Abstract

A new optical mode of propagation is described, which is the natural eigenmode (supermode) of a fiber (or any optical waveguide) with two cospatial periodic gratings. The mode frustrates the backward Bragg scattering from the grating by destructive interference of its two constituent submodes (which are eigenmodes of a uniform waveguide). It can be used in a new type of spatial mode conversion in optical guides.

© 1998 Optical Society of America

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References

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  1. T. Erdogan, J. Lightwave Technol. 15, 8 (1997).
    [CrossRef]
  2. A. Yariv, IEEE J. Quantum Electron. QE-9, 919 (1973).
    [CrossRef]
  3. D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974), p. 106.
  4. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).
  5. M. P. Fewel, B. W. Shore, and K. Bergmann, Aust. J. Phys. 50, 281 (1977).
    [CrossRef]

1997

T. Erdogan, J. Lightwave Technol. 15, 8 (1997).
[CrossRef]

1977

M. P. Fewel, B. W. Shore, and K. Bergmann, Aust. J. Phys. 50, 281 (1977).
[CrossRef]

1973

A. Yariv, IEEE J. Quantum Electron. QE-9, 919 (1973).
[CrossRef]

Bergmann, K.

M. P. Fewel, B. W. Shore, and K. Bergmann, Aust. J. Phys. 50, 281 (1977).
[CrossRef]

Erdogan, T.

T. Erdogan, J. Lightwave Technol. 15, 8 (1997).
[CrossRef]

Fewel, M. P.

M. P. Fewel, B. W. Shore, and K. Bergmann, Aust. J. Phys. 50, 281 (1977).
[CrossRef]

Love, J. D.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).

Marcuse, D.

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974), p. 106.

Shore, B. W.

M. P. Fewel, B. W. Shore, and K. Bergmann, Aust. J. Phys. 50, 281 (1977).
[CrossRef]

Snyder, A. W.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).

Yariv, A.

A. Yariv, IEEE J. Quantum Electron. QE-9, 919 (1973).
[CrossRef]

Aust. J. Phys.

M. P. Fewel, B. W. Shore, and K. Bergmann, Aust. J. Phys. 50, 281 (1977).
[CrossRef]

IEEE J. Quantum Electron.

A. Yariv, IEEE J. Quantum Electron. QE-9, 919 (1973).
[CrossRef]

J. Lightwave Technol.

T. Erdogan, J. Lightwave Technol. 15, 8 (1997).
[CrossRef]

Other

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974), p. 106.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman & Hall, London, 1983).

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Figures (1)

Fig. 1
Fig. 1

(a) A fiber (or optical waveguide) modulated spatially by a grating with a period Λ1, which Bragg scatters resonantly between forward mode |a> and backward mode |b>. A momentum diagram shows the initial and the final photon momenta, β, involved as well as the lattice momentum 2π/Λ1. (b) Fiber with a second grating Λ2, which Bragg scatters a higher-order forward mode |c> into backward mode |b>. (c) Dual-grating fiber, which can scatter resonantly and simultaneously between modes |a> and |c> and backward mode |b> but not between modes |a> and |c>.

Equations (12)

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

βa+βb=2πΛ1,
βb+βc=2πΛ2.
Ex,y,z=AzE1x,yexp-iβaz+BzE3x,y×expiβbz+CzE2x,yexp-iβcz.
dAdz=iK1B expiβa+βb-G1z,
dBdz=-iK1A exp-iβa+βb-G1z-iK2C×exp-iβb+βc-G2z,
dCdz=iK2B expiβc+βb-G2z,  G1,22πΛ1,2.
AC=-K2K1,
Δβc-βa+G1-G2=0,
dBdz=0.
E˜1=-K2K1 exp-iG1-G2z0exp-i2G2-G1zexp-iβa+βcz,
100,  whenK1zK2z=0
001,  whenK2zK1z=0;

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