Abstract

We analyze stimulated Raman scattering in normally dispersive highly birefringent fibers under dual-frequency, orthogonal polarization pumping. Experiments show that stimulated Raman scattering can be suppressed in anyone of the fiber axes by two distinct processes prevailing at large and small group-velocity mismatches (GVM’s), respectively, between the pumps. For a relatively large GVM, parametric four-wave mixing is the dominant process for the suppression of Raman–Stokes radiation. On the other hand, for a small GVM, the Raman–Stokes light is suppressed along the polarization direction of the highest-frequency pump, through a mechanism associated with the orthogonal component of the Raman gain. The sign of the GVM between the pumps allows for selecting the particular fiber axis where suppression of the Raman–Stokes radiation is desired. This selection is achieved by simply tuning the frequency spacing between the pumps.

© 1998 Optical Society of America

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  1. K. Tai, A. Hasegawa, and A. Tomita, Phys. Rev. Lett. 56, 135 (1986).
    [CrossRef] [PubMed]
  2. G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1989).
  3. R. H. Stolen, Phys. Chem. Glasses 11, 83 (1970).
  4. D. J. Dougherty, F. X. Kärtner, H. A. Haus, and E. Ippen, Opt. Lett. 20, 31 (1995).
    [CrossRef] [PubMed]
  5. R. Hellwarth, Prog. Quantum Electron. 5, 1 (1977).
    [CrossRef]
  6. E. Golovchenko, E. M. Dianov, P. V. Mamyshev, and A. N. Pilipetskii, JETP Lett. 50, 190 (1989).
  7. E. Golovchenko and A. N. Pilipetskii, Sov. Lightwave Commun. 1, 271 (1991).
  8. P. V. Mamyshev and A. P. Vertikov, in Quantum Electronics and Laser Science, Vol. 13 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992).
  9. S. Trillo and S. Wabnitz, J. Opt. Soc. Am. B 9, 1061 (1992).
    [CrossRef]
  10. J. K. Chee and J. M. Liu, Opt. Lett. 14, 820 (1989).
    [CrossRef] [PubMed]
  11. J. K. Chee and J. M. Liu, IEEE J. Quantum Electron. 26, 541 (1990).
    [CrossRef]
  12. P. Tchofo Dinda, G. Millot, and S. Wabnitz, Opt. Lett. 22, 1595–1597 (1997).
    [CrossRef]
  13. E. Seve, P. Tchofo Dinda, G. Millot, M. Remoissenet, J. M. Bilbault, and M. Haelterman, Phys. Rev. A 54, 3519 (1996).
    [CrossRef] [PubMed]
  14. P. Tchofo Dinda, G. Millot, E. Seve, and M. Haelterman, Opt. Lett. 21, 1640 (1996).
    [CrossRef]
  15. C. Lin, J. Opt. Commun. 4, 2 (1983).
    [CrossRef]

1997

1996

P. Tchofo Dinda, G. Millot, E. Seve, and M. Haelterman, Opt. Lett. 21, 1640 (1996).
[CrossRef]

E. Seve, P. Tchofo Dinda, G. Millot, M. Remoissenet, J. M. Bilbault, and M. Haelterman, Phys. Rev. A 54, 3519 (1996).
[CrossRef] [PubMed]

1995

1992

1991

E. Golovchenko and A. N. Pilipetskii, Sov. Lightwave Commun. 1, 271 (1991).

1990

J. K. Chee and J. M. Liu, IEEE J. Quantum Electron. 26, 541 (1990).
[CrossRef]

1989

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

J. K. Chee and J. M. Liu, Opt. Lett. 14, 820 (1989).
[CrossRef] [PubMed]

1986

K. Tai, A. Hasegawa, and A. Tomita, Phys. Rev. Lett. 56, 135 (1986).
[CrossRef] [PubMed]

1983

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

1977

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

1970

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

Bilbault, J. M.

E. Seve, P. Tchofo Dinda, G. Millot, M. Remoissenet, J. M. Bilbault, and M. Haelterman, Phys. Rev. A 54, 3519 (1996).
[CrossRef] [PubMed]

Chee, J. K.

J. K. Chee and J. M. Liu, IEEE J. Quantum Electron. 26, 541 (1990).
[CrossRef]

J. K. Chee and J. M. Liu, Opt. Lett. 14, 820 (1989).
[CrossRef] [PubMed]

Dianov, E. M.

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

Dougherty, D. J.

Golovchenko, E.

E. Golovchenko and A. N. Pilipetskii, Sov. Lightwave Commun. 1, 271 (1991).

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

Haelterman, M.

P. Tchofo Dinda, G. Millot, E. Seve, and M. Haelterman, Opt. Lett. 21, 1640 (1996).
[CrossRef]

E. Seve, P. Tchofo Dinda, G. Millot, M. Remoissenet, J. M. Bilbault, and M. Haelterman, Phys. Rev. A 54, 3519 (1996).
[CrossRef] [PubMed]

Hasegawa, A.

K. Tai, A. Hasegawa, and A. Tomita, Phys. Rev. Lett. 56, 135 (1986).
[CrossRef] [PubMed]

Haus, H. A.

Hellwarth, R.

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

Ippen, E.

Kärtner, F. X.

Lin, C.

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

Liu, J. M.

J. K. Chee and J. M. Liu, IEEE J. Quantum Electron. 26, 541 (1990).
[CrossRef]

J. K. Chee and J. M. Liu, Opt. Lett. 14, 820 (1989).
[CrossRef] [PubMed]

Mamyshev, P. V.

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

Millot, G.

Pilipetskii, A. N.

E. Golovchenko and A. N. Pilipetskii, Sov. Lightwave Commun. 1, 271 (1991).

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

Remoissenet, M.

E. Seve, P. Tchofo Dinda, G. Millot, M. Remoissenet, J. M. Bilbault, and M. Haelterman, Phys. Rev. A 54, 3519 (1996).
[CrossRef] [PubMed]

Seve, E.

E. Seve, P. Tchofo Dinda, G. Millot, M. Remoissenet, J. M. Bilbault, and M. Haelterman, Phys. Rev. A 54, 3519 (1996).
[CrossRef] [PubMed]

P. Tchofo Dinda, G. Millot, E. Seve, and M. Haelterman, Opt. Lett. 21, 1640 (1996).
[CrossRef]

Stolen, R. H.

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

Tai, K.

K. Tai, A. Hasegawa, and A. Tomita, Phys. Rev. Lett. 56, 135 (1986).
[CrossRef] [PubMed]

Tchofo Dinda, P.

Tomita, A.

K. Tai, A. Hasegawa, and A. Tomita, Phys. Rev. Lett. 56, 135 (1986).
[CrossRef] [PubMed]

Trillo, S.

Wabnitz, S.

IEEE J. Quantum Electron.

J. K. Chee and J. M. Liu, IEEE J. Quantum Electron. 26, 541 (1990).
[CrossRef]

J. Opt. Commun.

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

J. Opt. Soc. Am. B

JETP Lett.

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

Opt. Lett.

Phys. Chem. Glasses

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

Phys. Rev. A

E. Seve, P. Tchofo Dinda, G. Millot, M. Remoissenet, J. M. Bilbault, and M. Haelterman, Phys. Rev. A 54, 3519 (1996).
[CrossRef] [PubMed]

Phys. Rev. Lett.

K. Tai, A. Hasegawa, and A. Tomita, Phys. Rev. Lett. 56, 135 (1986).
[CrossRef] [PubMed]

Prog. Quantum Electron.

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

Sov. Lightwave Commun.

E. Golovchenko and A. N. Pilipetskii, Sov. Lightwave Commun. 1, 271 (1991).

Other

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

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1989).

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Figures (10)

Fig. 1
Fig. 1

Plots showing the frequency dependence of the orthogonal and parallel components of the Raman susceptibility: solid curve, Im(χ1212R)=Im[B(ω)/4]; dotted curve, Re(χ1212R)=Re[B(ω)/4]; dashed curve, Im(χ1111R)=Im{[A(ω)+B(ω)]/2}; +, Re(χ1111R)=Re{[A(ω)+B(ω)]/2}.

Fig. 2
Fig. 2

Spectra obtained from the linear stability analysis of a dual-frequency pumping system [Eq. (9)]. Gain spectrum: (a) the curves correspond (from the smallest to the largest) to z=0, z=L/2, and z=L; output spectrum: (b) fast axis, (c) slow axis. Here ωP1=522 THz, ωP2=520.26 THz; δ=0.61 ps/m, βP1=59.2 ps2/km, βP2=58.9 ps2/km, γP1=41.7 W-1 km-1, and γP2=41.4 W-1 km-1. The power spectra are shown in the same arbitrary units for all figures. The initial intensity of the spectral components at z=0 was a weak noise.

Fig. 3
Fig. 3

Theoretical output spectra with (a) single- and (b1) and (b2) dual-frequency pumps. Here ωP1=522 THz, ωP2=513.3THz; δ=-1.96 ps/m, βP2=57.9 ps2/km, and γP2=39.9 W-1 km-1. Quasi-cw operation is achieved with pump pulses of duration 100 ps (FWHM). The spectra are shown in the same arbitrary units for all figures. The initial intensity of the spectral components at z=0 was a weak noise. Bj, parametric sidebands; Sj, Raman Stokes waves; Pj, pumps. The index j=1(2) indicates the polarization along the fast (slow) axis.

Fig. 4
Fig. 4

Theoretical output spectra with (a) single- and (b1) and (b2) dual-frequency pumps. Here ωP2=522 THz, ωP1=515.4 THz; δ=3.6 ps/m, βP1=58.2 ps2/km, and γP1=40.4 W-1 km-1. Quasi-cw operation is achieved with pump pulses of duration 150 ps (FWHM). The spectra are shown in the same arbitrary units for all figures. The initial intensity of the spectral components at z=0 was a weak noise.

Fig. 5
Fig. 5

Experimental output spectra for ωP1=522 THz and ωP2=513.3 THz (δ=-1.96 ps/m) with (a) single- and (b) dual-frequency pumps (the pump lines are divided here by ten to produce the best clarity in the figures).

Fig. 6
Fig. 6

Experimental output spectra for ωP1=515.4 THz and ωP2=522 THz (δ=3.6 ps/m) with (a) single- and (b) dual-frequency pumps (the pump lines are divided here by ten to produce the best clarity in the figures).

Fig. 7
Fig. 7

Solid curves, theoretical variation of pump and Stokes powers versus fiber length, obtained from Eqs. (13); crosses, analytical solution [Eqs. (8)] for the energy cross transfer between pumps. Here ωP1=522 THz, ωP2=518.6 THz; δ=0, βP2=58.7 ps2/km, and γP2=41.0 W-1 km-1.

Fig. 8
Fig. 8

Theoretical output spectra obtained from NLSE’s (4) with (a) single- and (b1) and (b2) dual-frequency pumps. Here δ=0. Quasi-cw operation is achieved with pump pulses of duration 100 ps (FWHM). The spectra are shown in the same arbitrary units for all figures. The initial intensity of the spectral components at z=0 was a weak noise.

Fig. 9
Fig. 9

Experimental output spectra with (a) single- and (b) dual-frequency pumps (the pump lines are divided here by 10 to produce the best clarity in the figures). Here δ=0. P1(2) is the pump polarized along the fast (slow) axis. S1(2) is the Raman–Stokes wave on the fast (slow) axis.

Fig. 10
Fig. 10

Experimental output spectra measured in operating conditions of nonzero GVM: (a) δ=0.61 ps/m and (b) δ=-0.61 ps/m. P1(2) is the pump polarized along the fast (slow) axis. S1(2) is the Raman–Stokes wave on the fast (slow) axis.

Equations (42)

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Ej=½Aj(z, t)exp[i(kjz-ωPjt)]+c.c.,j=1, 2,
Pi(3)(t)=σijklEj(t)Ek(t)El(t)+Ej(t)×-tdt1σijklR(t-t1)Ek(t1)El(t1),
σijklR(ω)=A(ω)δijδkl+[B(ω)/2](δikδjl+δilδjk).
Ajz+(-1)jδ2 Ajt+12 iβPj 2Ajt2
=iγPj(1-ρ)|Aj|2+23 |A3-j|2Aj+iγPjρAj0χ1111R(s)|Aj|2(t-s)ds+0χ1122R(s)|A3-j|2(t-s)ds+iγPjρA3-j×0χ1212R(s)exp(iΔωs)Aj(t-s)A3-j*(t-s)ds,
χ1122R(ω)=σ1122R(ω)2=A(ω)2.
δ1/Vg(ωP2)-1/Vg(ωP1)Δn/c-Δω(βP1+βP2)/2,
Aj=Asj+uj exp(-iΩt)+vj exp(iΩt),j=1, 2,
Asj=Pj(z) exp[iγPj((1-ρ)[Pj(z)+P3-j(z)]+ρ{Pj(z)χ1111R(0)+P3-j(z)χ1122R(0)+P3-j(z)Re[χ1212R(Δω)]})z],j=1, 2,
P2(z)As2As2*=P2(0)[R(0)+γ]γ+R(0)exp[2ργP2 Im[χ1212R(Δω)]zP2(0)[R(0)+γ]],
P1(z)As1As1*=P1(0)+γ[P2(0)-P2(z)],
R(z)P1(z)/P2(z),
γγP1/γP2.
d[Y]dz=i[M][Y],[Y]T[u1,v1*,u2,v2*],
[M]M11γP1P1(z)ξlγP1η12(z)ξm1γP1η12(z)ξn1-γP1P1(z)ξlM22-γP1η12(z)ξn2-γP1η12(z)ξm2γP2η12(z)ξm2γP2η12(z)ξn2M33γP2P2(z)ξl-γP2η12(z)ξn1-γP2η12(z)ξm1-γP2P2(z)ξlM44,
η12(z)[P1(z)P2(z)]1/2,
ξl1-ρ+ρχ1111R(-Ω),
M11½(-δΩ+βP1Ω2)+γP1[P2(z)ρC11+P1(z)ξl],
C11χ1212R(-Ω-Δω)-Re[χ1212R(Δω)],
M22½(-δΩ-βP1Ω2)-γP1[P2(z)ρC22+P1(z)ξl],
C22χ1212R(-Ω+Δω)-Re[χ1212R(Δω)].
M33½(δΩ+βP2Ω2)+γP2[P1(z)ρC22+P2(z)ξl],
M44½(δΩ-βP2Ω2)-γP2[P1(z)ρC11+P2(z)ξl],
ξm1(1-ρ)+ρ[χ1122R(-Ω)+χ1212R(-Δω)],
ξn1(1-ρ)+ρ[χ1122R(-Ω)+χ1212R(-Ω-Δω)],
ξm2(1-ρ)+ρ[χ1122R(-Ω)+χ1212R(Δω)],
ξn2(1-ρ)+ρ[χ1122R(-Ω)+χ1212R(-Ω+Δω)].
GAIN(ω)2|Im(K)|.
Ω=2δβP1+βP22δ0βP1+βP2-Δω,δ0Δnc.
Ej(z, t)=½{UPj(z)exp[i(kPjz-ωPjt)]+USj(z)exp[i(kSjz-ωSjt)]}+c.c.,
j=1, 2
UPjz-i(-1)jδ2 ωPj+βPj2 ωPj2UPj=iγPj(HPjPjPj|UPj|2+HP3-jP3-jPj|UP3-j|2+HSjSjPj|USj|2+HS3-jS3-jPj|US3-j|2)UPj,
j=1, 2
USjz-i(-1)jδsj2 ωSj+βSj2 ωSj2USj
=iγSj(HSjSjSj|USj|2+HS3-jS3-jSj|US3-j|2+HPjPjSj|UPj|2+HP3-jP3-jSj|UP3-j|2)USj,
δsjδ+2(-1)j1vg(ωsj)-1vg(wpj),j=1, 2,
HPjPjPj=HSjSjSjχ1111R(0)+3σ4,
HSjSjPjχ1111R(-ΩR)+χ1111R(0)+3σ2,
HP3-jP3-jPj=HS3-jS3-jSjχ1212R[(-1)jΔω]+A(0)2+σ2,
HS3-jS3-jPjA(0)2+χ1212R[(-1)jΔω-ΩR]+σ2,
HPjPjSjχ1111R(ΩR)+χ1111R(0)+3σ2,
HP3-jP3-jSjA(0)2+χ1212R[(-1)jΔω+ΩR]+σ2,

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