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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 23 — Nov. 18, 2013
  • pp: 28948–28959
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Optic-null medium: realization and applications

Qiong He, Shiyi Xiao, Xin Li, and Lei Zhou  »View Author Affiliations


Optics Express, Vol. 21, Issue 23, pp. 28948-28959 (2013)
http://dx.doi.org/10.1364/OE.21.028948


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Abstract

Optic-null medium (ONM), an electromagnetic (EM) space representing optically nothing, has many interesting applications but is difficult to realize practically due to its extreme EM parameters. Here we demonstrate that a holey metallic plate with periodic array of subwavelength apertures can well mimic an ONM. We develop an effective-medium theory to extract the EM parameters of the designed ONM, and employ full-wave simulations to demonstrate its optical functionalities. Microwave experiments, in excellent agreement with full-wave simulations, are performed to illustrate several applications of the ONM, including the radiation cancellation effect and the hyperlensing effect.

© 2013 Optical Society of America

1. Introduction

Controlling electromagnetic (EM) waves at will has always been fascinating, but conventional materials exhibit limited abilities to achieve this aim. Transformation optics (TO) theory, proposed independently by J. Pendry et al. [1

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

] and U. Leonhardt [2

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

] in 2006, is a powerful tool to engineer the EM space so as to control the flow of light at a desired manner. Since its establishment, many fascinating wave-manipulation phenomena have been predicted based on the TO theory, such as invisibility cloaking [1

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

,2

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

], illusion optics [3

3. Y. Lai, J. Ng, H. Y. Chen, D. Z. Han, J. J. Xiao, Z. Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102(25), 253902 (2009). [CrossRef] [PubMed]

,4

4. Y. Lai, J. Ng, H. Y. Chen, Z. Q. Zhang, and C. T. Chan, “Illusion optics,” Front. Phys. China 5(3), 308–318 (2010). [CrossRef]

], field rotator/shifter /transformer [5

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

7

7. W. X. Jiang, T. J. Cui, H. F. Ma, X. Y. Zhou, and Q. Cheng, “Cylindrical-to-plane-wave conversion via embedded optical transformation,” Appl. Phys. Lett. 92(26), 261903 (2008). [CrossRef]

], chirality switching [8

8. Y. Shen, K. Ding, W. Sun, and L. Zhou, “A chirality switching device designed with transformation optics,” Opt. Express 18(20), 21419–21426 (2010). [CrossRef] [PubMed]

], image transformer [9

9. S. Han, Y. Xiong, D. Genov, Z. Liu, G. Bartal, and X. Zhang, “Ray optics at a deep-subwavelength scale: a transformation optics approach,” Nano Lett. 8(12), 4243–4247 (2008). [CrossRef] [PubMed]

] and hyperlensing [10

10. A. V. Kildishev and E. E. Narimanov, “Impedance-matched hyperlens,” Opt. Lett. 32(23), 3432–3434 (2007). [CrossRef] [PubMed]

]. However, to realize these predicted effects, the EM space should be filled with certain inhomogeneous/anisotropic materials, which are hard to realize by naturally existing materials but have to rely on metamaterials (MTM).

MTMs are artificial materials composed by subwavelength microstructures with tailored EM responses, which exhibit exotic optical properties not existing in nature. Although MTMs have enabled realizing certain physical effects including negative refraction [11

11. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001). [CrossRef] [PubMed]

,12

12. D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (2004). [CrossRef] [PubMed]

], subwavelength imaging [13

13. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000). [CrossRef] [PubMed]

,14

14. N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-Diffraction-Limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005). [CrossRef] [PubMed]

], and more recently anomalous reflection/refraction [15

15. N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011). [CrossRef] [PubMed]

,16

16. S. Sun, Q. He, S. Xiao, Q. Xu, X. Li, and L. Zhou, “Gradient-index meta-surfaces as a bridge linking propagating waves and surface waves,” Nat. Mater. 11(5), 426–431 (2012). [CrossRef] [PubMed]

], still, a large body of TO-based devices are hard to realize with MTMs. The inherent difficulty is that those TO devices require the filling materials to exhibit extreme EM parameters (either very large or very small) which are hard to realize with current technologies. As a result, the number of experimental demonstrations is much smaller than available theoretical proposals. It is thus highly desired to realize certain TO media employing the MTM concept, based on which the TO predictions can be verified.

In this work, we describe a practical way to achieve a certain type of TO medium—“optic-null medium” (ONM), which presents an optically non-existing space, and experimentally demonstrate several applications of the ONM. We first briefly describe the physical concept of an ONM and its interesting properties (Sec. 2), and then introduce our approach to practically realize such a medium (Sec. 3). Specifically, we develop an effective medium theory (EMT) based on the rigorous mode-expansion method to successfully retrieve the effective EM parameters of the proposed system, and employ full wave simulations to demonstrate that such a medium can indeed mimic an ONM optically. Finally, we perform both experiments and simulations to illustrate several applications of the ONM in Sec. 4, and conclude our paper in Sec. 5.

2. Physical concept and basic properties of the optics-null medium

According to the TO theory [1

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

], it is straightforward to derive the EM parameters of the ONM (shown in Fig. 1(c)) as
ε=μ=(Δ/b000Δ/b000b/Δ)Δ0(00000000)
(1)
in which the last expression is valid for the limiting case of Δ0. Here the permittivity and permeability tensors are written based on Cartesian coordinate system, where the matrix index i=1,2,3 represent x,y,z, respectively. The same technique can be applied to the cylindrical coordinate system, where the operation is to stretch a zero-thickness (along the radial direction) space (Fig. 1(d)) to a finite-thickness space (Fig. 1(e)). In this case, the required ONM (Fig. 1(f)) filling the physical space should have the following EM parameters [10

10. A. V. Kildishev and E. E. Narimanov, “Impedance-matched hyperlens,” Opt. Lett. 32(23), 3432–3434 (2007). [CrossRef] [PubMed]

],
ε=μ=(00000000),
(2)
where the matrix index i=1,2,3 represent r,θ,z, respectively.

To visualize the key properties of an ONM, we performed full-wave simulations based on the finite-element method (FEM) [17

17. COMSOL Multi-physics 3.5, developed by COMSOL ©, network license (2008).

] to study the ONM described by Eq. (1). In our simulations, we shined plane waves with different incident angle and polarization onto a slab of ONM and then computed the transmission/reflection coefficients as well as the field distributions. We took very large values for εz and μz to mimic in our simulations [18

18. In our simulations, we tookΔ/b=10000.

]. We found that in all cases studied, the incident plane waves transmit perfectly through the ONM without any reflections, independent of the incident angle and polarization (see solid circles in Fig. 2(a)
Fig. 2 (a) FEM-computed transmission amplitudes |T| for EM waves with different incident angle and polarization passing through a 2λ-thick slab of ONM (solid circles), ENZ (green dash line, withε=0.1) or ZIM (red line), correspondingly. (b)-(d) FEM simulated electric field (Ey) distributions for TE-polarized EM waves passing through a 2λ-thick ONM slab with parallel wave-vectors: (b) kx=0 (c) kx=0.5k0 and (d) kx=1.2k0. Here, k0 is the wave-vector in vacuum and the shadow areas represent the ONM.
). In addition, field distributions (see Figs. 2(b)2(d)) show that the transmitted waves do not acquire any phase accumulations, as if the ONM does not exist at all [19

19. Here, we only present the field distributions for TE-polarized excitation since the TM case is quite similar to the TE case.

]. Note that this conclusion is valid even in the case of an evanescent wave excitation (see Fig. 2(d)) where the field amplitude keeps at a constant value inside the ONM. Therefore, when a source is placed on the front surface of an ONM, every Fourier components radiated from the source can perfectly transmit through the ONM, and the re-interference of those transmitted waves will form an image which is an exact replica of the source, on the exit plane of the ONM. Such a super-lensing effect is actually a straightforward consequence of the stretch operation as depicted in Fig. 1, since the “source” and “image” represents the same point in the original space. We emphasize that an ONM is fundamentally different from an epsilon-near-zero (ENZ) material {with ε0,μ=μ0} [20

20. A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: tailoring the radiation phase pattern,” Phys. Rev. B 75(15), 155410 (2007). [CrossRef]

22

22. J. Luo, P. Xu, H. Chen, B. Hou, L. Gao, and Y. Lai, “Realizing almost perfect bending waveguides with anisotropic epsilon-near-zero metamaterials,” Appl. Phys. Lett. 100(22), 221903 (2012). [CrossRef]

] and an isotropic zero-index material (ZIM) {ε=μ=0} [23

23. I. C. Khoo, D. H. Werner, X. Liang, A. Diaz, and B. Weiner, “Nanosphere dispersed liquid crystals for tunable negative-zero-positive index of refraction in the optical and terahertz regimes,” Opt. Lett. 31(17), 2592–2594 (2006). [CrossRef] [PubMed]

,24

24. N. M. Litchinitser, A. I. Maimistov, I. R. Gabitov, R. Z. Sagdeev, and V. M. Shalaev, “Metamaterials: electromagnetic enhancement at zero-index transition,” Opt. Lett. 33(20), 2350–2352 (2008). [CrossRef] [PubMed]

]. As shown in Fig. 2(a), both ENZ and ZIM are perfectly transparent only for certain incident angles but induce strong reflections in most other cases, including particularly the cases of evanescent wave excitations. The inherent physics is that the impedance does not match in an ENZ and ZIM material under general incidence conditions.

We note that an ONM can also be realized by combining a slab of ordinary material with a carefully chosen negative-index material slab, based on the idea of complementary medium [25

25. J. B. Pendry and S. A. Ramakrishna, “Focusing light using negative refraction,” J. Phys. Condens. Matter 15(37), 6345–6364 (2003). [CrossRef]

28

28. W. Yan, M. Yan, and M. Qiu, “Generalized nihility media from transformation optics,” J. Opt. 13(2), 024005 (2011). [CrossRef]

]. However, so far it is still a great challenge to practically realize a high-quality negative-index material, and thus it is even more difficult to homogenize such a bilayer system to achieve the desired ONM effect.

3. Practical realization of the ONM

Although an ONM exhibits very attractive optical properties, how to realize it remains a great challenge for MTM researchers due to its extreme EM parameters required (0 and ). Instead of combining different EM resonant units to achieve such extreme parameters, here we demonstrate that a specific photonic system can well mimic an ONM. The system is schematically depicted in Fig. 3(a)
Fig. 3 (a) Geometry of a HMP. (b) Scheme of mapping a HMP to a homogeneous anisotropic effective medium.
, which is a holey metallic plate (HMP) [29

29. J. B. Pendry, L. Martín-Moreno, and F. J. García-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004). [CrossRef] [PubMed]

32

32. J. Bravo-Abad, F. J. García-Vidal, and L. Martín-Moreno, “Resonant transmission of light through finite chains of subwavelength holes in a metallic film,” Phys. Rev. Lett. 93(22), 227401 (2004). [CrossRef] [PubMed]

] with subwavelength apertures arranged in a square lattice with periodicity d. Here we only consider the microwave frequency domain so that metallic can be treated as a perfect electric conductor (PEC). The aperture can take any symmetrical complex shape as long as the resonance wavelength associated with it is much longer than its own size (i.e.,λ>>d). We first extend a previously established EMT for simple-shaped aperture case [30

30. F. J. García-Vidal, L. Martín-Moreno, and J. B. Pendry, “Surface with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt. 7(2), S97–S101 (2005). [CrossRef]

] to a general situation. Symmetry argument tells us that the effective permittivity/permeability tensor of the MTM should be
εeff=ε0(εeff||000εeff||000εeff),μeff=μ0(μeff||000μeff||000μeff).
(3)
In what follows, we determine the 4 unknowns (εeff|| εeff μeff|| μeff) by requesting that the two systems (e.g., model and the realistic one) exhibit the same optical responses with respect to general excitations (see Fig. 3(b)), under certain approximations.

Suppose that the realistic system is illuminated by a transverse-electric (TE) - polarized light with a parallel wave vector k||0x^. The scattering properties of such a system can be solved by the standard mode-expansion method [30

30. F. J. García-Vidal, L. Martín-Moreno, and J. B. Pendry, “Surface with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt. 7(2), S97–S101 (2005). [CrossRef]

32

32. J. Bravo-Abad, F. J. García-Vidal, and L. Martín-Moreno, “Resonant transmission of light through finite chains of subwavelength holes in a metallic film,” Phys. Rev. Lett. 93(22), 227401 (2004). [CrossRef] [PubMed]

]. Wave in region I can be expressed as EI=ESin+nrnESref,n, where ESinrepresents the TE-polarized incident plane wave and ESref,n the reflected plane waves along the n-th diffraction channel (with k||n=k||0+nπ/d) with reflection coefficient rn. H field can be derived from the E-field easily. Meanwhile, E-field in region II can be expressed as EII=qtqeik||RjEqWG when r is inside an aperture located at Rj and is 0 elsewhere, where tq is the expansion coefficient for the q-th waveguide mode with wave-function given by EqWG. For general aperture shapes, while it is difficult to obtain analytical expressions for EqWG, one can always employ numerical simulations to get EqWG for each mode. An important property of these eigenmodes is that they are orthogonal to each other. Again, H-field in this region can be derived from the E-field easily. By matching the boundary conditions at the interface located at z=0 and fully utilizing the orthonormal properties of these eigenmodes, we can in principle determine all the coefficients rn,tq [30

30. F. J. García-Vidal, L. Martín-Moreno, and J. B. Pendry, “Surface with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt. 7(2), S97–S101 (2005). [CrossRef]

,31

31. S. Xiao, Q. He, X. Huang, and L. Zhou, “Super imaging with a plasmonic metamaterial: role of aperture shape,” Metamaterials (Amst.) 5(2–3), 112–118 (2011). [CrossRef]

]. However, the final expressions of these coefficients are quite complicated and physically less transparent.

We now take two approximations to derive an analytical solution for the given problem, based on which the effective parameters can be obtained. First, we retain only the fundamental modes in both regions (i.e., the specular reflection in region I and the fundamental waveguide mode inside the aperture) but neglect all the high-order modes. This single-mode approximation is widely used and is physically sound here since we assume λ>>d so that all high-order modes are evanescent waves. Under this approximation, we found that the specular reflection coefficient is written as
r0=|S0|2kzair/kzWG1|S0|2kzair/kzWG+1,
(4)
in which
|S0|2=|u.c.dr||(E||in)E0,||WG|2u.c.dr|||E||in|2u.c.dr|||E0,||WG|2
(5)
represents the overlapping between the incident plane wave E||in and the fundamental waveguide mode E0,||WG. Here only the parallel field components are relevant, and the integrals are performed within a unit cell. kzair,kzWGare the z-components of k vectors of waves in different regions. Explicitly,
kzWG=εhω2ωc2/c,
(6)
where εh is the relative permittivity of the medium filling the aperture and ωc is the cut-off frequency of the fundamental waveguide mode, again obtainable by numerical simulations for general aperture cases.

We now derive the effective-medium parameters of the structure. Under exactly the same external illumination, we find that the reflection coefficient of the model system (i.e., the anisotropic MTM) is
r=μeff||kzair/kzMTM1μeff||kzair/kzMTM+1,
(7)
where
kzMTM=(ω/c)2εeff||μeff||k||2μeff||/μeff
(8)
is the z-component of the k vector for a TE-polarized wave traveling inside such an anisotropic MTM. The effective-medium parameters can be fixed by equating Eqs. (7) and (8) with Eqs. (4) and (6) [33

33. Here one can also impose the condition that the two systems exhibit the same transmission properties, although the mathematics are a bit complicated.

]. A careful analysis tells us that
εeff||=(1ωc2/ω2)εh/|S0|2μeff||=|S0|2.μeff=
(9)
Similar calculations for transverse-magnetic (TM) - polarized excitations can give us the values of εeff||,μeff||,εeff. For εeff||,μeff||, the TM calculations yield the same expressions as recorded in Eq. (9), which justified our TE calculations independently. Meanwhile, we get additionally from the TM calculations that
εeff=.
(10)
Note that εeff=μeff= is physically understandable, since a bulk medium of our system does not allow EM waves to propagate along a direction within the xy-plane, due to the existence of PEC walls separating different apertures.

Set the working frequency as the waveguide cut-off (ω=ωc), we find that
εeff=ε0(00000000),μeff=μ0(|S0|2000|S0|2000).
(11)
Therefore, if we can design a HMP exhibiting |S0|20, then such a system (at the frequency ω=ωc) can well mimic an ONM optically, since it exhibits almost identical optical responses as an ONM under excitations with arbitrary polarizations and incident angles.

It is helpful to discuss what kind of aperture shape can better achieve the desired functionality. Apparently, such an aperture should exhibit |S0|20 and deep-subwavelength response (λc>>d with λc being the cut-off wavelength), simultaneously. Unfortunately, the simple square shape is not a good choice. According to the analytical expression S0=22a/πd for a square-shape aperture, we need a/d0 to make |S0|20. However, in such a case εh would be extremely large to satisfy the second condition λc>>d (Note λc=εha). Alternatively, we find that the fractal-like aperture shape is a much better choice (see Fig. 4(a)
Fig. 4 (a) Designed HMP slab with parameters d = 20 mm, l1 = 10 mm, l2 = 5 mm, l3 = l4 = 4 mm, w = 1 mm and h = 50 mm. (b) Transmission amplitudes (red line and circles, left axis) and phases (blue line and circles, right axis) for EM waves with different parallel wave-vector and polarization passing through the designed HMP (circles, calculated by FDTD simulations) and the corresponding effective-medium slab (lines). (c) Distributions of |Ey| along z-axis for the system shined with a TE-polarized incident evanescent wave with k|| = π/3d (left panel) and a TM-polarized incident evanescent wave with k|| = π/2d (right panel), calculated by FDTD simulations (|Ey| is averaged over a unit cell) for realistic HMP (triangles) and the effective-medium slab (lines). Here, the shadow areas represent the HMP, and the working frequency is 2.0 GHz in all calculations.
), because the line width w of such structure is an additional and independent parameter to control the overlapping integral |S0|2, without affecting the deep-subwavelength property of the whole aperture shape [31

31. S. Xiao, Q. He, X. Huang, and L. Zhou, “Super imaging with a plasmonic metamaterial: role of aperture shape,” Metamaterials (Amst.) 5(2–3), 112–118 (2011). [CrossRef]

].

4. Experimental verifications and applications of ONM

In this section, we fabricate realistic ONM structures based on the theory described in last section, and experimentally demonstrate a couple of applications of such systems. Instead of using the isotropic fractal-like aperture as in Fig. 4, here we chose an anisotropic fractal-like shape (see Fig. 5(a)
Fig. 5 (a) Picture of the fabricated sample with parameters L1 = 12 mm, L2 = 13 mm, L3 = 6 mm, Px = 18 mm, Py = 31 mm, w = 1 mm (b) Return loss (|S11|) spectra of a dipole antenna put on top of standing-alone ONM slabs (black), ONM slabs backed by a PEC substrate (red) and air gaps backed by a PEC substrate (green), obtained by experiment (symbols) and FDTD simulations (lines). Here the working frequency is 2.63 GHz.
) to design and fabricate our ONM. Our EMT can be easily extended to such anisotropic cases, where ωc, |S0|2can take different values for {εeffx,μeffy} and {εeffy,μeffx} dictated by different waveguide modes polarized along x or y directions. In certain applications with fixed in-plane E directions (see below), such anisotropic aperture shape is enough since the incident waves can only detect a certain set of parameters. We can thus utilize this property to design a deep-subwavelength aperture within a confined area, even without using high-index insertions.

For the designed aperture, we performed FDTD simulations to study its fundamental-mode (for E||y^) properties and found that ωc=2π×2.63 GHz and |S0|2=0.07. Therefore, at the working frequency ω=ωc, the effective parameters of this system are εeffy=0, εeffz=, μeffx=0.07μ0, μeffz=, according to the EMT described in last section. We then fabricated a series of HMP slabs with different thicknesses and performed microwave experiments to demonstrate several fascinating properties/applications of such systems.

Finally, we experimentally demonstrated a particular application of the ONM, which can work as a hyperlens as predicted in [10

10. A. V. Kildishev and E. E. Narimanov, “Impedance-matched hyperlens,” Opt. Lett. 32(23), 3432–3434 (2007). [CrossRef] [PubMed]

]. The working principle is shown in Fig. 6(c)
Fig. 6 (a) Top-view and (b) side-view pictures of the experiment sample. |E/Eref| distributions for the hyperlensing effect realized by (c) a cylindrical ONM with parameter given by Eq. (2) and (d) our designed sample obtained by FDTD simulations at frequency 2.63 GHz.
. Put two line sources on the inner surface of a cylindrical-shaped ONM layer, FDTD simulations show that the image formed on the outer surface of the ONM is just the original source magnified by a factor of Rout/Rin, with Rout,Rin denoting the radii of the outer and inner surfaces, respectively. Such a hyperlensing effect is a straightforward consequence of the “stretching” operation as depicted in Fig. 1. To fabricate the cylindrical ONM, we cut a 65mm-thick HMP slab (with the same parameters as in Fig. 5(a)) into 18 mm-wide stripes (each containing 7 unit elements) and then arrange them into a cylindrical shape. Adjacent stripes are metallically connected to avoid wave tunneling effects. Figures 6(a) and 6(b) show the top-view and side-view pictures of the sample. The inner and outer radii of the realized sample are 235 and 300 mm, respectively, and samples with other radii can be easily fabricated. It is straightforward to derive the effective-medium parameters of such a cylindrical HMP. We find that, at the working frequency, εof our system is identical to that of a cylindrical ONM (Eq. (2)) and μ is very close to that of a cylindrical ONM with only μθ slightly modified by a metric term but still approaching to zero. We have performed FDTD simulations on the designed realistic sample to study the hyperlensing effect at the frequency 2.63 GHz. Figure 6(d) depicts the calculated field distribution on the central xy-plane of the realistic sample, which is in excellent agreement with the field distribution of the ideal cylindrical ONM (Fig. 6(c)).

All these features are consistent with the theoretical predictions based on an ONM. FDTD simulations were performed on the realistic system, and the obtained results (lines in Figs. 7(b) and 7(d)) are in good agreement with the experimental ones. However, the working band width of our fabricated ONM is quite narrow, which is only 0.05GHz for the 65 mm-thick sample estimated by FDTD simulations [35

35. To estimate the working bandwidth, we define the frequencies at which the transmittance of our sample decreases to 0.5 as two boundaries of the working range.

]. As the working frequency significantly deviates from the waveguide cut-off, the effective permittivity of our sample will change dramatically from zero so that our device cannot work as an ONM.

Two things are worthy being mentioned. First, our experiments demonstrated that the hyperlensing effect is independent of δϕ(see Figs. 7(a) and 7(c)), which is the desired result according to the “stretching” operation (see Fig. 1). Such an interesting property offers the ONM more freedoms in future applications. Second, although the magnification factor is only ~1.3 in present demonstration, this factor can be easily improved by increasing the curvature or the thickness of our device. FDTD simulations were performed on a thicker sample (with realistic structure) withRout/Rin2 to demonstrate this point. Put two sources separated by 0.32λ at the inner surface of this new ONM, FDTD simulations show that the resulting images formed on the outer surface are separated by a distance0.64λ, which can now be distinguished in the far field (see Fig. 8
Fig. 8 FDTD simulated |E/Eref| distributions on the (a) x-z plane, (b) source plane, and (c) image plane for the hyperlensing effect realized by a cylindrical ONM with Rout=475mmand Rin=235mm at the working frequency 2.63 GHz.
).

5. Conclusions

In summary, based on an extended effective medium theory, we designed and fabricated a realistic structure to mimic the optical-null medium, and experimentally demonstrated several interesting physical effects and applications of such a system. Experimental results are in excellent agreement with full-wave simulations and model analyses. More applications can be expected for such a system.

Acknowledgments

This work was supported by NSFC (60990321, 11174055,11204040), the Program of Shanghai Subject Chief Scientist (12XD1400700) and MOE of China (B06011). Q. He acknowledges financial supports from China Postdoctoral Science Foundation (2012M520039, 2013T60412).

References and links

1.

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

2.

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

3.

Y. Lai, J. Ng, H. Y. Chen, D. Z. Han, J. J. Xiao, Z. Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102(25), 253902 (2009). [CrossRef] [PubMed]

4.

Y. Lai, J. Ng, H. Y. Chen, Z. Q. Zhang, and C. T. Chan, “Illusion optics,” Front. Phys. China 5(3), 308–318 (2010). [CrossRef]

5.

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

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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(6), 063903 (2008). [CrossRef] [PubMed]

7.

W. X. Jiang, T. J. Cui, H. F. Ma, X. Y. Zhou, and Q. Cheng, “Cylindrical-to-plane-wave conversion via embedded optical transformation,” Appl. Phys. Lett. 92(26), 261903 (2008). [CrossRef]

8.

Y. Shen, K. Ding, W. Sun, and L. Zhou, “A chirality switching device designed with transformation optics,” Opt. Express 18(20), 21419–21426 (2010). [CrossRef] [PubMed]

9.

S. Han, Y. Xiong, D. Genov, Z. Liu, G. Bartal, and X. Zhang, “Ray optics at a deep-subwavelength scale: a transformation optics approach,” Nano Lett. 8(12), 4243–4247 (2008). [CrossRef] [PubMed]

10.

A. V. Kildishev and E. E. Narimanov, “Impedance-matched hyperlens,” Opt. Lett. 32(23), 3432–3434 (2007). [CrossRef] [PubMed]

11.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001). [CrossRef] [PubMed]

12.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305(5685), 788–792 (2004). [CrossRef] [PubMed]

13.

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000). [CrossRef] [PubMed]

14.

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-Diffraction-Limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005). [CrossRef] [PubMed]

15.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011). [CrossRef] [PubMed]

16.

S. Sun, Q. He, S. Xiao, Q. Xu, X. Li, and L. Zhou, “Gradient-index meta-surfaces as a bridge linking propagating waves and surface waves,” Nat. Mater. 11(5), 426–431 (2012). [CrossRef] [PubMed]

17.

COMSOL Multi-physics 3.5, developed by COMSOL ©, network license (2008).

18.

In our simulations, we tookΔ/b=10000.

19.

Here, we only present the field distributions for TE-polarized excitation since the TM case is quite similar to the TE case.

20.

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: tailoring the radiation phase pattern,” Phys. Rev. B 75(15), 155410 (2007). [CrossRef]

21.

M. 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]

22.

J. Luo, P. Xu, H. Chen, B. Hou, L. Gao, and Y. Lai, “Realizing almost perfect bending waveguides with anisotropic epsilon-near-zero metamaterials,” Appl. Phys. Lett. 100(22), 221903 (2012). [CrossRef]

23.

I. C. Khoo, D. H. Werner, X. Liang, A. Diaz, and B. Weiner, “Nanosphere dispersed liquid crystals for tunable negative-zero-positive index of refraction in the optical and terahertz regimes,” Opt. Lett. 31(17), 2592–2594 (2006). [CrossRef] [PubMed]

24.

N. M. Litchinitser, A. I. Maimistov, I. R. Gabitov, R. Z. Sagdeev, and V. M. Shalaev, “Metamaterials: electromagnetic enhancement at zero-index transition,” Opt. Lett. 33(20), 2350–2352 (2008). [CrossRef] [PubMed]

25.

J. B. Pendry and S. A. Ramakrishna, “Focusing light using negative refraction,” J. Phys. Condens. Matter 15(37), 6345–6364 (2003). [CrossRef]

26.

Y. Lai, H. Chen, Z. Q. Zhang, and C. T. Chan, “Complementary Media Invisibility Cloak that Cloaks Objects at a Distance Outside the Cloaking Shell,” Phys. Rev. Lett. 102(9), 093901 (2009). [CrossRef] [PubMed]

27.

W. Yan, M. Yan, and M. Qiu, “Generalized compensated bilayer structure from the transformation optics perspective,” J. Opt. Soc. Am. B 26(12), 32–35 (2009). [CrossRef]

28.

W. Yan, M. Yan, and M. Qiu, “Generalized nihility media from transformation optics,” J. Opt. 13(2), 024005 (2011). [CrossRef]

29.

J. B. Pendry, L. Martín-Moreno, and F. J. García-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004). [CrossRef] [PubMed]

30.

F. J. García-Vidal, L. Martín-Moreno, and J. B. Pendry, “Surface with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt. 7(2), S97–S101 (2005). [CrossRef]

31.

S. Xiao, Q. He, X. Huang, and L. Zhou, “Super imaging with a plasmonic metamaterial: role of aperture shape,” Metamaterials (Amst.) 5(2–3), 112–118 (2011). [CrossRef]

32.

J. Bravo-Abad, F. J. García-Vidal, and L. Martín-Moreno, “Resonant transmission of light through finite chains of subwavelength holes in a metallic film,” Phys. Rev. Lett. 93(22), 227401 (2004). [CrossRef] [PubMed]

33.

Here one can also impose the condition that the two systems exhibit the same transmission properties, although the mathematics are a bit complicated.

34.

CONCERTO 7.0, developed by Vector Fields Ltd, England (2008).

35.

To estimate the working bandwidth, we define the frequencies at which the transmittance of our sample decreases to 0.5 as two boundaries of the working range.

OCIS Codes
(080.2710) Geometric optics : Inhomogeneous optical media
(230.0230) Optical devices : Optical devices
(260.2110) Physical optics : Electromagnetic optics
(260.2065) Physical optics : Effective medium theory
(160.3918) Materials : Metamaterials

ToC Category:
Metamaterials

History
Original Manuscript: September 23, 2013
Revised Manuscript: November 8, 2013
Manuscript Accepted: November 12, 2013
Published: November 15, 2013

Citation
Qiong He, Shiyi Xiao, Xin Li, and Lei Zhou, "Optic-null medium: realization and applications," Opt. Express 21, 28948-28959 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-23-28948


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References

  1. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312(5781), 1780–1782 (2006). [CrossRef] [PubMed]
  2. U. Leonhardt, “Optical conformal mapping,” Science312(5781), 1777–1780 (2006). [CrossRef] [PubMed]
  3. Y. Lai, J. Ng, H. Y. Chen, D. Z. Han, J. J. Xiao, Z. Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett.102(25), 253902 (2009). [CrossRef] [PubMed]
  4. Y. Lai, J. Ng, H. Y. Chen, Z. Q. Zhang, and C. T. Chan, “Illusion optics,” Front. Phys. China5(3), 308–318 (2010). [CrossRef]
  5. H. Y. Chen and C. T. Chan, “Transformation media that rotate electromagnetic fields,” Appl. Phys. Lett.90(24), 241105 (2007). [CrossRef]
  6. 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(6), 063903 (2008). [CrossRef] [PubMed]
  7. W. X. Jiang, T. J. Cui, H. F. Ma, X. Y. Zhou, and Q. Cheng, “Cylindrical-to-plane-wave conversion via embedded optical transformation,” Appl. Phys. Lett.92(26), 261903 (2008). [CrossRef]
  8. Y. Shen, K. Ding, W. Sun, and L. Zhou, “A chirality switching device designed with transformation optics,” Opt. Express18(20), 21419–21426 (2010). [CrossRef] [PubMed]
  9. S. Han, Y. Xiong, D. Genov, Z. Liu, G. Bartal, and X. Zhang, “Ray optics at a deep-subwavelength scale: a transformation optics approach,” Nano Lett.8(12), 4243–4247 (2008). [CrossRef] [PubMed]
  10. A. V. Kildishev and E. E. Narimanov, “Impedance-matched hyperlens,” Opt. Lett.32(23), 3432–3434 (2007). [CrossRef] [PubMed]
  11. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science292(5514), 77–79 (2001). [CrossRef] [PubMed]
  12. D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science305(5685), 788–792 (2004). [CrossRef] [PubMed]
  13. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett.85(18), 3966–3969 (2000). [CrossRef] [PubMed]
  14. N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-Diffraction-Limited optical imaging with a silver superlens,” Science308(5721), 534–537 (2005). [CrossRef] [PubMed]
  15. N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science334(6054), 333–337 (2011). [CrossRef] [PubMed]
  16. S. Sun, Q. He, S. Xiao, Q. Xu, X. Li, and L. Zhou, “Gradient-index meta-surfaces as a bridge linking propagating waves and surface waves,” Nat. Mater.11(5), 426–431 (2012). [CrossRef] [PubMed]
  17. COMSOL Multi-physics 3.5, developed by COMSOL ©, network license (2008).
  18. In our simulations, we tookΔ/b=10000.
  19. Here, we only present the field distributions for TE-polarized excitation since the TM case is quite similar to the TE case.
  20. A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: tailoring the radiation phase pattern,” Phys. Rev. B75(15), 155410 (2007). [CrossRef]
  21. M. 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]
  22. J. Luo, P. Xu, H. Chen, B. Hou, L. Gao, and Y. Lai, “Realizing almost perfect bending waveguides with anisotropic epsilon-near-zero metamaterials,” Appl. Phys. Lett.100(22), 221903 (2012). [CrossRef]
  23. I. C. Khoo, D. H. Werner, X. Liang, A. Diaz, and B. Weiner, “Nanosphere dispersed liquid crystals for tunable negative-zero-positive index of refraction in the optical and terahertz regimes,” Opt. Lett.31(17), 2592–2594 (2006). [CrossRef] [PubMed]
  24. N. M. Litchinitser, A. I. Maimistov, I. R. Gabitov, R. Z. Sagdeev, and V. M. Shalaev, “Metamaterials: electromagnetic enhancement at zero-index transition,” Opt. Lett.33(20), 2350–2352 (2008). [CrossRef] [PubMed]
  25. J. B. Pendry and S. A. Ramakrishna, “Focusing light using negative refraction,” J. Phys. Condens. Matter15(37), 6345–6364 (2003). [CrossRef]
  26. Y. Lai, H. Chen, Z. Q. Zhang, and C. T. Chan, “Complementary Media Invisibility Cloak that Cloaks Objects at a Distance Outside the Cloaking Shell,” Phys. Rev. Lett.102(9), 093901 (2009). [CrossRef] [PubMed]
  27. W. Yan, M. Yan, and M. Qiu, “Generalized compensated bilayer structure from the transformation optics perspective,” J. Opt. Soc. Am. B26(12), 32–35 (2009). [CrossRef]
  28. W. Yan, M. Yan, and M. Qiu, “Generalized nihility media from transformation optics,” J. Opt.13(2), 024005 (2011). [CrossRef]
  29. J. B. Pendry, L. Martín-Moreno, and F. J. García-Vidal, “Mimicking surface plasmons with structured surfaces,” Science305(5685), 847–848 (2004). [CrossRef] [PubMed]
  30. F. J. García-Vidal, L. Martín-Moreno, and J. B. Pendry, “Surface with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt.7(2), S97–S101 (2005). [CrossRef]
  31. S. Xiao, Q. He, X. Huang, and L. Zhou, “Super imaging with a plasmonic metamaterial: role of aperture shape,” Metamaterials (Amst.)5(2–3), 112–118 (2011). [CrossRef]
  32. J. Bravo-Abad, F. J. García-Vidal, and L. Martín-Moreno, “Resonant transmission of light through finite chains of subwavelength holes in a metallic film,” Phys. Rev. Lett.93(22), 227401 (2004). [CrossRef] [PubMed]
  33. Here one can also impose the condition that the two systems exhibit the same transmission properties, although the mathematics are a bit complicated.
  34. CONCERTO 7.0, developed by Vector Fields Ltd, England (2008).
  35. To estimate the working bandwidth, we define the frequencies at which the transmittance of our sample decreases to 0.5 as two boundaries of the working range.

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