Abstract

An effective method for designing wave shape transformers (WSTs) is investigated by adopting the coordinate transformation theory. Following this method, the devices employed to transform electromagnetic (EM) wave fronts from one style with arbitrary shape and size to another style, can be designed. To verify this method, three examples in 2D spaces are also presented. Compared with the methods proposed in other literatures, this method offers the general procedure in designing WSTs, and thus is of great importance for the potential and practical applications possessed by such kinds of devices.

©2008 Optical Society of America

1. Introduction

Based on the form-invariant of Maxwell’s equations, the coordinate transformation theory is stated by Pendry et al.[14], which is firstly adopted to design invisibility cloaks [1, 510]. Besides, with the increasing interests of this method, several other electromagnetic (EM) devices with new functionalities have been suggested: beam shifters [3] translate the incoming wave in the direction perpendicular to the propagating direction without altering the shapes of the wave fronts; concentrators [4, 1113] collect the energy to a small region; field rotators [13, 14] rotate the fields in a region and thus made the information from the outside appears as if it comes from a different angle; photon funnels [15] are used as the devices to compress wave beams from large width to the thin, and phase transformers [16, 17], transform the wave front shape from one style to another, for example, cylindrical waves to plane waves.

Among these devices mentioned above, photon funnels and phase transformers can be classified as wave shape transformers (WSTs). A WST is a device that can transform wave fronts from one style (having the certain shape and size) to another style. Such a device is popular in conventional fields and has many potential and practical applications. The literatures [1517] have discussed these devices and shown several examples, including devices that transform the wave shapes from cylindrical to plane, and devices that shift wave beams along parallel directions. However, these discussions were limited to the simple cases that the wave shapes are cylindrical or plane. In the more general cases, if we consider the complicated situations that to transform a wave front from arbitrary shapes to another arbitrary style, what the method and procedures should we adopt to design the corresponding WSTs? In this paper, we will introduce a general method of designing WSTs. By adopting this method, a WST that transform wave fronts with arbitrary shape and size to another arbitrary style can be designed.

2. The general method

In the free space, waves propagate perpendicular to the phase fronts, thus the wave shape and size of a non-plane wave will be changed momentarily. If a device is adopted to limit the propagation of a wave in one region and to transform the wave shape to another style at the moment the wave leaves, the device is used as a WST. Geometrically speaking, such a device causes the spatial deformation by mapping the position points traced by the wave propagating in the free space to the points within the device region. Therefore the constitutive parameters (permittivity and permeability) in the device region can be established by using the coordinate transformation theory.

We start our discussions by considering the situation that an EM wave propagates in the free space, and at one moment, is incident onto a WST with a certain phase front. After propagating in the WST, this wave changes its phase front to another style. As shown in Fig. 1, we call these two phase fronts as the original front and the new front, and denote them by S1 and S2, respectively. In our scheme, we limit our discussions to the cases that the wave propagates in the right half space, thus the shapes of these two fronts, surfaces S1 and S2, are assumed to be arbitrary under the limitation that both the two surfaces must intersect only once with an arbitrary line that is along the x-axis and within the WST region. In the following derivation, we suppose the wave propagates along the x-axis within the WST region, and that surfaces S1 and S2 have the general expressions in Cartesian systems as follows:

S1:f(x,y,z)=0,
S2:g(x,y,z)=0.

Shown by Fig. 1, during a given time interval, an arbitrary point A on S1, will move to P, then to C, when the wave propagates in the free space; and will move to P′, then to B, when the wave propagates in the WST region. As a result, after the time interval, the set of point C forms the imaginary wave front in the free space, and the set of point B the transformed wave front in the WST region ∑. Geometrically, there must be a unique mapping between P and P′ as well as C and B, and the mapping can be also used as the description of the spatial deformation. To mathematically describe such a mapping, we define four distance variables: lp=|AP|, lp′=|AP′|, L=|AC|, L′=|AB|, and adopt the following expression:

lpL=lpL.
 figure: Fig. 1.

Fig. 1. The wave front is transformed from surface S1 to surface S2. As a result, starting from an arbitrary point A on S1, the wave vector line will be AC when the wave propagates in the free space, and will be AB when the wave propagates in the WST, respectively.

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Equation (3) establishes a linear mapping between P and P′ by proportionally changing lp to lp′, and the validity is obvious. First of all, the mapping expressed by Eq. (3) is homeomorphous; secondly, when the point P tends to C, the point P′ correspondingly tends to B, which means that the mapping has no singularity; thirdly, from the viewpoint of physics, Eq. (3) prescribes the relationship between the points (denoted by P) traced by the imaginary waves in the old space and the points (denoted by P′) traced by the real waves in the transformed space, which well meets the requirement of the coordinate transformation theory [4].

In Eq. (3), parameter L is the wave path traveled by the wave in the free space during the given time interval. Since waves propagate at the same speed in the free space, L must be a constant for arbitrary starting point A in S1. In principle, L can be an arbitrary constant, larger or smaller than the length of the WST. But in practice, we usually assign L with several wavelengths and make it close to the length of the WST, for that such a choice avoids the too sharp deformation when we carry out the coordinate transformation and thus obtain a comparatively smooth distribution of the constitutive parameters. In one word, choosing of parameter L as well as the length of the WST only limits to the requirements of applications and the fabrication level.

Then, we need to express lp, lp′ and L′ with the coordinate variables, and by solving Eqs. (1–3), to obtain the exact relationship between P and P′. Supposing the coordinate of P is (xp, yp, zp), the line that includes P is written as:

xxpkx=yypky=zzpkz,

where (kx, ky, kz) is the line direction vector. Shown in Fig. 1, A is the intersection point of line AP and surface S1, so the coordinate (xa, ya, za) is involved in the simultaneous Eqs. (1, 4). Obviously, (xa, ya, za) and (kx, ky, kz) are associated to each other. By further considering the principle that when a wave propagates in the free space, the direction AP must be perpendicular to the tangent plane of the front surface S1 at A, we thus have

fi(xa,ya,za)=ki,i=x,y,z,

where, fi(xa, ya, za) is the partial differential coefficient of function f (x, y, z) cited in Eq. (1). Equation (5) together with (1, 4) determine (xa, ya, za) uniquely. Thereupon, the coordinate of B, (xb, yb, zb), can be also obtained by substituting y=ya and z=za into Eq. (2).

Supposing (xp′, yp′, zp′) is the coordinate of P′, we have:

L=xbxa,lp=xpxa.

Solving Eqs. (3, 6), we get:

xp=LLlp+xa,yp=ya,zp=za.

Equation (7) is a general formula derived from Eq. (3), describing the geometrical mapping between the points traced by waves propagating in the free space and in the WST region.

Finally, we can use the method prescribed by Rahm et al. [4] to obtain the relative permittivity and permeability of a WST via

α(xp,yp,zp)=Qα(xp,yp,zp)QTdetQ.

Where, α(xp, yp, zp) (before transformation, especially in the free space, it is equal to unit matrix) and α(xp′, yp′, zp′) (after transformation), respectively, denote the permittivity or permeability tensors; Q is the Jacobian transformation matrix between (xp, yp, zp) and (xp′, yp′, zp′) with its elements defined as

Qλη=λpηp,λ,η=x,y,z.

According to Eqs. (6, 7), Eq. (9) is thus expressed as

Qxη=xpηp=1L[lp(xbηpxaηp)+Llpηp]xaηp,
Qλη=λpηp=λaηp,λ=y,z;η=x,y,z.

In Eq. (10), ∂lp/∂ηp and ∂λa/∂η p are determined by Eqs. (1–5), and should be solved concretely when Eqs. (1, 2) are given. By now, the general method of designing WSTs that transform wave fronts between two arbitrary shapes has been established. Especially, Eq. (8) offers a general form in obtaining the relative permittivity and permeability, so, what we need to do in special designing is mainly to establish the Jacobian transformation matrix Q according to Eq. (10), and then to apply the matrix Q to Eq. (8) to obtain the constitutive parameters.

Note that, we have investigated the above method by using the coordinate transformation theory which is based on the form-invariant of Maxwell’s equations. In the derivation, the frequency dispersion is not involved, so the results are wavelength-independent.

3. Examples in 2D spaces

3.1 Convex cylindrical waves to concave cylindrical waves

Transforming a convex cylindrical wave to a concave cylindrical wave, the corresponding spatial deformation occurs in 2D spaces. Shown in Fig. 2(a), the centers of the original front circle and the new front circle are located at (x 1,0) and (x 2,0), respectively, and the functions of these two circles are

Si:x=Ricosθi+xi,y=Risinθi,i=1,2.
 figure: Fig. 2.

Fig. 2. The sketch of the geometrical relationship employed in designing a WST, where, the WST transforms the wave front (a) from convex cylindrical to concave cylindrical, or (b), from cylindrical to plane.

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After a simple deduction according to the method introduced in section 2, we obtain:

xa=R1cosθ1+x1,ya=R1sinθ1,
xb=R2cosθ2+x2,yb=ya,
lb=(xpxa)1+tan2θ1,

where,

θ1=arctan(ypxpx1),θ2=πarctan(R1R2sinθ1).

As the results,

θ1xp=yp(xpx1)2+yp2,θ1yp=xpx1(xpx1)2+yp2,
θ2ηp=R1cosθ1R22R12sin2θ1×θ1ηp,
xaηp=R1sinθ1θ1ηp,yaηp=R1cosθ1θ1ηp,
xbηp=R2sinθ2θ2ηp,
lpηp=(xpxa)11+tan2θ1tanθ1cos2θ1θ1ηp
+(s+xaηp)1+tan2θ1·s={1,η=x0,η=y

Substituting Eqs. (6, 12–14) into (10), we obtain the Jacobian transformation matrix with the elements as follows:

Qxη=1L{(xpR1cosθ1x1)(R2sinθ2cosθ1R22R12sin2θ1+sinθ1)R11+tan2θ1θ1ηp
+(R2cosθ2R1cosθ1+x2x1)[(xpR1cosθ1x1)11+tan2θ1tanθ1cos2θ1θ1ηp
+(sR1sinθ1θ1ηp)1+tan2θ1]}+R1sinθ1θ1ηp,s={1,η=x0,η=y
Qyη=R1cosθ1θ1ηp,η=x,y.

Where, ∂θ 1/∂η p is defined in Eq. (14).

In practical designs, the converse mapping from P′ to P is required, so, we should treat P′ as the known point and assign y=yp′. Substituting the results into (11), we get

θ1=arcsinypR1,θ2=πarcsinypR2,

and,

xp=LxpR1cosθ1x1R2cosθ2R1cosθ1+x2x111+tan2θ1+R1cosθ1+x1,
yp=(xpx1)tanθ1.

Equations (16, 17) are necessary in establishing the final form of Eq. (15). Once the final form of Eq. (15) is offered, the relative permittivity and permeability of the WST can be easily obtained by solving Eq. (8).

3.2 Cylindrical waves to plane waves

Similarly, transforming a cylindrical wave to a plane wave also occurs in 2D spaces. Shown in Fig. 2(b), the front surface functions are

S1:x=R1cosθ1+x1,y=R1sinθ1,
S2:y=k(xx2),

where k is the slope of S2.

Solving equations (3–10, 18), all variables except θ 2 and (xb, yb), have the same results as that in Eqs. (12–14). Here, θ 2 is not cited, and (xb, yb) has another form:

xb=R1sinθ1+kx2k,yb=ya.

Accordingly, the partial differential coefficient of xb is

xbηp=R1cosθ1kθ1ηp,η=x,y.

Substituting Eqs. (6, 12–14, 19 and 20) into (10), we obtain the Jacobian transformation matrix with the elements as follows:

Qxη=1L{(xpR1cosθ1x1)(cosθ1k+sinθ1)R11+tan2θ1θ1ηp
+(R1sinθ1+kx2kR1cosθ1x1)[(xpR1cosθ1x1)11+tan2θ1tanθ1cos2θ1θ1ηp
+(sR1sinθ1θ1ηp)1+tan2θ1]}+R1sinθ1θ1ηp,s={1,η=x0,η=y
Qyη=R1cosθ1θ1ηp,η=x,y.

Where,

θ1xp=yp(xpx1)2+yp2,θ1yp=xpx1(xpx1)2+yp2,
θ1=arcsinyp'R1,
xp=Lxp'R1cosθ1x1R1sinθ1+kx2kR1cosθ1x111+tan2θ1+R1cosθ1+x1,
yp=(xpx1)tanθ1.

3.3 Photon funnels

A photon funnel can be employed as a device to compress EM wave beams, which is in fact a wave shape transformer. The method we introduced in section 2 is also available in designing such devices, yet the special procedure should be adjusted slightly. In this example, we consider a 2D photon funnel, which is used to compress a plane wave beam. For the sake of simplicity, we suppose that wave beams propagate along the x-axis and are compressed in the y-axis direction. Shown in Fig. 3, a right traveling wave beam will be compressed from the width of |y 1| to the width of |y 2|.

In Fig. 3, once (x 1, y 1) and (x 2, y 2) are given, the top boundary of the WST is determined by

y=k(xx1)+y1,

where k=(y 2-y 1)/(x 2-x 1). Since the spatial compression is in the y-axis direction, the variables cited in Eq. (3) should be redefined: lp′=|AP′|=yp′|, lp=|AP|=|yp|, L′=|AB|=|yb, and L=|AC|=|yc|. Then, according to Eq. (3), we have

yp'yb=ypyc=ypy1,

where yb=kxp-kx 1+y 1. As the results,

yp'=ypy1yb,xp'=xp.

Finally, we get the Jacobian transformation matrix as follows:

Qxx=1,Qxy=0,Qyx=kypy1,Qyy=yby1.
 figure: Fig. 3.

Fig. 3. The sketch of the geometrical relationship employed in designing a photon funnel, where the incident wave is supposed to be right traveling and is compressed in the y-axis direction.

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4. Full-wave simulations and discussions

Full-wave finite-element simulations by using COMSOL Multiphysics software were performed to verify our conclusions in section 3. Figs. 4 and 5 display the cuts in the x-y plane of the simulation results using TE-mode harmonic waves. The computation domains, ∑(∑1 and ∑2 in Fig. 5(b)), are configured by media with the parameters (permittivity and permeability) governed by the equations deduced in section 3, and other regions are assumed to be the free space. The inner boundaries in Fig. 4 are set to be continuous. Whereas in Fig. 5, the funnel′s boundaries are set to be perfect electric conducting (PEC), by doing so, the compression performance can be seen clearly.

Figure 4(a) shows a WST through which a convex cylindrical wave with radius of R 1 is transformed to be a concave cylindrical wave with radius of R 2. Such a device is actually a perfect concave lens. Comparing with this WST, a conventional concave lens will produce large image dispersing when the flare angle of the incident wave is large, whereas this WST can overcome such limits. Theoretically, the flare angle of the incident beam into this WST can be large toπ. Another application of this WST is long-distance transmitting and focusing of energy when the radius of the second cylindrical surface is large enough.

In Fig. 4(b), we show a device through which a cylindrical wave is transformed to a plane wave. Obviously, such a device provides the capability of transforming the wave shape between cylindrical and plane, and thus can be used as perfect convex lens. We notice that, this case was already discussed by Lin and Jiang et al.[16, 17], however, our design is more general and more effective. For that, under the control of our designed WST, the direction of the transformed plane wave can be of any angles with respect to the main direction (the x-axis), which therefore has the capability to easily control the beam directions.

 figure: Fig. 4.

Fig. 4. (Color online) The electric-field distributions when waves propagate in WSTs, where, the wave shape is transformed (a) from convex cylindrical to concave cylindrical, or (b), from cylindrical to plane. The dashed lines (green) sketch the time-average power flows. The parameter L in the two parts is 20 wavelengths.

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Figure 5 shows the performance of photon funnels. In (a), a plane wave beam with large width is compressed to a thin beam without changing the wave shape, and therefore, the wave energy is concentrated. In principle, such compressions and concentrations are perfect compared with conventional devices. Another application of such devices is to enlarge wave beams when the wave is incident onto the right end (see Fig. 5(a)), in other words, such photon funnels can be used as perfect magnifiers and microscopes.

What is shown in Fig. 5(b) is the complex of a wave transformer (cylindrical to plane) and a photon funnel. Firstly, a cylindrical wave is transformed to a plane wave. Then, the plane wave with large width is compressed to a thin beam. As a whole, a cylindrical wave is collimated and compressed to be a thin beam. This complex is in fact a complicated photon funnel which is applied to cylindrical waves.

 figure: Fig. 5.

Fig. 5. (Color online) The electric-field distributions when waves propagate in photon funnels. Here two cases are considered: (a), using a photon funnel, a plane wave is compressed; and (b), using the complex of a WST and a photon funnel, a cylindrical wave is transformed to a plane wave and then is compressed to be a thin beam. The dashed lines (green) sketch the timeaverage power flows. The parameter L corresponding to regions ∑ and ∑2 is 7 wavelengths, and to region ∑1 is 20 wavelengths, respectively.

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5. Conclusions

By using the coordinate transformation theory in designing the desired WST, the derived relative permeability and permittivity have the tensor form, and some elements have the values varying from near zero to the higher. When the values of the relative permeability and permittivity fall into (0, 1), the conventional materials can not be applied any more, therefore we should rely on the meta-materials. Besides, the constitutive parameters of the WST are position-dependent, and even may be highly anisotropic for some complicated WSTs. Fortunately, the recently developed meta-material techniques, for instance, the split ring resonator (SRR) [18, 19] and the dielectric resonator (DR) [20], can be used to achieve the materials with the values of their effective relative permeability and permittivity below one. Adopting meta-materials, it is possible to manufacture some simple WSTs supposing that their constitutive parameters are not highly anisotropic and the distributions are comparatively uniform. However, in the complicated cases, there are difficulties in practical applications of the WSTs at the present technique situations. So the practical WSTs will depend on the further developments of meta-materials.

In summary, we have investigated the general method of designing WSTs to transform EM wave fronts from one style with arbitrary shape and size to another style, and presented some examples as the verification. Though the examples have limited to some special conditions, the generalization of this method is obvious according to the analysis in section 2.

For instance, a WST to transform the wave front from ellipsoid-shaped surface to paraboloid-shaped surface can be designed as well. Also, our method is available in cases with acoustic waves and the other types of waves.

Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant Nos.50632030, 10474077 and 60871027) and the 973-project of the Ministry of Science and Technology of China (Grant No. 2009CB613306). A Shaanxi National Science Foundation, also supported this work.

References and links

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

2. D. Schurig, J. B. Pendry, and D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express 14, 9794–9804 (2006). [CrossRef]   [PubMed]  

3. M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical Design of Reflectionless Complex Media by Finite Embedded Coordinate Transformations,” Phys. Rev. Lett. 100, 063903 (2008). [CrossRef]   [PubMed]  

4. M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photon. Nanostruct.: Fundam. Applic. 6, 87–95 (2008). [CrossRef]  

5. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006). [CrossRef]   [PubMed]  

6. H. Ma, S. Qu, Z. Xu, J. Zhang, B. Chen, and J. Wang, “Material parameter equation for elliptical cylindrical cloaks,” Phys. Rev. A 77, 013825 (2008). [CrossRef]  

7. D. -Hoon Kwon and D. H. Werner, “Two-dimensional eccentric elliptic electromagnetic cloaks,” Appl. Phys. Lett. 92, 013505 (2008). [CrossRef]  

8. Y. You, G. W. Kattawar, P.-W. Zhai, and P. Yang, “Invisibility cloaks for irregular particles using coordinate transformations,” Opt. Express 16, 6134–6145 (2008). [CrossRef]   [PubMed]  

9. W. Yan, M. Yan, Z. Ruan, and M. Qiu, “Coordinate transformations make perfect invisibility cloaks with arbitrary shape,” New J. Phys. 10, 043040 (2008). [CrossRef]  

10. W. Jiang, J. Y. Chin, Z. Li, Q. Cheng, R. Liu, and T. Cui, “Analytical design of conformally invisible cloaks for arbitrarily shaped Objects,” Phys. Rev. E 77, 066607 (2008). [CrossRef]  

11. L, Lin, W. Wang, C. Du, and X. Luo, “A cone-shaped concentrator with varying performances of concentrating,” Opt. Express 16, 6809–6814 (2008). [CrossRef]   [PubMed]  

12. W. Jiang, T. Cui, Q. Cheng, J. Y. Chin, X. Yang, R. Liu, and D. R. Smith, “Design of arbitrarily shaped concentrators based on conformally optical transformation of nonuniform rational B-spline surfaces,” Appl. Phys. Lett. 92, 264101 (2008). [CrossRef]  

13. Y. Luo, H. Chen, J. Zhang, L. Ran, and J. A. Kong, “Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations,” Phys. Rev. B 77, 125127 (2008). [CrossRef]  

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

15. H. Ma, S. Qu, Z. Xu, and J. Wang, “Using photon funnels based on metamaterial cloaks to compress electromagnetic wave beams,” Appl. Opt. 47, 4193 (2008). [CrossRef]   [PubMed]  

16. L. Lin, W. Wang, J. Cui, C. Du, and X. Luo, “Design of electromagnetic refractor and phase transformer using coordinate transformation theory,” Opt. Express 16, 6815–6821 (2008). [CrossRef]   [PubMed]  

17. W. Jiang, T. Cui, H. Ma, X. Zhou, and Q. Cheng, “Cylindrical-to-plane-wave conversion via embedded optical transformation,” Appl. Phys. Lett. 92, 261903 (2008). [CrossRef]  

18. 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, 4184 (2000). [CrossRef]   [PubMed]  

19. F. Zhang, G. Houzet, E. Lheurette, D. Lippens, M. Chaubet, and X. Zhao, “Negative-zero-positive metamaterial with omega-type metal inclusions,” J. Appl. Phys. 103, 084312 (2008). [CrossRef]  

20. B.-I. Popa and S. A. Cummer, “Compact Dielectric Particles as a Building Block for Low-Loss Magnetic Metamaterials,” Phys. Rev. Lett. 100, 207401 (2008). [CrossRef]   [PubMed]  

References

  • View by:

  1. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling Electromagnetic Fields,” Science 312, 1780–1782 (2006).
    [Crossref] [PubMed]
  2. D. Schurig, J. B. Pendry, and D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express 14, 9794–9804 (2006).
    [Crossref] [PubMed]
  3. M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical Design of Reflectionless Complex Media by Finite Embedded Coordinate Transformations,” Phys. Rev. Lett. 100, 063903 (2008).
    [Crossref] [PubMed]
  4. M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photon. Nanostruct.: Fundam. Applic. 6, 87–95 (2008).
    [Crossref]
  5. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
    [Crossref] [PubMed]
  6. H. Ma, S. Qu, Z. Xu, J. Zhang, B. Chen, and J. Wang, “Material parameter equation for elliptical cylindrical cloaks,” Phys. Rev. A 77, 013825 (2008).
    [Crossref]
  7. D. -Hoon Kwon and D. H. Werner, “Two-dimensional eccentric elliptic electromagnetic cloaks,” Appl. Phys. Lett. 92, 013505 (2008).
    [Crossref]
  8. Y. You, G. W. Kattawar, P.-W. Zhai, and P. Yang, “Invisibility cloaks for irregular particles using coordinate transformations,” Opt. Express 16, 6134–6145 (2008).
    [Crossref] [PubMed]
  9. W. Yan, M. Yan, Z. Ruan, and M. Qiu, “Coordinate transformations make perfect invisibility cloaks with arbitrary shape,” New J. Phys. 10, 043040 (2008).
    [Crossref]
  10. W. Jiang, J. Y. Chin, Z. Li, Q. Cheng, R. Liu, and T. Cui, “Analytical design of conformally invisible cloaks for arbitrarily shaped Objects,” Phys. Rev. E 77, 066607 (2008).
    [Crossref]
  11. L, Lin, W. Wang, C. Du, and X. Luo, “A cone-shaped concentrator with varying performances of concentrating,” Opt. Express 16, 6809–6814 (2008).
    [Crossref] [PubMed]
  12. W. Jiang, T. Cui, Q. Cheng, J. Y. Chin, X. Yang, R. Liu, and D. R. Smith, “Design of arbitrarily shaped concentrators based on conformally optical transformation of nonuniform rational B-spline surfaces,” Appl. Phys. Lett. 92, 264101 (2008).
    [Crossref]
  13. Y. Luo, H. Chen, J. Zhang, L. Ran, and J. A. Kong, “Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations,” Phys. Rev. B 77, 125127 (2008).
    [Crossref]
  14. H. Chen and C. T. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Lett. 90, 241105 (2007).
    [Crossref]
  15. H. Ma, S. Qu, Z. Xu, and J. Wang, “Using photon funnels based on metamaterial cloaks to compress electromagnetic wave beams,” Appl. Opt. 47, 4193 (2008).
    [Crossref] [PubMed]
  16. L. Lin, W. Wang, J. Cui, C. Du, and X. Luo, “Design of electromagnetic refractor and phase transformer using coordinate transformation theory,” Opt. Express 16, 6815–6821 (2008).
    [Crossref] [PubMed]
  17. W. Jiang, T. Cui, H. Ma, X. Zhou, and Q. Cheng, “Cylindrical-to-plane-wave conversion via embedded optical transformation,” Appl. Phys. Lett. 92, 261903 (2008).
    [Crossref]
  18. 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, 4184 (2000).
    [Crossref] [PubMed]
  19. F. Zhang, G. Houzet, E. Lheurette, D. Lippens, M. Chaubet, and X. Zhao, “Negative-zero-positive metamaterial with omega-type metal inclusions,” J. Appl. Phys. 103, 084312 (2008).
    [Crossref]
  20. B.-I. Popa and S. A. Cummer, “Compact Dielectric Particles as a Building Block for Low-Loss Magnetic Metamaterials,” Phys. Rev. Lett. 100, 207401 (2008).
    [Crossref] [PubMed]

2008 (15)

H. Ma, S. Qu, Z. Xu, J. Zhang, B. Chen, and J. Wang, “Material parameter equation for elliptical cylindrical cloaks,” Phys. Rev. A 77, 013825 (2008).
[Crossref]

D. -Hoon Kwon and D. H. Werner, “Two-dimensional eccentric elliptic electromagnetic cloaks,” Appl. Phys. Lett. 92, 013505 (2008).
[Crossref]

Y. You, G. W. Kattawar, P.-W. Zhai, and P. Yang, “Invisibility cloaks for irregular particles using coordinate transformations,” Opt. Express 16, 6134–6145 (2008).
[Crossref] [PubMed]

W. Yan, M. Yan, Z. Ruan, and M. Qiu, “Coordinate transformations make perfect invisibility cloaks with arbitrary shape,” New J. Phys. 10, 043040 (2008).
[Crossref]

W. Jiang, J. Y. Chin, Z. Li, Q. Cheng, R. Liu, and T. Cui, “Analytical design of conformally invisible cloaks for arbitrarily shaped Objects,” Phys. Rev. E 77, 066607 (2008).
[Crossref]

L, Lin, W. Wang, C. Du, and X. Luo, “A cone-shaped concentrator with varying performances of concentrating,” Opt. Express 16, 6809–6814 (2008).
[Crossref] [PubMed]

W. Jiang, T. Cui, Q. Cheng, J. Y. Chin, X. Yang, R. Liu, and D. R. Smith, “Design of arbitrarily shaped concentrators based on conformally optical transformation of nonuniform rational B-spline surfaces,” Appl. Phys. Lett. 92, 264101 (2008).
[Crossref]

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. A. Kong, “Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations,” Phys. Rev. B 77, 125127 (2008).
[Crossref]

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical Design of Reflectionless Complex Media by Finite Embedded Coordinate Transformations,” Phys. Rev. Lett. 100, 063903 (2008).
[Crossref] [PubMed]

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photon. Nanostruct.: Fundam. Applic. 6, 87–95 (2008).
[Crossref]

H. Ma, S. Qu, Z. Xu, and J. Wang, “Using photon funnels based on metamaterial cloaks to compress electromagnetic wave beams,” Appl. Opt. 47, 4193 (2008).
[Crossref] [PubMed]

L. Lin, W. Wang, J. Cui, C. Du, and X. Luo, “Design of electromagnetic refractor and phase transformer using coordinate transformation theory,” Opt. Express 16, 6815–6821 (2008).
[Crossref] [PubMed]

W. Jiang, T. Cui, H. Ma, X. Zhou, and Q. Cheng, “Cylindrical-to-plane-wave conversion via embedded optical transformation,” Appl. Phys. Lett. 92, 261903 (2008).
[Crossref]

F. Zhang, G. Houzet, E. Lheurette, D. Lippens, M. Chaubet, and X. Zhao, “Negative-zero-positive metamaterial with omega-type metal inclusions,” J. Appl. Phys. 103, 084312 (2008).
[Crossref]

B.-I. Popa and S. A. Cummer, “Compact Dielectric Particles as a Building Block for Low-Loss Magnetic Metamaterials,” Phys. Rev. Lett. 100, 207401 (2008).
[Crossref] [PubMed]

2007 (1)

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

2006 (3)

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[Crossref] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling Electromagnetic Fields,” Science 312, 1780–1782 (2006).
[Crossref] [PubMed]

D. Schurig, J. B. Pendry, and D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express 14, 9794–9804 (2006).
[Crossref] [PubMed]

2000 (1)

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, 4184 (2000).
[Crossref] [PubMed]

Chan, C. T.

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

Chaubet, M.

F. Zhang, G. Houzet, E. Lheurette, D. Lippens, M. Chaubet, and X. Zhao, “Negative-zero-positive metamaterial with omega-type metal inclusions,” J. Appl. Phys. 103, 084312 (2008).
[Crossref]

Chen, B.

H. Ma, S. Qu, Z. Xu, J. Zhang, B. Chen, and J. Wang, “Material parameter equation for elliptical cylindrical cloaks,” Phys. Rev. A 77, 013825 (2008).
[Crossref]

Chen, H.

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. A. Kong, “Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations,” Phys. Rev. B 77, 125127 (2008).
[Crossref]

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

Cheng, Q.

W. Jiang, T. Cui, Q. Cheng, J. Y. Chin, X. Yang, R. Liu, and D. R. Smith, “Design of arbitrarily shaped concentrators based on conformally optical transformation of nonuniform rational B-spline surfaces,” Appl. Phys. Lett. 92, 264101 (2008).
[Crossref]

W. Jiang, J. Y. Chin, Z. Li, Q. Cheng, R. Liu, and T. Cui, “Analytical design of conformally invisible cloaks for arbitrarily shaped Objects,” Phys. Rev. E 77, 066607 (2008).
[Crossref]

W. Jiang, T. Cui, H. Ma, X. Zhou, and Q. Cheng, “Cylindrical-to-plane-wave conversion via embedded optical transformation,” Appl. Phys. Lett. 92, 261903 (2008).
[Crossref]

Chin, J. Y.

W. Jiang, J. Y. Chin, Z. Li, Q. Cheng, R. Liu, and T. Cui, “Analytical design of conformally invisible cloaks for arbitrarily shaped Objects,” Phys. Rev. E 77, 066607 (2008).
[Crossref]

W. Jiang, T. Cui, Q. Cheng, J. Y. Chin, X. Yang, R. Liu, and D. R. Smith, “Design of arbitrarily shaped concentrators based on conformally optical transformation of nonuniform rational B-spline surfaces,” Appl. Phys. Lett. 92, 264101 (2008).
[Crossref]

Cui, J.

Cui, T.

W. Jiang, T. Cui, H. Ma, X. Zhou, and Q. Cheng, “Cylindrical-to-plane-wave conversion via embedded optical transformation,” Appl. Phys. Lett. 92, 261903 (2008).
[Crossref]

W. Jiang, J. Y. Chin, Z. Li, Q. Cheng, R. Liu, and T. Cui, “Analytical design of conformally invisible cloaks for arbitrarily shaped Objects,” Phys. Rev. E 77, 066607 (2008).
[Crossref]

W. Jiang, T. Cui, Q. Cheng, J. Y. Chin, X. Yang, R. Liu, and D. R. Smith, “Design of arbitrarily shaped concentrators based on conformally optical transformation of nonuniform rational B-spline surfaces,” Appl. Phys. Lett. 92, 264101 (2008).
[Crossref]

Cummer, S. A.

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical Design of Reflectionless Complex Media by Finite Embedded Coordinate Transformations,” Phys. Rev. Lett. 100, 063903 (2008).
[Crossref] [PubMed]

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photon. Nanostruct.: Fundam. Applic. 6, 87–95 (2008).
[Crossref]

B.-I. Popa and S. A. Cummer, “Compact Dielectric Particles as a Building Block for Low-Loss Magnetic Metamaterials,” Phys. Rev. Lett. 100, 207401 (2008).
[Crossref] [PubMed]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[Crossref] [PubMed]

Du, C.

-Hoon Kwon, D.

D. -Hoon Kwon and D. H. Werner, “Two-dimensional eccentric elliptic electromagnetic cloaks,” Appl. Phys. Lett. 92, 013505 (2008).
[Crossref]

Houzet, G.

F. Zhang, G. Houzet, E. Lheurette, D. Lippens, M. Chaubet, and X. Zhao, “Negative-zero-positive metamaterial with omega-type metal inclusions,” J. Appl. Phys. 103, 084312 (2008).
[Crossref]

Jiang, W.

W. Jiang, T. Cui, H. Ma, X. Zhou, and Q. Cheng, “Cylindrical-to-plane-wave conversion via embedded optical transformation,” Appl. Phys. Lett. 92, 261903 (2008).
[Crossref]

W. Jiang, T. Cui, Q. Cheng, J. Y. Chin, X. Yang, R. Liu, and D. R. Smith, “Design of arbitrarily shaped concentrators based on conformally optical transformation of nonuniform rational B-spline surfaces,” Appl. Phys. Lett. 92, 264101 (2008).
[Crossref]

W. Jiang, J. Y. Chin, Z. Li, Q. Cheng, R. Liu, and T. Cui, “Analytical design of conformally invisible cloaks for arbitrarily shaped Objects,” Phys. Rev. E 77, 066607 (2008).
[Crossref]

Justice, B. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[Crossref] [PubMed]

Kattawar, G. W.

Kong, J. A.

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. A. Kong, “Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations,” Phys. Rev. B 77, 125127 (2008).
[Crossref]

Lheurette, E.

F. Zhang, G. Houzet, E. Lheurette, D. Lippens, M. Chaubet, and X. Zhao, “Negative-zero-positive metamaterial with omega-type metal inclusions,” J. Appl. Phys. 103, 084312 (2008).
[Crossref]

Li, Z.

W. Jiang, J. Y. Chin, Z. Li, Q. Cheng, R. Liu, and T. Cui, “Analytical design of conformally invisible cloaks for arbitrarily shaped Objects,” Phys. Rev. E 77, 066607 (2008).
[Crossref]

Lin, L,

Lin, L.

Lippens, D.

F. Zhang, G. Houzet, E. Lheurette, D. Lippens, M. Chaubet, and X. Zhao, “Negative-zero-positive metamaterial with omega-type metal inclusions,” J. Appl. Phys. 103, 084312 (2008).
[Crossref]

Liu, R.

W. Jiang, T. Cui, Q. Cheng, J. Y. Chin, X. Yang, R. Liu, and D. R. Smith, “Design of arbitrarily shaped concentrators based on conformally optical transformation of nonuniform rational B-spline surfaces,” Appl. Phys. Lett. 92, 264101 (2008).
[Crossref]

W. Jiang, J. Y. Chin, Z. Li, Q. Cheng, R. Liu, and T. Cui, “Analytical design of conformally invisible cloaks for arbitrarily shaped Objects,” Phys. Rev. E 77, 066607 (2008).
[Crossref]

Luo, X.

Luo, Y.

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. A. Kong, “Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations,” Phys. Rev. B 77, 125127 (2008).
[Crossref]

Ma, H.

H. Ma, S. Qu, Z. Xu, and J. Wang, “Using photon funnels based on metamaterial cloaks to compress electromagnetic wave beams,” Appl. Opt. 47, 4193 (2008).
[Crossref] [PubMed]

H. Ma, S. Qu, Z. Xu, J. Zhang, B. Chen, and J. Wang, “Material parameter equation for elliptical cylindrical cloaks,” Phys. Rev. A 77, 013825 (2008).
[Crossref]

W. Jiang, T. Cui, H. Ma, X. Zhou, and Q. Cheng, “Cylindrical-to-plane-wave conversion via embedded optical transformation,” Appl. Phys. Lett. 92, 261903 (2008).
[Crossref]

Mock, J. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[Crossref] [PubMed]

Nemat-Nasser, S. C.

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, 4184 (2000).
[Crossref] [PubMed]

Padilla, W. J.

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, 4184 (2000).
[Crossref] [PubMed]

Pendry, J. B.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photon. Nanostruct.: Fundam. Applic. 6, 87–95 (2008).
[Crossref]

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical Design of Reflectionless Complex Media by Finite Embedded Coordinate Transformations,” Phys. Rev. Lett. 100, 063903 (2008).
[Crossref] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling Electromagnetic Fields,” Science 312, 1780–1782 (2006).
[Crossref] [PubMed]

D. Schurig, J. B. Pendry, and D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express 14, 9794–9804 (2006).
[Crossref] [PubMed]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[Crossref] [PubMed]

Popa, B.-I.

B.-I. Popa and S. A. Cummer, “Compact Dielectric Particles as a Building Block for Low-Loss Magnetic Metamaterials,” Phys. Rev. Lett. 100, 207401 (2008).
[Crossref] [PubMed]

Qiu, M.

W. Yan, M. Yan, Z. Ruan, and M. Qiu, “Coordinate transformations make perfect invisibility cloaks with arbitrary shape,” New J. Phys. 10, 043040 (2008).
[Crossref]

Qu, S.

H. Ma, S. Qu, Z. Xu, and J. Wang, “Using photon funnels based on metamaterial cloaks to compress electromagnetic wave beams,” Appl. Opt. 47, 4193 (2008).
[Crossref] [PubMed]

H. Ma, S. Qu, Z. Xu, J. Zhang, B. Chen, and J. Wang, “Material parameter equation for elliptical cylindrical cloaks,” Phys. Rev. A 77, 013825 (2008).
[Crossref]

Rahm, M.

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical Design of Reflectionless Complex Media by Finite Embedded Coordinate Transformations,” Phys. Rev. Lett. 100, 063903 (2008).
[Crossref] [PubMed]

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photon. Nanostruct.: Fundam. Applic. 6, 87–95 (2008).
[Crossref]

Ran, L.

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. A. Kong, “Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations,” Phys. Rev. B 77, 125127 (2008).
[Crossref]

Roberts, D. A.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photon. Nanostruct.: Fundam. Applic. 6, 87–95 (2008).
[Crossref]

Ruan, Z.

W. Yan, M. Yan, Z. Ruan, and M. Qiu, “Coordinate transformations make perfect invisibility cloaks with arbitrary shape,” New J. Phys. 10, 043040 (2008).
[Crossref]

Schultz, S.

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, 4184 (2000).
[Crossref] [PubMed]

Schurig, D.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photon. Nanostruct.: Fundam. Applic. 6, 87–95 (2008).
[Crossref]

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical Design of Reflectionless Complex Media by Finite Embedded Coordinate Transformations,” Phys. Rev. Lett. 100, 063903 (2008).
[Crossref] [PubMed]

D. Schurig, J. B. Pendry, and D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express 14, 9794–9804 (2006).
[Crossref] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling Electromagnetic Fields,” Science 312, 1780–1782 (2006).
[Crossref] [PubMed]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[Crossref] [PubMed]

Smith, D. R.

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photon. Nanostruct.: Fundam. Applic. 6, 87–95 (2008).
[Crossref]

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical Design of Reflectionless Complex Media by Finite Embedded Coordinate Transformations,” Phys. Rev. Lett. 100, 063903 (2008).
[Crossref] [PubMed]

W. Jiang, T. Cui, Q. Cheng, J. Y. Chin, X. Yang, R. Liu, and D. R. Smith, “Design of arbitrarily shaped concentrators based on conformally optical transformation of nonuniform rational B-spline surfaces,” Appl. Phys. Lett. 92, 264101 (2008).
[Crossref]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling Electromagnetic Fields,” Science 312, 1780–1782 (2006).
[Crossref] [PubMed]

D. Schurig, J. B. Pendry, and D. R. Smith, “Calculation of material properties and ray tracing in transformation media,” Opt. Express 14, 9794–9804 (2006).
[Crossref] [PubMed]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[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, 4184 (2000).
[Crossref] [PubMed]

Starr, A. F.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[Crossref] [PubMed]

Vier, D. C.

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, 4184 (2000).
[Crossref] [PubMed]

Wang, J.

H. Ma, S. Qu, Z. Xu, and J. Wang, “Using photon funnels based on metamaterial cloaks to compress electromagnetic wave beams,” Appl. Opt. 47, 4193 (2008).
[Crossref] [PubMed]

H. Ma, S. Qu, Z. Xu, J. Zhang, B. Chen, and J. Wang, “Material parameter equation for elliptical cylindrical cloaks,” Phys. Rev. A 77, 013825 (2008).
[Crossref]

Wang, W.

Werner, D. H.

D. -Hoon Kwon and D. H. Werner, “Two-dimensional eccentric elliptic electromagnetic cloaks,” Appl. Phys. Lett. 92, 013505 (2008).
[Crossref]

Xu, Z.

H. Ma, S. Qu, Z. Xu, J. Zhang, B. Chen, and J. Wang, “Material parameter equation for elliptical cylindrical cloaks,” Phys. Rev. A 77, 013825 (2008).
[Crossref]

H. Ma, S. Qu, Z. Xu, and J. Wang, “Using photon funnels based on metamaterial cloaks to compress electromagnetic wave beams,” Appl. Opt. 47, 4193 (2008).
[Crossref] [PubMed]

Yan, M.

W. Yan, M. Yan, Z. Ruan, and M. Qiu, “Coordinate transformations make perfect invisibility cloaks with arbitrary shape,” New J. Phys. 10, 043040 (2008).
[Crossref]

Yan, W.

W. Yan, M. Yan, Z. Ruan, and M. Qiu, “Coordinate transformations make perfect invisibility cloaks with arbitrary shape,” New J. Phys. 10, 043040 (2008).
[Crossref]

Yang, P.

Yang, X.

W. Jiang, T. Cui, Q. Cheng, J. Y. Chin, X. Yang, R. Liu, and D. R. Smith, “Design of arbitrarily shaped concentrators based on conformally optical transformation of nonuniform rational B-spline surfaces,” Appl. Phys. Lett. 92, 264101 (2008).
[Crossref]

You, Y.

Zhai, P.-W.

Zhang, F.

F. Zhang, G. Houzet, E. Lheurette, D. Lippens, M. Chaubet, and X. Zhao, “Negative-zero-positive metamaterial with omega-type metal inclusions,” J. Appl. Phys. 103, 084312 (2008).
[Crossref]

Zhang, J.

H. Ma, S. Qu, Z. Xu, J. Zhang, B. Chen, and J. Wang, “Material parameter equation for elliptical cylindrical cloaks,” Phys. Rev. A 77, 013825 (2008).
[Crossref]

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. A. Kong, “Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations,” Phys. Rev. B 77, 125127 (2008).
[Crossref]

Zhao, X.

F. Zhang, G. Houzet, E. Lheurette, D. Lippens, M. Chaubet, and X. Zhao, “Negative-zero-positive metamaterial with omega-type metal inclusions,” J. Appl. Phys. 103, 084312 (2008).
[Crossref]

Zhou, X.

W. Jiang, T. Cui, H. Ma, X. Zhou, and Q. Cheng, “Cylindrical-to-plane-wave conversion via embedded optical transformation,” Appl. Phys. Lett. 92, 261903 (2008).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (4)

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

W. Jiang, T. Cui, Q. Cheng, J. Y. Chin, X. Yang, R. Liu, and D. R. Smith, “Design of arbitrarily shaped concentrators based on conformally optical transformation of nonuniform rational B-spline surfaces,” Appl. Phys. Lett. 92, 264101 (2008).
[Crossref]

D. -Hoon Kwon and D. H. Werner, “Two-dimensional eccentric elliptic electromagnetic cloaks,” Appl. Phys. Lett. 92, 013505 (2008).
[Crossref]

W. Jiang, T. Cui, H. Ma, X. Zhou, and Q. Cheng, “Cylindrical-to-plane-wave conversion via embedded optical transformation,” Appl. Phys. Lett. 92, 261903 (2008).
[Crossref]

J. Appl. Phys. (1)

F. Zhang, G. Houzet, E. Lheurette, D. Lippens, M. Chaubet, and X. Zhao, “Negative-zero-positive metamaterial with omega-type metal inclusions,” J. Appl. Phys. 103, 084312 (2008).
[Crossref]

New J. Phys. (1)

W. Yan, M. Yan, Z. Ruan, and M. Qiu, “Coordinate transformations make perfect invisibility cloaks with arbitrary shape,” New J. Phys. 10, 043040 (2008).
[Crossref]

Opt. Express (4)

Photon. Nanostruct.: Fundam. Applic. (1)

M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photon. Nanostruct.: Fundam. Applic. 6, 87–95 (2008).
[Crossref]

Phys. Rev. A (1)

H. Ma, S. Qu, Z. Xu, J. Zhang, B. Chen, and J. Wang, “Material parameter equation for elliptical cylindrical cloaks,” Phys. Rev. A 77, 013825 (2008).
[Crossref]

Phys. Rev. B (1)

Y. Luo, H. Chen, J. Zhang, L. Ran, and J. A. Kong, “Design and analytical full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations,” Phys. Rev. B 77, 125127 (2008).
[Crossref]

Phys. Rev. E (1)

W. Jiang, J. Y. Chin, Z. Li, Q. Cheng, R. Liu, and T. Cui, “Analytical design of conformally invisible cloaks for arbitrarily shaped Objects,” Phys. Rev. E 77, 066607 (2008).
[Crossref]

Phys. Rev. Lett. (3)

M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical Design of Reflectionless Complex Media by Finite Embedded Coordinate Transformations,” Phys. Rev. Lett. 100, 063903 (2008).
[Crossref] [PubMed]

B.-I. Popa and S. A. Cummer, “Compact Dielectric Particles as a Building Block for Low-Loss Magnetic Metamaterials,” Phys. Rev. Lett. 100, 207401 (2008).
[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, 4184 (2000).
[Crossref] [PubMed]

Science (2)

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314, 977–980 (2006).
[Crossref] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling Electromagnetic Fields,” Science 312, 1780–1782 (2006).
[Crossref] [PubMed]

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Figures (5)

Fig. 1.
Fig. 1. The wave front is transformed from surface S1 to surface S2. As a result, starting from an arbitrary point A on S1, the wave vector line will be AC when the wave propagates in the free space, and will be AB when the wave propagates in the WST, respectively.
Fig. 2.
Fig. 2. The sketch of the geometrical relationship employed in designing a WST, where, the WST transforms the wave front (a) from convex cylindrical to concave cylindrical, or (b), from cylindrical to plane.
Fig. 3.
Fig. 3. The sketch of the geometrical relationship employed in designing a photon funnel, where the incident wave is supposed to be right traveling and is compressed in the y-axis direction.
Fig. 4.
Fig. 4. (Color online) The electric-field distributions when waves propagate in WSTs, where, the wave shape is transformed (a) from convex cylindrical to concave cylindrical, or (b), from cylindrical to plane. The dashed lines (green) sketch the time-average power flows. The parameter L in the two parts is 20 wavelengths.
Fig. 5.
Fig. 5. (Color online) The electric-field distributions when waves propagate in photon funnels. Here two cases are considered: (a), using a photon funnel, a plane wave is compressed; and (b), using the complex of a WST and a photon funnel, a cylindrical wave is transformed to a plane wave and then is compressed to be a thin beam. The dashed lines (green) sketch the timeaverage power flows. The parameter L corresponding to regions ∑ and ∑2 is 7 wavelengths, and to region ∑1 is 20 wavelengths, respectively.

Equations (45)

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S 1 : f ( x , y , z ) = 0 ,
S 2 : g ( x , y , z ) = 0 .
l p L = l p L .
x x p k x = y y p k y = z z p k z ,
f i ( x a , y a , z a ) = k i , i = x , y , z ,
L = x b x a , l p = x p x a .
x p = L L l p + x a , y p = y a , z p = z a .
α ( x p , y p , z p ) = Q α ( x p , y p , z p ) Q T det Q .
Q λ η = λ p η p , λ , η = x , y , z .
Q x η = x p η p = 1 L [ l p ( x b η p x a η p ) + L l p η p ] x a η p ,
Q λ η = λ p η p = λ a η p , λ = y , z ; η = x , y , z .
S i : x = R i cos θ i + x i , y = R i sin θ i , i = 1 , 2 .
x a = R 1 cos θ 1 + x 1 , y a = R 1 sin θ 1 ,
x b = R 2 cos θ 2 + x 2 , y b = y a ,
l b = ( x p x a ) 1 + tan 2 θ 1 ,
θ 1 = arctan ( y p x p x 1 ) , θ 2 = π arctan ( R 1 R 2 sin θ 1 ) .
θ 1 x p = y p ( x p x 1 ) 2 + y p 2 , θ 1 y p = x p x 1 ( x p x 1 ) 2 + y p 2 ,
θ 2 η p = R 1 cos θ 1 R 2 2 R 1 2 sin 2 θ 1 × θ 1 η p ,
x a η p = R 1 sin θ 1 θ 1 η p , y a η p = R 1 cos θ 1 θ 1 η p ,
x b η p = R 2 sin θ 2 θ 2 η p ,
l p η p = ( x p x a ) 1 1 + tan 2 θ 1 tan θ 1 cos 2 θ 1 θ 1 η p
+ ( s + x a η p ) 1 + tan 2 θ 1 · s = { 1 , η = x 0 , η = y
Q x η = 1 L { ( x p R 1 cos θ 1 x 1 ) ( R 2 sin θ 2 cos θ 1 R 2 2 R 1 2 sin 2 θ 1 + sin θ 1 ) R 1 1 + tan 2 θ 1 θ 1 η p
+ ( R 2 cos θ 2 R 1 cos θ 1 + x 2 x 1 ) [ ( x p R 1 cos θ 1 x 1 ) 1 1 + tan 2 θ 1 tan θ 1 cos 2 θ 1 θ 1 η p
+ ( s R 1 sin θ 1 θ 1 η p ) 1 + tan 2 θ 1 ] } + R 1 sin θ 1 θ 1 η p , s = { 1 , η = x 0 , η = y
Q y η = R 1 cos θ 1 θ 1 η p , η = x , y .
θ 1 = arcsin y p R 1 , θ 2 = π arcsin y p R 2 ,
x p = L x p R 1 cos θ 1 x 1 R 2 cos θ 2 R 1 cos θ 1 + x 2 x 1 1 1 + tan 2 θ 1 + R 1 cos θ 1 + x 1 ,
y p = ( x p x 1 ) tan θ 1 .
S 1 : x = R 1 cos θ 1 + x 1 , y = R 1 sin θ 1 ,
S 2 : y = k ( x x 2 ) ,
x b = R 1 sin θ 1 + k x 2 k , y b = y a .
x b η p = R 1 cos θ 1 k θ 1 η p , η = x , y .
Q x η = 1 L { ( x p R 1 cos θ 1 x 1 ) ( cos θ 1 k + sin θ 1 ) R 1 1 + tan 2 θ 1 θ 1 η p
+ ( R 1 sin θ 1 + k x 2 k R 1 cos θ 1 x 1 ) [ ( x p R 1 cos θ 1 x 1 ) 1 1 + tan 2 θ 1 tan θ 1 cos 2 θ 1 θ 1 η p
+ ( s R 1 sin θ 1 θ 1 η p ) 1 + tan 2 θ 1 ] } + R 1 sin θ 1 θ 1 η p , s = { 1 , η = x 0 , η = y
Q y η = R 1 cos θ 1 θ 1 η p , η = x , y .
θ 1 x p = y p ( x p x 1 ) 2 + y p 2 , θ 1 y p = x p x 1 ( x p x 1 ) 2 + y p 2 ,
θ 1 = arcsin y p ' R 1 ,
x p = L x p ' R 1 cos θ 1 x 1 R 1 sin θ 1 + k x 2 k R 1 cos θ 1 x 1 1 1 + tan 2 θ 1 + R 1 cos θ 1 + x 1 ,
y p = ( x p x 1 ) tan θ 1 .
y = k ( x x 1 ) + y 1 ,
y p ' y b = y p y c = y p y 1 ,
y p ' = y p y 1 y b , x p ' = x p .
Q xx = 1 , Q xy = 0 , Q yx = k y p y 1 , Q yy = y b y 1 .

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