OSA's Digital Library

Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 16 — Aug. 12, 2013
  • pp: 19082–19090
« Show journal navigation

A Broadband and omnidirectional electromagnetic wave concentrator with gradient woodpile structure

Ming Yin, Xiao Yong Tian, Ling Ling Wu, and Di Chen Li  »View Author Affiliations


Optics Express, Vol. 21, Issue 16, pp. 19082-19090 (2013)
http://dx.doi.org/10.1364/OE.21.019082


View Full Text Article

Acrobat PDF (3934 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We present the first realized three-dimensional (3D) practical implementation of the so called “optical black hole” in microwave frequencies, an electromagnetic (EM) concentrator. The 3D EM wave concentrator was designed with non-resonant gradient index (GRIN) 3D woodpile photonic crystals (PCs) structure in metamaterial regime, and fabricated by Stereolithography (SL) process. Omnidirectional EM wave capture and absorbing ability of the device in a broad bandwidth (12GHz-15GHz) were validated by full-wave simulation and experiments. Such devices may have applications in microwave energy harvesting and radiation detector.

© 2013 OSA

1. Introduction

Artificial metamaterials made scientists magicians in the EM wave world with Transformation Optics (TO) [1

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

,2

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

], the magic wands in their hands. TO theory has demonstrated its magic power in the design of novel EM devices with specific material parameters distribution profile, which offered a way to manipulate the propagation of EM waves. “Tricks” like cloak [3

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]

5

5. Y. Urzhumov, N. Landy, T. Driscoll, D. Basov, and D. R. Smith, “Thin low-loss dielectric coatings for free-space cloaking,” Opt. Lett. 38(10), 1606 (2013). [CrossRef]

], field rotators [6

6. H. Chen and C. T. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Lett. 90(24), 241105 (2007). [CrossRef]

] and novel lens [7

7. Y. G. Ma, C. K. Ong, T. Tyc, and U. Leonhardt, “An omnidirectional retroreflector based on the transmutation of dielectric singularities,” Nat. Mater. 8(8), 639–642 (2009). [CrossRef] [PubMed]

,8

8. U. Leonhardt and T. G. Philbin, “General relativity in electrical engineering,” New J. Phys. 8(10), 247–247 (2006). [CrossRef]

] have been realized with metamaterials. Motivated by imitating celestial mechanics, researchers have proposed devices as the optical analogues of cosmic phenomena [8

8. U. Leonhardt and T. G. Philbin, “General relativity in electrical engineering,” New J. Phys. 8(10), 247–247 (2006). [CrossRef]

10

10. M. Li, R. X. Miao, and Y. Pang, “More studies on metamaterials mimicking de Sitter space,” Opt. Express 18(9), 9026–9033 (2010). [CrossRef] [PubMed]

]. One example is termed as the effective “optical black hole” or “EM black hole”. Different approaches were suggested to realize the interesting issue [8

8. U. Leonhardt and T. G. Philbin, “General relativity in electrical engineering,” New J. Phys. 8(10), 247–247 (2006). [CrossRef]

,11

11. D. A. Genov, S. Zhang, and X. Zhang, “Mimicking celestial mechanics in metamaterials,” Nat. Phys. 5(9), 687–692 (2009). [CrossRef]

13

13. H. Y. Chen, R. X. Miao, and M. A. Li, “Transformation optics that mimics the system outside a Schwarzschild black hole,” Opt. Express 18(14), 15183–15188 (2010). [CrossRef] [PubMed]

]. The isotropic and non-resonant approach proposed by Narimanov and Kildishev [12

12. E. E. Narimanov and A. V. Kildishev, “Optical black hole: Broadband omnidirectional light absorber,” Appl. Phys. Lett. 95(4), 041106 (2009). [CrossRef]

] was further demonstrated theoretically [14

14. A. V. Kildishev, L. J. Prokopeva, and E. E. Narimanov, “Cylinder light concentrator and absorber: theoretical description,” Opt. Express 18(16), 16646–16662 (2010). [CrossRef] [PubMed]

17

17. W. Lu, J. Jin, Z. Lin, and H. Chen, “A simple design of an artificial electromagnetic black hole,” J. Appl. Phys. 108(6), 064517 (2010). [CrossRef]

] and implemented in microwave regime [18

18. Q. Cheng, T. J. Cui, W. X. Jiang, and B. G. Cai, “An omnidirectional electromagnetic absorber made of metamaterials,” New J. Phys. 12(6), 063006 (2010). [CrossRef]

20

20. Y. R. Yang, L. Y. Leng, N. Wang, Y. G. Ma, and C. K. Ong, “Electromagnetic field attractor made of gradient index metamaterials,” J. Opt. Soc. Am. A 29(4), 473–475 (2012). [CrossRef] [PubMed]

]. The so called “black hole” devices behave more like omnidirectional and broadband EM wave concentrators. The scheme has also inspired analogy work in other realm, such as the acoustic and the elastic wave “black hole” [21

21. R.-Q. Li, X.-F. Zhu, B. Liang, Y. Li, X.-Y. Zou, and J.-C. Cheng, “A broadband acoustic omnidirectional absorber comprising positive-index materials,” Appl. Phys. Lett. 99(19), 193507 (2011). [CrossRef]

23

23. Z. Chang and G. Hu, “Elastic wave omnidirectional absorbers designed by transformation method,” Appl. Phys. Lett. 101(5), 054102 (2012). [CrossRef]

]. However, the implementations mentioned above were all cylindrical versions of the “black hole”, which were limited to 2D situation with waveguide geometry. 3D implementation of such devices would broaden the potential applications, but it also increases the difficulty in design and fabrication.

In this article, we present the first practical implementation of a 3D spherical effective “EM black hole”. The device consists of an inner core and an outer shell. The lossy core was realized with liquid dielectric medium. The shell with radially varying permittivity profile was designed with non-resonant 3D gradient index (GRIN) woodpile photonic crystals (PCs) structures in metamaterial regime. The highly integrated complex 3D GRIN structure, which was used to manipulate the local EM field propagation in the device, was fabricated by SL process using photosensitive resin as raw material. 3D full-wave simulation and experimental results validated the broadband performance of the device. The 3D EM wave concentrator proposed may find potential applications in energy harvesting and radiation detector.

2. Design of the 3D EM wave concentrator

The permittivity distribution profile ϵ(r) of the non-magnetic 3D EM wave concentrator derived from the equation in [12

12. E. E. Narimanov and A. V. Kildishev, “Optical black hole: Broadband omnidirectional light absorber,” Appl. Phys. Lett. 95(4), 041106 (2009). [CrossRef]

]:
ϵ(r)={ϵb,                         rRϵb(Rr)n,     Rc<r<Rϵc+iγ,                  rRc,
(1)
where ϵ(r) defines a GRIN shell and a lossy core, Rc and R represent the radius of the inner core and the outer radius of the spherical shell respectively, ϵc+ represents the complex permittivity of the lossy core and ϵb stands for the permittivity of the background medium. ϵbwas taken as 1 in the research, meaning the system was matched to free-space (air). The radius of the core was defined as   Rc=Rϵbϵc according to the impedance-matched condition at the core-shell interface. Integer power index n2 leads to incident wave falling into the core [12

12. E. E. Narimanov and A. V. Kildishev, “Optical black hole: Broadband omnidirectional light absorber,” Appl. Phys. Lett. 95(4), 041106 (2009). [CrossRef]

,14

14. A. V. Kildishev, L. J. Prokopeva, and E. E. Narimanov, “Cylinder light concentrator and absorber: theoretical description,” Opt. Express 18(16), 16646–16662 (2010). [CrossRef] [PubMed]

,15

15. S. Liu, L. Li, Z. Lin, H. Chen, J. Zi, and C. Chan, “Graded index photonic hole: Analytical and rigorous full wave solution,” Phys. Rev. B 82, 054204 (2010).

]. Higher orders n results in stronger and more efficient beam trap ability of the system. But it also increases the difficulty to realize, for the correspondingly growing values and gradients of the permittivity index. Thus, n=2 which constitutes the criterion for beam capture was chosen in the research.

To fulfill the inhomogeneous isotropic permittivity distribution, woodpile PCs structure [24

24. K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band-gaps in three-dmensions - new layer-by-layer periodic structure,” Solid State Commun. 89(5), 413–416 (1994). [CrossRef]

] in metmaterial regime was utilized as 3D GRIN medium in this letter. In long-wavelength limit, PCs structure can be homogenized and served as GRIN medium [4

4. T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science 328(5976), 337–339 (2010). [CrossRef] [PubMed]

,25

25. B. Vasić, G. Isić, R. Gajić, and K. Hingerl, “Controlling electromagnetic fields with graded photonic crystals in metamaterial regime,” Opt. Express 18(19), 20321–20333 (2010). [CrossRef] [PubMed]

]. Diamond-structured woodpile PCs in metamaterial regime with highly symmetrical face-centered cubic lattice can be used to realize 3D GRIN designs. Its approximate spherical equifrequency surface satisfies the requirement of homogenization under effective medium approximation in a broad bandwidth, which results in 3D isotropic EM properties [4

4. T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science 328(5976), 337–339 (2010). [CrossRef] [PubMed]

,26

26. C. Luo, S. G. Johnson, and J. D. Joannopoulos, “All-angle negative refraction in a three-dimensionally periodic photonic crystal,” Appl. Phys. Lett. 81(13), 2352 (2002). [CrossRef]

]. The effective medium approximation would work well when the wavelength of the incident wave is much longer than the rod spacing of the woodpile PCs unit cells. But as demonstrated in [4

4. T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science 328(5976), 337–339 (2010). [CrossRef] [PubMed]

], the effective medium limit is more forgiving than that. In order to simplify the analysis process to determine the effective permittivity of the GRIN PCs, effective medium theory was employed in the research. The obtained effective permittivity show good conformity with those derived from the dispersion curves of a PC based on photonic band gap calculations [4

4. T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science 328(5976), 337–339 (2010). [CrossRef] [PubMed]

,25

25. B. Vasić, G. Isić, R. Gajić, and K. Hingerl, “Controlling electromagnetic fields with graded photonic crystals in metamaterial regime,” Opt. Express 18(19), 20321–20333 (2010). [CrossRef] [PubMed]

]. In fact, by modifying the dispersion properties and engineering the equifrequency contours or surfaces of PCs, precise control of the EM waves propagation can be achieved [27

27. D. W. Prather, “Photonic crystals: theory, applications, and fabrication”,(Wiley, Hoboken, N.J., 2009).

29

29. Z. Liang and J. Li, “Scaling two-dimensional photonic crystals for transformation optics,” Opt. Express 19(18), 16821–16829 (2011). [CrossRef] [PubMed]

]. But in our research, we only exploited the local isotropic properties and the relationship between volume fraction of the constituent material and the local effective permittivity to fulfill the required discrete permittivity distribution. For practical engineering realization, the continuous gradient permittivity profile of the shell was divided into multiple layers. More non-uniform layers could improve the performance of the “EM black hole”. Considering the design and fabrication factors, 12 layers with equal thickness was adopted in the present research, which has been proved adequate to provide absorption efficiency comparable with the theoretical ideal case [14

14. A. V. Kildishev, L. J. Prokopeva, and E. E. Narimanov, “Cylinder light concentrator and absorber: theoretical description,” Opt. Express 18(16), 16646–16662 (2010). [CrossRef] [PubMed]

,17

17. W. Lu, J. Jin, Z. Lin, and H. Chen, “A simple design of an artificial electromagnetic black hole,” J. Appl. Phys. 108(6), 064517 (2010). [CrossRef]

]. Concerning the fabrication capability and the desired working frequency range of the device which satisfies the long wavelength limit, the rod spacing of the PCs was set to be a = 5mm. The thickness of each spherical layer of the EM wave concentrator shell was also accordingly set as 5mm. A nearly non-dispersive photosensitive resin with a permittivity εresin of 3.0, which was measured using a well-established waveguide-based retrieval method [30

30. H. Chen, J. Zhang, Y. Bai, Y. Luo, L. Ran, Q. Jiang, and J. A. Kong, “Experimental retrieval of the effective parameters of metamaterials based on a waveguide method,” Opt. Express 14(26), 12944–12949 (2006). [CrossRef] [PubMed]

] from 8 GHz to 18 GHz, was used as the structure material of the GRIN shell. The effective permittivity can be varied from 1.0 (full air) to 3.0 (full resin) and the real part of the complex permittivity of the lossy core was set to be ϵc= 3.0. Then, from Eq. (1), R and Rc can be determined as 142.0mm and 82.0mm respectively. As previously described, employing effective medium theory, the effective permittivity of the PCs can be calculated as εeff=fεresin+(1f)εair, where f is the volume filling fraction of the photosensitive resin. The local effective permittivity is controlled by altering the logs width ω of the woodpile PCs unit cells within each spherical layer area while the rod spacing of the unit cells keeps unchanged as 5mm. The relationship between local effective permittivity and logs width is shown in Fig. 1
Fig. 1 Fabricated sample of the 3D EM wave concentrator shell with GRIN woodpile PCs structure. (a) The sample of the EM wave concentrator. (b) Partial view of the cross-section along the axis of the spherical shell. (c) The relation between the local effective permittivity and log width of woodpile PCs with a rod spacing of 5mm. (d) The schematic of woodpile PCs structure.
. With rods remaining connected, the integrated structure is self-supporting and presents considerable mechanical strength. The 3D EM wave concentrator was fabricated on a SL process based 3D printing machine (SPS450B, Institute of Advanced Manufacturing Technology, Xi’an Jiaotong University), as shown in Figs. 1(a) and 1(b). Comparing with the Fused Deposition Modeling 3D printing process employed in [5

5. Y. Urzhumov, N. Landy, T. Driscoll, D. Basov, and D. R. Smith, “Thin low-loss dielectric coatings for free-space cloaking,” Opt. Lett. 38(10), 1606 (2013). [CrossRef]

], the precision of the SL process is relatively higher. But it also comes at higher cost because of the use of laser.

3. Simulation results

The use of isotropic 3D GRIN PCs structure ensures the device to be independent on polarization of the incident EM waves. To examine the broadband and omnidirectional EM wave capturing performance, the near-field wave propagating in the device was simulated in CST MICROWAVE STUDIO. A beam at a side position from the axis was incident on the model. The power flow in space and inside the device at 10 GHz was examined. As shown in Fig. 2
Fig. 2 Power flow in space and in the 3D EM wave concentrator” when an off-centre beam is incident on the structure. (a) Perspective view. (b) Front view (c) Side view.
, the power flow rapidly bends toward the core, indicating that the incoming field powerwas effectively concentrated. To further visualize the simulation results, we investigated the field intensity at different frequencies in the cross section of the system along the axis with incident beam on centre [Figs. 3(a)
Fig. 3 Simulation results of the electric field intensity distributions in the cross section of the system. (a-c) Incident beam on centre at 8 GHz, 13 GHz and 18GHz. (d) Incident beam on centre to the reference sample at 13 GHz. (e-g) Incident beam off centre at 8 GHz, 13 GHz and 18 GHz. (h) Incident beam off centre to the reference sample at 13 GHz.
-3(c)] and off centre [Figs. 3(e)-3(g)]. This is equivalent to simulating incident beam from different direction because of the circular symmetry. The incident wave followed a bending path when entering the shell. The broad bandwidth performance was also demonstrated in simulation covering X and Ku band as Fig. 3 shows. For comparison, the gradient index shell was substituted with homogenous woodpile PCs structure as a reference sample. The unit cell lattice constant and sample dimensions kept the same. From Figs. 3(d) and 3(h), it can be seen that for the reference sample, the incident beam was severely scattered at the core-shell and shell-air interface in comparison with Fig. 3(b) and 3(e), respectively. Figure 4
Fig. 4 Simulation results of the electric field intensity distributions in the cross section under the incidence of a plane wave at 13GHz. (a) The EM wave concentrator. (b) Reference sample.
demonstrates the field intensity distribution under the incidence of plane waves at the frequency of 13 GHz. From Fig. 4(a), it’s clear that nearly all incident waves hitting the “black hole” were trapped at the core and did not emerge. While for the same reference sample used in Figs. 3(d) and 3(h), the incident waves severely emerged [shown in Fig. 4(b)]. The simulation results demonstrate omnidirectional and broadband wave trapping ability of the proposed 3D EM wave concentrator.

4. Realization and experimental performance of the 3D EM wave concentrator

Two hemispheres of the woodpile shell were fabricated by SL process and assembled with liquid medium core. High shaping precision of the process ensures the continuous changing of the unit cell parameters and smooth GRIN to realize the designed permittivity profile accurately, which reduces the impedance-mismatch and the EM wave scattering. The lossy core was realized via a compound liquid medium approach [31

31. L. Wu, X. Tian, H. Ma, M. Yin, and D. Li, “Broadband flattened Luneburg lens with ultra-wide angle based on a liquid medium,” Appl. Phys. Lett. 102(7), 074103 (2013). [CrossRef]

]. Mixture of ethanol and oleic acid was chosen in the research, for ethanol is a damping medium with high dielectric constant and oleic acid is a lossless medium with relatively low dielectric constant. The required complex dielectric constant was fulfilled, when volume ratio between ethanol and oleic acid reaches 60:40, as demonstrates in Fig. 5
Fig. 5 Dielectric properties of ethanol, oleic acid and the compound medium. (a) Dielectric constants of ethanol, oleic acid and their mixture at a volume ratio of 60:40 in the frequency range of 5 GHz – 20 GHz. The oleic acid has nearly no loss (b) Dielectric constants of the mixture with different volume ratio at the frequency of 12 GHz, 13 GHz, 14 GHz and 15 GHz.
. Broadband performance is ensured by the weak frequency dependence of the dielectric constants. A spherical shell with a radius of82.0 mm was used to contain the compound liquid medium. The shell was also made by SL with photosensitive resin and was only 200 μm thick, and would not affect the impedance-match condition at the core-shell interface, which was demonstrated with simulation.

The cross-sectional slice along the axis of the spherical EM wave concentrator was measured in a 2D field mapping device [5

5. Y. Urzhumov, N. Landy, T. Driscoll, D. Basov, and D. R. Smith, “Thin low-loss dielectric coatings for free-space cloaking,” Opt. Lett. 38(10), 1606 (2013). [CrossRef]

,32

32. B. J. Justice, J. J. Mock, L. H. Guo, A. Degiron, D. Schurig, and D. R. Smith, “Spatial mapping of the internal and external electromagnetic fields of negative index metamaterials,” Opt. Express 14(19), 8694–8705 (2006). [CrossRef] [PubMed]

] to determine its electric field intensity distribution with a beam obliquely incident on the structure. A slice of 3D EM wave concentrator with a height of 8.8mm can be considered as a quasi 2D “EM black hole”. In comparison with the simulation, similar wave trapping behavior was observed in a relatively narrower bandwidth from 12 GHz to 15 GHz, as illustrated in Fig. 6
Fig. 6 Measured electric field intensity distributions for the cross-sectional slice along the axis of the device. (a-d) At 12 GHz, 13 GHz, 14 GHz and 15GHz, respectively.
. The reduced operationalfrequency range for the quasi 2D sample was mainly restricted by experiment limitations and the frequency dispersion characteristic of the core material. Standing wave pattern appears, when the frequency of the incident wave exceeds 15 GHz, which is the cutoff frequency of the higher order modes for the test device. Coexistence of the high-order modes and the main mode will affect the proper measurement. Also, the absorbing effect begins to deteriorate due to the smaller dielectric loss of the core material in higher frequencies. For incident wave below 12 GHz, distortion in electric field map introduced by the hardware flaws (e.g. the sag and the unevenness of the chamber plates in the test device) becomes significant. Thus, the incident beam scattered severely in propagation. The 2D near-field experiment results reflect an overall good wave trapping performance of the device, though it exhibits limitations compared with the simulation.

The far-field scattering pattern for the 3D sample was also measured in an anechoic chamber with a pair of Ku-band horn antennas. One served as a feeding source generating incident wave on the device along the axis, which is the representative situation, while the other one acted as a detector of far-field scattering waves. For comparison, we also measured the far-field pattern when the spherical outer shell was removed. The measured far-field pattern at 12, 13, 14 and 15 GHz are illustrated in Fig. 7
Fig. 7 Measured far-field scattering pattern of EM waves for the 3D “EM black hole” and the bare core. Feeding source is along the axis. (a-d) at 12 GHz, 13 GHz, 14 GHz and 15 GHz, respectively.
, respectively. Compared with the bare core situation, scattering fields are significantly reduced with the existence of the shell, reflecting a good EM wave absorbing performance. The reduced backscattering also suggests a relatively small monostatic RCS. The absorbing behavior of the 3D EM wave concentrator was verified by the contrast experiments.

5. Conclusion

In conclusion, a 3D EM wave concentrator was designed and realized with GRIN 3D PCs structure in metamaterial regime and a liquid medium approach. The complicated structure was fabricated by SL. Simulations and experimental results validated the capability for the concentrator in capturing and absorbing the broadband and omnidirectional EM wave. The proposed device may find applications in energy harvesting and radiation detector for 3D situation. Furthermore, by changing the photosensitive material used in SL process, and the composition in the compound liquid medium, more flexible effective index range can be realized. Also, the proposed structure is all dielectric and non-resonant, which can be extended to optical regime. The approach in this report presents promising prospects for practical implementation of novel 3D EM GRIN designs.

Acknowledgments

This work is supported by National Natural Science Foundation of China (51105300), Ph.D. Program Foundation of Ministry of Education of China (20110201120075), the Scientific Research Foundation for the Returned Overseas Chinese Scholars, Ministry of Education of China, and the Fundamental Research Funds for the Central Universities of China.

References and links

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.

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science 328(5976), 337–339 (2010). [CrossRef] [PubMed]

5.

Y. Urzhumov, N. Landy, T. Driscoll, D. Basov, and D. R. Smith, “Thin low-loss dielectric coatings for free-space cloaking,” Opt. Lett. 38(10), 1606 (2013). [CrossRef]

6.

H. Chen and C. T. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Lett. 90(24), 241105 (2007). [CrossRef]

7.

Y. G. Ma, C. K. Ong, T. Tyc, and U. Leonhardt, “An omnidirectional retroreflector based on the transmutation of dielectric singularities,” Nat. Mater. 8(8), 639–642 (2009). [CrossRef] [PubMed]

8.

U. Leonhardt and T. G. Philbin, “General relativity in electrical engineering,” New J. Phys. 8(10), 247–247 (2006). [CrossRef]

9.

A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Electromagnetic wormholes and virtual magnetic monopoles from metamaterials,” Phys. Rev. Lett. 99(18), 183901 (2007). [CrossRef] [PubMed]

10.

M. Li, R. X. Miao, and Y. Pang, “More studies on metamaterials mimicking de Sitter space,” Opt. Express 18(9), 9026–9033 (2010). [CrossRef] [PubMed]

11.

D. A. Genov, S. Zhang, and X. Zhang, “Mimicking celestial mechanics in metamaterials,” Nat. Phys. 5(9), 687–692 (2009). [CrossRef]

12.

E. E. Narimanov and A. V. Kildishev, “Optical black hole: Broadband omnidirectional light absorber,” Appl. Phys. Lett. 95(4), 041106 (2009). [CrossRef]

13.

H. Y. Chen, R. X. Miao, and M. A. Li, “Transformation optics that mimics the system outside a Schwarzschild black hole,” Opt. Express 18(14), 15183–15188 (2010). [CrossRef] [PubMed]

14.

A. V. Kildishev, L. J. Prokopeva, and E. E. Narimanov, “Cylinder light concentrator and absorber: theoretical description,” Opt. Express 18(16), 16646–16662 (2010). [CrossRef] [PubMed]

15.

S. Liu, L. Li, Z. Lin, H. Chen, J. Zi, and C. Chan, “Graded index photonic hole: Analytical and rigorous full wave solution,” Phys. Rev. B 82, 054204 (2010).

16.

C. Argyropoulos, E. Kallos, and Y. Hao, “FDTD analysis of the optical black hole,” J. Opt. Soc. Am. B 27(10), 2020–2025 (2010). [CrossRef]

17.

W. Lu, J. Jin, Z. Lin, and H. Chen, “A simple design of an artificial electromagnetic black hole,” J. Appl. Phys. 108(6), 064517 (2010). [CrossRef]

18.

Q. Cheng, T. J. Cui, W. X. Jiang, and B. G. Cai, “An omnidirectional electromagnetic absorber made of metamaterials,” New J. Phys. 12(6), 063006 (2010). [CrossRef]

19.

J. Zhou, X. Cai, Z. Chang, and G. Hu, “Experimental study on a broadband omnidirectional electromagnetic absorber,” J. Opt. 13(8), 085103 (2011). [CrossRef]

20.

Y. R. Yang, L. Y. Leng, N. Wang, Y. G. Ma, and C. K. Ong, “Electromagnetic field attractor made of gradient index metamaterials,” J. Opt. Soc. Am. A 29(4), 473–475 (2012). [CrossRef] [PubMed]

21.

R.-Q. Li, X.-F. Zhu, B. Liang, Y. Li, X.-Y. Zou, and J.-C. Cheng, “A broadband acoustic omnidirectional absorber comprising positive-index materials,” Appl. Phys. Lett. 99(19), 193507 (2011). [CrossRef]

22.

A. Climente, D. Torrent, and J. Sánchez-Dehesa, “Omnidirectional broadband acoustic absorber based on metamaterials,” Appl. Phys. Lett. 100(14), 144103 (2012). [CrossRef]

23.

Z. Chang and G. Hu, “Elastic wave omnidirectional absorbers designed by transformation method,” Appl. Phys. Lett. 101(5), 054102 (2012). [CrossRef]

24.

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band-gaps in three-dmensions - new layer-by-layer periodic structure,” Solid State Commun. 89(5), 413–416 (1994). [CrossRef]

25.

B. Vasić, G. Isić, R. Gajić, and K. Hingerl, “Controlling electromagnetic fields with graded photonic crystals in metamaterial regime,” Opt. Express 18(19), 20321–20333 (2010). [CrossRef] [PubMed]

26.

C. Luo, S. G. Johnson, and J. D. Joannopoulos, “All-angle negative refraction in a three-dimensionally periodic photonic crystal,” Appl. Phys. Lett. 81(13), 2352 (2002). [CrossRef]

27.

D. W. Prather, “Photonic crystals: theory, applications, and fabrication”,(Wiley, Hoboken, N.J., 2009).

28.

Y. A. Urzhumov and D. R. Smith, “Transformation Optics with Photonic Band Gap Media,” Phys. Rev. Lett. 105(16), 163901 (2010). [CrossRef] [PubMed]

29.

Z. Liang and J. Li, “Scaling two-dimensional photonic crystals for transformation optics,” Opt. Express 19(18), 16821–16829 (2011). [CrossRef] [PubMed]

30.

H. Chen, J. Zhang, Y. Bai, Y. Luo, L. Ran, Q. Jiang, and J. A. Kong, “Experimental retrieval of the effective parameters of metamaterials based on a waveguide method,” Opt. Express 14(26), 12944–12949 (2006). [CrossRef] [PubMed]

31.

L. Wu, X. Tian, H. Ma, M. Yin, and D. Li, “Broadband flattened Luneburg lens with ultra-wide angle based on a liquid medium,” Appl. Phys. Lett. 102(7), 074103 (2013). [CrossRef]

32.

B. J. Justice, J. J. Mock, L. H. Guo, A. Degiron, D. Schurig, and D. R. Smith, “Spatial mapping of the internal and external electromagnetic fields of negative index metamaterials,” Opt. Express 14(19), 8694–8705 (2006). [CrossRef] [PubMed]

OCIS Codes
(220.0220) Optical design and fabrication : Optical design and fabrication
(160.3918) Materials : Metamaterials
(160.5298) Materials : Photonic crystals

ToC Category:
Metamaterials

History
Original Manuscript: June 18, 2013
Revised Manuscript: July 25, 2013
Manuscript Accepted: July 25, 2013
Published: August 2, 2013

Citation
Ming Yin, Xiao Yong Tian, Ling Ling Wu, and Di Chen Li, "A Broadband and omnidirectional electromagnetic wave concentrator with gradient woodpile structure," Opt. Express 21, 19082-19090 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-16-19082


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312(5781), 1780–1782 (2006). [CrossRef] [PubMed]
  2. U. Leonhardt, “Optical conformal mapping,” Science312(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,” Science314(5801), 977–980 (2006). [CrossRef] [PubMed]
  4. T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science328(5976), 337–339 (2010). [CrossRef] [PubMed]
  5. Y. Urzhumov, N. Landy, T. Driscoll, D. Basov, and D. R. Smith, “Thin low-loss dielectric coatings for free-space cloaking,” Opt. Lett.38(10), 1606 (2013). [CrossRef]
  6. H. Chen and C. T. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Lett.90(24), 241105 (2007). [CrossRef]
  7. Y. G. Ma, C. K. Ong, T. Tyc, and U. Leonhardt, “An omnidirectional retroreflector based on the transmutation of dielectric singularities,” Nat. Mater.8(8), 639–642 (2009). [CrossRef] [PubMed]
  8. U. Leonhardt and T. G. Philbin, “General relativity in electrical engineering,” New J. Phys.8(10), 247–247 (2006). [CrossRef]
  9. A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Electromagnetic wormholes and virtual magnetic monopoles from metamaterials,” Phys. Rev. Lett.99(18), 183901 (2007). [CrossRef] [PubMed]
  10. M. Li, R. X. Miao, and Y. Pang, “More studies on metamaterials mimicking de Sitter space,” Opt. Express18(9), 9026–9033 (2010). [CrossRef] [PubMed]
  11. D. A. Genov, S. Zhang, and X. Zhang, “Mimicking celestial mechanics in metamaterials,” Nat. Phys.5(9), 687–692 (2009). [CrossRef]
  12. E. E. Narimanov and A. V. Kildishev, “Optical black hole: Broadband omnidirectional light absorber,” Appl. Phys. Lett.95(4), 041106 (2009). [CrossRef]
  13. H. Y. Chen, R. X. Miao, and M. A. Li, “Transformation optics that mimics the system outside a Schwarzschild black hole,” Opt. Express18(14), 15183–15188 (2010). [CrossRef] [PubMed]
  14. A. V. Kildishev, L. J. Prokopeva, and E. E. Narimanov, “Cylinder light concentrator and absorber: theoretical description,” Opt. Express18(16), 16646–16662 (2010). [CrossRef] [PubMed]
  15. S. Liu, L. Li, Z. Lin, H. Chen, J. Zi, and C. Chan, “Graded index photonic hole: Analytical and rigorous full wave solution,” Phys. Rev. B82, 054204 (2010).
  16. C. Argyropoulos, E. Kallos, and Y. Hao, “FDTD analysis of the optical black hole,” J. Opt. Soc. Am. B27(10), 2020–2025 (2010). [CrossRef]
  17. W. Lu, J. Jin, Z. Lin, and H. Chen, “A simple design of an artificial electromagnetic black hole,” J. Appl. Phys.108(6), 064517 (2010). [CrossRef]
  18. Q. Cheng, T. J. Cui, W. X. Jiang, and B. G. Cai, “An omnidirectional electromagnetic absorber made of metamaterials,” New J. Phys.12(6), 063006 (2010). [CrossRef]
  19. J. Zhou, X. Cai, Z. Chang, and G. Hu, “Experimental study on a broadband omnidirectional electromagnetic absorber,” J. Opt.13(8), 085103 (2011). [CrossRef]
  20. Y. R. Yang, L. Y. Leng, N. Wang, Y. G. Ma, and C. K. Ong, “Electromagnetic field attractor made of gradient index metamaterials,” J. Opt. Soc. Am. A29(4), 473–475 (2012). [CrossRef] [PubMed]
  21. R.-Q. Li, X.-F. Zhu, B. Liang, Y. Li, X.-Y. Zou, and J.-C. Cheng, “A broadband acoustic omnidirectional absorber comprising positive-index materials,” Appl. Phys. Lett.99(19), 193507 (2011). [CrossRef]
  22. A. Climente, D. Torrent, and J. Sánchez-Dehesa, “Omnidirectional broadband acoustic absorber based on metamaterials,” Appl. Phys. Lett.100(14), 144103 (2012). [CrossRef]
  23. Z. Chang and G. Hu, “Elastic wave omnidirectional absorbers designed by transformation method,” Appl. Phys. Lett.101(5), 054102 (2012). [CrossRef]
  24. K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band-gaps in three-dmensions - new layer-by-layer periodic structure,” Solid State Commun.89(5), 413–416 (1994). [CrossRef]
  25. B. Vasić, G. Isić, R. Gajić, and K. Hingerl, “Controlling electromagnetic fields with graded photonic crystals in metamaterial regime,” Opt. Express18(19), 20321–20333 (2010). [CrossRef] [PubMed]
  26. C. Luo, S. G. Johnson, and J. D. Joannopoulos, “All-angle negative refraction in a three-dimensionally periodic photonic crystal,” Appl. Phys. Lett.81(13), 2352 (2002). [CrossRef]
  27. D. W. Prather, “Photonic crystals: theory, applications, and fabrication”,(Wiley, Hoboken, N.J., 2009).
  28. Y. A. Urzhumov and D. R. Smith, “Transformation Optics with Photonic Band Gap Media,” Phys. Rev. Lett.105(16), 163901 (2010). [CrossRef] [PubMed]
  29. Z. Liang and J. Li, “Scaling two-dimensional photonic crystals for transformation optics,” Opt. Express19(18), 16821–16829 (2011). [CrossRef] [PubMed]
  30. H. Chen, J. Zhang, Y. Bai, Y. Luo, L. Ran, Q. Jiang, and J. A. Kong, “Experimental retrieval of the effective parameters of metamaterials based on a waveguide method,” Opt. Express14(26), 12944–12949 (2006). [CrossRef] [PubMed]
  31. L. Wu, X. Tian, H. Ma, M. Yin, and D. Li, “Broadband flattened Luneburg lens with ultra-wide angle based on a liquid medium,” Appl. Phys. Lett.102(7), 074103 (2013). [CrossRef]
  32. B. J. Justice, J. J. Mock, L. H. Guo, A. Degiron, D. Schurig, and D. R. Smith, “Spatial mapping of the internal and external electromagnetic fields of negative index metamaterials,” Opt. Express14(19), 8694–8705 (2006). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited