Abstract

We show theoretically and experimentally that the polarization sensitivity of asymmetric nondegenerate fiber four-wave mixing can be eliminated by using circularly polarized pump waves in a twisted fiber. By twisting a fiber at 15 turns/m and aligning the pump waves to a circular state of polarization, we successfully reduce the polarization sensitivity from 5.8 dB to 0.9 dB. Although the polarization-mode dispersion (PMD) of the twisted fiber sets the limitation to the conversion bandwidth, its effect is relatively small owing to the small PMD of the twisted fiber. The demonstrated scheme should be a simple and efficient way of realizing all-optical tunable wavelength converters and wavelength-exchange devices without polarization dependence.

© 2005 Optical Society of America

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References

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  1. K. Inoue, �??Tunable and selective wavelength conversion using fiber four-wave mixing with two pump lights,�?? IEEE Photonics Technol. Lett. 6, 1451-1453 (1994).
    [CrossRef]
  2. T. Tanemura, C. S. Goh, K. Kikuchi, and S. Y. Set, �??Highly efficient arbitrary wavelength conversion within entire C-band based on nondegenerate fiber four-wave mixing,�?? IEEE Photonics Technol. Lett. 16, 551-553 (2004).
    [CrossRef]
  3. M. E. Marhic, Y. Park, F. S. Yang, and L. G. Kazovsky, �??Widely tunable spectrum translation and wavelength exchange by four-wave mixing in optical fibers,�?? Opt. Lett. 21, 1906-1908 (1996).
    [CrossRef] [PubMed]
  4. K. Uesaka, K. K. Y. Wong, M. E. Marhic, and L. G. Kazovsky, �??Polarization-insensitive wavelength exchange in highly-nonlinear dispersion-shifted fiber,�?? in Proc. Optical Fiber Communications (OFC) 2002, Paper ThY3 (2002).
  5. S. Radic, C. J. McKinstrie, R. M. Jopson, J. C. Centanni, A. R. Chraplyvy, C. G. Jorgensen, K. Brar, and C. Headley, �??Selective suppression of idler spectral broadening in two-pump parametric architectures,�?? IEEE Photonics Technol. Lett. 15, 673-675 (2003).
    [CrossRef]
  6. R. M. Jopson and R. E. Tench, �??Polarization-independent phase conjugation of lightwave signals,�?? Electron. Lett. 29, 2216-2217 (1993).
    [CrossRef]
  7. K. Inoue, �??Polarization independent wavelength conversion using fiber four-wave mixing with two orthogonal pump lights of different frequencies,�?? J. Lightwave Technol. 12, 1916-1920 (1994).
    [CrossRef]
  8. C. J. McKinstrie, H. Kogelnik, R. M. Jopson, S. Radic, and A. V. Kanaev, �??Four-wave mixing in fibers with random birefringence,�?? Opt. Express 12, 2033-2055 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-10-2033.">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-10-2033.</a>
    [CrossRef] [PubMed]
  9. Y. Liang, J. W. Lou, J. K. Andersen, J. C. Stocker, O. Boyraz, M. N. Islam, and D. A. Nolan, �??Polarization-insensitive nonlinear optical loop mirror demultiplexer with twisted fiber,�?? Opt. Lett. 24, 726-728 (1999).
    [CrossRef]
  10. T. Tanemura, J. Suzuki, K. Katoh, and K. Kikuchi, �??Polarization-insensitive all-optical wavelength conversion using cross-phase modulation in twisted fiber and optical filtering,�?? IEEE Photonics Technol. Lett. 17, 1052-1054 (2005).
    [CrossRef]
  11. P. D. Maker and R. W. Terhune, �??Study of optical effects due to an induced polarization third order in the electric field strength,�?? Phys. Rev. 137, A801-A818 (1965).
    [CrossRef]
  12. Q. Lin and G. P. Agrawal, �??Vector theory of four-wave mixing: polarization effects in fiber-optic parametric amplifiers,�?? J. Opt. Soc. Am. B 21, 1216-1224 (2004).
    [CrossRef]
  13. M. E. Marhic, K. K. Y. Wong, and L. G. Kazovsky, �??Fiber optical parametric amplifiers with linearly or circularly polarized waves,�?? J. Opt. Soc. Am. B 20, -2433 (2003).
    [CrossRef]
  14. R. Ulrich and A. Simon, �??Polarization optics of twisted single-mode fibers,�?? Appl. Opt. 18, 2241-2251 (1979)
    [CrossRef] [PubMed]
  15. D. N. Payne, A. J. Barlow, and J. J. R. Hansen, �??Development of low- and high-birefringence optical fibers,�?? IEEE J. Quantum Electron. 18, 477-488 (1982).
    [CrossRef]
  16. E. Brinkmeyer, �??Forward-backward transmission in birefringent single-mode fibers: interpretation of polarization-sensitive measurements,�?? Opt. Lett. 6, 575-577 (1981).
    [CrossRef] [PubMed]

Appl. Opt. (1)

Electron. Lett. (1)

R. M. Jopson and R. E. Tench, �??Polarization-independent phase conjugation of lightwave signals,�?? Electron. Lett. 29, 2216-2217 (1993).
[CrossRef]

IEEE J. Quantum Electron. (1)

D. N. Payne, A. J. Barlow, and J. J. R. Hansen, �??Development of low- and high-birefringence optical fibers,�?? IEEE J. Quantum Electron. 18, 477-488 (1982).
[CrossRef]

IEEE Photonics Technol. Lett. (4)

S. Radic, C. J. McKinstrie, R. M. Jopson, J. C. Centanni, A. R. Chraplyvy, C. G. Jorgensen, K. Brar, and C. Headley, �??Selective suppression of idler spectral broadening in two-pump parametric architectures,�?? IEEE Photonics Technol. Lett. 15, 673-675 (2003).
[CrossRef]

K. Inoue, �??Tunable and selective wavelength conversion using fiber four-wave mixing with two pump lights,�?? IEEE Photonics Technol. Lett. 6, 1451-1453 (1994).
[CrossRef]

T. Tanemura, C. S. Goh, K. Kikuchi, and S. Y. Set, �??Highly efficient arbitrary wavelength conversion within entire C-band based on nondegenerate fiber four-wave mixing,�?? IEEE Photonics Technol. Lett. 16, 551-553 (2004).
[CrossRef]

T. Tanemura, J. Suzuki, K. Katoh, and K. Kikuchi, �??Polarization-insensitive all-optical wavelength conversion using cross-phase modulation in twisted fiber and optical filtering,�?? IEEE Photonics Technol. Lett. 17, 1052-1054 (2005).
[CrossRef]

J. Lightwave Technol. (1)

K. Inoue, �??Polarization independent wavelength conversion using fiber four-wave mixing with two orthogonal pump lights of different frequencies,�?? J. Lightwave Technol. 12, 1916-1920 (1994).
[CrossRef]

J. Opt. Soc. Am. B (2)

OFC 2002 (1)

K. Uesaka, K. K. Y. Wong, M. E. Marhic, and L. G. Kazovsky, �??Polarization-insensitive wavelength exchange in highly-nonlinear dispersion-shifted fiber,�?? in Proc. Optical Fiber Communications (OFC) 2002, Paper ThY3 (2002).

Opt. Express (1)

Opt. Lett. (3)

Phys. Rev. (1)

P. D. Maker and R. W. Terhune, �??Study of optical effects due to an induced polarization third order in the electric field strength,�?? Phys. Rev. 137, A801-A818 (1965).
[CrossRef]

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Figures (7)

Fig. 1.
Fig. 1.

Wavelength allocation of the asymmetric FWM.

Fig. 2.
Fig. 2.

(a) Experimental setup for the P-OTDR measurement. PC: polarization controller. (b) Measured P-OTDR traces. Black and gray traces show two different cases as we varied PC.

Fig. 3.
Fig. 3.

Experimental setup of the polarization-insensitive FWM using a twisted fiber. MZ: LiNbO3 Mach-Zehnder modulator, PM: LiNbO3 phase modulator, ECL: external-cavity CW laser, P: polarizer, HWP: half-wave plate, PC: polarization controller.

Fig. 4.
Fig. 4.

Eye diagrams of the output idler wave with the polarization scrambler OFF (left) and ON (right), when we employ the non-twisted DSF (a) and twisted DSF (b).

Fig. 5.
Fig. 5.

Polarization sensitivity of the conversion efficiency measured with the non-twisted DSF (dots) and twisted DSF (circle).

Fig. 6.
Fig. 6.

Polarization sensitivity versus the pump SOP. Dots and circles are the maximum and minimum conversion efficiency, respectively, measured by varying the signal SOP, while triangles are the ratio of those two, representing the polarization sensitivity.

Fig. 7.
Fig. 7.

The maximum (dots) and minimum (circles) conversion efficiency and their ratios (triangles), representing the polarization sensitivity, as functions of the pump-wavelength separation. Theoretical curves are calculated from Eqs. (17) and (23).

Equations (25)

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P ( 3 ) ( r , t ) = ε 0 χ ( 3 ) [ E ( r , t ) · E ( r , t ) ] E ( r , t ) ,
E ( r , t ) = Re [ E 1 ( r ) exp ( i ω 1 t ) + E 2 ( r ) exp ( i ω 2 t ) + E 3 ( r ) exp ( i ω 3 t ) + E 4 ( r ) exp ( i ω 4 t ) ] ,
P 1 ( 3 ) ( r ) = ε 0 χ ( 3 ) 4 { E 1 2 E 1 [ 2 e 1 + ( e 1 · e 1 ) e 1 * ] + 2 E 2 2 E 1 [ e 1 + ( e 1 · e 2 * ) e 2 + ( e 1 · e 2 ) e 2 * ] } ,
P 2 ( 3 ) ( r ) = ε 0 χ ( 3 ) 4 { E 2 2 E 2 [ 2 e 2 + ( e 2 · e 2 ) e 2 * ] + 2 E 1 2 E 2 [ e 2 + ( e 1 · e 2 * ) e 1 + ( e 1 · e 2 ) e 1 * ] } ,
P 3 ( 3 ) ( r ) = ε 0 χ ( 3 ) 2 { E 1 2 E 3 [ e 3 + ( e 1 * · e 3 ) e 1 + ( e 1 · e 3 ) e 1 * ] + E 2 2 E 3 [ e 3 + ( e 2 * · e 3 ) e 2 + ( e 2 · e 3 ) e 2 * ]
+ E 1 * E 2 E 4 [ ( e 1 * · e 2 ) e 4 + ( e 1 * · e 4 ) e 2 + ( e 2 · e 4 ) e 1 * ] } ,
P 4 ( 3 ) ( r ) = ε 0 χ ( 3 ) 2 { E 1 2 E 4 [ e 4 + ( e 1 * · e 4 ) e 1 + ( e 1 · e 4 ) e 1 * ] + E 2 2 E 4 [ e 4 + ( e 2 * · e 4 ) e 2 + ( e 2 · e 4 ) e 2 * ]
+ E 1 E 2 * E 3 [ ( e 1 · e 2 * ) e 3 + ( e 2 * · e 3 ) e 1 + ( e 1 · e 3 ) e 2 * ] } ,
P 1 ( 3 ) ( r ) = ε 0 χ ( 3 ) 2 ( E 1 2 + 2 E 2 2 ) E 1 ,
P 2 ( 3 ) ( r ) = ε 0 χ ( 3 ) 2 ( E 2 2 + 2 E 1 2 ) E 2 ,
P 3 ( 3 ) ( r ) = ε 0 χ ( 3 ) ( E 1 2 + E 2 2 ) E 3 + E 1 * E 2 E 4 ,
P 4 ( 3 ) ( r ) = ε 0 χ ( 3 ) ( E 1 2 + E 2 2 ) E 4 + E 1 E 2 * E 3 .
d A 1 dz = 2 i γ 3 ( A 1 2 + 2 A 2 2 ) A 1 ,
d A 2 dz = 2 i γ 3 ( A 2 2 + 2 A 1 2 ) A 2 ,
d A 3 dz = 4 i γ 3 [ ( A 1 2 + A 2 2 ) A 3 + A 1 * A 2 A 4 exp ( i Δ kz ) ] ,
d A 4 dz = 4 i γ 3 [ ( A 1 2 + A 2 2 ) A 4 + A 2 * A 1 A 3 exp ( i Δkz ) ] ,
A 4 ( L ) A 3 ( 0 ) 2 = 16 γ 2 P 1 P 2 9 g 2 sin 2 ( gL ) ,
g 2 = [ 2 γ ( P 1 P 2 ) / 3 Δ k 2 ] 2 + 16 9 γ 2 P 1 P 2 .
A 4 ( L ) A 3 ( 0 ) 2 = 16 γ 2 P 2 L 2 9 [ sin ( Δ kL / 2 ) Δ kL / 2 ] 2 .
Δk = β 2 ( Δ ω 1 2 Δ ω 2 2 ) ,
k 1 = k 0 R β 1 R Δ ω 1 + β 2 Δ ω 1 2 / 2 ,
k 2 = k 0 R β 1 R Δ ω 2 + β 2 Δ ω 2 2 / 2 ,
k 3 = k 0 L + β 1 L Δ ω 1 + β 2 Δ ω 1 2 / 2 ,
k 4 = k 0 L + β 1 L Δ ω 2 + β 2 Δ ω 2 2 / 2 ,
Δ k = β 2 ( Δ ω 1 2 Δ ω 2 2 ) τ ( Δ ω 1 Δ ω 2 ) ,

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