Abstract

Complex electromagnetic structures can be designed by exploiting the concept of spatial coordinate transformations. In this paper, we define a coordinate transformation scheme that enables one to taper the electric field between two waveguides of different cross-sections. The electromagnetic field launched from the wide input waveguide is compressed in the proposed field tapering device and guided into the narrow output waveguide. In closed rectangular waveguide configurations, the taper can further play the role of a mode selector due to the output waveguide’s cut-off frequency. Realizable permittivity and permeability values that can be achieved with common existing metamaterials are determined from the transformation equations and simplified by a proposed parameter reduction method. Both a 2D continuous design model and a potential 3D discretized realization model are presented at microwave frequencies and the performances of the tapering devices are verified by full-wave finite element numerical simulations. Finally, near-field distributions are shown to demonstrate the field tapering functionality.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
    [Crossref] [PubMed]
  2. U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
    [Crossref] [PubMed]
  3. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
    [Crossref] [PubMed]
  4. D. Schurig, J. B. Pendry, and D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express 14(21), 9794–9804 (2006).
    [Crossref] [PubMed]
  5. Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z. Q. Zhang, and C. T. Chan, “Illusion optics: The optical transformation of an object into another object,” Phys. Rev. Lett. 102(25), 253902 (2009).
    [Crossref] [PubMed]
  6. W. X. Jiang and T. J. Cui, “Radar illusion via metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(2), 026601 (2011).
    [Crossref] [PubMed]
  7. W. X. Jiang, T. J. Cui, X. M. Yang, H. F. Ma, and Q. Cheng, “Shrinking an arbitrary object as one desires using metamaterials,” Appl. Phys. Lett. 98(20), 204101 (2011).
    [Crossref]
  8. W. X. Jiang, C. W. Qiu, T. Han, S. Zhang, and T. J. Cui, “Creation of ghost illusions using wave dynamics in metamaterials,” Adv. Funct. Mater. 23(32), 4028–4034 (2013).
    [Crossref]
  9. J. Yi, P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Illusion optics: Optically transforming the nature and the location of electromagnetic emissions,” J. Appl. Phys. 117(8), 084903 (2015).
    [Crossref]
  10. D. H. Werner and D.-H. Kwon, Transformation Electromagnetics and Metamaterials: Fundamental Principles and Applications (Springer, 2014).
  11. M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett. 100(6), 063903 (2008).
    [Crossref] [PubMed]
  12. M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, “Transformation-optical design of adaptive beam bends and beam expanders,” Opt. Express 16(15), 11555–11567 (2008).
    [Crossref] [PubMed]
  13. D. A. Roberts, M. Rahm, J. B. Pendry, and D. R. Smith, “Transformation-optical design of sharp waveguide bends and corners,” Appl. Phys. Lett. 93(25), 251111 (2008).
    [Crossref]
  14. P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Waveguide taper engineering using coordinate transformation technology,” Opt. Express 18(2), 767–772 (2010).
    [Crossref] [PubMed]
  15. J. Yi, G.-P. Piau, A. de Lustrac, and S. N. Burokur, “Electromagnetic field tapering using all-dielectric gradient index materials,” Sci. Rep. 6(1), 30661 (2016).
    [Crossref] [PubMed]
  16. D. H. Kwon and D. H. Werner, “Transformation optical designs for wave collimators, flat lenses and right-angle bends,” New J. Phys. 10(11), 115023 (2008).
    [Crossref]
  17. N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater. 9(2), 129–132 (2010).
    [Crossref] [PubMed]
  18. J. Yi, S. N. Burokur, and A. de Lustrac, “Experimental validation of a transformation optics based lens for beam steering,” Appl. Phys. Lett. 107(15), 154101 (2015).
    [Crossref]
  19. H. F. Ma and T. J. Cui, “Three-dimensional broadband and broad-angle transformation-optics lens,” Nat. Commun. 1(8), 124 (2010).
    [Crossref] [PubMed]
  20. C. Mateo-Segura, A. Dyke, H. Dyke, S. Haq, and Y. Hao, “Flat Luneburg lens via transformation optics for directive antenna applications,” IEEE Trans. Antenn. Propag. 62(4), 1945–1953 (2014).
    [Crossref]
  21. P.-H. Tichit, S. N. Burokur, C.-W. Qiu, and A. de Lustrac, “Experimental verification of isotropic radiation from a coherent dipole source via electric-field-driven LC resonator metamaterials,” Phys. Rev. Lett. 111(13), 133901 (2013).
    [Crossref] [PubMed]
  22. J. Yi, S. N. Burokur, G. P. Piau, and A. de Lustrac, “Coherent beam control with an all-dielectric transformation optics based lens,” Sci. Rep. 6(1), 18819 (2016).
    [Crossref] [PubMed]
  23. J. Yi, S. N. Burokur, G. P. Piau, and A. de Lustrac, “Restoring in-phase emissions from non-planar radiating elements using a transformation optics based lens,” Appl. Phys. Lett. 107(2), 024101 (2015).
    [Crossref]
  24. R. Yang, Z. Lei, L. Chen, Z. Wang, and Y. Hao, “Surface wave transformation lens antennas,” IEEE Trans. Antenn. Propag. 62(2), 973–977 (2014).
    [Crossref]
  25. J. Yi, S. N. Burokur, and A. de Lustrac, “Conceptual design of a beam steering lens through transformation electromagnetics,” Opt. Express 23(10), 12942–12951 (2015).
    [Crossref] [PubMed]
  26. A. Sellier, S. N. Burokur, B. Kanté, and A. de Lustrac, “Negative refractive index metamaterials using only metallic cut wires,” Opt. Express 17(8), 6301–6310 (2009).
    [Crossref] [PubMed]
  27. D. Schurig, J. J. Mock, and D. R. Smith, “Electric-field-coupled resonators for negative permittivity metamaterials,” Appl. Phys. Lett. 88(4), 041109 (2006).
    [Crossref]
  28. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
    [Crossref]

2016 (2)

J. Yi, G.-P. Piau, A. de Lustrac, and S. N. Burokur, “Electromagnetic field tapering using all-dielectric gradient index materials,” Sci. Rep. 6(1), 30661 (2016).
[Crossref] [PubMed]

J. Yi, S. N. Burokur, G. P. Piau, and A. de Lustrac, “Coherent beam control with an all-dielectric transformation optics based lens,” Sci. Rep. 6(1), 18819 (2016).
[Crossref] [PubMed]

2015 (4)

J. Yi, S. N. Burokur, G. P. Piau, and A. de Lustrac, “Restoring in-phase emissions from non-planar radiating elements using a transformation optics based lens,” Appl. Phys. Lett. 107(2), 024101 (2015).
[Crossref]

J. Yi, S. N. Burokur, and A. de Lustrac, “Experimental validation of a transformation optics based lens for beam steering,” Appl. Phys. Lett. 107(15), 154101 (2015).
[Crossref]

J. Yi, P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Illusion optics: Optically transforming the nature and the location of electromagnetic emissions,” J. Appl. Phys. 117(8), 084903 (2015).
[Crossref]

J. Yi, S. N. Burokur, and A. de Lustrac, “Conceptual design of a beam steering lens through transformation electromagnetics,” Opt. Express 23(10), 12942–12951 (2015).
[Crossref] [PubMed]

2014 (2)

C. Mateo-Segura, A. Dyke, H. Dyke, S. Haq, and Y. Hao, “Flat Luneburg lens via transformation optics for directive antenna applications,” IEEE Trans. Antenn. Propag. 62(4), 1945–1953 (2014).
[Crossref]

R. Yang, Z. Lei, L. Chen, Z. Wang, and Y. Hao, “Surface wave transformation lens antennas,” IEEE Trans. Antenn. Propag. 62(2), 973–977 (2014).
[Crossref]

2013 (2)

W. X. Jiang, C. W. Qiu, T. Han, S. Zhang, and T. J. Cui, “Creation of ghost illusions using wave dynamics in metamaterials,” Adv. Funct. Mater. 23(32), 4028–4034 (2013).
[Crossref]

P.-H. Tichit, S. N. Burokur, C.-W. Qiu, and A. de Lustrac, “Experimental verification of isotropic radiation from a coherent dipole source via electric-field-driven LC resonator metamaterials,” Phys. Rev. Lett. 111(13), 133901 (2013).
[Crossref] [PubMed]

2011 (2)

W. X. Jiang and T. J. Cui, “Radar illusion via metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(2), 026601 (2011).
[Crossref] [PubMed]

W. X. Jiang, T. J. Cui, X. M. Yang, H. F. Ma, and Q. Cheng, “Shrinking an arbitrary object as one desires using metamaterials,” Appl. Phys. Lett. 98(20), 204101 (2011).
[Crossref]

2010 (3)

H. F. Ma and T. J. Cui, “Three-dimensional broadband and broad-angle transformation-optics lens,” Nat. Commun. 1(8), 124 (2010).
[Crossref] [PubMed]

N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater. 9(2), 129–132 (2010).
[Crossref] [PubMed]

P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Waveguide taper engineering using coordinate transformation technology,” Opt. Express 18(2), 767–772 (2010).
[Crossref] [PubMed]

2009 (2)

A. Sellier, S. N. Burokur, B. Kanté, and A. de Lustrac, “Negative refractive index metamaterials using only metallic cut wires,” Opt. Express 17(8), 6301–6310 (2009).
[Crossref] [PubMed]

Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z. Q. Zhang, and C. T. Chan, “Illusion optics: The optical transformation of an object into another object,” Phys. Rev. Lett. 102(25), 253902 (2009).
[Crossref] [PubMed]

2008 (4)

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett. 100(6), 063903 (2008).
[Crossref] [PubMed]

D. H. Kwon and D. H. Werner, “Transformation optical designs for wave collimators, flat lenses and right-angle bends,” New J. Phys. 10(11), 115023 (2008).
[Crossref]

D. A. Roberts, M. Rahm, J. B. Pendry, and D. R. Smith, “Transformation-optical design of sharp waveguide bends and corners,” Appl. Phys. Lett. 93(25), 251111 (2008).
[Crossref]

M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, “Transformation-optical design of adaptive beam bends and beam expanders,” Opt. Express 16(15), 11555–11567 (2008).
[Crossref] [PubMed]

2006 (5)

D. Schurig, J. B. Pendry, and D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express 14(21), 9794–9804 (2006).
[Crossref] [PubMed]

D. Schurig, J. J. Mock, and D. R. Smith, “Electric-field-coupled resonators for negative permittivity metamaterials,” Appl. Phys. Lett. 88(4), 041109 (2006).
[Crossref]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[Crossref] [PubMed]

U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
[Crossref] [PubMed]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[Crossref] [PubMed]

1999 (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[Crossref]

Burokur, S. N.

J. Yi, G.-P. Piau, A. de Lustrac, and S. N. Burokur, “Electromagnetic field tapering using all-dielectric gradient index materials,” Sci. Rep. 6(1), 30661 (2016).
[Crossref] [PubMed]

J. Yi, S. N. Burokur, G. P. Piau, and A. de Lustrac, “Coherent beam control with an all-dielectric transformation optics based lens,” Sci. Rep. 6(1), 18819 (2016).
[Crossref] [PubMed]

J. Yi, S. N. Burokur, and A. de Lustrac, “Experimental validation of a transformation optics based lens for beam steering,” Appl. Phys. Lett. 107(15), 154101 (2015).
[Crossref]

J. Yi, S. N. Burokur, G. P. Piau, and A. de Lustrac, “Restoring in-phase emissions from non-planar radiating elements using a transformation optics based lens,” Appl. Phys. Lett. 107(2), 024101 (2015).
[Crossref]

J. Yi, P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Illusion optics: Optically transforming the nature and the location of electromagnetic emissions,” J. Appl. Phys. 117(8), 084903 (2015).
[Crossref]

J. Yi, S. N. Burokur, and A. de Lustrac, “Conceptual design of a beam steering lens through transformation electromagnetics,” Opt. Express 23(10), 12942–12951 (2015).
[Crossref] [PubMed]

P.-H. Tichit, S. N. Burokur, C.-W. Qiu, and A. de Lustrac, “Experimental verification of isotropic radiation from a coherent dipole source via electric-field-driven LC resonator metamaterials,” Phys. Rev. Lett. 111(13), 133901 (2013).
[Crossref] [PubMed]

P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Waveguide taper engineering using coordinate transformation technology,” Opt. Express 18(2), 767–772 (2010).
[Crossref] [PubMed]

A. Sellier, S. N. Burokur, B. Kanté, and A. de Lustrac, “Negative refractive index metamaterials using only metallic cut wires,” Opt. Express 17(8), 6301–6310 (2009).
[Crossref] [PubMed]

Chan, C. T.

Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z. Q. Zhang, and C. T. Chan, “Illusion optics: The optical transformation of an object into another object,” Phys. Rev. Lett. 102(25), 253902 (2009).
[Crossref] [PubMed]

Chen, H.

Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z. Q. Zhang, and C. T. Chan, “Illusion optics: The optical transformation of an object into another object,” Phys. Rev. Lett. 102(25), 253902 (2009).
[Crossref] [PubMed]

Chen, L.

R. Yang, Z. Lei, L. Chen, Z. Wang, and Y. Hao, “Surface wave transformation lens antennas,” IEEE Trans. Antenn. Propag. 62(2), 973–977 (2014).
[Crossref]

Cheng, Q.

W. X. Jiang, T. J. Cui, X. M. Yang, H. F. Ma, and Q. Cheng, “Shrinking an arbitrary object as one desires using metamaterials,” Appl. Phys. Lett. 98(20), 204101 (2011).
[Crossref]

Cui, T. J.

W. X. Jiang, C. W. Qiu, T. Han, S. Zhang, and T. J. Cui, “Creation of ghost illusions using wave dynamics in metamaterials,” Adv. Funct. Mater. 23(32), 4028–4034 (2013).
[Crossref]

W. X. Jiang and T. J. Cui, “Radar illusion via metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(2), 026601 (2011).
[Crossref] [PubMed]

W. X. Jiang, T. J. Cui, X. M. Yang, H. F. Ma, and Q. Cheng, “Shrinking an arbitrary object as one desires using metamaterials,” Appl. Phys. Lett. 98(20), 204101 (2011).
[Crossref]

H. F. Ma and T. J. Cui, “Three-dimensional broadband and broad-angle transformation-optics lens,” Nat. Commun. 1(8), 124 (2010).
[Crossref] [PubMed]

Cummer, S. A.

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett. 100(6), 063903 (2008).
[Crossref] [PubMed]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[Crossref] [PubMed]

de Lustrac, A.

J. Yi, S. N. Burokur, G. P. Piau, and A. de Lustrac, “Coherent beam control with an all-dielectric transformation optics based lens,” Sci. Rep. 6(1), 18819 (2016).
[Crossref] [PubMed]

J. Yi, G.-P. Piau, A. de Lustrac, and S. N. Burokur, “Electromagnetic field tapering using all-dielectric gradient index materials,” Sci. Rep. 6(1), 30661 (2016).
[Crossref] [PubMed]

J. Yi, P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Illusion optics: Optically transforming the nature and the location of electromagnetic emissions,” J. Appl. Phys. 117(8), 084903 (2015).
[Crossref]

J. Yi, S. N. Burokur, and A. de Lustrac, “Experimental validation of a transformation optics based lens for beam steering,” Appl. Phys. Lett. 107(15), 154101 (2015).
[Crossref]

J. Yi, S. N. Burokur, G. P. Piau, and A. de Lustrac, “Restoring in-phase emissions from non-planar radiating elements using a transformation optics based lens,” Appl. Phys. Lett. 107(2), 024101 (2015).
[Crossref]

J. Yi, S. N. Burokur, and A. de Lustrac, “Conceptual design of a beam steering lens through transformation electromagnetics,” Opt. Express 23(10), 12942–12951 (2015).
[Crossref] [PubMed]

P.-H. Tichit, S. N. Burokur, C.-W. Qiu, and A. de Lustrac, “Experimental verification of isotropic radiation from a coherent dipole source via electric-field-driven LC resonator metamaterials,” Phys. Rev. Lett. 111(13), 133901 (2013).
[Crossref] [PubMed]

P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Waveguide taper engineering using coordinate transformation technology,” Opt. Express 18(2), 767–772 (2010).
[Crossref] [PubMed]

A. Sellier, S. N. Burokur, B. Kanté, and A. de Lustrac, “Negative refractive index metamaterials using only metallic cut wires,” Opt. Express 17(8), 6301–6310 (2009).
[Crossref] [PubMed]

Dyke, A.

C. Mateo-Segura, A. Dyke, H. Dyke, S. Haq, and Y. Hao, “Flat Luneburg lens via transformation optics for directive antenna applications,” IEEE Trans. Antenn. Propag. 62(4), 1945–1953 (2014).
[Crossref]

Dyke, H.

C. Mateo-Segura, A. Dyke, H. Dyke, S. Haq, and Y. Hao, “Flat Luneburg lens via transformation optics for directive antenna applications,” IEEE Trans. Antenn. Propag. 62(4), 1945–1953 (2014).
[Crossref]

Han, D.

Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z. Q. Zhang, and C. T. Chan, “Illusion optics: The optical transformation of an object into another object,” Phys. Rev. Lett. 102(25), 253902 (2009).
[Crossref] [PubMed]

Han, T.

W. X. Jiang, C. W. Qiu, T. Han, S. Zhang, and T. J. Cui, “Creation of ghost illusions using wave dynamics in metamaterials,” Adv. Funct. Mater. 23(32), 4028–4034 (2013).
[Crossref]

Hao, Y.

C. Mateo-Segura, A. Dyke, H. Dyke, S. Haq, and Y. Hao, “Flat Luneburg lens via transformation optics for directive antenna applications,” IEEE Trans. Antenn. Propag. 62(4), 1945–1953 (2014).
[Crossref]

R. Yang, Z. Lei, L. Chen, Z. Wang, and Y. Hao, “Surface wave transformation lens antennas,” IEEE Trans. Antenn. Propag. 62(2), 973–977 (2014).
[Crossref]

Haq, S.

C. Mateo-Segura, A. Dyke, H. Dyke, S. Haq, and Y. Hao, “Flat Luneburg lens via transformation optics for directive antenna applications,” IEEE Trans. Antenn. Propag. 62(4), 1945–1953 (2014).
[Crossref]

Holden, A. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[Crossref]

Jiang, W. X.

W. X. Jiang, C. W. Qiu, T. Han, S. Zhang, and T. J. Cui, “Creation of ghost illusions using wave dynamics in metamaterials,” Adv. Funct. Mater. 23(32), 4028–4034 (2013).
[Crossref]

W. X. Jiang, T. J. Cui, X. M. Yang, H. F. Ma, and Q. Cheng, “Shrinking an arbitrary object as one desires using metamaterials,” Appl. Phys. Lett. 98(20), 204101 (2011).
[Crossref]

W. X. Jiang and T. J. Cui, “Radar illusion via metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(2), 026601 (2011).
[Crossref] [PubMed]

Justice, B. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[Crossref] [PubMed]

Kanté, B.

Kundtz, N.

N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater. 9(2), 129–132 (2010).
[Crossref] [PubMed]

Kwon, D. H.

D. H. Kwon and D. H. Werner, “Transformation optical designs for wave collimators, flat lenses and right-angle bends,” New J. Phys. 10(11), 115023 (2008).
[Crossref]

Lai, Y.

Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z. Q. Zhang, and C. T. Chan, “Illusion optics: The optical transformation of an object into another object,” Phys. Rev. Lett. 102(25), 253902 (2009).
[Crossref] [PubMed]

Lei, Z.

R. Yang, Z. Lei, L. Chen, Z. Wang, and Y. Hao, “Surface wave transformation lens antennas,” IEEE Trans. Antenn. Propag. 62(2), 973–977 (2014).
[Crossref]

Leonhardt, U.

U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
[Crossref] [PubMed]

Ma, H. F.

W. X. Jiang, T. J. Cui, X. M. Yang, H. F. Ma, and Q. Cheng, “Shrinking an arbitrary object as one desires using metamaterials,” Appl. Phys. Lett. 98(20), 204101 (2011).
[Crossref]

H. F. Ma and T. J. Cui, “Three-dimensional broadband and broad-angle transformation-optics lens,” Nat. Commun. 1(8), 124 (2010).
[Crossref] [PubMed]

Mateo-Segura, C.

C. Mateo-Segura, A. Dyke, H. Dyke, S. Haq, and Y. Hao, “Flat Luneburg lens via transformation optics for directive antenna applications,” IEEE Trans. Antenn. Propag. 62(4), 1945–1953 (2014).
[Crossref]

Mock, J. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[Crossref] [PubMed]

D. Schurig, J. J. Mock, and D. R. Smith, “Electric-field-coupled resonators for negative permittivity metamaterials,” Appl. Phys. Lett. 88(4), 041109 (2006).
[Crossref]

Ng, J.

Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z. Q. Zhang, and C. T. Chan, “Illusion optics: The optical transformation of an object into another object,” Phys. Rev. Lett. 102(25), 253902 (2009).
[Crossref] [PubMed]

Pendry, J. B.

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett. 100(6), 063903 (2008).
[Crossref] [PubMed]

D. A. Roberts, M. Rahm, J. B. Pendry, and D. R. Smith, “Transformation-optical design of sharp waveguide bends and corners,” Appl. Phys. Lett. 93(25), 251111 (2008).
[Crossref]

M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, “Transformation-optical design of adaptive beam bends and beam expanders,” Opt. Express 16(15), 11555–11567 (2008).
[Crossref] [PubMed]

D. Schurig, J. B. Pendry, and D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express 14(21), 9794–9804 (2006).
[Crossref] [PubMed]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[Crossref] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[Crossref] [PubMed]

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[Crossref]

Piau, G. P.

J. Yi, S. N. Burokur, G. P. Piau, and A. de Lustrac, “Coherent beam control with an all-dielectric transformation optics based lens,” Sci. Rep. 6(1), 18819 (2016).
[Crossref] [PubMed]

J. Yi, S. N. Burokur, G. P. Piau, and A. de Lustrac, “Restoring in-phase emissions from non-planar radiating elements using a transformation optics based lens,” Appl. Phys. Lett. 107(2), 024101 (2015).
[Crossref]

Piau, G.-P.

J. Yi, G.-P. Piau, A. de Lustrac, and S. N. Burokur, “Electromagnetic field tapering using all-dielectric gradient index materials,” Sci. Rep. 6(1), 30661 (2016).
[Crossref] [PubMed]

Qiu, C. W.

W. X. Jiang, C. W. Qiu, T. Han, S. Zhang, and T. J. Cui, “Creation of ghost illusions using wave dynamics in metamaterials,” Adv. Funct. Mater. 23(32), 4028–4034 (2013).
[Crossref]

Qiu, C.-W.

P.-H. Tichit, S. N. Burokur, C.-W. Qiu, and A. de Lustrac, “Experimental verification of isotropic radiation from a coherent dipole source via electric-field-driven LC resonator metamaterials,” Phys. Rev. Lett. 111(13), 133901 (2013).
[Crossref] [PubMed]

Rahm, M.

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett. 100(6), 063903 (2008).
[Crossref] [PubMed]

M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, “Transformation-optical design of adaptive beam bends and beam expanders,” Opt. Express 16(15), 11555–11567 (2008).
[Crossref] [PubMed]

D. A. Roberts, M. Rahm, J. B. Pendry, and D. R. Smith, “Transformation-optical design of sharp waveguide bends and corners,” Appl. Phys. Lett. 93(25), 251111 (2008).
[Crossref]

Robbins, D. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[Crossref]

Roberts, D. A.

M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, “Transformation-optical design of adaptive beam bends and beam expanders,” Opt. Express 16(15), 11555–11567 (2008).
[Crossref] [PubMed]

D. A. Roberts, M. Rahm, J. B. Pendry, and D. R. Smith, “Transformation-optical design of sharp waveguide bends and corners,” Appl. Phys. Lett. 93(25), 251111 (2008).
[Crossref]

Schurig, D.

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett. 100(6), 063903 (2008).
[Crossref] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[Crossref] [PubMed]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[Crossref] [PubMed]

D. Schurig, J. J. Mock, and D. R. Smith, “Electric-field-coupled resonators for negative permittivity metamaterials,” Appl. Phys. Lett. 88(4), 041109 (2006).
[Crossref]

D. Schurig, J. B. Pendry, and D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express 14(21), 9794–9804 (2006).
[Crossref] [PubMed]

Sellier, A.

Smith, D. R.

N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater. 9(2), 129–132 (2010).
[Crossref] [PubMed]

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett. 100(6), 063903 (2008).
[Crossref] [PubMed]

M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, “Transformation-optical design of adaptive beam bends and beam expanders,” Opt. Express 16(15), 11555–11567 (2008).
[Crossref] [PubMed]

D. A. Roberts, M. Rahm, J. B. Pendry, and D. R. Smith, “Transformation-optical design of sharp waveguide bends and corners,” Appl. Phys. Lett. 93(25), 251111 (2008).
[Crossref]

D. Schurig, J. J. Mock, and D. R. Smith, “Electric-field-coupled resonators for negative permittivity metamaterials,” Appl. Phys. Lett. 88(4), 041109 (2006).
[Crossref]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[Crossref] [PubMed]

D. Schurig, J. B. Pendry, and D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express 14(21), 9794–9804 (2006).
[Crossref] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[Crossref] [PubMed]

Starr, A. F.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[Crossref] [PubMed]

Stewart, W. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[Crossref]

Tichit, P.-H.

J. Yi, P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Illusion optics: Optically transforming the nature and the location of electromagnetic emissions,” J. Appl. Phys. 117(8), 084903 (2015).
[Crossref]

P.-H. Tichit, S. N. Burokur, C.-W. Qiu, and A. de Lustrac, “Experimental verification of isotropic radiation from a coherent dipole source via electric-field-driven LC resonator metamaterials,” Phys. Rev. Lett. 111(13), 133901 (2013).
[Crossref] [PubMed]

P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Waveguide taper engineering using coordinate transformation technology,” Opt. Express 18(2), 767–772 (2010).
[Crossref] [PubMed]

Wang, Z.

R. Yang, Z. Lei, L. Chen, Z. Wang, and Y. Hao, “Surface wave transformation lens antennas,” IEEE Trans. Antenn. Propag. 62(2), 973–977 (2014).
[Crossref]

Werner, D. H.

D. H. Kwon and D. H. Werner, “Transformation optical designs for wave collimators, flat lenses and right-angle bends,” New J. Phys. 10(11), 115023 (2008).
[Crossref]

Xiao, J.

Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z. Q. Zhang, and C. T. Chan, “Illusion optics: The optical transformation of an object into another object,” Phys. Rev. Lett. 102(25), 253902 (2009).
[Crossref] [PubMed]

Yang, R.

R. Yang, Z. Lei, L. Chen, Z. Wang, and Y. Hao, “Surface wave transformation lens antennas,” IEEE Trans. Antenn. Propag. 62(2), 973–977 (2014).
[Crossref]

Yang, X. M.

W. X. Jiang, T. J. Cui, X. M. Yang, H. F. Ma, and Q. Cheng, “Shrinking an arbitrary object as one desires using metamaterials,” Appl. Phys. Lett. 98(20), 204101 (2011).
[Crossref]

Yi, J.

J. Yi, G.-P. Piau, A. de Lustrac, and S. N. Burokur, “Electromagnetic field tapering using all-dielectric gradient index materials,” Sci. Rep. 6(1), 30661 (2016).
[Crossref] [PubMed]

J. Yi, S. N. Burokur, G. P. Piau, and A. de Lustrac, “Coherent beam control with an all-dielectric transformation optics based lens,” Sci. Rep. 6(1), 18819 (2016).
[Crossref] [PubMed]

J. Yi, S. N. Burokur, G. P. Piau, and A. de Lustrac, “Restoring in-phase emissions from non-planar radiating elements using a transformation optics based lens,” Appl. Phys. Lett. 107(2), 024101 (2015).
[Crossref]

J. Yi, S. N. Burokur, and A. de Lustrac, “Experimental validation of a transformation optics based lens for beam steering,” Appl. Phys. Lett. 107(15), 154101 (2015).
[Crossref]

J. Yi, P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Illusion optics: Optically transforming the nature and the location of electromagnetic emissions,” J. Appl. Phys. 117(8), 084903 (2015).
[Crossref]

J. Yi, S. N. Burokur, and A. de Lustrac, “Conceptual design of a beam steering lens through transformation electromagnetics,” Opt. Express 23(10), 12942–12951 (2015).
[Crossref] [PubMed]

Zhang, S.

W. X. Jiang, C. W. Qiu, T. Han, S. Zhang, and T. J. Cui, “Creation of ghost illusions using wave dynamics in metamaterials,” Adv. Funct. Mater. 23(32), 4028–4034 (2013).
[Crossref]

Zhang, Z. Q.

Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z. Q. Zhang, and C. T. Chan, “Illusion optics: The optical transformation of an object into another object,” Phys. Rev. Lett. 102(25), 253902 (2009).
[Crossref] [PubMed]

Adv. Funct. Mater. (1)

W. X. Jiang, C. W. Qiu, T. Han, S. Zhang, and T. J. Cui, “Creation of ghost illusions using wave dynamics in metamaterials,” Adv. Funct. Mater. 23(32), 4028–4034 (2013).
[Crossref]

Appl. Phys. Lett. (5)

W. X. Jiang, T. J. Cui, X. M. Yang, H. F. Ma, and Q. Cheng, “Shrinking an arbitrary object as one desires using metamaterials,” Appl. Phys. Lett. 98(20), 204101 (2011).
[Crossref]

J. Yi, S. N. Burokur, and A. de Lustrac, “Experimental validation of a transformation optics based lens for beam steering,” Appl. Phys. Lett. 107(15), 154101 (2015).
[Crossref]

J. Yi, S. N. Burokur, G. P. Piau, and A. de Lustrac, “Restoring in-phase emissions from non-planar radiating elements using a transformation optics based lens,” Appl. Phys. Lett. 107(2), 024101 (2015).
[Crossref]

D. A. Roberts, M. Rahm, J. B. Pendry, and D. R. Smith, “Transformation-optical design of sharp waveguide bends and corners,” Appl. Phys. Lett. 93(25), 251111 (2008).
[Crossref]

D. Schurig, J. J. Mock, and D. R. Smith, “Electric-field-coupled resonators for negative permittivity metamaterials,” Appl. Phys. Lett. 88(4), 041109 (2006).
[Crossref]

IEEE Trans. Antenn. Propag. (2)

R. Yang, Z. Lei, L. Chen, Z. Wang, and Y. Hao, “Surface wave transformation lens antennas,” IEEE Trans. Antenn. Propag. 62(2), 973–977 (2014).
[Crossref]

C. Mateo-Segura, A. Dyke, H. Dyke, S. Haq, and Y. Hao, “Flat Luneburg lens via transformation optics for directive antenna applications,” IEEE Trans. Antenn. Propag. 62(4), 1945–1953 (2014).
[Crossref]

IEEE Trans. Microw. Theory Tech. (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[Crossref]

J. Appl. Phys. (1)

J. Yi, P.-H. Tichit, S. N. Burokur, and A. de Lustrac, “Illusion optics: Optically transforming the nature and the location of electromagnetic emissions,” J. Appl. Phys. 117(8), 084903 (2015).
[Crossref]

Nat. Commun. (1)

H. F. Ma and T. J. Cui, “Three-dimensional broadband and broad-angle transformation-optics lens,” Nat. Commun. 1(8), 124 (2010).
[Crossref] [PubMed]

Nat. Mater. (1)

N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater. 9(2), 129–132 (2010).
[Crossref] [PubMed]

New J. Phys. (1)

D. H. Kwon and D. H. Werner, “Transformation optical designs for wave collimators, flat lenses and right-angle bends,” New J. Phys. 10(11), 115023 (2008).
[Crossref]

Opt. Express (5)

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

W. X. Jiang and T. J. Cui, “Radar illusion via metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83(2), 026601 (2011).
[Crossref] [PubMed]

Phys. Rev. Lett. (3)

Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z. Q. Zhang, and C. T. Chan, “Illusion optics: The optical transformation of an object into another object,” Phys. Rev. Lett. 102(25), 253902 (2009).
[Crossref] [PubMed]

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett. 100(6), 063903 (2008).
[Crossref] [PubMed]

P.-H. Tichit, S. N. Burokur, C.-W. Qiu, and A. de Lustrac, “Experimental verification of isotropic radiation from a coherent dipole source via electric-field-driven LC resonator metamaterials,” Phys. Rev. Lett. 111(13), 133901 (2013).
[Crossref] [PubMed]

Sci. Rep. (2)

J. Yi, S. N. Burokur, G. P. Piau, and A. de Lustrac, “Coherent beam control with an all-dielectric transformation optics based lens,” Sci. Rep. 6(1), 18819 (2016).
[Crossref] [PubMed]

J. Yi, G.-P. Piau, A. de Lustrac, and S. N. Burokur, “Electromagnetic field tapering using all-dielectric gradient index materials,” Sci. Rep. 6(1), 30661 (2016).
[Crossref] [PubMed]

Science (3)

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[Crossref] [PubMed]

U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006).
[Crossref] [PubMed]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[Crossref] [PubMed]

Other (1)

D. H. Werner and D.-H. Kwon, Transformation Electromagnetics and Metamaterials: Fundamental Principles and Applications (Springer, 2014).

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Figures (8)

Fig. 1
Fig. 1

Illustrations depicting of four different types of transformations. (a) cosinusoidal, (b) parabolic, (c) logarithmic and (d) reciprocal transformation.

Fig. 2
Fig. 2

Components of the permittivity and permeability tensors θ ¯ ¯ for the four different transformation techniques: (a) cosinusoidal, (b) parabolic, (c) logarithmic, and (d) reciprocal transformation.

Fig. 3
Fig. 3

Electric field distribution for the four different types of transformation techniques: (a) cosinusoidal, (b) parabolic, (c) logarithmic, and (d) reciprocal transformation. (e) Electric field distribution for transmission without taper between the two waveguides. (f) Transmission (S21) of the four tapering structures compared to the case without taper.

Fig. 4
Fig. 4

Electric field distribution of the TE3 mode in the case of the reciprocal transformation at 25 GHz.

Fig. 5
Fig. 5

Diagram of the two-step parameter simplification procedure. (a) Original Cartesian coordinate. (b) Eigenvectors of material properties matrix from (a). (c) Coordinate system of simplified parameters: (1) Calculation of eigenvectors from (a) to (b) and (2) parameter reduction by dispersion relation from (b) to (c).

Fig. 6
Fig. 6

Effective parameter distributions: (a) permeability μv’v’ and (b) permittivity εz’z’.

Fig. 7
Fig. 7

(a) Design of 3D discrete taper composed of three different types of unit cells. (b) Effective permittivity of the cell composed of an air hole in a dielectric host medium. (c) Effective permittivity of an E-LC resonator embedded in a dielectric cube. (d) Effective permeability of a SRR resonator embedded in a dielectric cube.

Fig. 8
Fig. 8

Simulated electric near-field distribution. (a) Original space without the tapering device. 3D discrete tapering device in the xy plane at (b) 9.2 GHz, (c) 10 GHz, and (d) 10.8 GHz. The lower row shows the field distribution in the yz plane at the output waveguide.

Tables (3)

Tables Icon

Table 1 Mathematical Expressions Defining the Transformation Techniques

Tables Icon

Table 2 S-parameters of the Transformation Techniques at 25 GHz for a TE3 Excitation Mode

Tables Icon

Table 3 Ratio of Throughput Between the Output and Input Ports

Equations (10)

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

ε i'j' = J i i' J j j' ε 0 δ ij det(J) and μ i'j' = J i i' J j j' μ 0 δ ij det(J) with J α α' = x ' α x α
θ ¯ ¯ =[ θ xx ( x',y' ) θ xy ( x',y' ) 0 θ xy ( x',y' ) θ yy ( x',y' ) 0 0 0 θ zz ( x',y' ) ].
( m n y n 0 y n n 2 + y 2 mn 0 0 0 m n )
α=[ m 2 + n 2 + y 2 + ( m 2 + n 2 + y 2 ) 2 4 m 2 n 2 2mn m 2 + n 2 + y 2 ( m 2 + n 2 + y 2 ) 2 4 m 2 n 2 2mn m n ]
λ=[ m 2 n 2 y 2 + ( m 2 + n 2 + y 2 ) 2 4 m 2 n 2 2my 1 0 m 2 n 2 y 2 ( m 2 + n 2 + y 2 ) 2 4 m 2 n 2 2my 1 0 0 0 1 ]
ε zz ( μ uv 2 μ uv μ vv )+ μ uu k u 2 + k v ( μ vv k v 2 μ uv k u )=0.
μ v'v' = m 2 + n 2 + y 2 ( m 2 + n 2 + y 2 ) 2 4 m 2 n 2 2 n 2
ε z'z' = m 2 + n 2 + y 2 + ( m 2 + n 2 + y 2 ) 2 4 m 2 n 2 m 2 + n 2 + y 2 ( m 2 + n 2 + y 2 ) 2 4 m 2 n 2 .
β= Cos 1 [ m 2 n 2 y 2 + ( m 2 + n 2 + y 2 ) 2 4 m 2 n 2 2my 1+ ( m 2 n 2 y 2 + ( m 2 + n 2 + y 2 ) 2 4 m 2 n 2 ) 2 4 m 2 y 2 ].
ε e = ε a f a + ε h f h