Abstract

We calculated the spectrum of normal scalar waves in a planar waveguide with absolutely soft randomly rough boundaries. Our approach is beyond perturbation theories in the roughness heights and slopes and is based instead on the exact boundary scattering potential. The spectrum is proved to be a nearly real nonanalytic function of the dispersion ζ2 of the roughness heights (with square-root singularity) as ζ20. The opposite case of large boundary defects is summarized.

© 1998 Optical Society of America

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References

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  1. F. G. Bass, V. D. Freilikher, and I. M. Fuks, Izv. Vuzov Radiofiz. 12, 1521 (1969) [Radiophys. Quantum Electron. 12, 1189 (1972)].
  2. F. G. Bass and I. M. Fuks, Wave Scattering from Statistically Rough Surfaces (Pergamon, New York, 1979).
  3. A. G. Voronovich, Sov. Phys. Acoust. 30, 444 (1984); Sov. Phys. JETP 62, 65 (1985).
  4. A. B. Isers, A. A. Puzenko, and I. M. Fuks, Sov. Phys. Acoust. 36, 253 (1990).
  5. S. Z. Dunin and G. A. Maksimov, Sov. Phys. JETP 71, 219 (1990); Sov. Phys. Acoust. 36, 150 (1990).
  6. V. I. Tatarskii, Waves Random Media 3, 127 (1993).
    [CrossRef]
  7. A. R. McGurn and A. A. Maradudin, Phys. Rev. B 30, 3136 (1984).
    [CrossRef]
  8. S. M. Rytov, Yu. A. Kravtsov, and V. I. Tatarskii, Principles of Statistical Radiophysics (Springer-Verlag, Berlin, 1989).

1993 (1)

V. I. Tatarskii, Waves Random Media 3, 127 (1993).
[CrossRef]

1990 (2)

A. B. Isers, A. A. Puzenko, and I. M. Fuks, Sov. Phys. Acoust. 36, 253 (1990).

S. Z. Dunin and G. A. Maksimov, Sov. Phys. JETP 71, 219 (1990); Sov. Phys. Acoust. 36, 150 (1990).

1984 (2)

A. G. Voronovich, Sov. Phys. Acoust. 30, 444 (1984); Sov. Phys. JETP 62, 65 (1985).

A. R. McGurn and A. A. Maradudin, Phys. Rev. B 30, 3136 (1984).
[CrossRef]

1969 (1)

F. G. Bass, V. D. Freilikher, and I. M. Fuks, Izv. Vuzov Radiofiz. 12, 1521 (1969) [Radiophys. Quantum Electron. 12, 1189 (1972)].

Bass, F. G.

F. G. Bass, V. D. Freilikher, and I. M. Fuks, Izv. Vuzov Radiofiz. 12, 1521 (1969) [Radiophys. Quantum Electron. 12, 1189 (1972)].

F. G. Bass and I. M. Fuks, Wave Scattering from Statistically Rough Surfaces (Pergamon, New York, 1979).

Dunin, S. Z.

S. Z. Dunin and G. A. Maksimov, Sov. Phys. JETP 71, 219 (1990); Sov. Phys. Acoust. 36, 150 (1990).

Freilikher, V. D.

F. G. Bass, V. D. Freilikher, and I. M. Fuks, Izv. Vuzov Radiofiz. 12, 1521 (1969) [Radiophys. Quantum Electron. 12, 1189 (1972)].

Fuks, I. M.

A. B. Isers, A. A. Puzenko, and I. M. Fuks, Sov. Phys. Acoust. 36, 253 (1990).

F. G. Bass, V. D. Freilikher, and I. M. Fuks, Izv. Vuzov Radiofiz. 12, 1521 (1969) [Radiophys. Quantum Electron. 12, 1189 (1972)].

F. G. Bass and I. M. Fuks, Wave Scattering from Statistically Rough Surfaces (Pergamon, New York, 1979).

Isers, A. B.

A. B. Isers, A. A. Puzenko, and I. M. Fuks, Sov. Phys. Acoust. 36, 253 (1990).

Kravtsov, Yu. A.

S. M. Rytov, Yu. A. Kravtsov, and V. I. Tatarskii, Principles of Statistical Radiophysics (Springer-Verlag, Berlin, 1989).

Maksimov, G. A.

S. Z. Dunin and G. A. Maksimov, Sov. Phys. JETP 71, 219 (1990); Sov. Phys. Acoust. 36, 150 (1990).

Maradudin, A. A.

A. R. McGurn and A. A. Maradudin, Phys. Rev. B 30, 3136 (1984).
[CrossRef]

McGurn, A. R.

A. R. McGurn and A. A. Maradudin, Phys. Rev. B 30, 3136 (1984).
[CrossRef]

Puzenko, A. A.

A. B. Isers, A. A. Puzenko, and I. M. Fuks, Sov. Phys. Acoust. 36, 253 (1990).

Rytov, S. M.

S. M. Rytov, Yu. A. Kravtsov, and V. I. Tatarskii, Principles of Statistical Radiophysics (Springer-Verlag, Berlin, 1989).

Tatarskii, V. I.

V. I. Tatarskii, Waves Random Media 3, 127 (1993).
[CrossRef]

S. M. Rytov, Yu. A. Kravtsov, and V. I. Tatarskii, Principles of Statistical Radiophysics (Springer-Verlag, Berlin, 1989).

Voronovich, A. G.

A. G. Voronovich, Sov. Phys. Acoust. 30, 444 (1984); Sov. Phys. JETP 62, 65 (1985).

Izv. Vuzov Radiofiz. (1)

F. G. Bass, V. D. Freilikher, and I. M. Fuks, Izv. Vuzov Radiofiz. 12, 1521 (1969) [Radiophys. Quantum Electron. 12, 1189 (1972)].

Phys. Rev. B (1)

A. R. McGurn and A. A. Maradudin, Phys. Rev. B 30, 3136 (1984).
[CrossRef]

Sov. Phys. Acoust. (2)

A. G. Voronovich, Sov. Phys. Acoust. 30, 444 (1984); Sov. Phys. JETP 62, 65 (1985).

A. B. Isers, A. A. Puzenko, and I. M. Fuks, Sov. Phys. Acoust. 36, 253 (1990).

Sov. Phys. JETP (1)

S. Z. Dunin and G. A. Maksimov, Sov. Phys. JETP 71, 219 (1990); Sov. Phys. Acoust. 36, 150 (1990).

Waves Random Media (1)

V. I. Tatarskii, Waves Random Media 3, 127 (1993).
[CrossRef]

Other (2)

S. M. Rytov, Yu. A. Kravtsov, and V. I. Tatarskii, Principles of Statistical Radiophysics (Springer-Verlag, Berlin, 1989).

F. G. Bass and I. M. Fuks, Wave Scattering from Statistically Rough Surfaces (Pergamon, New York, 1979).

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Equations (17)

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ξx=0, ξxξx=ζ2Wx-x.
Gx,x;z,z=G0x-x;z,z+-dxsdzsG0x-xs;z,zsΞˆxs,zsGxs,x;zs,z,
Ξˆxs,zs=δzs-ξxszs-dξxsdxsxs,
Gx,x;z,zG¯x-x;z,z=-dkx2πexpikxx-xG¯kx;z,z,
G¯kx;z,zG0kx;z,z1-kzcotkzdMkx.
Mkx=-dzsdzsdxssinkzzskzexp-ikxxsΞˆxs,zs×G0xs-xs;zs,zsΞˆxs,zsexpikxxssinkzzskz.
δkn=γn+i2Ln-1=-Mknπn/d2/knd.
δknΛn1, δknR˜c1.
γn=ζ22πn/d2kndn=1ndπn/d2kndW˜Skn,kn-W˜Skn,-kn-πn/d2kndM2kn+2ζ2πn/d2knd×n=nd+1πn/d2knd0dx exp-knx×Reexp-iknxW˜kn,ikn;x,
Ln-1=ζ2πn/d2kndn=1ndπn/d2kndW˜Ckn,kn+W˜Ckn,-kn.
W˜kx,qx;x=4kzqzζ2-1×kz+qz2+kz+qzkx-qxkxkz-qxqz-kx-qx2kxqxkzqzSkz+qz,kz+qz;x-kz-qz2+kz-qzkx-qxkxkz+qxqz+kx-qx2kxqxkzqzSkz-qz,kz-qz;x+2kx-qx×qxkzqz-kxqzkz+kx-qxkxqxkzqz×Skz+qz,kz-qz;x,
St1,t2;x=t1t2-1sinht1t2ζ2Wx×exp-t12+t22ζ2/2,
M2kx=k22kz2dn=12Skz+πn/d,kz-πn/d;0-Skz+πn/d,kz+πn/d;0-Skz-πn/d,kz-πn/d;0-kzk2πndSkz+πn/d,kz+πn/d;0-Skz-πn/d,kz-πn/d;0.
kζ21.
γnζπn/d2/knd.
kzζ2=πn/d2ζ2min1,Λn/Rc2.
kζ21,

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