. P. Ippen, C. E. Kerbage, R. S. Windeler, and B. J. Eggleton, "Highly nondegenerate femtosecond four-wave mixing in tapered microstructure fiber," Appl. Phys. Lett. 81, 1384-1386 (2002).
[CrossRef]

Abeeluck, A. K.

Akimov, D. A.

Bird, D. M.

Bolger, J. A.

Chernikov, S. V.

Coen, S.

S. Coen, D. A. Wardle, and J. D. Harvey, "Observation of Non-Phase-Matched Parametric Amplification in Resonant Nonlinear Optics," Phys. Rev. Lett. 89, 273901 (2002).
[CrossRef]

de Sterke, C. M.

P. Steinvurzel, C. M. de Sterke, B. J. Eggleton, B. T. Kuhlmey, and M. J. Steel, "Mode field distributions in solid core photonic bandgap fibers," Opt. Commun. 263, 207-213 (2006).
[CrossRef]

Delaye, P.

Dukel’skii, K. V.

Eggleton, B. J.

P. Steinvurzel, C. M. de Sterke, B. J. Eggleton, B. T. Kuhlmey, and M. J. Steel, "Mode field distributions in solid core photonic bandgap fibers," Opt. Commun. 263, 207-213 (2006).
[CrossRef]

A. Fuerbach, P. Steinvurzel, J. A. Bolger, A. Nulsen, and B. J. Eggleton, "Nonlinear propagation effects in antiresonant high-index inclusion photonic crystal fibers," Opt. Lett. 30, 830-832 (2005).
[CrossRef] [PubMed]

N. M. Litchinitser, A. K. Abeeluck, C. Headley, and B. J. Eggleton, "Antiresonant reflecting photonic crystal optical waveguides," Opt. Lett. 27, 1592-1594 (2002).
[CrossRef]

K. S. Abedin, J. T. Gopinath, E. P. Ippen, C. E. Kerbage, R. S. Windeler, and B. J. Eggleton, "Highly nondegenerate femtosecond four-wave mixing in tapered microstructure fiber," Appl. Phys. Lett. 81, 1384-1386 (2002).
[CrossRef]

Frey, R.

Fuerbach, A.

George, A. K.

Gopinath, J. T.

K. S. Abedin, J. T. Gopinath, E. P. Ippen, C. E. Kerbage, R. S. Windeler, and B. J. Eggleton, "Highly nondegenerate femtosecond four-wave mixing in tapered microstructure fiber," Appl. Phys. Lett. 81, 1384-1386 (2002).
[CrossRef]

Harvey, J. D.

S. Coen, D. A. Wardle, and J. D. Harvey, "Observation of Non-Phase-Matched Parametric Amplification in Resonant Nonlinear Optics," Phys. Rev. Lett. 89, 273901 (2002).
[CrossRef]

Headley, C.

Hedley, T. D.

Herrmann, J.

A. V. Husakou and J. Herrmann, "Supercontinuum Generation of Higher-Order Solitons by Fission in Photonic Crystal Fibers," Phys. Rev. Lett. 87, 203,901 (2001).

Husakou, A. V.

A. V. Husakou and J. Herrmann, "Supercontinuum Generation of Higher-Order Solitons by Fission in Photonic Crystal Fibers," Phys. Rev. Lett. 87, 203,901 (2001).

Ippen, E. P.

K. S. Abedin, J. T. Gopinath, E. P. Ippen, C. E. Kerbage, R. S. Windeler, and B. J. Eggleton, "Highly nondegenerate femtosecond four-wave mixing in tapered microstructure fiber," Appl. Phys. Lett. 81, 1384-1386 (2002).
[CrossRef]

Kerbage, C. E.

K. S. Abedin, J. T. Gopinath, E. P. Ippen, C. E. Kerbage, R. S. Windeler, and B. J. Eggleton, "Highly nondegenerate femtosecond four-wave mixing in tapered microstructure fiber," Appl. Phys. Lett. 81, 1384-1386 (2002).
[CrossRef]

Kiefer, W.

Knight, J. C.

Kondrat’ev, Y. N.

Kuhlmey, B. T.

P. Steinvurzel, C. M. de Sterke, B. J. Eggleton, B. T. Kuhlmey, and M. J. Steel, "Mode field distributions in solid core photonic bandgap fibers," Opt. Commun. 263, 207-213 (2006).
[CrossRef]

Lebrun, S.

Litchinitser, N. M.

Luan, F.

Maksimenka, R.

Mamyshev, P. V.

Nulsen, A.

Pearce, G. J.

Roosen, G.

Russell, P. St. J.

Schmitt, M.

Serebryannikov, E. E.

Shevandin, V. S.

Steel, M. J.

P. Steinvurzel, C. M. de Sterke, B. J. Eggleton, B. T. Kuhlmey, and M. J. Steel, "Mode field distributions in solid core photonic bandgap fibers," Opt. Commun. 263, 207-213 (2006).
[CrossRef]

Steinvurzel, P.

P. Steinvurzel, C. M. de Sterke, B. J. Eggleton, B. T. Kuhlmey, and M. J. Steel, "Mode field distributions in solid core photonic bandgap fibers," Opt. Commun. 263, 207-213 (2006).
[CrossRef]

A. Fuerbach, P. Steinvurzel, J. A. Bolger, A. Nulsen, and B. J. Eggleton, "Nonlinear propagation effects in antiresonant high-index inclusion photonic crystal fibers," Opt. Lett. 30, 830-832 (2005).
[CrossRef] [PubMed]

Toyoda, T.

T. Toyoda and M. Yabe, "The temperature dependence of the refractive indices of fused silica and crystal quartz," J. Phys. D 16, L97 (1983).
[CrossRef]

Wardle, D. A.

S. Coen, D. A. Wardle, and J. D. Harvey, "Observation of Non-Phase-Matched Parametric Amplification in Resonant Nonlinear Optics," Phys. Rev. Lett. 89, 273901 (2002).
[CrossRef]

Windeler, R. S.

K. S. Abedin, J. T. Gopinath, E. P. Ippen, C. E. Kerbage, R. S. Windeler, and B. J. Eggleton, "Highly nondegenerate femtosecond four-wave mixing in tapered microstructure fiber," Appl. Phys. Lett. 81, 1384-1386 (2002).
[CrossRef]

Yabe, M.

T. Toyoda and M. Yabe, "The temperature dependence of the refractive indices of fused silica and crystal quartz," J. Phys. D 16, L97 (1983).
[CrossRef]

Zheltikov, A. M.

Appl. Phys. Lett. (1)

K. S. Abedin, J. T. Gopinath, E. P. Ippen, C. E. Kerbage, R. S. Windeler, and B. J. Eggleton, "Highly nondegenerate femtosecond four-wave mixing in tapered microstructure fiber," Appl. Phys. Lett. 81, 1384-1386 (2002).
[CrossRef]

J. Lightwave Technol. (1)

J. Phys. D (1)

T. Toyoda and M. Yabe, "The temperature dependence of the refractive indices of fused silica and crystal quartz," J. Phys. D 16, L97 (1983).
[CrossRef]

Opt. Commun. (1)

P. Steinvurzel, C. M. de Sterke, B. J. Eggleton, B. T. Kuhlmey, and M. J. Steel, "Mode field distributions in solid core photonic bandgap fibers," Opt. Commun. 263, 207-213 (2006).
[CrossRef]

Opt. Lett. (6)

Phys. Rev. Lett. (2)

S. Coen, D. A. Wardle, and J. D. Harvey, "Observation of Non-Phase-Matched Parametric Amplification in Resonant Nonlinear Optics," Phys. Rev. Lett. 89, 273901 (2002).
[CrossRef]

A. V. Husakou and J. Herrmann, "Supercontinuum Generation of Higher-Order Solitons by Fission in Photonic Crystal Fibers," Phys. Rev. Lett. 87, 203,901 (2001).

Other (15)

I. Cristiani, R. Tediosi, L. Tartara, and V. Degiorgio, "Dispersive wave generation by solitons in microstructured optical fibers," Opt. Express 12, 124-135 (2004). URL >http://www.opticsexpress.org/abstract.cfm?URI=oe-12-1-124.
[CrossRef] [PubMed]

A. Argyros, T. Birks, S. Leon-Saval, C. M. Cordeiro, F. Luan, and P. St. J. Russell, "Photonic bandgap with an index step of one percent," Opt. Express 13, 309-314 (2005). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-13-1-309.
[CrossRef] [PubMed]

J. Laegsgaard, "Mode profile dispersion in the generalised nonlinear Schr¨odinger equation," Opt. Express 15, 16,110-16,123 (2007). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-15-24-16110.
[CrossRef]

T. Birks, D. Bird, T. Hedley, J. Pottage, and P. St. J. Russell, "Scaling laws and vector effects in bandgap-guiding fibres," Opt. Express 12, 69-74 (2004). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-12-1-69.
[CrossRef] [PubMed]

T. A. Birks, F. Luan, G. J. Pearce, A. Wang, J. C. Knight, and D. M. Bird, "Bend loss in all-solid bandgap fibres," Opt. Express 14, 5688-5698 (2006). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-14-12-5688.
[CrossRef] [PubMed]

W. H. Reeves, J. C. Knight, P. St. J. Russell, and P. J. Roberts, "Demonstration of ultra-flattened dispersion in photonic crystal fibers," Opt. Express 10, 609-613 (2002). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-10-14-609.
[PubMed]

G. P. Agrawal, Nonlinear Fiber Optics, third edition (Academic Press, San Diego, 2001).

Comsol Multiphysics 3.3a (2007) URLwww.comsol.com.

Cargille Laboratories, Specifications of Cargille Optical Liquids URL www.cargille.com.

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

R. T. Bise, R. S. Windeler, K. S. Kranz, C. Kerbage, B. J. Eggleton, and D. J. Trevor, "Tunable photonic bandgap fiber," in Optical Fiber Communications Conference, Post Conference vol. 70 of OSA Trends in Optics and Photonics Series Technical Digest (Optical Society of America, Washington, D.C., 2002), 466-468.

T. Larsen, A. Bjarklev, D. Hermann, and J. Broeng, "Optical devices based on liquid crystal photonic bandgap fibres," Opt. Express 11, 2589-2596 (2003). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-11-20-2589.
[CrossRef] [PubMed]

K. Saitoh, N. Florous, and M. Koshiba, "Ultra-flattened chromatic dispersion controllability using a defectedcore photonic crystal fiber with low confinement losses," Opt. Express 13, 8365-8371 (2005). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-13-21-8365.
[CrossRef] [PubMed]

R. W. Boyd, Nonlinear Optics, second edition (Academic Press, San Diego, 2003).

A. Fuerbach, P. Steinvurzel, J. A. Bolger, and B. J. Eggleton, "Nonlinear pulse propagation at zero dispersion wavelength in anti-resonant photonic crystal fibers," Opt. Express 13, 2977-2987 (2005). URL http://www.opticsexpress.org/abstract.cfm?URI=oe-13-8-2977.
[CrossRef] [PubMed]

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Figures (3)

Fig. 1.
Fig. 1.

Properties of the considered ARROW-fiber with Λ=3.1µm, d=1.23µm, and 6 rings of holes, as a function of wavelength. (a) Modal overlap η between guided mode and high index regions. (b) Leakage loss. (c) Propagation loss, i.e. the sum of the leakage loss and absorption loss. (d) Effective area of the guided mode in the infiltrated fiber, and an air-hole PCF with identical dimensions. Notice that the V-parameter of a high-index rod is shown on the upper x-axis on all the plots.

Fig. 2.
Fig. 2.

Phase difference as a function of wavelength in the 3rd. and 4th. bandgap when pumping at λ 0=532nm. (a) Three different designs where d/Λ is constant, but the whole structure has been up- and down-scaled by a half percent. (b) Effect of varying the temperature. (c) Group velocity as a function of wavelength for the ARROW-PCF and the similar air-hole PCF.

Fig. 3.
Fig. 3.

(a) Group velocity dispersion in the 3rd. and 4th. band-gap. The fiber parameters are the same as those used in Fig. 2(b) for the case where the fiber is heated 3°C above room temperature. (b) Pulse spectrum after 1.5m [dashed (black) line: Without the Raman effect included in the simulation, and solid (red) line: With the Raman effect included]. The initial pulse is a 10ps (FWHM) sech-pulse with a peak power of 10kW at 532nm. The two arrows in the top of the plot show the theoretically predicted positions of the Stokes and anti-Stokes wavelengths. (c) and (d): Spectrograms on a logarithmic scale at the propagation distance where the energy in the 4th bandgap is highest without and with the Raman effect, respectively. (e) Integrated energy in the 4th. bandgap pr. pulse as a function of propagation length [dashed (black) line: Raman effect neglected, solid (red) line: Raman effect included].

Equations (1)

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η λ = liquid E λ ( x , y ) 2 n ( x , y , λ ) dxdy SiO 2 + liquid E λ ( x , y ) 2 n ( x , y , λ ) dxdy ,

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