## Arbitrarily thin metamaterial structure for perfect absorption and giant magnification |

Optics Express, Vol. 19, Issue 12, pp. 11114-11119 (2011)

http://dx.doi.org/10.1364/OE.19.011114

Acrobat PDF (975 KB)

### Abstract

In our common understanding, for strong absorption or amplification in a slab structure, the desire of reducing the slab thickness seems contradictory to the condition of small loss or gain. In this paper, this common understanding is challenged. It is shown that an arbitrarily thin metamaterial layer can perfectly absorb or giantly amplify an incident plane wave at a critical angle when the real parts of the permittivity and permeability of the metamaterial are zero while the absolute imaginary parts can be arbitrarily small. The metamaterial layer needs a totally reflective substrate for perfect absorption, while this is not required for giant magnification. Detailed analysis for the existence of the critical angle and physical explanation for these abnormal phenomena are given.

© 2011 OSA

## 1. Introduction

2. N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. **100**(20), 207402 (2008). [CrossRef] [PubMed]

5. X. L. Liu, T. Starr, A. F. Starr, and W. J. Padilla, “Infrared spatial and frequency selective metamaterial with near-unity absorbance,” Phys. Rev. Lett. **104**(20), 207403 (2010). [CrossRef] [PubMed]

*ε*or permeability

*μ*provides us some special properties [6

6. S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. **89**(21), 213902 (2002). [CrossRef] [PubMed]

10. A. Ciattoni, C. Rizza, and E. Palange, “Transmissivity directional hysteresis of a nonlinear metamaterial slab with very small linear permittivity,” Opt. Lett. **35**(13), 2130–2132 (2010). [CrossRef] [PubMed]

6. S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. **89**(21), 213902 (2002). [CrossRef] [PubMed]

8. L. V. Alekseyev, E. E. Narimanov, T. Tumkur, H. Li, Y. A. Barnakov, and M. A. Noginov, “Uniaxial epsilon-near-zero metamaterial for angular filtering and polarization control,” Appl. Phys. Lett. **97**(13), 131107 (2010). [CrossRef]

9. M. G. Silveirinha and N. Engheta, “Tunneling of electromagnetic energy through subwavelength channels and bends using *ε*-near-zero materials,” Phys. Rev. Lett. **97**(15), 157403 (2006). [CrossRef] [PubMed]

10. A. Ciattoni, C. Rizza, and E. Palange, “Transmissivity directional hysteresis of a nonlinear metamaterial slab with very small linear permittivity,” Opt. Lett. **35**(13), 2130–2132 (2010). [CrossRef] [PubMed]

*ε*) and real(

*μ*) (hereinafter referred to as ZRMs) can find amazing applications in absorption and magnification. With the assumption of a time harmonic factor exp(−

*iωt*), positive imag(

*ε*) and imag(

*μ*) represent loss, and negative ones represent gain. A lossy or active ZRM layer can perfectly absorb or strongly amplify an incident plane wave, while amazingly the thickness of the ZRM layer, as well as |imag(

*ε*)| and |imag(

*μ*)|, can be arbitrarily small. Metamaterials hold the potential to realize ZRMs. By careful tuning the electric and magnetic resonant units that form a metamaterial [11

11. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. **84**(18), 4184–4187 (2000). [CrossRef] [PubMed]

*ε*) and real(

*μ*) may vanish at some frequency. At some Dirac point with a zero Bloch wave vector, a specially designed photonic crystal may be homogenized as a metamaterial with both effective

*ε*and

*μ*approaching zero [12

12. Y. Wu, J. S. Li, Z. Q. Zhang, and C. T. Chan, “Effective medium theory for magnetodielectric composites: beyond the long-wavelength limit,” Phys. Rev. B **74**(8), 085111 (2006). [CrossRef]

*ε*and

*μ*[13

13. M. Ö. Oktel and Ö. E. Müstecaplıoğlu, “Electromagnetically induced left-handedness in a dense gas of three-level atoms,” Phys. Rev. A **70**(5), 053806 (2004). [CrossRef]

*ε*) and real(

*μ*) vanish.

## 2. Perfect absorption and giant magnification

*n*are denoted by

*ε*and

_{n}*μ*, respectively. The magnetic field is along the

_{n}*z*axis (TM polarization). When a plane wave impinges in the downward direction on the slab (the incident angle is

*θ*and the corresponding transverse wave vector is

*k*), the magnetic and electric fields in layer

_{y}*n*can be expressed as

*k*

_{n}_{,}

*= (*

_{x}*k*

_{n}^{2}−

*k*

_{y}^{2})

^{1/2},

*k*is the wave number in layer

_{n}*n*, and

*H*

_{n}^{±}is the magnetic field amplitude of a down- or up-going plane wave component in layer

*n*as shown in Fig. 1. According to the electromagnetic boundary conditions, one can obtain

*H*

_{n}^{±}and the corresponding field distribution in layer

*n*. Due to the symmetry of the structure, it is sufficient to study the electromagnetic response for

*k*≥0.

_{y}*ε*

_{1}=

*iε*

_{1,}

*”*

_{r}*ε*

_{0}and

*μ*

_{1}=

*iμ*

_{1,}

*”*

_{r}*μ*

_{0}(

*ε*

_{1,}

*”≥0 and*

_{r}*μ*

_{1,}

*”≥0), and layer 2 is a PEC. The reflection coefficient of the slab iswhere*

_{r}*γ*= (

*ε*

_{1,}

*”*

_{r}*μ*

_{1,}

*”*

_{r}*k*

_{0}

^{2}+

*k*

_{y}^{2})

^{1/2}. Since all the variables on the right-hand side of Eq. (2) are real numbers when

*k*

_{y}<k_{0}, the reflected wave is either in phase or out of phase with respect to the incident wave. The numerator on the right-hand side of Eq. (2) is denoted by

*f*, and may become zero for some

_{loss}*k*

_{y}<k_{0}(corresponding to some incident angle) in some situations. The first term in

*f*decreases as

_{loss}*k*increases from 0 to

_{y}*k*

_{0}, and is always larger than or equal to 1. The second term in

*f*increases from a minimal value of (

_{loss}*μ*

_{1,}

*”/*

_{r}*ε*

_{1,}

*”)*

_{r}^{1/2}to infinity as

*k*increases from 0 to

_{y}*k*

_{0}. Thus, when

*μ*

_{1,}

*”/*

_{r}*ε*

_{1,}

*”≤1, there always exists some value of*

_{r}*k*(<

_{y}*k*

_{0}) making

*f*zero, no matter how small

_{loss}*d*

_{1}becomes. Then

*R*also becomes zero. This means that there exists an incident angle at which the incident plane wave is completely (100%) absorbed by the lossy slab since the absorptivity is equal to 1−|

_{loss}*R*|

_{loss}^{2}. This incident angle is referred to as the critical angle (denoted by

*θ*) hereafter. When

_{c}*μ*

_{1,}

*”/*

_{r}*ε*

_{1,}

*”>1, the existence of*

_{r}*θ*depends on the value of

_{c}*d*

_{1}. If

*d*

_{1}is too large compared with the wavelength in free space (

*λ*

_{0}),

*θ*does not exist, because the first term in

_{c}*f*is smaller than 1/tanh[(

_{loss}*ε*

_{1,}

*”*

_{r}*μ*

_{1,}

*”)*

_{r}^{1/2}(

*k*

_{0}

*d*

_{1})], which approaches 1 when

*d*

_{1}is very large, whereas the second term is always larger than 1. When

*ε*

_{1,}

*” and*

_{r}*μ*

_{1,}

*” are given with*

_{r}*μ*

_{1,}

*”/*

_{r}*ε*

_{1,}

*”>1, the threshold of*

_{r}*d*

_{1}allowing the existence of

*θ*is determined by the following equation

_{c}*R*|

_{loss}^{2}) of the slab for various

*k*. When

_{y}*μ*

_{1,}

*”/*

_{r}*ε*

_{1,}

*”≤1, there are always deep dips representing perfect absorption on the reflectivity curves [see curves 1−4 in Fig. 2(a) and curves 1 and 2 in Fig. 2(b)]. When*

_{r}*μ*

_{1,}

*”/*

_{r}*ε*

_{1,}

*”>1 and*

_{r}*d*

_{1}is large enough, such dips disappear [see curve 5 in Fig. 2(a) and curve 3 in Fig. 2(b); note that perfect absorption is still possible for some appropriate thickness

*d*

_{1}when

*μ*

_{1,}

*”/*

_{r}*ε*

_{1,}

*”>1]. Comparing Figs. 2(a) and 2(b), one sees that when*

_{r}*μ*

_{1,}

*” =*

_{r}*ε*

_{1,}

*” (i.e., matched impedance), if*

_{r}*ε*

_{1,}

*” and*

_{r}*μ*

_{1,}

*” are large,*

_{r}*θ*is near to zero (i.e., perfect absorption at nearly normal incidence) and strong absorption over a wide range of incidence angle can be achieved. If

_{c}*ε*

_{1,}

*” and*

_{r}*μ*

_{1,}

*” are small (i.e., small loss), perfect absorption near normal incidence can still be achieved when*

_{r}*ε*

_{1,}

*” is much smaller than*

_{r}*μ*

_{1,}

*” (see curve 4 of Fig. 2(a)). Note that contrary to all the absorbers reported previously, the values of*

_{r}*d*

_{1,}

*ε*

_{1,}

*” and*

_{r}*μ*

_{1,}

*” can be very small (arbitrarily small) in the situation of perfect absorption.*

_{r}*θ*depends on

_{c}*d*

_{1},

*ε*

_{1,}

*” and*

_{r}*μ*

_{1,}

*” as illustrated well in Fig. 2(a). The second term in*

_{r}*f*is approximately inversely proportional to

_{loss}*ε*

_{1,}

*”. As*

_{r}*ε*

_{1,}

*” decreases gradually (with fixed*

_{r}*μ*

_{1,}

*” and*

_{r}*d*

_{1}),

*θ*should approach zero so that the first term in

_{c}*f*can cancel the second term. If

_{loss}*ε*

_{1,}

*” decreases further and becomes smaller than some value which satisfies Eq. (3) with the other parameters given,*

_{r}*θ*will not exist. Similarly, as

_{c}*μ*

_{1,}

*” increases, the second term in*

_{r}*f*also increases, and

_{loss}*θ*should approach zero in order to make

_{c}*f*zero. And if

_{loss}*μ*

_{1,}

*” increases further,*

_{r}*θ*will not exist. When

_{c}*d*

_{1}is gradually reduced with fixed

*ε*

_{1,}

*” and*

_{r}*μ*

_{1,}

*”,*

_{r}*θ*becomes larger. Note that the first term in

_{c}*f*is very large when

_{loss}*d*

_{1}is very small. To make the second term in

*f*also large, |

_{loss}*k*| needs to approach

_{y}*k*

_{0}(i.e.,

*θ*approaches 90 degrees). On the other hand,

_{c}*θ*approaches zero as

_{c}*d*

_{1}increases.

*θ*will not exist any more when

_{c}*d*

_{1}increases further and becomes larger than some value satisfying Eq. (3).

*p*

_{0}) when the incident plane wave impinges on surface

*S*

_{0,1}. When the incident plane wave enters the slab and is multi-reflected between surfaces

*S*

_{0,1}and

*S*

_{1,2}, a part of it is refracted out of surface

*S*

_{0,1}and forms the other components which are denoted by

*p*(

_{n}*n*= 1,2,…). Based on this interpretation,

*R*can be rewritten aswhere

_{loss}*r*

_{0,1}= (1-

*γ*/

*ε*

_{1,}

*”*

_{r}*k*

_{0,}

*)/(1 +*

_{x}*γ*/

*ε*

_{1,}

*”*

_{r}*k*

_{0,}

*),*

_{x}*r*

_{1,0}= -

*r*

_{0,1},

*t*

_{0,1}= 2

*ε*

_{1,}

*”*

_{r}*k*

_{0,}

*/(*

_{x}*ε*

_{1,}

*”*

_{r}*k*

_{0,}

*+*

_{x}*γ*),

*t*

_{1,0}= 2

*γ*/(

*ε*

_{1,}

*”*

_{r}*k*

_{0,}

*+*

_{x}*γ*). The first term on the right-hand side of Eq. (4) represents component

*p*

_{0}in Fig. 1(b), and the second term represents the composition of the other components,

*p*(

_{n}*n*= 1,2,…). From Eq. (2), one sees that

*γ*/

*ε*

_{1,}

*”*

_{r}*k*

_{0,}

*must be larger than 1 to make*

_{x}*f*zero since tanh(

_{loss}*γd*

_{1})<1. Thus,

*r*

_{0,1}is negative and

*r*

_{1,0}is positive. Then, all components

*p*

_{1},

*p*

_{2}, … are in phase, and they are out of phase with component

*p*

_{0}. At critical angle

*θ*, the two groups cancel each other. This leads to the disappearing of the reflected wave in layer 0, and the incident plane wave is perfectly absorbed by the lossy slab. From Eq. (1), one sees that inside the slab,

_{c}*E*

_{1,}

*(*

_{x}**r**) is out of phase with

*H*

_{1,z}(

**r**), and time-averaged energy stream density

**P**

_{1}(

**r**) has a zero component along the

*y*axis. This indicates that when the incident plane wave enters the slab, it will just be normally multi-reflected by surface

*S*

_{0,1}and

*S*

_{1,2}and repeatedly absorbed. During this process, there is no phase introduced, leading to a result that the exponents in the square on the right-hand side of Eq. (4) just possess negative real variables (instead of complex variables). There is no transverse shift along the

*y*axis among components

*p*

_{0},

*p*

_{1}, … in Fig. 1(b). As a numerical example, Figs. 2(c)-2(e) show the electric and magnetic fields and time-averaged energy stream density (represented by arrows) around the slab when

*d*

_{1}= 0.4

*λ*

_{0},

*ε*

_{1,}

*” = 0.3,*

_{r}*μ*

_{1,}

*” = 0.1, and*

_{r}*θ*≈19.8 degrees. To show clearly the distributions of the field and time-averaged energy stream density inside the slab, a relatively large value of

_{c}*d*

_{1}is chosen for Figs. 2(c)-2(e). The distributions inside a thinner slab are similar. These distributions clearly show that there is no wave reflected by the slab. When the position approaches surface

*S*

_{1,2},

*E*

_{1,}

*(*

_{y}**r**) has to tend to zero as required by the boundary condition at PEC surface

*S*

_{1,2}, and so is

**P**

_{1}(

**r**), whereas

*E*

_{1,}

*(*

_{x}**r**) and

*H*

_{1,}

*(*

_{z}**r**) have no such tendency. For perfect absorption, a PEC as the substrate of the slab is necessary. If it is removed, the plane wave components refracted into the substrate (after being multi-reflected by surfaces

*S*

_{0,1}and

*S*

_{1,2}) cannot cancel each other, and the incident plane wave can partially transmit through the slab as a total effect.

*ε*

_{1}and

*μ*

_{1}are only of negative imaginary parts (i.e.,

*ε*

_{1}= -

*iε*

_{1,}

*”*

_{r}*ε*

_{0}and

*μ*

_{1}= -

*iμ*

_{1,}

*”*

_{r}*μ*

_{0}). Recently, there have been some efforts in active metamaterials [14

14. S. M. Xiao, V. P. Drachev, A. V. Kildishev, X. J. Ni, U. K. Chettiar, H. K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature **466**(7307), 735–738 (2010). [CrossRef] [PubMed]

15. N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics **2**(6), 351–354 (2008). [CrossRef]

*R*= [1/tanh(

_{gain}*γd*

_{1}) +

*γ*/

*ε*

_{1,}

*”*

_{r}*k*

_{0,}

*]/[1/tanh(*

_{x}*γd*

_{1})-

*γ*/

*ε*

_{1,}

*”*

_{r}*k*

_{0,}

*], which is reciprocal to Eq. (2) for*

_{x}*R*. When

_{loss}*R*is zero,

_{loss}*R*is infinite. Then, there exists a critical angle

_{gain}*θ*at which the plane wave impinging on the slab is infinitely magnified. The relation between

_{c}*θ*and the values of

_{c}*d*

_{1},

*ε*

_{1,}

*” and*

_{r}*μ*

_{1,}

*” is similar to that for the previous lossy slab. Especially, when*

_{r}*μ*

_{1,}

*”/*

_{r}*ε*

_{1,}

*”≤1,*

_{r}*θ*always exists even if the thickness and gain of the slab are arbitrarily small. Curve 1 in Fig. 3(a) shows a numerical example. The infinite magnification can be understood as follows. The condition of

_{c}*R*= ∞ determines the dispersion equation of the slab waveguide. Now, special waveguide modes can exist for

_{gain}*k*<

_{y}*k*

_{0}. The energy stream inside the slab is normally reflected back and forth by surfaces

*S*

_{1}and

*S*

_{2}(instead of propagating along the slab). Some electromagnetic energy runs away from the slab, but it can be compensated by the energy generated by the gain. When an incident wave excites a waveguide mode, the total reflected wave will be infinite. The infinite magnification is from the time-harmonic solution. In practice, it may take an infinitely long time to obtain this effect. However, one can still obtain giant magnification after long enough time.

*ε*

_{1}) and real(

*μ*

_{1}) possess different signs. Only the case of

*ε*

_{1}= −

*iε*

_{1,}

*”*

_{r}*ε*

_{0}and

*μ*

_{1}=

*iμ*

_{1,}

*”*

_{r}*μ*

_{0}is investigated here, and the contrary case can be analyzed similarly. The reflection coefficient of the slab then becomes where

*β*= (

*k*

_{y}^{2}−

*ε*

_{1,}

*”*

_{r}*μ*

_{1,}

*”*

_{r}*k*

_{0}

^{2})

^{1/2}. In Eq. (5), ctan(

*k*

_{1,}

_{x}d_{1}) is a periodic function with its value varying from + ∞ to −∞. Thus, both the numerator and denominator on the right-hand side of Eq. (5) have a possibility to be zero when

*k*<

_{y}*k*

_{0}. When

*d*

_{1}is large enough, many critical angles may exist at which the numerator or denominator on the right-hand side of Eq. (5) is zero. At the right-hand side of Eq. (6), the numerator is always larger than zero, and the denominator can be zero at some value of

*k*since

_{y}*β*/

*k*

_{0,}

_{x}ε_{1,}

*” increases from zero to infinite in the range of (*

_{r}*ε*

_{1,}

*”*

_{r}*μ*

_{1,}

*”)*

_{r}^{1/2}

*k*

_{0}<

*k*<

_{y}*k*

_{0}. This indicates that regardless of the values of

*d*

_{1},

*ε*

_{1,}

*”, and*

_{r}*μ*

_{1,}

*”, there always exists a critical angle*

_{r}*θ*at which the incident plane wave can be infinitely magnified when

_{c}*ε*

_{1,}

*”*

_{r}*μ*

_{1,}

*”<1. This is a quite interesting result that although*

_{r}*μ*

_{1,}

*” may be very large (representing large loss), small*

_{r}*ε*

_{1,}

*” (representing low gain) still can lead to infinite magnification, which may bring convenience in practical magnification. Curves 1 and 2 in Fig. 3(b) show the reflectivity for different thickness of the slab when*

_{r}*ε*

_{1,}

*” = −0.1 and*

_{r}*μ*

_{1,}

*” = 0.3. When*

_{r}*d*

_{1}= 0.1

*λ*

_{0}, there is only one peak on curve 1. When the slab becomes thick, e.g.,

*d*

_{1}= 0.5

*λ*

_{0}, both one dip and one peak appear on curve 2, which indicates that one can obtain both strong absorption and magnification at different special values of the incident angle.

*ε*

_{1}= −

*iε*

_{1,}

*”*

_{r}*ε*

_{0}and

*μ*

_{1}= −

*iμ*

_{1,}

*”*

_{r}*μ*

_{0}, one has the following reflection and transmission coefficients of the slab

*f*. The first term in

_{gain}*f*decreases as

_{gain}*k*increases from 0 to

_{y}*k*

_{0}, and is always larger or equal to 2. The second term in

*f*is infinite when

_{gain}*k*approaches

_{y}*k*

_{0}, and reaches a minimal value of 2 when

*γ*/

*k*

_{1,}

_{x}ε_{1,}

*” =*

_{r}*k*

_{1,}

_{x}ε_{1,}

*”/*

_{r}*γ*. When

*μ*

_{1,}

*”/*

_{r}*ε*

_{1,}

*”≤1, this condition can be fulfilled by some*

_{r}*k*(<

_{y}*k*

_{0}), and a critical angle

*θ*exists. Like in the case when layer 2 is a PEC, the incident plane wave at

_{c}*θ*can be infinitely magnified regardless of the values of

_{c}*d*

_{1},

*ε*

_{1,}

*” and*

_{r}*μ*

_{1,}

*”. If*

_{r}*μ*

_{1,}

*”/*

_{r}*ε*

_{1,}

*”>1, this property disappears. As shown in Fig. 3(a), the value of*

_{r}*θ*without a PEC substrate is different from that with a PEC substrate. Similarly, giant magnification can still be obtained in a hybrid case when layer 2 is of free space, as shown by the peaks of curves 3 and 4 in Fig. 3(b) as a numerical example. These two curves also indicate that perfect absorption does not occur in this case since transmissivity curve 4 has no dip although there is a dip on reflectivity curve 3. The second remark is that the deviation of real(

_{c}*ε*

_{1}) and real(

*μ*

_{1}) from zero may cause the disappearance of perfect absorption and giant magnification. However, as illustrated in Figs. 4(a) and 4(b), if |real(

*ε*

_{1})| and |real(

*μ*

_{1})| are moderately small compared with |imag(

*ε*

_{1})| and |imag(

*μ*

_{1})|, respectively, strong absorption and magnification effect can still be obtained. As shown in Fig. 4, the influence of the deviation of real(

*ε*

_{1}) from zero on the absorption and magnification is different from that of real(

*μ*

_{1}). In general, when |imag(

*ε*

_{1})| = |imag(

*μ*

_{1})|, the influence of the same deviation of real(

*ε*

_{1}) and real(

*μ*

_{1}) from zero (i.e., with impedance match kept) on the absorption and magnification is smaller.

## 3. Conclusion

*θ*has been analyzed for various situations. The thickness of the ZRM layer, as well as |imag(

_{c}*ε*)| and |imag(

*μ*)|, can be arbitrarily small. This challenges our common understanding that strong absorption and magnification seems impossible in a very thin layer of material with finite or small |imag(

*ε*)| and |imag(

*μ*)|. It should be noted that in principle the homogeneous ZRM can be arbitrarily thin. In practical realization, the smallest thickness of a ZRM layer is determined by the dimension of the resonant metamaterial units, which is usually one or two order smaller than the wavelength. However, if the ZRM layer can be realized by an EIT gas, the thickness can be reduced even further. Even if the ZRM layer cannot be very thin, it is still rather significant, especially for giant magnification.

## Acknowledgments

## References and links

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5. | X. L. Liu, T. Starr, A. F. Starr, and W. J. Padilla, “Infrared spatial and frequency selective metamaterial with near-unity absorbance,” Phys. Rev. Lett. |

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

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

8. | L. V. Alekseyev, E. E. Narimanov, T. Tumkur, H. Li, Y. A. Barnakov, and M. A. Noginov, “Uniaxial epsilon-near-zero metamaterial for angular filtering and polarization control,” Appl. Phys. Lett. |

9. | M. G. Silveirinha and N. Engheta, “Tunneling of electromagnetic energy through subwavelength channels and bends using |

10. | A. Ciattoni, C. Rizza, and E. Palange, “Transmissivity directional hysteresis of a nonlinear metamaterial slab with very small linear permittivity,” Opt. Lett. |

11. | D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. |

12. | Y. Wu, J. S. Li, Z. Q. Zhang, and C. T. Chan, “Effective medium theory for magnetodielectric composites: beyond the long-wavelength limit,” Phys. Rev. B |

13. | M. Ö. Oktel and Ö. E. Müstecaplıoğlu, “Electromagnetically induced left-handedness in a dense gas of three-level atoms,” Phys. Rev. A |

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

15. | N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics |

**OCIS Codes**

(260.0260) Physical optics : Physical optics

(310.0310) Thin films : Thin films

(160.3918) Materials : Metamaterials

**ToC Category:**

Metamaterials

**History**

Original Manuscript: March 30, 2011

Revised Manuscript: May 4, 2011

Manuscript Accepted: May 17, 2011

Published: May 23, 2011

**Citation**

Yi Jin, Sanshui Xiao, N. Asger Mortensen, and Sailing He, "Arbitrarily thin metamaterial structure for perfect absorption and giant magnification," Opt. Express **19**, 11114-11119 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-12-11114

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### References

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- M. G. Silveirinha and N. Engheta, “Tunneling of electromagnetic energy through subwavelength channels and bends using ε-near-zero materials,” Phys. Rev. Lett. 97(15), 157403 (2006). [CrossRef] [PubMed]
- A. Ciattoni, C. Rizza, and E. Palange, “Transmissivity directional hysteresis of a nonlinear metamaterial slab with very small linear permittivity,” Opt. Lett. 35(13), 2130–2132 (2010). [CrossRef] [PubMed]
- D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000). [CrossRef] [PubMed]
- Y. Wu, J. S. Li, Z. Q. Zhang, and C. T. Chan, “Effective medium theory for magnetodielectric composites: beyond the long-wavelength limit,” Phys. Rev. B 74(8), 085111 (2006). [CrossRef]
- M. Ö. Oktel and Ö. E. Müstecaplıoğlu, “Electromagnetically induced left-handedness in a dense gas of three-level atoms,” Phys. Rev. A 70(5), 053806 (2004). [CrossRef]
- S. M. Xiao, V. P. Drachev, A. V. Kildishev, X. J. Ni, U. K. Chettiar, H. K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466(7307), 735–738 (2010). [CrossRef] [PubMed]
- N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics 2(6), 351–354 (2008). [CrossRef]

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