Abstract

We analyze and experimentally realize coplanar imaging of transverse-electric (TE) modes surface waves using weakly anisotropic metasurface consisting of non-periodic subwavelength U-shaped metallic structures. Such metallic structures with the exciting coplanar dipole are integrated on the top surface of a thin dielectric board. A circuit model is utilized to analyze the characteristics of the surface waves supported by the metasurface. By varying the geometrical parameters of the U-shaped metallic structures, the phases of surface waves are modulated, from which a planar lens is presented for the TE-mode coplanar imaging. The analyses and measurements show that anisotropies of the U-shaped metallic structures have little influence on the imaging properties of the planar lens. The measurement results have good agreements to numerical simulations.

©2013 Optical Society of America

1. Introduction

Metamaterials provides concepts and methods of manipulating electromagnetic (EM) waves according to the predetermined designs. This has been mostly proceeding in three-dimensional situations for the past a few years. Recently, a single layer of metamaterials (or very thin metamaterials) also referred to as metasurface or metafilm has attracted increasingly interests due to the advantages of low cost, easy fabrication, low loss, and compact size over the bulk metamaterials. For two-dimensional (2D) metamaterials, various analysis methods are established and plenty of applications are realized. For example, a general sheet transition condition (GSTC) has been utilized to analyze the ungrounded metasurfaces [1], and a very thin cloak was presented using the method [2]. For grounded metasurfaces, impedance boundary condition has been adopted to design low profile antennas [3, 4]. A high efficiency bridge linking propagation waves and surface waves was realized by modulating the reflected phase of the metasurface [5]; the snell’s low was generalized to study the propagation phase discontinuity [6]; and the light polarization is manipulated with ultrathin metasurfaces [7].

In this letter, we focus on manipulating the surface waves on ungrounded metasurfaces. Specified structures supporting surface waves can be found in early works, such as corrugated metal surface [8, 9] or cylinder [10, 11]. These surface waves are analogy in their dispersion properties to surface plasmon polaritons (SPPs) existing on interfaces between a metal and a dielectric at the optical frequency. Actually, by structuring metal surfaces with subwavelength slits or holes, a concept of spoof SPPs has been introduced at the vicinity of metal surfaces in the terahertz and microwave frequencies [12, 13]. Broadband ultrasubwavelength waveguiding at terahertz and infraed freuquencies are also described based on strongly coupled interlaced charge density waves [14]. This concept offers the possibility to realize compact integrated plasmonic devices with well-designed metasurfaces. Ultrathin metafilms consisting of split-ring resonators (SRRs) [15] and complementary split-ring resonators (CSRRs) [16] were proposed for guiding the spoof SPPs. Grooved metal surface with nearly-zero lateral thickness was also demonstrated to be a good candidate for guiding the tightly bounded spoof SPPs [17]. By discretizing the periodical units of such grooved metallic surface and displacing them on a planar or curved object, an ultrathin metasurface consisting of U-shaped metallic structures can be produced for guiding spoof SPPs. Based on this, a planar lens is then presented for coplanar imaging by modulating the propagation phase of spoof SPPs. The phase modulation is accomplished by changing the geometric parameters of units. More complicated functional SPP devices can also be created by designing the units, and the presented metasurface can be another good candidate to realize integrated planar systems [18]. In the process of preparing this paper, the authors have noticed that in-plane focusing of terahertz surface waves has been reported [19].

Physically, the propagation of surface waves on these guiding structures relies on the coupling of units. By introducing a groove into each metal patch, the capacitive coupling of such units is stronger than the traditional split-ring resonators (SRRs), and the inductive coupling of such units is stronger than the traditional metal patches. Hence the working frequency of surface waves or the plasma frequency of the spoof SPPs is significantly lowered. It is worth noting that the excessive magnetic coupling between units may bring in magnetoinductive waves [20], because in this case the spatial dispersion of a single resonant unit is involved since the wavelength of the surface waves is comparable with the unit size. And it would be better to avoid the working frequency being close to the first Brillouin zone, otherwise higher-order Floquet modes may emerge.

2. Analysis

The waveguide model in Fig. 1(a) shows the configuration of solving the eigen modes using electromagnetic simulation software (CST Microwave Studio). Periodic boundaries are used in the x and y directions, and the perfect electric conductor (PEC) boundary is used in the z direction since the open boundary is not supported by the eigen-mode solver of CST. Because the surface waves decay rapidly in the z direction, the PEC boundary has little effect on the propagation properties of the surface waves when the distance between PEC and the unit is sufficiently large.

 figure: Fig. 1

Fig. 1 (a) The waveguide model to solve the eigen modes of unit cell, a rectangular metal patch with a rectangular groove. (b) The effective circuit model of the waveguide model.

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The circuit models shown in Fig. 1(b) are utilized to analyze the propagation characteristics of the metasurface. The thin anisotropic unit is represented by a tensor surface admittance matrix

Y¯¯s=[YxxYxyYyxYyy].
In the absence of losses, Y¯¯s is anti-Hermitian, implying that Yxx and Yyy are imaginary and Yxy=Yyx. The air regions together with the PEC boundary are equivalent to shorted transmission lines. Note that electromagnetic modes in air regions contain both TE and TM modes due to the anisotropy of the unit. Assuming that the surface wave possesses the wave number kt, we have Y0TM=Y0k0/kz and Y0TE=Y0kz/k0, where kz=k02kt2, and Y0 and k0 are the wave admittance and wavenumber in free space, respectively. Supporting surface waves on the metasurface composed of the unit cells needs to satisfy the transmission-line resonance equation
[YxxYxyYyxYyy]+2[jY0TMcot(kzH)00jY0TEcot(kzH)]=0,
Since kz is imaginary for surface waves on the metasurface, cot(kzH) goes to j when H is sufficiently large. Then the input admittance of the transmission line corresponds to the wave admittance with open boundary, and Eq. (2) can be written as
(Yxx2Y0TM)(Yyy2Y0TE)=YxyYyx,
For weak anisotropies, we have YxyYyxYxxYyy, and then
(Yxx2Y0TM)(Yyy2Y0TE)=0.
We observe that the TE and TM modes are separated if the propagation direction of surface waves is along the principle axis of the metasurface. Supposing kt=kx and ky=0, TM modes are supported by Yxx or TE modes are supported by Yyy. In the other word, for the separated case, the metasurface can be treated as isotropic surface with admittance Yxx for the TM modes or Yyy for the TE modes. The presented metasurface consisting of U-shaped metallic structures is excited by a coplanar-placed dipole, hence only the TE modes (with respect to z) interact with the metasurface.

3. Simulations and design

With the configuration shown in Fig. 2(a), we obtain the dispersion relation of the U-shaped unit by sweeping the phase variations in the x and y directions using the eigen-mode solver of CST. From the dispersion surface shown in Fig. 2(b), we notice that the surface waves on the presented ultrathin metasurface is able to mimic spoof SPPs in two dimensions. To manipulate the behaviors of the surface wave, we need to know how the geometrical parameters of the element affect the phase changes at a specified frequency.

 figure: Fig. 2

Fig. 2 (a) The detailed geometrical parameters of a single U-shaped metallic structure, in which px=3.4mm, py=4.6mm, dx=3mm, dy=4mm, w=1.5mm, h=2.2mm, and t=1mm. The thickness of the U-shaped metallic structure is 0.018mm. The lossless dielectric constant is 2.2. (b) The 2D dispersion surface of the single element with the same geometric parameters as in Fig. 2(a).

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Figure 3 illustrates the iso-frequency curves of the unit elements with different groove heights at 11 GHz which is far away from the edge of Brillouin zone. From Fig. 3, we clearly observe that the isofrequency curve approaches a circle when the groove length becomes smaller and smaller, implying that the degree of anisotropy decreases.

 figure: Fig. 3

Fig. 3 Isofrequency curves of the U-shaped metallic structure at 11GHz when the groove length h increases from 1 mm to 3.4 mm with a step of 0.3 mm. The dashed red arrow shows the tendency of the curves with increasing h.

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In the design of a coplanar lens presented in Fig. 4, the elements with deep grooves are placed in the middle of the lens. Then the surface wave passes through these elements in a line nearly parallel to the x axis. According to previous analysis, the TE surface waves feel these elements as isotropic ones with admittance Yyy and the wave number of the surface wave is kx. The elements with shallow grooves can be safely treated as isotropic since their dispersion curves are close to circles no matter whether the propagation direction of the surface wave is along the principle axis or not. When calculating the phase changes of the surface wave when passing through the coplanar lens, the propagation direction is assumed to be along the x axis. Thereby the phase of surface wave can be modulated by relating the groove lengths and phase changes in the x direction. The imaging system is illustrated in Fig. 4, in which a coax-fed dipole which is parallel to the lens is used to excite the TE surface waves. As the phases of surface waves are purposely modulated, an image of the source is formed by focusing the transmitted waves.

 figure: Fig. 4

Fig. 4 (a) The schematic diagram of the dipole source, whose length is 12mm. (b) The schematic diagram of the metasurface lens.

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Figure 5(a) displays the relationship of the phase change in the x direction to the groove length at specific frequencies. The operating frequency is designed as 11 GHz, and both positions of the source and image are designed to be 50 mm away from the lens.

 figure: Fig. 5

Fig. 5 (a) Relationship of phase changes in the x direction of the unit φx to the depths of grooves h. (b) The phase distribution φs at the left edge of the lens and the designed distribution of groove depth h along the y direction. The horizontal coordinate represents the positions of the U-shaped metallic structures along the y direction.

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As the dipole is not a perfect point source, the phase distribution φs at the left edge of the lens, which is closer to the source, is extracted from CST as is depicted by the blue line in Fig. 5(b). Because the source distance equals to the image distance, the optical length from the source to the lens is symmetrical to that from the image to the lens. Then the equality of optical length leads to the following equation

2φs(i)+mφx(i)+2nπ=2φs(1)+mφx(1),
where φx represents the phase change when the surface wave pass through a single unit, m is the number of units along the x direction which is design to be 12, and n is an integer. i=1,2,...9 is the row index of the upper half of the lens. The design of the lower half part is symmetrical to that of the upper half. Using the results shown in Fig. 5(a), we obtain the distribution of groove lengths h along the y direction, as demonstrated by the green line in Fig. 5(b). Note that the grooves with heights less than 1mm have been represented by grooves with heights of 1mm as the phase changes of these units are almost identical.

4. Experimental results

After obtaining all the necessary information for designing the metasurface lens, we have fabricated the imaging system using the standard printed circuit board. In the process of designing the lens, we assume the propagation paths of the waves are parallel to x axis so as to utilize the theory of geometrical optics. Because the propagation path of the surface wave on the planar lens is not strictly along x axis as in the theoretical design, a deviation of 4.5mm of the focus point between the theory and the structural simulations is observed. The structural simulations show that the working frequency of the lens is 10.5GHz and image distance is 45.5mm. In measurements, the sample is fixed on a motor station, another dipole having the same size as the source is fixed 1mm above the metasurface by a trestle. Both dipoles are connected to an Agilent N5230C network analyzer with coaxial lines. By moving the motor station, the y components of the electric fields on the measuring plane shown in Fig. 6(c) is recorded. In the measurement, there is no metal cover placed above the sample. That is, the measurement is processed in an open environment. Because the record results by the test probe are actually the amplitudes and phase of S21, extra propagation losses between the two dipoles are introduced, and the mismatch of the probe with the connecting coaxial line will also reduce the amplitudes of S21. As a result, Differences in quantities between the simulation and measurements are emerged as shown in Fig. 6(c). Nevertheless, the relative phases at each position are not affected by the losses and have been recorded by the probe. As can be seen from Fig. 6(c), the measured distributions of the y-component electric fields on the measurement plane are in good agreements with the simulated results.

 figure: Fig. 6

Fig. 6 The simulation and measurement results. (a) The measurement configuration, in which the measurement plane is 2 mm above the metasurface lens. (b) A section of the metasurface lens. Numbers below the section are detailed values of heights of the corresponding U-shaped units. (c) The measurement (upper) and simulation (lower) results of the y-component electric fields.

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Conclusions

In summary, U-shaped metallic structures are introduced to compose an ultrathin metasurface to support TE-mode surface waves, which is analogy in their dispersion properties to spoof SPPs. By varying the groove heights of the U-shaped units, phases of the surface waves are modulated and a metasurface lens is presented for coplanar imaging. More complicated functional metasurfaces or plasmonic devices are also able to design with these ultrathin U-shaped metallic structures.

Acknowledgments

This work was supported by the National Science Foundation of China under Grants 60990320, 60990324, 61138001, and 60921063, the National High Tech (863) Project under Grants 2011AA010202 and 2012AA030402, and the 111 Project under Grant 111-2-05.

References and links

1. C. L. Holloway, D. C. Love, E. F. Kuester, J. A. Gordon, and D. A. Hill, “Use of Generalized Sheet Transition Conditions to Model Guided Waves on Metasurfaces/Metafilms,” IEEE Trans. Antenn. Propag. 60(11), 5173–5186 (2012). [CrossRef]  

2. P. Y. Chen and A. Alu, “Mantle cloaking using thin patterned metasurfaces,” Phys. Rev. B 84(20), 205110 (2011). [CrossRef]  

3. S. Maci, G. Minatti, M. Casaletti, and M. Bosiljevac, “Metasurfing: Addressing Waves on Impenetrable Metasurfaces,” IEEE Antennas Wirel. Propag. Lett. 10, 1499–1502 (2011). [CrossRef]  

4. M. Bosiljevac, M. Casaletti, F. Caminita, Z. Sipus, and S. Maci, “Non-Uniform Metasurface Luneburg Lens Antenna Design,” IEEE Trans. Antenn. Propag. 60(9), 4065–4073 (2012). [CrossRef]  

5. S. L. Sun, Q. He, S. Y. Xiao, Q. Xu, X. Li, and L. Zhou, “Gradient-index meta-surfaces as a bridge linking propagating waves and surface waves,” Nat. Mater. 11(5), 426–431 (2012). [CrossRef]   [PubMed]  

6. N. F. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction,” Science 334(6054), 333–337 (2011). [CrossRef]   [PubMed]  

7. Y. Zhao and A. Alu, “Manipulating light polarization with ultrathin plasmonic metasurfaces,” Phys. Rev. B 84(20), 205428 (2011). [CrossRef]  

8. R. A. Hurd, “The propagation of an electromagnetic wave along an infinite corrugated surface,” Can. J. Phys. 32(12), 727–734 (1954). [CrossRef]  

9. R. S. Elliott, “On the theory of corrugated plane surfaces,” Trans. IRE professional group on Antennas and Propagation. (71–81) 1954.

10. W. Rotman, “A study of single-surface corrugated guides,” Proceedings of the IRE (951–959)1951.

11. H. E. M. Barlow and A. E. Karbowiak, “An experimental investigation of the properties of corrugated cylindrical surface waveguides,” Proceedings of the IEEE-part III: Radio and Communication Engineering 101, 182–188 (1954).

12. J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004). [CrossRef]   [PubMed]  

13. F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt. 7(2), S97–S101 (2005). [CrossRef]  

14. T. A. Morgado, J. S. Marcos, M. G. Silveirinha, and S. I. Maslovski, “Ultraconfined interlaced plasmons,” Phys. Rev. Lett. 107(6), 063903 (2011). [CrossRef]   [PubMed]  

15. B. Reinhard, O. Paul, R. Beigang, and M. Rahm, “Experimental and numerical studies of terahertz surface waves on a thin metamaterial film,” Opt. Lett. 35(9), 1320–1322 (2010). [CrossRef]   [PubMed]  

16. M. Navarro-Cía, M. Beruete, S. Agrafiotis, F. Falcone, M. Sorolla, and S. A. Maier, “Broadband spoof plasmons and subwavelength electromagnetic energy confinement on ultrathin metafilms,” Opt. Express 17(20), 18184–18195 (2009). [CrossRef]   [PubMed]  

17. X. P. Shen, T. J. Cui, D. Martin-Cano, and F. J. Garcia-Vidal, “Conformal surface plasmons propagating on ultrathin and flexible films,” Proc. Natl. Acad. Sci. U.S.A. 110(1), 40–45 (2013). [CrossRef]   [PubMed]  

18. Q. Wu, J. P. Turpin, and D. H. Werner, “Integrated photonic systems based on transformation optics enabled gradient index devices,” Light Sci. Appl. 1(11), e38 (2012). [CrossRef]  

19. M. F. Volk, B. Reinhard, J. Neu, R. Beigang, and M. Rahm, “In-plane focusing of terahertz surface waves on a gradient index metamaterial film,” Opt. Lett. 38(12), 2156–2158 (2013). [CrossRef]  

20. E. Shamonina, V. A. Kalinin, K. H. Ringhofer, and L. Solymar, “Magnetoinductive waves in one, two, and three dimensions,” J. Appl. Phys. 92(10), 6252–6261 (2002). [CrossRef]  

References

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  1. C. L. Holloway, D. C. Love, E. F. Kuester, J. A. Gordon, and D. A. Hill, “Use of Generalized Sheet Transition Conditions to Model Guided Waves on Metasurfaces/Metafilms,” IEEE Trans. Antenn. Propag. 60(11), 5173–5186 (2012).
    [Crossref]
  2. P. Y. Chen and A. Alu, “Mantle cloaking using thin patterned metasurfaces,” Phys. Rev. B 84(20), 205110 (2011).
    [Crossref]
  3. S. Maci, G. Minatti, M. Casaletti, and M. Bosiljevac, “Metasurfing: Addressing Waves on Impenetrable Metasurfaces,” IEEE Antennas Wirel. Propag. Lett. 10, 1499–1502 (2011).
    [Crossref]
  4. M. Bosiljevac, M. Casaletti, F. Caminita, Z. Sipus, and S. Maci, “Non-Uniform Metasurface Luneburg Lens Antenna Design,” IEEE Trans. Antenn. Propag. 60(9), 4065–4073 (2012).
    [Crossref]
  5. S. L. Sun, Q. He, S. Y. Xiao, Q. Xu, X. Li, and L. Zhou, “Gradient-index meta-surfaces as a bridge linking propagating waves and surface waves,” Nat. Mater. 11(5), 426–431 (2012).
    [Crossref] [PubMed]
  6. N. F. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction,” Science 334(6054), 333–337 (2011).
    [Crossref] [PubMed]
  7. Y. Zhao and A. Alu, “Manipulating light polarization with ultrathin plasmonic metasurfaces,” Phys. Rev. B 84(20), 205428 (2011).
    [Crossref]
  8. R. A. Hurd, “The propagation of an electromagnetic wave along an infinite corrugated surface,” Can. J. Phys. 32(12), 727–734 (1954).
    [Crossref]
  9. R. S. Elliott, “On the theory of corrugated plane surfaces,” Trans. IRE professional group on Antennas and Propagation. (71–81) 1954.
  10. W. Rotman, “A study of single-surface corrugated guides,” Proceedings of the IRE (951–959)1951.
  11. H. E. M. Barlow and A. E. Karbowiak, “An experimental investigation of the properties of corrugated cylindrical surface waveguides,” Proceedings of the IEEE-part III: Radio and Communication Engineering 101, 182–188 (1954).
  12. J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004).
    [Crossref] [PubMed]
  13. F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt. 7(2), S97–S101 (2005).
    [Crossref]
  14. T. A. Morgado, J. S. Marcos, M. G. Silveirinha, and S. I. Maslovski, “Ultraconfined interlaced plasmons,” Phys. Rev. Lett. 107(6), 063903 (2011).
    [Crossref] [PubMed]
  15. B. Reinhard, O. Paul, R. Beigang, and M. Rahm, “Experimental and numerical studies of terahertz surface waves on a thin metamaterial film,” Opt. Lett. 35(9), 1320–1322 (2010).
    [Crossref] [PubMed]
  16. M. Navarro-Cía, M. Beruete, S. Agrafiotis, F. Falcone, M. Sorolla, and S. A. Maier, “Broadband spoof plasmons and subwavelength electromagnetic energy confinement on ultrathin metafilms,” Opt. Express 17(20), 18184–18195 (2009).
    [Crossref] [PubMed]
  17. X. P. Shen, T. J. Cui, D. Martin-Cano, and F. J. Garcia-Vidal, “Conformal surface plasmons propagating on ultrathin and flexible films,” Proc. Natl. Acad. Sci. U.S.A. 110(1), 40–45 (2013).
    [Crossref] [PubMed]
  18. Q. Wu, J. P. Turpin, and D. H. Werner, “Integrated photonic systems based on transformation optics enabled gradient index devices,” Light Sci. Appl. 1(11), e38 (2012).
    [Crossref]
  19. M. F. Volk, B. Reinhard, J. Neu, R. Beigang, and M. Rahm, “In-plane focusing of terahertz surface waves on a gradient index metamaterial film,” Opt. Lett. 38(12), 2156–2158 (2013).
    [Crossref]
  20. E. Shamonina, V. A. Kalinin, K. H. Ringhofer, and L. Solymar, “Magnetoinductive waves in one, two, and three dimensions,” J. Appl. Phys. 92(10), 6252–6261 (2002).
    [Crossref]

2013 (2)

X. P. Shen, T. J. Cui, D. Martin-Cano, and F. J. Garcia-Vidal, “Conformal surface plasmons propagating on ultrathin and flexible films,” Proc. Natl. Acad. Sci. U.S.A. 110(1), 40–45 (2013).
[Crossref] [PubMed]

M. F. Volk, B. Reinhard, J. Neu, R. Beigang, and M. Rahm, “In-plane focusing of terahertz surface waves on a gradient index metamaterial film,” Opt. Lett. 38(12), 2156–2158 (2013).
[Crossref]

2012 (4)

Q. Wu, J. P. Turpin, and D. H. Werner, “Integrated photonic systems based on transformation optics enabled gradient index devices,” Light Sci. Appl. 1(11), e38 (2012).
[Crossref]

M. Bosiljevac, M. Casaletti, F. Caminita, Z. Sipus, and S. Maci, “Non-Uniform Metasurface Luneburg Lens Antenna Design,” IEEE Trans. Antenn. Propag. 60(9), 4065–4073 (2012).
[Crossref]

S. L. Sun, Q. He, S. Y. Xiao, Q. Xu, X. Li, and L. Zhou, “Gradient-index meta-surfaces as a bridge linking propagating waves and surface waves,” Nat. Mater. 11(5), 426–431 (2012).
[Crossref] [PubMed]

C. L. Holloway, D. C. Love, E. F. Kuester, J. A. Gordon, and D. A. Hill, “Use of Generalized Sheet Transition Conditions to Model Guided Waves on Metasurfaces/Metafilms,” IEEE Trans. Antenn. Propag. 60(11), 5173–5186 (2012).
[Crossref]

2011 (5)

P. Y. Chen and A. Alu, “Mantle cloaking using thin patterned metasurfaces,” Phys. Rev. B 84(20), 205110 (2011).
[Crossref]

S. Maci, G. Minatti, M. Casaletti, and M. Bosiljevac, “Metasurfing: Addressing Waves on Impenetrable Metasurfaces,” IEEE Antennas Wirel. Propag. Lett. 10, 1499–1502 (2011).
[Crossref]

N. F. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Y. Zhao and A. Alu, “Manipulating light polarization with ultrathin plasmonic metasurfaces,” Phys. Rev. B 84(20), 205428 (2011).
[Crossref]

T. A. Morgado, J. S. Marcos, M. G. Silveirinha, and S. I. Maslovski, “Ultraconfined interlaced plasmons,” Phys. Rev. Lett. 107(6), 063903 (2011).
[Crossref] [PubMed]

2010 (1)

2009 (1)

2005 (1)

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt. 7(2), S97–S101 (2005).
[Crossref]

2004 (1)

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004).
[Crossref] [PubMed]

2002 (1)

E. Shamonina, V. A. Kalinin, K. H. Ringhofer, and L. Solymar, “Magnetoinductive waves in one, two, and three dimensions,” J. Appl. Phys. 92(10), 6252–6261 (2002).
[Crossref]

1954 (2)

R. A. Hurd, “The propagation of an electromagnetic wave along an infinite corrugated surface,” Can. J. Phys. 32(12), 727–734 (1954).
[Crossref]

H. E. M. Barlow and A. E. Karbowiak, “An experimental investigation of the properties of corrugated cylindrical surface waveguides,” Proceedings of the IEEE-part III: Radio and Communication Engineering 101, 182–188 (1954).

Agrafiotis, S.

Aieta, F.

N. F. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Alu, A.

Y. Zhao and A. Alu, “Manipulating light polarization with ultrathin plasmonic metasurfaces,” Phys. Rev. B 84(20), 205428 (2011).
[Crossref]

P. Y. Chen and A. Alu, “Mantle cloaking using thin patterned metasurfaces,” Phys. Rev. B 84(20), 205110 (2011).
[Crossref]

Barlow, H. E. M.

H. E. M. Barlow and A. E. Karbowiak, “An experimental investigation of the properties of corrugated cylindrical surface waveguides,” Proceedings of the IEEE-part III: Radio and Communication Engineering 101, 182–188 (1954).

Beigang, R.

Beruete, M.

Bosiljevac, M.

M. Bosiljevac, M. Casaletti, F. Caminita, Z. Sipus, and S. Maci, “Non-Uniform Metasurface Luneburg Lens Antenna Design,” IEEE Trans. Antenn. Propag. 60(9), 4065–4073 (2012).
[Crossref]

S. Maci, G. Minatti, M. Casaletti, and M. Bosiljevac, “Metasurfing: Addressing Waves on Impenetrable Metasurfaces,” IEEE Antennas Wirel. Propag. Lett. 10, 1499–1502 (2011).
[Crossref]

Caminita, F.

M. Bosiljevac, M. Casaletti, F. Caminita, Z. Sipus, and S. Maci, “Non-Uniform Metasurface Luneburg Lens Antenna Design,” IEEE Trans. Antenn. Propag. 60(9), 4065–4073 (2012).
[Crossref]

Capasso, F.

N. F. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Casaletti, M.

M. Bosiljevac, M. Casaletti, F. Caminita, Z. Sipus, and S. Maci, “Non-Uniform Metasurface Luneburg Lens Antenna Design,” IEEE Trans. Antenn. Propag. 60(9), 4065–4073 (2012).
[Crossref]

S. Maci, G. Minatti, M. Casaletti, and M. Bosiljevac, “Metasurfing: Addressing Waves on Impenetrable Metasurfaces,” IEEE Antennas Wirel. Propag. Lett. 10, 1499–1502 (2011).
[Crossref]

Chen, P. Y.

P. Y. Chen and A. Alu, “Mantle cloaking using thin patterned metasurfaces,” Phys. Rev. B 84(20), 205110 (2011).
[Crossref]

Cui, T. J.

X. P. Shen, T. J. Cui, D. Martin-Cano, and F. J. Garcia-Vidal, “Conformal surface plasmons propagating on ultrathin and flexible films,” Proc. Natl. Acad. Sci. U.S.A. 110(1), 40–45 (2013).
[Crossref] [PubMed]

Falcone, F.

Gaburro, Z.

N. F. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Garcia-Vidal, F. J.

X. P. Shen, T. J. Cui, D. Martin-Cano, and F. J. Garcia-Vidal, “Conformal surface plasmons propagating on ultrathin and flexible films,” Proc. Natl. Acad. Sci. U.S.A. 110(1), 40–45 (2013).
[Crossref] [PubMed]

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt. 7(2), S97–S101 (2005).
[Crossref]

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004).
[Crossref] [PubMed]

Genevet, P.

N. F. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Gordon, J. A.

C. L. Holloway, D. C. Love, E. F. Kuester, J. A. Gordon, and D. A. Hill, “Use of Generalized Sheet Transition Conditions to Model Guided Waves on Metasurfaces/Metafilms,” IEEE Trans. Antenn. Propag. 60(11), 5173–5186 (2012).
[Crossref]

He, Q.

S. L. Sun, Q. He, S. Y. Xiao, Q. Xu, X. Li, and L. Zhou, “Gradient-index meta-surfaces as a bridge linking propagating waves and surface waves,” Nat. Mater. 11(5), 426–431 (2012).
[Crossref] [PubMed]

Hill, D. A.

C. L. Holloway, D. C. Love, E. F. Kuester, J. A. Gordon, and D. A. Hill, “Use of Generalized Sheet Transition Conditions to Model Guided Waves on Metasurfaces/Metafilms,” IEEE Trans. Antenn. Propag. 60(11), 5173–5186 (2012).
[Crossref]

Holloway, C. L.

C. L. Holloway, D. C. Love, E. F. Kuester, J. A. Gordon, and D. A. Hill, “Use of Generalized Sheet Transition Conditions to Model Guided Waves on Metasurfaces/Metafilms,” IEEE Trans. Antenn. Propag. 60(11), 5173–5186 (2012).
[Crossref]

Hurd, R. A.

R. A. Hurd, “The propagation of an electromagnetic wave along an infinite corrugated surface,” Can. J. Phys. 32(12), 727–734 (1954).
[Crossref]

Kalinin, V. A.

E. Shamonina, V. A. Kalinin, K. H. Ringhofer, and L. Solymar, “Magnetoinductive waves in one, two, and three dimensions,” J. Appl. Phys. 92(10), 6252–6261 (2002).
[Crossref]

Karbowiak, A. E.

H. E. M. Barlow and A. E. Karbowiak, “An experimental investigation of the properties of corrugated cylindrical surface waveguides,” Proceedings of the IEEE-part III: Radio and Communication Engineering 101, 182–188 (1954).

Kats, M. A.

N. F. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Kuester, E. F.

C. L. Holloway, D. C. Love, E. F. Kuester, J. A. Gordon, and D. A. Hill, “Use of Generalized Sheet Transition Conditions to Model Guided Waves on Metasurfaces/Metafilms,” IEEE Trans. Antenn. Propag. 60(11), 5173–5186 (2012).
[Crossref]

Li, X.

S. L. Sun, Q. He, S. Y. Xiao, Q. Xu, X. Li, and L. Zhou, “Gradient-index meta-surfaces as a bridge linking propagating waves and surface waves,” Nat. Mater. 11(5), 426–431 (2012).
[Crossref] [PubMed]

Love, D. C.

C. L. Holloway, D. C. Love, E. F. Kuester, J. A. Gordon, and D. A. Hill, “Use of Generalized Sheet Transition Conditions to Model Guided Waves on Metasurfaces/Metafilms,” IEEE Trans. Antenn. Propag. 60(11), 5173–5186 (2012).
[Crossref]

Maci, S.

M. Bosiljevac, M. Casaletti, F. Caminita, Z. Sipus, and S. Maci, “Non-Uniform Metasurface Luneburg Lens Antenna Design,” IEEE Trans. Antenn. Propag. 60(9), 4065–4073 (2012).
[Crossref]

S. Maci, G. Minatti, M. Casaletti, and M. Bosiljevac, “Metasurfing: Addressing Waves on Impenetrable Metasurfaces,” IEEE Antennas Wirel. Propag. Lett. 10, 1499–1502 (2011).
[Crossref]

Maier, S. A.

Marcos, J. S.

T. A. Morgado, J. S. Marcos, M. G. Silveirinha, and S. I. Maslovski, “Ultraconfined interlaced plasmons,” Phys. Rev. Lett. 107(6), 063903 (2011).
[Crossref] [PubMed]

Martin-Cano, D.

X. P. Shen, T. J. Cui, D. Martin-Cano, and F. J. Garcia-Vidal, “Conformal surface plasmons propagating on ultrathin and flexible films,” Proc. Natl. Acad. Sci. U.S.A. 110(1), 40–45 (2013).
[Crossref] [PubMed]

Martin-Moreno, L.

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt. 7(2), S97–S101 (2005).
[Crossref]

Martín-Moreno, L.

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004).
[Crossref] [PubMed]

Maslovski, S. I.

T. A. Morgado, J. S. Marcos, M. G. Silveirinha, and S. I. Maslovski, “Ultraconfined interlaced plasmons,” Phys. Rev. Lett. 107(6), 063903 (2011).
[Crossref] [PubMed]

Minatti, G.

S. Maci, G. Minatti, M. Casaletti, and M. Bosiljevac, “Metasurfing: Addressing Waves on Impenetrable Metasurfaces,” IEEE Antennas Wirel. Propag. Lett. 10, 1499–1502 (2011).
[Crossref]

Morgado, T. A.

T. A. Morgado, J. S. Marcos, M. G. Silveirinha, and S. I. Maslovski, “Ultraconfined interlaced plasmons,” Phys. Rev. Lett. 107(6), 063903 (2011).
[Crossref] [PubMed]

Navarro-Cía, M.

Neu, J.

Paul, O.

Pendry, J. B.

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt. 7(2), S97–S101 (2005).
[Crossref]

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004).
[Crossref] [PubMed]

Rahm, M.

Reinhard, B.

Ringhofer, K. H.

E. Shamonina, V. A. Kalinin, K. H. Ringhofer, and L. Solymar, “Magnetoinductive waves in one, two, and three dimensions,” J. Appl. Phys. 92(10), 6252–6261 (2002).
[Crossref]

Rotman, W.

W. Rotman, “A study of single-surface corrugated guides,” Proceedings of the IRE (951–959)1951.

Shamonina, E.

E. Shamonina, V. A. Kalinin, K. H. Ringhofer, and L. Solymar, “Magnetoinductive waves in one, two, and three dimensions,” J. Appl. Phys. 92(10), 6252–6261 (2002).
[Crossref]

Shen, X. P.

X. P. Shen, T. J. Cui, D. Martin-Cano, and F. J. Garcia-Vidal, “Conformal surface plasmons propagating on ultrathin and flexible films,” Proc. Natl. Acad. Sci. U.S.A. 110(1), 40–45 (2013).
[Crossref] [PubMed]

Silveirinha, M. G.

T. A. Morgado, J. S. Marcos, M. G. Silveirinha, and S. I. Maslovski, “Ultraconfined interlaced plasmons,” Phys. Rev. Lett. 107(6), 063903 (2011).
[Crossref] [PubMed]

Sipus, Z.

M. Bosiljevac, M. Casaletti, F. Caminita, Z. Sipus, and S. Maci, “Non-Uniform Metasurface Luneburg Lens Antenna Design,” IEEE Trans. Antenn. Propag. 60(9), 4065–4073 (2012).
[Crossref]

Solymar, L.

E. Shamonina, V. A. Kalinin, K. H. Ringhofer, and L. Solymar, “Magnetoinductive waves in one, two, and three dimensions,” J. Appl. Phys. 92(10), 6252–6261 (2002).
[Crossref]

Sorolla, M.

Sun, S. L.

S. L. Sun, Q. He, S. Y. Xiao, Q. Xu, X. Li, and L. Zhou, “Gradient-index meta-surfaces as a bridge linking propagating waves and surface waves,” Nat. Mater. 11(5), 426–431 (2012).
[Crossref] [PubMed]

Tetienne, J. P.

N. F. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Turpin, J. P.

Q. Wu, J. P. Turpin, and D. H. Werner, “Integrated photonic systems based on transformation optics enabled gradient index devices,” Light Sci. Appl. 1(11), e38 (2012).
[Crossref]

Volk, M. F.

Werner, D. H.

Q. Wu, J. P. Turpin, and D. H. Werner, “Integrated photonic systems based on transformation optics enabled gradient index devices,” Light Sci. Appl. 1(11), e38 (2012).
[Crossref]

Wu, Q.

Q. Wu, J. P. Turpin, and D. H. Werner, “Integrated photonic systems based on transformation optics enabled gradient index devices,” Light Sci. Appl. 1(11), e38 (2012).
[Crossref]

Xiao, S. Y.

S. L. Sun, Q. He, S. Y. Xiao, Q. Xu, X. Li, and L. Zhou, “Gradient-index meta-surfaces as a bridge linking propagating waves and surface waves,” Nat. Mater. 11(5), 426–431 (2012).
[Crossref] [PubMed]

Xu, Q.

S. L. Sun, Q. He, S. Y. Xiao, Q. Xu, X. Li, and L. Zhou, “Gradient-index meta-surfaces as a bridge linking propagating waves and surface waves,” Nat. Mater. 11(5), 426–431 (2012).
[Crossref] [PubMed]

Yu, N. F.

N. F. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Zhao, Y.

Y. Zhao and A. Alu, “Manipulating light polarization with ultrathin plasmonic metasurfaces,” Phys. Rev. B 84(20), 205428 (2011).
[Crossref]

Zhou, L.

S. L. Sun, Q. He, S. Y. Xiao, Q. Xu, X. Li, and L. Zhou, “Gradient-index meta-surfaces as a bridge linking propagating waves and surface waves,” Nat. Mater. 11(5), 426–431 (2012).
[Crossref] [PubMed]

Can. J. Phys. (1)

R. A. Hurd, “The propagation of an electromagnetic wave along an infinite corrugated surface,” Can. J. Phys. 32(12), 727–734 (1954).
[Crossref]

IEEE Antennas Wirel. Propag. Lett. (1)

S. Maci, G. Minatti, M. Casaletti, and M. Bosiljevac, “Metasurfing: Addressing Waves on Impenetrable Metasurfaces,” IEEE Antennas Wirel. Propag. Lett. 10, 1499–1502 (2011).
[Crossref]

IEEE Trans. Antenn. Propag. (2)

M. Bosiljevac, M. Casaletti, F. Caminita, Z. Sipus, and S. Maci, “Non-Uniform Metasurface Luneburg Lens Antenna Design,” IEEE Trans. Antenn. Propag. 60(9), 4065–4073 (2012).
[Crossref]

C. L. Holloway, D. C. Love, E. F. Kuester, J. A. Gordon, and D. A. Hill, “Use of Generalized Sheet Transition Conditions to Model Guided Waves on Metasurfaces/Metafilms,” IEEE Trans. Antenn. Propag. 60(11), 5173–5186 (2012).
[Crossref]

J. Appl. Phys. (1)

E. Shamonina, V. A. Kalinin, K. H. Ringhofer, and L. Solymar, “Magnetoinductive waves in one, two, and three dimensions,” J. Appl. Phys. 92(10), 6252–6261 (2002).
[Crossref]

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

F. J. Garcia-Vidal, L. Martin-Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt. 7(2), S97–S101 (2005).
[Crossref]

Light Sci. Appl. (1)

Q. Wu, J. P. Turpin, and D. H. Werner, “Integrated photonic systems based on transformation optics enabled gradient index devices,” Light Sci. Appl. 1(11), e38 (2012).
[Crossref]

Nat. Mater. (1)

S. L. Sun, Q. He, S. Y. Xiao, Q. Xu, X. Li, and L. Zhou, “Gradient-index meta-surfaces as a bridge linking propagating waves and surface waves,” Nat. Mater. 11(5), 426–431 (2012).
[Crossref] [PubMed]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. B (2)

Y. Zhao and A. Alu, “Manipulating light polarization with ultrathin plasmonic metasurfaces,” Phys. Rev. B 84(20), 205428 (2011).
[Crossref]

P. Y. Chen and A. Alu, “Mantle cloaking using thin patterned metasurfaces,” Phys. Rev. B 84(20), 205110 (2011).
[Crossref]

Phys. Rev. Lett. (1)

T. A. Morgado, J. S. Marcos, M. G. Silveirinha, and S. I. Maslovski, “Ultraconfined interlaced plasmons,” Phys. Rev. Lett. 107(6), 063903 (2011).
[Crossref] [PubMed]

Proc. Natl. Acad. Sci. U.S.A. (1)

X. P. Shen, T. J. Cui, D. Martin-Cano, and F. J. Garcia-Vidal, “Conformal surface plasmons propagating on ultrathin and flexible films,” Proc. Natl. Acad. Sci. U.S.A. 110(1), 40–45 (2013).
[Crossref] [PubMed]

Proceedings of the IEEE-part III: Radio and Communication Engineering (1)

H. E. M. Barlow and A. E. Karbowiak, “An experimental investigation of the properties of corrugated cylindrical surface waveguides,” Proceedings of the IEEE-part III: Radio and Communication Engineering 101, 182–188 (1954).

Science (2)

J. B. Pendry, L. Martín-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004).
[Crossref] [PubMed]

N. F. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Other (2)

R. S. Elliott, “On the theory of corrugated plane surfaces,” Trans. IRE professional group on Antennas and Propagation. (71–81) 1954.

W. Rotman, “A study of single-surface corrugated guides,” Proceedings of the IRE (951–959)1951.

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Figures (6)

Fig. 1
Fig. 1 (a) The waveguide model to solve the eigen modes of unit cell, a rectangular metal patch with a rectangular groove. (b) The effective circuit model of the waveguide model.
Fig. 2
Fig. 2 (a) The detailed geometrical parameters of a single U-shaped metallic structure, in which p x =3.4mm , p y =4.6mm , d x =3mm , d y =4mm , w=1.5mm , h=2.2mm , and t=1mm . The thickness of the U-shaped metallic structure is 0.018mm. The lossless dielectric constant is 2.2. (b) The 2D dispersion surface of the single element with the same geometric parameters as in Fig. 2(a).
Fig. 3
Fig. 3 Isofrequency curves of the U-shaped metallic structure at 11GHz when the groove length h increases from 1 mm to 3.4 mm with a step of 0.3 mm. The dashed red arrow shows the tendency of the curves with increasing h.
Fig. 4
Fig. 4 (a) The schematic diagram of the dipole source, whose length is 12mm. (b) The schematic diagram of the metasurface lens.
Fig. 5
Fig. 5 (a) Relationship of phase changes in the x direction of the unit φ x to the depths of grooves h. (b) The phase distribution φ s at the left edge of the lens and the designed distribution of groove depth h along the y direction. The horizontal coordinate represents the positions of the U-shaped metallic structures along the y direction.
Fig. 6
Fig. 6 The simulation and measurement results. (a) The measurement configuration, in which the measurement plane is 2 mm above the metasurface lens. (b) A section of the metasurface lens. Numbers below the section are detailed values of heights of the corresponding U-shaped units. (c) The measurement (upper) and simulation (lower) results of the y-component electric fields.

Equations (5)

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

Y ¯ ¯ s =[ Y xx Y xy Y yx Y yy ].
[ Y xx Y xy Y yx Y yy ]+2[ j Y 0 TM cot( k z H) 0 0 j Y 0 TE cot( k z H) ]=0,
( Y xx 2 Y 0 TM )( Y yy 2 Y 0 TE )= Y xy Y yx ,
( Y xx 2 Y 0 TM )( Y yy 2 Y 0 TE )=0.
2 φ s (i)+m φ x (i)+2nπ=2 φ s (1)+m φ x (1),

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