## Giant omnidirectional radiation enhancement via radially anisotropic zero-index metamaterial |

Optics Express, Vol. 21, Issue 20, pp. 23712-23723 (2013)

http://dx.doi.org/10.1364/OE.21.023712

Acrobat PDF (1382 KB)

### Abstract

We demonstrate a remarkable enhancement of isotropic radiation via radially anisotropic zero-index metamaterial (RAZIM). The radiation power can be enhanced by an order of magnitude when a line source and a dielectric particle is enclosed by a RAZIM shell. Based on the extended Mie theory, we illustrate that the basic physics of this isotropic radiation enhancement lies in the confinement of higher order anisotropic modes by the RAZIM shell. The confinement results in some high field regions within the RAZIM shell and thus enables strong scattering from the dielectric particle therein, giving rise to a giant amplification of isotropic radiation out of the system. The influence of the loss inherent in the RAZIM shell is also examined. It is found that the attenuation of omnidirectional power enhancement due to the loss in the RAZIM can be compensated by gain particles.

© 2013 OSA

## 1. Introduction

2. C. J. Boukamp and H. B. G. Casimir, “On multipole expansions in the theory of electromagnetic radiation,” Physica **20**, 539–554 (1954). [CrossRef]

4. Y. Yuan, N. Wang, and J. H. Lim, “On the omnidirectional radiation via radially anisotropic zero-index metamaterials,” Europhys. Lett. **100**, 34005 (2012). [CrossRef]

5. T. J. Judasz and B. B. Balsley, “Improved theoretical and experimental models for the coaxial colinear antenna,” IEEE Trans. Antennas and Propagat. **37**, 289–296 (1989). [CrossRef]

6. R. Bancroft, “Design parameters of an omnidirectional planar microstrip antenna,” Microw. Opt. Technol. Lett. **47**, 414–418 (2005). [CrossRef]

7. H. X. Xu, G. M. Wang, M. Q. Qi, and Z. M. Xu, “A metamaterial antenna with frequency-scanning omnidirectional radiation patterns,” Appl. Phys. Lett. **101**, 173501 (2012). [CrossRef]

8. J. Ahn, H. Jang, H. Moon, J. W. Lee, and B. Lee, “Inductively coupled compact RFID tag antenna at 910 MHz with near-isotropic radar cross-section (RCS) patterns,” IEEE Antennas Wirel. Propag. Lett. **6**, 518–520 (2007). [CrossRef]

9. S. L. Chen, K. H. Lin, and R. Mittra, “Miniature and near-3D omnidirectional radiation pattern RFID tag antenna design,” Electron. Lett. **45**, 923–924 (2009). [CrossRef]

10. R. A. York and R. C. Compton, “Quasi-optical power combining using mutually synchronized oscillator arrays,” IEEE Trans. Microwave Theory Tech. **39**, 1000–1009 (1991). [CrossRef]

12. M. P. DeLisio and R. A. York, “Quasi-optical and spatial power combining,” IEEE Trans. Microwave Theory Tech. **50**, 929–936 (2002). [CrossRef]

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

15. D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science **305**, 788–792 (2004). [CrossRef] [PubMed]

*ε*and permeability

*μ*, are employed to realize spatial power combination [16

16. Q. Cheng, W. X. Jiang, and T. J. Cui, “Spatial power combination for omnidirectional radiation via anisotropic metamaterials,” Phys. Rev. Lett. **108**, 213903 (2012). [CrossRef] [PubMed]

*ε*-near-zero (ENZ) [17

17. N. Garcia, E. V. Ponizovskaya, and John Q. Xiao, “Zero permittivity materials: Band gaps at the visible,” Appl. Phys. Lett. **80**, 1120–1122 (2002). [CrossRef]

21. R. P. Liu, Q. Cheng, T. Hand, J. J. Mock, T. J. Cui, S. A. Cummer, and D. R. Smith, “Experimental demonstration of electromagnetic tunneling through an epsilon-near-zero metamaterial at microwave frequencies,” Phys. Rev. Lett. **100**, 023903 (2008). [CrossRef] [PubMed]

*μ*-near-zero (MNZ) [22

22. M. G. Silveirinha and P. A. Belov, “Spatial dispersion in lattices of split ring resonators with permeability near zero,” Phys. Rev. B **77**, 233104 (2008). [CrossRef]

24. Y. Jin and S. L. He, “Enhancing and suppressing radiation with some permeability-near-zero structures,” Opt. Express **18**, 16587–16593 (2010). [CrossRef] [PubMed]

*ε*and

*μ*near zero, a matched ZIM (MZIM) [25

25. R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E **70**, 046608 (2004). [CrossRef]

27. X. Q. Huang, Y. Lai, Z. H. Hang, H. H. Zheng, and C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. **10**, 582–586 (2011). [CrossRef] [PubMed]

16. Q. Cheng, W. X. Jiang, and T. J. Cui, “Spatial power combination for omnidirectional radiation via anisotropic metamaterials,” Phys. Rev. Lett. **108**, 213903 (2012). [CrossRef] [PubMed]

28. Y. Yuan, L. F. Shen, L. X. Ran, T. Jiang, J. T. Huangfu, and J. A. Kong, “Directive emission based on anisotropic metamaterials,” Phys. Rev. A **77**, 053821 (2008). [CrossRef]

32. W. R. Zhu, I. D. Rukhlenko, and M. Premaratne, “Application of zero-index metamaterials for surface plasmon guiding,” Appl. Phys. Lett. **102**, 011910 (2013). [CrossRef]

19. B. Edwards, A. Alù, M. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett. **100**, 033903 (2008). [CrossRef] [PubMed]

21. R. P. Liu, Q. Cheng, T. Hand, J. J. Mock, T. J. Cui, S. A. Cummer, and D. R. Smith, “Experimental demonstration of electromagnetic tunneling through an epsilon-near-zero metamaterial at microwave frequencies,” Phys. Rev. Lett. **100**, 023903 (2008). [CrossRef] [PubMed]

34. M. G. Silveirinha and N. Engheta, “Theory of supercoupling, squeezing wave energy, and field confinement in narrow channels and tight bends using ε near-zero metamaterials,” Phys. Rev. B **76**, 245109 (2007). [CrossRef]

28. Y. Yuan, L. F. Shen, L. X. Ran, T. Jiang, J. T. Huangfu, and J. A. Kong, “Directive emission based on anisotropic metamaterials,” Phys. Rev. A **77**, 053821 (2008). [CrossRef]

29. Y. G. Ma, P. Wang, X. Chen, and C. K. Ong, “Near-field plane-wave-like beam emitting antenna fabricated by anisotropic metamaterial,” Appl. Phys. Lett. **94**, 044107 (2009). [CrossRef]

31. Q. Cheng, W. X. Jiang, and T. J. Cui, “Multi-beam generations at pre-designed directions based on anisotropic zero-index metamaterials,” Appl. Phys. Lett. **99**, 131913 (2011). [CrossRef]

35. S. Enoch, G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. **89**, 213902 (2002). [CrossRef] [PubMed]

27. X. Q. Huang, Y. Lai, Z. H. Hang, H. H. Zheng, and C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. **10**, 582–586 (2011). [CrossRef] [PubMed]

36. A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B **75**, 155410 (2007). [CrossRef]

37. S. M. Feng, “Loss-induced omnidirectional bending to the normal in ε-near-zero metamaterials,” Phys. Rev. Lett. **108**, 193904 (2012). [CrossRef]

38. B. Edwards, A. Alù, M. G. Silveirinha, and N. Engheta, “Reflectionless sharp bends and corners in waveguides using epsilon-near-zero effects,” J. Appl. Phys. **105**, 044905 (2009). [CrossRef]

39. J. Luo, P. Xu, H. Y. Chen, B. Hou, L. Gao, and Y. Lai, “Realizing almost perfect bending waveguides with anisotropic epsilon-near-zero metamaterials,” Appl. Phys. Lett. **100**, 221903 (2012). [CrossRef]

27. X. Q. Huang, Y. Lai, Z. H. Hang, H. H. Zheng, and C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. **10**, 582–586 (2011). [CrossRef] [PubMed]

40. J. Hao, W. Yan, and M. Qiu, “Super-reflection and cloaking based on zero index metamaterial,” Appl. Phys. Lett. **96**, 101109 (2010). [CrossRef]

42. Y. Xu and H. Chen, “Total reflection and transmission by epsilon-near-zero metamaterials with defects,” Appl. Phys. Lett. **98**, 113501 (2011). [CrossRef]

16. Q. Cheng, W. X. Jiang, and T. J. Cui, “Spatial power combination for omnidirectional radiation via anisotropic metamaterials,” Phys. Rev. Lett. **108**, 213903 (2012). [CrossRef] [PubMed]

43. S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature (London) **466**, 735–738 (2010). [CrossRef]

45. Z. Huang, T. Koschny, and C. M. Soukoulis, “Theory of pump-probe experiments of metallic metamaterials coupled to a gain medium,” Phys. Rev. Lett. **108**, 187402 (2012). [CrossRef] [PubMed]

46. W. R. Zhu, I. D. Rukhlenko, and M. Premaratne, “Light amplification in zero-index metamaterial with gain inserts,” Appl. Phys. Lett. **101**, 031907 (2012). [CrossRef]

25. R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E **70**, 046608 (2004). [CrossRef]

45. Z. Huang, T. Koschny, and C. M. Soukoulis, “Theory of pump-probe experiments of metallic metamaterials coupled to a gain medium,” Phys. Rev. Lett. **108**, 187402 (2012). [CrossRef] [PubMed]

46. W. R. Zhu, I. D. Rukhlenko, and M. Premaratne, “Light amplification in zero-index metamaterial with gain inserts,” Appl. Phys. Lett. **101**, 031907 (2012). [CrossRef]

## 2. Geometry and formulations

*a*and

*b*the inner and outer shell radii, and the positions of the dielectric rod and the line source are denoted by

*D*and

*S*, respectively. In the cylindrical coordinate, the permittivity and the permeability tensors of the RAZIM are characterized by [4

4. Y. Yuan, N. Wang, and J. H. Lim, “On the omnidirectional radiation via radially anisotropic zero-index metamaterials,” Europhys. Lett. **100**, 34005 (2012). [CrossRef]

**108**, 213903 (2012). [CrossRef] [PubMed]

47. Y. X. Ni, L. Gao, and C. W. Qiu, “Achieving invisibility of homegeneous cylindrically anisotropic cylinders,” Plamonics **5**, 251–258 (2010). [CrossRef]

*μ*→ 0. The origin of the cylindrical coordinate is at the center of the RAZIM shell. In our work, radiation behavior of a transverse magnetic (TM) line source with the electric field polarized along

_{r}*z*direction is considered. For convenience in illustrating physics, we first consider a simple system schematically illustrated in Fig. 1(a), based on which we can then solve the system when a dielectric particle is introduced as shown in Fig. 1(b) by taking account of the scattering effect between the particle and the RAZIM shell.

### 2.1. The system with a single line source

**108**, 213903 (2012). [CrossRef] [PubMed]

47. Y. X. Ni, L. Gao, and C. W. Qiu, “Achieving invisibility of homegeneous cylindrically anisotropic cylinders,” Plamonics **5**, 251–258 (2010). [CrossRef]

*k*the wavenumber in the vacuum,

*J*and

_{ν}*H*are, respectively, the

_{ν}*ν*-th order Bessel functions and Hankel functions of first kind, with

*m*runs from −∞ to ∞. The corresponding magnetic field in the transverse

*xoy*plane can be calculated by for the TM waves. The electric field radiated by a line source can also be expanded around the RAZIM shell center [48, 49] where

**is the position vector, and**

*r**denotes the position of the line source, with*

**l**_{s}*s*=

*l*= |

_{s}*| denoting the separation between the line source and the RAZIM shell center. For convenience and without loss of generality, the line source is supposed to be located at (*

**l**_{s}*x*,

_{s}*y*) with

_{s}*y*= 0. With these expansions, we can write the total electric field in different regions according to where coefficients

_{s}*A*characterize the reflection of EM wave from the RAZIM shell, and

_{m}*D*describes the EM wave radiating out of the shell.

_{m}*E*and

_{z}*H*should be continuous at the interface, based on which we can work out the partial wave expansion coefficients for the electric fields in different regions, where the generalized Mie coefficients are given by

_{ϕ}*μ*→ 0, suggesting that the order of the cylindrical functions

_{r}*J*and

_{ν}*H*in Eqs. (2), (5), and (7)

_{ν}*ν*→ ∞ for

*m*≠ 0. Therefore, |

*H*| → ∞ and |

_{ν}*J*| → 0, resulting in the Mie coefficient

_{ν}*p′*→ 0 for

_{m}*m*≠ 0. It follows from (6) that

*B*→ 0,

_{m}*C*→ 0 and

_{m}*D*→ 0 for

_{m}*m*≠ 0. This reveals that the permitted propagating EM waves in the RAZIM shell is nearly independent on the azimuthal angle

*ϕ*, as can be seen from Eqs. (2) and (5). In particular, for the case when

*ε*=

_{z}*μ*= 1, the Mie coefficients

_{ϕ}*p*

_{0}=

*p′*

_{0}= 1,

*q*

_{0}=

*q′*

_{0}= 0, and

*D*

_{0}=

*J*

_{0}(

*kd*). Accordingly, only the 0-th order of the isotropic cylindrical EM wave can be radiated out of the RAZIM shell, ensuring its omnidirectionality (

*ϕ*independent), consistent with the results obtained by Cheng and coworkers [16

**108**, 213903 (2012). [CrossRef] [PubMed]

4. Y. Yuan, N. Wang, and J. H. Lim, “On the omnidirectional radiation via radially anisotropic zero-index metamaterials,” Europhys. Lett. **100**, 34005 (2012). [CrossRef]

**108**, 213903 (2012). [CrossRef] [PubMed]

50. Z. C. Chen, R. Mohsen, Y. D. Gong, T. W. Chong, and M. H. Hong, “Realization of variable three-dimensional terahertz metamaterial tubes for passive resonance tunability,” Adv. Mater. **24**, OP143–OP147 (2012). [CrossRef]

### 2.2. The system with an addition of dielectric rod

*D*in space enclosed by the RAZIM shell as illustrated in Fig. 1(b). In this case, the dielectric particle re-scatters the EM wave and transforms the waves into the isotropic modes, which can be radiated through the RZAIM shell. So the radiation out of the RAZIM shell orginate not only the isotropic component from the line source

*S*, but also the isotropic component due to the dielectric particle

*D*. In the presence of dielectric rod, the equations in place of Eq. (6b) to determine the partial wave expansion coefficients

*A*,

_{m}*B*,

_{m}*C*and

_{m}*D*read where

_{m}*E*are the expansion coefficients of the scattered EM wave by the dielectric rod

_{m}*D*. Since the RZAIM shell is intact when the dielectric rod

*D*is inserted inside, the coefficients

*p*,

_{m}*q*,

_{m}*p′*, and

_{m}*q′*that characterize the scattering property of the RAZIM shell remain the same in the new system.

_{m}*E*, we transform the expanding terms of the EM wave from the shell center to the center of the dielectric rod

_{m}*D*. In this way, the electric field inside the dielectric rod

*denotes the position of the dielectric rod, with*

**l**_{d}*d*=

*l*= |

_{d}*| denoting the separation between the dielectric rod center and the RAZIM shell center, and*

**l**_{d}*r*is the radius of the dielectric rod

_{d}*D*. The partial wave expansion coefficients are given by with

*I*and

_{m}*R*corresponding to the contribution from the line source and the EM wave scattered inside by the RAZIM shell, In Eq. (11),

_{m}*ϕ*= ∠

_{c}*AOS*,

*ϕ′*= ∠

*ASO*,

*l*

^{2}=

*d*

^{2}+

*s*

^{2}−2

*ds*cos

*ϕ*is the distances from the dielectric rod to the line source

_{c}*S*, with

*l*/sin

*ϕ*=

_{c}*d*/ sin

*ϕ′. a*and

_{m}*b*are the Mie coefficients of the dielectric rod, which can easily obtained from the Mie theory [51] where

_{m}*ε*and

_{d}*μ*being the permittivity and permeability of dielectric rod, respectively. Note that when the RAZIM shell is removed from the system, the scattering from the shell vanishes, corresponding to

_{d}*R*= 0. Combining Eqs. (8), (10), and (11), we can arrive at This is a set of linear equations governing the coefficients

_{m}*E*, with the Mie coefficients

_{n}*a*and

_{m}*q′*given by (12b) and (7d), respectively, whereas the partial wave expansion coefficient

_{m}*I*is given by (11a).

_{m}## 3. Results and discussion

*a*= 0.5,

*b*= 1,

*μ*= 0.01,

_{r}*μ*= 1,

_{ϕ}*ε*= 1, and for the dielectric rod are

_{z}*r*= 0.15,

_{d}*ε*= 2, and

_{d}*μ*= 1. The wavelength of the line source is set as unit

_{d}*λ*= 1. The present theory can even be used to model system for a gain particle or a lossy particle inserted inside the RAZIM shell.

### 3.1. Field pattern simulation

*E*| pattern inside RAZIM shell, the result is shown in Fig. 2(a), where a line source is positioned at (0.1, 0) and no dielectric rod is inserted. Thus, the role of the RAZIM shell can be illustrated. We can observe a standing wave characterized by strong inhomogeneity, which is created by the higher order partial waves in Eq. (4) due to the high reflection from the RAZIM shell. Accordingly, the RAZIM shell is operated similarly as a filter in that only 0-th order of the partial wave can be radiated out, ensuring the isotropy of the radiation. Simultaneously, it confines all the higher order partial waves inside the system, facilitating the enhancement of the radiation power by the introduction of a dielectric rod. The EM wave radiating outside the RAZIM shell can be calculated approximately by Accordingly, the performance of the dielectric rod can be evaluated by calculating the amplitude of |

_{z}*D*

_{0}| given by (6). In Fig. 2(b), we present the map of |

*D*

_{0}| as the function of the dielectric rod position (

*x*,

_{d}*y*), where we can find the optimal position is near to the area where the electric field amplitude |

_{d}*E*| is strongest. In addition, |

_{z}*D*

_{0}| bears a much larger value than that of a free line source in a large area, illustrating the outstanding effect of the dielectric rod on the radiation enhancement. Besides, the introduction of a dielectric rod inside the RAZIM shell doesn’t destroy the homogeneity of the RAZIM. This makes the designed system experimentally feasible.

### 3.2. Amplification of the radiation power

**is the Poynting vector, the integral curve**

*S**L*is the circle centered at the origin

*O*with the radius larger than the RAZIM shell radius

*b*. For the system showing in Fig. 1(b), only the 0-th order cylindrical wave is radiated out. The radiating power can be approximately evaluated according to For comparison, we also calculate the radiating power

*P*when the RAZIM shell is removed from the system, which can be measured by In Fig. 3, we present the radiating power normalized by the radiating power

_{wo}*P*

_{s}_{0}of the line source in free space. Both

*P*

_{wi}/P_{s}_{0}and

*P*

_{wo}/P_{s}_{0}are plotted as the functions of the dielectric rod position

*x*while keeping

_{d}*y*= 0. Panels (a) and (b) correspond to the cases when the line source is positioned at (0.1, 0) and (0, 0), respectively. For

_{d}*P*

_{wo}/P_{s}_{0}, its value experiences nearly no change with the change of the dielectric rod position, as shown by the blue dashed line in panels (a) and (b). Our simulation shows that even when the dielectric rod is replaced by a gain particle, the value of

*P*

_{wo}/P_{s}_{0}remains close to 1, suggesting that an insertion of particle, either passive or active, has nearly no effect on the radiating behavior of the system in the absence of the RAZIM shell. The reason lies in that in free space the line source does not demonstrate the position with a strong electric field amplitude. This explains why Zhu and coworkers have to use multiple gain particles to obtain a strong radiation [46

46. W. R. Zhu, I. D. Rukhlenko, and M. Premaratne, “Light amplification in zero-index metamaterial with gain inserts,” Appl. Phys. Lett. **101**, 031907 (2012). [CrossRef]

*P*

_{wi}/P_{s}_{0}, the radiating power can be significantly improved, as can be observed from the red solid lines shown in panels (a) and (b), indicating that the RAZIM shell plays a crucial role for the amplification of the radiation. The maximum enhancement appears close to the position with the strongest electric field amplitude. It is also noted that the position of the line source has an obvious effect on the radiating power by comparing panels (a) and (b), which arises from the dependence of the standing wave on the source position. In our system, an enhancement of over 10 times is achieved with the insertion of a dielectric rod.

52. S. Arslanagic, Y. Liu, R. Malureanu, and R. W. Ziolkowki, “Impact of the excitation source and plasmonic material on cylindrical active coated nano-particles,” Sensors **11**, 9109–9120 (2011). [CrossRef] [PubMed]

53. A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, “Band gap formation and multiple scattering in photonic quasicrystals with a Penrose-type lattice,” Phys. Rev. Lett. **94**, 183903 (2005). [CrossRef] [PubMed]

*I/I*

_{0}by that of the line source in free space

*I*

_{0}where the irradiance is defined as

*x*,

_{s}*y*) = (0.1, 0) and the dielectric rod is located at (

_{s}*x*,

_{d}*y*) = (−0.24, 0) close to the position of the strongest electric field amplitude. The red solid line is 1/4 of the irradiance

_{d}*I*for the system with the RAZIM shell, from which we can find that the system can amplify the irradiance by over 10 times, consistent with the result shown in Fig. 3(a). In addition, the radiation demonstrates an obvious isotropic characteristic. For comparison, we also present the result when the RAZIM shell is removed from the system. The corresponding irradiance

_{wi}*I*is shown by the blue dash line, which is not isotropic and no obvious enhancement can be achieved with the dielectric rod or even a gain particle. The performance of the dielectric rod can be evaluated by comparing

_{wo}*I*to irradiance

_{wi}**108**, 213903 (2012). [CrossRef] [PubMed]

*μ*= 0.01, not exactly equal to 0, suggesting a finite bandwidth of the operating frequency.

_{r}### 3.3. Influence of the loss due to the RAZIM shell

52. S. Arslanagic, Y. Liu, R. Malureanu, and R. W. Ziolkowki, “Impact of the excitation source and plasmonic material on cylindrical active coated nano-particles,” Sensors **11**, 9109–9120 (2011). [CrossRef] [PubMed]

54. S. Arslanagic and R. W. Ziolkowki, “Active coated nano-particle excited by an arbitrarily located electric Hertzian dipolelresonance and transparency effects,” J. Opt. **12**, 024014 (2010). [CrossRef]

56. S. Arslanagic, “Power flow in the interior and exterior of cylindrical coated nanoparticles,” Appl. Phys. A **109**, 921–925 (2012). [CrossRef]

50. Z. C. Chen, R. Mohsen, Y. D. Gong, T. W. Chong, and M. H. Hong, “Realization of variable three-dimensional terahertz metamaterial tubes for passive resonance tunability,” Adv. Mater. **24**, OP143–OP147 (2012). [CrossRef]

52. S. Arslanagic, Y. Liu, R. Malureanu, and R. W. Ziolkowki, “Impact of the excitation source and plasmonic material on cylindrical active coated nano-particles,” Sensors **11**, 9109–9120 (2011). [CrossRef] [PubMed]

54. S. Arslanagic and R. W. Ziolkowki, “Active coated nano-particle excited by an arbitrarily located electric Hertzian dipolelresonance and transparency effects,” J. Opt. **12**, 024014 (2010). [CrossRef]

*ε*= 2.5 − 0.5

_{d}*i*. The results are illustrated by the red solid line in Fig. 5, where we can find that an enhancement of the output radiating power is achieved by a factor of about 7. Meanwhile, the omnidirectionality is ensured as well despite of the position of the line source. For comparison, we also present the result for the system without the RAZIM shell but with a gain particle only, which is indicated by the blue solid line. It can be found that neither significant increase nor isotropy in radiation is achieved, imlying once again that the RAZIM shell plays a crucial role in enhancing radiation power and keeping radiation isotropic.

## 4. Conclusion

## Acknowledgments

## References and links

1. | J. D. Kraus and R. J. Marhefka, |

2. | C. J. Boukamp and H. B. G. Casimir, “On multipole expansions in the theory of electromagnetic radiation,” Physica |

3. | H. F. Mathis, “A short proof that an isotropic antenna is impossible,” Proc. IRE |

4. | Y. Yuan, N. Wang, and J. H. Lim, “On the omnidirectional radiation via radially anisotropic zero-index metamaterials,” Europhys. Lett. |

5. | T. J. Judasz and B. B. Balsley, “Improved theoretical and experimental models for the coaxial colinear antenna,” IEEE Trans. Antennas and Propagat. |

6. | R. Bancroft, “Design parameters of an omnidirectional planar microstrip antenna,” Microw. Opt. Technol. Lett. |

7. | H. X. Xu, G. M. Wang, M. Q. Qi, and Z. M. Xu, “A metamaterial antenna with frequency-scanning omnidirectional radiation patterns,” Appl. Phys. Lett. |

8. | J. Ahn, H. Jang, H. Moon, J. W. Lee, and B. Lee, “Inductively coupled compact RFID tag antenna at 910 MHz with near-isotropic radar cross-section (RCS) patterns,” IEEE Antennas Wirel. Propag. Lett. |

9. | S. L. Chen, K. H. Lin, and R. Mittra, “Miniature and near-3D omnidirectional radiation pattern RFID tag antenna design,” Electron. Lett. |

10. | R. A. York and R. C. Compton, “Quasi-optical power combining using mutually synchronized oscillator arrays,” IEEE Trans. Microwave Theory Tech. |

11. | S. Nogi, J. S. Lin, and T. Itoh, “Mode analysis and stabilization of a spatial power combining array with strongly coupled oscillators,” IEEE Trans. Microwave Theory Tech. |

12. | M. P. DeLisio and R. A. York, “Quasi-optical and spatial power combining,” IEEE Trans. Microwave Theory Tech. |

13. | J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. |

14. | R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science |

15. | D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science |

16. | Q. Cheng, W. X. Jiang, and T. J. Cui, “Spatial power combination for omnidirectional radiation via anisotropic metamaterials,” Phys. Rev. Lett. |

17. | N. Garcia, E. V. Ponizovskaya, and John Q. Xiao, “Zero permittivity materials: Band gaps at the visible,” Appl. Phys. Lett. |

18. | M. Silveirinha and N. Engheta, “Tunneling of electromagnetic energy through subwavelength channels and bends using ε-near-zero materials,” Phys. Rev. Lett. |

19. | B. Edwards, A. Alù, M. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett. |

20. | A. Alù, M. G. Silveirinha, and N. Engheta, “Transmission-line analysis of ε-near-zero–filled narrow channels,” Phys. Rev. E |

21. | R. P. Liu, Q. Cheng, T. Hand, J. J. Mock, T. J. Cui, S. A. Cummer, and D. R. Smith, “Experimental demonstration of electromagnetic tunneling through an epsilon-near-zero metamaterial at microwave frequencies,” Phys. Rev. Lett. |

22. | M. G. Silveirinha and P. A. Belov, “Spatial dispersion in lattices of split ring resonators with permeability near zero,” Phys. Rev. B |

23. | Y. Jin, P. Zhang, and S. L. He, “Squeezing electromagnetic energy with a dielectric split ring inside a permeability-near-zero metamaterial,” Phys. Rev. B |

24. | Y. Jin and S. L. He, “Enhancing and suppressing radiation with some permeability-near-zero structures,” Opt. Express |

25. | R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E |

26. | M. Silveirinha and Nader Engheta, “Design of matched zero-index metamaterials using nonmagnetic inclusions in epsilon-near-zero media,” Phys. Rev. B, |

27. | X. Q. Huang, Y. Lai, Z. H. Hang, H. H. Zheng, and C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater. |

28. | Y. Yuan, L. F. Shen, L. X. Ran, T. Jiang, J. T. Huangfu, and J. A. Kong, “Directive emission based on anisotropic metamaterials,” Phys. Rev. A |

29. | Y. G. Ma, P. Wang, X. Chen, and C. K. Ong, “Near-field plane-wave-like beam emitting antenna fabricated by anisotropic metamaterial,” Appl. Phys. Lett. |

30. | Q. Cheng, W. X. Jiang, and T. J. Cui, “Radiation of planar electromagnetic waves by a line source in anisotropic metamaterials,” J. Phys. D: Appl. Phys. |

31. | Q. Cheng, W. X. Jiang, and T. J. Cui, “Multi-beam generations at pre-designed directions based on anisotropic zero-index metamaterials,” Appl. Phys. Lett. |

32. | W. R. Zhu, I. D. Rukhlenko, and M. Premaratne, “Application of zero-index metamaterials for surface plasmon guiding,” Appl. Phys. Lett. |

33. | Q. Cheng, R. P. Liu, D. Huang, T. J. Cui, and D. R. Smith, “Circuit verification of tunneling effect in zero permittivity medium,” Appl. Phys. Lett. |

34. | M. G. Silveirinha and N. Engheta, “Theory of supercoupling, squeezing wave energy, and field confinement in narrow channels and tight bends using ε near-zero metamaterials,” Phys. Rev. B |

35. | S. Enoch, G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. |

36. | A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B |

37. | S. M. Feng, “Loss-induced omnidirectional bending to the normal in ε-near-zero metamaterials,” Phys. Rev. Lett. |

38. | B. Edwards, A. Alù, M. G. Silveirinha, and N. Engheta, “Reflectionless sharp bends and corners in waveguides using epsilon-near-zero effects,” J. Appl. Phys. |

39. | J. Luo, P. Xu, H. Y. Chen, B. Hou, L. Gao, and Y. Lai, “Realizing almost perfect bending waveguides with anisotropic epsilon-near-zero metamaterials,” Appl. Phys. Lett. |

40. | J. Hao, W. Yan, and M. Qiu, “Super-reflection and cloaking based on zero index metamaterial,” Appl. Phys. Lett. |

41. | V. C. Nguyen, L. Chen, and K. Halterman, “Total transmission and total reflection by zero index metamaterials with defects,” Phys. Rev. Lett. |

42. | Y. Xu and H. Chen, “Total reflection and transmission by epsilon-near-zero metamaterials with defects,” Appl. Phys. Lett. |

43. | S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature (London) |

44. | A. Veltri and A. Aradian, “Optical response of a metallic nanoparticle immersed in a medium with optical gain,” Phys. Rev. B |

45. | Z. Huang, T. Koschny, and C. M. Soukoulis, “Theory of pump-probe experiments of metallic metamaterials coupled to a gain medium,” Phys. Rev. Lett. |

46. | W. R. Zhu, I. D. Rukhlenko, and M. Premaratne, “Light amplification in zero-index metamaterial with gain inserts,” Appl. Phys. Lett. |

47. | Y. X. Ni, L. Gao, and C. W. Qiu, “Achieving invisibility of homegeneous cylindrically anisotropic cylinders,” Plamonics |

48. | M. Abramowitz and I. A. Stegun, |

49. | W. C. Chew, |

50. | Z. C. Chen, R. Mohsen, Y. D. Gong, T. W. Chong, and M. H. Hong, “Realization of variable three-dimensional terahertz metamaterial tubes for passive resonance tunability,” Adv. Mater. |

51. | C. F. Bohren and D. R. Huffman, |

52. | S. Arslanagic, Y. Liu, R. Malureanu, and R. W. Ziolkowki, “Impact of the excitation source and plasmonic material on cylindrical active coated nano-particles,” Sensors |

53. | A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, “Band gap formation and multiple scattering in photonic quasicrystals with a Penrose-type lattice,” Phys. Rev. Lett. |

54. | S. Arslanagic and R. W. Ziolkowki, “Active coated nano-particle excited by an arbitrarily located electric Hertzian dipolelresonance and transparency effects,” J. Opt. |

55. | S. Arslanagic and R. W. Ziolkowki, “Achieve coated nanoparticles: impact of plasmonic material choice,” Appl. Phys. A |

56. | S. Arslanagic, “Power flow in the interior and exterior of cylindrical coated nanoparticles,” Appl. Phys. A |

**OCIS Codes**

(290.4020) Scattering : Mie theory

(350.5610) Other areas of optics : Radiation

(160.3918) Materials : Metamaterials

**ToC Category:**

Metamaterials

**History**

Original Manuscript: August 19, 2013

Revised Manuscript: September 5, 2013

Manuscript Accepted: September 5, 2013

Published: September 27, 2013

**Citation**

Neng Wang, Huajin Chen, Wanli Lu, Shiyang Liu, and Zhifang Lin, "Giant omnidirectional radiation enhancement via radially anisotropic zero-index metamaterial," Opt. Express **21**, 23712-23723 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-20-23712

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### References

- J. D. Kraus and R. J. Marhefka, Antennas: For All Applications (McGraw Hill, 2002).
- C. J. Boukamp and H. B. G. Casimir, “On multipole expansions in the theory of electromagnetic radiation,” Physica20, 539–554 (1954). [CrossRef]
- H. F. Mathis, “A short proof that an isotropic antenna is impossible,” Proc. IRE39, 970 (1951).
- Y. Yuan, N. Wang, and J. H. Lim, “On the omnidirectional radiation via radially anisotropic zero-index metamaterials,” Europhys. Lett.100, 34005 (2012). [CrossRef]
- T. J. Judasz and B. B. Balsley, “Improved theoretical and experimental models for the coaxial colinear antenna,” IEEE Trans. Antennas and Propagat.37, 289–296 (1989). [CrossRef]
- R. Bancroft, “Design parameters of an omnidirectional planar microstrip antenna,” Microw. Opt. Technol. Lett.47, 414–418 (2005). [CrossRef]
- H. X. Xu, G. M. Wang, M. Q. Qi, and Z. M. Xu, “A metamaterial antenna with frequency-scanning omnidirectional radiation patterns,” Appl. Phys. Lett.101, 173501 (2012). [CrossRef]
- J. Ahn, H. Jang, H. Moon, J. W. Lee, and B. Lee, “Inductively coupled compact RFID tag antenna at 910 MHz with near-isotropic radar cross-section (RCS) patterns,” IEEE Antennas Wirel. Propag. Lett.6, 518–520 (2007). [CrossRef]
- S. L. Chen, K. H. Lin, and R. Mittra, “Miniature and near-3D omnidirectional radiation pattern RFID tag antenna design,” Electron. Lett.45, 923–924 (2009). [CrossRef]
- R. A. York and R. C. Compton, “Quasi-optical power combining using mutually synchronized oscillator arrays,” IEEE Trans. Microwave Theory Tech.39, 1000–1009 (1991). [CrossRef]
- S. Nogi, J. S. Lin, and T. Itoh, “Mode analysis and stabilization of a spatial power combining array with strongly coupled oscillators,” IEEE Trans. Microwave Theory Tech.41, 1827–1837 (1993). [CrossRef]
- M. P. DeLisio and R. A. York, “Quasi-optical and spatial power combining,” IEEE Trans. Microwave Theory Tech.50, 929–936 (2002). [CrossRef]
- J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett.85, 3966–3969 (2000). [CrossRef] [PubMed]
- R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science292, 77–79 (2001). [CrossRef] [PubMed]
- D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science305, 788–792 (2004). [CrossRef] [PubMed]
- Q. Cheng, W. X. Jiang, and T. J. Cui, “Spatial power combination for omnidirectional radiation via anisotropic metamaterials,” Phys. Rev. Lett.108, 213903 (2012). [CrossRef] [PubMed]
- N. Garcia, E. V. Ponizovskaya, and John Q. Xiao, “Zero permittivity materials: Band gaps at the visible,” Appl. Phys. Lett.80, 1120–1122 (2002). [CrossRef]
- M. Silveirinha and N. Engheta, “Tunneling of electromagnetic energy through subwavelength channels and bends using ε-near-zero materials,” Phys. Rev. Lett.97, 157403 (2006). [CrossRef]
- B. Edwards, A. Alù, M. Young, M. Silveirinha, and N. Engheta, “Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide,” Phys. Rev. Lett.100, 033903 (2008). [CrossRef] [PubMed]
- A. Alù, M. G. Silveirinha, and N. Engheta, “Transmission-line analysis of ε-near-zero–filled narrow channels,” Phys. Rev. E78, 016604 (2008). [CrossRef]
- R. P. Liu, Q. Cheng, T. Hand, J. J. Mock, T. J. Cui, S. A. Cummer, and D. R. Smith, “Experimental demonstration of electromagnetic tunneling through an epsilon-near-zero metamaterial at microwave frequencies,” Phys. Rev. Lett.100, 023903 (2008). [CrossRef] [PubMed]
- M. G. Silveirinha and P. A. Belov, “Spatial dispersion in lattices of split ring resonators with permeability near zero,” Phys. Rev. B77, 233104 (2008). [CrossRef]
- Y. Jin, P. Zhang, and S. L. He, “Squeezing electromagnetic energy with a dielectric split ring inside a permeability-near-zero metamaterial,” Phys. Rev. B81, 085117 (2010). [CrossRef]
- Y. Jin and S. L. He, “Enhancing and suppressing radiation with some permeability-near-zero structures,” Opt. Express18, 16587–16593 (2010). [CrossRef] [PubMed]
- R. W. Ziolkowski, “Propagation in and scattering from a matched metamaterial having a zero index of refraction,” Phys. Rev. E70, 046608 (2004). [CrossRef]
- M. Silveirinha and Nader Engheta, “Design of matched zero-index metamaterials using nonmagnetic inclusions in epsilon-near-zero media,” Phys. Rev. B,75, 075119 (2007). [CrossRef]
- X. Q. Huang, Y. Lai, Z. H. Hang, H. H. Zheng, and C. T. Chan, “Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials,” Nat. Mater.10, 582–586 (2011). [CrossRef] [PubMed]
- Y. Yuan, L. F. Shen, L. X. Ran, T. Jiang, J. T. Huangfu, and J. A. Kong, “Directive emission based on anisotropic metamaterials,” Phys. Rev. A77, 053821 (2008). [CrossRef]
- Y. G. Ma, P. Wang, X. Chen, and C. K. Ong, “Near-field plane-wave-like beam emitting antenna fabricated by anisotropic metamaterial,” Appl. Phys. Lett.94, 044107 (2009). [CrossRef]
- Q. Cheng, W. X. Jiang, and T. J. Cui, “Radiation of planar electromagnetic waves by a line source in anisotropic metamaterials,” J. Phys. D: Appl. Phys.43, 335406 (2010). [CrossRef]
- Q. Cheng, W. X. Jiang, and T. J. Cui, “Multi-beam generations at pre-designed directions based on anisotropic zero-index metamaterials,” Appl. Phys. Lett.99, 131913 (2011). [CrossRef]
- W. R. Zhu, I. D. Rukhlenko, and M. Premaratne, “Application of zero-index metamaterials for surface plasmon guiding,” Appl. Phys. Lett.102, 011910 (2013). [CrossRef]
- Q. Cheng, R. P. Liu, D. Huang, T. J. Cui, and D. R. Smith, “Circuit verification of tunneling effect in zero permittivity medium,” Appl. Phys. Lett.91, 2341052007.
- M. G. Silveirinha and N. Engheta, “Theory of supercoupling, squeezing wave energy, and field confinement in narrow channels and tight bends using ε near-zero metamaterials,” Phys. Rev. B76, 245109 (2007). [CrossRef]
- S. Enoch, G. Tayeb, P. Sabouroux, N. Guerin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett.89, 213902 (2002). [CrossRef] [PubMed]
- A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B75, 155410 (2007). [CrossRef]
- S. M. Feng, “Loss-induced omnidirectional bending to the normal in ε-near-zero metamaterials,” Phys. Rev. Lett.108, 193904 (2012). [CrossRef]
- B. Edwards, A. Alù, M. G. Silveirinha, and N. Engheta, “Reflectionless sharp bends and corners in waveguides using epsilon-near-zero effects,” J. Appl. Phys.105, 044905 (2009). [CrossRef]
- J. Luo, P. Xu, H. Y. Chen, B. Hou, L. Gao, and Y. Lai, “Realizing almost perfect bending waveguides with anisotropic epsilon-near-zero metamaterials,” Appl. Phys. Lett.100, 221903 (2012). [CrossRef]
- J. Hao, W. Yan, and M. Qiu, “Super-reflection and cloaking based on zero index metamaterial,” Appl. Phys. Lett.96, 101109 (2010). [CrossRef]
- V. C. Nguyen, L. Chen, and K. Halterman, “Total transmission and total reflection by zero index metamaterials with defects,” Phys. Rev. Lett.105, 233908 (2010). [CrossRef]
- Y. Xu and H. Chen, “Total reflection and transmission by epsilon-near-zero metamaterials with defects,” Appl. Phys. Lett.98, 113501 (2011). [CrossRef]
- S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature (London)466, 735–738 (2010). [CrossRef]
- A. Veltri and A. Aradian, “Optical response of a metallic nanoparticle immersed in a medium with optical gain,” Phys. Rev. B85, 115429 (2012). [CrossRef]
- Z. Huang, T. Koschny, and C. M. Soukoulis, “Theory of pump-probe experiments of metallic metamaterials coupled to a gain medium,” Phys. Rev. Lett.108, 187402 (2012). [CrossRef] [PubMed]
- W. R. Zhu, I. D. Rukhlenko, and M. Premaratne, “Light amplification in zero-index metamaterial with gain inserts,” Appl. Phys. Lett.101, 031907 (2012). [CrossRef]
- Y. X. Ni, L. Gao, and C. W. Qiu, “Achieving invisibility of homegeneous cylindrically anisotropic cylinders,” Plamonics5, 251–258 (2010). [CrossRef]
- M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graph, and Mathematical Tables(Dover, 1964).
- W. C. Chew, Waves and Fields in Inhomogeneous Media (IEEE Press, 1995).
- Z. C. Chen, R. Mohsen, Y. D. Gong, T. W. Chong, and M. H. Hong, “Realization of variable three-dimensional terahertz metamaterial tubes for passive resonance tunability,” Adv. Mater.24, OP143–OP147 (2012). [CrossRef]
- C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley, 1983).
- S. Arslanagic, Y. Liu, R. Malureanu, and R. W. Ziolkowki, “Impact of the excitation source and plasmonic material on cylindrical active coated nano-particles,” Sensors11, 9109–9120 (2011). [CrossRef] [PubMed]
- A. Della Villa, S. Enoch, G. Tayeb, V. Pierro, V. Galdi, and F. Capolino, “Band gap formation and multiple scattering in photonic quasicrystals with a Penrose-type lattice,” Phys. Rev. Lett.94, 183903 (2005). [CrossRef] [PubMed]
- S. Arslanagic and R. W. Ziolkowki, “Active coated nano-particle excited by an arbitrarily located electric Hertzian dipolelresonance and transparency effects,” J. Opt.12, 024014 (2010). [CrossRef]
- S. Arslanagic and R. W. Ziolkowki, “Achieve coated nanoparticles: impact of plasmonic material choice,” Appl. Phys. A103, 795–798 (2011). [CrossRef]
- S. Arslanagic, “Power flow in the interior and exterior of cylindrical coated nanoparticles,” Appl. Phys. A109, 921–925 (2012). [CrossRef]

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