Tunable Graphene Antennas for Selective Enhancement of THz-Emission

R. Filter,1, ∗ M. Farhat,1 M. Steglich,2 R. Alaee,1 C. Rockstuhl,1 and F. Lederer11Institute of Condensed Matter Theory and Solid State Optics,

Abbe Center of Photonics, Friedrich-Schiller-Universität Jena, D-07743 Jena, Germany2Laboratory Astrophysics Group of the Max Planck Institute for Astronomy,

Friedrich-Schiller-Universität Jena, D-07743 Jena, Germany

In this paper, we will introduce THz graphene antennas that strongly enhance the emissionrate of quantum systems at specific frequencies. The tunability of these antennas can be used toselectively enhance individual spectral features. We will show as an example that any weak transitionin the spectrum of coronene can become the dominant contribution. This selective and tunableenhancement establishes a new class of graphene-based THz devices, which will find applications insensors, novel light sources, spectroscopy, and quantum communication devices.

PACS numbers: 73.20.Mf, 42.50.Hz, 32.70.Cs, 33.20.-t

I. INTRODUCTION

The advance of optical antennas has led to incredi-ble new possibilities to control light-matter-interactions;including the directive emission of quantum systems orthe modification of radiative rates at which such hybridsystems emit light.1–3 The parameter usually used toquantify modified emission rates of quantum systems isthe Purcell factor F defined as F = γa

rad/γfsrad with the

radiative emission rate γrad. The superscripts “a” and“fs” denote the presence of the antenna or an emissionin free space, respectively. For a cavity, F is propor-tional to the quality factor Q and λ3/V , where λ is thewavelength and V is the mode volume. High Purcellfactors have been achieved either in high-Q resonators,tolerating larger mode volumes,4 or in systems support-ing localized surface plasmon polaritons (LSPP) with ex-tremely small mode volumes, therefore tolerating lowerQ-factors.5–8 However, since comparable Purcell factorsappear for modes at higher frequencies in most of suchimplementations, these approaches are inappropriate forthe selective enhancement of emissions at individual fre-quencies exclusively. Moreover, the impossibility to tunethe spectral response of metal-based antennas over ex-tended spectral domains is extremely restrictive for manyapplications.

Recently, graphene has been suggested as a possi-ble material that may remedy at least some of theselimitations.7 Moreover, since its operational domainwould be in the THz frequency range (ν ≈ 0.1−30 THz),it may also be used for long-needed functional devicesin the so-called THz gap. In this frequency domain,graphene offers low-loss SPPs9–11 whose effective wave-lengths are two to three orders of magnitude smaller thanthe free space wavelengths at the same frequency.12 Inaddition, the electronic properties of graphene can bewidely tuned using the electric field effect.13,14 A finaladvantage of graphene is the much weaker interactionwith light in the visible when compared to THz frequen-cies. This property is extremely useful for the selectiveenhancement of THz emission bands since optical emis-

Figure 1: (color online) A graphene antenna to selectivelyenhance THz emissions: A molecule gets excited in the vis-ible/UV. Subsequentially, it strongly emits at a single fre-quency in the THz regime. The emission frequency can betuned by adjusting the chemical potential µc.

sion bands are only marginally influenced by grapheneantennas.

A referential example for an application in the THzdomain is the identification of specific molecules, e.g., inany transmission, fluorescence, or Raman spectroscopyexperiments which rely on previously collected spec-troscopic information.15 Although graphene-based op-tical antennas were already suggested to support suchprocesses7,16, in principle, metal-based antennas can alsobe used in such applications. Therefore, the two key ques-tions to be answered are: How can graphene antennas beused to observe effects which are fundamentally inacces-sible by metal antennas and how can basic limitations ofthe latter ones be overcome?

Here we introduce a concept that allows the selectiveenhancement emissions in molecules using tunable THzantennas made of graphene. It will be shown that dis-tinct and very weak spectral features at disparate fre-quencies can be enhanced without any structural mod-ification of the antenna. The scheme we are going tointroduce provides the possibility to probe for all spec-tral features of a certain molecule; thus simplifying thespectroscopic classification of the molecule tremendously.

2

To enhance spectrally weak features, it is essential thatthe enhancement is selective, i.e. no other transitionsshall be strongly enhanced except the desired one. Thisrequires carefully designed antennas where higher-orderresonances are shifted off the spectral domain of interest.

For this reason, we will discuss the optical propertiesof a graphene-based antenna and elaborate on the detailsof the ultimate design first. All spectral properties areclearly motivated by the requirements described above.We will also discuss the interaction of the antenna with aspecific molecule and outline how its spectral propertiescan be selectively enhanced.

II. EFFICIENT AND TUNABLE GRAPHENEANTENNAS FOR STRONG SPONTANEOUS

EMISSION ENHANCEMENT

Although graphene was suggested above as an idealmaterial, naturally its linear properties do not violateKramers-Kronig relations and the dispersive propertiesare accompanied by absorption. Therefore, the rate atwhich radiation can escape an antenna-emitter systemγrad is lower than the total emission rate γtot of the emit-ter, γtot = γloss+γrad. Both quantities are related by theantenna efficiency η = γrad/γtot. The enhancement Ftot

of the total emission rate γtot of a dipole emitter in thevicinity of an antenna compared to the case of free spacecan be calculated within the Weisskopf-Wigner approxi-mation as Ftot = γa

tot/γfstot = P a

tot/Pfstot .17 Here, P a/fs

tot isthe total power emitted by the dipole. Using the latterrelation, it is possible to calculate the emission rates inthe realm of classical electrodynamics. Assuming thatthe emission in free space is free of absorption (ηfs = 1),the Purcell factor with respect to the antenna reads asF = ηaFtot. In general, Ftot depends on the positionof the dipole, its polarization, and all properties of theantenna.

In the following, we will show how to achieve a highPurcell factor for a graphene-based antenna in the THzregime at a preselected frequency exclusively. The elec-tric field effect can be used to change Graphene’s chemi-cal potential µc and consequentially its conductivity. SeeApp. A for more information and details on our numer-ical implementation of the material. We further assumethat the devices required to apply the electric field effectdo not strongly influence the overall emission properties.This simplifies the analysis to free standing elements.

The design of plasmonic antennas with high efficiencyηa at a certain frequency strongly depends on geometricalparameters. Notably, the efficiency of sub-wavelength an-tennas can be quite low. To achieve a high Purcell factor,one thus encounters a trade-off between high Ftot and ηa.Plasmonic antennas consisting of two elements generallyexhibit a larger efficiency than single element antennas.18In consequence, a configuration is considered where thedipole is situated in the center between the two elementsof the antenna. The dipole is oriented in x-direction,

6 8 10 12 14 16 18ΛHµmL

105

106

107

Ftot

1.0 µm

1.0 µm

3

2

1

0

-1

-2

-3

-4

Ex (a.u.) 103Ex (a.u.)(a) (b)

(c)

Figure 2: (color online) (a) & (c) Two circular graphene ele-ments cause a strong enhancement of the total emission rateFtot for a dark antenna mode at λ ≈ 7.9 µm (ν ≈ 38 THz).To visualize the field outside the antenna, the colormap hasbeen truncated (white regions). (b) & (c) The antenna withtwo elliptical elements exhibits by far the strongest Ftot forthe desired dipolar mode at λ ≈ 12 µm (ν ≈ 26.6 THz).The scale shown in (b) applies for all field plots with order-ofmagnitude rescalings.

i.e. parallel to the connection line of both elements. Asa result of the strong confinement of the LSPP, a smallseparation between the antenna elements is required. Ini-tially we chose an antenna design consisting of two circu-lar elements. Such a device can be fabricated e.g. usingnanosphere lithography and the single discs may be de-scribed as Fabry-Perot resonators.19,20 A configurationwith radii of 200nm and separation of 30 nm was foundto exhibit Ftot ≈ 106...7, and an efficiency η ≈ 0.4 atν ≈ 26.6THz with µc = 1 eV. However, this structurealso permits the coupling of the dipole to higher-orderresonances of the antenna, see Fig. 2 (a). These higher-order resonances, sometimes called dark modes, have ex-tremely low efficiencies since they are only weakly cou-pled to the far-field. Nevertheless, they exhibit a strongFtot and are therefore undesired. For our present sce-nario, a dark mode at ν ≈ 38THz had an enhancementexceeding that of the dipole resonance with an efficiencyof only η ≈ 0.035. Therefore, these higher-order res-onances have to be suppressed in order to render thedevice useful.

We found that the problem can be circumvented bystretching the discs in the vertical (y) direction, i.e. per-pendicular to the dipole, by a factor of two. This stretch-ing results in an increase of the effective radiating area ofthe antenna and thus of its efficiency. This is accompa-nied by a blueshift of the undesired higher-order modes.18We observed a suppression of these dark modes by severalorders of magnitude for an antenna made of two ellipticalelements. Another aspect in favor of our design is a fur-ther enhancement of Ftot, see Fig. 2 (c). Generally, Ftot

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Figure 3: (color online) (a) A plane wave with amplitude E0

excites the dipolar resonance λ ≈ 12µm of the antenna. (b)& (c): Distribution of |E (r) /E0| in the plane of the grapheneellipses (x-y-plane) and in-between at x = 0 (y-z-plane). Theregion with strong enhancement is approximately 30× 100×20nm3 (blue region). For a dipole situated here, the Purcelleffect is comparable to a placement in the center.

at other frequencies than the antenna’s dipole resonanceis two or more orders of magnitude smaller. This offsetpermits the desired selective enhancement of molecularresonances if the resonance of the antenna coincides withone of the resonances of a quantum system as it will beoutlined in the following section.

One may furthermore ask the question how strongly lo-calized the Purcell enhancement is for the found efficientantenna. Because of the plasmonic nature of the mode,one expects a rather small region of enhancement. Tomeasure the size of this region, one can use the reciprocitytheorem:21,22 Illuminating the antenna with a plane wavecorresponds to an emitting dipole at infinity. We assumethat the plane wave excitation comes from a direction ofstrong emission of the antenna’s dipole mode. Then, thefield enhancement at some position is a measure for theradiated power of a dipole at that very position. We fur-ther assume that the dipole emitter couple to the dipolemode of the antenna. Then, radiation patterns do notchange strongly for different emitter positions. Conse-quentially, the ratios of field enhancements are propor-tional to the ratios of the overall radiated power and thusthe ratio of Purcell enhancements. We have made a cor-responding calculation. As expected, we found a regionof strong interaction confined in-between the antenna, seeFig. 3.

III. THE CHANGED SPECTRUM OFCORONENE

Up to this point, the enhancement of the total emis-sion rate Ftot was referring to a dipole in the vicinity ofa graphene antenna. To demonstrate the performanceof the suggested implementation, coronene (C24H12) hasbeen chosen as an example. It belongs to the group ofpolycyclic aromatic hydrocarbon (PAH) complexes andis of both great practical and theoretical interest.23 The

molecule exhibits resonances in the THz regime and itsproperties are well-documented.24,25

The emission process of coronene can be understood asa stepwise procedure following Ref. 23. First, upon ab-sorption of a UV photon, the electronic configuration ofthe molecule is transferred into an excited state. The ex-citation will be assumed in the near ultraviolet around afrequency of ∼ 990THz (300nm) where coronene absorbsstrongly. The absorbed energy is then almost instanta-neously redistributed to the different vibrational modesof the molecule. The characteristic time scale of this pro-cess is about 10−12 s. This redistribution obeys a Planckdistribution B (ω;Tm) over the respective eigenenergies~ωi. The temperature Tm refers to the microcanonicaltemperature of the molecule and can be approximatedby Tm ≃ 2000 (E (eV ) /Nc)

0.4K with the energy of the

exciting radiation E in electronvolts and the numberNc = 24 of carbon atoms of coronene. The expression forTm can be derived from the density of states of PAH’s.It has been proven correct within an error of ≈ 10% for35 . . . 1000K.23 For coronene and the given excitation, weget Tm ≈ 990K. The emission spectrum in free space isthen given by the oscillator strengths f (ωi) weighted byB (ω;Tm) .23

Close to the antenna, the emission of the molecule isstrongly modified. We assume here, that the redistribu-tion of energy into the different eigenmodes is much fasterthan any involved radiation process. This seems reason-able since the natural emission time for THz radiation isin the order of or even bigger than one second.23 There-fore, one might hypothesize that even an enhancement ofseveral orders of magnitude for the given THz transitionsin coronene should be possible without any noticeable in-fluence on the internal redistribution dynamics. Hence,by enhancing the emission rate for just one eigenmode,the emission of the remaining ones decreases. Then, onefinds different total emission rate enhancements for eachtransition Ftot (ωi), which deviate from the Purcell fac-tors of a single dipole, i.e. Ftot (ωi) ̸= Ftot (ωi). For alinear multiresonant system, modified emission rates arerelated to each other by a sum rule.26 Because of the in-ternal redistribution dynamics of coronene, this approachcannot be used. We assume that the power emitted uponexcitation does not change if the antenna is present, i.e.,P atot =

∑i ~ωiγiF (ωi)B (ωk;Tm)

!= P fs

tot implying en-ergy conservation. Then, the enhancement of the radia-tive rate with respect to the antenna efficiency is givenby

Frad (ωi) = η (ωi) · Ftot (ωi) ·∑k ~ωkγ

fstot (ωk)B (ωk;Tm)∑

k ~ωkFtot (ωk) γfstot (ωk)B (ωk;Tm)

.(1)

Since the characteristics of the graphene antenna can betuned by changing the chemical potential µc, the en-hancement also depends on µc. If now a certain transi-tion is selectively enhanced to a large extent, Ftot (ωi) ≫Ftot (ωk) (k ̸= i), the energy supplied to the molecule

4

1000meV425meV

200meV

free molecule

10 1005020 3015 70ΝHTHzL

0.2

0.4

0.6

0.8

IntensityHa.u.L

Figure 4: (color online) The modified emission spectrum ofcoronene in the vicinity of the graphene antenna as a functionof the chemical potential µc. For reference, the green curvedisplays the emission spectrum of the bare molecule exhibit-ing several peaks with different strengths. When tuning thechemical potential by taking advantage of the electric fieldeffect, the antenna may strongly and selectively enhance onlya single emission line, so that most of the energy leaves themolecule via this transition.

will predominantly leave it by exactly this transition.This result would also hold with respect to the sumrule in Ref. 26, for which we would find FBSL

tot (ωi) =Ftot (ωi) /

∑k Ftot (ωk). Hence, it might be expected that

the shift of emission processes in favor of a single transi-tion by a selective enhancement is likely to be a genericproperty of molecular systems. The spectral resolutionof the selective enhancement is limited by the antenna.It is naturally linked to the width of the antenna reso-nance which is approximately the relaxation rate Γ. So,if Γ is smaller than the minimum spectral distance be-tween certain resonances one wishes to distinguish, theselective enhancement should work. This is the case forcoronene; current fabrication techniques allow relaxationrates in the order of a few meV or THz, respectively.14

To demonstrate this selective and tunable enhance-ment, Fig. 4 shows how the emission spectrum ofcoronene changes if the antenna resonances are tuned.Although extensive simulations were performed, only afew selective results are shown where the resonance wastuned to enhance the emission at frequencies correspond-ing to "jumping-jack"-, "drumhead"- and a "C-H-out-of-plane"-vibrational motion at 11.3 THz, 16.5 THz and26.0 THz, respectively.27 The quantitative visualizationof the spectra is performed by assuming, as usual, acertain line width for each resonance. For PAH’s, weused a linewidth of 0.15THz, which is characteristic formolecules isolated from each other.27 It can be clearlyseen that by tuning the antenna it is possible to choosethe transition which is forced to emit light into the far-field; the main goal of this contribution. Various effectsmight broaden the lines as e.g. the coupling to surfacesor collisions with other molecules. Nevertheless, it canbe safely anticipated that the general characteristics ofthe spectrum survive.

IV. CONCLUSION

In conclusion, we have suggested and verified that dueto the unique properties of graphene, antennas made

from this material can be used to selectively enhance dif-ferent molecular transitions at THz frequencies by severalorders of magnitude. The achievable efficiencies and thesuppression of undesired modes were found to stronglydepend on the actual antenna geometry. A suitable im-plementation which consists of two closely placed ellip-tical graphene elements was introduced. Using this an-tenna, weak transitions can be made dominant in theemission spectrum. The potential of graphene antennasto selectively enhance molecular transitions can clearlybe anticipated to lead to new applications in THz spec-troscopy but will also contribute to the development ofnovel sensors, highly directed single photon light sources,and quantum communication and quantum computationdevices.28

Acknowledgements

We thank Karsten Verch (www.karstenverch.com) forhis artistic view of the theory in Fig. 1. Financial sup-port by the German Federal Ministry of Education andResearch (PhoNa), by the Thuringian State Government(MeMa) and the German Science Foundation (SPP 1391Ultrafast Nano-optics) is acknowledged.

Appendix A: NUMERICAL IMPLEMENTATIONOF GRAPHENE

At temperature T , the in-plane conductivity ofgraphene can be approximated using the Kubo formula

σs (ω) = i1

π~2e2kBT

ω + i2Γ

{µc

kBT+ 2 ln

[exp

(− µc

kBT

)+ 1

]}+i

e2

4π~ln

[2 |µc| − ~ (ω + i2Γ)

2 |µc|+ ~ (ω + i2Γ)

](A1)

with the chemical potential µc and the relaxation rateΓ.7,12 Γ was taken to be 0.1meV, consistent with valuesreported earlier.29 Note that the second interband termis not temperature dependent for kBT ≪ |µc|. This is invery good approximation for the values of the chemicalpotential used in our analysis, even at room tempera-ture, where kBT ≈ 26meV. Throughout, we assumed atime dependency according to exp (−iωt). In our calcula-tions, we represented graphene as a thin conductive layerwith thickness d = 1 nm ≪ λ and relative permittivityεg (ω) = 1 + iσs (ω) / (ε0 ω d), see also Refs. 7,12,30–32and 29. It was verified that none of the results are quan-titatively affected by that finite thickness. All simula-tions were performed using the Finite-Element Methodas implemented in COMSOL.33

5

∗ URL: http://www.robertfilter.de1 P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht,

and D. W. Pohl, Science 308, 1607 (Jun. 2005).2 A. Curto, G. Volpe, et al., Science 329, 930 (2010).3 P. Anger, P. Bharadwaj, and L. Novotny, Phys. Rev. Lett.

96, 113002 (2006).4 B. Song, S. Noda, T. Asano, and Y. Akahane, Nature Na-

terials 4, 207 (2005).5 A. J. Campillo, J. D. Eversole, and H.-B. Lin, Phys. Rev.

Lett. 67, 437 (Jul 1991).6 J.-J. Greffet, M. Laroche, and F. m. c. Marquier, Phys.

Rev. Lett. 105, 117701 (2010).7 F. H. L. Koppens, D. E. Chang, and F. J. Garcia de Abajo,

Nano Letters 11, 3370 (2011).8 R. Filter, S. Mühlig, T. Eichelkraut, C. Rockstuhl, and

F. Lederer, Phys. Rev. B 86, 035404 (2012).9 H. Boehm, A. Clauss, U. Hofmann, and G. Fischer, Z.

Naturforsch. B 17, 150 (1962).10 K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang,

Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A.Firsov, Science 306, 666 (2004).

11 A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S.Novoselov, and A. K. Geim, Rev. Mod. Phys. 81, 109 (Jan2009).

12 G. Hanson, Journal of Applied Physics 103, 064302 (2008).13 Y.-J. Yu, Y. Zhao, S. Ryu, L. E. Brus, K. S. Kim, and

P. Kim, Nano Letters 9, 3430 (2009).14 L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao,

H. Bechtel, X. Liang, A. Zettl, Y. Shen, et al., NatureNanotechnology 6, 630 (2011).

15 W. Schumacher, M. Kühnert, P. Rösch, and J. Popp, Jour-nal of Raman Spectroscopy 42, 383 (2011).

16 W. Xu, X. Ling, J. Xiao, M. Dresselhaus, J. Kong, H. Xu,Z. Liu, and J. Zhang, Proceedings of the National Academyof Sciences 109, 9281 (2012).

17 W. Vogel and D. G. Welsch, Quantum Optics (Wiley,

2006).18 L. Rogobete, F. Kaminski, M. Agio, and V. Sandoghdar,

Opt. Lett. 32, 1623 (Jun 2007).19 C. X. Cong, T. Yu, Z. H. Ni, L. Liu, Z. X. Shen, and

W. Huang, The Journal of Physical Chemistry C 113, 6529(2009).

20 R. Filter, J. Qi, C. Rockstuhl, and F. Lederer, Phys. Rev.B 85, 125429 (2012).

21 C. Balanis, Antenna Theory: Analysis and Design, 3rd ed.(J. Wiley, New York, 2005).

22 R. Esteban, M. Laroche, and J. Greffet, Journal of AppliedPhysics 105, 033107 (2009).

23 A. Tielens, The physics and chemistry of the interstellarmedium (Cambridge Univ Pr, 2005).

24 S. R. Langhoff, The Journal of Physical Chemistry 100,2819 (1996).

25 M. Steglich, C. Jäger, G. Rouillé, F. Huisken, H. Mutschke,and T. Henning, The Astrophysical Journal Letters 712,L16 (2010).

26 S. M. Barnett and R. Loudon, Phys. Rev. Lett. 77, 2444(1996).

27 A. Mattioda, A. Ricca, J. Tucker, C. Bauschlicher, andL. Allamandola, The Astronomical Journal 137, 4054(2009).

28 C. Rockstuhl and W. Zhang, Nature Photonics 3, 130(2009).

29 A. Vakil and N. Engheta, Science 332, 1291 (2011).30 G. Y. Slepyan, S. A. Maksimenko, A. Lakhtakia, O. Yev-

tushenko, and A. V. Gusakov, Phys. Rev. B 60, 17136 (Dec1999).

31 V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, Journalof Physics: Condensed Matter 19, 026222 (2007).

32 P.-Y. Chen and A. Alu, ACS Nano 5, 5855 (2011).33 “COMSOL Multiphysics 3.5,” comsol.com.