Abstract

An elliptic cylindrical omnidirectional light absorber forming a pseudo-optical black hole is studied both analytically and numerically. The conditions for permittivity tensors to trap optical rays are obtained from semiclassical analysis of the ray optic Hamiltonian. The dispersive finite-difference time-domain method is used to study the performance of these light-absorbing structures numerically. It is found that the permittivity of the structure in the form (1/sinhuu)(a/r)n traps the light ray efficiently into the elliptic absorber for n2, where u is the radial elliptic coordinate and a is the focal distance.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
    [CrossRef]
  2. U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (2006).
    [CrossRef]
  3. D. Schurig, J. Mock, B. Justice, S. A. Cummer, J. Pendry, A. Starr, and D. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
    [CrossRef]
  4. U. Leonhardt and T. G. Philbin, “General relativity in electrical engineering,” New J. Phys. 8, 247 (2006).
    [CrossRef]
  5. D. Ahn, “Calculation of permittivity tensors for invisibility devices by effective medium approach in general relativity,” J. Mod. Opt. 58, 700–710 (2011).
    [CrossRef]
  6. Y. Y. Lee and D. Ahn, “Dispersive full-wave finite-difference time-domain analysis of the bipolar cylindrical cloak based on the effective medium approach,” J. Opt. Soc. Am. B 30, 140–148 (2013).
    [CrossRef]
  7. V. G. Vaselago, “The electrodynamics of substances with simultaneous negative values of ε and μ,” Sov. Phys. Usp. 10, 509–514 (1968).
  8. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
    [CrossRef]
  9. T. G. Mackay, A. Lakhtakia, and S. Setiawan, “Gravitation and electromagnetic wave propagation with negative phase velocity,” New J. Phys. 7, 75 (2005).
    [CrossRef]
  10. T. G. Mackay and A. Lakhtakia, “Negative refraction, negative phase velocity, and counterposition in bianisotropic materials and metamaterials,” Phys. Rev. B 79, 235121 (2009).
  11. M. W. McCall, “On negative refraction in classical vacuum,” J. Mod. Opt. 54, 119–128 (2007).
    [CrossRef]
  12. M. W. McCall, “Classical gravity does not refract negatively,” Phys. Rev. Lett. 98, 91102 (2007).
    [CrossRef]
  13. Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Semiclassical theory of hyperlens,” J. Opt. Soc. Am. A 24, A52–A59 (2007).
    [CrossRef]
  14. W. Wang, L. Lin, J. Ma, C. Wang, J. Cui, C. Du, and X. Luo, “Electromagnetic concentrators with reduced material parameters based on coordinate transformation,” Opt. Express 16, 11431–11437 (2008).
    [CrossRef]
  15. D. A. Genov, S. Zhang, and X. Zhang, “Mimicking celestial mechanics in metamaterials,” Nat. Phys. 5, 687–692 (2009).
    [CrossRef]
  16. E. E. Narimanov and A. V. Kildishev, “Optical black hole: broadband omnidirectional light absorber,” Appl. Phys. Lett. 95, 041106 (2009).
    [CrossRef]
  17. C. Argyropoulous, E. Kallos, and Y. Hao, “FDTD analysis of the optical black hole,” J. Opt. Soc. Am. B 27, 2020–2025 (2010).
    [CrossRef]
  18. Q. Bai, J. Chen, N.-H. Shen, C. Cheng, and H.-T. Wang, “Controllable optical black hole in left-handed materials,” Opt. Express 18, 2106–2115 (2010).
    [CrossRef]
  19. Q. Cheng, T. J. Cui, W. X. Jiang, and B. G. Cai, “An omnidirectional electromagnetic absorber made of metamaterials,” New J. Phys. 12, 063006 (2010).
    [CrossRef]
  20. A. V. Kildishev, L. J. Prokopeva, and E. E. Narimanov, “Cylinder light concentrator and absorber: theoretical description,” Opt. Express 18, 16646–16662 (2010).
    [CrossRef]
  21. H.-W. Wang and L.-W. Chen, “A cylindrical optical black hole using graded index photonic crystals,” J. Appl. Phys. 109, 103104 (2011).
    [CrossRef]
  22. C. Sheng, H. Liu, Y. Wang, S. N. Zhu, and D. A. Genov, “Trapping light by mimicking gravitational lensing,” Nat. Photonics 7, 902–906 (2013).
    [CrossRef]
  23. Y. Cui, K. H. Fung, J. Xu, H. Ma, Y. Jin, S. He, and N. X. Fang, “Ultrabroadband light absorption by a sawtooth anisotropic metamaterial slab,” Nano Lett. 12, 1443–1447 (2012).
    [CrossRef]
  24. I. S. Gradshteyn and I. M. Ryzhil, “Indefinite integrals of elementary functions,” in Table of Integrals, Series and Products (Academic, 2007), pp. 63–246.
  25. A. Taflove and S. C. Hagness, Computational Electrodynamics (Artech House, 1995).
  26. D. M. Sullivan, Electromagnetic Simulation Using the FDTD Method (IEEE, 2000).

2013 (2)

C. Sheng, H. Liu, Y. Wang, S. N. Zhu, and D. A. Genov, “Trapping light by mimicking gravitational lensing,” Nat. Photonics 7, 902–906 (2013).
[CrossRef]

Y. Y. Lee and D. Ahn, “Dispersive full-wave finite-difference time-domain analysis of the bipolar cylindrical cloak based on the effective medium approach,” J. Opt. Soc. Am. B 30, 140–148 (2013).
[CrossRef]

2012 (1)

Y. Cui, K. H. Fung, J. Xu, H. Ma, Y. Jin, S. He, and N. X. Fang, “Ultrabroadband light absorption by a sawtooth anisotropic metamaterial slab,” Nano Lett. 12, 1443–1447 (2012).
[CrossRef]

2011 (2)

H.-W. Wang and L.-W. Chen, “A cylindrical optical black hole using graded index photonic crystals,” J. Appl. Phys. 109, 103104 (2011).
[CrossRef]

D. Ahn, “Calculation of permittivity tensors for invisibility devices by effective medium approach in general relativity,” J. Mod. Opt. 58, 700–710 (2011).
[CrossRef]

2010 (4)

2009 (3)

D. A. Genov, S. Zhang, and X. Zhang, “Mimicking celestial mechanics in metamaterials,” Nat. Phys. 5, 687–692 (2009).
[CrossRef]

E. E. Narimanov and A. V. Kildishev, “Optical black hole: broadband omnidirectional light absorber,” Appl. Phys. Lett. 95, 041106 (2009).
[CrossRef]

T. G. Mackay and A. Lakhtakia, “Negative refraction, negative phase velocity, and counterposition in bianisotropic materials and metamaterials,” Phys. Rev. B 79, 235121 (2009).

2008 (1)

2007 (3)

Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Semiclassical theory of hyperlens,” J. Opt. Soc. Am. A 24, A52–A59 (2007).
[CrossRef]

M. W. McCall, “On negative refraction in classical vacuum,” J. Mod. Opt. 54, 119–128 (2007).
[CrossRef]

M. W. McCall, “Classical gravity does not refract negatively,” Phys. Rev. Lett. 98, 91102 (2007).
[CrossRef]

2006 (4)

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[CrossRef]

U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (2006).
[CrossRef]

D. Schurig, J. Mock, B. Justice, S. A. Cummer, J. Pendry, A. Starr, and D. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[CrossRef]

U. Leonhardt and T. G. Philbin, “General relativity in electrical engineering,” New J. Phys. 8, 247 (2006).
[CrossRef]

2005 (1)

T. G. Mackay, A. Lakhtakia, and S. Setiawan, “Gravitation and electromagnetic wave propagation with negative phase velocity,” New J. Phys. 7, 75 (2005).
[CrossRef]

2000 (1)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[CrossRef]

1968 (1)

V. G. Vaselago, “The electrodynamics of substances with simultaneous negative values of ε and μ,” Sov. Phys. Usp. 10, 509–514 (1968).

Ahn, D.

Y. Y. Lee and D. Ahn, “Dispersive full-wave finite-difference time-domain analysis of the bipolar cylindrical cloak based on the effective medium approach,” J. Opt. Soc. Am. B 30, 140–148 (2013).
[CrossRef]

D. Ahn, “Calculation of permittivity tensors for invisibility devices by effective medium approach in general relativity,” J. Mod. Opt. 58, 700–710 (2011).
[CrossRef]

Alekseyev, L. V.

Argyropoulous, C.

Bai, Q.

Cai, B. G.

Q. Cheng, T. J. Cui, W. X. Jiang, and B. G. Cai, “An omnidirectional electromagnetic absorber made of metamaterials,” New J. Phys. 12, 063006 (2010).
[CrossRef]

Chen, J.

Chen, L.-W.

H.-W. Wang and L.-W. Chen, “A cylindrical optical black hole using graded index photonic crystals,” J. Appl. Phys. 109, 103104 (2011).
[CrossRef]

Cheng, C.

Cheng, Q.

Q. Cheng, T. J. Cui, W. X. Jiang, and B. G. Cai, “An omnidirectional electromagnetic absorber made of metamaterials,” New J. Phys. 12, 063006 (2010).
[CrossRef]

Cui, J.

Cui, T. J.

Q. Cheng, T. J. Cui, W. X. Jiang, and B. G. Cai, “An omnidirectional electromagnetic absorber made of metamaterials,” New J. Phys. 12, 063006 (2010).
[CrossRef]

Cui, Y.

Y. Cui, K. H. Fung, J. Xu, H. Ma, Y. Jin, S. He, and N. X. Fang, “Ultrabroadband light absorption by a sawtooth anisotropic metamaterial slab,” Nano Lett. 12, 1443–1447 (2012).
[CrossRef]

Cummer, S. A.

D. Schurig, J. Mock, B. Justice, S. A. Cummer, J. Pendry, A. Starr, and D. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[CrossRef]

Du, C.

Fang, N. X.

Y. Cui, K. H. Fung, J. Xu, H. Ma, Y. Jin, S. He, and N. X. Fang, “Ultrabroadband light absorption by a sawtooth anisotropic metamaterial slab,” Nano Lett. 12, 1443–1447 (2012).
[CrossRef]

Fung, K. H.

Y. Cui, K. H. Fung, J. Xu, H. Ma, Y. Jin, S. He, and N. X. Fang, “Ultrabroadband light absorption by a sawtooth anisotropic metamaterial slab,” Nano Lett. 12, 1443–1447 (2012).
[CrossRef]

Genov, D. A.

C. Sheng, H. Liu, Y. Wang, S. N. Zhu, and D. A. Genov, “Trapping light by mimicking gravitational lensing,” Nat. Photonics 7, 902–906 (2013).
[CrossRef]

D. A. Genov, S. Zhang, and X. Zhang, “Mimicking celestial mechanics in metamaterials,” Nat. Phys. 5, 687–692 (2009).
[CrossRef]

Gradshteyn, I. S.

I. S. Gradshteyn and I. M. Ryzhil, “Indefinite integrals of elementary functions,” in Table of Integrals, Series and Products (Academic, 2007), pp. 63–246.

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics (Artech House, 1995).

Hao, Y.

He, S.

Y. Cui, K. H. Fung, J. Xu, H. Ma, Y. Jin, S. He, and N. X. Fang, “Ultrabroadband light absorption by a sawtooth anisotropic metamaterial slab,” Nano Lett. 12, 1443–1447 (2012).
[CrossRef]

Jacob, Z.

Jiang, W. X.

Q. Cheng, T. J. Cui, W. X. Jiang, and B. G. Cai, “An omnidirectional electromagnetic absorber made of metamaterials,” New J. Phys. 12, 063006 (2010).
[CrossRef]

Jin, Y.

Y. Cui, K. H. Fung, J. Xu, H. Ma, Y. Jin, S. He, and N. X. Fang, “Ultrabroadband light absorption by a sawtooth anisotropic metamaterial slab,” Nano Lett. 12, 1443–1447 (2012).
[CrossRef]

Justice, B.

D. Schurig, J. Mock, B. Justice, S. A. Cummer, J. Pendry, A. Starr, and D. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[CrossRef]

Kallos, E.

Kildishev, A. V.

A. V. Kildishev, L. J. Prokopeva, and E. E. Narimanov, “Cylinder light concentrator and absorber: theoretical description,” Opt. Express 18, 16646–16662 (2010).
[CrossRef]

E. E. Narimanov and A. V. Kildishev, “Optical black hole: broadband omnidirectional light absorber,” Appl. Phys. Lett. 95, 041106 (2009).
[CrossRef]

Lakhtakia, A.

T. G. Mackay and A. Lakhtakia, “Negative refraction, negative phase velocity, and counterposition in bianisotropic materials and metamaterials,” Phys. Rev. B 79, 235121 (2009).

T. G. Mackay, A. Lakhtakia, and S. Setiawan, “Gravitation and electromagnetic wave propagation with negative phase velocity,” New J. Phys. 7, 75 (2005).
[CrossRef]

Lee, Y. Y.

Leonhardt, U.

U. Leonhardt and T. G. Philbin, “General relativity in electrical engineering,” New J. Phys. 8, 247 (2006).
[CrossRef]

U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (2006).
[CrossRef]

Lin, L.

Liu, H.

C. Sheng, H. Liu, Y. Wang, S. N. Zhu, and D. A. Genov, “Trapping light by mimicking gravitational lensing,” Nat. Photonics 7, 902–906 (2013).
[CrossRef]

Luo, X.

Ma, H.

Y. Cui, K. H. Fung, J. Xu, H. Ma, Y. Jin, S. He, and N. X. Fang, “Ultrabroadband light absorption by a sawtooth anisotropic metamaterial slab,” Nano Lett. 12, 1443–1447 (2012).
[CrossRef]

Ma, J.

Mackay, T. G.

T. G. Mackay and A. Lakhtakia, “Negative refraction, negative phase velocity, and counterposition in bianisotropic materials and metamaterials,” Phys. Rev. B 79, 235121 (2009).

T. G. Mackay, A. Lakhtakia, and S. Setiawan, “Gravitation and electromagnetic wave propagation with negative phase velocity,” New J. Phys. 7, 75 (2005).
[CrossRef]

McCall, M. W.

M. W. McCall, “On negative refraction in classical vacuum,” J. Mod. Opt. 54, 119–128 (2007).
[CrossRef]

M. W. McCall, “Classical gravity does not refract negatively,” Phys. Rev. Lett. 98, 91102 (2007).
[CrossRef]

Mock, J.

D. Schurig, J. Mock, B. Justice, S. A. Cummer, J. Pendry, A. Starr, and D. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[CrossRef]

Narimanov, E.

Narimanov, E. E.

A. V. Kildishev, L. J. Prokopeva, and E. E. Narimanov, “Cylinder light concentrator and absorber: theoretical description,” Opt. Express 18, 16646–16662 (2010).
[CrossRef]

E. E. Narimanov and A. V. Kildishev, “Optical black hole: broadband omnidirectional light absorber,” Appl. Phys. Lett. 95, 041106 (2009).
[CrossRef]

Pendry, J.

D. Schurig, J. Mock, B. Justice, S. A. Cummer, J. Pendry, A. Starr, and D. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[CrossRef]

Pendry, J. B.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[CrossRef]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[CrossRef]

Philbin, T. G.

U. Leonhardt and T. G. Philbin, “General relativity in electrical engineering,” New J. Phys. 8, 247 (2006).
[CrossRef]

Prokopeva, L. J.

Ryzhil, I. M.

I. S. Gradshteyn and I. M. Ryzhil, “Indefinite integrals of elementary functions,” in Table of Integrals, Series and Products (Academic, 2007), pp. 63–246.

Schurig, D.

D. Schurig, J. Mock, B. Justice, S. A. Cummer, J. Pendry, A. Starr, and D. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[CrossRef]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[CrossRef]

Setiawan, S.

T. G. Mackay, A. Lakhtakia, and S. Setiawan, “Gravitation and electromagnetic wave propagation with negative phase velocity,” New J. Phys. 7, 75 (2005).
[CrossRef]

Shen, N.-H.

Sheng, C.

C. Sheng, H. Liu, Y. Wang, S. N. Zhu, and D. A. Genov, “Trapping light by mimicking gravitational lensing,” Nat. Photonics 7, 902–906 (2013).
[CrossRef]

Smith, D.

D. Schurig, J. Mock, B. Justice, S. A. Cummer, J. Pendry, A. Starr, and D. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[CrossRef]

Smith, D. R.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[CrossRef]

Starr, A.

D. Schurig, J. Mock, B. Justice, S. A. Cummer, J. Pendry, A. Starr, and D. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[CrossRef]

Sullivan, D. M.

D. M. Sullivan, Electromagnetic Simulation Using the FDTD Method (IEEE, 2000).

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics (Artech House, 1995).

Vaselago, V. G.

V. G. Vaselago, “The electrodynamics of substances with simultaneous negative values of ε and μ,” Sov. Phys. Usp. 10, 509–514 (1968).

Wang, C.

Wang, H.-T.

Wang, H.-W.

H.-W. Wang and L.-W. Chen, “A cylindrical optical black hole using graded index photonic crystals,” J. Appl. Phys. 109, 103104 (2011).
[CrossRef]

Wang, W.

Wang, Y.

C. Sheng, H. Liu, Y. Wang, S. N. Zhu, and D. A. Genov, “Trapping light by mimicking gravitational lensing,” Nat. Photonics 7, 902–906 (2013).
[CrossRef]

Xu, J.

Y. Cui, K. H. Fung, J. Xu, H. Ma, Y. Jin, S. He, and N. X. Fang, “Ultrabroadband light absorption by a sawtooth anisotropic metamaterial slab,” Nano Lett. 12, 1443–1447 (2012).
[CrossRef]

Zhang, S.

D. A. Genov, S. Zhang, and X. Zhang, “Mimicking celestial mechanics in metamaterials,” Nat. Phys. 5, 687–692 (2009).
[CrossRef]

Zhang, X.

D. A. Genov, S. Zhang, and X. Zhang, “Mimicking celestial mechanics in metamaterials,” Nat. Phys. 5, 687–692 (2009).
[CrossRef]

Zhu, S. N.

C. Sheng, H. Liu, Y. Wang, S. N. Zhu, and D. A. Genov, “Trapping light by mimicking gravitational lensing,” Nat. Photonics 7, 902–906 (2013).
[CrossRef]

Appl. Phys. Lett. (1)

E. E. Narimanov and A. V. Kildishev, “Optical black hole: broadband omnidirectional light absorber,” Appl. Phys. Lett. 95, 041106 (2009).
[CrossRef]

J. Appl. Phys. (1)

H.-W. Wang and L.-W. Chen, “A cylindrical optical black hole using graded index photonic crystals,” J. Appl. Phys. 109, 103104 (2011).
[CrossRef]

J. Mod. Opt. (2)

D. Ahn, “Calculation of permittivity tensors for invisibility devices by effective medium approach in general relativity,” J. Mod. Opt. 58, 700–710 (2011).
[CrossRef]

M. W. McCall, “On negative refraction in classical vacuum,” J. Mod. Opt. 54, 119–128 (2007).
[CrossRef]

J. Opt. Soc. Am. A (1)

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

Nano Lett. (1)

Y. Cui, K. H. Fung, J. Xu, H. Ma, Y. Jin, S. He, and N. X. Fang, “Ultrabroadband light absorption by a sawtooth anisotropic metamaterial slab,” Nano Lett. 12, 1443–1447 (2012).
[CrossRef]

Nat. Photonics (1)

C. Sheng, H. Liu, Y. Wang, S. N. Zhu, and D. A. Genov, “Trapping light by mimicking gravitational lensing,” Nat. Photonics 7, 902–906 (2013).
[CrossRef]

Nat. Phys. (1)

D. A. Genov, S. Zhang, and X. Zhang, “Mimicking celestial mechanics in metamaterials,” Nat. Phys. 5, 687–692 (2009).
[CrossRef]

New J. Phys. (3)

Q. Cheng, T. J. Cui, W. X. Jiang, and B. G. Cai, “An omnidirectional electromagnetic absorber made of metamaterials,” New J. Phys. 12, 063006 (2010).
[CrossRef]

T. G. Mackay, A. Lakhtakia, and S. Setiawan, “Gravitation and electromagnetic wave propagation with negative phase velocity,” New J. Phys. 7, 75 (2005).
[CrossRef]

U. Leonhardt and T. G. Philbin, “General relativity in electrical engineering,” New J. Phys. 8, 247 (2006).
[CrossRef]

Opt. Express (3)

Phys. Rev. B (1)

T. G. Mackay and A. Lakhtakia, “Negative refraction, negative phase velocity, and counterposition in bianisotropic materials and metamaterials,” Phys. Rev. B 79, 235121 (2009).

Phys. Rev. Lett. (2)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[CrossRef]

M. W. McCall, “Classical gravity does not refract negatively,” Phys. Rev. Lett. 98, 91102 (2007).
[CrossRef]

Science (3)

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[CrossRef]

U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (2006).
[CrossRef]

D. Schurig, J. Mock, B. Justice, S. A. Cummer, J. Pendry, A. Starr, and D. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[CrossRef]

Sov. Phys. Usp. (1)

V. G. Vaselago, “The electrodynamics of substances with simultaneous negative values of ε and μ,” Sov. Phys. Usp. 10, 509–514 (1968).

Other (3)

I. S. Gradshteyn and I. M. Ryzhil, “Indefinite integrals of elementary functions,” in Table of Integrals, Series and Products (Academic, 2007), pp. 63–246.

A. Taflove and S. C. Hagness, Computational Electrodynamics (Artech House, 1995).

D. M. Sullivan, Electromagnetic Simulation Using the FDTD Method (IEEE, 2000).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1.
Fig. 1.

Elliptical coordinate system. The blue (solid) and the dark red (dashed) lines represent constant u and v contours, respectively. a represents the focal point, and k represents the maximal radius for constant u.

Fig. 2.
Fig. 2.

Trajectory of rays with incident angles of π/6, π/4, π/3 incident on the normalized elliptic cylinder a=1. We have assumed the normalized momentum pv=ωa/(2c) (ε0=1) for all rays. Note that rays are converging to the points on the focal plane.

Fig. 3.
Fig. 3.

Elliptic cylindrical absorber with inhomogeneous dielectric permittivity εu matching that of the outer medium and of the internal core at corresponding interfaces: ε={ε0,u>K2ε(u),K1<u<K2εc+iγ,u<K1.

Fig. 4.
Fig. 4.

Hz(A/m) field distributions when an elliptic cylindrical optical black hole is exposed to illumination in the x direction with different time steps: (a) 0.1 psec and (b) 0.8 psec. Hz(A/m) field distributions when an elliptic cylindrical optical black hole is exposed to illumination in the y direction with different time steps: (a) 0.1 psec and (b) 0.8 psec.

Fig. 5.
Fig. 5.

Hz(A/m) field distributions when an elliptic cylindrical optical black hole is exposed at the elapsed time of 0.8 psec for illumination in (a) x direction and (b) y direction for the dielectric permittivity of the form ε(u)=(ε0/sinhu). Hz(A/m) field distributions when an elliptic cylindrical optical black hole is exposed at the elapsed time of 0.8 psec for illumination in (a) x direction and (b) y direction for the dielectric permittivity of the form ε(u)=(ε0/sinh3u).

Fig. 6.
Fig. 6.

Hz(A/m) field distributions when an elliptic cylindrical optical black hole is exposed at the elapsed time of 0.2 psec for illumination in the x direction for the semi-focal distance a=15μm and n=2.

Equations (25)

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

×E=1cBt,×B⃗=1cD⃗t,·D=0,∇⃗·B⃗=0,
D=ε·E,B=μ0H,
×[ε1·(×B⃗)]=ω2c2B.
x=acoshucosv,y=asinhusinv,z=z,
×F=u^1hvhz{v(hzFz)z(hvFv)}+v^1hzhu{z(huFu)u(hzFz)}+z^1huhv{u(hvFv)v(huFu)},
hu=hv=a(sinh2u+sin2v)1/2,hz=1.
1a2(sinh2u+sin2v){u(1εv(u,v)Bzu)+v(1εu(u,v)Bzv)}+ω2c2Bz=0,
Bz(u,v)=B0exp(iS(u,v)),
u(1εvBzu)u(1εvB0u)eiS1εv(Su)2B0eiS+i2εvB0uSueiS+iu(1εvSu)B0eiS,
v(1εuBzv)v(1εuB0v)eiS1εu(Sv)2B0eiS+i2εuB0vSveiS+iv(1εuSv)B0eiS.
λεu,vu1,λεu,vv1.
λB0u,λB0v1.
1a2(sinh2u+sin2v){1εv(Su)2+1εu(Sv)2}Bz+ω2c2Bz=0,
H=1a2(sinh2u+sin2v){1εv(Su)2+1εu(Sv)2}=1a2(sinh2u+sin2v){1εv(pu)2+1εu(pv)2}.
dudt=Hpu,dvdt=Hpv.
dudt=2pua2(sinh2u+sin2v)ε(u,v),
dvdt=2pva2(sinh2u+sin2v)ε(u,v),
pu=a2ω2c2ε(u,v)(sinh2u+sin2v)pv2.
dvdu=pv[ω2a2c2(sinh2u+sin2v)ε(u,v)(pv)2]1/2.
vv0=u0udvdudu.
dvdu=pvsinhu[ω2a2c2ε0(sinh2u+sin2v)pv2sinh2u]1/2=pvsinhu(ω2a2ε0c2pv2)1/2(sinh2u+q2)1/2,
q2=ε0ω2a2sin2v(ω2a2ε0c2pv2).
νν0=log(coshucoshu0)pν(ω2c2ε0a2pν)1/2,
r2=x2+y2=a2cosh2ucos2v+a2sinh2usin2v=a2(sinh2u+cos2v)a2sinh2u.
ε={ε0,u>K2ε(u),K1<u<K2εc+iγ,u<K1.

Metrics