Abstract

Optical parametric interaction in isotropic third-order nonlinear media with magneto-optic properties is investigated. It is shown that new phase-matching conditions with a magneto-optic contribution are possible. In particular, we study four-wave mixing and electric field–induced three-wave parametric processes in the presence of a magnetic field applied along the direction of propagation of the interacting waves. Control of the new phase-matching branches can be achieved by tuning of the magnetic field.

© 2000 Optical Society of America

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References

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  1. H. Rabin and P. P. Bey, Phys. Rev. 156, 1010 (1967).
    [CrossRef]
  2. F. Jonsson and C. Flytzanis, Opt. Lett. 24, 1514 (1999).
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  3. R. H. Stolen and J. E. Bjorkholm, IEEE J. Quantum Electron. QE-18, 1062 (1982); G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, New York, 1995).
    [CrossRef]
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    [CrossRef]
  5. R. Kashyap, J. Opt. Soc. Am. B 6, 313 (1989).
    [CrossRef]
  6. V. Pruneri, G. Bonfrate, P. G. Kazansky, D. J. Richardson, N. G. Broderick, J. P. De Sandro, C. Simonneau, P. Vidakovic, and J. A. Levenson, Opt. Lett. 24, 208 (1999).
    [CrossRef]
  7. N. F. Borrelli, J. Chem. Phys. 41, 3289 (1964).
  8. V. Pruneri and S. Longhi are preparing a manuscript to be called “Modulational instability and four-wave mixing in anisotropic χ3 magneto-optic media.”
  9. N. F. Borrelli, B. G. Aitken, and M. A. Newhouse, J. Non-Cryst. Solids 185, 109 (1995).
    [CrossRef]
  10. Optical Glass, Schott Catalog (Schott Glass Technologies, Inc., Duryea, Pa., 1984).

1999 (2)

1997 (1)

1995 (1)

N. F. Borrelli, B. G. Aitken, and M. A. Newhouse, J. Non-Cryst. Solids 185, 109 (1995).
[CrossRef]

1989 (1)

1982 (1)

R. H. Stolen and J. E. Bjorkholm, IEEE J. Quantum Electron. QE-18, 1062 (1982); G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, New York, 1995).
[CrossRef]

1967 (1)

H. Rabin and P. P. Bey, Phys. Rev. 156, 1010 (1967).
[CrossRef]

1964 (1)

N. F. Borrelli, J. Chem. Phys. 41, 3289 (1964).

Aitken, B. G.

N. F. Borrelli, B. G. Aitken, and M. A. Newhouse, J. Non-Cryst. Solids 185, 109 (1995).
[CrossRef]

Bey, P. P.

H. Rabin and P. P. Bey, Phys. Rev. 156, 1010 (1967).
[CrossRef]

Bjorkholm, J. E.

R. H. Stolen and J. E. Bjorkholm, IEEE J. Quantum Electron. QE-18, 1062 (1982); G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, New York, 1995).
[CrossRef]

Bonfrate, G.

Borrelli, N. F.

N. F. Borrelli, B. G. Aitken, and M. A. Newhouse, J. Non-Cryst. Solids 185, 109 (1995).
[CrossRef]

N. F. Borrelli, J. Chem. Phys. 41, 3289 (1964).

Broderick, N. G.

De Sandro, J. P.

Flytzanis, C.

Jonsson, F.

Kashyap, R.

Kazansky, P. G.

Levenson, J. A.

Longhi, S.

V. Pruneri and S. Longhi are preparing a manuscript to be called “Modulational instability and four-wave mixing in anisotropic χ3 magneto-optic media.”

Newhouse, M. A.

N. F. Borrelli, B. G. Aitken, and M. A. Newhouse, J. Non-Cryst. Solids 185, 109 (1995).
[CrossRef]

Pruneri, V.

V. Pruneri, G. Bonfrate, P. G. Kazansky, D. J. Richardson, N. G. Broderick, J. P. De Sandro, C. Simonneau, P. Vidakovic, and J. A. Levenson, Opt. Lett. 24, 208 (1999).
[CrossRef]

V. Pruneri and S. Longhi are preparing a manuscript to be called “Modulational instability and four-wave mixing in anisotropic χ3 magneto-optic media.”

Rabin, H.

H. Rabin and P. P. Bey, Phys. Rev. 156, 1010 (1967).
[CrossRef]

Richardson, D. J.

Simonneau, C.

Stolen, R. H.

R. H. Stolen and J. E. Bjorkholm, IEEE J. Quantum Electron. QE-18, 1062 (1982); G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, New York, 1995).
[CrossRef]

Unsbo, P.

Vidakovic, P.

IEEE J. Quantum Electron. (1)

R. H. Stolen and J. E. Bjorkholm, IEEE J. Quantum Electron. QE-18, 1062 (1982); G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, New York, 1995).
[CrossRef]

J. Chem. Phys. (1)

N. F. Borrelli, J. Chem. Phys. 41, 3289 (1964).

J. Non-Cryst. Solids (1)

N. F. Borrelli, B. G. Aitken, and M. A. Newhouse, J. Non-Cryst. Solids 185, 109 (1995).
[CrossRef]

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

Opt. Lett. (2)

Phys. Rev. (1)

H. Rabin and P. P. Bey, Phys. Rev. 156, 1010 (1967).
[CrossRef]

Other (2)

V. Pruneri and S. Longhi are preparing a manuscript to be called “Modulational instability and four-wave mixing in anisotropic χ3 magneto-optic media.”

Optical Glass, Schott Catalog (Schott Glass Technologies, Inc., Duryea, Pa., 1984).

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Figures (2)

Fig. 1
Fig. 1

Parametric gain for EI-PDC as a function of residual PM, Δkres=Δkdisp-2πΛ, in the absence of (dotted curve) and with (solid curves) an applied magnetic field. The instability branches, 1, 2, and 3, correspond to the QPM conditions Δk1=0, Δk2=0, and Δk3=0. The dashed curves, which nearly overlap the solid curves, are the parametric instability branches as predicted by approximate uncoupled parametric processes (see text). The parameter values are θ=2 m-1, Δk1MO=-14 m-1, Δk2MO=-26 m-1, and Δk3MO=-34 m-1.

Fig. 2
Fig. 2

Parametric gain for near-degenerate EI-PDC as a function of signal (idler) wavelength in an SF57 fiber for different values of magnetic field. Dotted curve, Hz=0 mT; dashed curves, Hz=-200 mT; solid curves, Hz=-400 mT. The fiber has a numerical aperture of 0.2 and a core radius of 2.5 µm. The parameter values are pump wavelength λ3=775 nm, Λ=26.752 µm (corresponding to Δkdisp=0 at degeneracy λ1=λ2=1550 nm), and θ=0.3 m-1. For calculation of the wavelength-dependent term Δkdisp the Sellmeier equation given in Ref. 10 was used.

Equations (11)

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PxNLω1=0gdegχ3Exω4Exω3Exω2*+13Exω4Eyω3Eyω2*+13Eyω4Exω3Eyω2*+13Eyω4Eyω3Exω2*,
P+NLω1=230gdegχ3E+ω4E+ω3E+ω2*+E-ω4E+ω3E-ω2*+E+ω4E-ω3E-ω2*.
z2E±ω1,2+k±2ω1,2E±ω1,2=-μ0ω1,22P±NLω1,2,
E±ω1,2z=ω1,2nω1,2ω31/2A±ω1,2zexpik±ω1,2z.
zA+ω1=iθA+ω2* expiΔk1z+A-ω2* expiΔk3z,
zA-ω1=iθA+ω2* expiΔk2z,
zA+ω2*=-iθA+ω1 exp-iΔk1z+A-ω1 exp-iΔk2z,
zA-ω2*=-iθA+ω1 exp-iΔk3z,
Δk1MO=HzVω1+Vω2-Vω3,
Δk2MO=Hz-Vω1+Vω2-Vω3,
Δk3MO=HzVω1-Vω2-Vω3.

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