Abstract

We performed analysis of a planar waveguide with arbitrary index variations. We obtained numerical results for the propagation coefficient by using first-order Langer and Liouville transformations. The accuracy of the numerical results is confirmed by a comparison with those obtained by other methods.

© 2001 Optical Society of America

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References

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  1. Z. Nikolov, B. Pantchew, “Application of wave theory for two types of planar-diffused optical waveguide profiles,” IEEE J. Quantum Electron. 28, 658–662 (1992).
    [CrossRef]
  2. H. Ikuno, A. Yata, “Uniform asymptotic technique for analyzing wave propagation in inhomogeneous slab waveguides,” IEEE Trans. Microwave Theory Tech. 30, 1958–1963 (1982).
    [CrossRef]
  3. I. C. Goyal, R. L. Gallawa, A. K. Ghatak, “An approximate solution to the wave equation revisited,” J. Electromagn. Waves Appl. 5, 623–636 (1991).
    [CrossRef]
  4. H. Moriguchi, “An improvement of the WKB method in the presence of turning points and the asymptotic solutions of a class of Hill equations,” J. Phys. Soc. Jpn. 14, 1771–1796 (1959).
    [CrossRef]

1992 (1)

Z. Nikolov, B. Pantchew, “Application of wave theory for two types of planar-diffused optical waveguide profiles,” IEEE J. Quantum Electron. 28, 658–662 (1992).
[CrossRef]

1991 (1)

I. C. Goyal, R. L. Gallawa, A. K. Ghatak, “An approximate solution to the wave equation revisited,” J. Electromagn. Waves Appl. 5, 623–636 (1991).
[CrossRef]

1982 (1)

H. Ikuno, A. Yata, “Uniform asymptotic technique for analyzing wave propagation in inhomogeneous slab waveguides,” IEEE Trans. Microwave Theory Tech. 30, 1958–1963 (1982).
[CrossRef]

1959 (1)

H. Moriguchi, “An improvement of the WKB method in the presence of turning points and the asymptotic solutions of a class of Hill equations,” J. Phys. Soc. Jpn. 14, 1771–1796 (1959).
[CrossRef]

Gallawa, R. L.

I. C. Goyal, R. L. Gallawa, A. K. Ghatak, “An approximate solution to the wave equation revisited,” J. Electromagn. Waves Appl. 5, 623–636 (1991).
[CrossRef]

Ghatak, A. K.

I. C. Goyal, R. L. Gallawa, A. K. Ghatak, “An approximate solution to the wave equation revisited,” J. Electromagn. Waves Appl. 5, 623–636 (1991).
[CrossRef]

Goyal, I. C.

I. C. Goyal, R. L. Gallawa, A. K. Ghatak, “An approximate solution to the wave equation revisited,” J. Electromagn. Waves Appl. 5, 623–636 (1991).
[CrossRef]

Ikuno, H.

H. Ikuno, A. Yata, “Uniform asymptotic technique for analyzing wave propagation in inhomogeneous slab waveguides,” IEEE Trans. Microwave Theory Tech. 30, 1958–1963 (1982).
[CrossRef]

Moriguchi, H.

H. Moriguchi, “An improvement of the WKB method in the presence of turning points and the asymptotic solutions of a class of Hill equations,” J. Phys. Soc. Jpn. 14, 1771–1796 (1959).
[CrossRef]

Nikolov, Z.

Z. Nikolov, B. Pantchew, “Application of wave theory for two types of planar-diffused optical waveguide profiles,” IEEE J. Quantum Electron. 28, 658–662 (1992).
[CrossRef]

Pantchew, B.

Z. Nikolov, B. Pantchew, “Application of wave theory for two types of planar-diffused optical waveguide profiles,” IEEE J. Quantum Electron. 28, 658–662 (1992).
[CrossRef]

Yata, A.

H. Ikuno, A. Yata, “Uniform asymptotic technique for analyzing wave propagation in inhomogeneous slab waveguides,” IEEE Trans. Microwave Theory Tech. 30, 1958–1963 (1982).
[CrossRef]

IEEE J. Quantum Electron. (1)

Z. Nikolov, B. Pantchew, “Application of wave theory for two types of planar-diffused optical waveguide profiles,” IEEE J. Quantum Electron. 28, 658–662 (1992).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

H. Ikuno, A. Yata, “Uniform asymptotic technique for analyzing wave propagation in inhomogeneous slab waveguides,” IEEE Trans. Microwave Theory Tech. 30, 1958–1963 (1982).
[CrossRef]

J. Electromagn. Waves Appl. (1)

I. C. Goyal, R. L. Gallawa, A. K. Ghatak, “An approximate solution to the wave equation revisited,” J. Electromagn. Waves Appl. 5, 623–636 (1991).
[CrossRef]

J. Phys. Soc. Jpn. (1)

H. Moriguchi, “An improvement of the WKB method in the presence of turning points and the asymptotic solutions of a class of Hill equations,” J. Phys. Soc. Jpn. 14, 1771–1796 (1959).
[CrossRef]

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Tables (1)

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Table 1 Normalized Propagation Constant B 0 Versus V

Equations (18)

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n2x=n12+n22-n12fx, |x|<d,
d2Eydx2+QxEy=0,
Qx=k02n2x-β2
QX=V2fX-B,
V=k0dn22-n121/2,
B=β2/k02-n12n22-n12.
τPv dv=XQudu
ξ 0τsech2u-B1/2du=0XQv dv,
ξ τtτB-sech2u1/2du=XtX-Qv dv,
ξ=0XtQvdv0τtsech2u-B1/2du.
Eˆyτ=dXdτ-1/2EyX,
d2Eˆyτdτ2+ξ2sech2τ-B-RτEˆyτ=0,
Rτ=dτ/dX1/2d2dτ/dX-1/2dτ2.
EyX=constdτdX-1/2cosh-1XFa, b, c, χ,
a=r-s, b=r+s+1, c=r+1, r=ξB1/2, s=4ξ2+11/22, χ=121+tanhτX.
τX=Vξ X+V1-B2V2-ξ26ξ31-B X3+ .
B=2m+1-4ξ2+11/224ξ2  mode number m=0, 1, 2, .
a=r-s=-m  mode number m=0, 1, 2, 

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