## Doubly negative metamaterials in the near infrared and visible regimes based on thin film nanocomposites

Optics Express, Vol. 14, Issue 23, pp. 11164-11177 (2006)

http://dx.doi.org/10.1364/OE.14.011164

Acrobat PDF (1136 KB)

### Abstract

An optical metamaterial characterized simultaneously by negative permittivity and permeability, viz. doubly negative metamaterial (DNM), that comprises deeply subwavelength unit cells is introduced. The DNM can operate in the near infrared and visible spectra and can be manufactured using standard nanofabrication methods with compatible materials. The DNM”s unit cell comprise a continuous optically thin metal film sandwiched between two identical optically thin metal strips separated by a small distance form the film. The incorporation of the middle thin metal film avoids limitations of metamaterials comprised of arrays of paired wires/strips/patches to operate for large wavelength / unit cell ratios. A cavity model, which is a modification of the conventional patch antenna cavity model, is developed to elucidate the structure”s electromagnetic properties. A novel procedure for extracting the effective permittivity and permeability is developed for an arbitrary incident angle and those parameters were shown to be nearly angle-independent. Extensions of the presented two dimensional structure to three dimensions by using square patches are straightforward and will enable more isotropic DNMs.

© 2006 Optical Society of America

## 1. Introduction

1. V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ϵ and &mu,” Soviet Physics - Uspekhi **10**, 509–514 (1968). [CrossRef]

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

8. Z. Jiangfeng, T. Koschny, Z. Lei, G. Tuttle, and C. M. Soukoulis, “Experimental demonstration of negative index of refraction,” Appl. Phys. Lett. **88**, 221103-221101 (2006). [CrossRef]

10. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science **292**, 77–79 (2001). [CrossRef] [PubMed]

13. J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. **95**, 223902-223901 (2005). [CrossRef] [PubMed]

12. Z. Shuang, F. Wenjun, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, “Midinfrared resonant magnetic nanostructures exhibiting a negative permeability,” Phys. Rev. Lett. **94**, 037402-037401 (2005). [CrossRef]

14. V. M. Shalaev, C. Wenshan, U. K. Chettiar, Y. Hsiao-Kuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett. **30**, 3356–3358 (2005). [CrossRef]

17. G. Shvets and Y. A. Urzhumov, “Engineering the electromagnetic properties of periodic nanostructures using electrostatic resonances,” Phys. Rev. Lett. **93**, 243902-243901 (2004). [CrossRef]

18. A. Alu, A. Salandrino, and N. Engheta, “Negative effective permeability and left-handed materials at optical frequencies,” Opt. Express **14**, 1557 (2006). [CrossRef] [PubMed]

11. G. Shvets and Y. Urzhumov, “Negative index meta-materials based on two-dimensional metallic structures,” J. Opt. A **8**, S122 (2006). [CrossRef]

12. Z. Shuang, F. Wenjun, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, “Midinfrared resonant magnetic nanostructures exhibiting a negative permeability,” Phys. Rev. Lett. **94**, 037402-037401 (2005). [CrossRef]

14. V. M. Shalaev, C. Wenshan, U. K. Chettiar, Y. Hsiao-Kuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett. **30**, 3356–3358 (2005). [CrossRef]

11. G. Shvets and Y. Urzhumov, “Negative index meta-materials based on two-dimensional metallic structures,” J. Opt. A **8**, S122 (2006). [CrossRef]

11. G. Shvets and Y. Urzhumov, “Negative index meta-materials based on two-dimensional metallic structures,” J. Opt. A **8**, S122 (2006). [CrossRef]

14. V. M. Shalaev, C. Wenshan, U. K. Chettiar, Y. Hsiao-Kuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett. **30**, 3356–3358 (2005). [CrossRef]

**8**, S122 (2006). [CrossRef]

## 2. Layout of the unit cell

*x*and

*z*directions with periods

*L*

_{x}and

*L*

_{z}, respectively. The structure comprises a finite number of

*m*

_{l}layers in the

*z*direction and an infinite number of unit cells in the

*x*direction. Every layer comprises an infinite metal film of thickness

*d*

_{f}and an infinite array of metal strips of width

*w*and thickness

*d*

_{s}(Fig. 1). In the

*z*dimension, the strips are arranged in pairs symmetrically with respect to the unit cell’s symmetry plane (

*z*=0). The distance between the bottom face of the top strip and the top face of the bottom strip is 2

*h*. The structure is uniform in the

*y*dimension. The strips and the film are assumed to be made of an identical metal characterized by a relative permittivity

*ε*

_{m}with Re{

*ε*

_{m}}<0 in the optical frequency regime (e.g. silver or gold). It is assumed that

*d*

_{s},

*d*

_{f},

*h*,

*L*

_{x}and

*L*

_{z}are much smaller than the (free-space) wavelength of illumination

*λ*to assure that the unit cells’ geometry is much smaller than the effective wavelength of the incident radiation. In addition,

*d*

_{s},

*d*

_{f}are assumed to be smaller than

*w*such that possible charge and current distribution variations in the strips and film occur primarily in the horizontal (

*x*) dimension. The whole metallic structure is embedded into a dielectric material with permittivity

*ε*

_{d}of a total thickness

*H*=

*m*

_{l}

*L*

_{z}. A harmonic time dependence

*e*

^{j2πft}of the optical field is assumed and suppressed in what follows. Here,

*f*=

*c*/

*λ*is the frequency of illumination and

*c*is the speed of light in vacuum.

**8**, S122 (2006). [CrossRef]

*y*axis) and for special combinations of the structures’ parameters and frequency of illumination, the structure in Fig. 1 is equivalent to a slab made of a DNM characterized simultaneously by negative real parts of the effective permittivity, permeability, and index of refraction. It is noted that the introduced array of strips is a 2D counterpart of a 3D structure comprising doubly periodic arrays of rectangular/square patches and therefore the results presented here are directly extendable to more general 3D configurations leading to e DNMs with properties nearly independent of light polarization and plane of incidence.

## 3. Optical properties of DNM structures

### 3.1 Cavity model

*x*|<

*w*2 is closed by (virtual) vertical perfect magnetically conducting walls (Fig. 2). In the second step, the optically thin top and bottom metal strips and the central metal film are replaced by thin (inductive) admittance sheets characterized by normalized surface admittances

*k*

_{0}(

*ε*

_{m}-1)

*d*

_{s}at

*z*=±

*h*and

*jk*

_{0}(

*ε*

_{m}-1)

*d*

_{f}at

*z*=0, respectively [20];

*k*

_{0}=2

*π*/

*λ*is the free space wavenumber. Due to its symmetry around

*z*=0, the resulting simplified cavity supports resonances for which magnetic field has either even or odd parity with respect to the

*z*=0 plane.

### 3.2 Magnetic resonances

*z*=0) and hence this sheet has no effect on the modal field structure (Fig. 2). In contrast, the currents in the top and bottom strip admittance sheets (

*z*=±

*h*) are strong and they flow in opposite directions thus resulting in an effective magnetic dipole response; this resonance type will be referred to as magnetic. The magnetic field of the magnetic resonances behaves as

**H**=

**ŷ**

*A*(

*f*

_{magn},

*z*)sin(

*πq*(

*x*-

*w*/2)/

*w*), where

*q*is an integer counting the number of the field oscillations in the

*x*direction within

*w*,

*A*(

*f*

_{magn},

*z*) is an even function separately defined inside and outside the cavity, and

*f*

_{magn}are the magnetic resonance frequencies satisfying the following dispersion relation obtained by matching the fields outside and inside the cavity:

*ε*

_{m}-1)

*d*

_{s}| is large, then |cot

*k*

_{z}

*h*| should be large and as a result magnetic resonance frequencies,

*ε*

_{m}-1)

*d*

_{s}| is finite/small,

*f*

_{magn}can be made much smaller than the simple path antenna resonances, which is the crucial point in achieving a subwavelength DNM operation. To obtain an approximate expression for

*f*

_{magn}in this regime, it is assumed that |

*k*

_{z}

*h*|«1,

*ε*

_{m}(

*f*) is given by an approximate lossless Drude model

*ε*

_{m}(

*f*)≈-

*f*

^{2}, where

*f*

_{p}is the metal plasma frequency. Based on these assumptions,

21. A. K. Sarychev, G. Shvets, and V. M. Shalaev, “Magnetic Plasmon Resonance,” Phys. Rev. E **73**, 036609 (2006). [CrossRef]

*ϕ*

_{i}(

*E*⃗=-∇⃗

*ϕ*

_{i}) or by the stream function

*Ψ*

_{i}(

*E*⃗=

*e*⃗

_{y}×∇⃗

*Ψ*

_{i}) [17

17. G. Shvets and Y. A. Urzhumov, “Engineering the electromagnetic properties of periodic nanostructures using electrostatic resonances,” Phys. Rev. Lett. **93**, 243902-243901 (2004). [CrossRef]

*A*used above. Therefore, properties of such sub-wavelength structures are essentially scale-invariant.

### 3.3 Electric resonances

*z*=±

*h*) but also in the infinite thin film sheet (

*z*=0) and hence the latter affects the modal field significantly (Fig. 2). The currents in the top and bottom strip admittance sheets flow in the same direction thus resulting in an effective electric dipole response; these resonances will be referred to as electric resonance. The magnetic field is described by

**H**=

**ŷ**

*B*(

*f*

_{elect},

*z*)sin(

*πq*(

*x*-

*w*/2)/

*w*), where

*B*(

*ω*

_{elect},

*z*) is an odd function around

*z*=0 and

*f*

_{elect}are electric resonance frequencies satisfying

*i*=1, 2) that are frequencies of the electric resonances for each value of the integer

*q*. By setting Re{

*f*

_{magn}} holds. As |

*f*

_{magn}}, and in the limit

*f*

_{magn}as |

*d*

_{f}.

### 3.4 Model for effective parameters

22. W.J Padilla, D.R Smith, and D.N Basov, “Spectroscopy of metamaterials from infrared to optical frequencies,” J. Opt. Society America B **23**, 404 (2006). [CrossRef]

**µ̳**

_{eff}and

**ε̳**

_{eff}. For the TM excitation considered in the paper, the relevant tensor components affecting the structure’s electromagnetic properties are

*µ*

_{eff,yy},

*ε*

_{eff,xx}, and

*ε*

_{eff,zz}. As shown below, by judicious choice of parameters, simultaneously negative permeability and permittivity can be achieved for finite frequency bandwidths. Interactions of the magnetic and electric resonances with an external field can be described by the existence of effective magnetic and electric dipole moments,

**m**(

*f*)=

*m*

_{0}/(

*f*-

*f*

_{m})

**ŷ**, and

**p**

^{(i)}(

*f*)=

*f*-

**x̂**, respectively, where

*m*

_{0}and

*ii*=

*xx*or

*zz*. The effective parameters in (4) comprise non-resonant components

*µ*

_{0,eff,yy}and

*ε*

_{0,eff,ii}and resonant components described by the resonance frequencies

*f*

_{magn}and

*f*

_{p,magn,yy}and

*ii*=

*xx*and

*zz*(see further discussions in Sec. 4.1).

*ε*

_{eff,ii}can be derived rigorously based on quasi-static approximation,

*ε*

_{qs}(

*f*)=

*e*

_{d}(1-

*F*

_{0}/

*s*-Σ

_{i}

*F*

_{i}/(

*s*-

*s*

_{i})), where

*s*(

*f*)=(1-

*ε*

_{m}(

*f*)/

*ε*

_{d})

^{-1}, and

*s*

_{i}are the eigenvalues of the differential equation ∇(

*θ*(

**r**)∇

*ϕ*

_{i}(

**r**))=

*s*

_{i}∇

^{2}

*ϕ*

_{i}(

**r**). Here

*ϕ*

_{i}are the zero order scalar potential distributions in the nanostructure, and

*θ*(

**r**) is the Heaviside function equal to unity when

**r**is inside the metal and zero when

**r**is outside of the metal. Contributions of different quasi-static resonances are weighted by their strengths

*F*

_{i}that are determined numerically from the functional form of

*ϕ*

_{i}(

**r**) [23

23. D. J. Bergman and D. Stroud, “Properties of Macroscopically Inhomogeneous Media,” Solid State Phys. **46**, 147 (1992). [CrossRef]

*µ*

_{eff, yy}}, Re{

*ε*

_{eff, ii}} are negative. It is important to note that unlike in all previous studies, the effective parameters here can be tuned nearly independently in the entire range from near-IR to visible. Indeed, one can first choose

*w*,

*d*

_{s}and

*h*to tune the magnetic resonance frequency to a required frequency of DNM operation. Then the film thickness

*d*

_{f}can be chosen so as to bring the electric resonance frequency close to the magnetic one. This tuning is possible because the magnetic resonance is (nearly) independent of

*d*

_{f}.

*f*

_{magn}(at least for the same resonance order

*q*), these structures cannot operate as NIMs. This is the middle film that provides the existence of the lower frequency tunable resonance with

## 4. Numerical study

### 4.1 Extraction of the effective parameters

24. D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B **65**, 195104 (2002). [CrossRef]

*θ*on a slab of thickness

*H*made of isotropic or uniaxially anisotropic material can be written as

*n*

_{z,eff}is effective index for the field propagating in the

*z*direction, and

*Z*

_{z,eff}is the corresponding normalized impedance defined as the ratio between tangential components of the electric and magnetic fields in the

*x*-

*y*plane. From Eq. (5),

*n*

_{z,eff}and

*Z*

_{z,eff}are found as

*l*is an integer that is chosen as described by Smith at al [24

24. D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B **65**, 195104 (2002). [CrossRef]

*n*

_{z,eff}and

*Z*

_{z,eff}also satisfy

*µ*

_{eff,yy},

*ε*

_{eff,xx}, and

*ε*

_{eff,zz}has to be imposed. Different relations would lead to different results for the effective parameters (but all of them would result in the same structure’s scattering properties). In this paper, we choose a semi-empirical assumption that

*ε*

_{eff,zz}is a positive constant that is chosen further as

*ε*

_{d}. This assumption is based on the observation that the metal films/strips all are arranged along (

*x*-

*y*) planes so that the field components along the

*z*axis are weakly affected by the presented resonances so that the excitation constants

*ε*

_{eff,zz}extracted by assuming static fields is nearly constant in the range of interest. Based on this assumption the effective parameters

*µ*

_{eff,yy}and

*ε*

_{eff,xx}are found as

*n*

_{z},

_{eff}and

*Z*

_{z,eff}are given by Eq. (6) and

*ε*

_{eff,zz}=

*ε*

_{d}. In the remaining part of the manuscript we use the following notations:

*µ*

_{eff}=

*µ*

_{eff,yy},

*ε*

_{eff}=

*ε*

_{eff,xx},

*n*

_{eff}=(

*µ*

_{eff}

*ε*

_{eff})

^{1/2}.

### 4.2 Numerical simulations

25. M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, “Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings: enhanced transmittance matrix approach,” J. Opt. Soc. Am. A **12**, 1077–1086 (1995). [CrossRef]

26. P. Lalanne, “Improved formulation of the coupled-wave method for two-dimensional gratings,” J. Opt. Soc. Am. A **14**, 1592–1598 (1997). [CrossRef]

_{2}as an embedding dielectric with the dielectric constant value of

*ε*

_{d}=2.25. The metal was assumed to be gold with

*ε*

_{m}given by the Drude model

*ε*

_{m}=1-

*f*(

*f*-

*j*Γ)), where

*f*

_{p}is the plasma frequency and Γ is the scattering frequency characterizing the dissipation rate in the metal. Following Ref. [16

16. G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science **312**, 892–894 (2006). [CrossRef] [PubMed]

*f*

_{p}=1.32×10

^{4}/(2

*π*)THz and Γ=1.2×10

^{2}(2

*π*)THz.

*T*

_{0}for a single layer (

*m*

_{l}=1) in the absence of the middle slab for

*h*=7nm,

*d*

_{f}=0,

*L*

_{z}=44.5nm and in the presence of the middle slab for

*h*=10.25nm,

*d*

_{f}=6.5nm

*L*

_{z}=50.5nm as well as for

*h*=11.25nm,

*d*

_{f}=8.5nm,

*L*

_{z}=52.5nm. Other structure’s parameters were chosen as

*L*

_{x}=100nm,

*w*=50nm,

*d*

_{s}=15nm. In the absence of the central film, two non-overlapping electric and magnetic resonances are obtained for

*λ*=350nm and 600nm, respectively. In the presence of the middle film, for smaller film thickness (

*d*

_{f}=6.5nm), three separate resonance dips are observed around

*λ*=435nm and

*λ*=640nm, and

*λ*=800nm corresponding to electric, magnetic, and electric resonances, respectively. As

*d*

_{f}increases the two longer wavelength (magnetic and electric) resonances approach each other and they almost merge around

*λ*=680nm for

*d*

_{f}=8.5nm. The longer wavelength resonance for

*d*

_{f}=0 and the middle resonance for

*d*

_{f}0 in Fig. 3(a) correspond to bands of negative Re{

*µ*

_{eff}} in Fig. 3(b). The longest wavelength resonances for

*d*

_{f} 0 in Fig. 3(a) correspond to bands with negative Re{

*ε*

_{eff}} in Fig. 3(c). From the obtained results it is evident that in agreement with Shvets and Urzhumov [11

**8**, S122 (2006). [CrossRef]

*µ*

_{eff}} and Re{

*ε*

_{eff}} are obtained when the middle slab is absent. However, as predicted by the model and analysis described above, introducing the middle layer of thin metal film at z=0 causes simultaneously overlapping bands of negative Re{

*µ*

_{eff}} and Re{

*ε*

_{eff}} as required to construct a DNM. This is because Re{

*ε*

_{eff}} tends to be negative between the two electric resonance frequencies.

*µ*

_{eff}} and Re{

*ε*

_{eff}} in Fig. 3(b), we calculated the field distributions assuming static approximation. Figures 4(a) and 4(b) show the field distribution corresponding to magnetic and electric resonances within the cavity with the same parameters as those used in Fig. 3(a) for

*d*

_{f}=6.5nm and for

*λ*=640nm and

*λ*=800nm. It is observed that the fields for the middle and longer wavelength resonances exhibit even and odd symmetries with respect to the

*z*=0 plane. These symmetries explain the presence of the effective magnetic and electric dipoles and hence negative Re{

*µ*

_{eff}} and Re{

*ε*

_{eff}}, respectively. From the results in Figs. 3 and 4 it is evident that the structure in Fig. 1 indeed can operate as a DNM having a deeply subwavelength unit cell with a wavelength-to-period ratio of about 7, and that the cavity model predictions are valid.

*ε*

_{eff}very well. Note that the position of the resonance extracted from fully electromagnetic simulations is red shifted form its electrostatic value because of the finite retardation effects proportional to (

*L*/

*λ*)

^{2}[28

28. I. D. Mayergoyz, D. R. Fredkin, and Z. Zhang, “Electrostatic (plasmon) resonances in nanoparticles,” Phys. Rev. B **72**, 155412 (2005). [CrossRef]

*n*

_{eff}} and Im{

*n*

_{eff}} for three sets of structure parameters (i. e., set 1, 2 and 3), resulting in DNM operation in three wavelength ranges 820nm<

*λ*<1040nm, 550nm<

*λ*<670nm, and 500nm<

*λ*<560nm. Additional simulations confirm that DNM operation can be obtained in the entire range from 450nm to 1800 nm with wavelength-to-period ratios of about 7 and with sufficiently low loss. Notice, that the wavelength-to- period ratio can be further increased, but on the expense of increased losses.

*n*

_{eff}} for the structure parameters as those in Fig. 3 with

*d*

_{f}=8.5nm for different number of layers

*m*

_{l}to demonstrate that the structure can operate as a bulky material. It is evident that while Re{

*n*

_{eff}} slightly changes as the number of layers increases, it is reliably negative in the range 600nm<

*λ*<680nm for any

*m*

_{l}.

15. Z. Shuang, F. Wenjun, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. **95**, 137404-137401 (2005). [CrossRef]

18. A. Alu, A. Salandrino, and N. Engheta, “Negative effective permeability and left-handed materials at optical frequencies,” Opt. Express **14**, 1557 (2006). [CrossRef] [PubMed]

*µ*

_{eff}even without introducing any gain medium.

## 5. Summary

## Acknowledgments

## References and Links

1. | V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ϵ and &mu,” Soviet Physics - Uspekhi |

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

3. | D. R. Smith, D. Schurig, J. J. Mock, P. Kolinko, and P. Rye, “Partial focusing of radiation by a slab of indefinite media,” Appl. Phys. Lett. |

4. | Y. Horii, C. Caloz, and T. Itoh, “Super-compact multilayered left-handed transmission line and diplexer application,” IEEE Trans. Microwave Theory Tech. |

5. | A. Alu and N. Engheta, “Guided modes in a waveguide filled with a pair of single-negative (SNG), double-negative (DNG), and/or double-positive (DPS) layers,” IEEE Trans. Microwave Theory Tech. |

6. | N. Engheta and R. W. Ziolkowski, “A positive future for double-negative metamaterials,” IEEE Trans. Microwave Theory Tech. |

7. | R. W. Ziolkowski and E. Heyman, “Wave propagation in media having negative permittivity and permeability,” Phys. Rev. E |

8. | Z. Jiangfeng, T. Koschny, Z. Lei, G. Tuttle, and C. M. Soukoulis, “Experimental demonstration of negative index of refraction,” Appl. Phys. Lett. |

9. | P. Kolinko and D. R. Smith, “Numerical study of electromagnetic waves interacting with negative index materials,” Opt. Express |

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

11. | G. Shvets and Y. Urzhumov, “Negative index meta-materials based on two-dimensional metallic structures,” J. Opt. A |

12. | Z. Shuang, F. Wenjun, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, “Midinfrared resonant magnetic nanostructures exhibiting a negative permeability,” Phys. Rev. Lett. |

13. | J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, “Saturation of the magnetic response of split-ring resonators at optical frequencies,” Phys. Rev. Lett. |

14. | V. M. Shalaev, C. Wenshan, U. K. Chettiar, Y. Hsiao-Kuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett. |

15. | Z. Shuang, F. Wenjun, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. |

16. | G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science |

17. | G. Shvets and Y. A. Urzhumov, “Engineering the electromagnetic properties of periodic nanostructures using electrostatic resonances,” Phys. Rev. Lett. |

18. | A. Alu, A. Salandrino, and N. Engheta, “Negative effective permeability and left-handed materials at optical frequencies,” Opt. Express |

19. | J. R. James and P. S. Hall, |

20. | C. A. Balanis, |

21. | A. K. Sarychev, G. Shvets, and V. M. Shalaev, “Magnetic Plasmon Resonance,” Phys. Rev. E |

22. | W.J Padilla, D.R Smith, and D.N Basov, “Spectroscopy of metamaterials from infrared to optical frequencies,” J. Opt. Society America B |

23. | D. J. Bergman and D. Stroud, “Properties of Macroscopically Inhomogeneous Media,” Solid State Phys. |

24. | D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B |

25. | M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, “Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings: enhanced transmittance matrix approach,” J. Opt. Soc. Am. A |

26. | P. Lalanne, “Improved formulation of the coupled-wave method for two-dimensional gratings,” J. Opt. Soc. Am. A |

27. | J. Jin, |

28. | I. D. Mayergoyz, D. R. Fredkin, and Z. Zhang, “Electrostatic (plasmon) resonances in nanoparticles,” Phys. Rev. B |

29. | N. M. Lawandy, “Localized surface plasmon singularities in amplifying media,” Appl. Phys. Lett. |

30. | F. Hide, B. J. Schwartz, M. A. Diaz-Garcia, and A. J. Heeger, “Conjugated polymers as solid state laser materials,” Synth. Met. |

**OCIS Codes**

(160.4670) Materials : Optical materials

(310.6860) Thin films : Thin films, optical properties

**ToC Category:**

Metamaterials

**History**

Original Manuscript: August 16, 2006

Revised Manuscript: October 20, 2006

Manuscript Accepted: October 26, 2006

Published: November 13, 2006

**Citation**

Vitaliy Lomakin, Yeshaiahu Fainman, Yaroslav Urzhumov, and Gennady Shvets, "Doubly negative metamaterials in the near infrared and visible regimes based on thin film nanocomposites," Opt. Express **14**, 11164-11177 (2006)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-23-11164

Sort: Year | Journal | Reset

### References

- V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of ϵ and &mu," Soviet Physics - Uspekhi 10, 509-514 (1968). [CrossRef]
- J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000). [CrossRef] [PubMed]
- D. R. Smith, D. Schurig, J. J. Mock, P. Kolinko, and P. Rye, "Partial focusing of radiation by a slab of indefinite media," Appl. Phys. Lett. 84, 2244-2246 (2004). [CrossRef]
- Y. Horii, C. Caloz, and T. Itoh, "Super-compact multilayered left-handed transmission line and diplexer application," IEEE Trans. Microwave Theory Tech. 53, 1527-1534 (2005). [CrossRef]
- A. Alu and N. Engheta, "Guided modes in a waveguide filled with a pair of single-negative (SNG), double-negative (DNG), and/or double-positive (DPS) layers," IEEE Trans. Microwave Theory Tech. 52, 199-210 (2004). [CrossRef]
- N. Engheta and R. W. Ziolkowski, "A positive future for double-negative metamaterials," IEEE Trans. Microwave Theory Tech. 53, 1535-1556 (2005). [CrossRef]
- R. W. Ziolkowski and E. Heyman, "Wave propagation in media having negative permittivity and permeability," Phys. Rev. E 64, 056625-056621 (2001). [CrossRef]
- Z. Jiangfeng, T. Koschny, Z. Lei, G. Tuttle, and C. M. Soukoulis, "Experimental demonstration of negative index of refraction," Appl. Phys. Lett. 88, 221103-221101 (2006). [CrossRef]
- P. Kolinko and D. R. Smith, "Numerical study of electromagnetic waves interacting with negative index materials," Opt. Express 11, (2003). [CrossRef] [PubMed]
- R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001). [CrossRef] [PubMed]
- G. Shvets and Y. Urzhumov, "Negative index meta-materials based on two-dimensional metallic structures," J. Opt. A 8, S122 (2006). [CrossRef]
- Z. Shuang, F. Wenjun, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, "Midinfrared resonant magnetic nanostructures exhibiting a negative permeability," Phys. Rev. Lett. 94, 037402-037401 (2005). [CrossRef]
- J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, "Saturation of the magnetic response of split-ring resonators at optical frequencies," Phys. Rev. Lett. 95, 223902-223901 (2005). [CrossRef] [PubMed]
- V. M. Shalaev, C. Wenshan, U. K. Chettiar, Y. Hsiao-Kuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett. 30, 3356-3358 (2005). [CrossRef]
- Z. Shuang, F. Wenjun, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Experimental demonstration of near-infrared negative-index metamaterials," Phys. Rev. Lett. 95, 137404-137401 (2005). [CrossRef]
- G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, "Simultaneous negative phase and group velocity of light in a metamaterial," Science 312, 892-894 (2006). [CrossRef] [PubMed]
- G. Shvets and Y. A. Urzhumov, "Engineering the electromagnetic properties of periodic nanostructures using electrostatic resonances," Phys. Rev. Lett. 93, 243902-243901 (2004). [CrossRef]
- A. Alu, A. Salandrino, and N. Engheta, "Negative effective permeability and left-handed materials at optical frequencies," Opt. Express 14, 1557 (2006). [CrossRef] [PubMed]
- J. R. James and P. S. Hall, Handbook of Microstrip Antennas (1988).
- C. A. Balanis, Antenna Theory: Analysis and Design, Third Edition ed. (John Wiley, 2005).
- A. K. Sarychev, G. Shvets, and V. M. Shalaev, "Magnetic Plasmon Resonance," Phys. Rev. E 73, 036609 (2006). [CrossRef]
- W.J. Padilla, D.R. Smith, and D.N. Basov, "Spectroscopy of metamaterials from infrared to optical frequencies," J. Opt. Society America B 23, 404 (2006). [CrossRef]
- D. J. Bergman and D. Stroud, ``Properties of Macroscopically Inhomogeneous Media,' Solid State Phys. 46, 147 (1992). [CrossRef]
- D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, "Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients," Phys. Rev. B 65, 195104 (2002). [CrossRef]
- M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, "Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings: enhanced transmittance matrix approach," J. Opt. Soc. Am. A 12, 1077-1086 (1995). [CrossRef]
- P. Lalanne, "Improved formulation of the coupled-wave method for two-dimensional gratings," J. Opt. Soc. Am. A 14, 1592-1598 (1997). [CrossRef]
- J. Jin, The Finite Elements Method in Electromagnetics, Second Edition (Wiley, New York, 2002).
- I. D. Mayergoyz, D. R. Fredkin, and Z. Zhang, "Electrostatic (plasmon) resonances in nanoparticles," Phys. Rev. B 72, 155412 (2005). [CrossRef]
- N. M. Lawandy, "Localized surface plasmon singularities in amplifying media," Appl. Phys. Lett. 85, 5040 (2004). [CrossRef]
- F. Hide, B. J. Schwartz, M. A. Diaz-Garcia, and A. J. Heeger, "Conjugated polymers as solid state laser materials," Synth. Met. 91, 35 (1997). [CrossRef]

## 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.