Abstract

The Smith–Purcell radiation from a charge moving across a penetrable grating is studied. We account for the finite permittivity and the absorption effect of the grating and find that enhancement of the radiation will occur near particular angles of observation at which the phase-matching condition for the excitation of the surface-plasmon mode is satisfied.

© 1984 Optical Society of America

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References

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  1. R. P. Leavitt, D. E. Wortman, H. Dropkin, “Millimeter-wave orotron oscillation. Part I. Theory,” IEEE J. Quantum Electron. QE-17, 1333–1340 (1981).
    [CrossRef]
  2. D. E. Wortman, H. Dropkin, R. P. Leavitt, “Millimeter-wave oroton oscillation. Part II. Experiment,” IEEE J. Quantum Electron. QE-17, 1341–1348 (1981).
    [CrossRef]
  3. S. J. Smith, E. M. Purcell, “Visible light from localized surface charges moving across a grating,” Phys. Rev. 92, 1069 (1953).
    [CrossRef]
  4. K. Ishiguro, T. Tako, “An estimation of Smith–Purcell effect as the light source in the infrared region,” Opt. Acta 8, 25–31 (1961).
    [CrossRef]
  5. A. J. Fox, N. W. W. Smith, “Proposal for obtaining laser beat frequency radiation in the far infrared by the Smith–Purcell effect,” Proc. IEEE 52, 429–430 (1964).
    [CrossRef]
  6. G. Toraldo, Di Francia, “On the theory of some Čerenkovian effects,” Nuovo Cimento 16, 61–77 (1960).
    [CrossRef]
  7. L. B. Felsen, A. Hessel, “A network approach to the analysis of Čerenkov radiation problems,” Nuovo Cimento 19, 1065–1071 (1961).
    [CrossRef]
  8. I. Palocz, A. A. Oliner, “Leaky space-charge waves. I. Čerenkov radiation,” Proc IEEE 53, 24–36 (1965).
    [CrossRef]
  9. I. Palocz, A. A. Oliner, “Leaky space-charge waves. II. Smith–Purcell radiation,” Proc. IEEE 55, 46–56 (1967).
    [CrossRef]
  10. C. W. Barnes, K. G. Dedrick, “Radiation by an electron beam interacting with a diffraction grating. Two-dimensional theory,” J. Appl. Phys. 37, 411–418 (1966).
    [CrossRef]
  11. Eamon Lalor, “Three-dimensional theory of the Smith–Purcell effect,” Phys. Rev. A 7, 435–446 (1973).
    [CrossRef]
  12. Ye. V. Avdeyev, G. V. Voskresenskiy, “Calculation of diffraction radiation of a line source moving near a periodic delay structure,” Radiotekh. Elektron. 11, 1419–1427 (1966).
  13. Ye. V. Avdeyev, G. V. Voskresenskiy, “Radiation of a point charge which moves uniformly near a periodic system made up of perfectly conducting semiplanes,” Radiotekh. Elektron. 11, 1560–1570 (1966).
  14. Ye. V. Avdeyev, G. V. Voskresenskiy, “The radiation accompanying the uniform motion of a charged filament in the vicinity of a comb structure. General solution,” Radiotekh. Elektron. 12, 469–478 (1967).
  15. O. A. Tret’yakov, E. I. Chernyakov, V. P. Shestopalov, “Emission of electromagnetic waves by an electron beam moving above a diffraction grating,” Sov. Phys. Tech. Phys. 11, 22–25 (1966).
  16. B. M. Bolotovskii, G. V. Voskresenskii, “Diffraction radiation,” Usp. Fiz. Nauk 88, 209–251 (1966) [Sov. Phys. Usp. 9, 73–96 (1966)].
  17. B. M. Bolotovskii, G. V. Voskresenskii, “Emission from charged particles in periodic structures,” Usp. Fiz. Nauk 94, 377–416 (1968) [Sov. Phys. Usp. 11, 143–162 (1968)].
  18. P. M. van den Berg, “Smith–Purcell radiation from a line charge moving parallel to a reflection grating,”J. Opt. Soc. Am. 63, 689–698 (1973).
    [CrossRef]
  19. P. M. van den Berg, “Smith–Purcell radiation from a point charge moving parallel to a reflection grating,”J. Opt. Soc. Am. 63, 1588–1597 (1973).
    [CrossRef]
  20. P. M. van den Berg, T. H. Tan, “Smith–Purcell radiation from a line charge moving parallel to a reflection grating with rectangular profile,”J. Opt. Soc. Am. 64, 325–328 (1974).
    [CrossRef]
  21. M. C. Hutley, “An experimental study of the anomalies of sinusoidal diffraction gratings,” Opt. Acta 20, 607–624 (1973).
    [CrossRef]
  22. M. C. Hutley, V. M. Bird, “A detailed experimental study of the anomalies of a sinusoidal diffraction grating,” Opt. Acta 20, 771–782 (1973).
    [CrossRef]
  23. P. M. van den Berg, J. C. M. Borburgh, “Dispersion of surface plasmons in InSb gratings,” Appl. Phys. 3, 55–60 (1974).
    [CrossRef]
  24. S. L. Chuang, J. A. Kong, “Wave scattering from periodic rough surfaces,” Proc. IEEE 69, 1132–1144 (1981).
    [CrossRef]
  25. S. L. Chuang, J. A. Kong, “Wave scattering and guidance by dielectric waveguides with periodic surfaces,”J. Opt. Soc. Am. 73, 669–679 (1983).
    [CrossRef]
  26. P. C. Waterman, “Scattering by periodic surfaces,”J. Acoust. Soc. Am. 57, 791–802 (1975).
    [CrossRef]
  27. S. L. Chuang, “Electromagnetic and acoustic wave scattering from periodic and random rough surfaces,” Ph.D. Dissertation (Massachusetts Institute of Technology, Cambridge, Mass., 1983).
  28. L. F. Schultz, “The optical constants of silver, gold, copper, and aluminum. I. The absorption coefficient k,” J. Opt. Soc. Am. 44, 357–362 (1954).
    [CrossRef]
  29. L. G. Schulz, F. R. Tangherlini, “Optical constants of silver, gold, copper, and aluminum. II. The index of refraction,”J. Opt. Soc. Am. 44, 362–368 (1954).
    [CrossRef]
  30. L. F. Drummeter, G. Hass, “Solar absorptance and thermal emittance of evaporated coatings,” in Physics of Thin Films, G. Hass, R. E. Thun, eds. (Academic, New York, 1964).
  31. A. Hessel, “Resonance in the Smith–Purcell effect,” Can. J. Phys. 42, 1195–1211 (1964).
    [CrossRef]

1983 (1)

1981 (3)

S. L. Chuang, J. A. Kong, “Wave scattering from periodic rough surfaces,” Proc. IEEE 69, 1132–1144 (1981).
[CrossRef]

R. P. Leavitt, D. E. Wortman, H. Dropkin, “Millimeter-wave orotron oscillation. Part I. Theory,” IEEE J. Quantum Electron. QE-17, 1333–1340 (1981).
[CrossRef]

D. E. Wortman, H. Dropkin, R. P. Leavitt, “Millimeter-wave oroton oscillation. Part II. Experiment,” IEEE J. Quantum Electron. QE-17, 1341–1348 (1981).
[CrossRef]

1975 (1)

P. C. Waterman, “Scattering by periodic surfaces,”J. Acoust. Soc. Am. 57, 791–802 (1975).
[CrossRef]

1974 (2)

1973 (5)

M. C. Hutley, “An experimental study of the anomalies of sinusoidal diffraction gratings,” Opt. Acta 20, 607–624 (1973).
[CrossRef]

M. C. Hutley, V. M. Bird, “A detailed experimental study of the anomalies of a sinusoidal diffraction grating,” Opt. Acta 20, 771–782 (1973).
[CrossRef]

Eamon Lalor, “Three-dimensional theory of the Smith–Purcell effect,” Phys. Rev. A 7, 435–446 (1973).
[CrossRef]

P. M. van den Berg, “Smith–Purcell radiation from a line charge moving parallel to a reflection grating,”J. Opt. Soc. Am. 63, 689–698 (1973).
[CrossRef]

P. M. van den Berg, “Smith–Purcell radiation from a point charge moving parallel to a reflection grating,”J. Opt. Soc. Am. 63, 1588–1597 (1973).
[CrossRef]

1968 (1)

B. M. Bolotovskii, G. V. Voskresenskii, “Emission from charged particles in periodic structures,” Usp. Fiz. Nauk 94, 377–416 (1968) [Sov. Phys. Usp. 11, 143–162 (1968)].

1967 (2)

Ye. V. Avdeyev, G. V. Voskresenskiy, “The radiation accompanying the uniform motion of a charged filament in the vicinity of a comb structure. General solution,” Radiotekh. Elektron. 12, 469–478 (1967).

I. Palocz, A. A. Oliner, “Leaky space-charge waves. II. Smith–Purcell radiation,” Proc. IEEE 55, 46–56 (1967).
[CrossRef]

1966 (5)

C. W. Barnes, K. G. Dedrick, “Radiation by an electron beam interacting with a diffraction grating. Two-dimensional theory,” J. Appl. Phys. 37, 411–418 (1966).
[CrossRef]

O. A. Tret’yakov, E. I. Chernyakov, V. P. Shestopalov, “Emission of electromagnetic waves by an electron beam moving above a diffraction grating,” Sov. Phys. Tech. Phys. 11, 22–25 (1966).

B. M. Bolotovskii, G. V. Voskresenskii, “Diffraction radiation,” Usp. Fiz. Nauk 88, 209–251 (1966) [Sov. Phys. Usp. 9, 73–96 (1966)].

Ye. V. Avdeyev, G. V. Voskresenskiy, “Calculation of diffraction radiation of a line source moving near a periodic delay structure,” Radiotekh. Elektron. 11, 1419–1427 (1966).

Ye. V. Avdeyev, G. V. Voskresenskiy, “Radiation of a point charge which moves uniformly near a periodic system made up of perfectly conducting semiplanes,” Radiotekh. Elektron. 11, 1560–1570 (1966).

1965 (1)

I. Palocz, A. A. Oliner, “Leaky space-charge waves. I. Čerenkov radiation,” Proc IEEE 53, 24–36 (1965).
[CrossRef]

1964 (2)

A. J. Fox, N. W. W. Smith, “Proposal for obtaining laser beat frequency radiation in the far infrared by the Smith–Purcell effect,” Proc. IEEE 52, 429–430 (1964).
[CrossRef]

A. Hessel, “Resonance in the Smith–Purcell effect,” Can. J. Phys. 42, 1195–1211 (1964).
[CrossRef]

1961 (2)

K. Ishiguro, T. Tako, “An estimation of Smith–Purcell effect as the light source in the infrared region,” Opt. Acta 8, 25–31 (1961).
[CrossRef]

L. B. Felsen, A. Hessel, “A network approach to the analysis of Čerenkov radiation problems,” Nuovo Cimento 19, 1065–1071 (1961).
[CrossRef]

1960 (1)

G. Toraldo, Di Francia, “On the theory of some Čerenkovian effects,” Nuovo Cimento 16, 61–77 (1960).
[CrossRef]

1954 (2)

1953 (1)

S. J. Smith, E. M. Purcell, “Visible light from localized surface charges moving across a grating,” Phys. Rev. 92, 1069 (1953).
[CrossRef]

Avdeyev, Ye. V.

Ye. V. Avdeyev, G. V. Voskresenskiy, “The radiation accompanying the uniform motion of a charged filament in the vicinity of a comb structure. General solution,” Radiotekh. Elektron. 12, 469–478 (1967).

Ye. V. Avdeyev, G. V. Voskresenskiy, “Radiation of a point charge which moves uniformly near a periodic system made up of perfectly conducting semiplanes,” Radiotekh. Elektron. 11, 1560–1570 (1966).

Ye. V. Avdeyev, G. V. Voskresenskiy, “Calculation of diffraction radiation of a line source moving near a periodic delay structure,” Radiotekh. Elektron. 11, 1419–1427 (1966).

Barnes, C. W.

C. W. Barnes, K. G. Dedrick, “Radiation by an electron beam interacting with a diffraction grating. Two-dimensional theory,” J. Appl. Phys. 37, 411–418 (1966).
[CrossRef]

Bird, V. M.

M. C. Hutley, V. M. Bird, “A detailed experimental study of the anomalies of a sinusoidal diffraction grating,” Opt. Acta 20, 771–782 (1973).
[CrossRef]

Bolotovskii, B. M.

B. M. Bolotovskii, G. V. Voskresenskii, “Emission from charged particles in periodic structures,” Usp. Fiz. Nauk 94, 377–416 (1968) [Sov. Phys. Usp. 11, 143–162 (1968)].

B. M. Bolotovskii, G. V. Voskresenskii, “Diffraction radiation,” Usp. Fiz. Nauk 88, 209–251 (1966) [Sov. Phys. Usp. 9, 73–96 (1966)].

Borburgh, J. C. M.

P. M. van den Berg, J. C. M. Borburgh, “Dispersion of surface plasmons in InSb gratings,” Appl. Phys. 3, 55–60 (1974).
[CrossRef]

Chernyakov, E. I.

O. A. Tret’yakov, E. I. Chernyakov, V. P. Shestopalov, “Emission of electromagnetic waves by an electron beam moving above a diffraction grating,” Sov. Phys. Tech. Phys. 11, 22–25 (1966).

Chuang, S. L.

S. L. Chuang, J. A. Kong, “Wave scattering and guidance by dielectric waveguides with periodic surfaces,”J. Opt. Soc. Am. 73, 669–679 (1983).
[CrossRef]

S. L. Chuang, J. A. Kong, “Wave scattering from periodic rough surfaces,” Proc. IEEE 69, 1132–1144 (1981).
[CrossRef]

S. L. Chuang, “Electromagnetic and acoustic wave scattering from periodic and random rough surfaces,” Ph.D. Dissertation (Massachusetts Institute of Technology, Cambridge, Mass., 1983).

Dedrick, K. G.

C. W. Barnes, K. G. Dedrick, “Radiation by an electron beam interacting with a diffraction grating. Two-dimensional theory,” J. Appl. Phys. 37, 411–418 (1966).
[CrossRef]

Dropkin, H.

R. P. Leavitt, D. E. Wortman, H. Dropkin, “Millimeter-wave orotron oscillation. Part I. Theory,” IEEE J. Quantum Electron. QE-17, 1333–1340 (1981).
[CrossRef]

D. E. Wortman, H. Dropkin, R. P. Leavitt, “Millimeter-wave oroton oscillation. Part II. Experiment,” IEEE J. Quantum Electron. QE-17, 1341–1348 (1981).
[CrossRef]

Drummeter, L. F.

L. F. Drummeter, G. Hass, “Solar absorptance and thermal emittance of evaporated coatings,” in Physics of Thin Films, G. Hass, R. E. Thun, eds. (Academic, New York, 1964).

Felsen, L. B.

L. B. Felsen, A. Hessel, “A network approach to the analysis of Čerenkov radiation problems,” Nuovo Cimento 19, 1065–1071 (1961).
[CrossRef]

Fox, A. J.

A. J. Fox, N. W. W. Smith, “Proposal for obtaining laser beat frequency radiation in the far infrared by the Smith–Purcell effect,” Proc. IEEE 52, 429–430 (1964).
[CrossRef]

Francia, Di

G. Toraldo, Di Francia, “On the theory of some Čerenkovian effects,” Nuovo Cimento 16, 61–77 (1960).
[CrossRef]

Hass, G.

L. F. Drummeter, G. Hass, “Solar absorptance and thermal emittance of evaporated coatings,” in Physics of Thin Films, G. Hass, R. E. Thun, eds. (Academic, New York, 1964).

Hessel, A.

A. Hessel, “Resonance in the Smith–Purcell effect,” Can. J. Phys. 42, 1195–1211 (1964).
[CrossRef]

L. B. Felsen, A. Hessel, “A network approach to the analysis of Čerenkov radiation problems,” Nuovo Cimento 19, 1065–1071 (1961).
[CrossRef]

Hutley, M. C.

M. C. Hutley, “An experimental study of the anomalies of sinusoidal diffraction gratings,” Opt. Acta 20, 607–624 (1973).
[CrossRef]

M. C. Hutley, V. M. Bird, “A detailed experimental study of the anomalies of a sinusoidal diffraction grating,” Opt. Acta 20, 771–782 (1973).
[CrossRef]

Ishiguro, K.

K. Ishiguro, T. Tako, “An estimation of Smith–Purcell effect as the light source in the infrared region,” Opt. Acta 8, 25–31 (1961).
[CrossRef]

Kong, J. A.

S. L. Chuang, J. A. Kong, “Wave scattering and guidance by dielectric waveguides with periodic surfaces,”J. Opt. Soc. Am. 73, 669–679 (1983).
[CrossRef]

S. L. Chuang, J. A. Kong, “Wave scattering from periodic rough surfaces,” Proc. IEEE 69, 1132–1144 (1981).
[CrossRef]

Lalor, Eamon

Eamon Lalor, “Three-dimensional theory of the Smith–Purcell effect,” Phys. Rev. A 7, 435–446 (1973).
[CrossRef]

Leavitt, R. P.

D. E. Wortman, H. Dropkin, R. P. Leavitt, “Millimeter-wave oroton oscillation. Part II. Experiment,” IEEE J. Quantum Electron. QE-17, 1341–1348 (1981).
[CrossRef]

R. P. Leavitt, D. E. Wortman, H. Dropkin, “Millimeter-wave orotron oscillation. Part I. Theory,” IEEE J. Quantum Electron. QE-17, 1333–1340 (1981).
[CrossRef]

Oliner, A. A.

I. Palocz, A. A. Oliner, “Leaky space-charge waves. II. Smith–Purcell radiation,” Proc. IEEE 55, 46–56 (1967).
[CrossRef]

I. Palocz, A. A. Oliner, “Leaky space-charge waves. I. Čerenkov radiation,” Proc IEEE 53, 24–36 (1965).
[CrossRef]

Palocz, I.

I. Palocz, A. A. Oliner, “Leaky space-charge waves. II. Smith–Purcell radiation,” Proc. IEEE 55, 46–56 (1967).
[CrossRef]

I. Palocz, A. A. Oliner, “Leaky space-charge waves. I. Čerenkov radiation,” Proc IEEE 53, 24–36 (1965).
[CrossRef]

Purcell, E. M.

S. J. Smith, E. M. Purcell, “Visible light from localized surface charges moving across a grating,” Phys. Rev. 92, 1069 (1953).
[CrossRef]

Schultz, L. F.

Schulz, L. G.

Shestopalov, V. P.

O. A. Tret’yakov, E. I. Chernyakov, V. P. Shestopalov, “Emission of electromagnetic waves by an electron beam moving above a diffraction grating,” Sov. Phys. Tech. Phys. 11, 22–25 (1966).

Smith, N. W. W.

A. J. Fox, N. W. W. Smith, “Proposal for obtaining laser beat frequency radiation in the far infrared by the Smith–Purcell effect,” Proc. IEEE 52, 429–430 (1964).
[CrossRef]

Smith, S. J.

S. J. Smith, E. M. Purcell, “Visible light from localized surface charges moving across a grating,” Phys. Rev. 92, 1069 (1953).
[CrossRef]

Tako, T.

K. Ishiguro, T. Tako, “An estimation of Smith–Purcell effect as the light source in the infrared region,” Opt. Acta 8, 25–31 (1961).
[CrossRef]

Tan, T. H.

Tangherlini, F. R.

Toraldo, G.

G. Toraldo, Di Francia, “On the theory of some Čerenkovian effects,” Nuovo Cimento 16, 61–77 (1960).
[CrossRef]

Tret’yakov, O. A.

O. A. Tret’yakov, E. I. Chernyakov, V. P. Shestopalov, “Emission of electromagnetic waves by an electron beam moving above a diffraction grating,” Sov. Phys. Tech. Phys. 11, 22–25 (1966).

van den Berg, P. M.

Voskresenskii, G. V.

B. M. Bolotovskii, G. V. Voskresenskii, “Emission from charged particles in periodic structures,” Usp. Fiz. Nauk 94, 377–416 (1968) [Sov. Phys. Usp. 11, 143–162 (1968)].

B. M. Bolotovskii, G. V. Voskresenskii, “Diffraction radiation,” Usp. Fiz. Nauk 88, 209–251 (1966) [Sov. Phys. Usp. 9, 73–96 (1966)].

Voskresenskiy, G. V.

Ye. V. Avdeyev, G. V. Voskresenskiy, “The radiation accompanying the uniform motion of a charged filament in the vicinity of a comb structure. General solution,” Radiotekh. Elektron. 12, 469–478 (1967).

Ye. V. Avdeyev, G. V. Voskresenskiy, “Radiation of a point charge which moves uniformly near a periodic system made up of perfectly conducting semiplanes,” Radiotekh. Elektron. 11, 1560–1570 (1966).

Ye. V. Avdeyev, G. V. Voskresenskiy, “Calculation of diffraction radiation of a line source moving near a periodic delay structure,” Radiotekh. Elektron. 11, 1419–1427 (1966).

Waterman, P. C.

P. C. Waterman, “Scattering by periodic surfaces,”J. Acoust. Soc. Am. 57, 791–802 (1975).
[CrossRef]

Wortman, D. E.

R. P. Leavitt, D. E. Wortman, H. Dropkin, “Millimeter-wave orotron oscillation. Part I. Theory,” IEEE J. Quantum Electron. QE-17, 1333–1340 (1981).
[CrossRef]

D. E. Wortman, H. Dropkin, R. P. Leavitt, “Millimeter-wave oroton oscillation. Part II. Experiment,” IEEE J. Quantum Electron. QE-17, 1341–1348 (1981).
[CrossRef]

Appl. Phys. (1)

P. M. van den Berg, J. C. M. Borburgh, “Dispersion of surface plasmons in InSb gratings,” Appl. Phys. 3, 55–60 (1974).
[CrossRef]

Can. J. Phys. (1)

A. Hessel, “Resonance in the Smith–Purcell effect,” Can. J. Phys. 42, 1195–1211 (1964).
[CrossRef]

IEEE J. Quantum Electron. (2)

R. P. Leavitt, D. E. Wortman, H. Dropkin, “Millimeter-wave orotron oscillation. Part I. Theory,” IEEE J. Quantum Electron. QE-17, 1333–1340 (1981).
[CrossRef]

D. E. Wortman, H. Dropkin, R. P. Leavitt, “Millimeter-wave oroton oscillation. Part II. Experiment,” IEEE J. Quantum Electron. QE-17, 1341–1348 (1981).
[CrossRef]

J. Acoust. Soc. Am. (1)

P. C. Waterman, “Scattering by periodic surfaces,”J. Acoust. Soc. Am. 57, 791–802 (1975).
[CrossRef]

J. Appl. Phys. (1)

C. W. Barnes, K. G. Dedrick, “Radiation by an electron beam interacting with a diffraction grating. Two-dimensional theory,” J. Appl. Phys. 37, 411–418 (1966).
[CrossRef]

J. Opt. Soc. Am. (6)

Nuovo Cimento (2)

G. Toraldo, Di Francia, “On the theory of some Čerenkovian effects,” Nuovo Cimento 16, 61–77 (1960).
[CrossRef]

L. B. Felsen, A. Hessel, “A network approach to the analysis of Čerenkov radiation problems,” Nuovo Cimento 19, 1065–1071 (1961).
[CrossRef]

Opt. Acta (3)

K. Ishiguro, T. Tako, “An estimation of Smith–Purcell effect as the light source in the infrared region,” Opt. Acta 8, 25–31 (1961).
[CrossRef]

M. C. Hutley, “An experimental study of the anomalies of sinusoidal diffraction gratings,” Opt. Acta 20, 607–624 (1973).
[CrossRef]

M. C. Hutley, V. M. Bird, “A detailed experimental study of the anomalies of a sinusoidal diffraction grating,” Opt. Acta 20, 771–782 (1973).
[CrossRef]

Phys. Rev. (1)

S. J. Smith, E. M. Purcell, “Visible light from localized surface charges moving across a grating,” Phys. Rev. 92, 1069 (1953).
[CrossRef]

Phys. Rev. A (1)

Eamon Lalor, “Three-dimensional theory of the Smith–Purcell effect,” Phys. Rev. A 7, 435–446 (1973).
[CrossRef]

Proc IEEE (1)

I. Palocz, A. A. Oliner, “Leaky space-charge waves. I. Čerenkov radiation,” Proc IEEE 53, 24–36 (1965).
[CrossRef]

Proc. IEEE (3)

I. Palocz, A. A. Oliner, “Leaky space-charge waves. II. Smith–Purcell radiation,” Proc. IEEE 55, 46–56 (1967).
[CrossRef]

A. J. Fox, N. W. W. Smith, “Proposal for obtaining laser beat frequency radiation in the far infrared by the Smith–Purcell effect,” Proc. IEEE 52, 429–430 (1964).
[CrossRef]

S. L. Chuang, J. A. Kong, “Wave scattering from periodic rough surfaces,” Proc. IEEE 69, 1132–1144 (1981).
[CrossRef]

Radiotekh. Elektron. (3)

Ye. V. Avdeyev, G. V. Voskresenskiy, “Calculation of diffraction radiation of a line source moving near a periodic delay structure,” Radiotekh. Elektron. 11, 1419–1427 (1966).

Ye. V. Avdeyev, G. V. Voskresenskiy, “Radiation of a point charge which moves uniformly near a periodic system made up of perfectly conducting semiplanes,” Radiotekh. Elektron. 11, 1560–1570 (1966).

Ye. V. Avdeyev, G. V. Voskresenskiy, “The radiation accompanying the uniform motion of a charged filament in the vicinity of a comb structure. General solution,” Radiotekh. Elektron. 12, 469–478 (1967).

Sov. Phys. Tech. Phys. (1)

O. A. Tret’yakov, E. I. Chernyakov, V. P. Shestopalov, “Emission of electromagnetic waves by an electron beam moving above a diffraction grating,” Sov. Phys. Tech. Phys. 11, 22–25 (1966).

Usp. Fiz. Nauk (2)

B. M. Bolotovskii, G. V. Voskresenskii, “Diffraction radiation,” Usp. Fiz. Nauk 88, 209–251 (1966) [Sov. Phys. Usp. 9, 73–96 (1966)].

B. M. Bolotovskii, G. V. Voskresenskii, “Emission from charged particles in periodic structures,” Usp. Fiz. Nauk 94, 377–416 (1968) [Sov. Phys. Usp. 11, 143–162 (1968)].

Other (2)

S. L. Chuang, “Electromagnetic and acoustic wave scattering from periodic and random rough surfaces,” Ph.D. Dissertation (Massachusetts Institute of Technology, Cambridge, Mass., 1983).

L. F. Drummeter, G. Hass, “Solar absorptance and thermal emittance of evaporated coatings,” in Physics of Thin Films, G. Hass, R. E. Thun, eds. (Academic, New York, 1964).

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Figures (6)

Fig. 1
Fig. 1

The Smith–Purcell radiation from a charge moving across a grating.

Fig. 2
Fig. 2

Radiation pattern from a moving dipole v = 0.25c.

Fig. 3
Fig. 3

The radiation factors |R−1|2 from a perfectly conducting grating (dashed line) and from a silver grating (solid line). 2h/P = 0.1, v = 0.8c, and P = 1.67 μm.

Fig. 4
Fig. 4

The radiation factors for the reflected intensity |R−1|2 and the transmitted intensity ν3|T−1|2 as functions of the observation angles for a thin silver grating. P = 1.67 μm, h = 0.0835 μm, d1 = 0.12 μm, and v = 0.8c.

Fig. 5
Fig. 5

The radiation factor |R−1|2 as a function of the observation angle for a metallic grating with 1(ω) given by Eq. (24), τ = 10−14 sec, ωpτ = 20π, P = 2 μm, h = 0.1 μm, and v = 0.8c. The sharp peak at θ−1 = 71° is where the surface-plasmon mode is excited strongly.

Fig. 6
Fig. 6

Same as Fig. 5 except that v =0.84c. The sharp peak at θ−1 = 60° is due to the strong excitation of the surface-plasmon mode.

Equations (28)

Equations on this page are rendered with MathJax. Learn more.

J ( r , t ) = x ^ q v δ ( z - z 0 ) δ ( x - v t ) .
J ( r , ω ) = x ^ q δ ( z - z 0 ) exp ( i ω v x ) .
H ( r , ω ) = - y ^ q 2 exp [ i ω v x + i k z 0 ( z - z 0 ) ] ,
E ( r , ω ) = q 2 ω 0 ( z ^ ω v - x ^ k z 0 ) exp [ i ω v x + i k z 0 ( z - z 0 ) ] .
H ( r , ω ) = y ^ q 2 exp [ i ω v x - i k z 0 ( z - z 0 ) ] ,
E ( r , ω ) = q 2 ω 0 [ - z ^ ω v - x ^ k z 0 ] exp [ i ω v x - i k z 0 ( z - z 0 ) ] ,
H i ( r , ω ) = y ^ a 0 exp ( i k x 0 x - i k z 0 z ) k z 0 ,
a 0 = q 2 k z 0 exp ( i k z 0 z 0 ) ,
k x 0 = ω / v ,
H r ( r , ω ) = y ^ n b n exp ( i k x n x + i k z n z ) k z n .
H t ( r , ω ) = y ^ n A 3 n exp ( i k 3 x n x - i k 3 z n z ) ( ν 3 k 3 z n ) 1 / 2 ,
d W d ω = 1 π P d x d z Re [ E ( r , ω ) · J * ( r , ω ) ] = 2 π ω 0 Im ( b 0 a 0 * ) = 2 π ω 0 Im ( - a 0 b 0 * ) .
d W s 1 d ω = 2 π P S 1 d x ½ Re [ E ( r , ω ) × H * ( r , ω ) ] · ( - z ^ ) ,
H ( r , ω ) = H i ( r , ω ) + H r ( r , ω ) ,
E ( r , ω ) = E i ( r , ω ) + E r ( r , ω ) ,
d W s 1 d ω = 2 π ω 0 Im ( - a 0 b 0 * ) - 2 π k z n real b n 2 2 ω 0 .
d W s 3 d ω = 2 π n Re k 3 z n 2 ω 3 A 3 n 2 ν 3 k 3 z n exp [ 2 Im k 3 z n ( d 1 + d 2 ) ] .
k z n real η r n + k 3 z n real η t n = 1 ,
η r n = b n 2 2 Im ( - a 0 b 0 * )
η t n = 1 2 Im ( - a 0 b 0 * ) Re ν 3 k 3 z n A 3 n 2 ν 3 k 3 z n × exp [ - 2 Im k 3 z n ( d 1 + d 2 ) ] .
d I d ω = μ 0 π 2 2 c ( v P ) 4 p 1 2 ( sin θ - v / c ) 2 [ 1 - ( v / c ) sin θ ] 5 ,
b n k z n = R n q 2 exp [ i k z 0 ( z 0 - z max ) ] ,
A 3 n ( ν 3 k 3 z n ) 1 / 2 = T n q 2 exp [ i k z 0 ( z 0 - z max ) ] .
k x n = k x 0 + n 2 π P
sin θ n = c v + n λ P ,
1 ( ω ) = 0 [ 1 + i ω p 2 τ 2 ω τ ( 1 - i ω τ ) ] .
k s p = ω c [ 1 ( ω ) 1 ( ω ) + 0 ] 1 / 2
c v = [ 1 ( ω ) 1 ( ω ) + 0 ] 1 / 2 ,

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