Abstract

The effects of the presence of metal irises on guided-mode propagation through a symmetrical three-layer slab waveguide are examined by using the integral equation method. The aperture electric field distribution is expressed in terms of a finite series of Chebyshev polynomials. The modal reflection and transmission coefficients, the near-field structure, and the far-field radiation pattern are calculated, while numerical results are presented for several iris apertures.

© 2006 Optical Society of America

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References

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  1. M. Born and E. Wolf, Principles of Optics (Pergamon, 1964).
  2. H. Hönl, A. W. Maue, and K. Westpfahl, Theorie der Beugung (Springer, 1981).
  3. J. B. Keller, "Geometrical theory of diffraction," J. Opt. Soc. Am. 52, 116-130 (1962).
    [CrossRef] [PubMed]
  4. W. B. Dou and E. K. N. Yung, "Diffraction of an electromagnetic beam by an aperture in a conducting screen," J. Opt. Soc. Am. A 18, 801-806 (2001).
    [CrossRef]
  5. J. Meixner, "Behaviour of electromagnetic fields at edges," IEEE Trans. Antennas Propag. AP-20, 442-446 (1972).
    [CrossRef]
  6. A. G. Fox and T. Li, "Resonant modes in maser interferometer," Bell Syst. Tech. J. 40, 451-488 (1961).
  7. A. F. Goncharov, G. N. Zhizhin, S. A. Kiselev, L. A. Kuzik, and V. A. Sakovlev, "Determination of the dielectrical constant of YBa2Cu3O7−δ single crystals in the 10μm spectral range by sew phase spectroscopy," Phys. Lett. A 133, 163-166 (1988).
    [CrossRef]
  8. E. V. Alieva, V. A. Yakovlev, V. I. Silin, and A. Volkov, "Surface electromagnetic waves excitation from infrared to visible," Opt. Commun. 96, 218-220 (1993).
    [CrossRef]
  9. A. N. Chester, S. Martellucci, and A. M. Verga Scheggi, Optical Fiber Sensors (Nijhoff, 1967).
  10. A. V. Brovko and A. B. Manenkov, "Diffraction of the guided mode of a dielectric waveguide by metal plates," J. Commun. Technol. Electron. 49, 239-249 (2004).
  11. R. G. Hunsperger, Integrated Optics: Theory and Technology (Springer, 1984).
  12. J. Walsh, B. Johnson, G. Dattoli, and A. Renieri, "Undulator and Cherenkov free-electron lasers: a preliminary comparison," Phys. Rev. Lett. 53, 779-782 (1984).
    [CrossRef]
  13. F. Ciocci, A. Doria, G. P. Gallerano, I. Giabbai, M. F. Kimmitt, G. Messina, A. Renieri, and J. E. Walsh, "Observation of coherent millimeter and submillimeter emission from a microtron-driven Cherenkov free-electron laser," Phys. Rev. Lett. 66, 699-702 (1991).
    [CrossRef] [PubMed]
  14. L. Lewin, Theory of Waveguides (Newness-Butterworths, 1975).
  15. I. G. Tigelis and A. B. Manenkov, "Scattering from an abruptly terminated asymmetrical slab waveguide," J. Opt. Soc. Am. A 16, 523-532 (1999).
    [CrossRef]
  16. I. G. Tigelis and A. B. Manenkov, "Analysis of mode scattering from an abruptly ended dielectric slab waveguide by an accelerated iteration technique," J. Opt. Soc. Am. A 17, 2249-2259 (2000).
    [CrossRef]
  17. D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, 1974).
  18. N. F. Dasyras, I. G. Tigelis, A. D. Tsigopoulos, and A. B. Manenkov, "Calculation of the radiation modes by the Lanczos-Fourier expansion," J. Opt. Soc. Am. A 21, 1740-1749 (2004).
    [CrossRef]
  19. C. Lanczos, Applied Analysis (Prentice-Hall, 1956).
  20. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (National Bureau of Standards, 1964).
  21. P. A. Koukoutsaki, I. G. Tigelis, and A. B. Manenkov, "Guided-mode analysis by the Lanczos-Fourier expansion," J. Opt. Soc. Am. A 19, 2293-2300 (2002).
    [CrossRef]
  22. D. S. Jones, Theory of Electromagnetism (Macmillan, 1964), Chap. 8.
  23. A. B. Manenkov, "Propagation of a surface wave along a dielectric waveguide with an abrupt change of parameters. II: Solution by variational method," Izv. Vyssh. Uchebn. Zaved., Radiofiz. 25, 1484-1490 (1982).

2004 (2)

A. V. Brovko and A. B. Manenkov, "Diffraction of the guided mode of a dielectric waveguide by metal plates," J. Commun. Technol. Electron. 49, 239-249 (2004).

N. F. Dasyras, I. G. Tigelis, A. D. Tsigopoulos, and A. B. Manenkov, "Calculation of the radiation modes by the Lanczos-Fourier expansion," J. Opt. Soc. Am. A 21, 1740-1749 (2004).
[CrossRef]

2002 (1)

2001 (1)

2000 (1)

1999 (1)

1993 (1)

E. V. Alieva, V. A. Yakovlev, V. I. Silin, and A. Volkov, "Surface electromagnetic waves excitation from infrared to visible," Opt. Commun. 96, 218-220 (1993).
[CrossRef]

1991 (1)

F. Ciocci, A. Doria, G. P. Gallerano, I. Giabbai, M. F. Kimmitt, G. Messina, A. Renieri, and J. E. Walsh, "Observation of coherent millimeter and submillimeter emission from a microtron-driven Cherenkov free-electron laser," Phys. Rev. Lett. 66, 699-702 (1991).
[CrossRef] [PubMed]

1988 (1)

A. F. Goncharov, G. N. Zhizhin, S. A. Kiselev, L. A. Kuzik, and V. A. Sakovlev, "Determination of the dielectrical constant of YBa2Cu3O7−δ single crystals in the 10μm spectral range by sew phase spectroscopy," Phys. Lett. A 133, 163-166 (1988).
[CrossRef]

1984 (1)

J. Walsh, B. Johnson, G. Dattoli, and A. Renieri, "Undulator and Cherenkov free-electron lasers: a preliminary comparison," Phys. Rev. Lett. 53, 779-782 (1984).
[CrossRef]

1982 (1)

A. B. Manenkov, "Propagation of a surface wave along a dielectric waveguide with an abrupt change of parameters. II: Solution by variational method," Izv. Vyssh. Uchebn. Zaved., Radiofiz. 25, 1484-1490 (1982).

1972 (1)

J. Meixner, "Behaviour of electromagnetic fields at edges," IEEE Trans. Antennas Propag. AP-20, 442-446 (1972).
[CrossRef]

1962 (1)

1961 (1)

A. G. Fox and T. Li, "Resonant modes in maser interferometer," Bell Syst. Tech. J. 40, 451-488 (1961).

Abramowitz, M.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (National Bureau of Standards, 1964).

Alieva, E. V.

E. V. Alieva, V. A. Yakovlev, V. I. Silin, and A. Volkov, "Surface electromagnetic waves excitation from infrared to visible," Opt. Commun. 96, 218-220 (1993).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1964).

Brovko, A. V.

A. V. Brovko and A. B. Manenkov, "Diffraction of the guided mode of a dielectric waveguide by metal plates," J. Commun. Technol. Electron. 49, 239-249 (2004).

Chester, A. N.

A. N. Chester, S. Martellucci, and A. M. Verga Scheggi, Optical Fiber Sensors (Nijhoff, 1967).

Ciocci, F.

F. Ciocci, A. Doria, G. P. Gallerano, I. Giabbai, M. F. Kimmitt, G. Messina, A. Renieri, and J. E. Walsh, "Observation of coherent millimeter and submillimeter emission from a microtron-driven Cherenkov free-electron laser," Phys. Rev. Lett. 66, 699-702 (1991).
[CrossRef] [PubMed]

Dasyras, N. F.

Dattoli, G.

J. Walsh, B. Johnson, G. Dattoli, and A. Renieri, "Undulator and Cherenkov free-electron lasers: a preliminary comparison," Phys. Rev. Lett. 53, 779-782 (1984).
[CrossRef]

Doria, A.

F. Ciocci, A. Doria, G. P. Gallerano, I. Giabbai, M. F. Kimmitt, G. Messina, A. Renieri, and J. E. Walsh, "Observation of coherent millimeter and submillimeter emission from a microtron-driven Cherenkov free-electron laser," Phys. Rev. Lett. 66, 699-702 (1991).
[CrossRef] [PubMed]

Dou, W. B.

Fox, A. G.

A. G. Fox and T. Li, "Resonant modes in maser interferometer," Bell Syst. Tech. J. 40, 451-488 (1961).

Gallerano, G. P.

F. Ciocci, A. Doria, G. P. Gallerano, I. Giabbai, M. F. Kimmitt, G. Messina, A. Renieri, and J. E. Walsh, "Observation of coherent millimeter and submillimeter emission from a microtron-driven Cherenkov free-electron laser," Phys. Rev. Lett. 66, 699-702 (1991).
[CrossRef] [PubMed]

Giabbai, I.

F. Ciocci, A. Doria, G. P. Gallerano, I. Giabbai, M. F. Kimmitt, G. Messina, A. Renieri, and J. E. Walsh, "Observation of coherent millimeter and submillimeter emission from a microtron-driven Cherenkov free-electron laser," Phys. Rev. Lett. 66, 699-702 (1991).
[CrossRef] [PubMed]

Goncharov, A. F.

A. F. Goncharov, G. N. Zhizhin, S. A. Kiselev, L. A. Kuzik, and V. A. Sakovlev, "Determination of the dielectrical constant of YBa2Cu3O7−δ single crystals in the 10μm spectral range by sew phase spectroscopy," Phys. Lett. A 133, 163-166 (1988).
[CrossRef]

Hönl, H.

H. Hönl, A. W. Maue, and K. Westpfahl, Theorie der Beugung (Springer, 1981).

Hunsperger, R. G.

R. G. Hunsperger, Integrated Optics: Theory and Technology (Springer, 1984).

Johnson, B.

J. Walsh, B. Johnson, G. Dattoli, and A. Renieri, "Undulator and Cherenkov free-electron lasers: a preliminary comparison," Phys. Rev. Lett. 53, 779-782 (1984).
[CrossRef]

Jones, D. S.

D. S. Jones, Theory of Electromagnetism (Macmillan, 1964), Chap. 8.

Keller, J. B.

Kimmitt, M. F.

F. Ciocci, A. Doria, G. P. Gallerano, I. Giabbai, M. F. Kimmitt, G. Messina, A. Renieri, and J. E. Walsh, "Observation of coherent millimeter and submillimeter emission from a microtron-driven Cherenkov free-electron laser," Phys. Rev. Lett. 66, 699-702 (1991).
[CrossRef] [PubMed]

Kiselev, S. A.

A. F. Goncharov, G. N. Zhizhin, S. A. Kiselev, L. A. Kuzik, and V. A. Sakovlev, "Determination of the dielectrical constant of YBa2Cu3O7−δ single crystals in the 10μm spectral range by sew phase spectroscopy," Phys. Lett. A 133, 163-166 (1988).
[CrossRef]

Koukoutsaki, P. A.

Kuzik, L. A.

A. F. Goncharov, G. N. Zhizhin, S. A. Kiselev, L. A. Kuzik, and V. A. Sakovlev, "Determination of the dielectrical constant of YBa2Cu3O7−δ single crystals in the 10μm spectral range by sew phase spectroscopy," Phys. Lett. A 133, 163-166 (1988).
[CrossRef]

Lanczos, C.

C. Lanczos, Applied Analysis (Prentice-Hall, 1956).

Lewin, L.

L. Lewin, Theory of Waveguides (Newness-Butterworths, 1975).

Li, T.

A. G. Fox and T. Li, "Resonant modes in maser interferometer," Bell Syst. Tech. J. 40, 451-488 (1961).

Manenkov, A. B.

Marcuse, D.

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, 1974).

Martellucci, S.

A. N. Chester, S. Martellucci, and A. M. Verga Scheggi, Optical Fiber Sensors (Nijhoff, 1967).

Maue, A. W.

H. Hönl, A. W. Maue, and K. Westpfahl, Theorie der Beugung (Springer, 1981).

Meixner, J.

J. Meixner, "Behaviour of electromagnetic fields at edges," IEEE Trans. Antennas Propag. AP-20, 442-446 (1972).
[CrossRef]

Messina, G.

F. Ciocci, A. Doria, G. P. Gallerano, I. Giabbai, M. F. Kimmitt, G. Messina, A. Renieri, and J. E. Walsh, "Observation of coherent millimeter and submillimeter emission from a microtron-driven Cherenkov free-electron laser," Phys. Rev. Lett. 66, 699-702 (1991).
[CrossRef] [PubMed]

Renieri, A.

F. Ciocci, A. Doria, G. P. Gallerano, I. Giabbai, M. F. Kimmitt, G. Messina, A. Renieri, and J. E. Walsh, "Observation of coherent millimeter and submillimeter emission from a microtron-driven Cherenkov free-electron laser," Phys. Rev. Lett. 66, 699-702 (1991).
[CrossRef] [PubMed]

J. Walsh, B. Johnson, G. Dattoli, and A. Renieri, "Undulator and Cherenkov free-electron lasers: a preliminary comparison," Phys. Rev. Lett. 53, 779-782 (1984).
[CrossRef]

Sakovlev, V. A.

A. F. Goncharov, G. N. Zhizhin, S. A. Kiselev, L. A. Kuzik, and V. A. Sakovlev, "Determination of the dielectrical constant of YBa2Cu3O7−δ single crystals in the 10μm spectral range by sew phase spectroscopy," Phys. Lett. A 133, 163-166 (1988).
[CrossRef]

Silin, V. I.

E. V. Alieva, V. A. Yakovlev, V. I. Silin, and A. Volkov, "Surface electromagnetic waves excitation from infrared to visible," Opt. Commun. 96, 218-220 (1993).
[CrossRef]

Stegun, I. A.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (National Bureau of Standards, 1964).

Tigelis, I. G.

Tsigopoulos, A. D.

Verga Scheggi, A. M.

A. N. Chester, S. Martellucci, and A. M. Verga Scheggi, Optical Fiber Sensors (Nijhoff, 1967).

Volkov, A.

E. V. Alieva, V. A. Yakovlev, V. I. Silin, and A. Volkov, "Surface electromagnetic waves excitation from infrared to visible," Opt. Commun. 96, 218-220 (1993).
[CrossRef]

Walsh, J.

J. Walsh, B. Johnson, G. Dattoli, and A. Renieri, "Undulator and Cherenkov free-electron lasers: a preliminary comparison," Phys. Rev. Lett. 53, 779-782 (1984).
[CrossRef]

Walsh, J. E.

F. Ciocci, A. Doria, G. P. Gallerano, I. Giabbai, M. F. Kimmitt, G. Messina, A. Renieri, and J. E. Walsh, "Observation of coherent millimeter and submillimeter emission from a microtron-driven Cherenkov free-electron laser," Phys. Rev. Lett. 66, 699-702 (1991).
[CrossRef] [PubMed]

Westpfahl, K.

H. Hönl, A. W. Maue, and K. Westpfahl, Theorie der Beugung (Springer, 1981).

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1964).

Yakovlev, V. A.

E. V. Alieva, V. A. Yakovlev, V. I. Silin, and A. Volkov, "Surface electromagnetic waves excitation from infrared to visible," Opt. Commun. 96, 218-220 (1993).
[CrossRef]

Yung, E. K. N.

Zhizhin, G. N.

A. F. Goncharov, G. N. Zhizhin, S. A. Kiselev, L. A. Kuzik, and V. A. Sakovlev, "Determination of the dielectrical constant of YBa2Cu3O7−δ single crystals in the 10μm spectral range by sew phase spectroscopy," Phys. Lett. A 133, 163-166 (1988).
[CrossRef]

Bell Syst. Tech. J. (1)

A. G. Fox and T. Li, "Resonant modes in maser interferometer," Bell Syst. Tech. J. 40, 451-488 (1961).

IEEE Trans. Antennas Propag. (1)

J. Meixner, "Behaviour of electromagnetic fields at edges," IEEE Trans. Antennas Propag. AP-20, 442-446 (1972).
[CrossRef]

Izv. Vyssh. Uchebn. Zaved., Radiofiz. (1)

A. B. Manenkov, "Propagation of a surface wave along a dielectric waveguide with an abrupt change of parameters. II: Solution by variational method," Izv. Vyssh. Uchebn. Zaved., Radiofiz. 25, 1484-1490 (1982).

J. Commun. Technol. Electron. (1)

A. V. Brovko and A. B. Manenkov, "Diffraction of the guided mode of a dielectric waveguide by metal plates," J. Commun. Technol. Electron. 49, 239-249 (2004).

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (5)

Opt. Commun. (1)

E. V. Alieva, V. A. Yakovlev, V. I. Silin, and A. Volkov, "Surface electromagnetic waves excitation from infrared to visible," Opt. Commun. 96, 218-220 (1993).
[CrossRef]

Phys. Lett. A (1)

A. F. Goncharov, G. N. Zhizhin, S. A. Kiselev, L. A. Kuzik, and V. A. Sakovlev, "Determination of the dielectrical constant of YBa2Cu3O7−δ single crystals in the 10μm spectral range by sew phase spectroscopy," Phys. Lett. A 133, 163-166 (1988).
[CrossRef]

Phys. Rev. Lett. (2)

J. Walsh, B. Johnson, G. Dattoli, and A. Renieri, "Undulator and Cherenkov free-electron lasers: a preliminary comparison," Phys. Rev. Lett. 53, 779-782 (1984).
[CrossRef]

F. Ciocci, A. Doria, G. P. Gallerano, I. Giabbai, M. F. Kimmitt, G. Messina, A. Renieri, and J. E. Walsh, "Observation of coherent millimeter and submillimeter emission from a microtron-driven Cherenkov free-electron laser," Phys. Rev. Lett. 66, 699-702 (1991).
[CrossRef] [PubMed]

Other (9)

L. Lewin, Theory of Waveguides (Newness-Butterworths, 1975).

R. G. Hunsperger, Integrated Optics: Theory and Technology (Springer, 1984).

C. Lanczos, Applied Analysis (Prentice-Hall, 1956).

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (National Bureau of Standards, 1964).

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, 1974).

A. N. Chester, S. Martellucci, and A. M. Verga Scheggi, Optical Fiber Sensors (Nijhoff, 1967).

M. Born and E. Wolf, Principles of Optics (Pergamon, 1964).

H. Hönl, A. W. Maue, and K. Westpfahl, Theorie der Beugung (Springer, 1981).

D. S. Jones, Theory of Electromagnetism (Macmillan, 1964), Chap. 8.

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Figures (10)

Fig. 1
Fig. 1

Symmetrical three-layer slab waveguide with two metal irises at the plane z = 0 .

Fig. 2
Fig. 2

Reflection R g and transmission T g coefficients of the first even TE guided mode as a function of d s D for different values of M.

Fig. 3
Fig. 3

Variation of the electric field magnitude E y ( x ) at z = 0 for d s = 0.1 μ m .

Fig. 4
Fig. 4

Same as Fig. 3 but for d s = 0.2 μ m .

Fig. 5
Fig. 5

Same as Fig. 3 but for d s = 0.5 μ m .

Fig. 6
Fig. 6

Variation of E y ( x ) at z = 0 for d s = 0.025 , 0.05 , 0.1 , 0.2 , and 0.5 μ m and field distribution of the incident guided mode.

Fig. 7
Fig. 7

Electric field magnitude E y ( x ) at the near field for d s = 0.1 μ m .

Fig. 8
Fig. 8

Same as Fig. 7 but for d s = 0.2 μ m .

Fig. 9
Fig. 9

Same as Fig. 7 but for d s = 0.5 μ m .

Fig. 10
Fig. 10

Far-field pattern for three values of the iris half-aperture d s .

Equations (25)

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U g ( x ) = A g { cos ( h 2 D ) exp [ h 1 ( x D ) ] x D cos ( h 2 x ) 0 x D ,
Ψ ( x , ρ ) = { B r cos [ ρ ( x D ) + ϕ ( ρ ) ] , x D A r cos ( σ x ) , 0 x D ,
0 + U g ( x ) Ψ ( x , ρ ) d x = 0 .
E y I ( x , z ) = U g ( x ) exp ( j β g z ) + R g U g ( x ) exp ( + j β g z ) + 0 + R ( ρ ) Ψ ( x , ρ ) exp [ + j β ( ρ ) z ] d ρ ,
E y II ( x , z ) = T g U g ( x ) exp ( j β g z ) + 0 + T ( ρ ) Ψ ( x , ρ ) exp [ j β ( ρ ) z ] d ρ ,
1 + R g = T g = 0 + E ( x ) U g ( x ) d x ,
R ( ρ ) = T ( ρ ) = 0 + E ( x ) Ψ ( x , ρ ) d x .
0 + d s E ( x ) K ( x , x ) d x = β g U g ( x ) ,
K ( x , x ) = β g U g ( x ) U g ( x ) + 0 + β ( ρ ) Ψ ( x , ρ ) Ψ ( x , ρ ) d ρ .
E ( x ) = 1 ( x d s ) 2 m = 0 M 1 C m T 2 m ( x d s ) ,
x j = d s cos ( π 2 j + 1 4 M ) .
β g U g ( x j ) = β g U g ( x j ) 0 d s U g ( x ) 1 ( x d s ) 2 m = 0 M 1 C m T 2 m ( x d s ) d x + 0 + d ρ β ( ρ ) Ψ ( x j , ρ ) 0 d s Ψ ( x , ρ ) 1 ( x d s ) 2 m = 0 M 1 C m T 2 m ( x d s ) d x .
0 d s U g ( x ) 1 ( x d s ) 2 T 2 m ( x d s ) d x = P 2 m , g ,
0 d s Ψ ( x , ρ ) 1 ( x d s ) 2 T 2 m ( x d s ) d x = S 2 m , r ( ρ ) ,
R j = m = 0 M 1 C m Q j m ,
R j = β g U g ( x j ) ,
Q j m = R j P 2 m , g + 0 + β ( ρ ) Ψ ( x , ρ ) S 2 m , r ( ρ ) d ρ .
1 1 T m ( x ) T n ( x ) 1 x 2 d x = { 0 , m n π , m = n = 0 π 2 , m = n = 1 , 2 , 3 , ,
1 + R g = T g = m = 0 M 1 C m P 2 m , g ,
R ( ρ ) = T ( ρ ) = m = 0 M 1 C m S 2 m , r ( ρ ) .
E y R A D = 0 + T ( ρ ) Ψ ( x , ρ ) exp [ j β ( ρ ) z ] d ρ .
E y R A D ( r , θ ) = 2 π k 0 n 0 r B r ( ρ 0 ) T ( ρ 0 ) exp [ j k 0 n 0 ( D sin θ + r ) + j ( π 4 ) + j ϕ ( ρ 0 ) ] cos θ ,
R g ( υ ) R g ( υ ) 1 = 0 d ρ β ( ρ ) E ( x ) , Ψ ( x , ρ ) 2 β g E ( x ) , U g ( x ) 2 ,
E ( x ) , F ( x ) = d s d s E ( x ) F ( x ) d x .
E ( x ) = E 0 1 ( x d s ) 2 ,

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