Abstract

The contribution to polarization dynamics from a combination of linear birefringence, anisotropic nonlinear refraction, and a longitudinal magneto-optic effect is discussed. A Hamiltonian formalism is developed using Stokes parameters. It is found that by periodic reversal of the magnetic field, avenues are opened up to exploit Faraday rotation, for example, as an optical isolator, and polarization switching in an integrated optical environment. A practical implementation is discussed that uses semiconductors and a shaped-surface conductor.

© 2000 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. S. Aitchison, D. C. Hutchings, J. M. Arnold, J. U. Kang, G. I. Stegeman, E. Ostrovskaya, and N. Akhmediev, “Power-dependent polarization dynamics of mixed-mode spatial solitary waves in AlGaAs waveguides,” J. Opt. Soc. Am. B 14, 3032–3037 (1997).
    [CrossRef]
  2. A. D. Boardman and K. Xie, “Magneto-optic spatial solitons,” J. Opt. Soc. Am. B 14, 3102–3109 (1997).
    [CrossRef]
  3. D. C. Hutchings, J. S. Aitchison, and J. M. Arnold, “Nonlinear refractive coupling and vector solitons in anisotropic cubic media,” J. Opt. Soc. Am. B 14, 869–879 (1997).
    [CrossRef]
  4. D. C. Hutchings, J. M. Arnold, and J. S. Aitchison, “Theory of mixed-polarization propagation in anisotropic cubic media,” Opt. Quantum Electron. 30, 771–782 (1998).
    [CrossRef]
  5. M. S. Alber, G. G. Luther, J. E. Marsden, and J. M. Robbins, “Geometric phases, reduction and Lie–Poisson structure for the resonant three-wave interaction,” Physica D 123, 271–290 (1998).
    [CrossRef]
  6. G. G. Luther, M. S. Alber, J. E. Marsden, and J. M. Robbins, “Geometrical analysis of optical frequency conversion and its control in quadratic nonlinear media,” J. Opt. Soc. Am. B 17, 932–941 (2000).
    [CrossRef]
  7. D. C. Hutchings and B. S. Wherrett, “Theory of the anisotropy of ultrafast nonlinear refraction in zinc-blende semiconductors,” Phys. Rev. B 52, 8150–8159 (1995).
    [CrossRef]
  8. D. C. Hutchings, J. S. Aitchison, B. S. Wherrett, G. T. Kennedy, and W. S. Sibbett, “Polarization dependence of ultrafast nonlinear refraction in an AlGaAs waveguide at the half-gap,” Opt. Lett. 20, 991–993 (1995).
    [CrossRef]
  9. L. M. Roth, “Theory of Faraday effect in solids,” Phys. Rev. 133, A542–A553 (1964).
    [CrossRef]
  10. M. Balkanski, E. Amzallag, and D. Langer, “Interband Faraday rotation of II–VI compounds,” J. Phys. Chem. Solids 27, 299 (1966).
    [CrossRef]
  11. S. Hugonnard-Bruyère, C. Buss, F. Vouilloz, R. Frey, and C. Flytzanis, “Faraday-rotation spectra of semimagnetic semiconductors,” Phys. Rev. B 50, 2200–2207 (1994).
    [CrossRef]
  12. S. V. Mel’nichuk, P. I. Nikitin, A. I. Savchuk, and D. N. Trifonenko, “Faraday effect in semimagnetic Cd1−xFexTe semiconductor,” Semiconductors 30, 959–961 (1996).
  13. H. Akinaga, S. Miyanishi, K. Tanaka, W. Van Roy, and K. Onodera, “Magneto-optical properties and the potential application of GaAs with magnetic MnAs nanocluster,” Appl. Phys. Lett. 76, 97–99 (2000).
    [CrossRef]

2000

G. G. Luther, M. S. Alber, J. E. Marsden, and J. M. Robbins, “Geometrical analysis of optical frequency conversion and its control in quadratic nonlinear media,” J. Opt. Soc. Am. B 17, 932–941 (2000).
[CrossRef]

H. Akinaga, S. Miyanishi, K. Tanaka, W. Van Roy, and K. Onodera, “Magneto-optical properties and the potential application of GaAs with magnetic MnAs nanocluster,” Appl. Phys. Lett. 76, 97–99 (2000).
[CrossRef]

1998

D. C. Hutchings, J. M. Arnold, and J. S. Aitchison, “Theory of mixed-polarization propagation in anisotropic cubic media,” Opt. Quantum Electron. 30, 771–782 (1998).
[CrossRef]

M. S. Alber, G. G. Luther, J. E. Marsden, and J. M. Robbins, “Geometric phases, reduction and Lie–Poisson structure for the resonant three-wave interaction,” Physica D 123, 271–290 (1998).
[CrossRef]

1997

1996

S. V. Mel’nichuk, P. I. Nikitin, A. I. Savchuk, and D. N. Trifonenko, “Faraday effect in semimagnetic Cd1−xFexTe semiconductor,” Semiconductors 30, 959–961 (1996).

1995

D. C. Hutchings and B. S. Wherrett, “Theory of the anisotropy of ultrafast nonlinear refraction in zinc-blende semiconductors,” Phys. Rev. B 52, 8150–8159 (1995).
[CrossRef]

D. C. Hutchings, J. S. Aitchison, B. S. Wherrett, G. T. Kennedy, and W. S. Sibbett, “Polarization dependence of ultrafast nonlinear refraction in an AlGaAs waveguide at the half-gap,” Opt. Lett. 20, 991–993 (1995).
[CrossRef]

1994

S. Hugonnard-Bruyère, C. Buss, F. Vouilloz, R. Frey, and C. Flytzanis, “Faraday-rotation spectra of semimagnetic semiconductors,” Phys. Rev. B 50, 2200–2207 (1994).
[CrossRef]

1966

M. Balkanski, E. Amzallag, and D. Langer, “Interband Faraday rotation of II–VI compounds,” J. Phys. Chem. Solids 27, 299 (1966).
[CrossRef]

1964

L. M. Roth, “Theory of Faraday effect in solids,” Phys. Rev. 133, A542–A553 (1964).
[CrossRef]

Aitchison, J. S.

Akhmediev, N.

Akinaga, H.

H. Akinaga, S. Miyanishi, K. Tanaka, W. Van Roy, and K. Onodera, “Magneto-optical properties and the potential application of GaAs with magnetic MnAs nanocluster,” Appl. Phys. Lett. 76, 97–99 (2000).
[CrossRef]

Alber, M. S.

G. G. Luther, M. S. Alber, J. E. Marsden, and J. M. Robbins, “Geometrical analysis of optical frequency conversion and its control in quadratic nonlinear media,” J. Opt. Soc. Am. B 17, 932–941 (2000).
[CrossRef]

M. S. Alber, G. G. Luther, J. E. Marsden, and J. M. Robbins, “Geometric phases, reduction and Lie–Poisson structure for the resonant three-wave interaction,” Physica D 123, 271–290 (1998).
[CrossRef]

Amzallag, E.

M. Balkanski, E. Amzallag, and D. Langer, “Interband Faraday rotation of II–VI compounds,” J. Phys. Chem. Solids 27, 299 (1966).
[CrossRef]

Arnold, J. M.

Balkanski, M.

M. Balkanski, E. Amzallag, and D. Langer, “Interband Faraday rotation of II–VI compounds,” J. Phys. Chem. Solids 27, 299 (1966).
[CrossRef]

Boardman, A. D.

Buss, C.

S. Hugonnard-Bruyère, C. Buss, F. Vouilloz, R. Frey, and C. Flytzanis, “Faraday-rotation spectra of semimagnetic semiconductors,” Phys. Rev. B 50, 2200–2207 (1994).
[CrossRef]

Flytzanis, C.

S. Hugonnard-Bruyère, C. Buss, F. Vouilloz, R. Frey, and C. Flytzanis, “Faraday-rotation spectra of semimagnetic semiconductors,” Phys. Rev. B 50, 2200–2207 (1994).
[CrossRef]

Frey, R.

S. Hugonnard-Bruyère, C. Buss, F. Vouilloz, R. Frey, and C. Flytzanis, “Faraday-rotation spectra of semimagnetic semiconductors,” Phys. Rev. B 50, 2200–2207 (1994).
[CrossRef]

Hugonnard-Bruyère, S.

S. Hugonnard-Bruyère, C. Buss, F. Vouilloz, R. Frey, and C. Flytzanis, “Faraday-rotation spectra of semimagnetic semiconductors,” Phys. Rev. B 50, 2200–2207 (1994).
[CrossRef]

Hutchings, D. C.

Kang, J. U.

Kennedy, G. T.

Langer, D.

M. Balkanski, E. Amzallag, and D. Langer, “Interband Faraday rotation of II–VI compounds,” J. Phys. Chem. Solids 27, 299 (1966).
[CrossRef]

Luther, G. G.

G. G. Luther, M. S. Alber, J. E. Marsden, and J. M. Robbins, “Geometrical analysis of optical frequency conversion and its control in quadratic nonlinear media,” J. Opt. Soc. Am. B 17, 932–941 (2000).
[CrossRef]

M. S. Alber, G. G. Luther, J. E. Marsden, and J. M. Robbins, “Geometric phases, reduction and Lie–Poisson structure for the resonant three-wave interaction,” Physica D 123, 271–290 (1998).
[CrossRef]

Marsden, J. E.

G. G. Luther, M. S. Alber, J. E. Marsden, and J. M. Robbins, “Geometrical analysis of optical frequency conversion and its control in quadratic nonlinear media,” J. Opt. Soc. Am. B 17, 932–941 (2000).
[CrossRef]

M. S. Alber, G. G. Luther, J. E. Marsden, and J. M. Robbins, “Geometric phases, reduction and Lie–Poisson structure for the resonant three-wave interaction,” Physica D 123, 271–290 (1998).
[CrossRef]

Mel’nichuk, S. V.

S. V. Mel’nichuk, P. I. Nikitin, A. I. Savchuk, and D. N. Trifonenko, “Faraday effect in semimagnetic Cd1−xFexTe semiconductor,” Semiconductors 30, 959–961 (1996).

Miyanishi, S.

H. Akinaga, S. Miyanishi, K. Tanaka, W. Van Roy, and K. Onodera, “Magneto-optical properties and the potential application of GaAs with magnetic MnAs nanocluster,” Appl. Phys. Lett. 76, 97–99 (2000).
[CrossRef]

Nikitin, P. I.

S. V. Mel’nichuk, P. I. Nikitin, A. I. Savchuk, and D. N. Trifonenko, “Faraday effect in semimagnetic Cd1−xFexTe semiconductor,” Semiconductors 30, 959–961 (1996).

Onodera, K.

H. Akinaga, S. Miyanishi, K. Tanaka, W. Van Roy, and K. Onodera, “Magneto-optical properties and the potential application of GaAs with magnetic MnAs nanocluster,” Appl. Phys. Lett. 76, 97–99 (2000).
[CrossRef]

Ostrovskaya, E.

Robbins, J. M.

G. G. Luther, M. S. Alber, J. E. Marsden, and J. M. Robbins, “Geometrical analysis of optical frequency conversion and its control in quadratic nonlinear media,” J. Opt. Soc. Am. B 17, 932–941 (2000).
[CrossRef]

M. S. Alber, G. G. Luther, J. E. Marsden, and J. M. Robbins, “Geometric phases, reduction and Lie–Poisson structure for the resonant three-wave interaction,” Physica D 123, 271–290 (1998).
[CrossRef]

Roth, L. M.

L. M. Roth, “Theory of Faraday effect in solids,” Phys. Rev. 133, A542–A553 (1964).
[CrossRef]

Savchuk, A. I.

S. V. Mel’nichuk, P. I. Nikitin, A. I. Savchuk, and D. N. Trifonenko, “Faraday effect in semimagnetic Cd1−xFexTe semiconductor,” Semiconductors 30, 959–961 (1996).

Sibbett, W. S.

Stegeman, G. I.

Tanaka, K.

H. Akinaga, S. Miyanishi, K. Tanaka, W. Van Roy, and K. Onodera, “Magneto-optical properties and the potential application of GaAs with magnetic MnAs nanocluster,” Appl. Phys. Lett. 76, 97–99 (2000).
[CrossRef]

Trifonenko, D. N.

S. V. Mel’nichuk, P. I. Nikitin, A. I. Savchuk, and D. N. Trifonenko, “Faraday effect in semimagnetic Cd1−xFexTe semiconductor,” Semiconductors 30, 959–961 (1996).

Van Roy, W.

H. Akinaga, S. Miyanishi, K. Tanaka, W. Van Roy, and K. Onodera, “Magneto-optical properties and the potential application of GaAs with magnetic MnAs nanocluster,” Appl. Phys. Lett. 76, 97–99 (2000).
[CrossRef]

Vouilloz, F.

S. Hugonnard-Bruyère, C. Buss, F. Vouilloz, R. Frey, and C. Flytzanis, “Faraday-rotation spectra of semimagnetic semiconductors,” Phys. Rev. B 50, 2200–2207 (1994).
[CrossRef]

Wherrett, B. S.

D. C. Hutchings, J. S. Aitchison, B. S. Wherrett, G. T. Kennedy, and W. S. Sibbett, “Polarization dependence of ultrafast nonlinear refraction in an AlGaAs waveguide at the half-gap,” Opt. Lett. 20, 991–993 (1995).
[CrossRef]

D. C. Hutchings and B. S. Wherrett, “Theory of the anisotropy of ultrafast nonlinear refraction in zinc-blende semiconductors,” Phys. Rev. B 52, 8150–8159 (1995).
[CrossRef]

Xie, K.

Appl. Phys. Lett.

H. Akinaga, S. Miyanishi, K. Tanaka, W. Van Roy, and K. Onodera, “Magneto-optical properties and the potential application of GaAs with magnetic MnAs nanocluster,” Appl. Phys. Lett. 76, 97–99 (2000).
[CrossRef]

J. Opt. Soc. Am. B

J. Phys. Chem. Solids

M. Balkanski, E. Amzallag, and D. Langer, “Interband Faraday rotation of II–VI compounds,” J. Phys. Chem. Solids 27, 299 (1966).
[CrossRef]

Opt. Lett.

Opt. Quantum Electron.

D. C. Hutchings, J. M. Arnold, and J. S. Aitchison, “Theory of mixed-polarization propagation in anisotropic cubic media,” Opt. Quantum Electron. 30, 771–782 (1998).
[CrossRef]

Phys. Rev.

L. M. Roth, “Theory of Faraday effect in solids,” Phys. Rev. 133, A542–A553 (1964).
[CrossRef]

Phys. Rev. B

D. C. Hutchings and B. S. Wherrett, “Theory of the anisotropy of ultrafast nonlinear refraction in zinc-blende semiconductors,” Phys. Rev. B 52, 8150–8159 (1995).
[CrossRef]

S. Hugonnard-Bruyère, C. Buss, F. Vouilloz, R. Frey, and C. Flytzanis, “Faraday-rotation spectra of semimagnetic semiconductors,” Phys. Rev. B 50, 2200–2207 (1994).
[CrossRef]

Physica D

M. S. Alber, G. G. Luther, J. E. Marsden, and J. M. Robbins, “Geometric phases, reduction and Lie–Poisson structure for the resonant three-wave interaction,” Physica D 123, 271–290 (1998).
[CrossRef]

Semiconductors

S. V. Mel’nichuk, P. I. Nikitin, A. I. Savchuk, and D. N. Trifonenko, “Faraday effect in semimagnetic Cd1−xFexTe semiconductor,” Semiconductors 30, 959–961 (1996).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

Poincaré sphere representation of the polarization state.

Fig. 2
Fig. 2

Polarization-evolution trajectory for a periodically modulated magnetic field in a birefringent medium.

Fig. 3
Fig. 3

Calculated polarization-evolution trajectories for [100] propagation in AlGaAs for Δkmag/ΔkNL equal to (a) 0, (b) 0.2, and (c) 0.4. Here we have plotted the surface of the Poincaré sphere on a two-dimensional surface using the spherical polar coordinates (θ, ϕ).

Fig. 4
Fig. 4

Calculated polarization-evolution trajectories for [110] propagation in AlGaAs for Δkmag/ΔkNL equal to (a) 0, (b) 0.2, and (c) 0.4.

Fig. 5
Fig. 5

Calculated polarization-evolution trajectories for [110] propagation in a birefringent AlGaAs waveguide with a perturbing magnetic field. The solid and the dashed curves indicate opposite magnetic field polarity. By selecting the appropriate segment lengths for each field direction, a trajectory can be followed between a pair of stable stationary points.

Fig. 6
Fig. 6

Schematic of current-carrying contact deposited on top of a rib-loaded waveguide, which results in a spatially alternating longitudinal magnetic field.

Fig. 7
Fig. 7

Form of the function F1(x), which gives the spectral dependence of the interband contribution to the Faraday rotation.

Tables (1)

Tables Icon

Table 1 Typical Values for the Verdet Coefficient (Defined θF=VHd) for a Range of Semiconductors in the Near-Infrared at Room Temperaturea

Equations (24)

Equations on this page are rendered with MathJax. Learn more.

=n021-iQl-iQp+iQl1-iQt+iQp+iQt1,
ξjz=-i ξj*H(ξTE,ξTE*,ξTM,ξTM*),
s0=|ξp|2+|ξq|2,
s1=|ξp|2-|ξq|2,
s2=ξp*ξq+ξpξq*,
s3=-i(ξp*ξq-ξpξq*).
dsjdz=-i{sj, H},
{sj, sk}=2ijklsl,
H=Hbrf+Hmag=12Δkbrfs1+12Δkmags3.
(s1, s2, s3)=±ΔkbrfΔkbrf2+Δkmag2, 0,±ΔkmagΔkbrf2+Δkmag2.
Lbeat=πΔkbrf2+Δkmag2.
12Δkbrf sin θn+1-12Δkmag cos θn+1
=12Δkbrf sin θn+12Δkmag cos θn.
ΔθΔθ dLbeat2πΔkmagd,
HNL=-14ΔkNLσi[(s0+s1)|pi|2+(s0-s1)|qi|2]×[pi*qi(s2+is3)+piqi*(s2-is3)]+12 δ+σi(pi*)2qi2-12(s2+is3)2+12 δ+σ˙ipi2(qi*)2-12(s2-is3)2+1-δ+σ2i|pi|2|qi|2-12×(s0+s1)(s0-s1)+12 1+σi|pi|4-1(s0+s1)2+12 1+σi|qi|4-1(s0-s1)2.
HNL[100]=-12ΔkNL1-δs32-σ2s22.
s3=-Δkmag(2δ-σ)ΔkNL.
HNL[110]=-12ΔkNL1-δs32-σ2 s22+14(1+s1)2.
HNL[111]=-12ΔkNL1-σ2-δ-σ3s32.
s3=-Δkmag2(δ-σ/3)ΔkNL.
s1=13 1+4ΔkbrfσΔkNL.
θF=VHd.
V=V0F1(ω/Eg),
F1(x)=1x[(1-x)-1/2-(1+x)-1/2]-4x˙2[2-(1-x)1/2-(1+x)1/2].

Metrics