Abstract

We have developed a coupled-mode theory to describe light propagation in triple-core photonic crystal fibers (PCFs) in the nonlinear regime. The propagation equations including nonlinearities have been solved analytically. The nonlinear coupling for symmetric and asymmetric fibers is modeled for different coupling and nonlinear parameters. We investigate nonlinear inter-core coupling experimentally with a single high intensity pump beam. Optical switching of a signal beam in the presence of a control pump beam at a different wavelength is also demonstrated. The self-phase modulation (SPM) parameter γ in the triple-core PCF studied is determined.

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References

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  1. G. P. Agrawal, Nonlinear Fiber Optics (Academic, 1995).
  2. P. Miller, J. S. Aitchison, J. U. Kang, G. I. Stegeman, A. Villeneuve, G. T. Kennedy, and W. Sibbett, “Nonlinear waveguide arrays in AlGaAs,” J. Opt. Soc. Am. B 14, 11 (1997).
  3. A. Betlej, S. Suntsov, K. G. Makris, L. Jankovic, D. N. Christodoulides, G. I. Stegeman, J. Fini, R. T. Bise, and D. J. Digiovanni, “All-optical switching and multifrequency generation in a dual-core photonic crystal fiber,” Opt. Lett. 31(10), 1480–1482 (2006).
    [CrossRef] [PubMed]
  4. G. P. Agrawal, Applications of Nonlinear Fiber Optics (Academic, 2001).
  5. Y. Yan, J. Toulouse, I. Velchev, and S. V. Rotkin, “Decoupling and asymmetric coupling in triple-core photonic crystal fibers,” J. Opt. Soc. Am. B 25(9), 1488 (2008).
    [CrossRef]
  6. S. M. Jensen, “The nonlinear coherent coupler,” IEEE J. Quantum Electron. 18(10), 1580–1583 (1982).
    [CrossRef]
  7. I. D. Chremmos, G. Kakarantzas, and N. K. Uzunoglu, “Modeling of a highly nonlinear chalcogenide dual-core photonic crystal fiber coupler,” Opt. Commun. 251(4-6), 339–345 (2005).
    [CrossRef]
  8. A. I. Siahlo, L. K. Oxenlowe, K. S. Berg, A. T. Clausen, P. A. Anderson, C. Peucheret, A. Tersigni, P. Jeppesen, K. P. Hansen, and J. R. Folkenberg, “A high-speed demultiplexer based on a nonlinear optical loop mirror with a photonic crystal fiber,” IEEE Photon. Technol. Lett. 15(8), 1147–1149 (2003).
    [CrossRef]
  9. R. Jiang, R. Saperstein, N. Alic, M. Nezhad, C. McKinstrie, J. Ford, Y. Fainman, and S. Radic, “375THz parametric translation of modulated signal from 1550nm to visible band,” OFC, PDP16, (2006).

2008

Y. Yan, J. Toulouse, I. Velchev, and S. V. Rotkin, “Decoupling and asymmetric coupling in triple-core photonic crystal fibers,” J. Opt. Soc. Am. B 25(9), 1488 (2008).
[CrossRef]

2006

2005

I. D. Chremmos, G. Kakarantzas, and N. K. Uzunoglu, “Modeling of a highly nonlinear chalcogenide dual-core photonic crystal fiber coupler,” Opt. Commun. 251(4-6), 339–345 (2005).
[CrossRef]

2003

A. I. Siahlo, L. K. Oxenlowe, K. S. Berg, A. T. Clausen, P. A. Anderson, C. Peucheret, A. Tersigni, P. Jeppesen, K. P. Hansen, and J. R. Folkenberg, “A high-speed demultiplexer based on a nonlinear optical loop mirror with a photonic crystal fiber,” IEEE Photon. Technol. Lett. 15(8), 1147–1149 (2003).
[CrossRef]

1997

1982

S. M. Jensen, “The nonlinear coherent coupler,” IEEE J. Quantum Electron. 18(10), 1580–1583 (1982).
[CrossRef]

Aitchison, J. S.

Anderson, P. A.

A. I. Siahlo, L. K. Oxenlowe, K. S. Berg, A. T. Clausen, P. A. Anderson, C. Peucheret, A. Tersigni, P. Jeppesen, K. P. Hansen, and J. R. Folkenberg, “A high-speed demultiplexer based on a nonlinear optical loop mirror with a photonic crystal fiber,” IEEE Photon. Technol. Lett. 15(8), 1147–1149 (2003).
[CrossRef]

Berg, K. S.

A. I. Siahlo, L. K. Oxenlowe, K. S. Berg, A. T. Clausen, P. A. Anderson, C. Peucheret, A. Tersigni, P. Jeppesen, K. P. Hansen, and J. R. Folkenberg, “A high-speed demultiplexer based on a nonlinear optical loop mirror with a photonic crystal fiber,” IEEE Photon. Technol. Lett. 15(8), 1147–1149 (2003).
[CrossRef]

Betlej, A.

Bise, R. T.

Chremmos, I. D.

I. D. Chremmos, G. Kakarantzas, and N. K. Uzunoglu, “Modeling of a highly nonlinear chalcogenide dual-core photonic crystal fiber coupler,” Opt. Commun. 251(4-6), 339–345 (2005).
[CrossRef]

Christodoulides, D. N.

Clausen, A. T.

A. I. Siahlo, L. K. Oxenlowe, K. S. Berg, A. T. Clausen, P. A. Anderson, C. Peucheret, A. Tersigni, P. Jeppesen, K. P. Hansen, and J. R. Folkenberg, “A high-speed demultiplexer based on a nonlinear optical loop mirror with a photonic crystal fiber,” IEEE Photon. Technol. Lett. 15(8), 1147–1149 (2003).
[CrossRef]

Digiovanni, D. J.

Fini, J.

Folkenberg, J. R.

A. I. Siahlo, L. K. Oxenlowe, K. S. Berg, A. T. Clausen, P. A. Anderson, C. Peucheret, A. Tersigni, P. Jeppesen, K. P. Hansen, and J. R. Folkenberg, “A high-speed demultiplexer based on a nonlinear optical loop mirror with a photonic crystal fiber,” IEEE Photon. Technol. Lett. 15(8), 1147–1149 (2003).
[CrossRef]

Hansen, K. P.

A. I. Siahlo, L. K. Oxenlowe, K. S. Berg, A. T. Clausen, P. A. Anderson, C. Peucheret, A. Tersigni, P. Jeppesen, K. P. Hansen, and J. R. Folkenberg, “A high-speed demultiplexer based on a nonlinear optical loop mirror with a photonic crystal fiber,” IEEE Photon. Technol. Lett. 15(8), 1147–1149 (2003).
[CrossRef]

Jankovic, L.

Jensen, S. M.

S. M. Jensen, “The nonlinear coherent coupler,” IEEE J. Quantum Electron. 18(10), 1580–1583 (1982).
[CrossRef]

Jeppesen, P.

A. I. Siahlo, L. K. Oxenlowe, K. S. Berg, A. T. Clausen, P. A. Anderson, C. Peucheret, A. Tersigni, P. Jeppesen, K. P. Hansen, and J. R. Folkenberg, “A high-speed demultiplexer based on a nonlinear optical loop mirror with a photonic crystal fiber,” IEEE Photon. Technol. Lett. 15(8), 1147–1149 (2003).
[CrossRef]

Kakarantzas, G.

I. D. Chremmos, G. Kakarantzas, and N. K. Uzunoglu, “Modeling of a highly nonlinear chalcogenide dual-core photonic crystal fiber coupler,” Opt. Commun. 251(4-6), 339–345 (2005).
[CrossRef]

Kang, J. U.

Kennedy, G. T.

Makris, K. G.

Miller, P.

Oxenlowe, L. K.

A. I. Siahlo, L. K. Oxenlowe, K. S. Berg, A. T. Clausen, P. A. Anderson, C. Peucheret, A. Tersigni, P. Jeppesen, K. P. Hansen, and J. R. Folkenberg, “A high-speed demultiplexer based on a nonlinear optical loop mirror with a photonic crystal fiber,” IEEE Photon. Technol. Lett. 15(8), 1147–1149 (2003).
[CrossRef]

Peucheret, C.

A. I. Siahlo, L. K. Oxenlowe, K. S. Berg, A. T. Clausen, P. A. Anderson, C. Peucheret, A. Tersigni, P. Jeppesen, K. P. Hansen, and J. R. Folkenberg, “A high-speed demultiplexer based on a nonlinear optical loop mirror with a photonic crystal fiber,” IEEE Photon. Technol. Lett. 15(8), 1147–1149 (2003).
[CrossRef]

Rotkin, S. V.

Y. Yan, J. Toulouse, I. Velchev, and S. V. Rotkin, “Decoupling and asymmetric coupling in triple-core photonic crystal fibers,” J. Opt. Soc. Am. B 25(9), 1488 (2008).
[CrossRef]

Siahlo, A. I.

A. I. Siahlo, L. K. Oxenlowe, K. S. Berg, A. T. Clausen, P. A. Anderson, C. Peucheret, A. Tersigni, P. Jeppesen, K. P. Hansen, and J. R. Folkenberg, “A high-speed demultiplexer based on a nonlinear optical loop mirror with a photonic crystal fiber,” IEEE Photon. Technol. Lett. 15(8), 1147–1149 (2003).
[CrossRef]

Sibbett, W.

Stegeman, G. I.

Suntsov, S.

Tersigni, A.

A. I. Siahlo, L. K. Oxenlowe, K. S. Berg, A. T. Clausen, P. A. Anderson, C. Peucheret, A. Tersigni, P. Jeppesen, K. P. Hansen, and J. R. Folkenberg, “A high-speed demultiplexer based on a nonlinear optical loop mirror with a photonic crystal fiber,” IEEE Photon. Technol. Lett. 15(8), 1147–1149 (2003).
[CrossRef]

Toulouse, J.

Y. Yan, J. Toulouse, I. Velchev, and S. V. Rotkin, “Decoupling and asymmetric coupling in triple-core photonic crystal fibers,” J. Opt. Soc. Am. B 25(9), 1488 (2008).
[CrossRef]

Uzunoglu, N. K.

I. D. Chremmos, G. Kakarantzas, and N. K. Uzunoglu, “Modeling of a highly nonlinear chalcogenide dual-core photonic crystal fiber coupler,” Opt. Commun. 251(4-6), 339–345 (2005).
[CrossRef]

Velchev, I.

Y. Yan, J. Toulouse, I. Velchev, and S. V. Rotkin, “Decoupling and asymmetric coupling in triple-core photonic crystal fibers,” J. Opt. Soc. Am. B 25(9), 1488 (2008).
[CrossRef]

Villeneuve, A.

Yan, Y.

Y. Yan, J. Toulouse, I. Velchev, and S. V. Rotkin, “Decoupling and asymmetric coupling in triple-core photonic crystal fibers,” J. Opt. Soc. Am. B 25(9), 1488 (2008).
[CrossRef]

IEEE J. Quantum Electron.

S. M. Jensen, “The nonlinear coherent coupler,” IEEE J. Quantum Electron. 18(10), 1580–1583 (1982).
[CrossRef]

IEEE Photon. Technol. Lett.

A. I. Siahlo, L. K. Oxenlowe, K. S. Berg, A. T. Clausen, P. A. Anderson, C. Peucheret, A. Tersigni, P. Jeppesen, K. P. Hansen, and J. R. Folkenberg, “A high-speed demultiplexer based on a nonlinear optical loop mirror with a photonic crystal fiber,” IEEE Photon. Technol. Lett. 15(8), 1147–1149 (2003).
[CrossRef]

J. Opt. Soc. Am. B

P. Miller, J. S. Aitchison, J. U. Kang, G. I. Stegeman, A. Villeneuve, G. T. Kennedy, and W. Sibbett, “Nonlinear waveguide arrays in AlGaAs,” J. Opt. Soc. Am. B 14, 11 (1997).

Y. Yan, J. Toulouse, I. Velchev, and S. V. Rotkin, “Decoupling and asymmetric coupling in triple-core photonic crystal fibers,” J. Opt. Soc. Am. B 25(9), 1488 (2008).
[CrossRef]

Opt. Commun.

I. D. Chremmos, G. Kakarantzas, and N. K. Uzunoglu, “Modeling of a highly nonlinear chalcogenide dual-core photonic crystal fiber coupler,” Opt. Commun. 251(4-6), 339–345 (2005).
[CrossRef]

Opt. Lett.

Other

G. P. Agrawal, Applications of Nonlinear Fiber Optics (Academic, 2001).

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 1995).

R. Jiang, R. Saperstein, N. Alic, M. Nezhad, C. McKinstrie, J. Ford, Y. Fainman, and S. Radic, “375THz parametric translation of modulated signal from 1550nm to visible band,” OFC, PDP16, (2006).

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Figures (11)

Fig. 1
Fig. 1

(a) Fiber geometry, with cores marked by large circles for illustration purpose only. (b) Microscope image of the cross section of the fiber used in the experiments.

Fig. 2
Fig. 2

(color online) Nonlinear coupling computed for symmetric triple-core PCF. P 20 is the initial power launched into core 2. The continuous curves and the dashed curves represent P 2 and P 1 = P 3, respectively. (a) P 20 = 1W (b) P 20 = 400W (c) P 20 = 625W (d) P 20 = 729W (e) P 20 = 900W (f) P 20 = 1.6kW.

Fig. 3
Fig. 3

Interaction length versus the incident power P 20.

Fig. 4
Fig. 4

(color online) Nonlinear coupling computed for asymmetric triple-core PCF. P 20 is the initial power launched into core 2. The continuous curves, the dotted curves, and the dashed curves represent P 2, P 1, and P 3, respectively. (a) P 20 = 1W (b) P 20 = 400W (c) P 20 = 625W (d) P 20 = 729W (e) P 20 = 900W (f) P 20 = 1.6kW

Fig. 5
Fig. 5

Experimental setup for SPM inter-core coupling.

Fig. 6
Fig. 6

(color online) Output beam and intensity profiles at wavelength λ = 811nm for P 20 = 0.017W (a) and (b) and P 20 = 520W (c) and (d)

Fig. 7
Fig. 7

(color online) Output beam and intensity profiles at wavelength λ = 769nm for P 20 = 1 (a) and (b) and P 20 = 887W (c) and (d)

Fig. 8
Fig. 8

(color online) Computations under the same launching conditions as the experimental results presented in Fig. 6. The wavelength λ = 811nm. The continuous curves and the dashed curves represent P 2 and P 1 = P 3, respectively. (a) P 20 = 0.017W (b) P 20 = 520W

Fig. 9
Fig. 9

(color online) Computations under the same launching conditions as the experimental results presented in Fig. 7. The wavelength λ = 769nm. The continuous curves and the dashed curves represent P 2 and P 1 = P 3, respectively. (a) P 20 = 1W (b) P 20 = 887W

Fig. 10
Fig. 10

Experimental setup for optical switching with two beams.

Fig. 11
Fig. 11

Output of the signal beam of wavelength λ = 1580nm. (a) and (b) output beam and intensity profiles with pump off; (c) and (d) output beam and intensity profiles with pump on.

Equations (2)

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{dA1dz=iκ1A2+iγ|A1|2A1dA2dz=iκ1A1+iκ2A3+iγ|A2|2A2dA3dz=iκ2A2+iγ|A3|2A3
Pc=4κγ(1σ)

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