Ultrafast multi-wavelength switch based on dynamics of spectrally-shifted solitons in a dual‑core photonic crystal fiber

Pavol Stajanca; Dariusz Pysz; Giedrius Andriukaitis; Tadas Balciunas; Guangyu Fan; Andrius Baltuska; Ignac Bugar

doi:10.1364/OE.22.031092

Ultrafast multi-wavelength switch based on dynamics of spectrally-shifted solitons in a dual‑core photonic crystal fiber

Pavol Stajanca, Dariusz Pysz, Giedrius Andriukaitis, Tadas Balciunas, Guangyu Fan, Andrius Baltuska, and Ignac Bugar

Optics Express
Vol. 22,
Issue 25,
pp. 31092-31101
(2014)
•https://doi.org/10.1364/OE.22.031092

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Pavol Stajanca, Dariusz Pysz, Giedrius Andriukaitis, Tadas Balciunas, Guangyu Fan, Andrius Baltuska, and Ignac Bugar, "Ultrafast multi-wavelength switch based on dynamics of spectrally-shifted solitons in a dual‑core photonic crystal fiber," Opt. Express 22, 31092-31101 (2014)

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Related Topics
Table of Contents Category
- Fiber Optics
Optics & Photonics Topics
?

The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Photonic crystal fibers (060.5295)
- Pulse propagation and temporal solitons (190.5530)
- Switching (200.6715)

About this Article
History
- Original Manuscript: September 3, 2014
- Revised Manuscript: October 31, 2014
- Manuscript Accepted: November 1, 2014
- Published: December 8, 2014

Accessible

Open Access

Abstract

Nonlinear propagation of ultrafast near infrared pulses in anomalous dispersion region of dual-core photonic crystal fiber was studied. Polarization tunable soliton-based nonlinear switching at multiple non-excitation wavelengths was demonstrated experimentally for fiber excitation by 100 fs pulses at 1650 nm. The highest-contrast switching was obtained with the fiber length of just 14 mm, which is significantly shorter compared to the conventional non-solitonic in-fiber switching based on nonlinear optical loop mirror. Advanced numerical simulations show good agreement with the experimental results, suggesting that the underlying dual-core soliton fission process supports nonlinear optical switching and simultaneous pulse compression to few-cycle durations at the level of 20 fs.

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References

View by:
Article Order
|
Year
|
Author
|
Publication

S. M. Jensen, “The nonlinear coherent coupler,” IEEE J. Quantum Electron. QE-18, 15801583 (1982).
A. A. Maĭer, “Optical transistors and bistable devices utilizing nonlinear transmission of light in systems with unidirectional coupled waves,” Sov. J. Quantum Electron. 12(11), 1490–1494 (1982).
[Crossref]
G. P. Agrawal, Application of nonlinear fibre optics: 2nd edition (Elsevier, 2008), Chap. 2.
S. R. Friberg, A. M. Weiner, Y. Silberberg, B. G. Sfez, and P. S. Smith, “Femotosecond switching in a dual-core-fiber nonlinear coupler,” Opt. Lett. 13(10), 904–906 (1988).
[Crossref] [PubMed]
G. I. Stegeman and A. Miller, “Physics of all-optical switching devices,” in Photonics in switching, J. E. Midwinter, ed. (Academic, 1993).
S. Trillo, S. Wabnitz, E. M. Wright, and G. I. Stegeman, “Soliton switching in fiber nonlinear directional couplers,” Opt. Lett. 13(8), 672–674 (1988).
[Crossref] [PubMed]
M. Romagnoli, S. Trillo, and S. Wabnitz, “Soliton switching in nonlinear couplers,” Opt. Quantum Electron. 24(11), 1237–1267 (1992).
[Crossref]
Y. S. Kivshar, “Switching dynamics of solitons in fiber directional couplers,” Opt. Lett. 18(1), 7–9 (1993).
[Crossref] [PubMed]
P. L. Chu, Y. S. Kivshar, B. A. Malomed, G.-D. Peng, and M. L. Quiroga-Teixeiro, “Soliton controlling, switching, and splitting in nonlinear fused-fiber couplers,” J. Opt. Soc. B 12(5), 898–903 (1995).
[Crossref]
P. St. J. Russell, “Photonic crystal fibers,” Science 299(5605), 358–362 (2003).
[Crossref] [PubMed]
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]
K. R. Khan, T. X. Wu, D. N. Christodoulides, and G. I. Stegeman, “Soliton switching and multi-frequency generation in a nonlinear photonic crystal fiber coupler,” Opt. Express 16(13), 9417–9428 (2008).
[Crossref] [PubMed]
D. Lorenc, I. Bugar, M. Aranyaosiova, R. Buczynski, D. Pysz, D. Velic, and D. Chorvat, “Linear and nonlinear properties of multicomponent glass photonic crystal fibers,” Laser Phys. 18(3), 270–276 (2008).
[Crossref]
M. Koys, I. Bugar, I. Hrebikova, V. Mesaros, R. Buczynski, and F. Uherek, “Spectral switching control of ultrafast pulses in dual core photonic crystal fibre,” J. Europ. Opt. Soc. Rap. Public 8, 13041 (2013).
[Crossref]
P. Stajanca, D. Pysz, M. Michalka, G. Andriukaitis, T. Balciunas, G. Fan, A. Baltuska, and I. Bugar, “Soliton-based ultrafast multi-wavelength nonlinear switch in dual-core photonic crystal fibre,” Laser Phys. 24(6), 065103 (2014).
[Crossref]
R. Buczynski, “Photonic crystal fibres,” Acta. Phys. Pol. A 106, 141–168 (2004).
M. Koys, I. Bugar, V. Mesaros, F. Uherek, and R. Buczynski, “Supercontinuum generation in dual core photonic crystal fiber,” Proc. SPIE 7746, 11 (2010).
[Crossref]
D. Lorenc, M. Aranyosiova, R. Buczynski, R. Stepien, I. Bugar, A. Vincze, and D. Velic, “Nonlinear refractive index of multicomponent glasses designed for fabrication of photonic crystal fibers,” Appl. Phys. B 93(2-3), 531–538 (2008).
[Crossref]
K. J. Blow and D. Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 25(12), 2665–2673 (1989).
[Crossref]
J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fibers,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
[Crossref]
M. Murawski, G. Stępniewski, T. Tenderenda, M. Napierala, Z. Holdynski, L. Szostkiewicz, M. Slowikowski, M. Szymanski, L. Ostrowski, L. R. Jaroszewicz, R. Buczynski, and T. Nasilowski, “Low loss coupling and splicing of standard single mode fibers with all-solid soft-glass microstructured fibers for supercontinuum generation,” Proc. SPIE 8982, 28 (2014).
C. C. Lee, P. K. A. Wai, H. Y. Tam, L. Xu, and C. Wu, “10-Gb/s wavelength transparent optically controlled buffer using photonic-crystal-fiber-based nonlinear optical loop mirror,” IEEE Photon. Technol. Lett. 19(12), 898–900 (2007).
[Crossref]
D. Yoshitomi and K. Torizuka, “Long-term stable passive synchronization between two-color mode-locked lasers with the aid of temperature stabilization,” Opt. Express 22(4), 4091–4097 (2014).
[Crossref] [PubMed]
P. Stajanca, R. Buczynski, G. Andriukaitis, T. Balciunas, G. Fan, A. Baltuska, and I. Bugar, “Ultrafast solitonic nonlinear directional couplers utilizing multicomponent glass dual-core photonic crystal fibres,” in Proceedings of the 16th International Conference on Transparent Optical Networks (IEEE, 2014), We.A6.4.
[Crossref]

2014 (3)

P. Stajanca, D. Pysz, M. Michalka, G. Andriukaitis, T. Balciunas, G. Fan, A. Baltuska, and I. Bugar, “Soliton-based ultrafast multi-wavelength nonlinear switch in dual-core photonic crystal fibre,” Laser Phys. 24(6), 065103 (2014).
[Crossref]

M. Murawski, G. Stępniewski, T. Tenderenda, M. Napierala, Z. Holdynski, L. Szostkiewicz, M. Slowikowski, M. Szymanski, L. Ostrowski, L. R. Jaroszewicz, R. Buczynski, and T. Nasilowski, “Low loss coupling and splicing of standard single mode fibers with all-solid soft-glass microstructured fibers for supercontinuum generation,” Proc. SPIE 8982, 28 (2014).

D. Yoshitomi and K. Torizuka, “Long-term stable passive synchronization between two-color mode-locked lasers with the aid of temperature stabilization,” Opt. Express 22(4), 4091–4097 (2014).
[Crossref] [PubMed]

2013 (1)

M. Koys, I. Bugar, I. Hrebikova, V. Mesaros, R. Buczynski, and F. Uherek, “Spectral switching control of ultrafast pulses in dual core photonic crystal fibre,” J. Europ. Opt. Soc. Rap. Public 8, 13041 (2013).
[Crossref]

2010 (1)

M. Koys, I. Bugar, V. Mesaros, F. Uherek, and R. Buczynski, “Supercontinuum generation in dual core photonic crystal fiber,” Proc. SPIE 7746, 11 (2010).
[Crossref]

2008 (3)

D. Lorenc, M. Aranyosiova, R. Buczynski, R. Stepien, I. Bugar, A. Vincze, and D. Velic, “Nonlinear refractive index of multicomponent glasses designed for fabrication of photonic crystal fibers,” Appl. Phys. B 93(2-3), 531–538 (2008).
[Crossref]

D. Lorenc, I. Bugar, M. Aranyaosiova, R. Buczynski, D. Pysz, D. Velic, and D. Chorvat, “Linear and nonlinear properties of multicomponent glass photonic crystal fibers,” Laser Phys. 18(3), 270–276 (2008).
[Crossref]

K. R. Khan, T. X. Wu, D. N. Christodoulides, and G. I. Stegeman, “Soliton switching and multi-frequency generation in a nonlinear photonic crystal fiber coupler,” Opt. Express 16(13), 9417–9428 (2008).
[Crossref] [PubMed]

2007 (1)

C. C. Lee, P. K. A. Wai, H. Y. Tam, L. Xu, and C. Wu, “10-Gb/s wavelength transparent optically controlled buffer using photonic-crystal-fiber-based nonlinear optical loop mirror,” IEEE Photon. Technol. Lett. 19(12), 898–900 (2007).
[Crossref]

2006 (2)

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fibers,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
[Crossref]

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]

2004 (1)

R. Buczynski, “Photonic crystal fibres,” Acta. Phys. Pol. A 106, 141–168 (2004).

2003 (1)

P. St. J. Russell, “Photonic crystal fibers,” Science 299(5605), 358–362 (2003).
[Crossref] [PubMed]

1995 (1)

P. L. Chu, Y. S. Kivshar, B. A. Malomed, G.-D. Peng, and M. L. Quiroga-Teixeiro, “Soliton controlling, switching, and splitting in nonlinear fused-fiber couplers,” J. Opt. Soc. B 12(5), 898–903 (1995).
[Crossref]

1993 (1)

Y. S. Kivshar, “Switching dynamics of solitons in fiber directional couplers,” Opt. Lett. 18(1), 7–9 (1993).
[Crossref] [PubMed]

1992 (1)

M. Romagnoli, S. Trillo, and S. Wabnitz, “Soliton switching in nonlinear couplers,” Opt. Quantum Electron. 24(11), 1237–1267 (1992).
[Crossref]

1989 (1)

K. J. Blow and D. Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 25(12), 2665–2673 (1989).
[Crossref]

1988 (2)

S. Trillo, S. Wabnitz, E. M. Wright, and G. I. Stegeman, “Soliton switching in fiber nonlinear directional couplers,” Opt. Lett. 13(8), 672–674 (1988).
[Crossref] [PubMed]

S. R. Friberg, A. M. Weiner, Y. Silberberg, B. G. Sfez, and P. S. Smith, “Femotosecond switching in a dual-core-fiber nonlinear coupler,” Opt. Lett. 13(10), 904–906 (1988).
[Crossref] [PubMed]

1982 (2)

S. M. Jensen, “The nonlinear coherent coupler,” IEEE J. Quantum Electron. QE-18, 15801583 (1982).

A. A. Maĭer, “Optical transistors and bistable devices utilizing nonlinear transmission of light in systems with unidirectional coupled waves,” Sov. J. Quantum Electron. 12(11), 1490–1494 (1982).
[Crossref]

Andriukaitis, G.

Aranyaosiova, M.

Aranyosiova, M.

Balciunas, T.

Baltuska, A.

Betlej, A.

Bise, R. T.

Blow, K. J.

K. J. Blow and D. Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 25(12), 2665–2673 (1989).
[Crossref]

Buczynski, R.

M. Koys, I. Bugar, V. Mesaros, F. Uherek, and R. Buczynski, “Supercontinuum generation in dual core photonic crystal fiber,” Proc. SPIE 7746, 11 (2010).
[Crossref]

R. Buczynski, “Photonic crystal fibres,” Acta. Phys. Pol. A 106, 141–168 (2004).

Bugar, I.

M. Koys, I. Bugar, V. Mesaros, F. Uherek, and R. Buczynski, “Supercontinuum generation in dual core photonic crystal fiber,” Proc. SPIE 7746, 11 (2010).
[Crossref]

Chorvat, D.

Christodoulides, D. N.

Chu, P. L.

Coen, S.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fibers,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
[Crossref]

Digiovanni, D. J.

Dudley, J. M.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fibers,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
[Crossref]

Fan, G.

Fini, J.

Friberg, S. R.

S. R. Friberg, A. M. Weiner, Y. Silberberg, B. G. Sfez, and P. S. Smith, “Femotosecond switching in a dual-core-fiber nonlinear coupler,” Opt. Lett. 13(10), 904–906 (1988).
[Crossref] [PubMed]

Genty, G.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fibers,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
[Crossref]

Holdynski, Z.

Hrebikova, I.

Jankovic, L.

Jaroszewicz, L. R.

Jensen, S. M.

S. M. Jensen, “The nonlinear coherent coupler,” IEEE J. Quantum Electron. QE-18, 15801583 (1982).

Khan, K. R.

Kivshar, Y. S.

Y. S. Kivshar, “Switching dynamics of solitons in fiber directional couplers,” Opt. Lett. 18(1), 7–9 (1993).
[Crossref] [PubMed]

Koys, M.

M. Koys, I. Bugar, V. Mesaros, F. Uherek, and R. Buczynski, “Supercontinuum generation in dual core photonic crystal fiber,” Proc. SPIE 7746, 11 (2010).
[Crossref]

Lee, C. C.

Lorenc, D.

Maier, A. A.

Makris, K. G.

Malomed, B. A.

Mesaros, V.

M. Koys, I. Bugar, V. Mesaros, F. Uherek, and R. Buczynski, “Supercontinuum generation in dual core photonic crystal fiber,” Proc. SPIE 7746, 11 (2010).
[Crossref]

Michalka, M.

Murawski, M.

Napierala, M.

Nasilowski, T.

Ostrowski, L.

Peng, G.-D.

Pysz, D.

Quiroga-Teixeiro, M. L.

Romagnoli, M.

M. Romagnoli, S. Trillo, and S. Wabnitz, “Soliton switching in nonlinear couplers,” Opt. Quantum Electron. 24(11), 1237–1267 (1992).
[Crossref]

Russell, P. St. J.

P. St. J. Russell, “Photonic crystal fibers,” Science 299(5605), 358–362 (2003).
[Crossref] [PubMed]

Sfez, B. G.

S. R. Friberg, A. M. Weiner, Y. Silberberg, B. G. Sfez, and P. S. Smith, “Femotosecond switching in a dual-core-fiber nonlinear coupler,” Opt. Lett. 13(10), 904–906 (1988).
[Crossref] [PubMed]

Silberberg, Y.

S. R. Friberg, A. M. Weiner, Y. Silberberg, B. G. Sfez, and P. S. Smith, “Femotosecond switching in a dual-core-fiber nonlinear coupler,” Opt. Lett. 13(10), 904–906 (1988).
[Crossref] [PubMed]

Slowikowski, M.

Smith, P. S.

S. R. Friberg, A. M. Weiner, Y. Silberberg, B. G. Sfez, and P. S. Smith, “Femotosecond switching in a dual-core-fiber nonlinear coupler,” Opt. Lett. 13(10), 904–906 (1988).
[Crossref] [PubMed]

Stajanca, P.

Stegeman, G. I.

S. Trillo, S. Wabnitz, E. M. Wright, and G. I. Stegeman, “Soliton switching in fiber nonlinear directional couplers,” Opt. Lett. 13(8), 672–674 (1988).
[Crossref] [PubMed]

Stepien, R.

Stepniewski, G.

Suntsov, S.

Szostkiewicz, L.

Szymanski, M.

Tam, H. Y.

Tenderenda, T.

Torizuka, K.

Trillo, S.

M. Romagnoli, S. Trillo, and S. Wabnitz, “Soliton switching in nonlinear couplers,” Opt. Quantum Electron. 24(11), 1237–1267 (1992).
[Crossref]

S. Trillo, S. Wabnitz, E. M. Wright, and G. I. Stegeman, “Soliton switching in fiber nonlinear directional couplers,” Opt. Lett. 13(8), 672–674 (1988).
[Crossref] [PubMed]

Uherek, F.

M. Koys, I. Bugar, V. Mesaros, F. Uherek, and R. Buczynski, “Supercontinuum generation in dual core photonic crystal fiber,” Proc. SPIE 7746, 11 (2010).
[Crossref]

Velic, D.

Vincze, A.

Wabnitz, S.

M. Romagnoli, S. Trillo, and S. Wabnitz, “Soliton switching in nonlinear couplers,” Opt. Quantum Electron. 24(11), 1237–1267 (1992).
[Crossref]

S. Trillo, S. Wabnitz, E. M. Wright, and G. I. Stegeman, “Soliton switching in fiber nonlinear directional couplers,” Opt. Lett. 13(8), 672–674 (1988).
[Crossref] [PubMed]

Wai, P. K. A.

Weiner, A. M.

S. R. Friberg, A. M. Weiner, Y. Silberberg, B. G. Sfez, and P. S. Smith, “Femotosecond switching in a dual-core-fiber nonlinear coupler,” Opt. Lett. 13(10), 904–906 (1988).
[Crossref] [PubMed]

Wood, D.

K. J. Blow and D. Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 25(12), 2665–2673 (1989).
[Crossref]

Wright, E. M.

S. Trillo, S. Wabnitz, E. M. Wright, and G. I. Stegeman, “Soliton switching in fiber nonlinear directional couplers,” Opt. Lett. 13(8), 672–674 (1988).
[Crossref] [PubMed]

Wu, C.

Wu, T. X.

Xu, L.

Yoshitomi, D.

Acta. Phys. Pol. A (1)

R. Buczynski, “Photonic crystal fibres,” Acta. Phys. Pol. A 106, 141–168 (2004).

Appl. Phys. B (1)

IEEE J. Quantum Electron. (2)

K. J. Blow and D. Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 25(12), 2665–2673 (1989).
[Crossref]

S. M. Jensen, “The nonlinear coherent coupler,” IEEE J. Quantum Electron. QE-18, 15801583 (1982).

IEEE Photon. Technol. Lett. (1)

J. Europ. Opt. Soc. Rap. Public (1)

J. Opt. Soc. B (1)

Laser Phys. (2)

Opt. Express (2)

Opt. Lett. (4)

S. Trillo, S. Wabnitz, E. M. Wright, and G. I. Stegeman, “Soliton switching in fiber nonlinear directional couplers,” Opt. Lett. 13(8), 672–674 (1988).
[Crossref] [PubMed]

S. R. Friberg, A. M. Weiner, Y. Silberberg, B. G. Sfez, and P. S. Smith, “Femotosecond switching in a dual-core-fiber nonlinear coupler,” Opt. Lett. 13(10), 904–906 (1988).
[Crossref] [PubMed]

Y. S. Kivshar, “Switching dynamics of solitons in fiber directional couplers,” Opt. Lett. 18(1), 7–9 (1993).
[Crossref] [PubMed]

Opt. Quantum Electron. (1)

M. Romagnoli, S. Trillo, and S. Wabnitz, “Soliton switching in nonlinear couplers,” Opt. Quantum Electron. 24(11), 1237–1267 (1992).
[Crossref]

Proc. SPIE (2)

M. Koys, I. Bugar, V. Mesaros, F. Uherek, and R. Buczynski, “Supercontinuum generation in dual core photonic crystal fiber,” Proc. SPIE 7746, 11 (2010).
[Crossref]

Rev. Mod. Phys. (1)

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fibers,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
[Crossref]

Science (1)

P. St. J. Russell, “Photonic crystal fibers,” Science 299(5605), 358–362 (2003).
[Crossref] [PubMed]

Sov. J. Quantum Electron. (1)

Other (3)

G. P. Agrawal, Application of nonlinear fibre optics: 2nd edition (Elsevier, 2008), Chap. 2.

G. I. Stegeman and A. Miller, “Physics of all-optical switching devices,” in Photonics in switching, J. E. Midwinter, ed. (Academic, 1993).

P. Stajanca, R. Buczynski, G. Andriukaitis, T. Balciunas, G. Fan, A. Baltuska, and I. Bugar, “Ultrafast solitonic nonlinear directional couplers utilizing multicomponent glass dual-core photonic crystal fibres,” in Proceedings of the 16th International Conference on Transparent Optical Networks (IEEE, 2014), We.A6.4.
[Crossref]

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Fig. 1 (a) SEM image of fiber microstructure with labeling of cores and polarization directions as considered in experiment (U-upper, L-lower). (b) Calculated fiber coupling length L_c and upper core dispersion.

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Fig. 2 Simulated dual-core temporal and spectral evolution of Y-polarized, 24 nJ, 100 fs pulse at 1650 nm propagating along 50 mm of investigated DC PCF.

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Fig. 3 Simulated dual-core temporal and spectral evolution of Y-polarized, 55 nJ, 100 fs pulse at 1650 nm propagating along 50 mm of investigated DC PCF.

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Fig. 4 Excited core output spectral intensity normalized to overall spectral intensity registered from both cores for (a) 5 mm, (b) 10 mm and (c) 14 mm fiber sample. Upper fiber core was excited with X-polarized pulses.

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Fig. 5 (a) Experimental and (b) simulated excited core output spectral intensity normalized to overall spectral intensity registered from both cores for 14 mm fiber length. Upper fiber core was excited with Y-polarized pulses.

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Tables (1)

Table 1 Selected input parameters for coupled GNLSE model

View Table

Equations (2)

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

\begin{matrix} \frac{\partial A^{(r)}}{\partial z} = i (^{- 1) r + 1} δ_{0} A^{(r)} + (^{- 1) r} δ_{1} \frac{\partial A^{(r)}}{\partial T} + \sum_{p \geq 2} \frac{i^{p + 1}}{p!} β_{p}^{(r)} \frac{\partial^{p} A^{(r)}}{\partial T^{p}} - \frac{α^{(r)}}{2} A^{(r)} + \\ \sum_{q \geq 0} \frac{i^{q + 1}}{q!} κ_{q}^{(r)} \frac{\partial^{q} A^{(3 - r)}}{\partial T^{q}} + i γ^{(r)} [(1 + i τ_{s h o c k}^{(r)} \frac{\partial}{\partial T}) (R * {| A^{(r)} |}^{2}) + η {| A^{(3 - r)} |}^{2}] A^{(r)} \end{matrix}

τ_{s h o c k} = \frac{1}{ω_{0}} + \frac{d}{d ω} {[\ln (\frac{1}{n_{e f f} (ω) A_{e f f} (ω)})]}_{ω_{0}}

	Upper core		Lower core
	X-pol	Y-pol	X-pol	Y-pol
$γ$ [W⁻¹km⁻¹]	25,737	26,023	25,632	26,092
$η$	1,971E-28	2,612E-28	1,980E-28	2,605E-28
$τ_{s h o c k}$ [fs]	1,309	1,301	1,311	1,280
$β_{2}$ [ps²/km]	−105,730	−104,490	−107,130	−107,940
$β_{3}$ [ps³/km]	0,203	0,201	0,215	0,231
$κ_{0}$ [m⁻¹]	968,287	976,820	968,287	976,820
$κ_{1}$ [ps/m]	−2,709	−2,711	−2,709	−2,711