Abstract

Third-order Kerr nonlinearities and Raman gain are studied experimentally in high-purity As2Se3 optical fibers for wavelengths near 1.55 µm. Kerr nonlinear coefficients are measured to be nearly 1000 times higher than those for silica fibers. In pulsed mode, nonlinear phase shifts near 1.2-π rad are measured in fibers only 85 cm long with peak pulse powers near 3 W. However, there are nonlinear losses near 20% for nonlinear phase shifts near π. By use of a cw optical pump, large Raman gains nearly 800 times that of silica were measured. In the cw case there were losses in the form of index gratings formed from standing waves at the exit face of the fiber. Discrete Raman amplifiers and optical regenerators are discussed as possible applications.

© 2004 Optical Society of America

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2003 (2)

J. S. Sanghera, L. B. Shaw, and I. D. Aggrawal, “Applications of chalcogenide glass optical fibers,” C.R. Acad. Sci., Ser. IIc: Chim 5, 1–11 (2003).

P. A. Thielen, L. B. Shaw, P. C. Pureza, V. Q. Nguyen, J. S. Sanghera, and I. D. Aggrawal, “Small-core As–Se fiber for Raman amplification,” Opt. Lett. 28, 1406–1408 (2003).
[CrossRef] [PubMed]

2002 (3)

J. M. Harbold, F. O. Ilday, F. W. Wise, J. S. Sanghera, V. Q. Nguyen, L. B. Shaw, and I. D. Aggarwal, “Highly nonlinear As–S–Se glasses for all-optical switching,” Opt. Lett. 27, 119–121 (2002).
[CrossRef]

P. S. Westbrook, T. H. Her, B. J. Eggleton, S. Hunsche, and G. Raybon, “Measurement of pulse degradation using opti-cal 2D regenerator,” Electron. Lett. 38, 1193–1194 (2002).
[CrossRef]

J. M. Harbold, F. O. Ilday, F. W. Wise, and B. G. Aitken, “Highly nonlinear Ge–As–Se and Ge–As–S–Se glasses for all-optical switching,” IEEE Photon. Technol. Lett. 14, 822–824 (2002).
[CrossRef]

2001 (1)

2000 (2)

1999 (2)

J. S. Sanghera and I. D. Aggarwal, “Active and passive chalcogenide glass optical fibers for IR applications: a review,” J. Non-Cryst. Solids 257, 6–16 (1999).
[CrossRef]

S. Smolorz, I. Kang, F. W. Wise, B. G. Aitken, and N. F. Borrelli, “Studies of optical non-linearities of chalcogenide and heavy-metal oxide glasses,” J. Non-Cryst. Solids 256–257, 310–317 (1999).
[CrossRef]

1998 (1)

K. A. Richardson, J. M. McKinley, B. Lawrence, S. Joshi, and A. Villeneuve, “Comparison of nonlinear optical properties of sulfide glasses in bulk and thin film form,” Opt. Mater. 10, 155–159 (1998).
[CrossRef]

1997 (1)

M. Asobe, “Nonlinear optical properties of chalcogenide glass fibers and their applications in all-optical switching,” Opt. Fiber Technol. 3, 142–148 (1997).
[CrossRef]

1991 (2)

M. E. Lines, “Oxide glasses for fast photonic switching: a comparison study,” J. Appl. Phys. 69, 6876–6884 (1991).
[CrossRef]

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electron nonlinear refraction in solids,” IEEE J. Quantum Electron. 27, 1296–1309 (1991).
[CrossRef]

1990 (1)

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

1986 (1)

1978 (1)

K. O. Hill, Y. Fuji, D. C. Johnson, and B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: application to reflection filter fabrication,” Appl. Phys. Lett. 32, 647–649 (1978).
[CrossRef]

1977 (1)

N. Kumagai, J. Shirafuji, and Y. Inuishi, “Raman and infrared studies on vibrational properties of Ge–Se glasses,” J. Phys. Soc. Jpn. 42, 1262–1268 (1977).
[CrossRef]

1971 (1)

S. H. Wemple and M. DiDomenico, “Behavior of the electronic dielectric constant in covalent and ionic materials,” Phys. Rev. B 3, 1338–1351 (1971).
[CrossRef]

1970 (1)

F. Kosek and J. Tauc, “Optical properties of As2S3,” Czech. J. Phys. Sect. B 20, 94–100 (1970).
[CrossRef]

1966 (1)

J. T. Edmond, “Electronic conduction in As2Se3, As2Se2Te and similar materials,” Br. J. Appl. Phys. 17, 979–989 (1966).
[CrossRef]

Aggarwal, I. D.

J. M. Harbold, F. O. Ilday, F. W. Wise, J. S. Sanghera, V. Q. Nguyen, L. B. Shaw, and I. D. Aggarwal, “Highly nonlinear As–S–Se glasses for all-optical switching,” Opt. Lett. 27, 119–121 (2002).
[CrossRef]

J. S. Sanghera and I. D. Aggarwal, “Active and passive chalcogenide glass optical fibers for IR applications: a review,” J. Non-Cryst. Solids 257, 6–16 (1999).
[CrossRef]

Aggrawal, I. D.

Aitken, B. G.

J. M. Harbold, F. O. Ilday, F. W. Wise, and B. G. Aitken, “Highly nonlinear Ge–As–Se and Ge–As–S–Se glasses for all-optical switching,” IEEE Photon. Technol. Lett. 14, 822–824 (2002).
[CrossRef]

S. Smolorz, I. Kang, F. W. Wise, B. G. Aitken, and N. F. Borrelli, “Studies of optical non-linearities of chalcogenide and heavy-metal oxide glasses,” J. Non-Cryst. Solids 256–257, 310–317 (1999).
[CrossRef]

Asobe, M.

M. Asobe, “Nonlinear optical properties of chalcogenide glass fibers and their applications in all-optical switching,” Opt. Fiber Technol. 3, 142–148 (1997).
[CrossRef]

Borrelli, N. F.

S. Smolorz, I. Kang, F. W. Wise, B. G. Aitken, and N. F. Borrelli, “Studies of optical non-linearities of chalcogenide and heavy-metal oxide glasses,” J. Non-Cryst. Solids 256–257, 310–317 (1999).
[CrossRef]

Broderick, N. G. R.

T. M. Monro, Y. D. West, D. W. Hewak, N. G. R. Broderick, and D. J. Richardson, “Chalcogenide holey fibres,” Electron. Lett. 36, 1998–2000 (2000).
[CrossRef]

Chemla, D. S.

Cheong, S.-W.

DiDomenico, M.

S. H. Wemple and M. DiDomenico, “Behavior of the electronic dielectric constant in covalent and ionic materials,” Phys. Rev. B 3, 1338–1351 (1971).
[CrossRef]

Edmond, J. T.

J. T. Edmond, “Electronic conduction in As2Se3, As2Se2Te and similar materials,” Br. J. Appl. Phys. 17, 979–989 (1966).
[CrossRef]

Eggleton, B. J.

P. S. Westbrook, T. H. Her, B. J. Eggleton, S. Hunsche, and G. Raybon, “Measurement of pulse degradation using opti-cal 2D regenerator,” Electron. Lett. 38, 1193–1194 (2002).
[CrossRef]

B. J. Eggleton, C. Kerbage, P. S. Westbrook, R. S. Windeler, and A. Hale, “Microstructured optical fiber devices,” Opt. Express 9, 698–713 (2001).
[CrossRef] [PubMed]

Fuji, Y.

K. O. Hill, Y. Fuji, D. C. Johnson, and B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: application to reflection filter fabrication,” Appl. Phys. Lett. 32, 647–649 (1978).
[CrossRef]

Hagan, D. J.

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electron nonlinear refraction in solids,” IEEE J. Quantum Electron. 27, 1296–1309 (1991).
[CrossRef]

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

Hale, A.

Harbold, J. M.

J. M. Harbold, F. O. Ilday, F. W. Wise, J. S. Sanghera, V. Q. Nguyen, L. B. Shaw, and I. D. Aggarwal, “Highly nonlinear As–S–Se glasses for all-optical switching,” Opt. Lett. 27, 119–121 (2002).
[CrossRef]

J. M. Harbold, F. O. Ilday, F. W. Wise, and B. G. Aitken, “Highly nonlinear Ge–As–Se and Ge–As–S–Se glasses for all-optical switching,” IEEE Photon. Technol. Lett. 14, 822–824 (2002).
[CrossRef]

Her, T. H.

P. S. Westbrook, T. H. Her, B. J. Eggleton, S. Hunsche, and G. Raybon, “Measurement of pulse degradation using opti-cal 2D regenerator,” Electron. Lett. 38, 1193–1194 (2002).
[CrossRef]

Hewak, D. W.

T. M. Monro, Y. D. West, D. W. Hewak, N. G. R. Broderick, and D. J. Richardson, “Chalcogenide holey fibres,” Electron. Lett. 36, 1998–2000 (2000).
[CrossRef]

Hill, K. O.

K. O. Hill, Y. Fuji, D. C. Johnson, and B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: application to reflection filter fabrication,” Appl. Phys. Lett. 32, 647–649 (1978).
[CrossRef]

Hunsche, S.

P. S. Westbrook, T. H. Her, B. J. Eggleton, S. Hunsche, and G. Raybon, “Measurement of pulse degradation using opti-cal 2D regenerator,” Electron. Lett. 38, 1193–1194 (2002).
[CrossRef]

Hutchings, D. C.

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electron nonlinear refraction in solids,” IEEE J. Quantum Electron. 27, 1296–1309 (1991).
[CrossRef]

Hwang, H. Y.

Ilday, F. O.

J. M. Harbold, F. O. Ilday, F. W. Wise, and B. G. Aitken, “Highly nonlinear Ge–As–Se and Ge–As–S–Se glasses for all-optical switching,” IEEE Photon. Technol. Lett. 14, 822–824 (2002).
[CrossRef]

J. M. Harbold, F. O. Ilday, F. W. Wise, J. S. Sanghera, V. Q. Nguyen, L. B. Shaw, and I. D. Aggarwal, “Highly nonlinear As–S–Se glasses for all-optical switching,” Opt. Lett. 27, 119–121 (2002).
[CrossRef]

Inuishi, Y.

N. Kumagai, J. Shirafuji, and Y. Inuishi, “Raman and infrared studies on vibrational properties of Ge–Se glasses,” J. Phys. Soc. Jpn. 42, 1262–1268 (1977).
[CrossRef]

Johnson, D. C.

K. O. Hill, Y. Fuji, D. C. Johnson, and B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: application to reflection filter fabrication,” Appl. Phys. Lett. 32, 647–649 (1978).
[CrossRef]

Joshi, S.

K. A. Richardson, J. M. McKinley, B. Lawrence, S. Joshi, and A. Villeneuve, “Comparison of nonlinear optical properties of sulfide glasses in bulk and thin film form,” Opt. Mater. 10, 155–159 (1998).
[CrossRef]

Kang, I.

S. Smolorz, I. Kang, F. W. Wise, B. G. Aitken, and N. F. Borrelli, “Studies of optical non-linearities of chalcogenide and heavy-metal oxide glasses,” J. Non-Cryst. Solids 256–257, 310–317 (1999).
[CrossRef]

Katsufuji, T.

Kawasaki, B. S.

K. O. Hill, Y. Fuji, D. C. Johnson, and B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: application to reflection filter fabrication,” Appl. Phys. Lett. 32, 647–649 (1978).
[CrossRef]

Kerbage, C.

Kosek, F.

F. Kosek and J. Tauc, “Optical properties of As2S3,” Czech. J. Phys. Sect. B 20, 94–100 (1970).
[CrossRef]

Kumagai, N.

N. Kumagai, J. Shirafuji, and Y. Inuishi, “Raman and infrared studies on vibrational properties of Ge–Se glasses,” J. Phys. Soc. Jpn. 42, 1262–1268 (1977).
[CrossRef]

Lawrence, B.

K. A. Richardson, J. M. McKinley, B. Lawrence, S. Joshi, and A. Villeneuve, “Comparison of nonlinear optical properties of sulfide glasses in bulk and thin film form,” Opt. Mater. 10, 155–159 (1998).
[CrossRef]

Lenz, G.

Lines, M. E.

McKinley, J. M.

K. A. Richardson, J. M. McKinley, B. Lawrence, S. Joshi, and A. Villeneuve, “Comparison of nonlinear optical properties of sulfide glasses in bulk and thin film form,” Opt. Mater. 10, 155–159 (1998).
[CrossRef]

Miller, D. A. B.

Monro, T. M.

T. M. Monro, Y. D. West, D. W. Hewak, N. G. R. Broderick, and D. J. Richardson, “Chalcogenide holey fibres,” Electron. Lett. 36, 1998–2000 (2000).
[CrossRef]

Nguyen, V. Q.

Pureza, P. C.

Raybon, G.

P. S. Westbrook, T. H. Her, B. J. Eggleton, S. Hunsche, and G. Raybon, “Measurement of pulse degradation using opti-cal 2D regenerator,” Electron. Lett. 38, 1193–1194 (2002).
[CrossRef]

Richardson, D. J.

T. M. Monro, Y. D. West, D. W. Hewak, N. G. R. Broderick, and D. J. Richardson, “Chalcogenide holey fibres,” Electron. Lett. 36, 1998–2000 (2000).
[CrossRef]

Richardson, K. A.

K. A. Richardson, J. M. McKinley, B. Lawrence, S. Joshi, and A. Villeneuve, “Comparison of nonlinear optical properties of sulfide glasses in bulk and thin film form,” Opt. Mater. 10, 155–159 (1998).
[CrossRef]

Said, A. A.

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

Sanghera, J. S.

Shaw, L. B.

Sheik-Bahae, M.

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electron nonlinear refraction in solids,” IEEE J. Quantum Electron. 27, 1296–1309 (1991).
[CrossRef]

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

Shirafuji, J.

N. Kumagai, J. Shirafuji, and Y. Inuishi, “Raman and infrared studies on vibrational properties of Ge–Se glasses,” J. Phys. Soc. Jpn. 42, 1262–1268 (1977).
[CrossRef]

Slusher, R. E.

Smolorz, S.

S. Smolorz, I. Kang, F. W. Wise, B. G. Aitken, and N. F. Borrelli, “Studies of optical non-linearities of chalcogenide and heavy-metal oxide glasses,” J. Non-Cryst. Solids 256–257, 310–317 (1999).
[CrossRef]

Spalter, S.

Tauc, J.

F. Kosek and J. Tauc, “Optical properties of As2S3,” Czech. J. Phys. Sect. B 20, 94–100 (1970).
[CrossRef]

Thielen, P. A.

Van Stryland, E. W.

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electron nonlinear refraction in solids,” IEEE J. Quantum Electron. 27, 1296–1309 (1991).
[CrossRef]

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

Villeneuve, A.

K. A. Richardson, J. M. McKinley, B. Lawrence, S. Joshi, and A. Villeneuve, “Comparison of nonlinear optical properties of sulfide glasses in bulk and thin film form,” Opt. Mater. 10, 155–159 (1998).
[CrossRef]

Wei, T.-H.

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

Wemple, S. H.

S. H. Wemple and M. DiDomenico, “Behavior of the electronic dielectric constant in covalent and ionic materials,” Phys. Rev. B 3, 1338–1351 (1971).
[CrossRef]

West, Y. D.

T. M. Monro, Y. D. West, D. W. Hewak, N. G. R. Broderick, and D. J. Richardson, “Chalcogenide holey fibres,” Electron. Lett. 36, 1998–2000 (2000).
[CrossRef]

Westbrook, P. S.

P. S. Westbrook, T. H. Her, B. J. Eggleton, S. Hunsche, and G. Raybon, “Measurement of pulse degradation using opti-cal 2D regenerator,” Electron. Lett. 38, 1193–1194 (2002).
[CrossRef]

B. J. Eggleton, C. Kerbage, P. S. Westbrook, R. S. Windeler, and A. Hale, “Microstructured optical fiber devices,” Opt. Express 9, 698–713 (2001).
[CrossRef] [PubMed]

Windeler, R. S.

Wise, F. W.

J. M. Harbold, F. O. Ilday, F. W. Wise, J. S. Sanghera, V. Q. Nguyen, L. B. Shaw, and I. D. Aggarwal, “Highly nonlinear As–S–Se glasses for all-optical switching,” Opt. Lett. 27, 119–121 (2002).
[CrossRef]

J. M. Harbold, F. O. Ilday, F. W. Wise, and B. G. Aitken, “Highly nonlinear Ge–As–Se and Ge–As–S–Se glasses for all-optical switching,” IEEE Photon. Technol. Lett. 14, 822–824 (2002).
[CrossRef]

S. Smolorz, I. Kang, F. W. Wise, B. G. Aitken, and N. F. Borrelli, “Studies of optical non-linearities of chalcogenide and heavy-metal oxide glasses,” J. Non-Cryst. Solids 256–257, 310–317 (1999).
[CrossRef]

Zimmermann, J.

Appl. Phys. Lett. (1)

K. O. Hill, Y. Fuji, D. C. Johnson, and B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: application to reflection filter fabrication,” Appl. Phys. Lett. 32, 647–649 (1978).
[CrossRef]

Br. J. Appl. Phys. (1)

J. T. Edmond, “Electronic conduction in As2Se3, As2Se2Te and similar materials,” Br. J. Appl. Phys. 17, 979–989 (1966).
[CrossRef]

C.R. Acad. Sci., Ser. IIc: Chim (1)

J. S. Sanghera, L. B. Shaw, and I. D. Aggrawal, “Applications of chalcogenide glass optical fibers,” C.R. Acad. Sci., Ser. IIc: Chim 5, 1–11 (2003).

Czech. J. Phys. Sect. B (1)

F. Kosek and J. Tauc, “Optical properties of As2S3,” Czech. J. Phys. Sect. B 20, 94–100 (1970).
[CrossRef]

Electron. Lett. (2)

P. S. Westbrook, T. H. Her, B. J. Eggleton, S. Hunsche, and G. Raybon, “Measurement of pulse degradation using opti-cal 2D regenerator,” Electron. Lett. 38, 1193–1194 (2002).
[CrossRef]

T. M. Monro, Y. D. West, D. W. Hewak, N. G. R. Broderick, and D. J. Richardson, “Chalcogenide holey fibres,” Electron. Lett. 36, 1998–2000 (2000).
[CrossRef]

IEEE J. Quantum Electron. (2)

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
[CrossRef]

M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electron nonlinear refraction in solids,” IEEE J. Quantum Electron. 27, 1296–1309 (1991).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

J. M. Harbold, F. O. Ilday, F. W. Wise, and B. G. Aitken, “Highly nonlinear Ge–As–Se and Ge–As–S–Se glasses for all-optical switching,” IEEE Photon. Technol. Lett. 14, 822–824 (2002).
[CrossRef]

J. Appl. Phys. (1)

M. E. Lines, “Oxide glasses for fast photonic switching: a comparison study,” J. Appl. Phys. 69, 6876–6884 (1991).
[CrossRef]

J. Non-Cryst. Solids (2)

J. S. Sanghera and I. D. Aggarwal, “Active and passive chalcogenide glass optical fibers for IR applications: a review,” J. Non-Cryst. Solids 257, 6–16 (1999).
[CrossRef]

S. Smolorz, I. Kang, F. W. Wise, B. G. Aitken, and N. F. Borrelli, “Studies of optical non-linearities of chalcogenide and heavy-metal oxide glasses,” J. Non-Cryst. Solids 256–257, 310–317 (1999).
[CrossRef]

J. Phys. Soc. Jpn. (1)

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M. Asobe, “Nonlinear optical properties of chalcogenide glass fibers and their applications in all-optical switching,” Opt. Fiber Technol. 3, 142–148 (1997).
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Opt. Mater. (1)

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Figures (13)

Fig. 1
Fig. 1

Three absorption spectral regions in a glass are shown schematically. Region C corresponds to the Sellmeier gap where the absorption varies as a polynomial with frequency, region B is the Urbach gap region where absorption varies exponentially with frequency, and region A is where the absorption is dominated by impurities.

Fig. 2
Fig. 2

Linear optical absorption edges (Urbach tails) for chalcogenide glasses: As2Se3 used in the present experiments (solid curve with dotted extension, Eg=1.78 eV), As2S3 (dashed–dotted curve, Eg=2.4 eV), Ge0.25Se0.75 (dotted curve, Eg=2.07 eV), and Ge0.25Se0.65Te0.1 (dashed–dotted–dotted curve, Eg=1.72 eV). The linear extensions (on this log plot) of the measured data to the level of 103 cm-1 are shown as short dashed lines. The curves for As2S3 and As2Se3 (solid curve, Eg=1.77 eV) over a large range of energies are taken from Refs. 11-13. The horizontal dashed–dotted line is the absorption level used as a measure of Eg.

Fig. 3
Fig. 3

Theoretical group-velocity dispersion as a function of wavelength for As2Se3 glass.

Fig. 4
Fig. 4

FOM, the ratio of the nonlinear phase shift to the nonlinear loss [see Eq. (10)], is shown as a function of percentage of the incident light energy exiting the fiber, i.e., the total transmission including both nonlinear and linear losses. This calculation assumes a 1-dB linear loss. For total transmission near 65% observed in the experiments, FOM2.5.

Fig. 5
Fig. 5

Calculated dispersion of the Kerr response (solid curve) and TPA (dashed curve).

Fig. 6
Fig. 6

Measured dispersion delay in a 40-cm length of As–Se fiber used in the experiments.

Fig. 7
Fig. 7

Average power output as a function of power input for cw excitation of the fiber. There is no hysteresis in this case. The shaded portion corresponds to fluctuations in the output power. The dotted line is a linear extrapolation of the linear low-power range. The linear transmission of the experimental fiber is approximately 0.8.

Fig. 8
Fig. 8

Average power output as a function of average power input for pulsed excitation of fiber. The shaded area corresponds to fluctuations in the output power level as the power level is increased. The lower set of curves with no shading is the range of powers measured as the power is decreased. Note that there is some hysteretic effect. The dotted line is a linear extrapolation of the linear low-power range. The linear transmission of the experimental fiber is approximately 0.8.

Fig. 9
Fig. 9

Transmission spectra of fiber after exposure to a 450-mW cw Raman pump light at a wavelength of 1540 nm. The transmission spectrum is taken (a) immediately after exposure and (b) several months after exposure.

Fig. 10
Fig. 10

Average power output as a function of the average power input for the pulsed experiments shown in Figs. 11 and 12. The upper data points correspond to output powers measured as the power increased, and the lower points correspond to output powers as the power decreased. The dotted line is a linear extrapolation of the low-power data.

Fig. 11
Fig. 11

Experimental measurements of the SPM spectra at peak powers of 2.7 W (double-peaked solid curve), 1.5 W (dotted curve), and 0.1 W (single-peaked solid curve).

Fig. 12
Fig. 12

Numerical simulations of the SPM spectra as a function of wavelength for peak powers of 2.7 W (double-peaked solid curve), 1.5 W (dotted curve), and 0.1 W (single-peaked solid curve). The pulse width is 3.2-ps FWHM, the dispersion is -670 ps/(nm km), and the fiber attenuation is 2.9 dB/m (including nonlinear absorption at 2.7-W peak power).

Fig. 13
Fig. 13

Raman gain spectra measured in an 85-cm-long As–Se fiber (solid curve) compared with Raman spectrum in bulk material (dotted curve). The ratio of the power output to the power input, normalized to the ratio well removed from the Raman gain region, is shown as a function of wavelength.

Equations (13)

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n2-1=EdEs/[(Es)2-(hν)2],
β2=(λ3/2πc2)(d2n/dλ2),
β2=1.5α2Ed/(πc2Es3λn),
β2=5269Ed/Es3n.
D[ps/(nm km)]=-(2πc/λ2)β2(ps2/km)=-0.781β2(ps2/km)=-565[ps/(nm km)].
LD=τ2/β2
τc2=4 ln(2β2L).
τ0=τi[1+(τc/τi)4]1/2,
ϕNL(L)=2π(n2/βλ)ln[1+βI(0)Leff],
ϕNL(L)=2πFOM ln[exp(-αL)/T(L)],
n2(ν)=1.7×10-14(n2+2)3(n2-1)×(d/nEs)2F(hν/Eg)cm2/W,
FOMD=LD/πLNL={2n2/β2λ[µm2/(pJ ps)]}{Pτ/Aeff[(pJ ps)/µm2]},
Iout=Iin exp(gRIpL),

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