Abstract

The time reversibility of optical propagation impedes the definite performance of many optical devices, such as couplers, polarization converters, etc. We suggest a novel concept in which we use media with loss and gain, thus breaking the time-reversal characteristics, to achieve a unidirectional optical mode interference and coupling, which is a desirable feature for light-wave circuits. Using a matched periodic modulation of both the index of refraction and loss (gain) of the medium, we implement a spatially single sideband perturbation, which breaks the symmetry to allow only a unidirectional energy transfer from mode m to mode n of the optical structure. We elaborate on this phenomenon in coupling between two modes of a multimode optical waveguide.

© 2004 Optical Society of America

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References

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  1. Y. Nakano, Y. Luo, and K. Tada, Appl. Phys. Lett. 55, 1606 (1989).
    [CrossRef]
  2. D. Marcuse, in Theory of Dielectric Optical Waveguides, P. F. Liao and P. L. Kelley, eds. (Academic, Boston, 1972), pp. 97–133.
  3. W. P. Huang and C. L. Xu, IEEE J. Quantum Electron. 29, 2639 (1993).
    [CrossRef]

1993 (1)

W. P. Huang and C. L. Xu, IEEE J. Quantum Electron. 29, 2639 (1993).
[CrossRef]

1989 (1)

Y. Nakano, Y. Luo, and K. Tada, Appl. Phys. Lett. 55, 1606 (1989).
[CrossRef]

Huang, W. P.

W. P. Huang and C. L. Xu, IEEE J. Quantum Electron. 29, 2639 (1993).
[CrossRef]

Luo, Y.

Y. Nakano, Y. Luo, and K. Tada, Appl. Phys. Lett. 55, 1606 (1989).
[CrossRef]

Marcuse, D.

D. Marcuse, in Theory of Dielectric Optical Waveguides, P. F. Liao and P. L. Kelley, eds. (Academic, Boston, 1972), pp. 97–133.

Nakano, Y.

Y. Nakano, Y. Luo, and K. Tada, Appl. Phys. Lett. 55, 1606 (1989).
[CrossRef]

Tada, K.

Y. Nakano, Y. Luo, and K. Tada, Appl. Phys. Lett. 55, 1606 (1989).
[CrossRef]

Xu, C. L.

W. P. Huang and C. L. Xu, IEEE J. Quantum Electron. 29, 2639 (1993).
[CrossRef]

Appl. Phys. Lett. (1)

Y. Nakano, Y. Luo, and K. Tada, Appl. Phys. Lett. 55, 1606 (1989).
[CrossRef]

IEEE J. Quantum Electron. (1)

W. P. Huang and C. L. Xu, IEEE J. Quantum Electron. 29, 2639 (1993).
[CrossRef]

Other (1)

D. Marcuse, in Theory of Dielectric Optical Waveguides, P. F. Liao and P. L. Kelley, eds. (Academic, Boston, 1972), pp. 97–133.

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Figures (4)

Fig. 1
Fig. 1

(a) Square-wave perturbation. (b) Upper chart, cross section of relative field distributions: thin line, profile of imaginary index perturbation; solid curve, first mode; dashed curve, second mode. Lower chart, total power in the first half-period exhibiting a larger fraction of power in the amplifying region.

Fig. 2
Fig. 2

Modal power for imaginary perturbation fz=i sinΔβz. First mode is initially excited.

Fig. 3
Fig. 3

Modal power for the complex single sideband perturbation fz=expiΔβz. Initial conditions: c10=1, c20=0. Solid curve, numerical simulation; dashed curve, analytical result.

Fig. 4
Fig. 4

Modal power for the complex single sideband perturbation fz=expiΔβz. Initial conditions: c10=0, c20=1. Maximum power transfer to the first mode is less than -25 dB.

Equations (15)

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

Pm,nz0zfzexp-iβm-βnzdz,
dc1dz=-ifzK11c1-ifzK12c2 expiβ1-β2z,
dc2dz=-ifzK21c1 expiβ2-β1z-ifzK22c2,
Kmn=ωε04i-+-+n2-n02Emt*Entdxdy,
Δx,y=+Δx<0-Δx>0.
c˙1=K11 sinΔβzc1+K12 sinΔβzc2 expiΔβz,
c˙2=K21 sinΔβzc1 exp-iΔβz+K22 sinΔβzc2.
c˙1=-12iK12c2,
c˙2=-12iK21c1.
c1=12expαz+12exp-αz=coshαz,
c2=-i2expαz+i2exp-αz=-i sinhαz,
c˙1=-i expiΔβzK11c1-i expiΔβzK12c2×expiΔβz,
c˙2=-i expiΔβzK21c1 exp-iΔβz-i×expiΔβzK22c2.
c1=exp-K11Δβ1-expiΔβz1,
c2=-iK21,

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