Abstract

The nonlinear index of refraction in a resonant region has been determined by the use of a fiber-based Mach–Zehnder interferometer to measure the temporal fringe shift between two signals. The measurement technique is direct and does not require additional amplitude information for the extraction of the nonlinear index of refraction. This technique has been used to measure the temporal response of an InGaAsP semiconductor optical amplifier at 1.313 μm.

© 1996 Optical Society of America

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References

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  1. W. K. Burns, N. Bloembergen, “Third-harmonic generation in absorbing media of cubic or isotropic symmetry,” Phys. Rev. B 4, 3437–3450 (1971).
  2. G. R. Olbright, N. Peyghambarian, “Interferometric measurement of the nonlinear index of refraction, n2, of CdSxSe1−x-doped glasses,” Appl. Phys. Lett. 48, 1184–1186 (1986).
  3. R. Jin, C. L. Chuang, H. M. Gibbs, S. W. Koch, J. N. Polky, G. A. Pubanz, “Picosecond all-optical switching in single-mode GaAs/AlGaAs strip-loaded nonlinear directional couplers,” Appl. Phys. Lett. 53, 1791–1794 (1988).
  4. D. Cotter, C. N. Ironside, B. J. Ainslie, H. P. Girdlestone, “Picosecond pump-probe interferometric measurement of optical nonlinearity in semiconductor-doped fibers,” Opt. Lett. 14, 317–319 (1989).
  5. M. L. LaGasse, K. K. Anderson, H. A. Haus, J. G. Fujimoto, “Femtosecond all-optical switching in AlGaAs waveguides using a time division interferometer,” Appl. Phys. Lett. 54, 2068–2070 (1989).
  6. M. Sheik-bahae, A. A. Said, E. W. Van Stryland, “High-sensitivity, single-beam n2 measurements,” Opt. Lett. 14, 955–957 (1989).
  7. M. C. Gabriel, N. A. Whitaker, C. W. Dirk, M. G. Kuzyk, M. Thaker, “Measurement of ultrafast optical nonlinearities using a modified Sagnac interferometer,” Opt. Lett. 16, 1334–1336 (1991).
  8. K. L. Hall, A. M. Darwish, E. P. Ippen, U. Koren, G. Raybon, “Femtosecond index nonlinearities in InGaAsP optical amplifiers,” Appl. Phys. Lett. 62, 1320–1322 (1993).
  9. S. Nakamura, K. Tajima, Y. Sugimoto, “Experimental investigation on high-speed switching characteristic of a novel symmetric Mach–Zehnder all-optical switch,” Appl. Phys. Lett. 65, 283–286 (1994).
  10. P. Horowitz, W. Hill, The Art of Electronics, 2nd ed. (Cambridge, New York, 1989), p. 644.

1994 (1)

S. Nakamura, K. Tajima, Y. Sugimoto, “Experimental investigation on high-speed switching characteristic of a novel symmetric Mach–Zehnder all-optical switch,” Appl. Phys. Lett. 65, 283–286 (1994).

1993 (1)

K. L. Hall, A. M. Darwish, E. P. Ippen, U. Koren, G. Raybon, “Femtosecond index nonlinearities in InGaAsP optical amplifiers,” Appl. Phys. Lett. 62, 1320–1322 (1993).

1991 (1)

1989 (3)

1988 (1)

R. Jin, C. L. Chuang, H. M. Gibbs, S. W. Koch, J. N. Polky, G. A. Pubanz, “Picosecond all-optical switching in single-mode GaAs/AlGaAs strip-loaded nonlinear directional couplers,” Appl. Phys. Lett. 53, 1791–1794 (1988).

1986 (1)

G. R. Olbright, N. Peyghambarian, “Interferometric measurement of the nonlinear index of refraction, n2, of CdSxSe1−x-doped glasses,” Appl. Phys. Lett. 48, 1184–1186 (1986).

1971 (1)

W. K. Burns, N. Bloembergen, “Third-harmonic generation in absorbing media of cubic or isotropic symmetry,” Phys. Rev. B 4, 3437–3450 (1971).

Ainslie, B. J.

Anderson, K. K.

M. L. LaGasse, K. K. Anderson, H. A. Haus, J. G. Fujimoto, “Femtosecond all-optical switching in AlGaAs waveguides using a time division interferometer,” Appl. Phys. Lett. 54, 2068–2070 (1989).

Bloembergen, N.

W. K. Burns, N. Bloembergen, “Third-harmonic generation in absorbing media of cubic or isotropic symmetry,” Phys. Rev. B 4, 3437–3450 (1971).

Burns, W. K.

W. K. Burns, N. Bloembergen, “Third-harmonic generation in absorbing media of cubic or isotropic symmetry,” Phys. Rev. B 4, 3437–3450 (1971).

Chuang, C. L.

R. Jin, C. L. Chuang, H. M. Gibbs, S. W. Koch, J. N. Polky, G. A. Pubanz, “Picosecond all-optical switching in single-mode GaAs/AlGaAs strip-loaded nonlinear directional couplers,” Appl. Phys. Lett. 53, 1791–1794 (1988).

Cotter, D.

Darwish, A. M.

K. L. Hall, A. M. Darwish, E. P. Ippen, U. Koren, G. Raybon, “Femtosecond index nonlinearities in InGaAsP optical amplifiers,” Appl. Phys. Lett. 62, 1320–1322 (1993).

Dirk, C. W.

Fujimoto, J. G.

M. L. LaGasse, K. K. Anderson, H. A. Haus, J. G. Fujimoto, “Femtosecond all-optical switching in AlGaAs waveguides using a time division interferometer,” Appl. Phys. Lett. 54, 2068–2070 (1989).

Gabriel, M. C.

Gibbs, H. M.

R. Jin, C. L. Chuang, H. M. Gibbs, S. W. Koch, J. N. Polky, G. A. Pubanz, “Picosecond all-optical switching in single-mode GaAs/AlGaAs strip-loaded nonlinear directional couplers,” Appl. Phys. Lett. 53, 1791–1794 (1988).

Girdlestone, H. P.

Hall, K. L.

K. L. Hall, A. M. Darwish, E. P. Ippen, U. Koren, G. Raybon, “Femtosecond index nonlinearities in InGaAsP optical amplifiers,” Appl. Phys. Lett. 62, 1320–1322 (1993).

Haus, H. A.

M. L. LaGasse, K. K. Anderson, H. A. Haus, J. G. Fujimoto, “Femtosecond all-optical switching in AlGaAs waveguides using a time division interferometer,” Appl. Phys. Lett. 54, 2068–2070 (1989).

Hill, W.

P. Horowitz, W. Hill, The Art of Electronics, 2nd ed. (Cambridge, New York, 1989), p. 644.

Horowitz, P.

P. Horowitz, W. Hill, The Art of Electronics, 2nd ed. (Cambridge, New York, 1989), p. 644.

Ippen, E. P.

K. L. Hall, A. M. Darwish, E. P. Ippen, U. Koren, G. Raybon, “Femtosecond index nonlinearities in InGaAsP optical amplifiers,” Appl. Phys. Lett. 62, 1320–1322 (1993).

Ironside, C. N.

Jin, R.

R. Jin, C. L. Chuang, H. M. Gibbs, S. W. Koch, J. N. Polky, G. A. Pubanz, “Picosecond all-optical switching in single-mode GaAs/AlGaAs strip-loaded nonlinear directional couplers,” Appl. Phys. Lett. 53, 1791–1794 (1988).

Koch, S. W.

R. Jin, C. L. Chuang, H. M. Gibbs, S. W. Koch, J. N. Polky, G. A. Pubanz, “Picosecond all-optical switching in single-mode GaAs/AlGaAs strip-loaded nonlinear directional couplers,” Appl. Phys. Lett. 53, 1791–1794 (1988).

Koren, U.

K. L. Hall, A. M. Darwish, E. P. Ippen, U. Koren, G. Raybon, “Femtosecond index nonlinearities in InGaAsP optical amplifiers,” Appl. Phys. Lett. 62, 1320–1322 (1993).

Kuzyk, M. G.

LaGasse, M. L.

M. L. LaGasse, K. K. Anderson, H. A. Haus, J. G. Fujimoto, “Femtosecond all-optical switching in AlGaAs waveguides using a time division interferometer,” Appl. Phys. Lett. 54, 2068–2070 (1989).

Nakamura, S.

S. Nakamura, K. Tajima, Y. Sugimoto, “Experimental investigation on high-speed switching characteristic of a novel symmetric Mach–Zehnder all-optical switch,” Appl. Phys. Lett. 65, 283–286 (1994).

Olbright, G. R.

G. R. Olbright, N. Peyghambarian, “Interferometric measurement of the nonlinear index of refraction, n2, of CdSxSe1−x-doped glasses,” Appl. Phys. Lett. 48, 1184–1186 (1986).

Peyghambarian, N.

G. R. Olbright, N. Peyghambarian, “Interferometric measurement of the nonlinear index of refraction, n2, of CdSxSe1−x-doped glasses,” Appl. Phys. Lett. 48, 1184–1186 (1986).

Polky, J. N.

R. Jin, C. L. Chuang, H. M. Gibbs, S. W. Koch, J. N. Polky, G. A. Pubanz, “Picosecond all-optical switching in single-mode GaAs/AlGaAs strip-loaded nonlinear directional couplers,” Appl. Phys. Lett. 53, 1791–1794 (1988).

Pubanz, G. A.

R. Jin, C. L. Chuang, H. M. Gibbs, S. W. Koch, J. N. Polky, G. A. Pubanz, “Picosecond all-optical switching in single-mode GaAs/AlGaAs strip-loaded nonlinear directional couplers,” Appl. Phys. Lett. 53, 1791–1794 (1988).

Raybon, G.

K. L. Hall, A. M. Darwish, E. P. Ippen, U. Koren, G. Raybon, “Femtosecond index nonlinearities in InGaAsP optical amplifiers,” Appl. Phys. Lett. 62, 1320–1322 (1993).

Said, A. A.

Sheik-bahae, M.

Sugimoto, Y.

S. Nakamura, K. Tajima, Y. Sugimoto, “Experimental investigation on high-speed switching characteristic of a novel symmetric Mach–Zehnder all-optical switch,” Appl. Phys. Lett. 65, 283–286 (1994).

Tajima, K.

S. Nakamura, K. Tajima, Y. Sugimoto, “Experimental investigation on high-speed switching characteristic of a novel symmetric Mach–Zehnder all-optical switch,” Appl. Phys. Lett. 65, 283–286 (1994).

Thaker, M.

Van Stryland, E. W.

Whitaker, N. A.

Appl. Phys. Lett. (5)

G. R. Olbright, N. Peyghambarian, “Interferometric measurement of the nonlinear index of refraction, n2, of CdSxSe1−x-doped glasses,” Appl. Phys. Lett. 48, 1184–1186 (1986).

R. Jin, C. L. Chuang, H. M. Gibbs, S. W. Koch, J. N. Polky, G. A. Pubanz, “Picosecond all-optical switching in single-mode GaAs/AlGaAs strip-loaded nonlinear directional couplers,” Appl. Phys. Lett. 53, 1791–1794 (1988).

M. L. LaGasse, K. K. Anderson, H. A. Haus, J. G. Fujimoto, “Femtosecond all-optical switching in AlGaAs waveguides using a time division interferometer,” Appl. Phys. Lett. 54, 2068–2070 (1989).

K. L. Hall, A. M. Darwish, E. P. Ippen, U. Koren, G. Raybon, “Femtosecond index nonlinearities in InGaAsP optical amplifiers,” Appl. Phys. Lett. 62, 1320–1322 (1993).

S. Nakamura, K. Tajima, Y. Sugimoto, “Experimental investigation on high-speed switching characteristic of a novel symmetric Mach–Zehnder all-optical switch,” Appl. Phys. Lett. 65, 283–286 (1994).

Opt. Lett. (3)

Phys. Rev. B (1)

W. K. Burns, N. Bloembergen, “Third-harmonic generation in absorbing media of cubic or isotropic symmetry,” Phys. Rev. B 4, 3437–3450 (1971).

Other (1)

P. Horowitz, W. Hill, The Art of Electronics, 2nd ed. (Cambridge, New York, 1989), p. 644.

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Figures (3)

Fig. 1
Fig. 1

Experimental setup for the fiber-based Mach–Zehnder interferometer. Optical propagation in free space is indicated by dotted curves, and optical fibers are indicated by the solid curves. Electrical signal connections are shown by the dashed curves. The input optical pulse train is split by the polarization beam splitter (PBS) to provide the pump and probe signals. The polarization is adjusted by the loop polarizers (LP's), and a small incremental change is achieved by the piezotranslator (PZT) on one of adjustable delay units (AD's). The semiconductor optical amplifier (SOA) is inside one of the Mach–Zehnder arms.

Fig. 2
Fig. 2

Two sinusoidal signals obtained by the use of different pump pulse energies as a function of relative optical delay. Dotted and solid curves are with and without the presence of pump pulse, respectively. With the assumption of a −3-dB coupling loss at the amplifier input, the incident pump pulse energies at the amplifier are (a) 0 fJ, (b) 190 fJ, (c) 280 fJ, (d) 570 fJ.

Fig. 3
Fig. 3

Nonlinear temporal responses of a SOA: (a) nonlinear phase change, (b) signal output. These measurements were taken with 380 fJ of pump pulse energy and a bias current of 60 mA.

Equations (3)

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I out ( t ) = I 1 ( t ) + I 2 ( t ) + 2 [ I 1 ( t ) I 2 ( t ) ] 1 / 2 cos [ Δϕ ( t ) + ϕ nl ( t ) ] ,
E       [ I 1 ( t ) + I 2 ( t ) ] d t + 2   cos ( Δϕ + ϕ nl )       [ I 1 ( t ) I 2 ( t ) ] 1 / 2 d t .
Δ n = λ 2 π L Δ ϕ nl ,

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