Abstract

The evolution of modulated light in a nonlinear medium, when described in terms of intensity waves, depends critically on a phase-matching condition for the intensity waves. We formally develop the conditions for quasi-phase matching of the interacting intensity waves and show that a periodic nonlinearity can be utilized to eliminate the dephasing between them. This is verified using stimulated Brillouin scattering with a periodically nonlinear optical fiber that has a period length equal to one-half of the (modulation) wavelength of the intensity waves.

© 2006 Optical Society of America

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References

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  1. J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
    [CrossRef]
  2. D. A. Fishman and J. A. Nagel, J. Lightwave Technol. 11, 1721 (1993).
    [CrossRef]
  3. A. Djupsjobacka, G. Jacobsen, and B. Tromborg, J. Lightwave Technol. 18, 416 (2000).
    [CrossRef]
  4. C. R. S. Fludger, V. Handerek, and R. J. Mears, J. Lightwave Technol. 19, 1140 (2001).
    [CrossRef]
  5. S. Sternklar and E. Granot, Opt. Lett. 28, 977 (2003).
    [CrossRef] [PubMed]
  6. E. Granot, S. Sternklar, D. Kwiat, T. Arditi, and M. Tur, Opt. Commun. 259, 328 (2006).
    [CrossRef]
  7. S. Sternklar, E. Granot, D. Kwiat, T. Arditi, and M. Tur, in Quantum Electronics and Laser Science Conference (Optical Society of America, 2006), paper QWF6.
  8. R. W. Boyd, Nonlinear Optics, 2nd ed. (Academic, 2003).
  9. Usually the modified Bessel functions are denoted by Im [as in M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, 1972)]; however, to distinguish it from the intensity we adopt the notation I.
  10. J. U. Kang, Y. J. Ding, W. K. Burns, and J. S. Melinger, Opt. Lett. 22, 862 (1997).
    [CrossRef] [PubMed]
  11. V. I. Kovalev and R. G. Harrison, Opt. Lett. 27, 2022 (2002).
    [CrossRef]
  12. N. S. Makarov and V. G. Bespalov, J. Opt. Soc. Am. B 22, 835 (2005).
    [CrossRef]
  13. D. L. Williams, D. P. West, and T. A. King, Opt. Commun. 148, 208 (1998).
    [CrossRef]

2006 (1)

E. Granot, S. Sternklar, D. Kwiat, T. Arditi, and M. Tur, Opt. Commun. 259, 328 (2006).
[CrossRef]

2005 (1)

2003 (1)

2002 (1)

2001 (1)

2000 (1)

1998 (1)

D. L. Williams, D. P. West, and T. A. King, Opt. Commun. 148, 208 (1998).
[CrossRef]

1997 (1)

1993 (1)

D. A. Fishman and J. A. Nagel, J. Lightwave Technol. 11, 1721 (1993).
[CrossRef]

1962 (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Abramowitz, M.

Usually the modified Bessel functions are denoted by Im [as in M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, 1972)]; however, to distinguish it from the intensity we adopt the notation I.

Arditi, T.

E. Granot, S. Sternklar, D. Kwiat, T. Arditi, and M. Tur, Opt. Commun. 259, 328 (2006).
[CrossRef]

S. Sternklar, E. Granot, D. Kwiat, T. Arditi, and M. Tur, in Quantum Electronics and Laser Science Conference (Optical Society of America, 2006), paper QWF6.

Armstrong, J. A.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Bespalov, V. G.

Bloembergen, N.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Boyd, R. W.

R. W. Boyd, Nonlinear Optics, 2nd ed. (Academic, 2003).

Burns, W. K.

Ding, Y. J.

Djupsjobacka, A.

Ducuing, J.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Fishman, D. A.

D. A. Fishman and J. A. Nagel, J. Lightwave Technol. 11, 1721 (1993).
[CrossRef]

Fludger, C. R. S.

Granot, E.

E. Granot, S. Sternklar, D. Kwiat, T. Arditi, and M. Tur, Opt. Commun. 259, 328 (2006).
[CrossRef]

S. Sternklar and E. Granot, Opt. Lett. 28, 977 (2003).
[CrossRef] [PubMed]

S. Sternklar, E. Granot, D. Kwiat, T. Arditi, and M. Tur, in Quantum Electronics and Laser Science Conference (Optical Society of America, 2006), paper QWF6.

Handerek, V.

Harrison, R. G.

Jacobsen, G.

Kang, J. U.

King, T. A.

D. L. Williams, D. P. West, and T. A. King, Opt. Commun. 148, 208 (1998).
[CrossRef]

Kovalev, V. I.

Kwiat, D.

E. Granot, S. Sternklar, D. Kwiat, T. Arditi, and M. Tur, Opt. Commun. 259, 328 (2006).
[CrossRef]

S. Sternklar, E. Granot, D. Kwiat, T. Arditi, and M. Tur, in Quantum Electronics and Laser Science Conference (Optical Society of America, 2006), paper QWF6.

Makarov, N. S.

Mears, R. J.

Melinger, J. S.

Nagel, J. A.

D. A. Fishman and J. A. Nagel, J. Lightwave Technol. 11, 1721 (1993).
[CrossRef]

Pershan, P. S.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Stegun, I. A.

Usually the modified Bessel functions are denoted by Im [as in M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, 1972)]; however, to distinguish it from the intensity we adopt the notation I.

Sternklar, S.

E. Granot, S. Sternklar, D. Kwiat, T. Arditi, and M. Tur, Opt. Commun. 259, 328 (2006).
[CrossRef]

S. Sternklar and E. Granot, Opt. Lett. 28, 977 (2003).
[CrossRef] [PubMed]

S. Sternklar, E. Granot, D. Kwiat, T. Arditi, and M. Tur, in Quantum Electronics and Laser Science Conference (Optical Society of America, 2006), paper QWF6.

Tromborg, B.

Tur, M.

E. Granot, S. Sternklar, D. Kwiat, T. Arditi, and M. Tur, Opt. Commun. 259, 328 (2006).
[CrossRef]

S. Sternklar, E. Granot, D. Kwiat, T. Arditi, and M. Tur, in Quantum Electronics and Laser Science Conference (Optical Society of America, 2006), paper QWF6.

West, D. P.

D. L. Williams, D. P. West, and T. A. King, Opt. Commun. 148, 208 (1998).
[CrossRef]

Williams, D. L.

D. L. Williams, D. P. West, and T. A. King, Opt. Commun. 148, 208 (1998).
[CrossRef]

J. Lightwave Technol. (3)

J. Opt. Soc. Am. B (1)

Opt. Commun. (2)

D. L. Williams, D. P. West, and T. A. King, Opt. Commun. 148, 208 (1998).
[CrossRef]

E. Granot, S. Sternklar, D. Kwiat, T. Arditi, and M. Tur, Opt. Commun. 259, 328 (2006).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Other (3)

S. Sternklar, E. Granot, D. Kwiat, T. Arditi, and M. Tur, in Quantum Electronics and Laser Science Conference (Optical Society of America, 2006), paper QWF6.

R. W. Boyd, Nonlinear Optics, 2nd ed. (Academic, 2003).

Usually the modified Bessel functions are denoted by Im [as in M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, 1972)]; however, to distinguish it from the intensity we adopt the notation I.

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Figures (3)

Fig. 1
Fig. 1

Schematic of counterpropagating SBS and the implementation of IQPM with a periodic nonlinearity, with the governing k-vector diagram to fulfill IQPM. The pump IW (dashed curve) and Stokes (dotted curve) IWs are shown at the onset of the Stokes generation for the case K g = 2 K .

Fig. 2
Fig. 2

Experimental schematic for IQPM: LAS, laser, modulator, and EDFA amplifier; D, detector; ESA, electronic spectrum analyzer; dark fiber, SMF-28; light fiber, LEAF. (a)–(c) Three separate experiments, as described in the text.

Fig. 3
Fig. 3

Theoretical model (solid curves) and experimental data (symbols) of I 2 f without IQPM, IQPM with 1.5 periods, and IQPM with 2.5 periods.

Equations (4)

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I 1 ( z , t ) z 1 v g 1 I 1 ( z , t ) t = I 2 ( z , t ) z + 1 v g 2 I 2 ( z , t ) t = g ( z ) I 1 ( z , t ) I 2 ( z , t ) ,
i 2 ( L ) = i 2 ( 0 ) e G + α I 2 ( 0 ) G e G e i K L sinc ( Δ K L 2 ) ,
I 2 ( z = N Λ g , t ) = R I 1 [ 1 + α cos ( π K K g Ω t ) ] exp ( G g N ) exp { α G g 2 π K K g cos [ 2 π K K g ( N 1 ) + Ω t ] sin ( 2 π N K K g ) cos ( π K K g ) } ,
I 2 f = R I 1 e G N ( { α I 0 ( A ) cos ( q ) + 2 I 1 ( A ) cos [ 2 q ( N 1 ) ] + α I 2 ( A ) cos [ 4 q ( N 3 4 ) ] } 2 + { α I 0 ( A ) sin ( q ) 2 I 1 ( A ) sin [ 2 q ( N 1 ) ] α I 2 ( A ) sin [ 4 q ( N 3 4 ) ] } 2 ) 1 2 ,

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