Abstract

Mid-infrared fiber optical parametric oscillators (MIR FOPOs) based on the degenerate four-wave mixing (DFWM) of tellurite photonic crystal fibers (PCFs) are proposed and modeled for the first time. Using the DFWM coupled-wave equations, numerical simulations are performed to analyze the effects of tellurite PCFs, single-resonant cavity, and pump source on the MIR FOPO performances. The numerical results show that: (1) although a longer tellurite PCF can decrease the pump threshold of MIR FOPOs to a few watts only, the high conversion-efficiency of MIR idler usually requires a short-length optimum PCF with low loss; (2) compared with the single-pass DFWM configurations of the MIR fiber sources published previously, the stable oscillation of signal light in single-resonant cavity can significantly promote the MIR idler output efficiency. With a suggested tellurite PCF as parametric gain medium, the theoretical prediction indicates that such a MIR FOPO could obtain a wide MIR-tunable range and a high conversion efficiency of more than 10%.

© 2013 Optical Society of America

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  1. P. Q. Liu, A. J. Hoffman, M. D. Escarra, K. J. Franz, J. B. Khurgin, Y. Dikmelik, X. Wang, J.-Y. Fan, and C. F. Gmachl, “Highly power-efficient quantum cascade lasers,” Nat. Photonics 4, 95–98 (2010).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2012 (1)

2010 (2)

P. Q. Liu, A. J. Hoffman, M. D. Escarra, K. J. Franz, J. B. Khurgin, Y. Dikmelik, X. Wang, J.-Y. Fan, and C. F. Gmachl, “Highly power-efficient quantum cascade lasers,” Nat. Photonics 4, 95–98 (2010).
[CrossRef]

L. Lavoute, J. C. Knight, P. Dupriez, and W. J. Wadsworth, “High power red and near-IR generation using four wave mixing in all integrated fibre laser systems,” Opt. Express 18, 16193–16205 (2010).
[CrossRef]

2009 (2)

2008 (2)

2005 (1)

2004 (1)

2003 (1)

2002 (2)

2001 (1)

L. J. Wang, C. K. Hong, and S. R. Friberg, “Generation of correlated photons via four-wave mixing in optical fibers,” J. Opt. B 3, 346–352 (2001).
[CrossRef]

1996 (1)

Agrawal, G. P.

Aozasa, S.

A. Mori, K. Shikano, K. Enbutsu, K. Oikawa, K. Naganuma, M. Kato, and S. Aozasa, “1.5 μm band zero-dispersion shifted tellurite photonic crystal fiber with a nonlinear coefficient γ of 675  W−1 km−1,” in European Conference on Optical Communication (IEEE, 2004), paper Th3.3.6.

Auerbach, M.

Boller, E.-J.

Camerlingo, A.

Chaudhari, C.

Chiang, T.-K.

Dasgupta, S.

de Matos, C. J. S.

Deng, Y.

Dikmelik, Y.

P. Q. Liu, A. J. Hoffman, M. D. Escarra, K. J. Franz, J. B. Khurgin, Y. Dikmelik, X. Wang, J.-Y. Fan, and C. F. Gmachl, “Highly power-efficient quantum cascade lasers,” Nat. Photonics 4, 95–98 (2010).
[CrossRef]

Dupriez, P.

Ebendorff-Heidepriem, H.

Enbutsu, K.

A. Mori, K. Shikano, K. Enbutsu, K. Oikawa, K. Naganuma, M. Kato, and S. Aozasa, “1.5 μm band zero-dispersion shifted tellurite photonic crystal fiber with a nonlinear coefficient γ of 675  W−1 km−1,” in European Conference on Optical Communication (IEEE, 2004), paper Th3.3.6.

Escarra, M. D.

P. Q. Liu, A. J. Hoffman, M. D. Escarra, K. J. Franz, J. B. Khurgin, Y. Dikmelik, X. Wang, J.-Y. Fan, and C. F. Gmachl, “Highly power-efficient quantum cascade lasers,” Nat. Photonics 4, 95–98 (2010).
[CrossRef]

Fallnich, C.

Fan, J.-Y.

P. Q. Liu, A. J. Hoffman, M. D. Escarra, K. J. Franz, J. B. Khurgin, Y. Dikmelik, X. Wang, J.-Y. Fan, and C. F. Gmachl, “Highly power-efficient quantum cascade lasers,” Nat. Photonics 4, 95–98 (2010).
[CrossRef]

Feng, X.

Fiorentino, M.

Flanagan, J. C.

Foo, T.

Frampton, K. E.

Franz, K. J.

P. Q. Liu, A. J. Hoffman, M. D. Escarra, K. J. Franz, J. B. Khurgin, Y. Dikmelik, X. Wang, J.-Y. Fan, and C. F. Gmachl, “Highly power-efficient quantum cascade lasers,” Nat. Photonics 4, 95–98 (2010).
[CrossRef]

Friberg, S. R.

L. J. Wang, C. K. Hong, and S. R. Friberg, “Generation of correlated photons via four-wave mixing in optical fibers,” J. Opt. B 3, 346–352 (2001).
[CrossRef]

George, A.

Gmachl, C. F.

P. Q. Liu, A. J. Hoffman, M. D. Escarra, K. J. Franz, J. B. Khurgin, Y. Dikmelik, X. Wang, J.-Y. Fan, and C. F. Gmachl, “Highly power-efficient quantum cascade lasers,” Nat. Photonics 4, 95–98 (2010).
[CrossRef]

Gross, P.

Hansen, K. P.

Hemming, A.

Herzog, A.

Hoffman, A. J.

P. Q. Liu, A. J. Hoffman, M. D. Escarra, K. J. Franz, J. B. Khurgin, Y. Dikmelik, X. Wang, J.-Y. Fan, and C. F. Gmachl, “Highly power-efficient quantum cascade lasers,” Nat. Photonics 4, 95–98 (2010).
[CrossRef]

Hong, C. K.

L. J. Wang, C. K. Hong, and S. R. Friberg, “Generation of correlated photons via four-wave mixing in optical fibers,” J. Opt. B 3, 346–352 (2001).
[CrossRef]

Horak, P.

Ishaaya, A. A.

Jauregui, C.

Kagi, N.

Kato, M.

A. Mori, K. Shikano, K. Enbutsu, K. Oikawa, K. Naganuma, M. Kato, and S. Aozasa, “1.5 μm band zero-dispersion shifted tellurite photonic crystal fiber with a nonlinear coefficient γ of 675  W−1 km−1,” in European Conference on Optical Communication (IEEE, 2004), paper Th3.3.6.

Kazovsky, L. G.

Khurgin, J. B.

P. Q. Liu, A. J. Hoffman, M. D. Escarra, K. J. Franz, J. B. Khurgin, Y. Dikmelik, X. Wang, J.-Y. Fan, and C. F. Gmachl, “Highly power-efficient quantum cascade lasers,” Nat. Photonics 4, 95–98 (2010).
[CrossRef]

Klein, M. E.

Knight, J.

Knight, J. C.

Knox, W. H.

Kumar, P.

Lancaster, D. G.

Lavoute, L.

Li, Y.

Liao, M.

Limpert, J.

Lin, Q.

Liu, P. Q.

P. Q. Liu, A. J. Hoffman, M. D. Escarra, K. J. Franz, J. B. Khurgin, Y. Dikmelik, X. Wang, J.-Y. Fan, and C. F. Gmachl, “Highly power-efficient quantum cascade lasers,” Nat. Photonics 4, 95–98 (2010).
[CrossRef]

Loh, W. H.

Lu, F.

Marhic, M. E.

Monro, T. M.

Moore, R. C.

Mori, A.

A. Mori, K. Shikano, K. Enbutsu, K. Oikawa, K. Naganuma, M. Kato, and S. Aozasa, “1.5 μm band zero-dispersion shifted tellurite photonic crystal fiber with a nonlinear coefficient γ of 675  W−1 km−1,” in European Conference on Optical Communication (IEEE, 2004), paper Th3.3.6.

Naganuma, K.

A. Mori, K. Shikano, K. Enbutsu, K. Oikawa, K. Naganuma, M. Kato, and S. Aozasa, “1.5 μm band zero-dispersion shifted tellurite photonic crystal fiber with a nonlinear coefficient γ of 675  W−1 km−1,” in European Conference on Optical Communication (IEEE, 2004), paper Th3.3.6.

Nodop, D.

Ohishi, Y.

Oikawa, K.

A. Mori, K. Shikano, K. Enbutsu, K. Oikawa, K. Naganuma, M. Kato, and S. Aozasa, “1.5 μm band zero-dispersion shifted tellurite photonic crystal fiber with a nonlinear coefficient γ of 675  W−1 km−1,” in European Conference on Optical Communication (IEEE, 2004), paper Th3.3.6.

Petropoulos, P.

Price, J. H.

Qin, G.

Ravi Kanth Kumar, V. V.

Richardson, D. J.

Russell, P.

Rutt, H. N.

Schimpf, D.

Shamir, A.

Sharping, J. E.

Shikano, K.

A. Mori, K. Shikano, K. Enbutsu, K. Oikawa, K. Naganuma, M. Kato, and S. Aozasa, “1.5 μm band zero-dispersion shifted tellurite photonic crystal fiber with a nonlinear coefficient γ of 675  W−1 km−1,” in European Conference on Optical Communication (IEEE, 2004), paper Th3.3.6.

Suzuki, T.

Taylor, J. R.

Tünnermann, A.

Wadsworth, W. J.

Walde, T.

Wang, L. J.

L. J. Wang, C. K. Hong, and S. R. Friberg, “Generation of correlated photons via four-wave mixing in optical fibers,” J. Opt. B 3, 346–352 (2001).
[CrossRef]

Wang, X.

P. Q. Liu, A. J. Hoffman, M. D. Escarra, K. J. Franz, J. B. Khurgin, Y. Dikmelik, X. Wang, J.-Y. Fan, and C. F. Gmachl, “Highly power-efficient quantum cascade lasers,” Nat. Photonics 4, 95–98 (2010).
[CrossRef]

Wessels, P.

White, N. M.

Windeler, R. S.

Yan, X.

Zhang, W.

J. Opt. B (1)

L. J. Wang, C. K. Hong, and S. R. Friberg, “Generation of correlated photons via four-wave mixing in optical fibers,” J. Opt. B 3, 346–352 (2001).
[CrossRef]

Nat. Photonics (1)

P. Q. Liu, A. J. Hoffman, M. D. Escarra, K. J. Franz, J. B. Khurgin, Y. Dikmelik, X. Wang, J.-Y. Fan, and C. F. Gmachl, “Highly power-efficient quantum cascade lasers,” Nat. Photonics 4, 95–98 (2010).
[CrossRef]

Opt. Express (4)

Opt. Lett. (8)

H. Ebendorff-Heidepriem, T. Foo, R. C. Moore, W. Zhang, Y. Li, T. M. Monro, A. Hemming, and D. G. Lancaster, “Fluoride glass microstructured optical fiber with large mode area and mid-infrared transmission,” Opt. Lett. 33, 2861–2863 (2008).
[CrossRef]

A. Herzog, A. Shamir, and A. A. Ishaaya, “Wavelength conversion of nanosecond pulses to the mid-IR in photonic crystal fibers,” Opt. Lett. 37, 82–84 (2012).
[CrossRef]

M. E. Marhic, N. Kagi, T.-K. Chiang, and L. G. Kazovsky, “Broadband fiber optical parametric amplifiers,” Opt. Lett. 21, 573–575 (1996).
[CrossRef]

J. E. Sharping, M. Fiorentino, P. Kumar, and R. S. Windeler, “Optical parametric oscillator based on four-wave mixing in microstructure fiber,” Opt. Lett. 27, 1675–1677 (2002).
[CrossRef]

P. Gross, M. E. Klein, T. Walde, E.-J. Boller, M. Auerbach, P. Wessels, and C. Fallnich, “Fiber-laser-pumped continuous-wave singly resonant optical parametric oscillator,” Opt. Lett. 27, 418–420 (2002).
[CrossRef]

C. J. S. de Matos, J. R. Taylor, and K. P. Hansen, “Continuous-wave, totally fiber integrated optical parametric oscillator using holey fiber,” Opt. Lett. 29, 983–985 (2004).
[CrossRef]

Y. Deng, Q. Lin, F. Lu, G. P. Agrawal, and W. H. Knox, “Broadly tunable femtosecond parametric oscillator using a photonic crystal fiber,” Opt. Lett. 30, 1234–1236 (2005).
[CrossRef]

D. Nodop, C. Jauregui, D. Schimpf, J. Limpert, and A. Tünnermann, “Efficient high-power generation of visible and mid-infrared light by degenerate four-wave-mixing in a large-mode-area photonic-crystal fiber,” Opt. Lett. 34, 3499–3501 (2009).
[CrossRef]

Other (1)

A. Mori, K. Shikano, K. Enbutsu, K. Oikawa, K. Naganuma, M. Kato, and S. Aozasa, “1.5 μm band zero-dispersion shifted tellurite photonic crystal fiber with a nonlinear coefficient γ of 675  W−1 km−1,” in European Conference on Optical Communication (IEEE, 2004), paper Th3.3.6.

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Figures (7)

Fig. 1.
Fig. 1.

Schematic of the MIR FOPO. Inset: the principle for generation of MIR idler based on the degenerate FWM.

Fig. 2.
Fig. 2.

Calculated phase-matching diagram for the tellurite PCF at pump power P=20W. Inset: a cross section of the PCF (left) and the calculated transverse intensity distribution of fundamental mode at wavelength of 3.105 μm (right).

Fig. 3.
Fig. 3.

Output power of MIR idler as a function of the number of signal round trip for Pp=10W, L=28.7cm.

Fig. 4.
Fig. 4.

Threshold pump power of the MIR FOPO as a function of the length of PCF. Inset: the pump and idler power evolutions as a function of the longitudinal distance along the fiber for pump power Pp=10W, L=1m.

Fig. 5.
Fig. 5.

Conversion efficiency of MIR idler as a function of length of PCF, for the pump power of 10 W (dash dot), 30 W (solid), and 50 W (dot), respectively.

Fig. 6.
Fig. 6.

Output power of MIR idler as a function of input pump power for the PCF length of 4.4 cm (dash dot), 7.7 cm (solid), and 28.7 cm (dot), respectively.

Fig. 7.
Fig. 7.

Maximum conversion efficiency of 3.105 μm MIR idler as a function of loss of tellurite PCF at pump power of 10 W.

Equations (4)

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

Apz+i2β22Apt2i24β44Apt4=3iωp2χ(3)2Aeffpβpc2[2AsAiAp*eiΔβz+(|Ap|2+2|As|2+2|Ai|2)Ap]12αpAp,
Asz+i2β22Ast2i24β44Ast4=3iωs2χ(3)2Aeffsβsc2[Ap2Ai*eiΔβz+(2|Ap|2+|As|2+2|Ai|2)As]12αsAs,
Aiz+i2β22Ait2i24β44Ait4=3iωi2χ(3)2Aeffiβic2[Ap2As*eiΔβz+(2|Ap|2+2|As|2+|Ai|2)Ai]12αiAi.
|As(z=0,t)|2=(1αlinear)|As(z=L,t)|2|Ap(z=0,t)|2=Pp.

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