Abstract

Considered is the beam wave guidance and scattering by 2D quasi-optical reflectors modeling the components of beam waveguides. The incident field is taken as the complex-source-point field to simulate a finite-width beam generated by a small-aperture source. A numerical solution is obtained from the coupled singular integral equations (SIEs) for the surface currents on reflectors, discretized by using the recently introduced Nystrom-type quadrature formulas. This analysis is applied to study what effect the edge illumination has on the performance of a chain of confocal elliptic reflectors. We also develop a semianalytical approach for shaped reflector synthesis after a prescribed near-field pattern. Here a new point is the use of auxiliary SIEs of the same type as in the scattering analysis problem, however, for the gradient of the objective function. Sample results are presented for the synthesis of a reflector-type beam splitter.

© 2007 Optical Society of America

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References

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  1. Feature issue, "Diffractive optics applications," Appl. Opt. 34, 2399-2559 (1995).
    [PubMed]
  2. J. M. Bendickson, E. M. Glytsis, and T. K. Gaylord, "Metallic surface-relief on-axis and off-axis focusing diffractive cylindrical mirrors," J. Opt. Soc. Am. A 16, 113-130 (1999).
    [Crossref]
  3. J. M. Bendickson, E. N. Glytsis, and T. K. Gaylord, "Focusing diffractive cylindrical mirrors: rigorous evaluation of various design methods," J. Opt. Soc. Am. A 18, 1487-1494 (2001).
    [Crossref]
  4. B. Z. Katsenelenbaum, "Transmission of millimetric waves by reflection from a series of focusing mirrors (Approximate theory of millimetric wave transmission, using reflections from row of focusing mirrors)," Radio Eng. Electron. Phys. 8, 1455-1460 (1963) B. Z. Katsenelenbaum[Radiotekh. Elektron. (Moscow) 8, 1516-1522 (1963)].
  5. J. E. Degenford, M. D. Sirkis, and W. H. Steier, "The reflecting beam waveguide," IEEE Trans. Microwave Theory Tech. 12, 445-453 (1964).
    [Crossref]
  6. B. Z. Katsenelenbaum, "Quasioptical methods of generation and transmission of millimeter waves," Sov. Phys. Usp. 7, 385-400 (1964) B. Z. Katsenelenbaum[Usp. Fiz. Nauk 83, 31-105 (1964)].
    [Crossref]
  7. V. S. Averbakh, S. N. Vlasov, and V. I. Talanov, "Methods of mode selection in quasioptical systems," Radiophys. Quantum Electron. 10, 747-760 (1967) V. S. Averbakh, S. N. Vlasov, and V. I. Talanov, [Izv. Vyssh. Uchebn. Zaved. 10, 1333-1357 (1967)].
    [Crossref]
  8. R. Tremblay and A. Boivin, "Concepts and techniques of microwave optics," Appl. Opt. 5, 249-278 (1966).
    [Crossref] [PubMed]
  9. G. Goubau and P. D. Coleman, "Beam waveguides," in E.C.Okress, ed., Microwave Power Engineering (Academic, 1968), Vol. 1, pp. 228-255 (1968).
  10. P. F. Goldsmith, Quasioptical Systems: Gaussian Beam, Quasioptical Propagation and Applications (IEEE, 1998).
  11. A. Fernandez, K. M. Likin, P. Turullols, J. Teniente, R. Gonzalo, C. del Rio, J. Marti-Canales, M. Sorolla, R. Martin, "Quasioptical transmission lines for ECRH at TJ-II stellarator," Int. J. Infrared Millim. Waves 21, 1945-1957 (2000).
    [Crossref]
  12. M. K. Thumm and W. Kasparek, "Passive high-power microwave components," IEEE Trans. Plasma Sci. 30, 755-786 (2002).
    [Crossref]
  13. P. F. Goldsmith, "A quasi-optical feed system for radio-astronomical observations at mm wavelength," Bell Syst. Tech. J. 56, 1483-1501 (1977).
  14. L. B. Felsen, "Quasi-optic diffraction," in Proceedings of Symposium on Quasi-Optics (P. I. Brooklyn Press, 1964), pp. 1-40.
  15. J. A. Murphy, "Distortion of a simple Gaussian beam on reflection from off-axis ellipsoidal mirrors," Int. J. Infrared Millim. Waves 8, 1165-1187 (1987).
    [Crossref]
  16. L. Empacher and W. Kasparek, "Analysis of a multiple-beam waveguide for free-space transmission of microwaves," IEEE Trans. Antennas Propag. 49, 483-493 (2001).
    [Crossref]
  17. T. Bondo and S. B. Sorensen, "Physical optics analysis of beam waveguides using auxiliary planes," IEEE Trans. Antennas Propag. 53, 1062-1068 (2005).
    [Crossref]
  18. D. W. Prather, M. S. Mirotznik, and J. N. Mait, "Boundary integral methods applied to the analysis of diffractive optical elements," J. Opt. Soc. Am. A 14, 34-43 (1997).
    [Crossref]
  19. J. M. Bendickson, E. N. Glytsis, and T. K. Gaylord, "Scalar integral diffraction methods: unification, accuracy, and comparison with a rigorous boundary element method with application to diffractive cylindrical lenses," J. Opt. Soc. Am. A 15, 1822-1837 (1998).
    [Crossref]
  20. M. Testorf, "On the zero-thickness model of diffractive optical elements," J. Opt. Soc. Am. A 17, 1132-1133 (2000).
    [Crossref]
  21. T. Oguzer, A. I. Nosich, and A. Altintas, "E-polarized beam scattering by an open cylindrical PEC strip having arbitrary "conical-section" profile," Microwave Opt. Technol. Lett. 31, 480-484 (2001).
    [Crossref]
  22. A. A. Nosich and Y. V. Gandel, "Numerical analysis of quasi-optical multireflector antennas in 2-D with the method of discrete singularities," IEEE Trans. Antennas Propag. 55, 399-406 (2007).
    [Crossref]
  23. J. Tsalamengas, "Exponentially converging Nystrom's methods for systems of SIEs with applications to open/closed strip or slot-loaded 2-D structures," IEEE Trans. Antennas Propag. 54, 1549-1558 (2006).
    [Crossref]

2007 (1)

A. A. Nosich and Y. V. Gandel, "Numerical analysis of quasi-optical multireflector antennas in 2-D with the method of discrete singularities," IEEE Trans. Antennas Propag. 55, 399-406 (2007).
[Crossref]

2006 (1)

J. Tsalamengas, "Exponentially converging Nystrom's methods for systems of SIEs with applications to open/closed strip or slot-loaded 2-D structures," IEEE Trans. Antennas Propag. 54, 1549-1558 (2006).
[Crossref]

2005 (1)

T. Bondo and S. B. Sorensen, "Physical optics analysis of beam waveguides using auxiliary planes," IEEE Trans. Antennas Propag. 53, 1062-1068 (2005).
[Crossref]

2002 (1)

M. K. Thumm and W. Kasparek, "Passive high-power microwave components," IEEE Trans. Plasma Sci. 30, 755-786 (2002).
[Crossref]

2001 (3)

L. Empacher and W. Kasparek, "Analysis of a multiple-beam waveguide for free-space transmission of microwaves," IEEE Trans. Antennas Propag. 49, 483-493 (2001).
[Crossref]

J. M. Bendickson, E. N. Glytsis, and T. K. Gaylord, "Focusing diffractive cylindrical mirrors: rigorous evaluation of various design methods," J. Opt. Soc. Am. A 18, 1487-1494 (2001).
[Crossref]

T. Oguzer, A. I. Nosich, and A. Altintas, "E-polarized beam scattering by an open cylindrical PEC strip having arbitrary "conical-section" profile," Microwave Opt. Technol. Lett. 31, 480-484 (2001).
[Crossref]

2000 (2)

M. Testorf, "On the zero-thickness model of diffractive optical elements," J. Opt. Soc. Am. A 17, 1132-1133 (2000).
[Crossref]

A. Fernandez, K. M. Likin, P. Turullols, J. Teniente, R. Gonzalo, C. del Rio, J. Marti-Canales, M. Sorolla, R. Martin, "Quasioptical transmission lines for ECRH at TJ-II stellarator," Int. J. Infrared Millim. Waves 21, 1945-1957 (2000).
[Crossref]

1999 (1)

1998 (1)

1997 (1)

1995 (1)

1987 (1)

J. A. Murphy, "Distortion of a simple Gaussian beam on reflection from off-axis ellipsoidal mirrors," Int. J. Infrared Millim. Waves 8, 1165-1187 (1987).
[Crossref]

1977 (1)

P. F. Goldsmith, "A quasi-optical feed system for radio-astronomical observations at mm wavelength," Bell Syst. Tech. J. 56, 1483-1501 (1977).

1967 (1)

V. S. Averbakh, S. N. Vlasov, and V. I. Talanov, "Methods of mode selection in quasioptical systems," Radiophys. Quantum Electron. 10, 747-760 (1967) V. S. Averbakh, S. N. Vlasov, and V. I. Talanov, [Izv. Vyssh. Uchebn. Zaved. 10, 1333-1357 (1967)].
[Crossref]

V. S. Averbakh, S. N. Vlasov, and V. I. Talanov, "Methods of mode selection in quasioptical systems," Radiophys. Quantum Electron. 10, 747-760 (1967) V. S. Averbakh, S. N. Vlasov, and V. I. Talanov, [Izv. Vyssh. Uchebn. Zaved. 10, 1333-1357 (1967)].
[Crossref]

1966 (1)

1964 (2)

J. E. Degenford, M. D. Sirkis, and W. H. Steier, "The reflecting beam waveguide," IEEE Trans. Microwave Theory Tech. 12, 445-453 (1964).
[Crossref]

B. Z. Katsenelenbaum, "Quasioptical methods of generation and transmission of millimeter waves," Sov. Phys. Usp. 7, 385-400 (1964) B. Z. Katsenelenbaum[Usp. Fiz. Nauk 83, 31-105 (1964)].
[Crossref]

B. Z. Katsenelenbaum, "Quasioptical methods of generation and transmission of millimeter waves," Sov. Phys. Usp. 7, 385-400 (1964) B. Z. Katsenelenbaum[Usp. Fiz. Nauk 83, 31-105 (1964)].
[Crossref]

1963 (1)

B. Z. Katsenelenbaum, "Transmission of millimetric waves by reflection from a series of focusing mirrors (Approximate theory of millimetric wave transmission, using reflections from row of focusing mirrors)," Radio Eng. Electron. Phys. 8, 1455-1460 (1963) B. Z. Katsenelenbaum[Radiotekh. Elektron. (Moscow) 8, 1516-1522 (1963)].

B. Z. Katsenelenbaum, "Transmission of millimetric waves by reflection from a series of focusing mirrors (Approximate theory of millimetric wave transmission, using reflections from row of focusing mirrors)," Radio Eng. Electron. Phys. 8, 1455-1460 (1963) B. Z. Katsenelenbaum[Radiotekh. Elektron. (Moscow) 8, 1516-1522 (1963)].

Altintas, A.

T. Oguzer, A. I. Nosich, and A. Altintas, "E-polarized beam scattering by an open cylindrical PEC strip having arbitrary "conical-section" profile," Microwave Opt. Technol. Lett. 31, 480-484 (2001).
[Crossref]

Averbakh, V. S.

V. S. Averbakh, S. N. Vlasov, and V. I. Talanov, "Methods of mode selection in quasioptical systems," Radiophys. Quantum Electron. 10, 747-760 (1967) V. S. Averbakh, S. N. Vlasov, and V. I. Talanov, [Izv. Vyssh. Uchebn. Zaved. 10, 1333-1357 (1967)].
[Crossref]

V. S. Averbakh, S. N. Vlasov, and V. I. Talanov, "Methods of mode selection in quasioptical systems," Radiophys. Quantum Electron. 10, 747-760 (1967) V. S. Averbakh, S. N. Vlasov, and V. I. Talanov, [Izv. Vyssh. Uchebn. Zaved. 10, 1333-1357 (1967)].
[Crossref]

Bendickson, J. M.

Boivin, A.

Bondo, T.

T. Bondo and S. B. Sorensen, "Physical optics analysis of beam waveguides using auxiliary planes," IEEE Trans. Antennas Propag. 53, 1062-1068 (2005).
[Crossref]

Coleman, P. D.

G. Goubau and P. D. Coleman, "Beam waveguides," in E.C.Okress, ed., Microwave Power Engineering (Academic, 1968), Vol. 1, pp. 228-255 (1968).

Degenford, J. E.

J. E. Degenford, M. D. Sirkis, and W. H. Steier, "The reflecting beam waveguide," IEEE Trans. Microwave Theory Tech. 12, 445-453 (1964).
[Crossref]

del Rio, C.

A. Fernandez, K. M. Likin, P. Turullols, J. Teniente, R. Gonzalo, C. del Rio, J. Marti-Canales, M. Sorolla, R. Martin, "Quasioptical transmission lines for ECRH at TJ-II stellarator," Int. J. Infrared Millim. Waves 21, 1945-1957 (2000).
[Crossref]

Empacher, L.

L. Empacher and W. Kasparek, "Analysis of a multiple-beam waveguide for free-space transmission of microwaves," IEEE Trans. Antennas Propag. 49, 483-493 (2001).
[Crossref]

Felsen, L. B.

L. B. Felsen, "Quasi-optic diffraction," in Proceedings of Symposium on Quasi-Optics (P. I. Brooklyn Press, 1964), pp. 1-40.

Fernandez, A.

A. Fernandez, K. M. Likin, P. Turullols, J. Teniente, R. Gonzalo, C. del Rio, J. Marti-Canales, M. Sorolla, R. Martin, "Quasioptical transmission lines for ECRH at TJ-II stellarator," Int. J. Infrared Millim. Waves 21, 1945-1957 (2000).
[Crossref]

Gandel, Y. V.

A. A. Nosich and Y. V. Gandel, "Numerical analysis of quasi-optical multireflector antennas in 2-D with the method of discrete singularities," IEEE Trans. Antennas Propag. 55, 399-406 (2007).
[Crossref]

Gaylord, T. K.

Glytsis, E. M.

Glytsis, E. N.

Goldsmith, P. F.

P. F. Goldsmith, "A quasi-optical feed system for radio-astronomical observations at mm wavelength," Bell Syst. Tech. J. 56, 1483-1501 (1977).

P. F. Goldsmith, Quasioptical Systems: Gaussian Beam, Quasioptical Propagation and Applications (IEEE, 1998).

Gonzalo, R.

A. Fernandez, K. M. Likin, P. Turullols, J. Teniente, R. Gonzalo, C. del Rio, J. Marti-Canales, M. Sorolla, R. Martin, "Quasioptical transmission lines for ECRH at TJ-II stellarator," Int. J. Infrared Millim. Waves 21, 1945-1957 (2000).
[Crossref]

Goubau, G.

G. Goubau and P. D. Coleman, "Beam waveguides," in E.C.Okress, ed., Microwave Power Engineering (Academic, 1968), Vol. 1, pp. 228-255 (1968).

Kasparek, W.

M. K. Thumm and W. Kasparek, "Passive high-power microwave components," IEEE Trans. Plasma Sci. 30, 755-786 (2002).
[Crossref]

L. Empacher and W. Kasparek, "Analysis of a multiple-beam waveguide for free-space transmission of microwaves," IEEE Trans. Antennas Propag. 49, 483-493 (2001).
[Crossref]

Katsenelenbaum, B. Z.

B. Z. Katsenelenbaum, "Quasioptical methods of generation and transmission of millimeter waves," Sov. Phys. Usp. 7, 385-400 (1964) B. Z. Katsenelenbaum[Usp. Fiz. Nauk 83, 31-105 (1964)].
[Crossref]

B. Z. Katsenelenbaum, "Quasioptical methods of generation and transmission of millimeter waves," Sov. Phys. Usp. 7, 385-400 (1964) B. Z. Katsenelenbaum[Usp. Fiz. Nauk 83, 31-105 (1964)].
[Crossref]

B. Z. Katsenelenbaum, "Transmission of millimetric waves by reflection from a series of focusing mirrors (Approximate theory of millimetric wave transmission, using reflections from row of focusing mirrors)," Radio Eng. Electron. Phys. 8, 1455-1460 (1963) B. Z. Katsenelenbaum[Radiotekh. Elektron. (Moscow) 8, 1516-1522 (1963)].

B. Z. Katsenelenbaum, "Transmission of millimetric waves by reflection from a series of focusing mirrors (Approximate theory of millimetric wave transmission, using reflections from row of focusing mirrors)," Radio Eng. Electron. Phys. 8, 1455-1460 (1963) B. Z. Katsenelenbaum[Radiotekh. Elektron. (Moscow) 8, 1516-1522 (1963)].

Likin, K. M.

A. Fernandez, K. M. Likin, P. Turullols, J. Teniente, R. Gonzalo, C. del Rio, J. Marti-Canales, M. Sorolla, R. Martin, "Quasioptical transmission lines for ECRH at TJ-II stellarator," Int. J. Infrared Millim. Waves 21, 1945-1957 (2000).
[Crossref]

Mait, J. N.

Marti-Canales, J.

A. Fernandez, K. M. Likin, P. Turullols, J. Teniente, R. Gonzalo, C. del Rio, J. Marti-Canales, M. Sorolla, R. Martin, "Quasioptical transmission lines for ECRH at TJ-II stellarator," Int. J. Infrared Millim. Waves 21, 1945-1957 (2000).
[Crossref]

Martin, R.

A. Fernandez, K. M. Likin, P. Turullols, J. Teniente, R. Gonzalo, C. del Rio, J. Marti-Canales, M. Sorolla, R. Martin, "Quasioptical transmission lines for ECRH at TJ-II stellarator," Int. J. Infrared Millim. Waves 21, 1945-1957 (2000).
[Crossref]

Mirotznik, M. S.

Murphy, J. A.

J. A. Murphy, "Distortion of a simple Gaussian beam on reflection from off-axis ellipsoidal mirrors," Int. J. Infrared Millim. Waves 8, 1165-1187 (1987).
[Crossref]

Nosich, A. A.

A. A. Nosich and Y. V. Gandel, "Numerical analysis of quasi-optical multireflector antennas in 2-D with the method of discrete singularities," IEEE Trans. Antennas Propag. 55, 399-406 (2007).
[Crossref]

Nosich, A. I.

T. Oguzer, A. I. Nosich, and A. Altintas, "E-polarized beam scattering by an open cylindrical PEC strip having arbitrary "conical-section" profile," Microwave Opt. Technol. Lett. 31, 480-484 (2001).
[Crossref]

Oguzer, T.

T. Oguzer, A. I. Nosich, and A. Altintas, "E-polarized beam scattering by an open cylindrical PEC strip having arbitrary "conical-section" profile," Microwave Opt. Technol. Lett. 31, 480-484 (2001).
[Crossref]

Prather, D. W.

Sirkis, M. D.

J. E. Degenford, M. D. Sirkis, and W. H. Steier, "The reflecting beam waveguide," IEEE Trans. Microwave Theory Tech. 12, 445-453 (1964).
[Crossref]

Sorensen, S. B.

T. Bondo and S. B. Sorensen, "Physical optics analysis of beam waveguides using auxiliary planes," IEEE Trans. Antennas Propag. 53, 1062-1068 (2005).
[Crossref]

Sorolla, M.

A. Fernandez, K. M. Likin, P. Turullols, J. Teniente, R. Gonzalo, C. del Rio, J. Marti-Canales, M. Sorolla, R. Martin, "Quasioptical transmission lines for ECRH at TJ-II stellarator," Int. J. Infrared Millim. Waves 21, 1945-1957 (2000).
[Crossref]

Steier, W. H.

J. E. Degenford, M. D. Sirkis, and W. H. Steier, "The reflecting beam waveguide," IEEE Trans. Microwave Theory Tech. 12, 445-453 (1964).
[Crossref]

Talanov, V. I.

V. S. Averbakh, S. N. Vlasov, and V. I. Talanov, "Methods of mode selection in quasioptical systems," Radiophys. Quantum Electron. 10, 747-760 (1967) V. S. Averbakh, S. N. Vlasov, and V. I. Talanov, [Izv. Vyssh. Uchebn. Zaved. 10, 1333-1357 (1967)].
[Crossref]

V. S. Averbakh, S. N. Vlasov, and V. I. Talanov, "Methods of mode selection in quasioptical systems," Radiophys. Quantum Electron. 10, 747-760 (1967) V. S. Averbakh, S. N. Vlasov, and V. I. Talanov, [Izv. Vyssh. Uchebn. Zaved. 10, 1333-1357 (1967)].
[Crossref]

Teniente, J.

A. Fernandez, K. M. Likin, P. Turullols, J. Teniente, R. Gonzalo, C. del Rio, J. Marti-Canales, M. Sorolla, R. Martin, "Quasioptical transmission lines for ECRH at TJ-II stellarator," Int. J. Infrared Millim. Waves 21, 1945-1957 (2000).
[Crossref]

Testorf, M.

Thumm, M. K.

M. K. Thumm and W. Kasparek, "Passive high-power microwave components," IEEE Trans. Plasma Sci. 30, 755-786 (2002).
[Crossref]

Tremblay, R.

Tsalamengas, J.

J. Tsalamengas, "Exponentially converging Nystrom's methods for systems of SIEs with applications to open/closed strip or slot-loaded 2-D structures," IEEE Trans. Antennas Propag. 54, 1549-1558 (2006).
[Crossref]

Turullols, P.

A. Fernandez, K. M. Likin, P. Turullols, J. Teniente, R. Gonzalo, C. del Rio, J. Marti-Canales, M. Sorolla, R. Martin, "Quasioptical transmission lines for ECRH at TJ-II stellarator," Int. J. Infrared Millim. Waves 21, 1945-1957 (2000).
[Crossref]

Vlasov, S. N.

V. S. Averbakh, S. N. Vlasov, and V. I. Talanov, "Methods of mode selection in quasioptical systems," Radiophys. Quantum Electron. 10, 747-760 (1967) V. S. Averbakh, S. N. Vlasov, and V. I. Talanov, [Izv. Vyssh. Uchebn. Zaved. 10, 1333-1357 (1967)].
[Crossref]

V. S. Averbakh, S. N. Vlasov, and V. I. Talanov, "Methods of mode selection in quasioptical systems," Radiophys. Quantum Electron. 10, 747-760 (1967) V. S. Averbakh, S. N. Vlasov, and V. I. Talanov, [Izv. Vyssh. Uchebn. Zaved. 10, 1333-1357 (1967)].
[Crossref]

Appl. Opt. (2)

Bell Syst. Tech. J. (1)

P. F. Goldsmith, "A quasi-optical feed system for radio-astronomical observations at mm wavelength," Bell Syst. Tech. J. 56, 1483-1501 (1977).

IEEE Trans. Antennas Propag. (4)

L. Empacher and W. Kasparek, "Analysis of a multiple-beam waveguide for free-space transmission of microwaves," IEEE Trans. Antennas Propag. 49, 483-493 (2001).
[Crossref]

T. Bondo and S. B. Sorensen, "Physical optics analysis of beam waveguides using auxiliary planes," IEEE Trans. Antennas Propag. 53, 1062-1068 (2005).
[Crossref]

A. A. Nosich and Y. V. Gandel, "Numerical analysis of quasi-optical multireflector antennas in 2-D with the method of discrete singularities," IEEE Trans. Antennas Propag. 55, 399-406 (2007).
[Crossref]

J. Tsalamengas, "Exponentially converging Nystrom's methods for systems of SIEs with applications to open/closed strip or slot-loaded 2-D structures," IEEE Trans. Antennas Propag. 54, 1549-1558 (2006).
[Crossref]

IEEE Trans. Microwave Theory Tech. (1)

J. E. Degenford, M. D. Sirkis, and W. H. Steier, "The reflecting beam waveguide," IEEE Trans. Microwave Theory Tech. 12, 445-453 (1964).
[Crossref]

IEEE Trans. Plasma Sci. (1)

M. K. Thumm and W. Kasparek, "Passive high-power microwave components," IEEE Trans. Plasma Sci. 30, 755-786 (2002).
[Crossref]

Int. J. Infrared Millim. Waves (2)

J. A. Murphy, "Distortion of a simple Gaussian beam on reflection from off-axis ellipsoidal mirrors," Int. J. Infrared Millim. Waves 8, 1165-1187 (1987).
[Crossref]

A. Fernandez, K. M. Likin, P. Turullols, J. Teniente, R. Gonzalo, C. del Rio, J. Marti-Canales, M. Sorolla, R. Martin, "Quasioptical transmission lines for ECRH at TJ-II stellarator," Int. J. Infrared Millim. Waves 21, 1945-1957 (2000).
[Crossref]

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

Microwave Opt. Technol. Lett. (1)

T. Oguzer, A. I. Nosich, and A. Altintas, "E-polarized beam scattering by an open cylindrical PEC strip having arbitrary "conical-section" profile," Microwave Opt. Technol. Lett. 31, 480-484 (2001).
[Crossref]

Radio Eng. Electron. Phys. (1)

B. Z. Katsenelenbaum, "Transmission of millimetric waves by reflection from a series of focusing mirrors (Approximate theory of millimetric wave transmission, using reflections from row of focusing mirrors)," Radio Eng. Electron. Phys. 8, 1455-1460 (1963) B. Z. Katsenelenbaum[Radiotekh. Elektron. (Moscow) 8, 1516-1522 (1963)].

Radiophys. Quantum Electron. (1)

V. S. Averbakh, S. N. Vlasov, and V. I. Talanov, "Methods of mode selection in quasioptical systems," Radiophys. Quantum Electron. 10, 747-760 (1967) V. S. Averbakh, S. N. Vlasov, and V. I. Talanov, [Izv. Vyssh. Uchebn. Zaved. 10, 1333-1357 (1967)].
[Crossref]

Sov. Phys. Usp. (1)

B. Z. Katsenelenbaum, "Quasioptical methods of generation and transmission of millimeter waves," Sov. Phys. Usp. 7, 385-400 (1964) B. Z. Katsenelenbaum[Usp. Fiz. Nauk 83, 31-105 (1964)].
[Crossref]

Other (3)

G. Goubau and P. D. Coleman, "Beam waveguides," in E.C.Okress, ed., Microwave Power Engineering (Academic, 1968), Vol. 1, pp. 228-255 (1968).

P. F. Goldsmith, Quasioptical Systems: Gaussian Beam, Quasioptical Propagation and Applications (IEEE, 1998).

L. B. Felsen, "Quasi-optic diffraction," in Proceedings of Symposium on Quasi-Optics (P. I. Brooklyn Press, 1964), pp. 1-40.

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Figures (12)

Fig. 1
Fig. 1

Geometry of confocal three-reflector beam waveguide.

Fig. 2
Fig. 2

Geometry of elliptic reflector fed by an in-focus CSP feed.

Fig. 3
Fig. 3

Field amplitude at the focus F 2 normalized to the source field amplitude in the center of its aperture as a function of k b , for one elliptic reflector of the size d = 20 λ and β = 140 ° .

Fig. 4
Fig. 4

Near fields of focusers shaped as (a) a 1 4 ellipse, d = 12 λ k b = 2 , β = 80 ° (b) a and 1 6 ellipse with d = 12 λ k b = 10 , β = 15 ° , both with a 2 a 1 = 0.8 .

Fig. 5
Fig. 5

Field amplitudes at the focuses F 2 , F 3 , and F 4 normalized to the source field amplitude as a function of k b , for a three-reflector confocal beam waveguide fed by in-focus CSP source. The reflector size is d = 20 λ with a 2 a 1 = 0.8 , and the feed looking angle is β = 140 ° .

Fig. 6
Fig. 6

Same values as in Fig. 5 as a function of the feed orientation angle β for the same configuration of a three-reflector elliptic beam waveguide and a CSP source.

Fig. 7
Fig. 7

Edge illuminations of the first reflector as function of β for the same configuration of the three-reflector confocal elliptic beam waveguide and in-focus CSP source as in Fig. 6

Fig. 8
Fig. 8

Near field of three confocal elliptic reflectors of the size d = 20 λ with a 2 a 1 = 0.8 in-focus CSP feed parameters are k b = 4 and β = 140 ° .

Fig. 9
Fig. 9

Geometry of the reflector-type beam splitter and basic notations.

Fig. 10
Fig. 10

Near field of the initial d = 35 λ elliptic reflector with a 2 a 1 = 0.8 fed by an in-focus CSP source.

Fig. 11
Fig. 11

Initial, prescribed, and synthesized field amplitudes on a semicircular normalized contour S 2 for a nonsymmetrically fed reflector (see Fig. 10).

Fig. 12
Fig. 12

Near field of the synthesized reflector beam splitter.

Equations (8)

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U 0 ( r ) = H 0 ( 1 ) ( k r r c ) ,
i 4 q = 1 Q S q H 0 ( 1 ) ( k r q ( s q ) r p ( s p 0 ) ) j q ( s q ) d s q = U 0 ( r p ( s p 0 ) ) ,
ρ ( t 2 ) = U ( t 2 ) U ̃ ( t 2 ) , t 2 S 2 .
I [ x 1 , y 1 ] = ρ S 2 2 = ρ , ρ S 2 min .
( G ̂ i j ψ ) ( t j ) = 1 1 G i j ( t j , t i ) w ( t i ) ψ ( t i ) d t i ,
I x 1 , δ x 1 S 1 = 2 Re ρ , δ x 1 ρ S 2 .
I x 1 = 2 Re { ( U x 10 0 + G ̂ x 10 , 11 j ) ¯ ξ j ¯ ( G ̂ x 1 , 11 * ξ G ̂ x 10 , 21 * ρ ) } ,
G ̂ 11 * ξ = G ̂ 21 * ρ .

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