Abstract

The interplay between the optical focusing and wavelength-scale resonant features of extended hemielliptical (EHE) and extended hemispherical (EHS) lenses is studied in the two-dimensional (2-D) formulation using highly accurate in-house software based on the Muller boundary integral equations. The influence of the half-bowtie (HBT) resonances on the focusing and collimating capabilities of medium-size EHE and EHS lenses made of silicon is characterized as a function of lens parameters and excitation conditions. As a result, factors determining the parasitic impacts of the HBT resonances on the performance of integrated lens antennas are highlighted.

© 2010 Optical Society of America

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  1. D. F. Filipovic, S. S. Gearhart, and G. M. Rebeiz, “Double slot antennas on extended hemispherical and elliptical silicon dielectric lenses,” IEEE Trans. Microwave Theory Tech. 41, 1738–1749 (1993).
    [CrossRef]
  2. T. H. Buttgenbach, “An improved solution for integrated array optics in quasioptical mm and submm receivers: The hybrid antenna,” IEEE Trans. Microwave Theory Tech. 41, 1750–1761 (1993).
    [CrossRef]
  3. S. Raman and G. M. Rebeiz, “Single- and dual-polarized millimeter-wave slot-ring antennas,” IEEE Trans. Antennas Propag. 44, 1438–1444 (1996).
    [CrossRef]
  4. P. Otero, G. V. Eleftheriades, and J. R. Mosig, “Integrated modified rectangular loop slot antenna on substrate lenses for millimeter- and submillimeter-wave frequencies mixer applications,” IEEE Trans. Antennas Propag. 46, 1489–1497 (1998).
    [CrossRef]
  5. J. van Rudd and D. Mittleman, “Influence of substrate-lens design in terahertz time-domain spectroscopy,” J. Opt. Soc. Am. B 19, 319–329 (2002).
    [CrossRef]
  6. G. Godi, R. Sauleau, and D. Thouroude, “Performance of reduced size substrate lens antennas for mm-wave communications,” IEEE Trans. Antennas Propag. 53, 1278–1286 (2005).
    [CrossRef]
  7. S. Cherednichenko, V. Drakinskiy, T. Berg, P. Khosropanah, and E. Kollberg, “Hot-electron bolometer terahertz mixers for the Herschel Space Observatory,” Rev. Sci. Instrum. 79, 034501 (2008).
    [CrossRef] [PubMed]
  8. A. Neto, “UWB, non dispersive radiation from the planarly fed leaky lens antenna. Part 1: theory and design,” IEEE Trans. Antennas Propag. 58, 2238–2247 (2010).
    [CrossRef]
  9. P. Varga, “Focusing of electromagnetic radiation by hyperboloidal and ellipsoidal lenses,” J. Opt. Soc. Am. A 19, 1658–1667 (2002).
    [CrossRef]
  10. S. V. Boriskina, T. M. Benson, P. D. Sewell, and A. I. Nosich, “Directional emission, increased free spectral range, and mode Q-factors in 2-D wavelength-scale optical microcavity structures,” IEEE J. Sel. Top. Quantum Electron. 12, 1175–1182 (2006).
    [CrossRef]
  11. J. Wiersig, “Formation of long-lived, scarlike modes near avoided resonance crossings in optical microcavities,” Phys. Rev. Lett. 97, 253901 (2006).
    [CrossRef]
  12. H. G. L. Schwefel, N. B. Rex, H. E. Tureci, R. K. Chang, A. D. Stone, T. Ben-Messaoud, and J. Zyss, “Dramatic shape sensitivity of directional emission patterns from similarly deformed cylindrical polymer lasers,” J. Opt. Soc. Am. B 21, 923–934 (2004).
    [CrossRef]
  13. C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nockel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280, 1556–1564 (1998).
    [CrossRef] [PubMed]
  14. S. Y. Lee, M. S. Kurdoglyan, S. Rim, and C. M. Kim, “Resonance patterns in a stadium-shaped microcavity,” Phys. Rev. A 70, 023809 (2004).
    [CrossRef]
  15. S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, “Accurate simulation of 2D optical microcavities with uniquely solvable boundary integral equations and trigonometric-Galerkin discretization,” J. Opt. Soc. Am. A 21, 393–402 (2004).
    [CrossRef]
  16. E. Heyman and L. B. Felson, “Gaussian beam and pulsed-beam dynamics: complex-source and complex-spectrum formulations within and beyond paraxial asymptotics,” J. Opt. Soc. Am. A 18, 1588–1611 (2001).
    [CrossRef]
  17. A. V. Boriskin, G. Godi, R. Sauleau, and A. I. Nosich, “Small hemielliptic dielectric lens antenna analysis in 2-D: boundary integral equations versus geometrical and physical optics,” IEEE Trans. Antennas Propag. 56, 485–492 (2008).
    [CrossRef]
  18. A. V. Boriskin, A. Rolland, R. Sauleau, and A. I. Nosich, “Assessment of FDTD accuracy in the compact hemielliptic dielectric lens antenna analysis,” IEEE Trans. Antennas Propag. 56, 758–764 (2008).
    [CrossRef]
  19. A. V. Boriskin and A. I. Nosich, “Whispering-gallery and Luneburg-lens effects in a beam-fed circularly-layered dielectric cylinder,” IEEE Trans. Antennas Propag. 50, 1245–1249 (2002).
    [CrossRef]
  20. A. V. Boriskin, R. Sauleau, and A. I. Nosich, “Exact off-resonance near fields of small-size extended hemielliptic 2–D lenses illuminated by plane waves,” J. Opt. Soc. Am. A 26, 259–264 (2009).
    [CrossRef]
  21. A. V. Boriskin, S. V. Boriskina, A. I. Nosich, T. M. Benson, P. Sewell, and A. Altintas, “Lens or resonator? electromagnetic behavior of an extended hemielliptical lens for a sub-mm wave receiver,” Microwave Opt. Technol. Lett. 43, 515–518 (2004).
    [CrossRef]
  22. A. D. Semenov, H. Richter, H.-W. Hübers, B. Günther, A. Smirnov, K. S. Il’in, M. Siegel, and J. P. Karamarkovic, “Terahertz performance of integrated lens antennas with a hot-electron bolometer,” IEEE Trans. Microwave Theory Tech. 55, 239–247 (2007).
    [CrossRef]
  23. A. V. Boriskin, R. Sauleau, and A. I. Nosich, “Performance of hemielliptic dielectric lens antennas with optimal edge illumination,” IEEE Trans. Antennas Propag. 57, 2193–2198 (2009).
    [CrossRef]
  24. D. F. Filipovic, G. P. Gauthier, S. Raman, and G. M. Rebeiz, “Off-axis properties of silicon and quartz dielectric lens antennas,” IEEE Trans. Antennas Propag. 45, 760–766 (1997).
    [CrossRef]
  25. J. W. Lamb, “Miscellaneous data on materials for millimeter and submillimeter optics,” Int. J. Infrared Millim. Waves 17, 1997–2034 (1996).
    [CrossRef]
  26. X. Wu, G. V. Eleftheriades, and T. E. van Deventer-Perkins, “Design and characterization of single and multiple-beam mm-wave circularly polarized substrate lens antennas for wireless communications,” IEEE Trans. Microwave Theory Tech. 49, 431–441 (2001).
    [CrossRef]

2010

A. Neto, “UWB, non dispersive radiation from the planarly fed leaky lens antenna. Part 1: theory and design,” IEEE Trans. Antennas Propag. 58, 2238–2247 (2010).
[CrossRef]

2009

A. V. Boriskin, R. Sauleau, and A. I. Nosich, “Performance of hemielliptic dielectric lens antennas with optimal edge illumination,” IEEE Trans. Antennas Propag. 57, 2193–2198 (2009).
[CrossRef]

A. V. Boriskin, R. Sauleau, and A. I. Nosich, “Exact off-resonance near fields of small-size extended hemielliptic 2–D lenses illuminated by plane waves,” J. Opt. Soc. Am. A 26, 259–264 (2009).
[CrossRef]

2008

S. Cherednichenko, V. Drakinskiy, T. Berg, P. Khosropanah, and E. Kollberg, “Hot-electron bolometer terahertz mixers for the Herschel Space Observatory,” Rev. Sci. Instrum. 79, 034501 (2008).
[CrossRef] [PubMed]

A. V. Boriskin, G. Godi, R. Sauleau, and A. I. Nosich, “Small hemielliptic dielectric lens antenna analysis in 2-D: boundary integral equations versus geometrical and physical optics,” IEEE Trans. Antennas Propag. 56, 485–492 (2008).
[CrossRef]

A. V. Boriskin, A. Rolland, R. Sauleau, and A. I. Nosich, “Assessment of FDTD accuracy in the compact hemielliptic dielectric lens antenna analysis,” IEEE Trans. Antennas Propag. 56, 758–764 (2008).
[CrossRef]

2007

A. D. Semenov, H. Richter, H.-W. Hübers, B. Günther, A. Smirnov, K. S. Il’in, M. Siegel, and J. P. Karamarkovic, “Terahertz performance of integrated lens antennas with a hot-electron bolometer,” IEEE Trans. Microwave Theory Tech. 55, 239–247 (2007).
[CrossRef]

2006

S. V. Boriskina, T. M. Benson, P. D. Sewell, and A. I. Nosich, “Directional emission, increased free spectral range, and mode Q-factors in 2-D wavelength-scale optical microcavity structures,” IEEE J. Sel. Top. Quantum Electron. 12, 1175–1182 (2006).
[CrossRef]

J. Wiersig, “Formation of long-lived, scarlike modes near avoided resonance crossings in optical microcavities,” Phys. Rev. Lett. 97, 253901 (2006).
[CrossRef]

2005

G. Godi, R. Sauleau, and D. Thouroude, “Performance of reduced size substrate lens antennas for mm-wave communications,” IEEE Trans. Antennas Propag. 53, 1278–1286 (2005).
[CrossRef]

2004

S. Y. Lee, M. S. Kurdoglyan, S. Rim, and C. M. Kim, “Resonance patterns in a stadium-shaped microcavity,” Phys. Rev. A 70, 023809 (2004).
[CrossRef]

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

S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, “Accurate simulation of 2D optical microcavities with uniquely solvable boundary integral equations and trigonometric-Galerkin discretization,” J. Opt. Soc. Am. A 21, 393–402 (2004).
[CrossRef]

H. G. L. Schwefel, N. B. Rex, H. E. Tureci, R. K. Chang, A. D. Stone, T. Ben-Messaoud, and J. Zyss, “Dramatic shape sensitivity of directional emission patterns from similarly deformed cylindrical polymer lasers,” J. Opt. Soc. Am. B 21, 923–934 (2004).
[CrossRef]

2002

2001

X. Wu, G. V. Eleftheriades, and T. E. van Deventer-Perkins, “Design and characterization of single and multiple-beam mm-wave circularly polarized substrate lens antennas for wireless communications,” IEEE Trans. Microwave Theory Tech. 49, 431–441 (2001).
[CrossRef]

E. Heyman and L. B. Felson, “Gaussian beam and pulsed-beam dynamics: complex-source and complex-spectrum formulations within and beyond paraxial asymptotics,” J. Opt. Soc. Am. A 18, 1588–1611 (2001).
[CrossRef]

1998

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nockel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280, 1556–1564 (1998).
[CrossRef] [PubMed]

P. Otero, G. V. Eleftheriades, and J. R. Mosig, “Integrated modified rectangular loop slot antenna on substrate lenses for millimeter- and submillimeter-wave frequencies mixer applications,” IEEE Trans. Antennas Propag. 46, 1489–1497 (1998).
[CrossRef]

1997

D. F. Filipovic, G. P. Gauthier, S. Raman, and G. M. Rebeiz, “Off-axis properties of silicon and quartz dielectric lens antennas,” IEEE Trans. Antennas Propag. 45, 760–766 (1997).
[CrossRef]

1996

J. W. Lamb, “Miscellaneous data on materials for millimeter and submillimeter optics,” Int. J. Infrared Millim. Waves 17, 1997–2034 (1996).
[CrossRef]

S. Raman and G. M. Rebeiz, “Single- and dual-polarized millimeter-wave slot-ring antennas,” IEEE Trans. Antennas Propag. 44, 1438–1444 (1996).
[CrossRef]

1993

D. F. Filipovic, S. S. Gearhart, and G. M. Rebeiz, “Double slot antennas on extended hemispherical and elliptical silicon dielectric lenses,” IEEE Trans. Microwave Theory Tech. 41, 1738–1749 (1993).
[CrossRef]

T. H. Buttgenbach, “An improved solution for integrated array optics in quasioptical mm and submm receivers: The hybrid antenna,” IEEE Trans. Microwave Theory Tech. 41, 1750–1761 (1993).
[CrossRef]

Altintas, A.

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

Ben-Messaoud, T.

Benson, T. M.

S. V. Boriskina, T. M. Benson, P. D. Sewell, and A. I. Nosich, “Directional emission, increased free spectral range, and mode Q-factors in 2-D wavelength-scale optical microcavity structures,” IEEE J. Sel. Top. Quantum Electron. 12, 1175–1182 (2006).
[CrossRef]

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

S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, “Accurate simulation of 2D optical microcavities with uniquely solvable boundary integral equations and trigonometric-Galerkin discretization,” J. Opt. Soc. Am. A 21, 393–402 (2004).
[CrossRef]

Berg, T.

S. Cherednichenko, V. Drakinskiy, T. Berg, P. Khosropanah, and E. Kollberg, “Hot-electron bolometer terahertz mixers for the Herschel Space Observatory,” Rev. Sci. Instrum. 79, 034501 (2008).
[CrossRef] [PubMed]

Boriskin, A. V.

A. V. Boriskin, R. Sauleau, and A. I. Nosich, “Exact off-resonance near fields of small-size extended hemielliptic 2–D lenses illuminated by plane waves,” J. Opt. Soc. Am. A 26, 259–264 (2009).
[CrossRef]

A. V. Boriskin, R. Sauleau, and A. I. Nosich, “Performance of hemielliptic dielectric lens antennas with optimal edge illumination,” IEEE Trans. Antennas Propag. 57, 2193–2198 (2009).
[CrossRef]

A. V. Boriskin, G. Godi, R. Sauleau, and A. I. Nosich, “Small hemielliptic dielectric lens antenna analysis in 2-D: boundary integral equations versus geometrical and physical optics,” IEEE Trans. Antennas Propag. 56, 485–492 (2008).
[CrossRef]

A. V. Boriskin, A. Rolland, R. Sauleau, and A. I. Nosich, “Assessment of FDTD accuracy in the compact hemielliptic dielectric lens antenna analysis,” IEEE Trans. Antennas Propag. 56, 758–764 (2008).
[CrossRef]

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

A. V. Boriskin and A. I. Nosich, “Whispering-gallery and Luneburg-lens effects in a beam-fed circularly-layered dielectric cylinder,” IEEE Trans. Antennas Propag. 50, 1245–1249 (2002).
[CrossRef]

Boriskina, S. V.

S. V. Boriskina, T. M. Benson, P. D. Sewell, and A. I. Nosich, “Directional emission, increased free spectral range, and mode Q-factors in 2-D wavelength-scale optical microcavity structures,” IEEE J. Sel. Top. Quantum Electron. 12, 1175–1182 (2006).
[CrossRef]

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

S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, “Accurate simulation of 2D optical microcavities with uniquely solvable boundary integral equations and trigonometric-Galerkin discretization,” J. Opt. Soc. Am. A 21, 393–402 (2004).
[CrossRef]

Buttgenbach, T. H.

T. H. Buttgenbach, “An improved solution for integrated array optics in quasioptical mm and submm receivers: The hybrid antenna,” IEEE Trans. Microwave Theory Tech. 41, 1750–1761 (1993).
[CrossRef]

Capasso, F.

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nockel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280, 1556–1564 (1998).
[CrossRef] [PubMed]

Chang, R. K.

Cherednichenko, S.

S. Cherednichenko, V. Drakinskiy, T. Berg, P. Khosropanah, and E. Kollberg, “Hot-electron bolometer terahertz mixers for the Herschel Space Observatory,” Rev. Sci. Instrum. 79, 034501 (2008).
[CrossRef] [PubMed]

Cho, A. Y.

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nockel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280, 1556–1564 (1998).
[CrossRef] [PubMed]

Drakinskiy, V.

S. Cherednichenko, V. Drakinskiy, T. Berg, P. Khosropanah, and E. Kollberg, “Hot-electron bolometer terahertz mixers for the Herschel Space Observatory,” Rev. Sci. Instrum. 79, 034501 (2008).
[CrossRef] [PubMed]

Eleftheriades, G. V.

X. Wu, G. V. Eleftheriades, and T. E. van Deventer-Perkins, “Design and characterization of single and multiple-beam mm-wave circularly polarized substrate lens antennas for wireless communications,” IEEE Trans. Microwave Theory Tech. 49, 431–441 (2001).
[CrossRef]

P. Otero, G. V. Eleftheriades, and J. R. Mosig, “Integrated modified rectangular loop slot antenna on substrate lenses for millimeter- and submillimeter-wave frequencies mixer applications,” IEEE Trans. Antennas Propag. 46, 1489–1497 (1998).
[CrossRef]

Faist, J.

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nockel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280, 1556–1564 (1998).
[CrossRef] [PubMed]

Felson, L. B.

Filipovic, D. F.

D. F. Filipovic, G. P. Gauthier, S. Raman, and G. M. Rebeiz, “Off-axis properties of silicon and quartz dielectric lens antennas,” IEEE Trans. Antennas Propag. 45, 760–766 (1997).
[CrossRef]

D. F. Filipovic, S. S. Gearhart, and G. M. Rebeiz, “Double slot antennas on extended hemispherical and elliptical silicon dielectric lenses,” IEEE Trans. Microwave Theory Tech. 41, 1738–1749 (1993).
[CrossRef]

Gauthier, G. P.

D. F. Filipovic, G. P. Gauthier, S. Raman, and G. M. Rebeiz, “Off-axis properties of silicon and quartz dielectric lens antennas,” IEEE Trans. Antennas Propag. 45, 760–766 (1997).
[CrossRef]

Gearhart, S. S.

D. F. Filipovic, S. S. Gearhart, and G. M. Rebeiz, “Double slot antennas on extended hemispherical and elliptical silicon dielectric lenses,” IEEE Trans. Microwave Theory Tech. 41, 1738–1749 (1993).
[CrossRef]

Gmachl, C.

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nockel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280, 1556–1564 (1998).
[CrossRef] [PubMed]

Godi, G.

A. V. Boriskin, G. Godi, R. Sauleau, and A. I. Nosich, “Small hemielliptic dielectric lens antenna analysis in 2-D: boundary integral equations versus geometrical and physical optics,” IEEE Trans. Antennas Propag. 56, 485–492 (2008).
[CrossRef]

G. Godi, R. Sauleau, and D. Thouroude, “Performance of reduced size substrate lens antennas for mm-wave communications,” IEEE Trans. Antennas Propag. 53, 1278–1286 (2005).
[CrossRef]

Günther, B.

A. D. Semenov, H. Richter, H.-W. Hübers, B. Günther, A. Smirnov, K. S. Il’in, M. Siegel, and J. P. Karamarkovic, “Terahertz performance of integrated lens antennas with a hot-electron bolometer,” IEEE Trans. Microwave Theory Tech. 55, 239–247 (2007).
[CrossRef]

Heyman, E.

Hübers, H. -W.

A. D. Semenov, H. Richter, H.-W. Hübers, B. Günther, A. Smirnov, K. S. Il’in, M. Siegel, and J. P. Karamarkovic, “Terahertz performance of integrated lens antennas with a hot-electron bolometer,” IEEE Trans. Microwave Theory Tech. 55, 239–247 (2007).
[CrossRef]

Il’in, K. S.

A. D. Semenov, H. Richter, H.-W. Hübers, B. Günther, A. Smirnov, K. S. Il’in, M. Siegel, and J. P. Karamarkovic, “Terahertz performance of integrated lens antennas with a hot-electron bolometer,” IEEE Trans. Microwave Theory Tech. 55, 239–247 (2007).
[CrossRef]

Karamarkovic, J. P.

A. D. Semenov, H. Richter, H.-W. Hübers, B. Günther, A. Smirnov, K. S. Il’in, M. Siegel, and J. P. Karamarkovic, “Terahertz performance of integrated lens antennas with a hot-electron bolometer,” IEEE Trans. Microwave Theory Tech. 55, 239–247 (2007).
[CrossRef]

Khosropanah, P.

S. Cherednichenko, V. Drakinskiy, T. Berg, P. Khosropanah, and E. Kollberg, “Hot-electron bolometer terahertz mixers for the Herschel Space Observatory,” Rev. Sci. Instrum. 79, 034501 (2008).
[CrossRef] [PubMed]

Kim, C. M.

S. Y. Lee, M. S. Kurdoglyan, S. Rim, and C. M. Kim, “Resonance patterns in a stadium-shaped microcavity,” Phys. Rev. A 70, 023809 (2004).
[CrossRef]

Kollberg, E.

S. Cherednichenko, V. Drakinskiy, T. Berg, P. Khosropanah, and E. Kollberg, “Hot-electron bolometer terahertz mixers for the Herschel Space Observatory,” Rev. Sci. Instrum. 79, 034501 (2008).
[CrossRef] [PubMed]

Kurdoglyan, M. S.

S. Y. Lee, M. S. Kurdoglyan, S. Rim, and C. M. Kim, “Resonance patterns in a stadium-shaped microcavity,” Phys. Rev. A 70, 023809 (2004).
[CrossRef]

Lamb, J. W.

J. W. Lamb, “Miscellaneous data on materials for millimeter and submillimeter optics,” Int. J. Infrared Millim. Waves 17, 1997–2034 (1996).
[CrossRef]

Lee, S. Y.

S. Y. Lee, M. S. Kurdoglyan, S. Rim, and C. M. Kim, “Resonance patterns in a stadium-shaped microcavity,” Phys. Rev. A 70, 023809 (2004).
[CrossRef]

Mittleman, D.

Mosig, J. R.

P. Otero, G. V. Eleftheriades, and J. R. Mosig, “Integrated modified rectangular loop slot antenna on substrate lenses for millimeter- and submillimeter-wave frequencies mixer applications,” IEEE Trans. Antennas Propag. 46, 1489–1497 (1998).
[CrossRef]

Narimanov, E. E.

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nockel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280, 1556–1564 (1998).
[CrossRef] [PubMed]

Neto, A.

A. Neto, “UWB, non dispersive radiation from the planarly fed leaky lens antenna. Part 1: theory and design,” IEEE Trans. Antennas Propag. 58, 2238–2247 (2010).
[CrossRef]

Nockel, J. U.

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nockel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280, 1556–1564 (1998).
[CrossRef] [PubMed]

Nosich, A. I.

A. V. Boriskin, R. Sauleau, and A. I. Nosich, “Performance of hemielliptic dielectric lens antennas with optimal edge illumination,” IEEE Trans. Antennas Propag. 57, 2193–2198 (2009).
[CrossRef]

A. V. Boriskin, R. Sauleau, and A. I. Nosich, “Exact off-resonance near fields of small-size extended hemielliptic 2–D lenses illuminated by plane waves,” J. Opt. Soc. Am. A 26, 259–264 (2009).
[CrossRef]

A. V. Boriskin, A. Rolland, R. Sauleau, and A. I. Nosich, “Assessment of FDTD accuracy in the compact hemielliptic dielectric lens antenna analysis,” IEEE Trans. Antennas Propag. 56, 758–764 (2008).
[CrossRef]

A. V. Boriskin, G. Godi, R. Sauleau, and A. I. Nosich, “Small hemielliptic dielectric lens antenna analysis in 2-D: boundary integral equations versus geometrical and physical optics,” IEEE Trans. Antennas Propag. 56, 485–492 (2008).
[CrossRef]

S. V. Boriskina, T. M. Benson, P. D. Sewell, and A. I. Nosich, “Directional emission, increased free spectral range, and mode Q-factors in 2-D wavelength-scale optical microcavity structures,” IEEE J. Sel. Top. Quantum Electron. 12, 1175–1182 (2006).
[CrossRef]

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

S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, “Accurate simulation of 2D optical microcavities with uniquely solvable boundary integral equations and trigonometric-Galerkin discretization,” J. Opt. Soc. Am. A 21, 393–402 (2004).
[CrossRef]

A. V. Boriskin and A. I. Nosich, “Whispering-gallery and Luneburg-lens effects in a beam-fed circularly-layered dielectric cylinder,” IEEE Trans. Antennas Propag. 50, 1245–1249 (2002).
[CrossRef]

Otero, P.

P. Otero, G. V. Eleftheriades, and J. R. Mosig, “Integrated modified rectangular loop slot antenna on substrate lenses for millimeter- and submillimeter-wave frequencies mixer applications,” IEEE Trans. Antennas Propag. 46, 1489–1497 (1998).
[CrossRef]

Raman, S.

D. F. Filipovic, G. P. Gauthier, S. Raman, and G. M. Rebeiz, “Off-axis properties of silicon and quartz dielectric lens antennas,” IEEE Trans. Antennas Propag. 45, 760–766 (1997).
[CrossRef]

S. Raman and G. M. Rebeiz, “Single- and dual-polarized millimeter-wave slot-ring antennas,” IEEE Trans. Antennas Propag. 44, 1438–1444 (1996).
[CrossRef]

Rebeiz, G. M.

D. F. Filipovic, G. P. Gauthier, S. Raman, and G. M. Rebeiz, “Off-axis properties of silicon and quartz dielectric lens antennas,” IEEE Trans. Antennas Propag. 45, 760–766 (1997).
[CrossRef]

S. Raman and G. M. Rebeiz, “Single- and dual-polarized millimeter-wave slot-ring antennas,” IEEE Trans. Antennas Propag. 44, 1438–1444 (1996).
[CrossRef]

D. F. Filipovic, S. S. Gearhart, and G. M. Rebeiz, “Double slot antennas on extended hemispherical and elliptical silicon dielectric lenses,” IEEE Trans. Microwave Theory Tech. 41, 1738–1749 (1993).
[CrossRef]

Rex, N. B.

Richter, H.

A. D. Semenov, H. Richter, H.-W. Hübers, B. Günther, A. Smirnov, K. S. Il’in, M. Siegel, and J. P. Karamarkovic, “Terahertz performance of integrated lens antennas with a hot-electron bolometer,” IEEE Trans. Microwave Theory Tech. 55, 239–247 (2007).
[CrossRef]

Rim, S.

S. Y. Lee, M. S. Kurdoglyan, S. Rim, and C. M. Kim, “Resonance patterns in a stadium-shaped microcavity,” Phys. Rev. A 70, 023809 (2004).
[CrossRef]

Rolland, A.

A. V. Boriskin, A. Rolland, R. Sauleau, and A. I. Nosich, “Assessment of FDTD accuracy in the compact hemielliptic dielectric lens antenna analysis,” IEEE Trans. Antennas Propag. 56, 758–764 (2008).
[CrossRef]

Sauleau, R.

A. V. Boriskin, R. Sauleau, and A. I. Nosich, “Exact off-resonance near fields of small-size extended hemielliptic 2–D lenses illuminated by plane waves,” J. Opt. Soc. Am. A 26, 259–264 (2009).
[CrossRef]

A. V. Boriskin, R. Sauleau, and A. I. Nosich, “Performance of hemielliptic dielectric lens antennas with optimal edge illumination,” IEEE Trans. Antennas Propag. 57, 2193–2198 (2009).
[CrossRef]

A. V. Boriskin, G. Godi, R. Sauleau, and A. I. Nosich, “Small hemielliptic dielectric lens antenna analysis in 2-D: boundary integral equations versus geometrical and physical optics,” IEEE Trans. Antennas Propag. 56, 485–492 (2008).
[CrossRef]

A. V. Boriskin, A. Rolland, R. Sauleau, and A. I. Nosich, “Assessment of FDTD accuracy in the compact hemielliptic dielectric lens antenna analysis,” IEEE Trans. Antennas Propag. 56, 758–764 (2008).
[CrossRef]

G. Godi, R. Sauleau, and D. Thouroude, “Performance of reduced size substrate lens antennas for mm-wave communications,” IEEE Trans. Antennas Propag. 53, 1278–1286 (2005).
[CrossRef]

Schwefel, H. G. L.

Semenov, A. D.

A. D. Semenov, H. Richter, H.-W. Hübers, B. Günther, A. Smirnov, K. S. Il’in, M. Siegel, and J. P. Karamarkovic, “Terahertz performance of integrated lens antennas with a hot-electron bolometer,” IEEE Trans. Microwave Theory Tech. 55, 239–247 (2007).
[CrossRef]

Sewell, P.

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

S. V. Boriskina, T. M. Benson, P. Sewell, and A. I. Nosich, “Accurate simulation of 2D optical microcavities with uniquely solvable boundary integral equations and trigonometric-Galerkin discretization,” J. Opt. Soc. Am. A 21, 393–402 (2004).
[CrossRef]

Sewell, P. D.

S. V. Boriskina, T. M. Benson, P. D. Sewell, and A. I. Nosich, “Directional emission, increased free spectral range, and mode Q-factors in 2-D wavelength-scale optical microcavity structures,” IEEE J. Sel. Top. Quantum Electron. 12, 1175–1182 (2006).
[CrossRef]

Siegel, M.

A. D. Semenov, H. Richter, H.-W. Hübers, B. Günther, A. Smirnov, K. S. Il’in, M. Siegel, and J. P. Karamarkovic, “Terahertz performance of integrated lens antennas with a hot-electron bolometer,” IEEE Trans. Microwave Theory Tech. 55, 239–247 (2007).
[CrossRef]

Sivco, D. L.

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nockel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280, 1556–1564 (1998).
[CrossRef] [PubMed]

Smirnov, A.

A. D. Semenov, H. Richter, H.-W. Hübers, B. Günther, A. Smirnov, K. S. Il’in, M. Siegel, and J. P. Karamarkovic, “Terahertz performance of integrated lens antennas with a hot-electron bolometer,” IEEE Trans. Microwave Theory Tech. 55, 239–247 (2007).
[CrossRef]

Stone, A. D.

H. G. L. Schwefel, N. B. Rex, H. E. Tureci, R. K. Chang, A. D. Stone, T. Ben-Messaoud, and J. Zyss, “Dramatic shape sensitivity of directional emission patterns from similarly deformed cylindrical polymer lasers,” J. Opt. Soc. Am. B 21, 923–934 (2004).
[CrossRef]

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nockel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280, 1556–1564 (1998).
[CrossRef] [PubMed]

Thouroude, D.

G. Godi, R. Sauleau, and D. Thouroude, “Performance of reduced size substrate lens antennas for mm-wave communications,” IEEE Trans. Antennas Propag. 53, 1278–1286 (2005).
[CrossRef]

Tureci, H. E.

van Deventer-Perkins, T. E.

X. Wu, G. V. Eleftheriades, and T. E. van Deventer-Perkins, “Design and characterization of single and multiple-beam mm-wave circularly polarized substrate lens antennas for wireless communications,” IEEE Trans. Microwave Theory Tech. 49, 431–441 (2001).
[CrossRef]

van Rudd, J.

Varga, P.

Wiersig, J.

J. Wiersig, “Formation of long-lived, scarlike modes near avoided resonance crossings in optical microcavities,” Phys. Rev. Lett. 97, 253901 (2006).
[CrossRef]

Wu, X.

X. Wu, G. V. Eleftheriades, and T. E. van Deventer-Perkins, “Design and characterization of single and multiple-beam mm-wave circularly polarized substrate lens antennas for wireless communications,” IEEE Trans. Microwave Theory Tech. 49, 431–441 (2001).
[CrossRef]

Zyss, J.

IEEE J. Sel. Top. Quantum Electron.

S. V. Boriskina, T. M. Benson, P. D. Sewell, and A. I. Nosich, “Directional emission, increased free spectral range, and mode Q-factors in 2-D wavelength-scale optical microcavity structures,” IEEE J. Sel. Top. Quantum Electron. 12, 1175–1182 (2006).
[CrossRef]

IEEE Trans. Antennas Propag.

S. Raman and G. M. Rebeiz, “Single- and dual-polarized millimeter-wave slot-ring antennas,” IEEE Trans. Antennas Propag. 44, 1438–1444 (1996).
[CrossRef]

P. Otero, G. V. Eleftheriades, and J. R. Mosig, “Integrated modified rectangular loop slot antenna on substrate lenses for millimeter- and submillimeter-wave frequencies mixer applications,” IEEE Trans. Antennas Propag. 46, 1489–1497 (1998).
[CrossRef]

G. Godi, R. Sauleau, and D. Thouroude, “Performance of reduced size substrate lens antennas for mm-wave communications,” IEEE Trans. Antennas Propag. 53, 1278–1286 (2005).
[CrossRef]

A. V. Boriskin, G. Godi, R. Sauleau, and A. I. Nosich, “Small hemielliptic dielectric lens antenna analysis in 2-D: boundary integral equations versus geometrical and physical optics,” IEEE Trans. Antennas Propag. 56, 485–492 (2008).
[CrossRef]

A. V. Boriskin, A. Rolland, R. Sauleau, and A. I. Nosich, “Assessment of FDTD accuracy in the compact hemielliptic dielectric lens antenna analysis,” IEEE Trans. Antennas Propag. 56, 758–764 (2008).
[CrossRef]

A. V. Boriskin and A. I. Nosich, “Whispering-gallery and Luneburg-lens effects in a beam-fed circularly-layered dielectric cylinder,” IEEE Trans. Antennas Propag. 50, 1245–1249 (2002).
[CrossRef]

A. Neto, “UWB, non dispersive radiation from the planarly fed leaky lens antenna. Part 1: theory and design,” IEEE Trans. Antennas Propag. 58, 2238–2247 (2010).
[CrossRef]

A. V. Boriskin, R. Sauleau, and A. I. Nosich, “Performance of hemielliptic dielectric lens antennas with optimal edge illumination,” IEEE Trans. Antennas Propag. 57, 2193–2198 (2009).
[CrossRef]

D. F. Filipovic, G. P. Gauthier, S. Raman, and G. M. Rebeiz, “Off-axis properties of silicon and quartz dielectric lens antennas,” IEEE Trans. Antennas Propag. 45, 760–766 (1997).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

D. F. Filipovic, S. S. Gearhart, and G. M. Rebeiz, “Double slot antennas on extended hemispherical and elliptical silicon dielectric lenses,” IEEE Trans. Microwave Theory Tech. 41, 1738–1749 (1993).
[CrossRef]

T. H. Buttgenbach, “An improved solution for integrated array optics in quasioptical mm and submm receivers: The hybrid antenna,” IEEE Trans. Microwave Theory Tech. 41, 1750–1761 (1993).
[CrossRef]

X. Wu, G. V. Eleftheriades, and T. E. van Deventer-Perkins, “Design and characterization of single and multiple-beam mm-wave circularly polarized substrate lens antennas for wireless communications,” IEEE Trans. Microwave Theory Tech. 49, 431–441 (2001).
[CrossRef]

A. D. Semenov, H. Richter, H.-W. Hübers, B. Günther, A. Smirnov, K. S. Il’in, M. Siegel, and J. P. Karamarkovic, “Terahertz performance of integrated lens antennas with a hot-electron bolometer,” IEEE Trans. Microwave Theory Tech. 55, 239–247 (2007).
[CrossRef]

Int. J. Infrared Millim. Waves

J. W. Lamb, “Miscellaneous data on materials for millimeter and submillimeter optics,” Int. J. Infrared Millim. Waves 17, 1997–2034 (1996).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Microwave Opt. Technol. Lett.

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

Phys. Rev. A

S. Y. Lee, M. S. Kurdoglyan, S. Rim, and C. M. Kim, “Resonance patterns in a stadium-shaped microcavity,” Phys. Rev. A 70, 023809 (2004).
[CrossRef]

Phys. Rev. Lett.

J. Wiersig, “Formation of long-lived, scarlike modes near avoided resonance crossings in optical microcavities,” Phys. Rev. Lett. 97, 253901 (2006).
[CrossRef]

Rev. Sci. Instrum.

S. Cherednichenko, V. Drakinskiy, T. Berg, P. Khosropanah, and E. Kollberg, “Hot-electron bolometer terahertz mixers for the Herschel Space Observatory,” Rev. Sci. Instrum. 79, 034501 (2008).
[CrossRef] [PubMed]

Science

C. Gmachl, F. Capasso, E. E. Narimanov, J. U. Nockel, A. D. Stone, J. Faist, D. L. Sivco, and A. Y. Cho, “High-power directional emission from microlasers with chaotic resonators,” Science 280, 1556–1564 (1998).
[CrossRef] [PubMed]

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Figures (18)

Fig. 1
Fig. 1

EHE lens: (a) Geometry of the lens and schematic drawing of the ray-tracing focusing. The lens boundary is depicted by thick blue line. (b) Parameters of the EHE lenses designed with respect to the GO focusing rule versus lens material permittivity. Lens configurations marked by vertical dotted lines correspond to materials typically used for ILA design in the millimeter and sub-millimeter wave ranges.

Fig. 2
Fig. 2

Schematic drawing of different modes supported by the stadium-shaped resonator [12, 13].

Fig. 3
Fig. 3

Geometry and notations of the 2-D model of an EHE lens antenna excited by a plane wave (in the receiving mode) or by an aperture feed simulated by CSP (in the emitting mode). In the latter case, the curvy line indicates the branch cut in the real space due to CSP [16].

Fig. 4
Fig. 4

Free space radiation patterns of the 2-D CSP feed with different values of the k b parameter. The values of the CSP broadside directivity are given in parentheses.

Fig. 5
Fig. 5

Broadside directivity (linear scale) of the CSP feeds ( k b = 0 ) assisted by the EHE lens versus lens extension parameter ( ε = 11.7 , a = 4 λ 0 ) .

Fig. 6
Fig. 6

Normalized near-field maps ( | E z | ) for the EHE lenses illuminated by the E-polarized CSP feeds ( k b = 0 ) . Lens configurations correspond to A and B marks in Fig. 5.

Fig. 7
Fig. 7

Normalized radiation patterns of the E-polarized CSP feed ( k b = 0 ) assisted by two lenses whose designs correspond to marks A and B in Fig. 5. Solid line: non-resonant lens; dashed line: resonant lens.

Fig. 8
Fig. 8

Broadside directivity (linear scale) of the CSP feed ( k b = 0 ) assisted by the cut-through-focus EHE lens (see mark A in Fig. 5) versus frequency parameter that is lens bottom size normalized by the incident field wavelength.

Fig. 9
Fig. 9

Broadside directivity (linear scale) of the E-polarized CSP feeds with different radiation patterns (see Fig. 4) assisted by EHE lens ( ε = 11.7 , a = 4 λ 0 , l 2 = 1.046 ) versus lens extension parameter.

Fig. 10
Fig. 10

Broadside directivity (linear scale) of the E-polarized CSP feed ( k b = 0.5 ) assisted by EHE lenses ( ε = 11.7 , a = 4 λ 0 , l 2 = 1.046 ) with different extensions versus frequency parameter (i.e., lens bottom size normalized by the free space wavelength).

Fig. 11
Fig. 11

Same as Fig. 9 for EHS lens ( l 2 = 1.0 ) .

Fig. 12
Fig. 12

Same as Fig. 10 for EHS lens ( l 2 = 1.0 ) .

Fig. 13
Fig. 13

Normalized radiation patterns of the CSP feed ( k b = 0 ) assisted by EHE silicon lenses whose configurations are marked in Fig. 5. The family of four curves corresponding to the “in-resonance” case differ by the value of the material loss-factor (see legend). The value of the broadside directivity for each case is shown in parentheses.

Fig. 14
Fig. 14

Normalized near-field maps (focal spot region) for the silicon EHE lenses whose configurations are marked in Fig. 5 illuminated by the E-polarized plane waves: (a) off-resonance case, (b) in-resonance case.

Fig. 15
Fig. 15

Field amplitude distribution along the lens flat bottom for different angles of incidence of the unit-amplitude E-polarized plane wave illuminating the EHE silicon lenses ( ε = 11.7 , a = 4 λ 0 ) whose configurations are marked in Fig. 5: (a) non-resonant lens ( l 1 = 0.3 ) , (b) resonant lens ( l 1 = 0.343 ) .

Fig. 16
Fig. 16

Field amplitude in the hot spot of the EHE and EHS lenses versus length extension. The lenses ( ε = 11.7 , a = 4 λ 0 ) are illuminated by the unit-amplitude E-polarized plane waves under normal incidence ( γ = 0 ° ) .

Fig. 17
Fig. 17

Field amplitude in the hot spot of the (a) EHE and (b) EHS silicon lenses versus frequency parameter. The lenses are illuminated by the unit-amplitude E-polarized plane waves under normal incidence and differ by the extension lengths.

Fig. 18
Fig. 18

Field amplitude in the hot spot of the EHE lenses made of standard dielectric materials and illuminated by the unit-amplitude E-polarized plane waves versus lens extension parameter: (a) medium-size lens ( a = 4 λ 0 ) , (b) large-size lens ( a = 12 λ 0 ) .

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