Abstract

The near fields of small-size extended hemielliptic lenses made of rexolite and isotropic quartz and illuminated by E- and H-polarized plane waves are studied. Variations in the focal domain size, shape, and location are reported versus the angle of incidence of the incoming wave. The problem is solved numerically in a two-dimensional formulation. The accuracy of results is guaranteed by using a highly efficient numerical algorithm based on the combination of the Muller boundary integral equations, the method of analytical regularization, and the trigonometric Galerkin discretization scheme. The analysis fully accounts for the finite size of the lens as well as its curvature and thus can be considered as a reference solution for other electromagnetic solvers. Moreover, the trusted description of the focusing ability of a finite-size hemielliptic lens can be useful in the design of antenna receivers.

© 2009 Optical Society of America

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References

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  1. 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]
  2. J. Rudd and D. Mittleman, “Influence of substrate-lens design in terahertz time-domain spectroscopy,” J. Opt. Soc. Am. B 19, 319-329 (2002).
    [CrossRef]
  3. A. D. Greenwood and J.-M. Jin, “A field picture of wave propagation in inhomogeneous dielectric lenses,” IEEE Antennas Propag. Mag. 41, 9-18 (1999).
    [CrossRef]
  4. P. Varga, “Focusing of electromagnetic radiation by hyperboloidal and ellipsoidal lenses,” J. Opt. Soc. Am. A 19, 1658-1667 (2002).
    [CrossRef]
  5. 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]
  6. 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, 515-158 (2004).
    [CrossRef]
  7. J. Wiersig, “Formation of long-lived, scarlike modes near avoided resonance crossings in optical microcavities,” Phys. Rev. Lett. 97, 253901 (2006).
    [CrossRef]
  8. A. V. Boriskin, G. Godi, R. Sauleau, and A. I. Nosich, “Small hemielliptic dielectric lens antenna analysis in 2-D: boundary integral equations vs. geometrical and physical optics,” IEEE Trans. Antennas Propag. 56, 485-492 (2008).
    [CrossRef]
  9. J. V. Rudd, J. L. Johnson, and Daniel M. Mittleman, “Cross-polarized angular emission patterns from lens-coupled terahertz antennas,” J. Opt. Soc. Am. B 18, 1524-1533 (2001).
    [CrossRef]
  10. 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]
  11. D. Pasqualini and S. Maci, “High-frequency analysis of integrated dielectric lens antennas,” IEEE Trans. Antennas Propag. 52, 840-847 (2004).
    [CrossRef]
  12. A. V. Boriskin, A. Rolland, R. Sauleau, and A. I. Nosich, “Validation of FDTD accuracy in the compact hemielliptic dielectric lens antenna analysis,” IEEE Trans. Antennas Propag. 56, 758-764 (2008).
    [CrossRef]
  13. A. V. Boriskin, A. Rolland, R. Sauleau, and A. I. Nosich, “Test of the FDTD accuracy in the analysis of the scattering resonances associated with high-Q whispering-gallery modes of a circular cylinder,” J. Opt. Soc. Am. A 25, 1169-1173 (2008).
    [CrossRef]
  14. 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]
  15. D. Wilton, “Review of current status and trends in the use of integral equations in computational electromagnetics,” Electromagnetics 12, 287-341 (1992).
    [CrossRef]
  16. L. Rogobete and C. Henkel, “Spontaneous emission in a subwavelength environment characterized by boundary integral equations,” Phys. Rev. A 70, 063815 (2004).
    [CrossRef]
  17. J. Wiersig, “Boundary element method for resonances in dielectric microcavities,” J. Opt. A, Pure Appl. Opt. 5, 53-60 (2003).
    [CrossRef]
  18. M. S. Kurdoglyan, S.-Y. Lee, S. Rim, and C.-M. Kim, “Unidirectional lasing from a microcavity with a rounded isosceles triangle shape,” Opt. Lett. 29, 2758-2760 (2004).
    [CrossRef] [PubMed]
  19. V. Rokhlin, “Rapid solution of integral equations of scattering theory in two dimensions,” J. Comput. Phys. 86, 414-439 (1990).
    [CrossRef]
  20. J. L. Tsalamengas, “Exponentially convergent Nystrom methods applied to integral-integrodifferential equations of oblique scattering/hybrid wave propagation in presence of composite dielectric cylinders of arbitrary cross section,” IEEE Trans. Antennas Propag. 55, 3239-3250 (2007).
    [CrossRef]
  21. A. I. Nosich, E. I. Smotrova, S. V. Boriskina, T. M. Benson, and P. Sewell, “Trends in microdisk laser research and linear optical modelling,” Opt. Quantum Electron. 39, 1253-1272 (2007).
    [CrossRef]

2008 (3)

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

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

A. V. Boriskin, A. Rolland, R. Sauleau, and A. I. Nosich, “Test of the FDTD accuracy in the analysis of the scattering resonances associated with high-Q whispering-gallery modes of a circular cylinder,” J. Opt. Soc. Am. A 25, 1169-1173 (2008).
[CrossRef]

2007 (2)

J. L. Tsalamengas, “Exponentially convergent Nystrom methods applied to integral-integrodifferential equations of oblique scattering/hybrid wave propagation in presence of composite dielectric cylinders of arbitrary cross section,” IEEE Trans. Antennas Propag. 55, 3239-3250 (2007).
[CrossRef]

A. I. Nosich, E. I. Smotrova, S. V. Boriskina, T. M. Benson, and P. Sewell, “Trends in microdisk laser research and linear optical modelling,” Opt. Quantum Electron. 39, 1253-1272 (2007).
[CrossRef]

2006 (1)

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

2005 (1)

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 (5)

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, 515-158 (2004).
[CrossRef]

D. Pasqualini and S. Maci, “High-frequency analysis of integrated dielectric lens antennas,” IEEE Trans. Antennas Propag. 52, 840-847 (2004).
[CrossRef]

L. Rogobete and C. Henkel, “Spontaneous emission in a subwavelength environment characterized by boundary integral equations,” Phys. Rev. A 70, 063815 (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]

M. S. Kurdoglyan, S.-Y. Lee, S. Rim, and C.-M. Kim, “Unidirectional lasing from a microcavity with a rounded isosceles triangle shape,” Opt. Lett. 29, 2758-2760 (2004).
[CrossRef] [PubMed]

2003 (1)

J. Wiersig, “Boundary element method for resonances in dielectric microcavities,” J. Opt. A, Pure Appl. Opt. 5, 53-60 (2003).
[CrossRef]

2002 (3)

2001 (2)

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]

J. V. Rudd, J. L. Johnson, and Daniel M. Mittleman, “Cross-polarized angular emission patterns from lens-coupled terahertz antennas,” J. Opt. Soc. Am. B 18, 1524-1533 (2001).
[CrossRef]

1999 (1)

A. D. Greenwood and J.-M. Jin, “A field picture of wave propagation in inhomogeneous dielectric lenses,” IEEE Antennas Propag. Mag. 41, 9-18 (1999).
[CrossRef]

1992 (1)

D. Wilton, “Review of current status and trends in the use of integral equations in computational electromagnetics,” Electromagnetics 12, 287-341 (1992).
[CrossRef]

1990 (1)

V. Rokhlin, “Rapid solution of integral equations of scattering theory in two dimensions,” J. Comput. Phys. 86, 414-439 (1990).
[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, 515-158 (2004).
[CrossRef]

Benson, T. M.

A. I. Nosich, E. I. Smotrova, S. V. Boriskina, T. M. Benson, and P. Sewell, “Trends in microdisk laser research and linear optical modelling,” Opt. Quantum Electron. 39, 1253-1272 (2007).
[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, 515-158 (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]

Boriskin, A. V.

A. V. Boriskin, A. Rolland, R. Sauleau, and A. I. Nosich, “Test of the FDTD accuracy in the analysis of the scattering resonances associated with high-Q whispering-gallery modes of a circular cylinder,” J. Opt. Soc. Am. A 25, 1169-1173 (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 vs. geometrical and physical optics,” IEEE Trans. Antennas Propag. 56, 485-492 (2008).
[CrossRef]

A. V. Boriskin, A. Rolland, R. Sauleau, and A. I. Nosich, “Validation 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, 515-158 (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.

A. I. Nosich, E. I. Smotrova, S. V. Boriskina, T. M. Benson, and P. Sewell, “Trends in microdisk laser research and linear optical modelling,” Opt. Quantum Electron. 39, 1253-1272 (2007).
[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, 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, 515-158 (2004).
[CrossRef]

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]

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 vs. 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]

Greenwood, A. D.

A. D. Greenwood and J.-M. Jin, “A field picture of wave propagation in inhomogeneous dielectric lenses,” IEEE Antennas Propag. Mag. 41, 9-18 (1999).
[CrossRef]

Henkel, C.

L. Rogobete and C. Henkel, “Spontaneous emission in a subwavelength environment characterized by boundary integral equations,” Phys. Rev. A 70, 063815 (2004).
[CrossRef]

Jin, J.-M.

A. D. Greenwood and J.-M. Jin, “A field picture of wave propagation in inhomogeneous dielectric lenses,” IEEE Antennas Propag. Mag. 41, 9-18 (1999).
[CrossRef]

Johnson, J. L.

Kim, C.-M.

Kurdoglyan, M. S.

Lee, S.-Y.

Maci, S.

D. Pasqualini and S. Maci, “High-frequency analysis of integrated dielectric lens antennas,” IEEE Trans. Antennas Propag. 52, 840-847 (2004).
[CrossRef]

Mittleman, D.

Mittleman, Daniel M.

Nosich, A. I.

A. V. Boriskin, A. Rolland, R. Sauleau, and A. I. Nosich, “Test of the FDTD accuracy in the analysis of the scattering resonances associated with high-Q whispering-gallery modes of a circular cylinder,” J. Opt. Soc. Am. A 25, 1169-1173 (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 vs. geometrical and physical optics,” IEEE Trans. Antennas Propag. 56, 485-492 (2008).
[CrossRef]

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

A. I. Nosich, E. I. Smotrova, S. V. Boriskina, T. M. Benson, and P. Sewell, “Trends in microdisk laser research and linear optical modelling,” Opt. Quantum Electron. 39, 1253-1272 (2007).
[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, 515-158 (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]

Pasqualini, D.

D. Pasqualini and S. Maci, “High-frequency analysis of integrated dielectric lens antennas,” IEEE Trans. Antennas Propag. 52, 840-847 (2004).
[CrossRef]

Rim, S.

Rogobete, L.

L. Rogobete and C. Henkel, “Spontaneous emission in a subwavelength environment characterized by boundary integral equations,” Phys. Rev. A 70, 063815 (2004).
[CrossRef]

Rokhlin, V.

V. Rokhlin, “Rapid solution of integral equations of scattering theory in two dimensions,” J. Comput. Phys. 86, 414-439 (1990).
[CrossRef]

Rolland, A.

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

A. V. Boriskin, A. Rolland, R. Sauleau, and A. I. Nosich, “Test of the FDTD accuracy in the analysis of the scattering resonances associated with high-Q whispering-gallery modes of a circular cylinder,” J. Opt. Soc. Am. A 25, 1169-1173 (2008).
[CrossRef]

Rudd, J.

Rudd, J. V.

Sauleau, R.

A. V. Boriskin, A. Rolland, R. Sauleau, and A. I. Nosich, “Test of the FDTD accuracy in the analysis of the scattering resonances associated with high-Q whispering-gallery modes of a circular cylinder,” J. Opt. Soc. Am. A 25, 1169-1173 (2008).
[CrossRef]

A. V. Boriskin, A. Rolland, R. Sauleau, and A. I. Nosich, “Validation 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 vs. 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]

Sewell, P.

A. I. Nosich, E. I. Smotrova, S. V. Boriskina, T. M. Benson, and P. Sewell, “Trends in microdisk laser research and linear optical modelling,” Opt. Quantum Electron. 39, 1253-1272 (2007).
[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, 515-158 (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]

Smotrova, E. I.

A. I. Nosich, E. I. Smotrova, S. V. Boriskina, T. M. Benson, and P. Sewell, “Trends in microdisk laser research and linear optical modelling,” Opt. Quantum Electron. 39, 1253-1272 (2007).
[CrossRef]

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]

Tsalamengas, J. L.

J. L. Tsalamengas, “Exponentially convergent Nystrom methods applied to integral-integrodifferential equations of oblique scattering/hybrid wave propagation in presence of composite dielectric cylinders of arbitrary cross section,” IEEE Trans. Antennas Propag. 55, 3239-3250 (2007).
[CrossRef]

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]

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]

J. Wiersig, “Boundary element method for resonances in dielectric microcavities,” J. Opt. A, Pure Appl. Opt. 5, 53-60 (2003).
[CrossRef]

Wilton, D.

D. Wilton, “Review of current status and trends in the use of integral equations in computational electromagnetics,” Electromagnetics 12, 287-341 (1992).
[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]

Electromagnetics (1)

D. Wilton, “Review of current status and trends in the use of integral equations in computational electromagnetics,” Electromagnetics 12, 287-341 (1992).
[CrossRef]

IEEE Antennas Propag. Mag. (1)

A. D. Greenwood and J.-M. Jin, “A field picture of wave propagation in inhomogeneous dielectric lenses,” IEEE Antennas Propag. Mag. 41, 9-18 (1999).
[CrossRef]

IEEE Trans. Antennas Propag. (6)

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

D. Pasqualini and S. Maci, “High-frequency analysis of integrated dielectric lens antennas,” IEEE Trans. Antennas Propag. 52, 840-847 (2004).
[CrossRef]

A. V. Boriskin, A. Rolland, R. Sauleau, and A. I. Nosich, “Validation 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]

J. L. Tsalamengas, “Exponentially convergent Nystrom methods applied to integral-integrodifferential equations of oblique scattering/hybrid wave propagation in presence of composite dielectric cylinders of arbitrary cross section,” IEEE Trans. Antennas Propag. 55, 3239-3250 (2007).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

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]

J. Comput. Phys. (1)

V. Rokhlin, “Rapid solution of integral equations of scattering theory in two dimensions,” J. Comput. Phys. 86, 414-439 (1990).
[CrossRef]

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

J. Wiersig, “Boundary element method for resonances in dielectric microcavities,” J. Opt. A, Pure Appl. Opt. 5, 53-60 (2003).
[CrossRef]

J. Opt. Soc. Am. A (3)

J. Opt. Soc. Am. B (2)

Microwave Opt. Technol. Lett. (1)

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, 515-158 (2004).
[CrossRef]

Opt. Lett. (1)

Opt. Quantum Electron. (1)

A. I. Nosich, E. I. Smotrova, S. V. Boriskina, T. M. Benson, and P. Sewell, “Trends in microdisk laser research and linear optical modelling,” Opt. Quantum Electron. 39, 1253-1272 (2007).
[CrossRef]

Phys. Rev. A (1)

L. Rogobete and C. Henkel, “Spontaneous emission in a subwavelength environment characterized by boundary integral equations,” Phys. Rev. A 70, 063815 (2004).
[CrossRef]

Phys. Rev. Lett. (1)

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

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Figures (7)

Fig. 1
Fig. 1

Geometry and notations of the 2D model of the extended hemielliptic lens.

Fig. 2
Fig. 2

Near-field maps of rexolite extended hemielliptic lens ( ϵ = 2.53 , k a = 12.56 , l 1 = 0.8 , l 2 = 1.285 ) illuminated by unit-amplitude E- and H-polarized plane waves.

Fig. 3
Fig. 3

Near-field maps of quartz extended hemielliptic lens ( ϵ = 3.8 , k a = 12.56 , l 1 = 0.6 , l 2 = 1.165 ) illuminated by unit-amplitude E- and H-polarized plane waves.

Fig. 4
Fig. 4

(a) Normalized peak field values in the focal spots of the rexolite and quartz lenses and (b) normalized coordinates of the corresponding points versus the angle of incidence of plane waves. Dashed–dotted lines in (b) indicate the size of the lens extension ( a l 1 ) .

Fig. 5
Fig. 5

Normalized peak field values in the focal spots of the rexolite and quartz lenses symmetrically ( γ = 0 ° ) illuminated by unit-amplitude plane E- and H-waves versus the normalized frequency.

Fig. 6
Fig. 6

Horizontal coordinates ( k x ) of the points with the highest field values defined in the focal spots of the rexolite and quartz lenses illuminated symmetrically ( γ = 0 ° ) by plane E- and H-waves versus the normalized frequency. The dashed–dotted lines indicate the normalized sizes of the lens extensions for both lenses. The field values at the corresponding points are given in Fig. 5.

Fig. 7
Fig. 7

Intensity reflection coefficients for the E- (solid curves) and H-polarized (dashed curves) plane waves illuminating the flat air–dielectric surface of (a) rexolite, (b) quartz.

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