PHYSICAL REVIEW B 89, 245132 (2014)

Broadband electromagnetic metamaterials with reconfigurable fluid channels

Linde Liu, Alexander R. Katko, Dennis Li, and Steven A. Cummer*

Department of Electrical and Computer Engineering, Duke University, Durham, North Carolina 27708, USA(Received 17 January 2014; revised manuscript received 13 May 2014; published 25 June 2014)

We present the design, characterization, and experimental verification of broadband and tunable metamaterialsbased on reconfigurable fluid channels. We demonstrate through simulation that a finite-height cylinder of waterin a background medium behaves as a nonresonant metamaterial. By changing liquid type or adjusting liquidlevel, we tune the effective material parameters of the metamaterial through altering the composition and amountof water used. We verify the efficacy of the metamaterial through experiment, demonstrating a design procedurefor a metamaterial with broadband and tunable properties.

DOI: 10.1103/PhysRevB.89.245132 PACS number(s): 81.05.Xj, 78.67.Pt, 42.25.Gy

I. INTRODUCTION

Electromagnetic metamaterials employ subwavelength,structured composites to artificially engineer materials withunusual and versatile effective material properties. Since earlywork focusing on thin wire structures [1] and split-ringresonators (SRRs) [2], a variety of unit cell structures havebeen explored [3–5] and used for the design of interestingand useful devices, such as a superlens [6] and invisibilitycloak [7]. Many of these metamaterial unit cells have dependedon resonant effects, resulting in a narrow operating bandwidthand usually with high losses close to the resonant frequency.

Dynamic tunability has been used to partially address thebandwidth limitations of resonant metamaterials. Since typicalresonant metamaterial elements such as SRRs can be treated asresonant LC circuits, most of the work has involved embeddingelectric components such as varactor diodes into a resonantcell to create nonlinear effects and tune the capacitance ofthe unit cell [8–10]. Methods of mechanical tuning have alsobeen explored through methods such as pneumatic action [11]and adjustable metal rods in dielectric resonators [12]. Thesemethods all leverage the property of resonant elements thatthe resonant frequency can be shifted substantially by a verysmall change to the electric or physical properties of the cell.

In contrast, nonresonant metamaterial unit cells do notsuffer from narrow bandwidth limitations, bringing aboutdevices such as the broadband carpet cloak [13]. However,nonresonant elements can normally only be used to controlthe electric permittivity, and only values larger than unitycan be obtained. Creating tunable nonresonant cells is alsochallenging because altering the effective material propertiesrequires significant changes to the geometry of the cellstructure.

Our goal is to move towards metamaterials that exhibitboth nonresonant and dynamically tunable properties. Thecomposite liquid lens [14] achieves broadband tunable results,but the lens materials remain fixed after construction andthus exhibit a static tunability. In this paper, we propose theuse of liquid channels to create a metamaterial unit cell thatcan be easily tuned after initial construction by changing theliquid type or adjusting the liquid level within the structure’scolumns. With the ability to reconfigure the liquid volume

*cummer@ee.duke.edu

and conductivity in a cell, we consider the tunability tobe somewhat dynamic. True dynamic tunability could beachieved with our basic structure by employing microfluidicapproaches. This type of metamaterial unit cell could be usedto provide tunability for broadband, index-only metamaterialdevices. As an example, it could be used to realize a broadbandgraded-index (GRIN) lens. By adjusting the liquid height inthe metamaterial, properties of the lens such as the focal lengthwould gain tunability while retaining broadband performance.Other index-only devices that rely on broadband metamaterialsinclude the well-known carpet cloak [13]. By employingdynamically tunable metamaterials to realize such a device,the cloak would gain tunability and potentially the ability toadjust its size, all while retaining broadband operation.

This design approach offers a general tradeoff betweenrefractive index amplitude (n′) and loss (n′′) in the structure.Using a conductive fluid for the metamaterial, an increasein column number, spacing distance, and fluid volume willincrease both n′ and n′′. While we find through simulation thatloss can be mitigated by using fluid with a very high or lowconductivity, our approach focuses mainly on maximizing n′of the cell. With small volumes of fluid (less than 7% fluid perunit cell), tunable n′ from 1 to 2 can be achieved.

II. DESIGN AND CHARACTERIZATIONOF A SINGLE COLUMN

Our basic proposed unit cell is a cubic lattice containinga finite-height cylinder of dielectric material, as shownin Fig. 1(a), with column radius r = 4.5 mm and heighth = 28 mm. Replacing the dielectric with a perfect elec-tric conducting (PEC) material would yield a thin wiremedium. However, unlike low-frequency plasmons in metallicmesostructures [1], the cylinder used in this work is notinfinite in height. Due to its finite height, it has a nonzeroresonant frequency. The operational frequency range is heldwell below the resonant frequency in the quasistatic frequencyrange, yielding a nonresonant metamaterial unit cell. Thus, theproposed metamaterial exhibits a broadband response.

We first consider a dielectric fluid, i.e., either a losslessfluid (LF) or a conductive fluid (CF). If conductivity is largeenough, the lossy fluid dielectric is an effective conductor andthus behaves like a PEC inclusion. We confirm this behaviorthrough simulation using the Ansys HFSS software. Choosingthe dielectric material to be water based, the LF is characterized

1098-0121/2014/89(24)/245132(6) 245132-1 ©2014 American Physical Society

http://dx.doi.org/10.1103/PhysRevB.89.245132

LIU, KATKO, LI, AND CUMMER PHYSICAL REVIEW B 89, 245132 (2014)

−1

0

1

2

0.4 0.7 1

0

2

4

0.1 0.4 1

0

0.5

1

(a)

(c)

(b)

(d)

ε μn

0.70.1

PEC ImagPEC RealCF ImagCF RealLF ImagLF Real

Frequency (GHz) Frequency (GHz)

FIG. 1. (Color online) The single column unit cell. (a) Thesimulated model with parameters r and h labeled. (b)–(d) Theretrieved material parameters n, �, and μ, respectively. Both the realand imaginary parts are given for the perfect electric conductor (PEC),lossless fluid (LF), and conducting fluid (CF).

by �r = 81, modeling distilled water. The CF is characterizedby �r = 81 and σ = 4, a typical value for seawater.

From the simulated S parameters S11 and S21, we use thestandard S-parameter retrieval process [15] to calculate theeffective material parameters, focusing on the refractive indexn = n′ + jn′′. Figures 1(b)–1(d) show the effective materialparameters and demonstrate the broadband effective materialproperties for this metamaterial.

For 1 GHz, at which the unit cell is 1/10 the size of thefree-space wavelength, the PEC unit cell gives n′ = 1.66 andthe CF unit cell gives n′ = 1.65 [Fig. 1(b)]. The CF providescomparable results to a PEC, and thus we cannot use thehomogenization theory to accurately compute its materialparameters.

Although a CF such as saltwater can provide an effectiverefractive index comparable to that of a PEC, there is a smallamount of loss due to the finite conductivity [see Fig. 1(b)].The loss is significantly lower than that of a resonant cell, asn′′ < 0.1 across the decade sweep. However, if the structureis to be utilized for low-power applications where minimizingloss is critical, an LF unit cell may be used in place of theCF. For the LF, n′ = 1.60 at 1 GHz. Thus the tradeoff for thelossless character is a slight decrease in n′ when compared tothe CF case.

The nonresonant character of the unit cell provides abroadband response over a decade bandwidth from 100 MHzto 1 GHz. The PEC unit cell shows a 4.24% change, the CFunit cell shows a 3.11%, and the LF unit cell shows a 3.48%change across the decade.

Examining �r and μr in Figs. 1(c) and 1(d), we observethat μ remains close to 1 for all cases. Since changes in �alone affect n, we will only display n for the remainder of thesimulation characterization. In our experimental validation, wewill again examine the full set of effective material parameters.

To maximize the effective material response, we primarilywish to maximize n′. However, we also consider the lossfactor to accommodate for low-power scenarios and in theconsideration of physical applications such as lenses. Whereasresonant metamaterials produce significant loss, our nonreso-nant structure provides greater design freedom for the designerin selecting an acceptable loss for the structure. Devices such asPendry’s perfect lens [16] cannot exist without nearly losslessmaterials.

Physical structures are bound by the mechanical constraintsof size and weight, thus it is also important to minimize thevolume of water used when designing a cell.

III. PARAMETERS OF TUNABILITY

There are four basic properties that can be varied in thisstructure to manipulate the refractive index. Three involvecreating different fluid geometries by changing the number ofcolumns, the intercolumn spacing, and the dimensions of thecolumns. Composition of fluid through conductivity change isa fourth factor that can be altered in the structure. Throughtuning these parameters, we set a goal of maximizing effectiven′ while also minimizing the loss factor n′/n′′. Since the CFunit cell provides a larger n′ than LF, we focus on the use ofCF (σ = 4 S/m) for the inclusion. We are operating in thequasistatic limit, examining the unit cell at the upper limit ofour frequency range (1 GHz).

We use simulations because medium approximations donot accurately describe our cell’s properties. Given that ourwater inclusion of Fig. 1(a) has a volume ratio of 0.66 anddielectric constant of 81, a simple volume-weighted averageincorrectly predicts a refractive index of 2.5, while Maxwell-Garnett incorrectly predicts a refractive index of 1.1. We areworking with geometries that cannot be represented by theseapproximation models, and thus simulations are necessary foraccurate cell characterization.

A. Number of columns

To expand the number of columns in a single unit cell, webegin with a single column of r = 4.5 mm. We then dividethe single column into square arrays of columns, stepping thenumber of columns exponentially from 4 to 25. This presents adegree of freedom to our design: spacing distance d. Figure 2pictures a diagram of the 3×3 array case. While d = 5 mmand h = 28 mm throughout the simulations, we adjust r withevery array expansion to keep the volume of water consistentfor each design, using the water-volume percentage of the3×3 cell (6.60% of total unit cell volume, 1.7813×103 mm3of water per cell).

FIG. 2. (Color online) Diagram of the 3×3 column array. Thebase simulation design is shown with parameters r , h, and d .

245132-2

BROADBAND ELECTROMAGNETIC METAMATERIALS WITH . . . PHYSICAL REVIEW B 89, 245132 (2014)

1.6

1.7

1.8

1.9

2

n’

1 4 9 16 25

8

12

16

20

No. Columns

n’/n

’’

1.7

1.8

1.9

2

n’

4 6 8 10 128

10

12

14

Spacing Distance, d (mm)

(a)

(c) (d)

(b)

n’/n

’’

FIG. 3. (Color online) Parameter sweeps across (a), (c) numberof columns and (b), (d) spacing distance d . The real part of the refrac-tive index is shown in (a) and (b), while the loss factor is shown in(c) and (d).

The simulated results are shown below in Figs. 3(a)and 3(c). For an increasing number of square columns, thereis a monotonic increase in n′, as seen in Fig. 3(a). Figure 3(c)shows a monotonic decrease for the loss factor. Thus, for thesame volume of water, splitting the single column presents atradeoff by increasing n′ but also increasing n′/n′′.

The 3×3 array offers a compromise between large n′ andlow n′/n′′, so we examine a 3×3 array further.

B. Spacing distance between columns

Fixing r and h, the spacing distance d is stepped from 4 to13 mm by 1 mm increments. Seen in Fig. 3(b), as d increases, n′increases then decreases, reaching its peak around 10–12 mm.The loss [Fig. 3(d)] falls, then rises, for increasing d, inverselyrelated to n′.

Continuing our characterization, we examine thed = 10 mm model. At this value, n′ is reaching its peak, andthe columns are equidistant when multiple cells are lined uptogether. However, for applications where low loss is critical,it would be advantageous to select a model with closer columnspacing.

C. Column dimensions

The volume of water in each cell can be adjusted byvarying the dimensions of each column. Holding d = 10 mmfor the 3×3 array, we examine the effect of volume on n bydecreasing the parameters of radius and height of the cylindersindependently. We decrease r and hold h constant and viceversa, keeping the cylinders centered at the same points[see the diagram in Fig. 4(a)].

Figure 4(b) shows results for a sweep in radius with fixedheight h = 28 mm (blue) and for a sweep in height with afixed radius r = 1.5 mm (red). While an increase in volumeincreases n′ for both parameter sweeps, a maximum heightwith changes in radius provide higher n′ than a maximumradius with changes in height for the same amount of volume.This would suggest that height should be fixed to obtain thebest n′ performance.

0.6 1 1.4 1.80

100

200

300

n’/n

’’

1

1.5

2

n’

Radius SweepHeight Sweep

(a) (b)

(c)

Volume per cell (mm )3

FIG. 4. (Color online) Simulation results for parameter sweepsvarying column dimensions. (a) The two parameters: varying radius,height constant at h = 28 mm (top), and, varying height, radiusconstant at r = 1.5 mm (bottom). Both figures are shown with thesmallest simulated parameter. (b), (c) The refractive index plots.

However, examining n′/n′′ [Fig. 4(c)] shows that lossis much smaller for maximum r with changing h, andapproximately independent of changes in r for fixed h.

Thus there is a considerable tradeoff when considering anoptimal design. If volume of water (or, in particular, weight)is an important consideration, it is advantageous to maintain afixed height and vary the radius to obtain higher n′ for smallervolumes of water. However, to minimize the effects of loss,a design should maintain the largest radius possible whilevarying the height.

D. Fluid conductivity

We have a degree of freedom in the metamaterial designby selecting an appropriate fluid. We discussed two casesabove, namely, that of the LF and CF. With a large enoughconductivity, the CF behaves as a PEC inclusion. So far,we have discussed the CF in terms of the two limits ofconductivity—as either a lossless fluid (σ ≈ 0) or PEC(σ ≈ ∞). In both of these cases, as shown in Sec. II, themetamaterial structure is lossless. Introducing a finite σ causesthe metamaterial to become lossy. Because the metamaterialis lossless for both sides of the limit and we expect a finite lossfor finite σ , the loss must possess a local extremum by Rolle’stheorem. For a low-loss metamaterial, there are thus (at least)two ranges of σ values in which we should operate. We studyvariations in σ in order to examine the loss as a function ofσ using the baseline 3×3 array presented in Sec. III A. Thesimulated results are presented in Fig. 5.

As seen in Fig. 5, conductivities under 10−1 S/m and above105 S/m behave as very low-loss materials with a constant n′.Between these values, the loss in the metamaterial increasesgreatly. However, the strong electric field interaction alsoresults in a large n′. Examining the results, very conductivefluids (such as mercury, which has σ on the order of 106) couldbe used to provide a large n′ while also providing very low

245132-3

LIU, KATKO, LI, AND CUMMER PHYSICAL REVIEW B 89, 245132 (2014)

0

0.2

10−4 100 104 108

2

Conductivity (S/m)

n’ n’’

1.8

2.2

0.1

10−4 100 104 108

Conductivity (S/m)

)b()a(

FIG. 5. (Color online) Conductivity sweeps for the baseline 3×3array. (a) shows a rise, fall, then plateau of refractive index withincreasing fluid conductivity. (b) shows that there is no loss inthe structure when using fluids with very high and very lowconductivities.

loss. The saltwater we used in the experiments for this workis suboptimal for low-loss operation. However, as we noted,n′ is large for this range of σ . We note that for applicationsrequiring very low-loss metamaterials, the fluid should havevery large σ . However, if we can accept losses in order toobtain large n′, a CF such as saltwater is suitable.

IV. EXPERIMENTAL DESIGN

To fabricate and test our design, we manufactured a struc-ture that is five multichannel unit cells long in the transversedirection, pictured in Fig. 7. We make slight modificationsto the basic multichannel unit cell design of Fig. 2(a), wherer = 1.5 mm, h = 28 mm, and d = 10 mm. Using clear acrylicto hold the water channels, we set the radius to r = 1.5875 mmto accommodate a 1/8 inch drill bit in manufacturing. Columnheight was decreased to h = 25.75 mm to allow for top andbottom acrylic plates to hold the columns in place.

To make the cell reconfigurable and thus provide greaterfreedom for tunability, we chose to incorporate a base reservoirfrom which to fill and empty the fluid channels. The reservoirmeasures 30×12×2.5 mm in the k, H , and E directions,respectively. It overlaps the bottom of the columns in the E

−1

−0.5

0

n"

0

1

2

n’

0.6 0.7 0.8 0.9 10

2

4

6

8

Frequency (GHz)

ε

0

1

2

Frequency (GHz)

μ

PECPEC Base

DWDW Base

SWSW BaseSWhSWh Base

(a)

(d)(c)

(b)

0.6 0.7 0.8 0.9 1

FIG. 6. (Color online) Comparison of the 3×3 array design withbase reservoir (solid line) to original column design (dashed line) fora perfect electric conductor (PEC), distilled water (DW), saltwater(SW), and saltwater filled only halfway (SWh). Material parametersn′, n′′, real(�), and real(μ) are presented in (a)–(d), respectively.

FIG. 7. (Color online) Photographs of the fabricated structure(a) fully filled and (b) halfway filled. (c) The structure is placedin the transverse direction of the TEM waveguide.

direction, sitting 0.78 mm above the unit cell to account forthe thickness of the bottom of the acrylic plate.

Using simulation to compare the modified design to thebasic column design, Fig. 6 shows good agreement betweenthe two cases. We study PEC, saltwater (SW), saltwater filledhalfway (SWh), and distilled water (DW) inclusions.

With this reservoir in place, the fluid can be easily filled todifferent heights inside the structure from a single input valve.There is a hole in the reservoir of the top plate to allow air toescape during filling. Figure 7(a) shows the columns filled allthe way, while Fig. 7(b) shows the columns filled only halfway.

The structure is measured in a TEM waveguide, picturedin Fig. 7(c). The reservoir expands beyond the edge of thewaveguide to allow for easy access to the input valve.

V. EXPERIMENTAL RESULTS

We measure the S parameters using a vector networkanalyzer and obtain the effective material parameters, againusing the S-parameter retrieval process [15]. The structureis measured using saltwater with conductivity σ = 4 S/m,to match simulation. The filtered retrieved effective materialparameters are shown in Fig. 8.

We calibrate the experiment setup by retrieving effectivematerial parameters for a known material, rexolite, which hasn = 1.59, �r = 2.53, and μr = 1. We normalize the retrievedμr for each case to μrexolite, and multiply �r by μrexolite tomaintain n.

Figure 8 shows good agreement in n′ between measure-ments and the HFSS simulations of the structure with the basereservoir. There is slightly more loss than predicted in the upperfrequencies of the water trials, but all other material parametersshow results consistent with simulation predictions. The lown′ of air provides a baseline metric, showing that the acrylic

245132-4

BROADBAND ELECTROMAGNETIC METAMATERIALS WITH . . . PHYSICAL REVIEW B 89, 245132 (2014)

0

1

2

n’ε

0.6 0.7 0.8 0.9 10

Frequency (GHz) Frequency (GHz)

−1

−0.5

0

n’’

0

1

2

2

4

6

)b()a( Air Exp

DW SimDW Exp

SW SimSW ExpSWh SimSWh Exp(c) (d)

0.6 0.7 0.8 0.9 1

μ

FIG. 8. (Color online) Experimental data (solid line) compared to simulation data (dashed line) for the multichannel unit cell design withbase reservoir. The distilled water (DW), saltwater (SW), and saltwater filled halfway (SWh) conditions are presented. The air measurementprovides a baseline metric. Material parameters n′, n′′, real(�), and real(μ) are presented in (a)–(d), respectively. Experiment shows strongagreement to simulation.

support structure does not greatly affect the material propertiesof the liquid channels.

We demonstrate tunability in column height by taking ameasurement of the structure filled only halfway with saltwater(10.375 mm above the base reservoir). The good agreementwith simulation, seen in Fig. 8, shows that simulation canpredict the precise results of height tunability.

Tunability in fluid composition is exhibited by filling thechannels with distilled water (Fig. 8) rather than saltwater.Making predictions from the simulation of Fig. 5, decreasingconductivity from 4 S/m to about 0 S/m should decrease n′,and also decrease loss. The experimental results confirm thisprediction, showing that a nonconducting fluid can replacea conducting fluid to trade the maximum obtainable n′ forminimal loss.

Thus, after constructing a structure, we can reconfigureboth the composition and amount of fluid in the structure tosomewhat dynamically tune the effective material propertiesof the metamaterial.

VI. CONCLUSIONS

In this paper, we presented and demonstrated a nonresonantmetamaterial cell composed of liquid channels featuring finitecolumns of dielectric fluid. Liquid water was chosen for theinclusion because of its convenience and ease of tunability.The cell can be tuned by varying the height of the columnand the conductivity of the fluid. Through simulation, wecharacterized the four main degrees of design freedom of ourcell: number of columns, spacing distance between columns,dimensions of columns, and conductivity of liquid. In general,

as each parameter increases, we see an increase in the realpart of the refractive index, along with an increase in loss.Using a nonconducting fluid removes loss, but also lowers therefractive index amplitude when compared to the conductingfluid. Through simulation, an ideal conductivity range wasfound above 104 S/m, giving a high refractive index amplitudeand minimal loss.

To verify our simulation results, we fabricated and tested anarray of multichannel unit cells, with an added base reservoir toprovide easy and controlled filling of the channels. Measuringour structure with a saltwater inclusion, we obtained goodexperimental agreement to simulation. We were able to tunethe effective material properties of the metamaterial by varyingthe fill height of the saltwater columns and varying theconductivity of the fluid used. While our liquid configurationchanges did not implement a truly dynamic form of tunability,our structure offers the possibility of true dynamic tunabilitywith microfluidic approaches.

We have demonstrated a simple, tunable nonresonantmetamaterial, able to achieve n′ between 1 and 2 for avolume ratio less than 0.07. This provides an essentialtool for metamaterial designers, in particular for the designof index-only transformation optics or GRIN devices, byallowing the designer to dynamically alter the function of thedevices.

ACKNOWLEDGMENTS

This work was supported by a Multidisciplinary UniversityResearch Initiative from the US Army Research Office (GrantNo. W911NF-09-1-0539). We wish to thank Vrad Leveringfor useful discussions and fabrication assistance.

[1] J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs,Phys. Rev. Lett. 76, 4773 (1996).

[2] J. B. Pendry, A. Holden, D. Robbins, and W. Stewart,IEEE Trans. Microwave Theory Tech. 47, 2075 (1999).

245132-5

http://dx.doi.org/10.1103/PhysRevLett.76.4773http://dx.doi.org/10.1103/PhysRevLett.76.4773http://dx.doi.org/10.1103/PhysRevLett.76.4773http://dx.doi.org/10.1103/PhysRevLett.76.4773http://dx.doi.org/10.1109/22.798002http://dx.doi.org/10.1109/22.798002http://dx.doi.org/10.1109/22.798002http://dx.doi.org/10.1109/22.798002

LIU, KATKO, LI, AND CUMMER PHYSICAL REVIEW B 89, 245132 (2014)

[3] D. Schurig, J. J. Mock, and D. R. Smith, Appl. Phys. Lett. 88,041109 (2006).

[4] B.-I. Popa and S. A. Cummer, Phys. Rev. Lett. 100, 207401(2008).

[5] M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, Phys. Rev. B72, 193103 (2005).

[6] X. Xhang and Z. Liu, Nat. Mater. 7, 435 (2008).[7] D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry,

A. F. Starr, and D. R. Smith, Science 314, 977 (2006).[8] I. V. Shadrivov, S. K. Morrison, and Y. S. Kivshar, Opt. Express

14, 9344 (2006).[9] D. Huang, E. Poutrina, and D. R. Smith, Appl. Phys. Lett. 96,

104104 (2010).

[10] A. R. Katko, S. Gu, J. P. Barrett, B. I. Popa, G. Shvets, andS. A. Cummer, Phys. Rev. Lett. 105, 123905 (2010).

[11] I. E. Khodasevych, I. V. Shadrivov, D. A. Powell, W. S. T. Rowe,and A. Mitchell, Appl. Phys. Lett. 102, 031904 (2013).

[12] X. Q. Lin, T. J. Cui, J. Y. Chin, X. M. Yang, Q. Cheng, andR. Liu, Appl. Phys. Lett. 92, 131904 (2008).

[13] R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith,Science 323, 366 (2009).

[14] H. Han, L. Wu, X. Tian, D. Li, M. Yin, and Y. Wang, J. Appl.Phys. 112, 114913 (2012).

[15] X. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, Jr., andJ. A. Kong, Phys. Rev. E 70, 016608 (2004).

[16] J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).

245132-6

http://dx.doi.org/10.1063/1.2166681http://dx.doi.org/10.1063/1.2166681http://dx.doi.org/10.1063/1.2166681http://dx.doi.org/10.1063/1.2166681http://dx.doi.org/10.1103/PhysRevLett.100.207401http://dx.doi.org/10.1103/PhysRevLett.100.207401http://dx.doi.org/10.1103/PhysRevLett.100.207401http://dx.doi.org/10.1103/PhysRevLett.100.207401http://dx.doi.org/10.1103/PhysRevB.72.193103http://dx.doi.org/10.1103/PhysRevB.72.193103http://dx.doi.org/10.1103/PhysRevB.72.193103http://dx.doi.org/10.1103/PhysRevB.72.193103http://dx.doi.org/10.1038/nmat2141http://dx.doi.org/10.1038/nmat2141http://dx.doi.org/10.1038/nmat2141http://dx.doi.org/10.1038/nmat2141http://dx.doi.org/10.1126/science.1133628http://dx.doi.org/10.1126/science.1133628http://dx.doi.org/10.1126/science.1133628http://dx.doi.org/10.1126/science.1133628http://dx.doi.org/10.1364/OE.14.009344http://dx.doi.org/10.1364/OE.14.009344http://dx.doi.org/10.1364/OE.14.009344http://dx.doi.org/10.1364/OE.14.009344http://dx.doi.org/10.1063/1.3356223http://dx.doi.org/10.1063/1.3356223http://dx.doi.org/10.1063/1.3356223http://dx.doi.org/10.1063/1.3356223http://dx.doi.org/10.1103/PhysRevLett.105.123905http://dx.doi.org/10.1103/PhysRevLett.105.123905http://dx.doi.org/10.1103/PhysRevLett.105.123905http://dx.doi.org/10.1103/PhysRevLett.105.123905http://dx.doi.org/10.1063/1.4788918http://dx.doi.org/10.1063/1.4788918http://dx.doi.org/10.1063/1.4788918http://dx.doi.org/10.1063/1.4788918http://dx.doi.org/10.1063/1.2896308http://dx.doi.org/10.1063/1.2896308http://dx.doi.org/10.1063/1.2896308http://dx.doi.org/10.1063/1.2896308http://dx.doi.org/10.1126/science.1166949http://dx.doi.org/10.1126/science.1166949http://dx.doi.org/10.1126/science.1166949http://dx.doi.org/10.1126/science.1166949http://dx.doi.org/10.1063/1.4769344http://dx.doi.org/10.1063/1.4769344http://dx.doi.org/10.1063/1.4769344http://dx.doi.org/10.1063/1.4769344http://dx.doi.org/10.1103/PhysRevE.70.016608http://dx.doi.org/10.1103/PhysRevE.70.016608http://dx.doi.org/10.1103/PhysRevE.70.016608http://dx.doi.org/10.1103/PhysRevE.70.016608http://dx.doi.org/10.1103/PhysRevLett.85.3966http://dx.doi.org/10.1103/PhysRevLett.85.3966http://dx.doi.org/10.1103/PhysRevLett.85.3966http://dx.doi.org/10.1103/PhysRevLett.85.3966