Abstract

We analyze the stimulated-Raman-scattering-(SRS) process induced by a linearly polarized multifrequency pump field in a normally dispersive single-mode fiber. We show, by theoretical analysis and numerical simulations, that the SRS process may be either controlled by switching all the generated Stokes radiations to the lowest-frequency pump or suppressed for all the frequency components of the pump field. The suppression process is achieved by an appropriate choice of the frequency separation between the pumps and a particular power distribution among the frequency components of the pump field. We present experimental spectra showing the effectiveness of this suppression process for a dual-frequency pumping configuration.

© 1999 Optical Society of America

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References

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  1. R. H. Stolen, Phys. Chem. Glasses 11, 83 (1970).
  2. R. Hellwarth, Prog. Quantum Electron. 5, 1 (1977).
    [CrossRef]
  3. G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, San Diego, Calif., 1995).
  4. E. M. Dianov, P. V. Mamyshev, A. M. Prokhorov, and V. N. Serkin, Nonlinear Effects in Optical Fibers (Harwood Academic, Chur, Switzerland, 1989).
  5. D. J. Dougherty, F. X. Kärtner, H. A. Haus, and E. Ippen, Opt. Lett. 20, 31 (1995).
    [CrossRef] [PubMed]
  6. S. Kumar, A. Selvarajan, and G. V. Anand, Opt. Commun. 102, 329 (1993).
    [CrossRef]
  7. K. C. Chan and H. F. Liu, Opt. Lett. 14, 1150 (1993).
    [CrossRef]
  8. L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, Opt. Lett. 11, 659 (1986).
    [CrossRef]
  9. E. Golovchenko, E. M. Dianov, P. V. Mamyshev, and A. N. Pilipetskii, JETP Lett. 50, 190 (1989).
  10. P. V. Mamyshev and A. P. Vertikov, Quantum Electronics and Laser Science, Vol. 13 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), p. 130.
  11. S. Trillo and S. Wabnitz, J. Opt. Soc. Am. B 9, 1061 (1992).
    [CrossRef]
  12. P. Tchofo Dinda, G. Millot, and S. Wabnitz, J. Opt. Soc. Am. B 15, 1433 (1998).
    [CrossRef]
  13. S. Pitois, G. Millot, and P. Tchofo Dinda, Opt. Lett. 23, 1456 (1998).
    [CrossRef]
  14. P. Tchofo Dinda, G. Millot, and S. Wabnitz, Opt. Lett. 22, 1595 (1997).
    [CrossRef]
  15. T. Sylvestre, H. Maillotte, and E. Lantz, Electron. Lett. 34, 1417 (1998).
    [CrossRef]
  16. B. Colombeau, J. Monneret, F. Reynaud, B. Carquille, F. Louradour, and C. Froehly, in Proceedings of Dixièmes Journées Nationales d’Optique Guidée, J. P. Pocholle, ed. (Thomson-CSF-LCR, Orsay, France, 1989), p. 31.
  17. T. Sylvestre, H. Maillotte, P. Tchofo Dinda, and E. Coquet, Opt. Commun. 159, 32 (1999).
    [CrossRef]
  18. T. Sylvestre, H. Maillotte, and E. Lantz, “Optical wavelength switching by stimulated Raman scattering in a single-mode fiber,” in Conference on Lasers and Electro-Optics Europe (CLEO/Europe-European Quantum Electronics Conference), (Institute of Electronical and Electronics Engineers, Inc., Piscataway, N.J., 1998), paper CThH33.
  19. Chinlon Lin, J. Opt. Commun. 4, 2 (1983).
    [CrossRef]
  20. P. Tchofo Dinda, G. Millot, E. Seve, and M. Haelterman, Opt. Lett. 21, 1640 (1996).
    [CrossRef] [PubMed]

1999 (1)

T. Sylvestre, H. Maillotte, P. Tchofo Dinda, and E. Coquet, Opt. Commun. 159, 32 (1999).
[CrossRef]

1998 (3)

1997 (1)

1996 (1)

1995 (1)

1993 (2)

S. Kumar, A. Selvarajan, and G. V. Anand, Opt. Commun. 102, 329 (1993).
[CrossRef]

K. C. Chan and H. F. Liu, Opt. Lett. 14, 1150 (1993).
[CrossRef]

1992 (1)

1989 (1)

E. Golovchenko, E. M. Dianov, P. V. Mamyshev, and A. N. Pilipetskii, JETP Lett. 50, 190 (1989).

1986 (1)

1983 (1)

Chinlon Lin, J. Opt. Commun. 4, 2 (1983).
[CrossRef]

1977 (1)

R. Hellwarth, Prog. Quantum Electron. 5, 1 (1977).
[CrossRef]

1970 (1)

R. H. Stolen, Phys. Chem. Glasses 11, 83 (1970).

Anand, G. V.

S. Kumar, A. Selvarajan, and G. V. Anand, Opt. Commun. 102, 329 (1993).
[CrossRef]

Chan, K. C.

K. C. Chan and H. F. Liu, Opt. Lett. 14, 1150 (1993).
[CrossRef]

Coquet, E.

T. Sylvestre, H. Maillotte, P. Tchofo Dinda, and E. Coquet, Opt. Commun. 159, 32 (1999).
[CrossRef]

Dianov, E. M.

E. Golovchenko, E. M. Dianov, P. V. Mamyshev, and A. N. Pilipetskii, JETP Lett. 50, 190 (1989).

Dinda, P. Tchofo

Dougherty, D. J.

Golovchenko, E.

E. Golovchenko, E. M. Dianov, P. V. Mamyshev, and A. N. Pilipetskii, JETP Lett. 50, 190 (1989).

Gordon, J. P.

Haelterman, M.

Haus, H. A.

Hellwarth, R.

R. Hellwarth, Prog. Quantum Electron. 5, 1 (1977).
[CrossRef]

Ippen, E.

Kärtner, F. X.

Kumar, S.

S. Kumar, A. Selvarajan, and G. V. Anand, Opt. Commun. 102, 329 (1993).
[CrossRef]

Lantz, E.

T. Sylvestre, H. Maillotte, and E. Lantz, Electron. Lett. 34, 1417 (1998).
[CrossRef]

Lin, Chinlon

Chinlon Lin, J. Opt. Commun. 4, 2 (1983).
[CrossRef]

Liu, H. F.

K. C. Chan and H. F. Liu, Opt. Lett. 14, 1150 (1993).
[CrossRef]

Maillotte, H.

T. Sylvestre, H. Maillotte, P. Tchofo Dinda, and E. Coquet, Opt. Commun. 159, 32 (1999).
[CrossRef]

T. Sylvestre, H. Maillotte, and E. Lantz, Electron. Lett. 34, 1417 (1998).
[CrossRef]

Mamyshev, P. V.

E. Golovchenko, E. M. Dianov, P. V. Mamyshev, and A. N. Pilipetskii, JETP Lett. 50, 190 (1989).

Millot, G.

Mollenauer, L. F.

Pilipetskii, A. N.

E. Golovchenko, E. M. Dianov, P. V. Mamyshev, and A. N. Pilipetskii, JETP Lett. 50, 190 (1989).

Pitois, S.

Selvarajan, A.

S. Kumar, A. Selvarajan, and G. V. Anand, Opt. Commun. 102, 329 (1993).
[CrossRef]

Seve, E.

Stolen, R. H.

Sylvestre, T.

T. Sylvestre, H. Maillotte, P. Tchofo Dinda, and E. Coquet, Opt. Commun. 159, 32 (1999).
[CrossRef]

T. Sylvestre, H. Maillotte, and E. Lantz, Electron. Lett. 34, 1417 (1998).
[CrossRef]

Trillo, S.

Wabnitz, S.

Electron. Lett. (1)

T. Sylvestre, H. Maillotte, and E. Lantz, Electron. Lett. 34, 1417 (1998).
[CrossRef]

J. Opt. Commun. (1)

Chinlon Lin, J. Opt. Commun. 4, 2 (1983).
[CrossRef]

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

JETP Lett. (1)

E. Golovchenko, E. M. Dianov, P. V. Mamyshev, and A. N. Pilipetskii, JETP Lett. 50, 190 (1989).

Opt. Commun. (2)

S. Kumar, A. Selvarajan, and G. V. Anand, Opt. Commun. 102, 329 (1993).
[CrossRef]

T. Sylvestre, H. Maillotte, P. Tchofo Dinda, and E. Coquet, Opt. Commun. 159, 32 (1999).
[CrossRef]

Opt. Lett. (6)

Phys. Chem. Glasses (1)

R. H. Stolen, Phys. Chem. Glasses 11, 83 (1970).

Prog. Quantum Electron. (1)

R. Hellwarth, Prog. Quantum Electron. 5, 1 (1977).
[CrossRef]

Other (5)

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, San Diego, Calif., 1995).

E. M. Dianov, P. V. Mamyshev, A. M. Prokhorov, and V. N. Serkin, Nonlinear Effects in Optical Fibers (Harwood Academic, Chur, Switzerland, 1989).

P. V. Mamyshev and A. P. Vertikov, Quantum Electronics and Laser Science, Vol. 13 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), p. 130.

T. Sylvestre, H. Maillotte, and E. Lantz, “Optical wavelength switching by stimulated Raman scattering in a single-mode fiber,” in Conference on Lasers and Electro-Optics Europe (CLEO/Europe-European Quantum Electronics Conference), (Institute of Electronical and Electronics Engineers, Inc., Piscataway, N.J., 1998), paper CThH33.

B. Colombeau, J. Monneret, F. Reynaud, B. Carquille, F. Louradour, and C. Froehly, in Proceedings of Dixièmes Journées Nationales d’Optique Guidée, J. P. Pocholle, ed. (Thomson-CSF-LCR, Orsay, France, 1989), p. 31.

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Figures (10)

Fig. 1
Fig. 1

Plots showing the frequency dependence of the parallel components of the Raman susceptibility: solid curve, imaginary part I(χR); dotted curve, real part R(χR). The largest (smallest) dashed vertical lines indicate the gain at frequency detunings of 550 cm-1 and 888 cm-1.

Fig. 2
Fig. 2

Plot showing the coherence lengths 2π/Δkj versus Δω. The coherence length corresponding to a phase mismatch Δkj is indicated in the figures by the numerical j. The vertical dashed lines indicate the experimental operating condition considered in the present paper: Δω=888 cm-1, λP1=508 nm.

Fig. 3
Fig. 3

Theoretical variation of normalized pump and Stokes powers Qj/Pm(0), Q=S, P, j=1, N, versus propagation coordinate z for Δω=1760 cm-1 and Pj=Pm(0)=150 W. (a) N=2, (b) N=3, and (c) N=4. Cross, P1; barred cross, S1; square, P2; square on cross, S2; diamond, P3; diamond on plus, S3; plus sign, P4; barred plus, S4. ωP1=590.55 THz.

Fig. 4
Fig. 4

Plot showing the frequency dependence of the transverse overlapping of a pump ωP with its associated Raman Stokes wave ωSωP-ΩR: (a) ξ-1PPSS/ξ-1P0P0S0S0 versus ωP; (b) (ωS/ωS0)(ξ-1PPSS/ξ-1P0P0S0S0) versus ωP. ωP0=600 THz.

Fig. 5
Fig. 5

Theoretical variation of normalized pump and Stokes powers Qj/Pm(0), Q=S, P, j=1, N, versus propagation coordinate z for Δω=550 cm-1. (a) N=2, Pj(0)=Pm(0); (b) N=3, Pj(0)=Pm(0); (c) N=4, Pj(0)=Pm(0); (d) N=2, P1(0)=1.83Pm(0), P2(0)=0.17Pm(0); (e) N=3, P1(0)=1.84Pm(0), P2(0)=Pm(0), P3(0)=0.16Pm(0); (f) N=4, P1(0)=1.81Pm(0), P2(0)=P3(0)=Pm(0), P4(0)=0.19Pm(0). Cross, P1; barred cross, S1; square, P2; square on cross, S2; diamond, P3; diamond on plus, S3; plus sign, P4; barred plus, S4. ωP1=590.55 THz.

Fig. 6
Fig. 6

Plots showing the partial suppression of SRS. Theoretical variation of normalized pump and Stokes powers Qj/Pm(0), Q=S,P, j=1,N, versus propagation coordinate z for Δω=888 cm-1 and (a) N=2, (b) N=3, and (c) N=4. Cross, P1; barred cross, S1; square, P2; square on cross, S2; diamond, P3; diamond on plus, S3; plus sign, P4; barred plus, S4. ωP1=590.55 THz.

Fig. 7
Fig. 7

Plots showing the total suppression of SRS. Theoretical variation of normalized pump and Stokes powers Qj/Pm(0), Q=S,P, j=1,N, versus propagation coordinate z for Δω=888 cm-1 and (a) N=2, (b) N=3, and (c) N=4; and for Δω=840 cm-1 and (d) N=2, (e) N=3, and (f) N=4. Cross, P1; barred cross, S1; square, P2; square on cross, S2; diamond, P3; diamond on plus, S3; plus sign, P4; barred plus, S4. ωP1=590.55 THz.

Fig. 8
Fig. 8

Schematic diagram of the experimental apparatus. M, mirrors; B.S, beam splitter; O1,O2, microscope objectives; P’s, Glan polarizers; λ/2’s, half-wave plates; DL, prism delay-line for pulse synchronization. Polarizations of pumps P1 and P2 are parallel to the fast axis of the fiber.

Fig. 9
Fig. 9

Experimental output spectra measured under single-frequency pumping conditions (a) P1(0)=415 W and P2(0)=0 W and (b) P1(0)=0 W and P2(0)=415 W. ωP1=590.5 THz, ωP2=563.9 THz.

Fig. 10
Fig. 10

Experimental output spectra measured under dual-frequency pumping conditions. (a) Partial suppression of SRS (with equal pump powers): P1(0)=P2(0)=415 W. (b) Total suppression of SRS (with unbalanced pump powers): P1(0)=460 W, P2(0)=370 W. ωP1=590.5 THz, ωP2=563.9 THz.

Equations (51)

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P(t)=σE(t)E(t)E(t)+E(t)-tdsσR(t-s)E(s)E(s),
E=12j=13Q=P,SEQj+c.c.=12j=13Q=P,S1αNQjAQj(z)ψQj(x, y)×exp[i(kQjz-ωQjt)]+c.c.,
P(ωP1)=12j=13Q=S,PηQjQj*P1|EQj|2EP1+ηP2S2*S1 exp(-iΔk3z)EP2ES2*ES1+ηP3S3*S1 exp(-iΔk1z)EP3ES3*ES1+ηS2S3*P2 exp(-iΔk5z)ES2ES3*EP2+ηP2P3*P2 exp(-iΔk6z)EP22EP3*+[ηS1P2*S1 exp(-iΔk4z)ES12EP2*+ηS2P3*S1 exp(-iΔk2z)ES2EP3*ES1]δ(2ΩR)+c.c.,
ηQjQj*Qj3σ/4+χR(0),Q=S, P,j=1, 3,
ηQjQj*Gl3σ/2+χR(0)+χR(ωQj-ωGl),
Q, G=S, P,l=1, 3,QjGl,
ηP2S2*S13σ/2+χR(-ΩR)+χR(-Δω),
ηP3S3*S13σ/2+χR(-ΩR)+χR(-2Δω),
ηS2S3*P23σ/2+χR(-Δω)+χR(-Δω-ΩR),
ηP2P3*P23σ/4+χR(-Δω),
ηS1P2*S13σ/4+χR(-Δω+ΩR),
ηS2P3*S1=3σ/2+χR(-2Δω+ΩR)+χR(-Δω+ΩR).
AQjz=iγQj U,V,Wl,m,nHQjUlVmWn×exp(iΔkz)AUlAVm*AWn,
Δk1kP1-kP3+kS3-kS1,
Δk2kP1+kP3-kS1-kS2,
Δk3kP1-kP2+kS2-kS1,
Δk4kP1+kP2-2kS1,
Δk5=Δk1+Δk2-Δk4,
Δk6=Δk2+Δk3-Δk4,
Δk7=Δk4-Δk1,
Δk8=Δk2-Δk4,Δk9=Δk4-Δk3,
Δk10=Δk3-Δk5,
Δk11=Δk2-Δk3,Δk12=Δk1-Δk3,
Δk13=Δk2-Δk1.
HQjUlVmWnηUlVmWnξQjQjQjQjξQjUlVmWn,
(U, V, W)=S, P,(l, m, n)=1, N,
ξQjUlVmWn(NQjNUlNVmNWn)1/2ψQjψUlψVmψWndxdy,
(U, V, W)=S, P,(l, m, n)=1, N.
Qjz=AQjAQj*z+AQj*AQjz,
ϕQjz=i2QjAQjAQj*z-AQj*AQjz.
P1z=-2γP1j=13Q=S,PI(HQjQ*jP1P1)QjP1+[-R(HP2S*2S1P1)sin θ3+I(HP2S*2S1P1)cos θ3]S1S2P1P2+[-R(HP3S*3S1P1)sin θ1+I(HP3S*3S1P1)cos θ1]S1S3P1P3+[-R(HS2S*3P2P1)sin θ5+I(HS2S*3P2P1)cos θ5]S2S3P2P1+[-R(HP2P*3P2P1)sin θ6+I(HP2P*3P2P1)cos θ6]P2P1P3+[[-R(HS2P*3S1P1)sin θ2+I(HS2P*3S1P1)cos θ2]S1S2P3P1+[-R(HS1P*2S1P1)sin θ4+I(HS1P*2S1P1)cos θ4]S1P1P2]δ(2ΩR),
θ1z=Δk1+ϕP1z-ϕP3z+ϕS3z-ϕS1z,
θ2z=Δk2+ϕP1z+ϕP3z-ϕS1z-ϕS2z,
θ3z=Δk3+ϕP1z-ϕP2z+ϕS2z-ϕS1z,
θ4z=Δk4+ϕP1z+ϕP2z-2ϕS1z,
θ1zΔk1+ϕP1-ϕP3+ϕS3-ϕS1,
θ2zΔk2+ϕP1+ϕP3-ϕS1-ϕS2,
θ3zΔk3+ϕP1-ϕP2+ϕS2-ϕS1,
θ4zΔk4+ϕP1+ϕP2-2ϕS1,
θ5θ1+θ2-θ4,
θ6θ2+θ3-θ4.
ηQjQj *Qj3σ/4+χR(0),Q=S, P,j=1, N,
ηQjQj*Gl3σ/2+χR(0)+χR(ωQj-ωGl),
G=S, P,l=1, N,QjGl.
Qjz=-2γQjl=1NG=S,PI(HGlGlQjQj)GlQj,
Q=S, P,j=1, N.
Pj(0)=Pm(0)PT/N,j=2,N-1.
[PN(0)+P1(0)]/2=Pm(0)=PT/N.
ST(Δω)j=1NSj[Δω, Pj(0)]j=1NSj[Δω=4ΩR, Pj(0)=Pm(0)].
TST+ΔP,
ΔP1Nj=1N[Pj(L)-Pm(L)]2/Pm2(0)

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