
- Chinese Optics Letters
- Vol. 19, Issue 12, 123601 (2021)
Abstract
1. Introduction
In recent years, there have been many interests in studying electromagnetic superscattering because of its special applications[
All of the above-mentioned superscattering phenomena exhibit a single-frequency regime. Multifrequency superscattering may enable improved sensitivity and accuracy for extensive applications ranging from sensing, bioimaging, and optical tagging to spectroscopy[
2. Theory
In this work, we consider a two-dimensional subwavelength cylindrical structure. The structure consists of six layers of dielectric material, each of which is coated with a graphene shell, as shown in Fig. 1(a). Such a six-layer subwavelength structure is the main focus of this analysis, because six layers is sufficient for multifrequency superscattering and superscattering shaping. The conductivity of graphene can be expressed as the Kubo formula:
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Figure 1.(a) Illustration of a subwavelength multilayered cylindrical structure consisting of six layers of dielectric materials, each of which is coated with a graphene shell. Three-dimensional and two-dimensional views of the structure are shown in the left and right inset, respectively. Graphene shells are represented by black dotted lines. Here, the plane wave is TM-polarized and incident from the left side of the cylinder structure. (b) The scattering spectra (normalized scattering cross section) for the same structure in (a) under the ideal lossless assumption. Both the total scattering spectrum and the partial spectra of the first five scattering terms are shown. The inset in (b) shows the details at the resonance peak circled by a dotted blue line.
Here,
Then, from the recurrence relation of the coefficients of the adjacent layers, the relation between the coefficients of the innermost layer and the outermost layer can be described by the following formula:
Next, the scattering coefficient obtained according to Eqs. (12) and (13) can be expressed as
Here, NSCS is normalized by
3. Results and Discussions
To highlight the underlying physical properties, we first consider a lossless subwavelength cylindrical structure by setting
The underlying mechanism of the resonant overlapping of multipoles in the subwavelength cylinder structure can be qualitatively understood from the dispersion of plasmon polaritons supported by a corresponding planar structure in Fig. 2. Starting from resonance modes supported in the corresponding planar structure, the resonances of the subwavelength cylinder structure can be understood using the whispering gallery condition based on the Bohr model[
Figure 2.Dispersion of plasmon polaritons versus |RTM| (in logarithmic scale) under the ideal lossless assumption is shown. RTM is the reflection coefficient of the TM-polarized plane wave for the corresponding planar structure. The parameters of the corresponding planar structure are the same as those in Fig.
Figure 3 intuitively shows the performance of the superscattering pattern shaping in the form of far and near fields for the cylinder structure in Fig. 1(a) at the four superscattering resonant frequencies. Far-field angular scattering amplitude
Figure 3.Scattering angular distributions for the subwavelength cylinder structure in Fig.
Theoretically, various scattering pattern shaping can also be realized by resonantly overlapping different electromagnetic multipoles because these multipoles show different phase symmetries and parities[
Figure 3(a) shows the superscattering pattern shaping by resonantly overlapping ED and EQ at the resonant frequency of 3.79715 THz. Far-field scattering angular distribution is shown by a blue solid curve, and the scattering near field
Figure 3(c) illustrates the superscattering pattern shaping with resonantly overlapped EQ and MO by showing the scattering-field distribution at the frequency of 9.77464 THz. The far-field scattering angular distribution is plotted by a blue solid curve, which matches well with the scattering near field shown in the background pattern. Like Fig. 3(a), the scattering is enhanced in the forward direction but suppressed in the backward direction due to opposite parities of EQ and MO (even and odd, respectively). The two overlapped multipoles are in phase and out of phase, respectively, in the forward and backward directions. It is observed that the scattering is also suppressed from 30° to 45° and 315° to 330° in the forward half-scattering circle, which can be understood analytically by
Figure 3(e) illustrates the superscattering pattern shaping with resonantly overlapped ED and MO by showing the scattering-field distribution at the frequency of 12.65616 THz. The scattering near and far fields correspond to the background pattern and the blue solid curve, respectively, and they are well matched. Clearly, the scattering is enhanced symmetrically both in the forward and backward directions due to the same odd parity of the scatterings of ED and MO. Additionally, the interferences of overlapped ED and MO can also suppress the scattering at
Figure 3(g) shows the superscattering pattern shaping by resonantly overlapping EQ and EO at the frequency of 14.74908 THz in the form of the scattering far field plotted by the blue solid curve and the scattering near field shown in the bottom pattern. The scattering amplitudes are symmetrically enhanced both in forward and backward directions, which is caused by the same even parity of the EQ and EO. It can be also seen that the scattering is suppressed from 22.5° to 45°, 67.5° to 112.5°, 135° to 157.5°, 202.5° to 225°, 247.5° to 292.5°, and 315° to 337.5° according to
To facilitate the realization of the experiment and practical application, the effects of the material losses and the structural changes are analyzed in detail in Fig. 4. First, considering the optical losses of graphene, as shown in Fig. 4(a), the superscattering with resonantly overlapped multipoles still exists at corresponding resonant frequencies when changing the relaxation time
Figure 4.(a) Influence of graphene’s losses on multifrequency superscattering is shown through the total scattering spectra for different lossy cases. Except τ, other parameters are the same as those in the structure of Fig.
4. Conclusion
In conclusion, we propose that a graphene-based subwavelength structure can be a promising and versatile platform for the demonstration of simultaneous multifrequency superscattering and superscattering shaping with different engineered scattering patterns. Based on Bohr’s model and dispersion engineering, it is further demonstrated that such efficient superscattering pattern shaping is induced by the interferences of multipoles resonantly overlapped. In contrast with multilayer plasmonic structures, the performance of the proposed structure can be easily refined for the desired frequency by adjusting the chemical potential and loss of the graphene layer. Owing to multiple polaritonic dispersion lines in a graphene-based subwavelength structure, the phenomena of multifrequency superscattering are found to have a high tolerance to some structural variations and realistic graphene loss. In addition, more exotic scattering phenomena are expected in such a platform, such as dynamically tunable multifrequency cloaking and other multifrequency scattering-based devices.
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