Abstract

We show numerically that both coherent perfect absorption and transparency can be realized in a monolayer graphene. The graphene film, doped and patterned with a periodical array of holes, can support plasmonic resonances in the Mid-infrared range. Under the illumination of two counter-propagating coherent optical beams, resonant optical absorption may be tuned continuously from 99.93% to less than 0.01% by controlling their relative phase which gives a modulation contrast of 40 dB (about 30 dB for transmission). The phenomenon provides a versatile platform for manipulating the interaction between light and graphene and may serve applications in optical modulators, transducers, sensors and coherent detectors.

© 2014 Optical Society of America

Optical absorption plays an important role in a variety of applications such as photodetectors and photovoltaics. As a result, there has recently been lots of interest in realizing total light absorption and two different routes have generally been employed. Firstly, one can take advantage of diffusion or multi-scattering of light on very disordered lossy surfaces such as carbon nanotube arrays [1, 2]. The second method exploits the critical coupling effect [3]. When the coupling rate is equal to the dissipative rate of the structure and other energy loss channels such as diffraction and polarization conversion are blocked, critical coupling will lead to perfect absorption [4, 5]. Such kind of perfect absorption has been realized in various micro- and nano-structures such as plasmonic surfaces, metallic particle arrays and metamaterials [611].

Most perfect absorbers have only one port and critical coupling happens under the illumination of one beam. A generation to the two port situation leads to the so-called ’Coherent Perfect Absorption (CPA)’ [12]. Similar to the critical coupling effect, CPA relys on the coherent interference of light where two coherent beams are incident on the absorber from opposite sides and the reflected light of one beam interfere with the transmitted light of the other and vice versa [13, 14]. CPA was first realized using a silicon slab cavity [15], and has recently been reported in composite absorptive films, planar metamaterials, waveguides and so on [1623]. Coherent absorption provides an additional flexibility to tune the absorption by changing the relative phase of two beams and shows promising potentials for applications ranging from nanoscale light manipulations to data processing [19, 21, 24, 25].

Graphene, a single layer of carbon atoms arranged in plane with a honey comb lattice, shows promising potentials in optics and optoelectronics [26] and has recently attracted great attentions in many applications, such as photodetectors, optical modulators, tunable filters and polarizers [2730]. Even though the optical absorption of monolayer graphene is quite weak (about 2.3% in the visible range), enhanced absorption by unstructured graphene can be realized by placing it in an optical cavity or exploiting the critical coupling effect [3134]. Moreover, doped and patterned graphene can support localized plasmonic resonances in the infrared and THz ranges which significantly enhance the absorption [3537]. Specifically, complete light absorption has been reported in an array of doped graphene disks backed by a metallic mirror or a dielectric with high optical permittivity [38]. Graphene plasmonics provide an effective route to enhance light-graphene interactions.

Here we show CPA in a nanostructured graphene film. The graphene film, patterned with periodical arrays of holes, displays a strong plasmonic resonance in the Mid-infrared wavelength range. By controlling the relative phase of the two coherent beams incident on the graphene film, we are able to either enhance or suppress the resonant absorption in the graphene. Besides CPA, its opposite effect, coherent perfect transparency (CPT), can also be realized due to the extremely thin thickness of the graphene sheet which is less than one ten-thousandth of a wavelength thick.

It has been known that there is a universal limit to absorption by a thin layer with its thickness much smaller than the wavelength of light [38, 39]. We consider a thin film at the interface between two media, medium 1 and medium 2, with different refractive indices, n1 and n2. If light impinges on the film from medium 1 at normal incidence, the combined reflection and transmission coefficients are

R=r+(1+r)η,T=t+tη
where η is the self-consistent amplitude by the thin film, while r and t are the Fresnel coefficients of the bare n1 | n2 interface
r=n1n2n1+n2,t=2n1n1+n2

The absorption is

A=1|R|2n2n1|T|2=1|r+(1+r)η|2n2n1|t+tη|2]

The condition of maximum absorption is ∂A/∂η = 0 (2A/∂2η is real and negative) and we get

η=12
which leads to the absorption limit Amax = 1/(1 + χ), where χ = n2/n1. The corresponding reflection and transmission coefficients are
R=n2n1+n2,T=n1n1+n2

For any thin layer with symmetric environments, i.e., n1 = n2, the limit to maximum absorption is Amax = 0.5. The maximum absorption can be increased in asymmetric environments and most perfect absorbers employ a back mirror to block the transmission channel.

Now let’s consider two counter-propagating coherent beams, beam 1 and beam 2, impinge on the thin film at normal incidence from opposite sides, medium 1 and medium 2, respectively. We assume the electric field amplitude of beam 1 is 1 and that of beam 2 is α. The reflected part of one beam will interfere with the transmitted part of the other one and vice versa. Therefore, the amplitude of scattered light from each side of the thin film will be

s1=R1+T2αeiφ,s2=T1+R2αeiφ
where φ is the phase difference of beam 1 and beam 2. R1 and T1, R2 and T2 are the reflection and transmission coefficients of beam 1 and beam 2 respectively, which are given by Eq. (5)
R1=n2n1+n2,T1=n1n1+n2
R2=n1n1+n2,T2=n2n1+n2
So the coherent absorption is
Acoh=1|s1|2+χ|s2|21+χα2
Using Eqs. (6), (7) and (8), we have
Acoh=1χ1+χ1+α22αcosφ1+χα2

Apparently, Acoh gets its maximum of 1 only if α = 1 and φ = 2 (N is an integer). Therefore if a thin film can reach the incoherent absorption limit, coherent perfect absorption can be achieved under the illumination of two counter-propagating coherent beams with equal field amplitudes and a relative phase of zero. Once the amplitude of two coherent beams are fixed to be the same, the coherent absorption depends on their phase difference and can be tuned continuously between Amincoh=[(1χ)/(1+χ)]2 (at φ = (2N + 1)π) and Acohmax=1.

In this part, we study numerically the coherent absorption in a nanostructured graphene. The numerical simulations are conducted using a fully three-dimensional finite element technique (in Comsol MultiPhysics). In the simulation, the graphene is modelled as a conductive surface without thickness [38, 40, 41]. The optical conductivity of graphene can be derived within the random-phase approximation (RPA) in the local limit [42, 43]

σω=2e2kBTπh¯2iω+iτ1ln[2cosh(EF2kBT)]+e24h¯[12+1πarctan(h¯ω2EF2kBT)i2πln(h¯ω+2EF)2(h¯ω2EF)2+4(kBT)2]

Here kB is the Boltzmann constant, T is the temperature, ω is the frequency of light, τ is the carrier relaxation lifetime, and EF is the Fermi level. The first term in Eq. (11) corresponds to intra-band transitions and the second term is related to inter-band transitions. We restrict our calculations to energies below 0.2 eV in order to avoid the contribution of inter-band contribution and to the Fermi level EF ≫ 2kBT. Equation (11) reduces to the Drude model if we neglect both inter-band transitions and the effect of temperature (T = 0) [44, 45]

σω=e2EFπh¯2iω+iτ1
where EF depends on the concentration of charged doping and τ=μEF/evF2, where vF ≈ 1 × 106 m/s is the Fermi velocity and μ is the dc mobility. Here we use a moderate measured mobility μ = 10000 cm2 ·V−1 · s−1 [46]. The Fermi level of graphene is assumed to be EF = 0.6 eV which corresponds to an doping density of about 2.6 × 1013 cm−2 and may be realized by electrostatic or chemical doping [46, 47].

Figure 1(a) shows the schematic of coherent absorption in a freestanding graphene film patterned with a periodical array of square holes. Two coherent beams are incident on the graphene film from opposite sides and the coherent absorption is controlled by their relative phase. The geometric parameters of the patterned graphene are shown in Fig. 1(b). The width of hole is L = 220 nm and the period of unit cell is P = 400 nm in both x- and y- directions.

 figure: Fig. 1

Fig. 1 (a) Schematic of coherent absorption in a nanostructured graphene film. Two coherent optical beams impinge on the graphene film from opposite sides at normal incidence. Part of the energy may be absorbed while others will be scattered from both sides which can be controlled by changing the relative phase of the two beams. (b) A unit cell of the nanostructured graphene film with geometric parameters. The period is P = 400 nm and the size of hole is 220 nm.

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Figure 2 is the simulated spectra under incoherent as well as coherent illuminations. When a single beam of light is illuminated on the patterned graphene film at normal incidence, part of the energy will be absorbed while others will either be reflected or transmitted, as shown in Fig. 2(a). There is a plasmonic resonance centered at λ = 8.476 μm in the studied spectral range with a maximum absorption of A = 49.97%. When two coherent beams with equal intensities are incident on the graphene from opposite sides, they will interfere with each other, leading to coherent absorption. Now the absorption depends on the relative phase of the two counter-propagating beams.

 figure: Fig. 2

Fig. 2 Incoherent and coherent absorption in the nanostructured graphene film. (a) Simulated reflection, transmission and absorption of the nanostructured graphene film under the illumination of only one beam at normal incidence (or when the two input beams are incoherent). (b) Normalized total scattering output intensities |S|2 under the illumination of two counter-propagating coherent beams with the same intensities. The solid blue line and dashed red line show for parity-even mode and parity-odd mode, respectively. The geometric parameters of the patterned graphene is show in Fig. 1(b). Equation (12) is used to describe the conductivity of graphene and the Fermi level of graphene is assumed to beEF = 0.6 eV.

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Figure 2(b) shows the normalized total output intensities Stot = 1 − Atot (total input energy minus absorption) when their relative phase equals 0 and π, respectively. As the two beams have no phase difference, they are symmetric for the graphene film and form an parity-even mode. In this situation, the interference of the two beams suppresses their scattering and the absorption is enhanced (graphene is at the anti-node of the interference pattern formed by the two coherent beams). Particularly, the total output intensity drops more than 30 dB (A = 99.93%) at the plasmonic resonance of the nanostructured graphene film. On the contrary, they form an parity-odd mode when their phase difference is π and show reduced absorption due to constructive interference of scattered light at the two sides of the graphene film (graphene is at the node of the interference pattern formed by the two coherent beams). As a result, the normalized total output intensity is nearly unitary (A < 0.01%) at the whole studied spectral range. Thus, coherent absorption allows control of resonant absorption in the nanostructured graphene film, either an increase to nearly 100% (corresponding to CPA) or a suppression to almost zero (corresponding to CPT).

Figure 3 shows the normalized coherent absorption in the nanostructured graphene as a function of the relative phase. At the resonance wavelength of 8.476 μm, the coherent absorption varies continuously from 99.93% to less than 0.01% as the relative phase changes from 0 to π (see Fig. 3(a)), giving a modulation contrast of 40 dB. At the off-resonance wavelength, coherent perfect absorption cannot be realized and the maximum coherent absorption is about two times of the incoherent absorption (see Fig. 3(b)). Besides the variation of absorption, we also see transfer of energy between scattering at the two sides of the graphene film (S1 and S2) as the relative phase changes because of the interference between the reflected part of each beam with the transmitted part of the other.

 figure: Fig. 3

Fig. 3 Phase modulation of coherent absorption. Two coherent beams with equal intensities impinge on the nanostructured graphene film from opposite sides. (a) At the resonance wavelength of 8.476 μm, the coherent absorption decreases from 99.93% to less than 0.01% as the relative phase changes from 0 to π. (b) At the off-resonance wavelength of 8.4 μm, the coherent absorption (blue solid curve) varies from about 41% to less than 0.01%. Other energy will be scattered from the two sides of graphene (dashed red curve and dashed green curve).

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Coherent absorption in nanostructured graphene is a quite robust phenomenon and can also be implemented for graphene with asymmetric environments, i.e., on a substrate. We consider the same nanostructured graphene on a semi-infinite substrate with a refractive index of n = 1.5. To make our modeling more practical, instead of Eq. (12), here we use Eq. (11) for the conductivity of graphene in which both the intra-band contribution and temperature effect are considered. As in previous sections, we assume EF = 0.6 eV and μ = 10000 cm2 · V−1 · s−1. The temperature is assumed to be 300 K. Because of the substrate, the resonance wavelength redshifts from 8.476 μm to 10.61 μm. As the dielectric environment now becomes asymmetric for graphene, the incoherent absorption of patterned graphene film is 38.16% for light incident on the graphene from the air side and 57.23 % for light incident on the graphene from the substrate side at the resonance, respectively.

Figure 4 shows the interferometric control of coherent absorption in the nanostructured graphene on a substrate at the resonance wavelength of 10.61 μm. Two coherent beams with equal electric field amplitudes (relative intensity I1/I2 = 1/1.5) impinge on the graphene film from the air and the substrate side, respectively. The normalized coherent absorption varies from 95.4% to 3.8% as the relative phase changes from 0 to π. Here the minimum coherent absorption is very close to the ideal lower limit of Acohmin=[(1χ)/(1+χ)]2=4% while maximum absorption is slightly below coherent perfect absorption. This is because the maximum incoherent absorption of our nanostructured graphene at the resonance is a bit lower than the limit, i.e. 40% and 60% for incidence from the air and substrate side, respectively. Coherent perfect absorption may be realized by optimizing the doping level of graphene and the design of the nanostructures. We can also reduce the minimum absorption with a trade off of decreasing the maximum absorption by changing the relative intensities of input beams, which may increase the modulation contrast. For example, the coherent absorption here can be modulated between about 94.4% and 0.96% for two coherent beams with equal intensities (I1/I2 = 1/1).

 figure: Fig. 4

Fig. 4 Phase modulation of coherent absorption in a nanostructured graphene film with asymmetric environments. The graphene is on a semi-infinite substrate with a refractive index of 1.5. Two coherent beams, with equal field amplitudes, are incident on the graphene at normal direction from opposite sides.

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In summary, we have studied coherent absorption in a single layer of nanostructured graphene. The thickness of monolayer graphene is about 3.4 Ao which is less than one ten-thousandth of a wavelength. The coherent absorption can be tuned continuously from nearly 99.93% (corresponding to CPA) to less than 0.01% (corresponding to CPT) depending on the relative phase of the two counter-propagating coherent beams. This phenomenon relies on interplay of plasmonic resonances and the interference of optical beams on the patterned graphene and provides functionality that can be implemented freely across a broad Mid-infrared to THz range by varying the structural design and graphene doping level. Coherent absorption provides a very versatile platform for manipulating the interaction between graphene and light. It may serve applications in optical modulators, transducers, sensors or coherent detectors.

Acknowledgments

This work was supported by National Natural Science Foundation of China [Grant Nos. 11304389, 61177051 and 61205087] and the State Key Program for Basic Research of China [Grant No. 2012CB933501].

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References

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  1. Z.-P. Yang, L. Ci, J. A. Bur, S.-Y. Lin, P. M. Ajayan, “Experimental observation of an extremely dark material made by a low-density nanotube array,” Nano Lett. 8, 446–451 (2008).
    [Crossref] [PubMed]
  2. K. Mizuno, J. Ishii, H. Kishida, Y. Hayamizu, S. Yasuda, D. N. Futaba, M. Yumura, K. Hata, “A black body absorber from vertically aligned single-walled carbon nanotubes,” Proc. Natl. Acad. Sci. USA 106, 6044–6047 (2009).
    [Crossref] [PubMed]
  3. M. Cai, O. Painter, K. J. Vahala, “Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system,” Phys. Rev. Lett. 85, 74 (2000).
    [Crossref] [PubMed]
  4. K. Y. Bliokh, Y. P. Bliokh, V. Freilikher, S. SavelŁv, F. Nori, “Colloquium: Unusual resonators: Plasmonics, metamaterials, and random media,” Rev. Mod. Phys. 80, 1201 (2008).
    [Crossref]
  5. J. Zhang, J. Ou, K. MacDonald, N. Zheludev, “Optical response of plasmonic relief meta-surfaces,” Journal of Optics 14, 114002 (2012).
    [Crossref]
  6. T. V. Teperik, F. G. De Abajo, A. Borisov, M. Abdelsalam, P. Bartlett, Y. Sugawara, J. Baumberg, “Omnidirectional absorption in nanostructured metal surfaces,” Nat. Photonics 2, 299–301 (2008).
    [Crossref]
  7. N. Landy, S. Sajuyigbe, J. Mock, D. Smith, W. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100, 207402 (2008).
    [Crossref] [PubMed]
  8. N. Liu, M. Mesch, T. Weiss, M. Hentschel, H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10, 2342–2348 (2010).
    [Crossref] [PubMed]
  9. X. Liu, T. Starr, A. F. Starr, W. J. Padilla, “Infrared spatial and frequency selective metamaterial with near-unity absorbance,” Phys. Rev. Lett. 104, 207403 (2010).
    [Crossref] [PubMed]
  10. J. Hao, J. Wang, X. Liu, W. J. Padilla, L. Zhou, M. Qiu, “High performance optical absorber based on a plasmonic metamaterial,” Appl. Phys. Lett. 96, 251104 (2010).
    [Crossref]
  11. K. Aydin, V. E. Ferry, R. M. Briggs, H. A. Atwater, “Broadband polarization-independent resonant light absorption using ultrathin plasmonic super absorbers,” Nat. Comm. 2, 517 (2011).
    [Crossref]
  12. Y. Chong, L. Ge, H. Cao, A. D. Stone, “Coherent perfect absorbers: time-reversed lasers,” Phys. Rev. Lett. 105, 053901 (2010).
    [Crossref] [PubMed]
  13. A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Elect. Lett. 36, 321–322 (2000).
    [Crossref]
  14. L. Ken, “Phase effect on guided resonance in photonic crystal slabs,” Chin. Phys. Lett. 22, 2294 (2005).
    [Crossref]
  15. W. Wan, Y. Chong, L. Ge, H. Noh, A. D. Stone, H. Cao, “Time-reversed lasing and interferometric control of absorption,” Science 331, 889–892 (2011).
    [Crossref] [PubMed]
  16. S. Longhi, “Coherent perfect absorption in a homogeneously broadened two-level medium,” Phys. Rev. A 83, 055804 (2011).
    [Crossref]
  17. S. Dutta-Gupta, O. J. Martin, S. Dutta Gupta, G. Agarwal, “Controllable coherent perfect absorption in a composite film,” Opt. Express 20, 1330–1336 (2012).
    [Crossref] [PubMed]
  18. S. Feng, K. Halterman, “Coherent perfect absorption in epsilon-near-zero metamaterials,” Phys. Rev. B 86, 165103 (2012).
    [Crossref]
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2014 (3)

X. Fang, M. L. Tseng, J.-Y. Ou, K. F. MacDonald, D. P. Tsai, N. I. Zheludev, “Ultrafast all-optical switching via coherent modulation of metamaterial absorption,” Appl. Phys. Lett. 104, 141102 (2014).
[Crossref]

Z. Zhu, C. Guo, K. Liu, J. Zhang, W. Ye, X. Yuan, S. Qin, “Electrically tunable polarizer based on anisotropic absorption of graphene ribbons,” Appl. Phys. A 114, 1017–1021 (2014).

J. Piper, S. Fan, “Total absorption in a graphene monolayer in the optical regime by critical coupling with a photonic crystal guided resonance,” ACS Photonics 1, 347353 (2014).
[Crossref]

2013 (5)

N. Papasimakis, S. Thongrattanasiri, N. I. Zheludev, F. G. de Abajo, “The magnetic response of graphene split-ring metamaterials,” Light: Sci. Appl. 2, e78 (2013); doi:
[Crossref]

Y. Yao, M. A. Kats, P. Genevet, N. Yu, Y. Song, J. Kong, F. Capasso, “Broad electrical tuning of graphene-loaded plasmonic antennas,” Nano Lett. 13, 1257–1264 (2013).
[Crossref] [PubMed]

N. Gutman, A. A. Sukhorukov, Y. Chong, C. M. de Sterke, “Coherent perfect absorption and reflection in slow-light waveguides,” Opt. Lett. 38, 4970–4973 (2013).
[Crossref] [PubMed]

R. Bruck, O. L. Muskens, “Plasmonic nanoantennas as integrated coherent perfect absorbers on soi waveguides for modulators and all-optical switches,” Opt. Express 21, 27652–27661 (2013).
[Crossref]

Z. Fang, S. Thongrattanasiri, A. Schlather, Z. Liu, L. Ma, Y. Wang, P. M. Ajayan, P. Nordlander, N. J. Halas, F. J. García de Abajo, “Gated tunability and hybridization of localized plasmons in nanostructured graphene,” ACS Nano 7, 2388–2395 (2013).
[Crossref] [PubMed]

2012 (12)

M. Furchi, A. Urich, A. Pospischil, G. Lilley, K. Unterrainer, H. Detz, P. Klang, A. M. Andrews, W. Schrenk, G. Strasser, T. Mueller, “Microcavity-integrated graphene photodetector,” Nano Lett. 12, 2773–2777 (2012).
[Crossref] [PubMed]

J.-T. Liu, N.-H. Liu, J. Li, X. J. Li, J.-H. Huang, “Enhanced absorption of graphene with one-dimensional photonic crystal,” Appl. Phys. Lett. 101, 052104 (2012).
[Crossref]

H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, F. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol. 7, 330–334 (2012).
[Crossref] [PubMed]

S. Thongrattanasiri, F. H. Koppens, F. J. G. de Abajo, “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett. 108, 047401 (2012).
[Crossref] [PubMed]

A. Grigorenko, M. Polini, K. Novoselov, “Graphene plasmonics,” Nat. Photonics 6, 749–758 (2012).
[Crossref]

R. Alaee, M. Farhat, C. Rockstuhl, F. Lederer, “A perfect absorber made of a graphene micro-ribbon meta-material,” Opt. Express 20, 28017–28024 (2012).
[Crossref] [PubMed]

J. Zhang, J. Ou, K. MacDonald, N. Zheludev, “Optical response of plasmonic relief meta-surfaces,” Journal of Optics 14, 114002 (2012).
[Crossref]

S. Dutta-Gupta, O. J. Martin, S. Dutta Gupta, G. Agarwal, “Controllable coherent perfect absorption in a composite film,” Opt. Express 20, 1330–1336 (2012).
[Crossref] [PubMed]

S. Feng, K. Halterman, “Coherent perfect absorption in epsilon-near-zero metamaterials,” Phys. Rev. B 86, 165103 (2012).
[Crossref]

H. Noh, Y. Chong, A. D. Stone, H. Cao, “Perfect coupling of light to surface plasmons by coherent absorption,” Phys. Rev. Lett. 108, 186805 (2012).
[Crossref] [PubMed]

M. Pu, Q. Feng, M. Wang, C. Hu, C. Huang, X. Ma, Z. Zhao, C. Wang, X. Luo, “Ultrathin broadband nearly perfect absorber with symmetrical coherent illumination,” Opt. Express 20, 2246–2254 (2012).
[Crossref] [PubMed]

J. Zhang, K. F. MacDonald, N. I. Zheludev, “Controlling light-with-light without nonlinearity,” Light: Sci. Appl. 1, e18 (2012); doi:
[Crossref]

2011 (5)

K. Aydin, V. E. Ferry, R. M. Briggs, H. A. Atwater, “Broadband polarization-independent resonant light absorption using ultrathin plasmonic super absorbers,” Nat. Comm. 2, 517 (2011).
[Crossref]

W. Wan, Y. Chong, L. Ge, H. Noh, A. D. Stone, H. Cao, “Time-reversed lasing and interferometric control of absorption,” Science 331, 889–892 (2011).
[Crossref] [PubMed]

S. Longhi, “Coherent perfect absorption in a homogeneously broadened two-level medium,” Phys. Rev. A 83, 055804 (2011).
[Crossref]

A. Vakil, N. Engheta, “Transformation optics using graphene,” Science 332, 1291–1294 (2011).
[Crossref] [PubMed]

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64–67 (2011).
[Crossref] [PubMed]

2010 (5)

F. Bonaccorso, Z. Sun, T. Hasan, A. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4, 611–622 (2010).
[Crossref]

Y. Chong, L. Ge, H. Cao, A. D. Stone, “Coherent perfect absorbers: time-reversed lasers,” Phys. Rev. Lett. 105, 053901 (2010).
[Crossref] [PubMed]

N. Liu, M. Mesch, T. Weiss, M. Hentschel, H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10, 2342–2348 (2010).
[Crossref] [PubMed]

X. Liu, T. Starr, A. F. Starr, W. J. Padilla, “Infrared spatial and frequency selective metamaterial with near-unity absorbance,” Phys. Rev. Lett. 104, 207403 (2010).
[Crossref] [PubMed]

J. Hao, J. Wang, X. Liu, W. J. Padilla, L. Zhou, M. Qiu, “High performance optical absorber based on a plasmonic metamaterial,” Appl. Phys. Lett. 96, 251104 (2010).
[Crossref]

2009 (3)

K. Mizuno, J. Ishii, H. Kishida, Y. Hayamizu, S. Yasuda, D. N. Futaba, M. Yumura, K. Hata, “A black body absorber from vertically aligned single-walled carbon nanotubes,” Proc. Natl. Acad. Sci. USA 106, 6044–6047 (2009).
[Crossref] [PubMed]

F. Xia, T. Mueller, Y.-m. Lin, A. Valdes-Garcia, P. Avouris, “Ultrafast graphene photodetector,” Nat. Nanotechnol. 4, 839–843 (2009).
[Crossref] [PubMed]

M. Jablan, H. Buljan, M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80, 245435 (2009).
[Crossref]

2008 (5)

G. W. Hanson, “Quasi-transverse electromagnetic modes supported by a graphene parallel-plate waveguide,” Jour. Appl. Phys. 104, 084314 (2008).
[Crossref]

Z.-P. Yang, L. Ci, J. A. Bur, S.-Y. Lin, P. M. Ajayan, “Experimental observation of an extremely dark material made by a low-density nanotube array,” Nano Lett. 8, 446–451 (2008).
[Crossref] [PubMed]

K. Y. Bliokh, Y. P. Bliokh, V. Freilikher, S. SavelŁv, F. Nori, “Colloquium: Unusual resonators: Plasmonics, metamaterials, and random media,” Rev. Mod. Phys. 80, 1201 (2008).
[Crossref]

T. V. Teperik, F. G. De Abajo, A. Borisov, M. Abdelsalam, P. Bartlett, Y. Sugawara, J. Baumberg, “Omnidirectional absorption in nanostructured metal surfaces,” Nat. Photonics 2, 299–301 (2008).
[Crossref]

N. Landy, S. Sajuyigbe, J. Mock, D. Smith, W. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100, 207402 (2008).
[Crossref] [PubMed]

2007 (2)

L. Falkovsky, S. Pershoguba, “Optical far-infrared properties of a graphene monolayer and multilayer,” Phys. Rev. B 76, 153410 (2007).
[Crossref]

L. Falkovsky, A. Varlamov, “Space-time dispersion of graphene conductivity,” Eur. Phys. Jour. B 56, 281–284 (2007).
[Crossref]

2005 (1)

L. Ken, “Phase effect on guided resonance in photonic crystal slabs,” Chin. Phys. Lett. 22, 2294 (2005).
[Crossref]

2004 (1)

K. S. Novoselov, A. K. Geim, S. Morozov, D. Jiang, Y. Zhang, S. Dubonos, I. Grigorieva, A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[Crossref] [PubMed]

2000 (2)

M. Cai, O. Painter, K. J. Vahala, “Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system,” Phys. Rev. Lett. 85, 74 (2000).
[Crossref] [PubMed]

A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Elect. Lett. 36, 321–322 (2000).
[Crossref]

1947 (1)

Abdelsalam, M.

T. V. Teperik, F. G. De Abajo, A. Borisov, M. Abdelsalam, P. Bartlett, Y. Sugawara, J. Baumberg, “Omnidirectional absorption in nanostructured metal surfaces,” Nat. Photonics 2, 299–301 (2008).
[Crossref]

Adam, S.

F. Liu, Y. Chong, S. Adam, M. Polini, “Gate-tunable coherent perfect absorption of terahertz radiation in graphene,” arXiv preprint arXiv:1402.2368 (2014).

Agarwal, G.

Ajayan, P. M.

Z. Fang, S. Thongrattanasiri, A. Schlather, Z. Liu, L. Ma, Y. Wang, P. M. Ajayan, P. Nordlander, N. J. Halas, F. J. García de Abajo, “Gated tunability and hybridization of localized plasmons in nanostructured graphene,” ACS Nano 7, 2388–2395 (2013).
[Crossref] [PubMed]

Z.-P. Yang, L. Ci, J. A. Bur, S.-Y. Lin, P. M. Ajayan, “Experimental observation of an extremely dark material made by a low-density nanotube array,” Nano Lett. 8, 446–451 (2008).
[Crossref] [PubMed]

Alaee, R.

Andrews, A. M.

M. Furchi, A. Urich, A. Pospischil, G. Lilley, K. Unterrainer, H. Detz, P. Klang, A. M. Andrews, W. Schrenk, G. Strasser, T. Mueller, “Microcavity-integrated graphene photodetector,” Nano Lett. 12, 2773–2777 (2012).
[Crossref] [PubMed]

Atwater, H. A.

K. Aydin, V. E. Ferry, R. M. Briggs, H. A. Atwater, “Broadband polarization-independent resonant light absorption using ultrathin plasmonic super absorbers,” Nat. Comm. 2, 517 (2011).
[Crossref]

Avouris, P.

H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, F. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol. 7, 330–334 (2012).
[Crossref] [PubMed]

F. Xia, T. Mueller, Y.-m. Lin, A. Valdes-Garcia, P. Avouris, “Ultrafast graphene photodetector,” Nat. Nanotechnol. 4, 839–843 (2009).
[Crossref] [PubMed]

Aydin, K.

K. Aydin, V. E. Ferry, R. M. Briggs, H. A. Atwater, “Broadband polarization-independent resonant light absorption using ultrathin plasmonic super absorbers,” Nat. Comm. 2, 517 (2011).
[Crossref]

Bartlett, P.

T. V. Teperik, F. G. De Abajo, A. Borisov, M. Abdelsalam, P. Bartlett, Y. Sugawara, J. Baumberg, “Omnidirectional absorption in nanostructured metal surfaces,” Nat. Photonics 2, 299–301 (2008).
[Crossref]

Baumberg, J.

T. V. Teperik, F. G. De Abajo, A. Borisov, M. Abdelsalam, P. Bartlett, Y. Sugawara, J. Baumberg, “Omnidirectional absorption in nanostructured metal surfaces,” Nat. Photonics 2, 299–301 (2008).
[Crossref]

Bliokh, K. Y.

K. Y. Bliokh, Y. P. Bliokh, V. Freilikher, S. SavelŁv, F. Nori, “Colloquium: Unusual resonators: Plasmonics, metamaterials, and random media,” Rev. Mod. Phys. 80, 1201 (2008).
[Crossref]

Bliokh, Y. P.

K. Y. Bliokh, Y. P. Bliokh, V. Freilikher, S. SavelŁv, F. Nori, “Colloquium: Unusual resonators: Plasmonics, metamaterials, and random media,” Rev. Mod. Phys. 80, 1201 (2008).
[Crossref]

Bonaccorso, F.

F. Bonaccorso, Z. Sun, T. Hasan, A. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4, 611–622 (2010).
[Crossref]

Borisov, A.

T. V. Teperik, F. G. De Abajo, A. Borisov, M. Abdelsalam, P. Bartlett, Y. Sugawara, J. Baumberg, “Omnidirectional absorption in nanostructured metal surfaces,” Nat. Photonics 2, 299–301 (2008).
[Crossref]

Briggs, R. M.

K. Aydin, V. E. Ferry, R. M. Briggs, H. A. Atwater, “Broadband polarization-independent resonant light absorption using ultrathin plasmonic super absorbers,” Nat. Comm. 2, 517 (2011).
[Crossref]

Bruck, R.

Buljan, H.

M. Jablan, H. Buljan, M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80, 245435 (2009).
[Crossref]

Bur, J. A.

Z.-P. Yang, L. Ci, J. A. Bur, S.-Y. Lin, P. M. Ajayan, “Experimental observation of an extremely dark material made by a low-density nanotube array,” Nano Lett. 8, 446–451 (2008).
[Crossref] [PubMed]

Cai, M.

M. Cai, O. Painter, K. J. Vahala, “Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system,” Phys. Rev. Lett. 85, 74 (2000).
[Crossref] [PubMed]

Cao, H.

H. Noh, Y. Chong, A. D. Stone, H. Cao, “Perfect coupling of light to surface plasmons by coherent absorption,” Phys. Rev. Lett. 108, 186805 (2012).
[Crossref] [PubMed]

W. Wan, Y. Chong, L. Ge, H. Noh, A. D. Stone, H. Cao, “Time-reversed lasing and interferometric control of absorption,” Science 331, 889–892 (2011).
[Crossref] [PubMed]

Y. Chong, L. Ge, H. Cao, A. D. Stone, “Coherent perfect absorbers: time-reversed lasers,” Phys. Rev. Lett. 105, 053901 (2010).
[Crossref] [PubMed]

Capasso, F.

Y. Yao, M. A. Kats, P. Genevet, N. Yu, Y. Song, J. Kong, F. Capasso, “Broad electrical tuning of graphene-loaded plasmonic antennas,” Nano Lett. 13, 1257–1264 (2013).
[Crossref] [PubMed]

Chandra, B.

H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, F. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol. 7, 330–334 (2012).
[Crossref] [PubMed]

Chong, Y.

N. Gutman, A. A. Sukhorukov, Y. Chong, C. M. de Sterke, “Coherent perfect absorption and reflection in slow-light waveguides,” Opt. Lett. 38, 4970–4973 (2013).
[Crossref] [PubMed]

H. Noh, Y. Chong, A. D. Stone, H. Cao, “Perfect coupling of light to surface plasmons by coherent absorption,” Phys. Rev. Lett. 108, 186805 (2012).
[Crossref] [PubMed]

W. Wan, Y. Chong, L. Ge, H. Noh, A. D. Stone, H. Cao, “Time-reversed lasing and interferometric control of absorption,” Science 331, 889–892 (2011).
[Crossref] [PubMed]

Y. Chong, L. Ge, H. Cao, A. D. Stone, “Coherent perfect absorbers: time-reversed lasers,” Phys. Rev. Lett. 105, 053901 (2010).
[Crossref] [PubMed]

F. Liu, Y. Chong, S. Adam, M. Polini, “Gate-tunable coherent perfect absorption of terahertz radiation in graphene,” arXiv preprint arXiv:1402.2368 (2014).

Ci, L.

Z.-P. Yang, L. Ci, J. A. Bur, S.-Y. Lin, P. M. Ajayan, “Experimental observation of an extremely dark material made by a low-density nanotube array,” Nano Lett. 8, 446–451 (2008).
[Crossref] [PubMed]

de Abajo, F. G.

N. Papasimakis, S. Thongrattanasiri, N. I. Zheludev, F. G. de Abajo, “The magnetic response of graphene split-ring metamaterials,” Light: Sci. Appl. 2, e78 (2013); doi:
[Crossref]

T. V. Teperik, F. G. De Abajo, A. Borisov, M. Abdelsalam, P. Bartlett, Y. Sugawara, J. Baumberg, “Omnidirectional absorption in nanostructured metal surfaces,” Nat. Photonics 2, 299–301 (2008).
[Crossref]

de Abajo, F. J. G.

S. Thongrattanasiri, F. H. Koppens, F. J. G. de Abajo, “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett. 108, 047401 (2012).
[Crossref] [PubMed]

de Sterke, C. M.

Dennison, D.

Detz, H.

M. Furchi, A. Urich, A. Pospischil, G. Lilley, K. Unterrainer, H. Detz, P. Klang, A. M. Andrews, W. Schrenk, G. Strasser, T. Mueller, “Microcavity-integrated graphene photodetector,” Nano Lett. 12, 2773–2777 (2012).
[Crossref] [PubMed]

Dubonos, S.

K. S. Novoselov, A. K. Geim, S. Morozov, D. Jiang, Y. Zhang, S. Dubonos, I. Grigorieva, A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[Crossref] [PubMed]

Dutta Gupta, S.

Dutta-Gupta, S.

Engheta, N.

A. Vakil, N. Engheta, “Transformation optics using graphene,” Science 332, 1291–1294 (2011).
[Crossref] [PubMed]

Falkovsky, L.

L. Falkovsky, S. Pershoguba, “Optical far-infrared properties of a graphene monolayer and multilayer,” Phys. Rev. B 76, 153410 (2007).
[Crossref]

L. Falkovsky, A. Varlamov, “Space-time dispersion of graphene conductivity,” Eur. Phys. Jour. B 56, 281–284 (2007).
[Crossref]

Fan, S.

J. Piper, S. Fan, “Total absorption in a graphene monolayer in the optical regime by critical coupling with a photonic crystal guided resonance,” ACS Photonics 1, 347353 (2014).
[Crossref]

Fang, X.

X. Fang, M. L. Tseng, J.-Y. Ou, K. F. MacDonald, D. P. Tsai, N. I. Zheludev, “Ultrafast all-optical switching via coherent modulation of metamaterial absorption,” Appl. Phys. Lett. 104, 141102 (2014).
[Crossref]

Fang, Z.

Z. Fang, S. Thongrattanasiri, A. Schlather, Z. Liu, L. Ma, Y. Wang, P. M. Ajayan, P. Nordlander, N. J. Halas, F. J. García de Abajo, “Gated tunability and hybridization of localized plasmons in nanostructured graphene,” ACS Nano 7, 2388–2395 (2013).
[Crossref] [PubMed]

Farhat, M.

Feng, Q.

Feng, S.

S. Feng, K. Halterman, “Coherent perfect absorption in epsilon-near-zero metamaterials,” Phys. Rev. B 86, 165103 (2012).
[Crossref]

Ferrari, A.

F. Bonaccorso, Z. Sun, T. Hasan, A. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4, 611–622 (2010).
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X. Fang, M. L. Tseng, J.-Y. Ou, K. F. MacDonald, D. P. Tsai, N. I. Zheludev, “Ultrafast all-optical switching via coherent modulation of metamaterial absorption,” Appl. Phys. Lett. 104, 141102 (2014).
[Crossref]

Tseng, M. L.

X. Fang, M. L. Tseng, J.-Y. Ou, K. F. MacDonald, D. P. Tsai, N. I. Zheludev, “Ultrafast all-optical switching via coherent modulation of metamaterial absorption,” Appl. Phys. Lett. 104, 141102 (2014).
[Crossref]

Tulevski, G.

H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, F. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol. 7, 330–334 (2012).
[Crossref] [PubMed]

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M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64–67 (2011).
[Crossref] [PubMed]

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M. Furchi, A. Urich, A. Pospischil, G. Lilley, K. Unterrainer, H. Detz, P. Klang, A. M. Andrews, W. Schrenk, G. Strasser, T. Mueller, “Microcavity-integrated graphene photodetector,” Nano Lett. 12, 2773–2777 (2012).
[Crossref] [PubMed]

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M. Furchi, A. Urich, A. Pospischil, G. Lilley, K. Unterrainer, H. Detz, P. Klang, A. M. Andrews, W. Schrenk, G. Strasser, T. Mueller, “Microcavity-integrated graphene photodetector,” Nano Lett. 12, 2773–2777 (2012).
[Crossref] [PubMed]

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M. Cai, O. Painter, K. J. Vahala, “Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system,” Phys. Rev. Lett. 85, 74 (2000).
[Crossref] [PubMed]

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A. Vakil, N. Engheta, “Transformation optics using graphene,” Science 332, 1291–1294 (2011).
[Crossref] [PubMed]

Valdes-Garcia, A.

F. Xia, T. Mueller, Y.-m. Lin, A. Valdes-Garcia, P. Avouris, “Ultrafast graphene photodetector,” Nat. Nanotechnol. 4, 839–843 (2009).
[Crossref] [PubMed]

Varlamov, A.

L. Falkovsky, A. Varlamov, “Space-time dispersion of graphene conductivity,” Eur. Phys. Jour. B 56, 281–284 (2007).
[Crossref]

Wan, W.

W. Wan, Y. Chong, L. Ge, H. Noh, A. D. Stone, H. Cao, “Time-reversed lasing and interferometric control of absorption,” Science 331, 889–892 (2011).
[Crossref] [PubMed]

Wang, C.

Wang, F.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64–67 (2011).
[Crossref] [PubMed]

Wang, J.

J. Hao, J. Wang, X. Liu, W. J. Padilla, L. Zhou, M. Qiu, “High performance optical absorber based on a plasmonic metamaterial,” Appl. Phys. Lett. 96, 251104 (2010).
[Crossref]

Wang, M.

Wang, Y.

Z. Fang, S. Thongrattanasiri, A. Schlather, Z. Liu, L. Ma, Y. Wang, P. M. Ajayan, P. Nordlander, N. J. Halas, F. J. García de Abajo, “Gated tunability and hybridization of localized plasmons in nanostructured graphene,” ACS Nano 7, 2388–2395 (2013).
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N. Liu, M. Mesch, T. Weiss, M. Hentschel, H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10, 2342–2348 (2010).
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H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, F. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol. 7, 330–334 (2012).
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H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, F. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol. 7, 330–334 (2012).
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F. Xia, T. Mueller, Y.-m. Lin, A. Valdes-Garcia, P. Avouris, “Ultrafast graphene photodetector,” Nat. Nanotechnol. 4, 839–843 (2009).
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H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, F. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol. 7, 330–334 (2012).
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Z.-P. Yang, L. Ci, J. A. Bur, S.-Y. Lin, P. M. Ajayan, “Experimental observation of an extremely dark material made by a low-density nanotube array,” Nano Lett. 8, 446–451 (2008).
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K. Mizuno, J. Ishii, H. Kishida, Y. Hayamizu, S. Yasuda, D. N. Futaba, M. Yumura, K. Hata, “A black body absorber from vertically aligned single-walled carbon nanotubes,” Proc. Natl. Acad. Sci. USA 106, 6044–6047 (2009).
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Z. Zhu, C. Guo, K. Liu, J. Zhang, W. Ye, X. Yuan, S. Qin, “Electrically tunable polarizer based on anisotropic absorption of graphene ribbons,” Appl. Phys. A 114, 1017–1021 (2014).

Yin, X.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64–67 (2011).
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Y. Yao, M. A. Kats, P. Genevet, N. Yu, Y. Song, J. Kong, F. Capasso, “Broad electrical tuning of graphene-loaded plasmonic antennas,” Nano Lett. 13, 1257–1264 (2013).
[Crossref] [PubMed]

Yuan, X.

Z. Zhu, C. Guo, K. Liu, J. Zhang, W. Ye, X. Yuan, S. Qin, “Electrically tunable polarizer based on anisotropic absorption of graphene ribbons,” Appl. Phys. A 114, 1017–1021 (2014).

Yumura, M.

K. Mizuno, J. Ishii, H. Kishida, Y. Hayamizu, S. Yasuda, D. N. Futaba, M. Yumura, K. Hata, “A black body absorber from vertically aligned single-walled carbon nanotubes,” Proc. Natl. Acad. Sci. USA 106, 6044–6047 (2009).
[Crossref] [PubMed]

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M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64–67 (2011).
[Crossref] [PubMed]

Zhang, J.

Z. Zhu, C. Guo, K. Liu, J. Zhang, W. Ye, X. Yuan, S. Qin, “Electrically tunable polarizer based on anisotropic absorption of graphene ribbons,” Appl. Phys. A 114, 1017–1021 (2014).

J. Zhang, K. F. MacDonald, N. I. Zheludev, “Controlling light-with-light without nonlinearity,” Light: Sci. Appl. 1, e18 (2012); doi:
[Crossref]

J. Zhang, J. Ou, K. MacDonald, N. Zheludev, “Optical response of plasmonic relief meta-surfaces,” Journal of Optics 14, 114002 (2012).
[Crossref]

Zhang, X.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64–67 (2011).
[Crossref] [PubMed]

Zhang, Y.

K. S. Novoselov, A. K. Geim, S. Morozov, D. Jiang, Y. Zhang, S. Dubonos, I. Grigorieva, A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
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Zhao, Z.

Zheludev, N.

J. Zhang, J. Ou, K. MacDonald, N. Zheludev, “Optical response of plasmonic relief meta-surfaces,” Journal of Optics 14, 114002 (2012).
[Crossref]

Zheludev, N. I.

X. Fang, M. L. Tseng, J.-Y. Ou, K. F. MacDonald, D. P. Tsai, N. I. Zheludev, “Ultrafast all-optical switching via coherent modulation of metamaterial absorption,” Appl. Phys. Lett. 104, 141102 (2014).
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N. Papasimakis, S. Thongrattanasiri, N. I. Zheludev, F. G. de Abajo, “The magnetic response of graphene split-ring metamaterials,” Light: Sci. Appl. 2, e78 (2013); doi:
[Crossref]

J. Zhang, K. F. MacDonald, N. I. Zheludev, “Controlling light-with-light without nonlinearity,” Light: Sci. Appl. 1, e18 (2012); doi:
[Crossref]

S. A. Mousavi, E. Plum, J. Shi, N. I. Zheludev, “Coherent control of optical activity and optical anisotropy of thin metamaterials,” arXiv preprint arXiv:1312.0414 (2013).

Zhou, L.

J. Hao, J. Wang, X. Liu, W. J. Padilla, L. Zhou, M. Qiu, “High performance optical absorber based on a plasmonic metamaterial,” Appl. Phys. Lett. 96, 251104 (2010).
[Crossref]

Zhu, W.

H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, F. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol. 7, 330–334 (2012).
[Crossref] [PubMed]

Zhu, Z.

Z. Zhu, C. Guo, K. Liu, J. Zhang, W. Ye, X. Yuan, S. Qin, “Electrically tunable polarizer based on anisotropic absorption of graphene ribbons,” Appl. Phys. A 114, 1017–1021 (2014).

ACS Nano (1)

Z. Fang, S. Thongrattanasiri, A. Schlather, Z. Liu, L. Ma, Y. Wang, P. M. Ajayan, P. Nordlander, N. J. Halas, F. J. García de Abajo, “Gated tunability and hybridization of localized plasmons in nanostructured graphene,” ACS Nano 7, 2388–2395 (2013).
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ACS Photonics (1)

J. Piper, S. Fan, “Total absorption in a graphene monolayer in the optical regime by critical coupling with a photonic crystal guided resonance,” ACS Photonics 1, 347353 (2014).
[Crossref]

Appl. Phys. A (1)

Z. Zhu, C. Guo, K. Liu, J. Zhang, W. Ye, X. Yuan, S. Qin, “Electrically tunable polarizer based on anisotropic absorption of graphene ribbons,” Appl. Phys. A 114, 1017–1021 (2014).

Appl. Phys. Lett. (3)

X. Fang, M. L. Tseng, J.-Y. Ou, K. F. MacDonald, D. P. Tsai, N. I. Zheludev, “Ultrafast all-optical switching via coherent modulation of metamaterial absorption,” Appl. Phys. Lett. 104, 141102 (2014).
[Crossref]

J. Hao, J. Wang, X. Liu, W. J. Padilla, L. Zhou, M. Qiu, “High performance optical absorber based on a plasmonic metamaterial,” Appl. Phys. Lett. 96, 251104 (2010).
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J.-T. Liu, N.-H. Liu, J. Li, X. J. Li, J.-H. Huang, “Enhanced absorption of graphene with one-dimensional photonic crystal,” Appl. Phys. Lett. 101, 052104 (2012).
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L. Ken, “Phase effect on guided resonance in photonic crystal slabs,” Chin. Phys. Lett. 22, 2294 (2005).
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Elect. Lett. (1)

A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Elect. Lett. 36, 321–322 (2000).
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Eur. Phys. Jour. B (1)

L. Falkovsky, A. Varlamov, “Space-time dispersion of graphene conductivity,” Eur. Phys. Jour. B 56, 281–284 (2007).
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J. Opt. Soc. Am. (1)

Jour. Appl. Phys. (1)

G. W. Hanson, “Quasi-transverse electromagnetic modes supported by a graphene parallel-plate waveguide,” Jour. Appl. Phys. 104, 084314 (2008).
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Journal of Optics (1)

J. Zhang, J. Ou, K. MacDonald, N. Zheludev, “Optical response of plasmonic relief meta-surfaces,” Journal of Optics 14, 114002 (2012).
[Crossref]

Light: Sci. Appl. (2)

J. Zhang, K. F. MacDonald, N. I. Zheludev, “Controlling light-with-light without nonlinearity,” Light: Sci. Appl. 1, e18 (2012); doi:
[Crossref]

N. Papasimakis, S. Thongrattanasiri, N. I. Zheludev, F. G. de Abajo, “The magnetic response of graphene split-ring metamaterials,” Light: Sci. Appl. 2, e78 (2013); doi:
[Crossref]

Nano Lett. (4)

Y. Yao, M. A. Kats, P. Genevet, N. Yu, Y. Song, J. Kong, F. Capasso, “Broad electrical tuning of graphene-loaded plasmonic antennas,” Nano Lett. 13, 1257–1264 (2013).
[Crossref] [PubMed]

M. Furchi, A. Urich, A. Pospischil, G. Lilley, K. Unterrainer, H. Detz, P. Klang, A. M. Andrews, W. Schrenk, G. Strasser, T. Mueller, “Microcavity-integrated graphene photodetector,” Nano Lett. 12, 2773–2777 (2012).
[Crossref] [PubMed]

N. Liu, M. Mesch, T. Weiss, M. Hentschel, H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett. 10, 2342–2348 (2010).
[Crossref] [PubMed]

Z.-P. Yang, L. Ci, J. A. Bur, S.-Y. Lin, P. M. Ajayan, “Experimental observation of an extremely dark material made by a low-density nanotube array,” Nano Lett. 8, 446–451 (2008).
[Crossref] [PubMed]

Nat. Comm. (1)

K. Aydin, V. E. Ferry, R. M. Briggs, H. A. Atwater, “Broadband polarization-independent resonant light absorption using ultrathin plasmonic super absorbers,” Nat. Comm. 2, 517 (2011).
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Nat. Nanotechnol. (2)

H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, F. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol. 7, 330–334 (2012).
[Crossref] [PubMed]

F. Xia, T. Mueller, Y.-m. Lin, A. Valdes-Garcia, P. Avouris, “Ultrafast graphene photodetector,” Nat. Nanotechnol. 4, 839–843 (2009).
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Nat. Photonics (3)

F. Bonaccorso, Z. Sun, T. Hasan, A. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4, 611–622 (2010).
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A. Grigorenko, M. Polini, K. Novoselov, “Graphene plasmonics,” Nat. Photonics 6, 749–758 (2012).
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Nature (1)

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, X. Zhang, “A graphene-based broadband optical modulator,” Nature 474, 64–67 (2011).
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Opt. Express (4)

Opt. Lett. (1)

Phys. Rev. A (1)

S. Longhi, “Coherent perfect absorption in a homogeneously broadened two-level medium,” Phys. Rev. A 83, 055804 (2011).
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Phys. Rev. B (3)

S. Feng, K. Halterman, “Coherent perfect absorption in epsilon-near-zero metamaterials,” Phys. Rev. B 86, 165103 (2012).
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S. Thongrattanasiri, F. H. Koppens, F. J. G. de Abajo, “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett. 108, 047401 (2012).
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H. Noh, Y. Chong, A. D. Stone, H. Cao, “Perfect coupling of light to surface plasmons by coherent absorption,” Phys. Rev. Lett. 108, 186805 (2012).
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Y. Chong, L. Ge, H. Cao, A. D. Stone, “Coherent perfect absorbers: time-reversed lasers,” Phys. Rev. Lett. 105, 053901 (2010).
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N. Landy, S. Sajuyigbe, J. Mock, D. Smith, W. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100, 207402 (2008).
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X. Liu, T. Starr, A. F. Starr, W. J. Padilla, “Infrared spatial and frequency selective metamaterial with near-unity absorbance,” Phys. Rev. Lett. 104, 207403 (2010).
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M. Cai, O. Painter, K. J. Vahala, “Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system,” Phys. Rev. Lett. 85, 74 (2000).
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Proc. Natl. Acad. Sci. USA (1)

K. Mizuno, J. Ishii, H. Kishida, Y. Hayamizu, S. Yasuda, D. N. Futaba, M. Yumura, K. Hata, “A black body absorber from vertically aligned single-walled carbon nanotubes,” Proc. Natl. Acad. Sci. USA 106, 6044–6047 (2009).
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Rev. Mod. Phys. (1)

K. Y. Bliokh, Y. P. Bliokh, V. Freilikher, S. SavelŁv, F. Nori, “Colloquium: Unusual resonators: Plasmonics, metamaterials, and random media,” Rev. Mod. Phys. 80, 1201 (2008).
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Science (3)

W. Wan, Y. Chong, L. Ge, H. Noh, A. D. Stone, H. Cao, “Time-reversed lasing and interferometric control of absorption,” Science 331, 889–892 (2011).
[Crossref] [PubMed]

A. Vakil, N. Engheta, “Transformation optics using graphene,” Science 332, 1291–1294 (2011).
[Crossref] [PubMed]

K. S. Novoselov, A. K. Geim, S. Morozov, D. Jiang, Y. Zhang, S. Dubonos, I. Grigorieva, A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[Crossref] [PubMed]

Other (2)

S. A. Mousavi, E. Plum, J. Shi, N. I. Zheludev, “Coherent control of optical activity and optical anisotropy of thin metamaterials,” arXiv preprint arXiv:1312.0414 (2013).

F. Liu, Y. Chong, S. Adam, M. Polini, “Gate-tunable coherent perfect absorption of terahertz radiation in graphene,” arXiv preprint arXiv:1402.2368 (2014).

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Figures (4)

Fig. 1
Fig. 1 (a) Schematic of coherent absorption in a nanostructured graphene film. Two coherent optical beams impinge on the graphene film from opposite sides at normal incidence. Part of the energy may be absorbed while others will be scattered from both sides which can be controlled by changing the relative phase of the two beams. (b) A unit cell of the nanostructured graphene film with geometric parameters. The period is P = 400 nm and the size of hole is 220 nm.
Fig. 2
Fig. 2 Incoherent and coherent absorption in the nanostructured graphene film. (a) Simulated reflection, transmission and absorption of the nanostructured graphene film under the illumination of only one beam at normal incidence (or when the two input beams are incoherent). (b) Normalized total scattering output intensities |S|2 under the illumination of two counter-propagating coherent beams with the same intensities. The solid blue line and dashed red line show for parity-even mode and parity-odd mode, respectively. The geometric parameters of the patterned graphene is show in Fig. 1(b). Equation (12) is used to describe the conductivity of graphene and the Fermi level of graphene is assumed to beEF = 0.6 eV.
Fig. 3
Fig. 3 Phase modulation of coherent absorption. Two coherent beams with equal intensities impinge on the nanostructured graphene film from opposite sides. (a) At the resonance wavelength of 8.476 μm, the coherent absorption decreases from 99.93% to less than 0.01% as the relative phase changes from 0 to π. (b) At the off-resonance wavelength of 8.4 μm, the coherent absorption (blue solid curve) varies from about 41% to less than 0.01%. Other energy will be scattered from the two sides of graphene (dashed red curve and dashed green curve).
Fig. 4
Fig. 4 Phase modulation of coherent absorption in a nanostructured graphene film with asymmetric environments. The graphene is on a semi-infinite substrate with a refractive index of 1.5. Two coherent beams, with equal field amplitudes, are incident on the graphene at normal direction from opposite sides.

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

R = r + ( 1 + r ) η , T = t + t η
r = n 1 n 2 n 1 + n 2 , t = 2 n 1 n 1 + n 2
A = 1 | R | 2 n 2 n 1 | T | 2 = 1 | r + ( 1 + r ) η | 2 n 2 n 1 | t + t η | 2 ]
η = 1 2
R = n 2 n 1 + n 2 , T = n 1 n 1 + n 2
s 1 = R 1 + T 2 α e i φ , s 2 = T 1 + R 2 α e i φ
R 1 = n 2 n 1 + n 2 , T 1 = n 1 n 1 + n 2
R 2 = n 1 n 1 + n 2 , T 2 = n 2 n 1 + n 2
A coh = 1 | s 1 | 2 + χ | s 2 | 2 1 + χ α 2
A coh = 1 χ 1 + χ 1 + α 2 2 α cos φ 1 + χ α 2
σ ω = 2 e 2 k B T π h ¯ 2 i ω + i τ 1 ln [ 2 cosh ( E F 2 k B T ) ] + e 2 4 h ¯ [ 1 2 + 1 π arctan ( h ¯ ω 2 E F 2 k B T ) i 2 π ln ( h ¯ ω + 2 E F ) 2 ( h ¯ ω 2 E F ) 2 + 4 ( k B T ) 2 ]
σ ω = e 2 E F π h ¯ 2 i ω + i τ 1

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