Perfect subwavelength fishnetlike metamaterial-based film terahertz absorbers

D. Yu. Shchegolkov, A. K. Azad, J. F. O’Hara, and E. I. SimakovLos Alamos National Laboratory, Los Alamos, New Mexico 87545, USA

�Received 16 June 2010; revised manuscript received 14 October 2010; published 16 November 2010�

We present two different designs of robust, easily manufactured metamaterial-based films of subwavelengththickness capable of full absorption of incident terahertz radiation at certain frequencies. Both designs allow achoice between the total absorption of all polarizations or only one linear polarization while the other polar-ization is reflected. Even if the films are optimized for normal incidence, the absorption remains greater than99% for angles up to �35° in the TE and up to �65° in the TM case. In the first design, the maximumabsorption frequency shifts considerably with angle, and in the second design it is independent of angle.

DOI: 10.1103/PhysRevB.82.205117 PACS number�s�: 78.68.�m, 41.20.�q, 78.20.Ci

I. INTRODUCTION

In the past few years, the metamaterials concept has be-come a distinct paradigm by which some electromagneticmaterials and devices are born. In one common definitionmetamaterials are artificial media with engineered electricpermittivities � and magnetic permeabilities � �Refs. 1–3�obtained through geometric structuring of natural materialssuch as metals and insulators. Structuring is assumed to besufficiently smaller than a wavelength so that “effective” ma-terial parameters may be assumed, a notion that must beapproached with some caution4,5 but is often valid to theextent that diffraction effects may be neglected at the funda-mental operational frequency. In this interpretation, nonre-flecting media with wave impedance �� /� equal to that offree space6 may be envisioned. Creating reflectionless inter-faces is part of making high-performance absorbers, so natu-rally the metamaterial approach demands some investigation.

Many kinds of absorbers were developed over the pasthalf century based on frequency-selective surfaces �FSSs��Ref. 7� which are closely related to metamaterials. Theseabsorbers, often called Salisbury screens or Jaumann absorb-ers, operate on the same principle as optical antireflectioncoatings. Numerous stratified layers are stacked to createpartially reflected and transmitted components of the incidentwave. The transmitted component eventually reflects off bythe backmost layer, a metallic ground plane, and thereafterrecombines with the originally reflected wave except with a� phase shift, thereby creating perfect cancellation of theoverall reflection if absolute amplitudes of these waves arealso the same. The ground plane ensures zero transmission sothat the wave energy must be finally absorbed. Variations onthis theme enhance bandwidth or desensitize the dependenceon angle of incidence.

There are already many known metamaterial film ab-sorbers, including subwavelength film absorbers, whichwere demonstrated to have close to 100% absorptionefficiency.6,8–11 The main advantage of these designs is theirsmall thickness, on the order of � /10, whereas reported FSS-based absorbers are often � /2,7 though additional thicknessis often beneficial in improving bandwidth. Despite the im-maturity of terahertz �THz� technology, initial metamaterialabsorber work has been demonstrated in this frequency re-gime. At the beginning these were mostly bilayer absorbers

and both layers contained fine parts which required precisealignment between layers.6,9 Presently, they are being dis-placed by fully nontransparent single-layer absorbers havinga ground plane on the back.8,11,12 In this paper we presentimproved designs of THz absorbers that are superior to theprevious designs due to less complicated structure ofmetamaterial cells and greatly simplified fabrication.

II. DESIGN OF AN ABSORBER WITHFISHNETLIKE SURFACE

Our proposed absorbers are composed of a simple metal-lic FSS on a lossy dielectric film and a metal ground plane.Figure 1�a� shows one of our absorbers that utilizes a FSS ofa fishnet structure consisting of alternating metal and dielec-tric layers with rectangular openings. In our designs we use asolid gold ground plate on the back side of the absorber tolimit the absorber thickness and prevent any transmission.The first absorber design has a gold fishnet pattern on thefront side and the spacing between gold layers is filled witha lossy dielectric. In our case this dielectric was polyimide

(a) (b)

1210·6.11210·0.11110·3.71110·0.51110·3.31110·0.2

1010·3.4910·9.2

3mW

1110·1.1

(a) (b)

1210·6.11210·0.11110·3.71110·0.51110·3.31110·0.2

1010·3.4910·9.2

3mW

1110·1.1

EH

S

FIG. 1. �Color online� The elementary cell of the metamaterialfilm: an absorbing polyimide layer �dark gray, blue� is contained inbetween two layers of gold �light gray, yellow�, one of which has arectangular opening in it. The absorber consists of a two-dimensional array of the above elementary cells �a�. Losses in thecenter section of the film, proportional to the distribution of theelectric field energy density �b�: the central area corresponds to theminimum loss and two side areas are zones with maximum powerdissipation.

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with a loss tangent of 0.05 and permittivity of 3.4. The prin-ciple of operation is similar to absorbers based on FSS. Bywave cancellation the metamaterial has no reflection at theresonant frequency, and thus all of the power is absorbed.Importantly, our design retains a highly subwavelength thick-ness that is achieved by utilizing fishnetlike metamaterialcells having highly localized resonant electromagnetic fields.The absorption frequency can be easily tuned by geometricscaling or by varying only two parameters which, for ex-ample, can be the smaller dimension of the rectangular open-ing and the thickness of the dielectric layer, provided theparameters are still within operational limits.

The robustness of our design is determined by two fac-tors. First, the absorber performance depends mostly on theintegral geometric characteristics of the structure, so thatsmall variations in the openings from rectangular shape pre-serving the areas do not have any considerable effect on theperformance. Second, the electromagnetic power is dissi-pated mostly in the dielectric medium and only a very smallfraction is dissipated in the metal. This makes it less sensi-tive to the conducting properties of the metal surfaces, whichare harder to control. The simulated loss distribution insidethe polyimide is shown in Fig. 1�b�. All simulations wereperformed in CST MICROWAVE STUDIO®.13

III. FABRICATION AND TESTING

The fishnetlike absorber shown in Fig. 1�a� was fabricatedusing standard microfabrication. A bottom-up approach wasutilized. First, the ground metal plane was fabricated bye-beam evaporation of 200-nm-thick gold �Au� film on a1-mm-thick silicon substrate. On top of the Au film a thicklayer of polyimide was spin coated and subsequently cured at250 °C for 1 h. The cured-polyimide film had a thickness of23 �m. The metallic fishnet pattern was formed on the poly-imide layer using another 200-nm-thick Au layer. The size ofthe rectangular hole in the fishnet films was 150 �m�75 �m with a periodicity of 180 �m. The THz absorp-tion of this fishnet absorber was experimentally measuredusing a terahertz time domain spectrometer in reflectiongeometry.14 Our terahertz time-domain spectroscopy systemallowed us to measure reflection in the range of angles ofincidence from 20° to 60° and to use either the TE or the TMlinear polarizations.15 Independently, the sample could alsobe oriented so that the electric field had components parallelto either the short or the long sides of the rectangular fishnetopenings. Due to the small period of the pattern, diffractiveeffects did not occur at the frequencies of interest corre-sponding to peak absorption and there could only be a specu-lar reflection. Dimensions of the fabricated absorber are pre-

sented in Table I. According to simulations, the thickness of23 �m of the polyimide layer of the sample was bigger thanthe optimum value of 16 �m for the straight incidence but itwas close to the optimum for the 20° incident angle, espe-cially for the TE incidence case, as it can be seen from thesimulation data �Fig. 2�. In the experiment, the absorber be-haved very similarly to simulation, the absorption was closeto the 100% up to the very large angles of incidence �Figs.3�a� and 3�b��. The range of angles in which the absorptionremained very high was bigger for the TM incident waves�Fig. 3�a�� than for the TE waves incident in the other plane�Fig. 3�b��. In both cases, the electric field had components

TABLE I. Measured parameters of the fabricated absorber de-picted in Fig. 1�a�.

Period of the structure 180 �m

Rectangular openings dimensions 150�2 �m�75�2 �m

Polyimide layer thickness 23�2 �m

Gold layer thickness 0.3 �m

0.4 0.5 0.6 0.7 0.8

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Pabs./Pinc. ϑ = 0, 10, 20, 30, 40, 50, 60 deg

Frequency [THz]

0 deg60 deg

0.4 0.5 0.6 0.7 0.8 0.9

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Pabs./Pinc.

Frequency [THz]

ϑ = 0, 10, 20, 30, 40, 50, 60 deg

0 deg60

deg

(a)

(b)

FIG. 2. �Color online� Simulated absorption of metafilm whichwas used in the experiment with parameters from Table I for differ-ent angles of incidence for �a� the TM and �b� the TE incidentwaves. The polyimide thickness was different from its optimumvalue for straight incidence.

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parallel to the short side of the rectangular structure, asshown in Fig. 1�a�. Conversely, the absorber showed almostno absorption �less than 5% in the range between 0.5 and 1THz� when the electric field component was oriented parallelto the longer sides of the rectangular fishnet opening �Fig.3�c��.

IV. ALTERNATIVE DESIGNS OF ABSORBERS

We also came up with other absorber designs. Our seconddesign of the absorber �simulations only� is based on a natu-ral generalization of the fishnet structure pattern for polariza-tion insensitivity �Fig. 4�a��. Similar to the previous version�Fig. 1�a��, it can also be optimized to provide the full ab-sorption at any chosen frequency and works for a wide range

of incidence angles �Fig. 4�b��. The absorber thickness is11.5 �m and corresponds to a one-way wave phase advancein the polyimide as small as about 25° at 1 THz �Table II�.

In both design versions �Figs. 1�a� and 4�a��, the fre-quency corresponding to the absorption peak dependsstrongly on the angle of incidence �Figs. 3�a�, 3�b�, and4�b��. This can benefit some applications such as mechani-cally frequency tunable absorbers but can be a disadvantageto others. Our third design almost totally eliminates this an-gular dependence by implementing a complementary surfacepattern: noncontinuous stripes or crosses, both shown in Fig.5.

Note that the electromagnetic field orientation in Fig. 5�a�is different from the one in Fig. 1�a�. According to simula-tions, both absorbers, with rectangular openings and withmetal stripes, reflect about 99% of power for waves of thecomplementary field orientation.

The absorber in Fig. 5�b� resembles circuit analog absorb-ers in Ref. 7, which are known to have one of the best band-width for given thickness, the principle difference in our caseis that the loss is not in the metallic cross but inside of thedielectric. It also resembles a single layer of a bulk negativerefractive index material composed of pairs of parallel metalcrosses with a subwavelength gap in between the crossesdescribed in Ref. 16.

The simulated absorber performance of the cross-patterned film with parameters from Table III for angles ofincidence up to 80° is presented in Fig. 6. Peak absorptionfrequency shifts almost negligibly with incidence angle and

Frequency (THz)0.4 0.5 0.6 0.7 0.8 0.9 1.0

0.10.2

0.3

0.4

0.50.60.70.8

0.91.0

0.10.2

0.3

0.4

0.50.60.70.8

0.91.0

Abs

orpt

ion

Abs

orpt

ion

0.4 0.5 0.6 0.7 0.8 0.9 1.0

2030405060

Frequency (THz)

2030405060

deg

deg

20 deg

60 deg

Frequency (THz)0.4 0.5 0.6 0.7 0.8 0.9 1.0

0.10.2

0.3

0.4

0.50.60.70.8

0.91.0

0.10.2

0.3

0.4

0.50.60.70.8

0.91.0

Abs

orpt

ion

Abs

orpt

ion

0.4 0.5 0.6 0.7 0.8 0.9 1.0

2030405060

Frequency (THz)

2030405060

deg

deg

20 deg

60 degA

mpl

itud

eR

efle

ctio

n

0.2

0.4

0.6

0.8

1.0

1.00.80.60.4 0.5 0.7 0.9Frequency (THz) (c)

(b)

(a)

FIG. 3. �Color online� Measured absorption for �a� the TM and�b� the TE incident waves for different angles of incidence. Maxi-mum absorption frequency is redshifted with increasing angle forthe TM case, and blueshifted for the TE case. In �c� the measuredamplitude reflection coefficients are compared for the TM wavesincident at 20° with electric field component along the longer �thin-ner line, green� or shorter �thicker line, blue� sides of the rectangu-lar hole.

0.7 0.8 0.9 1 1.10

0.2

0.4

0.6

0.8

1Pabs./Pinc.

Frequency (THz)

ϑ= 0, 10 , 20, 30, 40, 50, 60 , 70 , 80 deg

0 deg

(a) (b)

FIG. 4. �Color online� The elementary cell of the polarizationinsensitive metamaterial film absorber. Dark gray �blue� is polyim-ide, light gray �yellow� is gold �a�. Corresponding absorptivity as afunction of frequency for different angles of incidence, , for theTM wave obtained from simulations for the parameters from TableII �b�. The loss in metal is neglected. The perfect absorption takesplace at both 0° angle and at about 55°.

TABLE II. Design parameters of the absorber depictured in Fig.4.

Period of the structure 125 �m

Cross opening dimensions 108 �m�length��28�width� �m

Polyimide layer thickness 11.5 �m

Metal layer thickness 0.2 �m

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the shift has the opposite sign compared to the first set ofabsorbers.

V. DISCUSSION AND EXPLANATION OF THE RESULTS

We have developed a simple physical model which ex-plains the subwavelength thickness and different frequencyshifts with the angle of incidence of the above absorber de-signs. First, let us consider a standard quarter-wavelengthdielectric Fabry-Perot resonant cavity with one side open andthe other side with a metallic mirror �Fig. 7�a��. If an opensurface is replaced with an impedance surface the resonantfrequency of the cavity will change. In order to bring theresonant frequency back to the desired value one has tomodify the cavity’s thickness �Fig. 7�b��. Depending on thesign of the reflection coefficient from the impedance surface,the cavity thickness will have to be either increased or de-creased to satisfy the relationship

2kL − � + imp = 0, �1�

where k=n� /c is a real part of wave propagation constant, Lis the thickness of the dielectric layer in the cavity, n is thereal part of refraction index, and imp is the phase of reflec-tion coefficient from the impedance surface. A specially de-signed impedance surface can provide a positive value ofimp partially compensating the 180° phase shift from thereflection from the metal surface. Thus, the length of thecavity which is necessary to satisfy Eq. �1� will be greatlyreduced.

As an example, let us consider a linearly polarized plane-wave incident from a semi-infinite space filled with a poly-imide dielectric �Fig. 7�c�� on a surface with a fishnet struc-ture with the dimensions of Table I. The phase change due tothe fishnet structure, imp0, becomes positive at above 0.71

GHz �Fig. 7�d�� and increases rapidly with frequency makingthe resonant length of the cavity much smaller than a quarterwavelength at these frequencies. It has to be mentioned,though, that the proximity of the metal wall on the other side

TABLE III. Design parameters of the absorber depictured inFigs. 5�b� and 6.

Period of the structure 115 �m

Metal cross dimensions 88 �m�length��10.5�width� �m

Polyimide layer thickness 10 �m

Metal layer thickness 0.2 �m

0.9 0.95 1 1.05 1.10

0.10.20.30.40.50.60.70.80.9

1

Frequency (THz)

Absorptivity for the TE incidence

0 deg10 deg20 deg30 deg40 deg50 deg60 deg70 deg

0.9 0.95 1 1.05 1.10

0.10.20.30.40.50.60.70.80.9

1

Frequency (THz)

Absorptivity for the TM incidence

0 deg10 deg20 deg30 deg40 deg50 deg60 deg70 deg

(a) (b)

FIG. 6. �Color online� Absorptivity of a cross-patterned filmshown in Fig. 5�b� with parameters from Table III as a function offrequency for different incidence angles and the two linear polar-izations. The loss in metal is neglected.

02

1

=−>π

εkL

02 =+− impkL ϕπL

impϕ 0impϕ

(a) (b) (c)

(d)

0.65 0.7 0.75 0.8 0.85

-90

-45

0

45

90

135

Frequency (THz)

ϕimp0 (deg)Phase of reflection coefficient,

FIG. 7. Dielectric quarter-wavelength Fabry-Perot resonatorwith one metal mirror and one open side �a�. The resonator thick-ness can be adjusted by introducing an impedance surface at theopen side �b�. Straight wave incidence from a half-infinite dielectricspace on an impedance surface �c� and the dependence of the phaseof the reflection coefficient on frequency for the impedance surfacewith a fishnet structure on the polyimide �d�.

HH

EESSSSSS

(a) (b)

FIG. 5. �Color online� Perfect absorbers of a complementaryshape to those shown in Figs. 1�a� and 4�a�. Periodic cell of theabsorber film suitable for a single linear polarization �a�, and for anarbitrary polarization �b� of the incident waves. Dark gray �blue� ispolyimide, light gray �yellow� is gold.

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of the resonator affects the properties of the impedance sur-face and thus the value of imp0 is somewhat different fromimp in an ideal quantitative analysis. Therefore, in this con-figuration it may be even more adequate to consider thewhole absorber film as a resonant surface, and not separatethe fishnet structure from the metal layer on the back.

The dependence of the peak absorption frequency on theangle of incidence for the incoming wave can be explainedby the following. According to Ref. 17, there may be twophysical mechanisms underlying the effect of the fishnetstructure being able to change the surface impedance. Thefishnet structure may resonate either in localized resonances,that is when resonating fields of neighboring metafilm cellsdo not interact, or in a surface wave, that is when there is noway to excite fields in one cell without exciting them in allthe others. For the surface waves, the resonant frequency isinversely proportional to the lattice period, and for the local-ized resonances it is independent of the lattice period. Oursimulations with small lattice period variations show that thefrequency of the absorption peak is inversely proportional tothe lattice period for the absorbers of Figs. 1�a� and 4�a�.However, it is almost independent of the lattice period for theabsorbers of Figs. 5�a� and 5�b�. Thus we can conclude thatthe absorbers of Figs. 1�a� and 4�a� resonate as a surfacewave, which is very common for structures having a largemetallization area with an in-plane period approaching thewavelength.17 Conversely, the absorbers of Figs. 5�a� and5�b� behave as a set of single resonators. The absence ofstrong coupling between neighboring resonators makes theabsorbers in Fig. 5 less sensitive to the incident angles ofradiation, and makes the peak absorption frequency indepen-dent of the angle of incidence. Note that as opposed to astandard Fabry-Perot cavity, where the resonant frequencyshifts with incidence angle because of the effective length, L,change in Eq. �1�, for subwavelength absorbers L is a verysmall factor to be accounted for.

The redshift and the blueshift of the maximum absorptionfrequency for the TM and the TE incidence �Figs. 3�a� and3�b�� can be explained by the following. Since the neighbor-ing cells of the absorbers in Figs. 1�a� and 4�a� interact as asurface wave, there is a coupling in between different reso-

nators �fishnet holes�. We noticed that neighboring resonatorsin the direction of magnetic field oscillate in phase, andneighboring resonators in the direction of electric field oscil-late in antiphase being described in terms of electric field.When the excitation wave is incident at a nonzero angle,there is a phase shift between the neighboring cells and con-sequently a phase shift between oscillations. Since oscilla-tions in-phase and out-of-phase have different dispersion,any phase change leads to different response: the blueshiftfor initially antiphased oscillations and to the redshift forinitially in phased oscillations.

VI. CONCLUSION

To conclude, we have designed a set of four perfect sub-wavelength film absorbers, which are easy to manufactureand have unique angular and polarization properties favor-able for different applications. We built one of the absorbersand carried out a thorough experiment in the THz frequencyband which fully confirmed simulated absorber performanceand proved its robustness to fabrication imperfections. Fi-nally, to explain absorbers operation we also provided asimple theory based on a Fabry-Perot resonator approach.

Notably, all the designs described above can be modifiedto dynamically tune the maximum absorption frequency byusing dielectrics with variable permittivity or to dynamicallycontrol the magnitude of the absorption peak by using semi-conductors with variable conductivity in place of metal.

The metafilm absorbers may be utilized in THzbolometer-type detectors, emissivity spectrum modifiers,nonreflecting surfaces, thermal imaging, and narrow-bandTHz sources. Low self-heat capacity makes these absorbers,combined with thermodetectors, especially attractive for pre-cise frequency-selective detection of THz radiation.

ACKNOWLEDGMENTS

The authors benefitted from discussions with AntoinetteTaylor and N.A. Moody and gratefully acknowledge the sup-port of the U.S. Department of Energy through the LANL/LDRD Program.

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