# Multiband and Broadband Absorption Enhancement of Monolayer Graphene at Optical Frequencies from Multiple Magnetic Dipole Resonances in Metamaterials

## Abstract

It is well known that a suspended monolayer graphene has a weak light absorption efficiency of about 2.3% at normal incidence, which is disadvantageous to some applications in optoelectronic devices. In this work, we will numerically study multiband and broadband absorption enhancement of monolayer graphene over the whole visible spectrum, due to multiple magnetic dipole resonances in metamaterials. The unit cell of the metamaterials is composed of a graphene monolayer sandwiched between four Ag nanodisks with different diameters and a SiO_{2} spacer on an Ag substrate. The near-field plasmon hybridizations between individual Ag nanodisks and the Ag substrate form four independent magnetic dipole modes, which result into multiband absorption enhancement of monolayer graphene at optical frequencies. When the resonance wavelengths of the magnetic dipole modes are tuned to approach one another by changing the diameters of the Ag nanodisks, a broadband absorption enhancement can be achieved. The position of the absorption band in monolayer graphene can be also controlled by varying the thickness of the SiO_{2} spacer or the distance between the Ag nanodisks. Our designed graphene light absorber may find some potential applications in optoelectronic devices, such as photodetectors.

## Keywords

Light absorption Monolayer graphene Magnetic dipole resonances Metamaterials Plasmonics## Abbreviations

- 1D
One-dimensional

- 2D
Two-dimensional

- FDTD
Finite difference time domain

## Background

Graphene, a monolayer of carbon atoms tightly arranged in two-dimensional (2D) honeycomb lattice, was first separated from graphite experimentally in 2004 [1]. Since then, graphene has attracted enormous attentions in the scientific community, partly owing to its exceptional electronic and optical properties, including fast carrier velocity, tunable conductivity, and high optical transparency [2]. As one kind of 2D emerging materials, graphene has promising potentials in a wide variety of fields ranging from optoelectronics [3, 4, 5, 6] to plasmonics [7, 8, 9, 10], to metamaterials [11, 12, 13, 14, 15], etc. Due to its unique conical band structure of Dirac fermions, the suspended and undoped graphene exhibits a universal absorption of approximately 2.3% within the visible and near-infrared regions, which is related to the fine structure constant in a monolayer atomic sheet [16, 17]. The optical absorption efficiency is impressive, considering that graphene is only about 0.34 nm thick. However, it is still too low to be useful for optoelectronic devices such as photodetectors and solar cells, which need considerably higher absorption values for efficient operation.

To overcome this problem, various physical mechanisms [18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43] to enhance absorption of graphene in the visible region have been proposed, which include strong photon localization on the defect layer in one-dimensional (1D) photonic crystals [18, 28, 33, 38], total internal reflection [19, 20, 23, 27], surface plasmon resonances [21, 22, 30, 31, 33], evanescent diffraction orders of the arrays of metal nanoparticles [34], and critical coupling to guided mode resonances [25, 26, 32, 34, 35, 37, 39, 40, 41]. Besides the absorption enhancement in graphene, achieving multiband and broadband light absorption in graphene is also important for some graphene-based optoelectronic devices from a practical point of view. But, it is still a challenge, as pointed out in the very recent reports [44, 45, 46]. At present, different approaches have been proposed to broaden the bandwidth of graphene absorption in wide frequency range from THz [44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62] and infrared [63, 64, 65] to optical frequencies [19, 23, 29, 31, 34, 35, 36, 38, 39, 40, 43]. Especially, a multi-resonator approach was proven to be a very effective method to resolve the bandwidth limitation of graphene absorption in the THz and infrared regions [45, 46, 62, 63]. In the multi-resonator approach, deep-subwavelength multiple resonators with different sizes are closely packed, which could extend the absorption bandwidth when their resonance frequencies overlap with each other. However, to the best of our knowledge, up to now there are only a few reports on such a multi-resonator approach to obtain multiband and broadband light absorption of graphene in the visible region.

In this work, by employing similar multi-resonator approach, we will numerically demonstrate multiband and broadband absorption enhancement of monolayer graphene in the whole visible wavelength range, which arise from a set of magnetic dipole resonances in metamaterials. The unit cell of metamaterials consists of a graphene monolayer sandwiched between four Ag nanodisks with different diameters and a SiO_{2} spacer on an Ag substrate. The near-field plasmon hybridizations between individual Ag nanodisks and the Ag substrate form four independent magnetic dipole modes, which result into four-band absorption enhancement of monolayer graphene. When the magnetic dipole modes are tuned to be overlapped spectrally by changing the diameters of Ag nanodisks, a broadband absorption enhancement is achieved. The position of the absorption band in monolayer graphene can be also controlled by varying the thickness of the SiO_{2} spacer or the distance between the Ag nanodisks.

## Methods/Experimental

_{2}spacer on an Ag substrate. We calculate the reflection and absorption spectra, and the distributions of electromagnetic fields by the commercial software package “EastFDTD, version 5.0,” which is based on finite difference time domain (FDTD) method (www.eastfdtd.com). In our numerical calculations, the refractive index of SiO

_{2}is 1.45, and the frequency-dependent relative permittivity of Ag is taken from experimental data [66]. Under the random-phase approximation, the complex surface conductivity

*σ*of graphene is the sum of the intraband term

*σ*

_{intra}and the interband term

*σ*

_{inter}[67, 68], which are expressed as follows:

*ω*is the frequency of incident light,

*e*is electron charge,

*ħ*is reduced Planck constant,

*E*

_{ f }is Fermi energy (or chemical potential),

*τ*is the relaxation time of electron-phonon,

*k*

_{ B }is Boltzmann constant,

*T*is temperature in K, and

*i*is the imaginary unit. Graphene has an anisotropic relative permittivity tensor of

*ε*

_{ g }expressed as

where *ε*_{ 0 } is the permittivity of the vacuum, and *t*_{ g } is the thickness of graphene sheet.

## Results and Discussion

*λ*

_{1}= 722.9 nm,

*λ*

_{2}= 655.7 nm,

*λ*

_{3}= 545.5 nm, and

*λ*

_{4}= 468.8 nm. At four absorption peaks, the light absorption in graphene can reach as high as 65.7, 61.2, 68.4, and 64.5%, respectively. Compared with a suspended monolayer graphene whose absorption efficiency is only 2.3% at optical frequencies [16, 17], the monolayer graphene in our designed metamaterials has an absorption enhancement of more than 26 times. It is also clearly seen in Fig. 2 that the absorbed light is mainly dissipated in graphene rather than in Ag. Moreover, the total absorption at the third peak exceeds 98.5%, very similar to much reported metamaterial electromagnetic wave perfect absorbers [69, 70, 71, 72, 73, 74, 75], which have many potential applications such as solar cells [76, 77, 78, 79, 80, 81].

*λ*

_{1},

*λ*

_{2},

*λ*

_{3}, and

*λ*

_{4}. At the resonance wavelength of

*λ*

_{1}, the electric fields are mainly concentrated near the left and right edges of the first Ag nanodisk with a diameter of

*d*

_{ 1 }(see Fig. 3a), and the magnetic fields are highly confined within the SiO

_{2}region under the first Ag nanodisk (see Fig. 4a). Such field distributions correspond to the excitation of a magnetic dipole mode [82, 83, 84, 85, 86], which steps from the near-field plasmon hybridization between the first Ag nanodisk and the Ag substrate. At the resonance wavelengths of

*λ*

_{2},

*λ*

_{3}, and

*λ*

_{4}, the electromagnetic fields have the same distribution properties, but are localized in the vicinity of the second, third, and fourth Ag nanodisks with diameters of

*d*

_{ 2 },

*d*

_{ 3 }, and

*d*

_{ 4 }, respectively. In short, the excitations of four independent magnetic dipole modes lead to the appearance of four absorption peaks in Fig. 2.

*d*

_{ 1 },

*d*

_{ 2 },

*d*

_{ 3 }, and

*d*

_{ 4 }of four Ag nanodisks are equal to 110, 90, 70, and 50 nm, respectively. In this case, a broadband absorption enhancement in the wavelength range from 450 to 650 nm is achieved by the spectral design on the overlapped absorption peaks, with the lowest (highest) absorption efficiency more than 50% (73%). For the diameters of the Ag nanodisks to be increased gradually, this broad high-absorption band is red-shifted, as shown in Fig. 5b, c.

*t*of the SiO

_{2}spacer. Figure 6 shows the normal-incidence absorption spectra in monolayer graphene, for

*t*to be increased from 25 to 45 nm. With the increasing

*t*, the absorption band in monolayer graphene will have an obvious blue-shift, because the near-field plasmon hybridizations between individual Ag nanodisks and the Ag substrate become weaker and thus magnetic dipole modes are blue-shifted [83].

*p*

_{ x }/4, ±

*p*

_{ y }/4), so the center distance

*l*between the nearest-neighbor Ag nanodisks is 200 nm. By varying

*l*, we can also tune the position of the absorption band in monolayer graphene. Figure 7 gives the normal-incidence absorption spectra in monolayer graphene, for

*l*to be decreased from 220 to 160 nm. With the decreasing

*l*, the absorption band in monolayer graphene is slightly blue-shifted, owing to the plasmon interactions among the Ag nanodisks.

## Conclusions

In this work, we have numerically investigated multiband and broadband absorption enhancement of monolayer graphene at optical frequencies from multiple magnetic dipole resonances in metamaterials. The unit cell of the metamaterials consists of a graphene monolayer sandwiched between four Ag nanodisks with different diameters and a SiO_{2} spacer on an Ag substrate. The near-field plasmon hybridizations between individual Ag nanodisks and the Ag substrate form four independent magnetic dipole modes, which result into multiband absorption enhancement of monolayer graphene in the visible wavelength range. When the magnetic dipole modes are tuned to be overlapped spectrally by changing the diameters of Ag nanodisks, a broadband absorption enhancement is achieved. The position of the absorption band in monolayer graphene can be also controlled, by varying the thickness of the SiO_{2} spacer or the distance between the Ag nanodisks. The numerical results may have some potential applications in optoelectronic devices, such as photodetectors.

## Notes

### Acknowledgements

This work is financially supported by the National Natural Science Foundation of China (NSFC) under Grant Nos. 11304159 and 11104136, the Natural Science Foundation of Zhejiang Province under Grant No. LY14A040004, the Natural Science Foundation of Jiangsu Province under Grant No. BK20161512, the Qing Lan Project of Jiangsu Province, the Open Project of State Key Laboratory of Millimeter Waves under Grant No. K201821, and the NUPTSF under Grant Nos. NY217045 and NY218022. J. Chen also acknowledges partial support from the National Research Foundation of Korea under “Young Scientist Exchange Program between The Republic of Korea and the People’s Republic of China”.

### Availability of Data and Materials

All data are fully available without restriction.

### Authors’ Contributions

BL, CT, and JC contributed equally to this work. BL, CT, and JC performed the design, analyzed the data, and drafted the manuscript. CT, JC, and GP guided the idea and the simulations, and checked the figures. All authors read and approved the final manuscript.

### Ethics Approval and Consent to Participate

We declare that there are no concerning data of human and animals.

### Competing Interests

The authors declare that they have no competing interests.

### Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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