Abstract

A new formulation of the classical scalar beam-propagation method is derived by use of the Wigner transform. The new method is faster than the classical beam-propagation method because no Fourier transform must be computed. An example given to illustrate the proposed method shows additional advantages.

© 1997 Optical Society of America

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References

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  1. R. März, Integrated Optics: Design and Modeling (Artech, Norwood, Mass., 1995), Chap. 4.
  2. G. R. Hadley, Opt. Lett. 17, 1743 (1992).
    [CrossRef] [PubMed]
  3. A. Splett, M. Majd, and K. Petermann, IEEE Photon. Technol. Lett. 3, 4666 (1991).
  4. L. Thylen and D. Yevick, Appl. Opt. 21, 2751 (1982).
    [CrossRef] [PubMed]
  5. D. Yevick, W. Bardyszewski, B. Hermansson, and M. Glasner, IEEE Photon. Technol. Lett. 3, 527 (1991).
    [CrossRef]
  6. C. Vassallo, J. Opt. Soc. Am. A 10, 2208 (1993).
    [CrossRef]
  7. D. Yevick, Opt. Quantum Electron. 26, 185 (1994).
    [CrossRef]
  8. E. Wigner, Phys. Rev. 40, 749 (1932).
    [CrossRef]
  9. N. Marcuvitz, Proc. IEEE 68, 1380 (1980).
    [CrossRef]
  10. D. Dragoman, Appl. Opt. 35, 4142 (1996).
    [CrossRef] [PubMed]
  11. A. Yariv, Optical Electronics (CBS College Publications, New York, 1985), Chap. 2.
  12. S. S. Allen and S. L. Richardson, J. Appl. Phys. 79, 886 (1996).
    [CrossRef]

1996 (2)

S. S. Allen and S. L. Richardson, J. Appl. Phys. 79, 886 (1996).
[CrossRef]

D. Dragoman, Appl. Opt. 35, 4142 (1996).
[CrossRef] [PubMed]

1994 (1)

D. Yevick, Opt. Quantum Electron. 26, 185 (1994).
[CrossRef]

1993 (1)

1992 (1)

1991 (2)

A. Splett, M. Majd, and K. Petermann, IEEE Photon. Technol. Lett. 3, 4666 (1991).

D. Yevick, W. Bardyszewski, B. Hermansson, and M. Glasner, IEEE Photon. Technol. Lett. 3, 527 (1991).
[CrossRef]

1982 (1)

1980 (1)

N. Marcuvitz, Proc. IEEE 68, 1380 (1980).
[CrossRef]

1932 (1)

E. Wigner, Phys. Rev. 40, 749 (1932).
[CrossRef]

Allen, S. S.

S. S. Allen and S. L. Richardson, J. Appl. Phys. 79, 886 (1996).
[CrossRef]

Bardyszewski, W.

D. Yevick, W. Bardyszewski, B. Hermansson, and M. Glasner, IEEE Photon. Technol. Lett. 3, 527 (1991).
[CrossRef]

Dragoman, D.

Glasner, M.

D. Yevick, W. Bardyszewski, B. Hermansson, and M. Glasner, IEEE Photon. Technol. Lett. 3, 527 (1991).
[CrossRef]

Hadley, G. R.

Hermansson, B.

D. Yevick, W. Bardyszewski, B. Hermansson, and M. Glasner, IEEE Photon. Technol. Lett. 3, 527 (1991).
[CrossRef]

Majd, M.

A. Splett, M. Majd, and K. Petermann, IEEE Photon. Technol. Lett. 3, 4666 (1991).

Marcuvitz, N.

N. Marcuvitz, Proc. IEEE 68, 1380 (1980).
[CrossRef]

März, R.

R. März, Integrated Optics: Design and Modeling (Artech, Norwood, Mass., 1995), Chap. 4.

Petermann, K.

A. Splett, M. Majd, and K. Petermann, IEEE Photon. Technol. Lett. 3, 4666 (1991).

Richardson, S. L.

S. S. Allen and S. L. Richardson, J. Appl. Phys. 79, 886 (1996).
[CrossRef]

Splett, A.

A. Splett, M. Majd, and K. Petermann, IEEE Photon. Technol. Lett. 3, 4666 (1991).

Thylen, L.

Vassallo, C.

Wigner, E.

E. Wigner, Phys. Rev. 40, 749 (1932).
[CrossRef]

Yariv, A.

A. Yariv, Optical Electronics (CBS College Publications, New York, 1985), Chap. 2.

Yevick, D.

D. Yevick, Opt. Quantum Electron. 26, 185 (1994).
[CrossRef]

D. Yevick, W. Bardyszewski, B. Hermansson, and M. Glasner, IEEE Photon. Technol. Lett. 3, 527 (1991).
[CrossRef]

L. Thylen and D. Yevick, Appl. Opt. 21, 2751 (1982).
[CrossRef] [PubMed]

Appl. Opt. (2)

IEEE Photon. Technol. Lett. (2)

A. Splett, M. Majd, and K. Petermann, IEEE Photon. Technol. Lett. 3, 4666 (1991).

D. Yevick, W. Bardyszewski, B. Hermansson, and M. Glasner, IEEE Photon. Technol. Lett. 3, 527 (1991).
[CrossRef]

J. Appl. Phys. (1)

S. S. Allen and S. L. Richardson, J. Appl. Phys. 79, 886 (1996).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Lett. (1)

Opt. Quantum Electron. (1)

D. Yevick, Opt. Quantum Electron. 26, 185 (1994).
[CrossRef]

Phys. Rev. (1)

E. Wigner, Phys. Rev. 40, 749 (1932).
[CrossRef]

Proc. IEEE (1)

N. Marcuvitz, Proc. IEEE 68, 1380 (1980).
[CrossRef]

Other (2)

A. Yariv, Optical Electronics (CBS College Publications, New York, 1985), Chap. 2.

R. März, Integrated Optics: Design and Modeling (Artech, Norwood, Mass., 1995), Chap. 4.

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Equations (16)

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Ψz=iHΨ,
Hr, ir; z=t2+k02n2r, z,
H=D+N,
n2r, z=n¯2z+Δn2r,
Ψr, z+Δz=expiD+N2k0n¯ΔzΨr, z,
Wr, p; z=Ψr+r2,zΨ*r-r2,zexp-irpdr,
iWz=Hr-i2p,p+i2r;z1/2-Hr+i2p,p-i2r;z1/2W,=-DW+NWW,
DW=n=022n+1!k02n¯2-p21/2p2n+1i2r2n+1,
NW=k02n¯n=022n+1!Δn2r2n+1-i2p2n+1,
Wr, p; z+Δz=expiDW+NWΔzWr, p; z.
n2x, z=n02-ax21+bz,
-iWΔz=ik0αx2n¯Wp+ik02n¯2-p21/2pWx-i243k02n¯2-p21/2p33Wx3+.
Wx, p; z+Δz=WDx-Bp,-Cx+Ap; z,
iWz=ik0a1+bzx2n0Wp-i2n0k0pWx,
π[AiyΓBiyAiy/ΓBiy],
Ψr, zΨ*0, z=14π2Wr/2, p; zexpirpdp.

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