Abstract

We adapt an iterative technique for calculating the reflection coefficient from abrupt junctions to optical waveguides.

© 1997 Optical Society of America

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References

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  1. D. Handelman, A. Hardy, A. Katzir, “Reflectivity of TE modes at the facets of buried heterostructure injection lasers,” IEEE J. Quantum Electron. QE-22, 498–500 (1986).
    [Crossref]
  2. C. Vassallo, “Reflectivity of multidielectric coatings deposited on the end facet of a weakly guiding dielectric slab waveguide,” J. Opt. Soc. Am. A 5, 1918–1928 (1988).
    [Crossref]
  3. J. Buus, M. C. Farries, D. J. Robbins, “Reflectivity of coated and tilted semiconductor facets,” IEEE J. Quantum Electron. 27, 1837–1842 (1991).
    [Crossref]
  4. M. D. Collins, R. B. Evans, “A two-way parabolic equation for acoustic backscattering in the ocean,” J. Acoust. Soc. Am. 91, 1357–1368 (1992).
    [Crossref]
  5. D. Yevick, W. Bardyszewski, B. Hermansson, M. Glasner, “Split-operator electric field reflection techniques,” Photon. Technol. Lett. 3, 527–529 (1991).
  6. D. Yevick, J. Xu, W. Bardyszewski, “Split-operator calculations of reflected electric field profiles,” Photon. Technol. Lett. 4, 1383–1386 (1992).
  7. J. Xu, D. Yevick, M. Gallant, “Approximate methods for electric field reflection at waveguide interfaces,” in OSA Annual Meeting, Vol. 16 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), p. 36.
  8. J. Xu, D. Yevick, M. Gallant, “Approximate methods for modal reflectivity at optical waveguide facets,” J. Opt. Soc. Am. A 12, 725–728 (1995).
    [Crossref]

1995 (1)

1992 (2)

D. Yevick, J. Xu, W. Bardyszewski, “Split-operator calculations of reflected electric field profiles,” Photon. Technol. Lett. 4, 1383–1386 (1992).

M. D. Collins, R. B. Evans, “A two-way parabolic equation for acoustic backscattering in the ocean,” J. Acoust. Soc. Am. 91, 1357–1368 (1992).
[Crossref]

1991 (2)

D. Yevick, W. Bardyszewski, B. Hermansson, M. Glasner, “Split-operator electric field reflection techniques,” Photon. Technol. Lett. 3, 527–529 (1991).

J. Buus, M. C. Farries, D. J. Robbins, “Reflectivity of coated and tilted semiconductor facets,” IEEE J. Quantum Electron. 27, 1837–1842 (1991).
[Crossref]

1988 (1)

1986 (1)

D. Handelman, A. Hardy, A. Katzir, “Reflectivity of TE modes at the facets of buried heterostructure injection lasers,” IEEE J. Quantum Electron. QE-22, 498–500 (1986).
[Crossref]

Bardyszewski, W.

D. Yevick, J. Xu, W. Bardyszewski, “Split-operator calculations of reflected electric field profiles,” Photon. Technol. Lett. 4, 1383–1386 (1992).

D. Yevick, W. Bardyszewski, B. Hermansson, M. Glasner, “Split-operator electric field reflection techniques,” Photon. Technol. Lett. 3, 527–529 (1991).

Buus, J.

J. Buus, M. C. Farries, D. J. Robbins, “Reflectivity of coated and tilted semiconductor facets,” IEEE J. Quantum Electron. 27, 1837–1842 (1991).
[Crossref]

Collins, M. D.

M. D. Collins, R. B. Evans, “A two-way parabolic equation for acoustic backscattering in the ocean,” J. Acoust. Soc. Am. 91, 1357–1368 (1992).
[Crossref]

Evans, R. B.

M. D. Collins, R. B. Evans, “A two-way parabolic equation for acoustic backscattering in the ocean,” J. Acoust. Soc. Am. 91, 1357–1368 (1992).
[Crossref]

Farries, M. C.

J. Buus, M. C. Farries, D. J. Robbins, “Reflectivity of coated and tilted semiconductor facets,” IEEE J. Quantum Electron. 27, 1837–1842 (1991).
[Crossref]

Gallant, M.

J. Xu, D. Yevick, M. Gallant, “Approximate methods for modal reflectivity at optical waveguide facets,” J. Opt. Soc. Am. A 12, 725–728 (1995).
[Crossref]

J. Xu, D. Yevick, M. Gallant, “Approximate methods for electric field reflection at waveguide interfaces,” in OSA Annual Meeting, Vol. 16 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), p. 36.

Glasner, M.

D. Yevick, W. Bardyszewski, B. Hermansson, M. Glasner, “Split-operator electric field reflection techniques,” Photon. Technol. Lett. 3, 527–529 (1991).

Handelman, D.

D. Handelman, A. Hardy, A. Katzir, “Reflectivity of TE modes at the facets of buried heterostructure injection lasers,” IEEE J. Quantum Electron. QE-22, 498–500 (1986).
[Crossref]

Hardy, A.

D. Handelman, A. Hardy, A. Katzir, “Reflectivity of TE modes at the facets of buried heterostructure injection lasers,” IEEE J. Quantum Electron. QE-22, 498–500 (1986).
[Crossref]

Hermansson, B.

D. Yevick, W. Bardyszewski, B. Hermansson, M. Glasner, “Split-operator electric field reflection techniques,” Photon. Technol. Lett. 3, 527–529 (1991).

Katzir, A.

D. Handelman, A. Hardy, A. Katzir, “Reflectivity of TE modes at the facets of buried heterostructure injection lasers,” IEEE J. Quantum Electron. QE-22, 498–500 (1986).
[Crossref]

Robbins, D. J.

J. Buus, M. C. Farries, D. J. Robbins, “Reflectivity of coated and tilted semiconductor facets,” IEEE J. Quantum Electron. 27, 1837–1842 (1991).
[Crossref]

Vassallo, C.

Xu, J.

J. Xu, D. Yevick, M. Gallant, “Approximate methods for modal reflectivity at optical waveguide facets,” J. Opt. Soc. Am. A 12, 725–728 (1995).
[Crossref]

D. Yevick, J. Xu, W. Bardyszewski, “Split-operator calculations of reflected electric field profiles,” Photon. Technol. Lett. 4, 1383–1386 (1992).

J. Xu, D. Yevick, M. Gallant, “Approximate methods for electric field reflection at waveguide interfaces,” in OSA Annual Meeting, Vol. 16 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), p. 36.

Yevick, D.

J. Xu, D. Yevick, M. Gallant, “Approximate methods for modal reflectivity at optical waveguide facets,” J. Opt. Soc. Am. A 12, 725–728 (1995).
[Crossref]

D. Yevick, J. Xu, W. Bardyszewski, “Split-operator calculations of reflected electric field profiles,” Photon. Technol. Lett. 4, 1383–1386 (1992).

D. Yevick, W. Bardyszewski, B. Hermansson, M. Glasner, “Split-operator electric field reflection techniques,” Photon. Technol. Lett. 3, 527–529 (1991).

J. Xu, D. Yevick, M. Gallant, “Approximate methods for electric field reflection at waveguide interfaces,” in OSA Annual Meeting, Vol. 16 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), p. 36.

IEEE J. Quantum Electron. (2)

J. Buus, M. C. Farries, D. J. Robbins, “Reflectivity of coated and tilted semiconductor facets,” IEEE J. Quantum Electron. 27, 1837–1842 (1991).
[Crossref]

D. Handelman, A. Hardy, A. Katzir, “Reflectivity of TE modes at the facets of buried heterostructure injection lasers,” IEEE J. Quantum Electron. QE-22, 498–500 (1986).
[Crossref]

J. Acoust. Soc. Am. (1)

M. D. Collins, R. B. Evans, “A two-way parabolic equation for acoustic backscattering in the ocean,” J. Acoust. Soc. Am. 91, 1357–1368 (1992).
[Crossref]

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

Photon. Technol. Lett. (2)

D. Yevick, W. Bardyszewski, B. Hermansson, M. Glasner, “Split-operator electric field reflection techniques,” Photon. Technol. Lett. 3, 527–529 (1991).

D. Yevick, J. Xu, W. Bardyszewski, “Split-operator calculations of reflected electric field profiles,” Photon. Technol. Lett. 4, 1383–1386 (1992).

Other (1)

J. Xu, D. Yevick, M. Gallant, “Approximate methods for electric field reflection at waveguide interfaces,” in OSA Annual Meeting, Vol. 16 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), p. 36.

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Figures (5)

Fig. 1
Fig. 1

Generic slab waveguide.

Fig. 2
Fig. 2

Artificial intermediate region AB employed to improve convergence.

Fig. 3
Fig. 3

Total reflected power computed with the three methods mentioned in the text for the first slab–waveguide interface.

Fig. 4
Fig. 4

Total reflected power computed with the three methods mentioned in the text for the second slab–waveguide interface.

Fig. 5
Fig. 5

Total reflected power computed with the three methods mentioned in the text for the third slab–waveguide interface.

Equations (20)

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nA(x)=ncoreA,|x|2dncladA,|x|>2d
2Eyz2+(2+k02n2)Ey=0
2=2x2+2y2
L={1+k0-2n0-2[2+k02(n2-n02)]}1/2
z+ik0n0Lz-ik0n0LEy=0.
z±ik0n0LEy=0.
Eyi+Eyr=Eyt,
Eyiz+Eyrz=Eytz,
(LA+LB)Eyr=(LA-LB)Eyi.
Eyr(k+1)=12(1-LB-1LA)(Eyr(k)-Eyi).
(LA+LAB)Eyr1=(LA-LAB)Eyi,
(LA+LB)(Eyr1+Eyr2)=(LA-LB)Eyi.
(LA+LB)Eyr2=(LAB-LB)(Eyi+Eyr1).
Eyr1(k+1)=Λ1(Eyr1(k)-Eyi),
Eyr2(k+1)=Λ1Eyr2(k)+Λ2(Eyi+Eyr1(k)+Eyr2(k)),
Λ1=12(1-LAB-1LA),
Λ2=12(1-LAB-1LB).
L=1+xj=1N 1+b2j-1,Nx1+b2j,Nx,
L-1=11+xj=1N 1+b2j,Nx1+b2j-1,Nx,
x=k0-2n0-2[2+k02(n2-n02)].

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