# Abnormal Fano Profile in Graphene-Wrapped Dielectric Particle Dimer

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

## 3. Results and Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Schematic diagram of the graphene-wrapped dielectric dimer in vacuum illuminated by the linear polarized light whose E direction is along the dimer axis. The radii of two particles are ${r}_{1}$ and ${r}_{2}$, respectively, and the center-to-center distance is $d$.

**Figure 2.**Internal field enhancement spectra for graphene-wrapped dielectric dimers with constant center-to-center distance of $d=210\text{\hspace{0.33em}}\mathrm{nm}$, for small particle (NP1, upper panels) and the large particle (NP2, middle panels) with various radii of small particle (

**I**) ${r}_{1}=50\text{}\mathrm{nm}$, (

**II**) ${r}_{1}=60\text{}\mathrm{nm}$, (

**III**) ${r}_{1}=70\text{}\mathrm{nm}$, and (

**IV**) ${r}_{1}=80\text{}\mathrm{nm}$, and with a fixed radius of large particle ${r}_{2}=100\text{}\mathrm{nm}$. The dashed line in each panel shows the analytical single particle field enhancement. Down panels illustrate the phase of each dipole moments in dimer calculated by Equation (6). The host medium is chosen as vacuum, $\epsilon =2.25$, ${E}_{F}=0.3\text{}\mathrm{eV}$, and $\tau =1\text{}\mathrm{ps}$.

**Figure 3.**The schematic diagram of the plasmon hybridization in the cascaded graphene-coated dimer. The Fano resonance arises due to the interference between antibonding and bonding modes.

**Figure 4.**(

**a**) Calculated results of denominator term $1-{\alpha}_{1}{\alpha}_{2}{A}_{12}{A}_{21}$ (black) and numerator terms $1-{\alpha}_{2,1}{A}_{12,21}$ (red for NP1 and blue for NP2) in the function of incident wavelength. (

**b**,

**c**) are the local enlarged images cut from (

**a**), located around $12.3\text{}\mathsf{\mu}\mathrm{m}$ and $13.8\text{}\mathsf{\mu}\mathrm{m}$, respectively. The physical parameters used in the calculation are the same as in Figure 2IV.

**Figure 5.**The same as in Figure 4 but with different relaxation times: (

**a**) $\tau =0.1\text{}\mathrm{ps}$, (

**b**) $\tau =0.5\text{}\mathrm{ps}$, (

**c**) $\tau =1\text{}\mathrm{ps}$. Corresponding internal field enhancements are shown in (

**d**–

**f**), respectively.

**Figure 6.**Extinction cross-section spectrum of total (black solid), NP1 (red dashed), and NP2 (blue dotted) contributions from the graphene-wrapped dimer.

**Figure 7.**Absorption cross-section spectrum of total (black solid), NP1 (red dashed), and NP2 (blue dotted) contributions from the graphene-wrapped dimer, respectively.

**Figure 8.**Internal field enhancement as the functions of center-to-center distance $d$ and incident wavelength $\lambda $ in NP1 (Upper panel) and NP2 (lower panel) with different Fermi energy levels: (

**a**,

**d**) ${E}_{F}=0.2\text{}\mathrm{eV}$, (

**b**,

**e**) ${E}_{F}=0.4\text{}\mathrm{eV}$, and (

**c**,

**f**) ${E}_{F}=0.6\text{}\mathrm{eV}$, respectively. The radius of NP1 is $80\text{}\mathrm{nm}$ and other parameters are the same as used in Figure 2.

**Figure 9.**Internal field enhancement spectra with different Fermi energy levels in (

**a**) NP1 and (

**b**) NP2, respectively. Other geometric parameters are the same as in Figure 2IV.

**Figure 10.**Internal field enhancement spectra in (

**a**) NP1 and (

**b**) NP2 with different polarization direction of incident wave: E perpendicular to dimer axis (solid) and E parallel to dimer axis (dashed). (

**c**) Phase of the dipole moments for NP1 and NP2 in case of E perpendicular to dimer axis. Other physical parameters are the same as in Figure 2IV. The insert denotes the plasmon hybridization.

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**MDPI and ACS Style**

Huang, Y.; Ma, P.; Wu, Y.M.
Abnormal Fano Profile in Graphene-Wrapped Dielectric Particle Dimer. *Photonics* **2020**, *7*, 124.
https://doi.org/10.3390/photonics7040124

**AMA Style**

Huang Y, Ma P, Wu YM.
Abnormal Fano Profile in Graphene-Wrapped Dielectric Particle Dimer. *Photonics*. 2020; 7(4):124.
https://doi.org/10.3390/photonics7040124

**Chicago/Turabian Style**

Huang, Yang, Pujuan Ma, and Ya Min Wu.
2020. "Abnormal Fano Profile in Graphene-Wrapped Dielectric Particle Dimer" *Photonics* 7, no. 4: 124.
https://doi.org/10.3390/photonics7040124