Abstract

We propose an advanced physical optics formulation for the accurate modeling of dielectric lenses used in quasi-optical systems of millimeter, submillimeter, and infrared wave applications. For comparison, we obtain an exact full-wave solution of a two-dimensional lens problem and use it as a benchmark for testing and validation of asymptotic models being considered.

© 2009 Optical Society of America

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  1. C. O'Sullivan, G. Cahill, J. A. Murphy, W. K. Gear, J. Harris, P. A. R. Ade, S. E. Church, K. L. Thompson, C. Pryke, J. Bock, M. Bowden, M. L. Brown, J. E. Carlstrom, P. G. Castro, T. Culverhouse, R. B. Friedman, K. M. Ganga, V. Haynes, J. R. Hinderks, J. Kovak, A. E. Lange, E. M. Leitch, O. E. Mallie, S. J. Melhuish, A. Orlando, L. Piccirillo, G. Pisano, N. Rajguru, B. A. Rusholme, R. Schwarz, A. N. Taylor, E. Y. S. Wu, and M. Zemcov, “The quasi-optical design of the QUaD telescope,” Infrared Phys. Technol. 51, 277-286 (2008).
  2. A. Walther, The Ray and Wave Theory of Lenses (Cambridge U. Press, 2006).
  3. C. A. Balanis, Advanced Engineering Electromagnetics (Wiley, 1989).
  4. P. Wenig, M. Schneider, and R. Weigel, “Performance analysis of a cylindric dielectric lens antenna for 77 GHz Automotive Radar,” in Proceedings of International Radar Symposium (IRS 2008), 21-23 May 2008, Wroclaw, Poland, A.Kawalec and P.Kaniewski, eds. (Institute of Radioelectronics, 2008), paper B1-1.
  5. D. Feng, Y. Yan, G. Jin, and S. Fan, “Axial focusing characteristics of diffractive microlenses based on a rigorous electromagnetic theory,” J. Opt. A, Pure Appl. Opt. 6, 1067-1071 (2004).
    [CrossRef]
  6. J.-S. Ye, B.-Z. Dong, B.-Y. Gu, G.-Z. Yang, and S.-T. Liu, “Analysis of a closed-boundary axilens with long focal depth and high transverse resolution based on rigorous electromagnetic theory,” J. Opt. Soc. Am. A 19, 2030-2035 (2002).
    [CrossRef]
  7. J.-S. Ye, B.-Y. Gu, B.-Z. Dong, and S.-T. Liu, “Application of improved first Rayleigh-Sommerfeld method to analyze the performance of cylindrical microlenses with different f-numbers,” J. Opt. Soc. Am. A 22, 862-869 (2005).
    [CrossRef]
  8. K. Duan and B. Lu, “Improved diffraction integral for studying the diffracted field of a spherical microlens,” J. Opt. Soc. Am. A 22, 2677-2681 (2005).
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  9. M. N. O. Sadiku, Numerical Techniques in Electromagnetics (CRC, 1992).
  10. C. Muller, Foundations of the Mathematical Theory of Electromagnetic Waves (Springer-Verlag, 1969).
  11. 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]
  12. G. Fikioris, “A note on the method of analytical regularization,” IEEE Antennas Propag. Mag. 43, 34-40 (2001).
    [CrossRef]
  13. S. V. Boriskina, P. Sewell, T. M. Benson, and A. I. Nosich, “Accurate simulation of two-dimensional optical microcavities with uniquely solvable boundary integral equations and trigonometric Galerkin discretization,” J. Opt. Soc. Am. A 21, 393-402 (2004).
    [CrossRef]
  14. A. V. Boriskin, A. I. Nosich, S. V. Boriskina, T. M. Benson, P. Sewell, and A. Altintas, “Lens or resonator? Electromagnetic behavior of an extended hemielliptic lens for a submillimeter-wave receiver,” Microwave Opt. Technol. Lett. 43, 515-518 (2004).
    [CrossRef]
  15. V. B. Yurchenko and A. Altintas, “Asymptotic wave-like modeling of dielectric lenses,” in Proceedings of the 6th International Conference on Antenna Theory and Techniques (ICATT 2007), 17-21 September 2007, Sevastopol, Ukraine, Y.S.Shifrin and N.N.Kolchigin, eds. (IEEE, 2007), pp. 93-98.
    [CrossRef]
  16. Y. Li and E. Wolf, “Focal shifts in diffracted converging spherical waves,” Opt. Commun. 39, 211-215 (1981).
    [CrossRef]

2008 (1)

C. O'Sullivan, G. Cahill, J. A. Murphy, W. K. Gear, J. Harris, P. A. R. Ade, S. E. Church, K. L. Thompson, C. Pryke, J. Bock, M. Bowden, M. L. Brown, J. E. Carlstrom, P. G. Castro, T. Culverhouse, R. B. Friedman, K. M. Ganga, V. Haynes, J. R. Hinderks, J. Kovak, A. E. Lange, E. M. Leitch, O. E. Mallie, S. J. Melhuish, A. Orlando, L. Piccirillo, G. Pisano, N. Rajguru, B. A. Rusholme, R. Schwarz, A. N. Taylor, E. Y. S. Wu, and M. Zemcov, “The quasi-optical design of the QUaD telescope,” Infrared Phys. Technol. 51, 277-286 (2008).

2005 (2)

2004 (3)

D. Feng, Y. Yan, G. Jin, and S. Fan, “Axial focusing characteristics of diffractive microlenses based on a rigorous electromagnetic theory,” J. Opt. A, Pure Appl. Opt. 6, 1067-1071 (2004).
[CrossRef]

A. V. Boriskin, A. I. Nosich, S. V. Boriskina, T. M. Benson, P. Sewell, and A. Altintas, “Lens or resonator? Electromagnetic behavior of an extended hemielliptic lens for a submillimeter-wave receiver,” Microwave Opt. Technol. Lett. 43, 515-518 (2004).
[CrossRef]

S. V. Boriskina, P. Sewell, T. M. Benson, and A. I. Nosich, “Accurate simulation of two-dimensional optical microcavities with uniquely solvable boundary integral equations and trigonometric Galerkin discretization,” J. Opt. Soc. Am. A 21, 393-402 (2004).
[CrossRef]

2002 (1)

2001 (1)

G. Fikioris, “A note on the method of analytical regularization,” IEEE Antennas Propag. Mag. 43, 34-40 (2001).
[CrossRef]

1997 (1)

1981 (1)

Y. Li and E. Wolf, “Focal shifts in diffracted converging spherical waves,” Opt. Commun. 39, 211-215 (1981).
[CrossRef]

Ade, P. A. R.

C. O'Sullivan, G. Cahill, J. A. Murphy, W. K. Gear, J. Harris, P. A. R. Ade, S. E. Church, K. L. Thompson, C. Pryke, J. Bock, M. Bowden, M. L. Brown, J. E. Carlstrom, P. G. Castro, T. Culverhouse, R. B. Friedman, K. M. Ganga, V. Haynes, J. R. Hinderks, J. Kovak, A. E. Lange, E. M. Leitch, O. E. Mallie, S. J. Melhuish, A. Orlando, L. Piccirillo, G. Pisano, N. Rajguru, B. A. Rusholme, R. Schwarz, A. N. Taylor, E. Y. S. Wu, and M. Zemcov, “The quasi-optical design of the QUaD telescope,” Infrared Phys. Technol. 51, 277-286 (2008).

Altintas, A.

A. V. Boriskin, A. I. Nosich, S. V. Boriskina, T. M. Benson, P. Sewell, and A. Altintas, “Lens or resonator? Electromagnetic behavior of an extended hemielliptic lens for a submillimeter-wave receiver,” Microwave Opt. Technol. Lett. 43, 515-518 (2004).
[CrossRef]

V. B. Yurchenko and A. Altintas, “Asymptotic wave-like modeling of dielectric lenses,” in Proceedings of the 6th International Conference on Antenna Theory and Techniques (ICATT 2007), 17-21 September 2007, Sevastopol, Ukraine, Y.S.Shifrin and N.N.Kolchigin, eds. (IEEE, 2007), pp. 93-98.
[CrossRef]

Balanis, C. A.

C. A. Balanis, Advanced Engineering Electromagnetics (Wiley, 1989).

Benson, T. M.

A. V. Boriskin, A. I. Nosich, S. V. Boriskina, T. M. Benson, P. Sewell, and A. Altintas, “Lens or resonator? Electromagnetic behavior of an extended hemielliptic lens for a submillimeter-wave receiver,” Microwave Opt. Technol. Lett. 43, 515-518 (2004).
[CrossRef]

S. V. Boriskina, P. Sewell, T. M. Benson, and A. I. Nosich, “Accurate simulation of two-dimensional optical microcavities with uniquely solvable boundary integral equations and trigonometric Galerkin discretization,” J. Opt. Soc. Am. A 21, 393-402 (2004).
[CrossRef]

Bock, J.

C. O'Sullivan, G. Cahill, J. A. Murphy, W. K. Gear, J. Harris, P. A. R. Ade, S. E. Church, K. L. Thompson, C. Pryke, J. Bock, M. Bowden, M. L. Brown, J. E. Carlstrom, P. G. Castro, T. Culverhouse, R. B. Friedman, K. M. Ganga, V. Haynes, J. R. Hinderks, J. Kovak, A. E. Lange, E. M. Leitch, O. E. Mallie, S. J. Melhuish, A. Orlando, L. Piccirillo, G. Pisano, N. Rajguru, B. A. Rusholme, R. Schwarz, A. N. Taylor, E. Y. S. Wu, and M. Zemcov, “The quasi-optical design of the QUaD telescope,” Infrared Phys. Technol. 51, 277-286 (2008).

Boriskin, A. V.

A. V. Boriskin, A. I. Nosich, S. V. Boriskina, T. M. Benson, P. Sewell, and A. Altintas, “Lens or resonator? Electromagnetic behavior of an extended hemielliptic lens for a submillimeter-wave receiver,” Microwave Opt. Technol. Lett. 43, 515-518 (2004).
[CrossRef]

Boriskina, S. V.

A. V. Boriskin, A. I. Nosich, S. V. Boriskina, T. M. Benson, P. Sewell, and A. Altintas, “Lens or resonator? Electromagnetic behavior of an extended hemielliptic lens for a submillimeter-wave receiver,” Microwave Opt. Technol. Lett. 43, 515-518 (2004).
[CrossRef]

S. V. Boriskina, P. Sewell, T. M. Benson, and A. I. Nosich, “Accurate simulation of two-dimensional optical microcavities with uniquely solvable boundary integral equations and trigonometric Galerkin discretization,” J. Opt. Soc. Am. A 21, 393-402 (2004).
[CrossRef]

Bowden, M.

C. O'Sullivan, G. Cahill, J. A. Murphy, W. K. Gear, J. Harris, P. A. R. Ade, S. E. Church, K. L. Thompson, C. Pryke, J. Bock, M. Bowden, M. L. Brown, J. E. Carlstrom, P. G. Castro, T. Culverhouse, R. B. Friedman, K. M. Ganga, V. Haynes, J. R. Hinderks, J. Kovak, A. E. Lange, E. M. Leitch, O. E. Mallie, S. J. Melhuish, A. Orlando, L. Piccirillo, G. Pisano, N. Rajguru, B. A. Rusholme, R. Schwarz, A. N. Taylor, E. Y. S. Wu, and M. Zemcov, “The quasi-optical design of the QUaD telescope,” Infrared Phys. Technol. 51, 277-286 (2008).

Brown, M. L.

C. O'Sullivan, G. Cahill, J. A. Murphy, W. K. Gear, J. Harris, P. A. R. Ade, S. E. Church, K. L. Thompson, C. Pryke, J. Bock, M. Bowden, M. L. Brown, J. E. Carlstrom, P. G. Castro, T. Culverhouse, R. B. Friedman, K. M. Ganga, V. Haynes, J. R. Hinderks, J. Kovak, A. E. Lange, E. M. Leitch, O. E. Mallie, S. J. Melhuish, A. Orlando, L. Piccirillo, G. Pisano, N. Rajguru, B. A. Rusholme, R. Schwarz, A. N. Taylor, E. Y. S. Wu, and M. Zemcov, “The quasi-optical design of the QUaD telescope,” Infrared Phys. Technol. 51, 277-286 (2008).

Cahill, G.

C. O'Sullivan, G. Cahill, J. A. Murphy, W. K. Gear, J. Harris, P. A. R. Ade, S. E. Church, K. L. Thompson, C. Pryke, J. Bock, M. Bowden, M. L. Brown, J. E. Carlstrom, P. G. Castro, T. Culverhouse, R. B. Friedman, K. M. Ganga, V. Haynes, J. R. Hinderks, J. Kovak, A. E. Lange, E. M. Leitch, O. E. Mallie, S. J. Melhuish, A. Orlando, L. Piccirillo, G. Pisano, N. Rajguru, B. A. Rusholme, R. Schwarz, A. N. Taylor, E. Y. S. Wu, and M. Zemcov, “The quasi-optical design of the QUaD telescope,” Infrared Phys. Technol. 51, 277-286 (2008).

Carlstrom, J. E.

C. O'Sullivan, G. Cahill, J. A. Murphy, W. K. Gear, J. Harris, P. A. R. Ade, S. E. Church, K. L. Thompson, C. Pryke, J. Bock, M. Bowden, M. L. Brown, J. E. Carlstrom, P. G. Castro, T. Culverhouse, R. B. Friedman, K. M. Ganga, V. Haynes, J. R. Hinderks, J. Kovak, A. E. Lange, E. M. Leitch, O. E. Mallie, S. J. Melhuish, A. Orlando, L. Piccirillo, G. Pisano, N. Rajguru, B. A. Rusholme, R. Schwarz, A. N. Taylor, E. Y. S. Wu, and M. Zemcov, “The quasi-optical design of the QUaD telescope,” Infrared Phys. Technol. 51, 277-286 (2008).

Castro, P. G.

C. O'Sullivan, G. Cahill, J. A. Murphy, W. K. Gear, J. Harris, P. A. R. Ade, S. E. Church, K. L. Thompson, C. Pryke, J. Bock, M. Bowden, M. L. Brown, J. E. Carlstrom, P. G. Castro, T. Culverhouse, R. B. Friedman, K. M. Ganga, V. Haynes, J. R. Hinderks, J. Kovak, A. E. Lange, E. M. Leitch, O. E. Mallie, S. J. Melhuish, A. Orlando, L. Piccirillo, G. Pisano, N. Rajguru, B. A. Rusholme, R. Schwarz, A. N. Taylor, E. Y. S. Wu, and M. Zemcov, “The quasi-optical design of the QUaD telescope,” Infrared Phys. Technol. 51, 277-286 (2008).

Church, S. E.

C. O'Sullivan, G. Cahill, J. A. Murphy, W. K. Gear, J. Harris, P. A. R. Ade, S. E. Church, K. L. Thompson, C. Pryke, J. Bock, M. Bowden, M. L. Brown, J. E. Carlstrom, P. G. Castro, T. Culverhouse, R. B. Friedman, K. M. Ganga, V. Haynes, J. R. Hinderks, J. Kovak, A. E. Lange, E. M. Leitch, O. E. Mallie, S. J. Melhuish, A. Orlando, L. Piccirillo, G. Pisano, N. Rajguru, B. A. Rusholme, R. Schwarz, A. N. Taylor, E. Y. S. Wu, and M. Zemcov, “The quasi-optical design of the QUaD telescope,” Infrared Phys. Technol. 51, 277-286 (2008).

Culverhouse, T.

C. O'Sullivan, G. Cahill, J. A. Murphy, W. K. Gear, J. Harris, P. A. R. Ade, S. E. Church, K. L. Thompson, C. Pryke, J. Bock, M. Bowden, M. L. Brown, J. E. Carlstrom, P. G. Castro, T. Culverhouse, R. B. Friedman, K. M. Ganga, V. Haynes, J. R. Hinderks, J. Kovak, A. E. Lange, E. M. Leitch, O. E. Mallie, S. J. Melhuish, A. Orlando, L. Piccirillo, G. Pisano, N. Rajguru, B. A. Rusholme, R. Schwarz, A. N. Taylor, E. Y. S. Wu, and M. Zemcov, “The quasi-optical design of the QUaD telescope,” Infrared Phys. Technol. 51, 277-286 (2008).

Dong, B.-Z.

Duan, K.

Fan, S.

D. Feng, Y. Yan, G. Jin, and S. Fan, “Axial focusing characteristics of diffractive microlenses based on a rigorous electromagnetic theory,” J. Opt. A, Pure Appl. Opt. 6, 1067-1071 (2004).
[CrossRef]

Feng, D.

D. Feng, Y. Yan, G. Jin, and S. Fan, “Axial focusing characteristics of diffractive microlenses based on a rigorous electromagnetic theory,” J. Opt. A, Pure Appl. Opt. 6, 1067-1071 (2004).
[CrossRef]

Fikioris, G.

G. Fikioris, “A note on the method of analytical regularization,” IEEE Antennas Propag. Mag. 43, 34-40 (2001).
[CrossRef]

Friedman, R. B.

C. O'Sullivan, G. Cahill, J. A. Murphy, W. K. Gear, J. Harris, P. A. R. Ade, S. E. Church, K. L. Thompson, C. Pryke, J. Bock, M. Bowden, M. L. Brown, J. E. Carlstrom, P. G. Castro, T. Culverhouse, R. B. Friedman, K. M. Ganga, V. Haynes, J. R. Hinderks, J. Kovak, A. E. Lange, E. M. Leitch, O. E. Mallie, S. J. Melhuish, A. Orlando, L. Piccirillo, G. Pisano, N. Rajguru, B. A. Rusholme, R. Schwarz, A. N. Taylor, E. Y. S. Wu, and M. Zemcov, “The quasi-optical design of the QUaD telescope,” Infrared Phys. Technol. 51, 277-286 (2008).

Ganga, K. M.

C. O'Sullivan, G. Cahill, J. A. Murphy, W. K. Gear, J. Harris, P. A. R. Ade, S. E. Church, K. L. Thompson, C. Pryke, J. Bock, M. Bowden, M. L. Brown, J. E. Carlstrom, P. G. Castro, T. Culverhouse, R. B. Friedman, K. M. Ganga, V. Haynes, J. R. Hinderks, J. Kovak, A. E. Lange, E. M. Leitch, O. E. Mallie, S. J. Melhuish, A. Orlando, L. Piccirillo, G. Pisano, N. Rajguru, B. A. Rusholme, R. Schwarz, A. N. Taylor, E. Y. S. Wu, and M. Zemcov, “The quasi-optical design of the QUaD telescope,” Infrared Phys. Technol. 51, 277-286 (2008).

Gear, W. K.

C. O'Sullivan, G. Cahill, J. A. Murphy, W. K. Gear, J. Harris, P. A. R. Ade, S. E. Church, K. L. Thompson, C. Pryke, J. Bock, M. Bowden, M. L. Brown, J. E. Carlstrom, P. G. Castro, T. Culverhouse, R. B. Friedman, K. M. Ganga, V. Haynes, J. R. Hinderks, J. Kovak, A. E. Lange, E. M. Leitch, O. E. Mallie, S. J. Melhuish, A. Orlando, L. Piccirillo, G. Pisano, N. Rajguru, B. A. Rusholme, R. Schwarz, A. N. Taylor, E. Y. S. Wu, and M. Zemcov, “The quasi-optical design of the QUaD telescope,” Infrared Phys. Technol. 51, 277-286 (2008).

Gu, B.-Y.

Harris, J.

C. O'Sullivan, G. Cahill, J. A. Murphy, W. K. Gear, J. Harris, P. A. R. Ade, S. E. Church, K. L. Thompson, C. Pryke, J. Bock, M. Bowden, M. L. Brown, J. E. Carlstrom, P. G. Castro, T. Culverhouse, R. B. Friedman, K. M. Ganga, V. Haynes, J. R. Hinderks, J. Kovak, A. E. Lange, E. M. Leitch, O. E. Mallie, S. J. Melhuish, A. Orlando, L. Piccirillo, G. Pisano, N. Rajguru, B. A. Rusholme, R. Schwarz, A. N. Taylor, E. Y. S. Wu, and M. Zemcov, “The quasi-optical design of the QUaD telescope,” Infrared Phys. Technol. 51, 277-286 (2008).

Haynes, V.

C. O'Sullivan, G. Cahill, J. A. Murphy, W. K. Gear, J. Harris, P. A. R. Ade, S. E. Church, K. L. Thompson, C. Pryke, J. Bock, M. Bowden, M. L. Brown, J. E. Carlstrom, P. G. Castro, T. Culverhouse, R. B. Friedman, K. M. Ganga, V. Haynes, J. R. Hinderks, J. Kovak, A. E. Lange, E. M. Leitch, O. E. Mallie, S. J. Melhuish, A. Orlando, L. Piccirillo, G. Pisano, N. Rajguru, B. A. Rusholme, R. Schwarz, A. N. Taylor, E. Y. S. Wu, and M. Zemcov, “The quasi-optical design of the QUaD telescope,” Infrared Phys. Technol. 51, 277-286 (2008).

Hinderks, J. R.

C. O'Sullivan, G. Cahill, J. A. Murphy, W. K. Gear, J. Harris, P. A. R. Ade, S. E. Church, K. L. Thompson, C. Pryke, J. Bock, M. Bowden, M. L. Brown, J. E. Carlstrom, P. G. Castro, T. Culverhouse, R. B. Friedman, K. M. Ganga, V. Haynes, J. R. Hinderks, J. Kovak, A. E. Lange, E. M. Leitch, O. E. Mallie, S. J. Melhuish, A. Orlando, L. Piccirillo, G. Pisano, N. Rajguru, B. A. Rusholme, R. Schwarz, A. N. Taylor, E. Y. S. Wu, and M. Zemcov, “The quasi-optical design of the QUaD telescope,” Infrared Phys. Technol. 51, 277-286 (2008).

Jin, G.

D. Feng, Y. Yan, G. Jin, and S. Fan, “Axial focusing characteristics of diffractive microlenses based on a rigorous electromagnetic theory,” J. Opt. A, Pure Appl. Opt. 6, 1067-1071 (2004).
[CrossRef]

Kovak, J.

C. O'Sullivan, G. Cahill, J. A. Murphy, W. K. Gear, J. Harris, P. A. R. Ade, S. E. Church, K. L. Thompson, C. Pryke, J. Bock, M. Bowden, M. L. Brown, J. E. Carlstrom, P. G. Castro, T. Culverhouse, R. B. Friedman, K. M. Ganga, V. Haynes, J. R. Hinderks, J. Kovak, A. E. Lange, E. M. Leitch, O. E. Mallie, S. J. Melhuish, A. Orlando, L. Piccirillo, G. Pisano, N. Rajguru, B. A. Rusholme, R. Schwarz, A. N. Taylor, E. Y. S. Wu, and M. Zemcov, “The quasi-optical design of the QUaD telescope,” Infrared Phys. Technol. 51, 277-286 (2008).

Lange, A. E.

C. O'Sullivan, G. Cahill, J. A. Murphy, W. K. Gear, J. Harris, P. A. R. Ade, S. E. Church, K. L. Thompson, C. Pryke, J. Bock, M. Bowden, M. L. Brown, J. E. Carlstrom, P. G. Castro, T. Culverhouse, R. B. Friedman, K. M. Ganga, V. Haynes, J. R. Hinderks, J. Kovak, A. E. Lange, E. M. Leitch, O. E. Mallie, S. J. Melhuish, A. Orlando, L. Piccirillo, G. Pisano, N. Rajguru, B. A. Rusholme, R. Schwarz, A. N. Taylor, E. Y. S. Wu, and M. Zemcov, “The quasi-optical design of the QUaD telescope,” Infrared Phys. Technol. 51, 277-286 (2008).

Leitch, E. M.

C. O'Sullivan, G. Cahill, J. A. Murphy, W. K. Gear, J. Harris, P. A. R. Ade, S. E. Church, K. L. Thompson, C. Pryke, J. Bock, M. Bowden, M. L. Brown, J. E. Carlstrom, P. G. Castro, T. Culverhouse, R. B. Friedman, K. M. Ganga, V. Haynes, J. R. Hinderks, J. Kovak, A. E. Lange, E. M. Leitch, O. E. Mallie, S. J. Melhuish, A. Orlando, L. Piccirillo, G. Pisano, N. Rajguru, B. A. Rusholme, R. Schwarz, A. N. Taylor, E. Y. S. Wu, and M. Zemcov, “The quasi-optical design of the QUaD telescope,” Infrared Phys. Technol. 51, 277-286 (2008).

Li, Y.

Y. Li and E. Wolf, “Focal shifts in diffracted converging spherical waves,” Opt. Commun. 39, 211-215 (1981).
[CrossRef]

Liu, S.-T.

Lu, B.

Mait, J. N.

Mallie, O. E.

C. O'Sullivan, G. Cahill, J. A. Murphy, W. K. Gear, J. Harris, P. A. R. Ade, S. E. Church, K. L. Thompson, C. Pryke, J. Bock, M. Bowden, M. L. Brown, J. E. Carlstrom, P. G. Castro, T. Culverhouse, R. B. Friedman, K. M. Ganga, V. Haynes, J. R. Hinderks, J. Kovak, A. E. Lange, E. M. Leitch, O. E. Mallie, S. J. Melhuish, A. Orlando, L. Piccirillo, G. Pisano, N. Rajguru, B. A. Rusholme, R. Schwarz, A. N. Taylor, E. Y. S. Wu, and M. Zemcov, “The quasi-optical design of the QUaD telescope,” Infrared Phys. Technol. 51, 277-286 (2008).

Melhuish, S. J.

C. O'Sullivan, G. Cahill, J. A. Murphy, W. K. Gear, J. Harris, P. A. R. Ade, S. E. Church, K. L. Thompson, C. Pryke, J. Bock, M. Bowden, M. L. Brown, J. E. Carlstrom, P. G. Castro, T. Culverhouse, R. B. Friedman, K. M. Ganga, V. Haynes, J. R. Hinderks, J. Kovak, A. E. Lange, E. M. Leitch, O. E. Mallie, S. J. Melhuish, A. Orlando, L. Piccirillo, G. Pisano, N. Rajguru, B. A. Rusholme, R. Schwarz, A. N. Taylor, E. Y. S. Wu, and M. Zemcov, “The quasi-optical design of the QUaD telescope,” Infrared Phys. Technol. 51, 277-286 (2008).

Mirotznik, M. S.

Muller, C.

C. Muller, Foundations of the Mathematical Theory of Electromagnetic Waves (Springer-Verlag, 1969).

Murphy, J. A.

C. O'Sullivan, G. Cahill, J. A. Murphy, W. K. Gear, J. Harris, P. A. R. Ade, S. E. Church, K. L. Thompson, C. Pryke, J. Bock, M. Bowden, M. L. Brown, J. E. Carlstrom, P. G. Castro, T. Culverhouse, R. B. Friedman, K. M. Ganga, V. Haynes, J. R. Hinderks, J. Kovak, A. E. Lange, E. M. Leitch, O. E. Mallie, S. J. Melhuish, A. Orlando, L. Piccirillo, G. Pisano, N. Rajguru, B. A. Rusholme, R. Schwarz, A. N. Taylor, E. Y. S. Wu, and M. Zemcov, “The quasi-optical design of the QUaD telescope,” Infrared Phys. Technol. 51, 277-286 (2008).

Nosich, A. I.

A. V. Boriskin, A. I. Nosich, S. V. Boriskina, T. M. Benson, P. Sewell, and A. Altintas, “Lens or resonator? Electromagnetic behavior of an extended hemielliptic lens for a submillimeter-wave receiver,” Microwave Opt. Technol. Lett. 43, 515-518 (2004).
[CrossRef]

S. V. Boriskina, P. Sewell, T. M. Benson, and A. I. Nosich, “Accurate simulation of two-dimensional optical microcavities with uniquely solvable boundary integral equations and trigonometric Galerkin discretization,” J. Opt. Soc. Am. A 21, 393-402 (2004).
[CrossRef]

Orlando, A.

C. O'Sullivan, G. Cahill, J. A. Murphy, W. K. Gear, J. Harris, P. A. R. Ade, S. E. Church, K. L. Thompson, C. Pryke, J. Bock, M. Bowden, M. L. Brown, J. E. Carlstrom, P. G. Castro, T. Culverhouse, R. B. Friedman, K. M. Ganga, V. Haynes, J. R. Hinderks, J. Kovak, A. E. Lange, E. M. Leitch, O. E. Mallie, S. J. Melhuish, A. Orlando, L. Piccirillo, G. Pisano, N. Rajguru, B. A. Rusholme, R. Schwarz, A. N. Taylor, E. Y. S. Wu, and M. Zemcov, “The quasi-optical design of the QUaD telescope,” Infrared Phys. Technol. 51, 277-286 (2008).

O'Sullivan, C.

C. O'Sullivan, G. Cahill, J. A. Murphy, W. K. Gear, J. Harris, P. A. R. Ade, S. E. Church, K. L. Thompson, C. Pryke, J. Bock, M. Bowden, M. L. Brown, J. E. Carlstrom, P. G. Castro, T. Culverhouse, R. B. Friedman, K. M. Ganga, V. Haynes, J. R. Hinderks, J. Kovak, A. E. Lange, E. M. Leitch, O. E. Mallie, S. J. Melhuish, A. Orlando, L. Piccirillo, G. Pisano, N. Rajguru, B. A. Rusholme, R. Schwarz, A. N. Taylor, E. Y. S. Wu, and M. Zemcov, “The quasi-optical design of the QUaD telescope,” Infrared Phys. Technol. 51, 277-286 (2008).

Piccirillo, L.

C. O'Sullivan, G. Cahill, J. A. Murphy, W. K. Gear, J. Harris, P. A. R. Ade, S. E. Church, K. L. Thompson, C. Pryke, J. Bock, M. Bowden, M. L. Brown, J. E. Carlstrom, P. G. Castro, T. Culverhouse, R. B. Friedman, K. M. Ganga, V. Haynes, J. R. Hinderks, J. Kovak, A. E. Lange, E. M. Leitch, O. E. Mallie, S. J. Melhuish, A. Orlando, L. Piccirillo, G. Pisano, N. Rajguru, B. A. Rusholme, R. Schwarz, A. N. Taylor, E. Y. S. Wu, and M. Zemcov, “The quasi-optical design of the QUaD telescope,” Infrared Phys. Technol. 51, 277-286 (2008).

Pisano, G.

C. O'Sullivan, G. Cahill, J. A. Murphy, W. K. Gear, J. Harris, P. A. R. Ade, S. E. Church, K. L. Thompson, C. Pryke, J. Bock, M. Bowden, M. L. Brown, J. E. Carlstrom, P. G. Castro, T. Culverhouse, R. B. Friedman, K. M. Ganga, V. Haynes, J. R. Hinderks, J. Kovak, A. E. Lange, E. M. Leitch, O. E. Mallie, S. J. Melhuish, A. Orlando, L. Piccirillo, G. Pisano, N. Rajguru, B. A. Rusholme, R. Schwarz, A. N. Taylor, E. Y. S. Wu, and M. Zemcov, “The quasi-optical design of the QUaD telescope,” Infrared Phys. Technol. 51, 277-286 (2008).

Prather, D. W.

Pryke, C.

C. O'Sullivan, G. Cahill, J. A. Murphy, W. K. Gear, J. Harris, P. A. R. Ade, S. E. Church, K. L. Thompson, C. Pryke, J. Bock, M. Bowden, M. L. Brown, J. E. Carlstrom, P. G. Castro, T. Culverhouse, R. B. Friedman, K. M. Ganga, V. Haynes, J. R. Hinderks, J. Kovak, A. E. Lange, E. M. Leitch, O. E. Mallie, S. J. Melhuish, A. Orlando, L. Piccirillo, G. Pisano, N. Rajguru, B. A. Rusholme, R. Schwarz, A. N. Taylor, E. Y. S. Wu, and M. Zemcov, “The quasi-optical design of the QUaD telescope,” Infrared Phys. Technol. 51, 277-286 (2008).

Rajguru, N.

C. O'Sullivan, G. Cahill, J. A. Murphy, W. K. Gear, J. Harris, P. A. R. Ade, S. E. Church, K. L. Thompson, C. Pryke, J. Bock, M. Bowden, M. L. Brown, J. E. Carlstrom, P. G. Castro, T. Culverhouse, R. B. Friedman, K. M. Ganga, V. Haynes, J. R. Hinderks, J. Kovak, A. E. Lange, E. M. Leitch, O. E. Mallie, S. J. Melhuish, A. Orlando, L. Piccirillo, G. Pisano, N. Rajguru, B. A. Rusholme, R. Schwarz, A. N. Taylor, E. Y. S. Wu, and M. Zemcov, “The quasi-optical design of the QUaD telescope,” Infrared Phys. Technol. 51, 277-286 (2008).

Rusholme, B. A.

C. O'Sullivan, G. Cahill, J. A. Murphy, W. K. Gear, J. Harris, P. A. R. Ade, S. E. Church, K. L. Thompson, C. Pryke, J. Bock, M. Bowden, M. L. Brown, J. E. Carlstrom, P. G. Castro, T. Culverhouse, R. B. Friedman, K. M. Ganga, V. Haynes, J. R. Hinderks, J. Kovak, A. E. Lange, E. M. Leitch, O. E. Mallie, S. J. Melhuish, A. Orlando, L. Piccirillo, G. Pisano, N. Rajguru, B. A. Rusholme, R. Schwarz, A. N. Taylor, E. Y. S. Wu, and M. Zemcov, “The quasi-optical design of the QUaD telescope,” Infrared Phys. Technol. 51, 277-286 (2008).

Sadiku, M. N. O.

M. N. O. Sadiku, Numerical Techniques in Electromagnetics (CRC, 1992).

Schneider, M.

P. Wenig, M. Schneider, and R. Weigel, “Performance analysis of a cylindric dielectric lens antenna for 77 GHz Automotive Radar,” in Proceedings of International Radar Symposium (IRS 2008), 21-23 May 2008, Wroclaw, Poland, A.Kawalec and P.Kaniewski, eds. (Institute of Radioelectronics, 2008), paper B1-1.

Schwarz, R.

C. O'Sullivan, G. Cahill, J. A. Murphy, W. K. Gear, J. Harris, P. A. R. Ade, S. E. Church, K. L. Thompson, C. Pryke, J. Bock, M. Bowden, M. L. Brown, J. E. Carlstrom, P. G. Castro, T. Culverhouse, R. B. Friedman, K. M. Ganga, V. Haynes, J. R. Hinderks, J. Kovak, A. E. Lange, E. M. Leitch, O. E. Mallie, S. J. Melhuish, A. Orlando, L. Piccirillo, G. Pisano, N. Rajguru, B. A. Rusholme, R. Schwarz, A. N. Taylor, E. Y. S. Wu, and M. Zemcov, “The quasi-optical design of the QUaD telescope,” Infrared Phys. Technol. 51, 277-286 (2008).

Sewell, P.

A. V. Boriskin, A. I. Nosich, S. V. Boriskina, T. M. Benson, P. Sewell, and A. Altintas, “Lens or resonator? Electromagnetic behavior of an extended hemielliptic lens for a submillimeter-wave receiver,” Microwave Opt. Technol. Lett. 43, 515-518 (2004).
[CrossRef]

S. V. Boriskina, P. Sewell, T. M. Benson, and A. I. Nosich, “Accurate simulation of two-dimensional optical microcavities with uniquely solvable boundary integral equations and trigonometric Galerkin discretization,” J. Opt. Soc. Am. A 21, 393-402 (2004).
[CrossRef]

Taylor, A. N.

C. O'Sullivan, G. Cahill, J. A. Murphy, W. K. Gear, J. Harris, P. A. R. Ade, S. E. Church, K. L. Thompson, C. Pryke, J. Bock, M. Bowden, M. L. Brown, J. E. Carlstrom, P. G. Castro, T. Culverhouse, R. B. Friedman, K. M. Ganga, V. Haynes, J. R. Hinderks, J. Kovak, A. E. Lange, E. M. Leitch, O. E. Mallie, S. J. Melhuish, A. Orlando, L. Piccirillo, G. Pisano, N. Rajguru, B. A. Rusholme, R. Schwarz, A. N. Taylor, E. Y. S. Wu, and M. Zemcov, “The quasi-optical design of the QUaD telescope,” Infrared Phys. Technol. 51, 277-286 (2008).

Thompson, K. L.

C. O'Sullivan, G. Cahill, J. A. Murphy, W. K. Gear, J. Harris, P. A. R. Ade, S. E. Church, K. L. Thompson, C. Pryke, J. Bock, M. Bowden, M. L. Brown, J. E. Carlstrom, P. G. Castro, T. Culverhouse, R. B. Friedman, K. M. Ganga, V. Haynes, J. R. Hinderks, J. Kovak, A. E. Lange, E. M. Leitch, O. E. Mallie, S. J. Melhuish, A. Orlando, L. Piccirillo, G. Pisano, N. Rajguru, B. A. Rusholme, R. Schwarz, A. N. Taylor, E. Y. S. Wu, and M. Zemcov, “The quasi-optical design of the QUaD telescope,” Infrared Phys. Technol. 51, 277-286 (2008).

Walther, A.

A. Walther, The Ray and Wave Theory of Lenses (Cambridge U. Press, 2006).

Weigel, R.

P. Wenig, M. Schneider, and R. Weigel, “Performance analysis of a cylindric dielectric lens antenna for 77 GHz Automotive Radar,” in Proceedings of International Radar Symposium (IRS 2008), 21-23 May 2008, Wroclaw, Poland, A.Kawalec and P.Kaniewski, eds. (Institute of Radioelectronics, 2008), paper B1-1.

Wenig, P.

P. Wenig, M. Schneider, and R. Weigel, “Performance analysis of a cylindric dielectric lens antenna for 77 GHz Automotive Radar,” in Proceedings of International Radar Symposium (IRS 2008), 21-23 May 2008, Wroclaw, Poland, A.Kawalec and P.Kaniewski, eds. (Institute of Radioelectronics, 2008), paper B1-1.

Wolf, E.

Y. Li and E. Wolf, “Focal shifts in diffracted converging spherical waves,” Opt. Commun. 39, 211-215 (1981).
[CrossRef]

Wu, E. Y. S.

C. O'Sullivan, G. Cahill, J. A. Murphy, W. K. Gear, J. Harris, P. A. R. Ade, S. E. Church, K. L. Thompson, C. Pryke, J. Bock, M. Bowden, M. L. Brown, J. E. Carlstrom, P. G. Castro, T. Culverhouse, R. B. Friedman, K. M. Ganga, V. Haynes, J. R. Hinderks, J. Kovak, A. E. Lange, E. M. Leitch, O. E. Mallie, S. J. Melhuish, A. Orlando, L. Piccirillo, G. Pisano, N. Rajguru, B. A. Rusholme, R. Schwarz, A. N. Taylor, E. Y. S. Wu, and M. Zemcov, “The quasi-optical design of the QUaD telescope,” Infrared Phys. Technol. 51, 277-286 (2008).

Yan, Y.

D. Feng, Y. Yan, G. Jin, and S. Fan, “Axial focusing characteristics of diffractive microlenses based on a rigorous electromagnetic theory,” J. Opt. A, Pure Appl. Opt. 6, 1067-1071 (2004).
[CrossRef]

Yang, G.-Z.

Ye, J.-S.

Yurchenko, V. B.

V. B. Yurchenko and A. Altintas, “Asymptotic wave-like modeling of dielectric lenses,” in Proceedings of the 6th International Conference on Antenna Theory and Techniques (ICATT 2007), 17-21 September 2007, Sevastopol, Ukraine, Y.S.Shifrin and N.N.Kolchigin, eds. (IEEE, 2007), pp. 93-98.
[CrossRef]

Zemcov, M.

C. O'Sullivan, G. Cahill, J. A. Murphy, W. K. Gear, J. Harris, P. A. R. Ade, S. E. Church, K. L. Thompson, C. Pryke, J. Bock, M. Bowden, M. L. Brown, J. E. Carlstrom, P. G. Castro, T. Culverhouse, R. B. Friedman, K. M. Ganga, V. Haynes, J. R. Hinderks, J. Kovak, A. E. Lange, E. M. Leitch, O. E. Mallie, S. J. Melhuish, A. Orlando, L. Piccirillo, G. Pisano, N. Rajguru, B. A. Rusholme, R. Schwarz, A. N. Taylor, E. Y. S. Wu, and M. Zemcov, “The quasi-optical design of the QUaD telescope,” Infrared Phys. Technol. 51, 277-286 (2008).

IEEE Antennas Propag. Mag. (1)

G. Fikioris, “A note on the method of analytical regularization,” IEEE Antennas Propag. Mag. 43, 34-40 (2001).
[CrossRef]

Infrared Phys. Technol. (1)

C. O'Sullivan, G. Cahill, J. A. Murphy, W. K. Gear, J. Harris, P. A. R. Ade, S. E. Church, K. L. Thompson, C. Pryke, J. Bock, M. Bowden, M. L. Brown, J. E. Carlstrom, P. G. Castro, T. Culverhouse, R. B. Friedman, K. M. Ganga, V. Haynes, J. R. Hinderks, J. Kovak, A. E. Lange, E. M. Leitch, O. E. Mallie, S. J. Melhuish, A. Orlando, L. Piccirillo, G. Pisano, N. Rajguru, B. A. Rusholme, R. Schwarz, A. N. Taylor, E. Y. S. Wu, and M. Zemcov, “The quasi-optical design of the QUaD telescope,” Infrared Phys. Technol. 51, 277-286 (2008).

J. Opt. A, Pure Appl. Opt. (1)

D. Feng, Y. Yan, G. Jin, and S. Fan, “Axial focusing characteristics of diffractive microlenses based on a rigorous electromagnetic theory,” J. Opt. A, Pure Appl. Opt. 6, 1067-1071 (2004).
[CrossRef]

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

Microwave Opt. Technol. Lett. (1)

A. V. Boriskin, A. I. Nosich, S. V. Boriskina, T. M. Benson, P. Sewell, and A. Altintas, “Lens or resonator? Electromagnetic behavior of an extended hemielliptic lens for a submillimeter-wave receiver,” Microwave Opt. Technol. Lett. 43, 515-518 (2004).
[CrossRef]

Opt. Commun. (1)

Y. Li and E. Wolf, “Focal shifts in diffracted converging spherical waves,” Opt. Commun. 39, 211-215 (1981).
[CrossRef]

Other (6)

V. B. Yurchenko and A. Altintas, “Asymptotic wave-like modeling of dielectric lenses,” in Proceedings of the 6th International Conference on Antenna Theory and Techniques (ICATT 2007), 17-21 September 2007, Sevastopol, Ukraine, Y.S.Shifrin and N.N.Kolchigin, eds. (IEEE, 2007), pp. 93-98.
[CrossRef]

M. N. O. Sadiku, Numerical Techniques in Electromagnetics (CRC, 1992).

C. Muller, Foundations of the Mathematical Theory of Electromagnetic Waves (Springer-Verlag, 1969).

A. Walther, The Ray and Wave Theory of Lenses (Cambridge U. Press, 2006).

C. A. Balanis, Advanced Engineering Electromagnetics (Wiley, 1989).

P. Wenig, M. Schneider, and R. Weigel, “Performance analysis of a cylindric dielectric lens antenna for 77 GHz Automotive Radar,” in Proceedings of International Radar Symposium (IRS 2008), 21-23 May 2008, Wroclaw, Poland, A.Kawalec and P.Kaniewski, eds. (Institute of Radioelectronics, 2008), paper B1-1.

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Figures (8)

Fig. 1
Fig. 1

Geometry of a 2D convex dielectric lens (cross section profile). The excitation wave (PW or CW) of either TM ( E z ̂ ) or TE ( H z ̂ ) polarizations is incident from the left.

Fig. 2
Fig. 2

Exact (solid curves) and asymptotic solutions (dashed curves for RS2 and dotted curves for KU models, see below) in the case of TM PW incidence on a symmetric 2D dielectric lens; (a) x and (b) y cuts of P z power distribution behind the lens. Here, n ̃ = 1.5 , R 1 = R 2 = D , θ 1 = θ 2 = 30 ° ; A and B groups of curves correspond to D = 12 λ ( x R = 8.7 λ ) and D = 6 λ ( x R = 4.3 λ ) , respectively.

Fig. 3
Fig. 3

(a) Exact solutions in TE (solid curves) and TM (dotted curves) cases of CW incidence on a lens with R 1 = 10 λ when (A) D = R 2 = 8 λ ( x R = 8.0 λ ) and (B) D = R 2 = 10 λ ( x R = 7.2 λ ) at L C = 30 λ ( L C L = 20 λ , n ̃ = 1.5 ) and (b) comparison of exact (solid curve) and asymptotic solutions (dashed curves for RS2 and dotted curves for KU models, see below) in case A of TE CW incidence.

Fig. 4
Fig. 4

Power patterns P z ( x , y ) behind the lens in case B of Fig. 3 in TE CW incidence. (a) Exact solution for a lens suspended in free space, (b) RS2 simulation for the same case, and (c) RS2 simulation for the same lens mounted into a stop.

Fig. 5
Fig. 5

Power density P z (TM PW case) in the focal domain of asymmetric lenses of diameter (a) D = 30 λ and (b) D = 90 λ ( n ̃ = 1.5 ) when either R 1 = 100 λ , R 2 = 60 λ (A orientation of lens), or R 1 = 60 λ , R 2 = 100 λ (B orientation) computed with KU (dotted curves) and RS2 (solid curves) asymptotic methods.

Fig. 6
Fig. 6

(a) Power density P z (TE PW case) in the focal domain of an essentially asymmetric lens of small size in A and B orientations ( n ̃ = 1.5 , D = 6 λ , R 1 = 10 λ , R 2 = 4 λ in case A when θ 1 = 17.5 ° , θ 2 = 48.6 ° ) computed with KU (dotted curves) and RS2 (dashed curves) asymptotic methods as compared to exact solutions (solid curves), and (b) total internal reflection near the lens rim in case A as illustrated by ray tracing (a few rays near the rim in this plot do not propagate through the lens).

Fig. 7
Fig. 7

(a) Power density P z ( y ) at x = x F (A curves) and P z ( x ) at y = 0 (B curves) computed by KU (dotted curve) and RS2 (dashed curve) asymptotic methods in the comparison with an exact solution (solid curve), and (b) set of rays in the case of CW incidence on an asymmetric lens in the B orientation when D = 8 λ , R 1 = 6 λ , R 2 = 10 λ , L C = 16 λ , and n ̃ = 1.5 (TE polarization).

Fig. 8
Fig. 8

(a) Power and (b) phase patterns computed by an exact method in the case of Fig. 7.

Equations (10)

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

U = n [ A n J n ( k r 1 ) + B n Y n ( k r 1 ) ] e i n ϕ 1 ,
( r 1 , ϕ 1 ) D L ,
U = n C n J n ( k r 1 ) e i n ϕ 1 ,
( r 1 , ϕ 1 ) D 1 i ,
U = n [ F n H n ( k r 1 ) + b n ( k r 1 ) ] e i n ϕ 1 ,
( r 1 , ϕ 1 ) D 1 e ,
n , m { [ A n J m n ( k d L ) + B n Y m n ( k d L ) ] J m ( k d R 2 ) C n J m n ( k L ) J m ( k R 2 ) } S mp ( θ 2 ) = 0 ,
n , m { η [ A n J m n ( k d L ) + B n Y m n ( k d L ) ] J m ( k d R 2 ) C n J m n ( k L ) J m ( k R 2 ) } S mp ( θ 2 ) = 0 ,
n { [ A n J n ( k d R 1 ) + B n Y n ( k d R 1 ) ] P np ( τ ) + C n J n ( k R 1 ) S np ( τ ) } F p H p ( k R 1 ) = b p ( k R 1 ) ,
n { η [ A n J n ( k d R 1 ) + B n Y n ( k d R 1 ) ] P np ( τ ) + C n J n ( k R 1 ) S np ( τ ) } F p H p ( k R 1 ) = b p ( k R 1 ) ,

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