Introduction

As one member of the third family in electromagnetic multipole theory1,2, toroidal dipole was proposed by Zel’dovich in 1957 to interpret the parity violation on the weak interaction in nuclear and particle physics3, which is a result of current flowing on the surface of a torus along its meridian4,5. However, due to weakly coupling to electromagnetic radiation, there is an obstacle to observe the toroidal dipolar response usually masked by electric and magnetic multipoles6. Fortunately, the appearance of metamaterials laid a solid foundation for overcoming it. Metamaterials are artificially constructed and own sub-wavelength unit cells in periodic arrays7,8. In basis of its various novel electromagnetic properties unobtainable in naturally occurring systems, such as negative refraction, super-imaging, perfect absorber and cloaking9,10,11, metamaterials have been a hot topic of artificial electromagnetic materials. K. Marinov et al. in 2007 theoretically put forward a toroidal metamaterial to suppress electric and magnetic multipoles and strength the toroidal dipole resonance12. In recent years, more toroidal metastructures were designed to further explore optical properties of toroidal dipole either theoretically or experimentally, for example, double disks6,13, asymmetric double bars14, multifold double rings15, oligomer nanocavities16, and other metallic metastructures based on split ring resonators5,17,18. To further avoid ohmic-damping loss in metals, all-dielectric metamaterials were also proposed to realize high-Q-factor toroidal dipole resonance19,20.

In optical physics, light-radiation manipulation is always a hot area of research21,22,23,24. There are a lot of ways to manipulate light scattering, such as (i) by electric dipole resonance25, (ii) by optically-induced magnetic dipole resonance26,27, and (iii) by the interference between electric and magnetic dipole resonances, showing the forward directional scattering while suppressing the backward scattering28,29,30. With the new member of toroidal dipole joining, it brings an extra degree of freedom for light scattering manipulation31. For example, in our previous work, a dipolar emitter coupling to the metastructure by double flat rings not only excites toroidal dipole but also controls both radiating direction and power of the dipolar emitter by tuning geometric parameters, acting like a nanoantenna13. Furthermore, a four-U-shaped toroidal metastructure with optical gain medium was proposed by Huang et al. in 2013, obtaining a high-Q-factor toroidal resonance and realizing the so-called toroidal lasing spaser5. In this paper, we embed the gain medium into the gap spacer between metallic double flat rings to explore the influence of optical gain on the far-field scattering properties based on the coupling interference between toroidal and electric dipole radiations.

Results and Discussion

The double metallic flat rings metastructure is illustrated in Fig. 1. The metal is chosen as silver following the Drude-type dispersion model , with the high-frequency permittivity , the plasma frequency and the collision frequency . The outer and inner radii of 40-nm-thick silver rings are 430 nm and 100 nm, respectively. A 40-nm silicon-oxide () gap layer with gain medium sparsely embedded in was assumed to have a gain coefficient as , where and are accordingly real and imaginary parts of permittivity for the gain layer5. To probe the far-field optical radiating property, the far-field probes B and D (marked by green arrows) are located on the y-axis as shown in Fig. 1. A dipolar emitter (labeled by red arrow), along the y-axis with 1-nm length and oscillating electric current of 1 A, is chosen as the excitation source. Δx is set as the radial displacement of the emitter with respect to the geometric center “O” of double-ring along the x-axis. Note that “O” is also the origin of coordinate system. The numerical simulation is performed based on the full-wave finite-element method (Ansoft HFSS).

Figure 1
figure 1

Schematic of the double-flat-ring toroidal metamaterial.

Full size image

In comparison to field probes in other directions13, the far-field radiating power, recorded by the probe B on the y-axis as shown in Fig. 1, is much appropriate for revealing the directional light radiating characteristic. When the dipolar emitter locates at the center of the metastructure (Δx = nm) and without considering the active feature of the gap layer (i.e., α = 0 cm−1), the far-field radiation shows two resonant peaks, namely, resonance R1 at 200 THz and R2 at 235 THz in Fig. 2(a), which actually corresponds to the peak and dip of the Fano-type spectrum in ref. 13, due to constructive and destructive interferences between toroidal and electric dipoles, respectively. It can be further verified by magnetic field distributions of resonance and in right panel of Fig. 2. Besides, the calculated scattered powers in terms of multipoles also sufficiently justify the excitation of a dominant toroidal dipole around 200 THz as shown in Fig. 3.

Figure 2: The spectra of far-field intensity monitored by probe B for different radial displacement Δx.
figure 2

Inset maps in the right pink box are magnetic field distributions of constructive (resonance R1) and destructive (resonance R2) interferences between toroidal and electric dipoles at 200 THz and 235 THz, respectively.

Full size image
Figure 3
figure 3

The scattered powers in terms of multipoles when Δx = 0 nm.

Full size image

Interestingly, when the position of dipole emitter has a small deviation from the center (e.g., Δx = 10 nm), the far-field radiating intensity of high frequency resonance R2 is gradually enhanced. With a continuing shift up to Δx = 80 nm, the far-field radiating power at resonance R2 is vastly enhanced to about 264000 times than the ones of Δx = 0 nm at 235 THz, undergoing a transformation from non- to super-radiating and making the emitter radiating like an optical nano-antenna with high directivity. Nevertheless, it should be emphasized that the low frequency resonance R1 does not disappear. In order to clarify it, Fig. 4 shows the dependence of the far-field radiating intensity of the resonance R1 on different radial displacements, monitored by the probe D: With the dipolar emitter moving along the x-axis, the far-field radiating power gradually increased and reached a maximum of when Δx = 80 nm.

Figure 4
figure 4

The spectra of far-field intensity monitored by probe D for different radial displacement Δx.

Full size image

To intuitively make clear the radiating evolution process from Δx = 0 nm to Δx = 80 nm, far-field radiating patterns for different radial displacement Δx are presented in Fig. 5. Obviously, before the dipolar emitter moving along the x-axis, it radiates light in an azimuthally symmetric torus-like pattern with respect to the y-axis. Nevertheless, once there is a small shift of 25 nm, directional radiations occur at 75- and 285-degree orientations (marked by pink dashed-lines) as shown in Fig. 5(c). By further moving to Δx = 80 nm, it will result in a directional radiating parallel to the y-axis with an angular width of 60 degree, radiating as an optical nano-antenna. In short, the ultimate physical mechanism is a hybridization interference between toroidal and electric dipoles due to an asymmetric configuration induced by the radial displacement Δx. It is necessary to note that, for the case of Δx = 80 nm, there still leaves a small radiation to the opposite x-axis direction on account of an insufficient interference.

Figure 5
figure 5

Three-dimensional far-field radiation patterns at 235 THz for different radial displacement Δx, and corresponding two-dimensional patterns in dependence of φ under θ = 90 degree (Radiation unit: 108 V.

Full size image

Then, Fig. 6 illustrates the magnetic-field distributions at 235 THz to better explain the interference mechanism. In phases and , the magnetic field of toroidal dipole response is always out-of-phase to the excitation field from the dipolar emitter. However, for and , the magnetic field forms a symmetric distribution respect to the y-z plane, implying a different interference process. Meanwhile, when , it seems to be a transition state from to . This is to say that the super-radiating characteristic of the single emitter actually results from asymmetric hybridization interference between toroidal and electric dipoles due to a radial displacement of the dipole emitter with respect to the double-flat-ring metastructure.

Figure 6
figure 6

The magnetic field vector distributions correspond to different phases under the geometric configuration of Δx = 80 nm.

Full size image

Since light radiating has great potential applications such as sensing and optical communications, it is of the great importance to enhance the light radiating power and direction of the single dipolar emitter when Δx = 80 nm at 235 THz. Such idea can be achieved by introducing optically active medium into this system. Here, the active medium (for example, PbSe semiconductor quantum dot) is embedded in the silicon-oxide gap layer, as described earlier. In order to provide an intuitive comparison, Fig. 7(a) displays the far-field radiating intensity with a peak of under an absence of gain medium (namely, ). Then, with the gain coefficient α increasing, the far-field radiating power is greatly strengthened and obtains a maximum value of under the moderate gain level of , which is 1.1×104 times stronger than ones of . Meanwhile, the sharp enhancement of the far-field radiating power at 235 THz, prompted by the gain medium, directly leads to a smaller full width at half maximum (FWHM), implying the potential for an excellent sensing performance32. In addition, the corresponding two dimensional (2D) radiating patterns of different gain values at 235 THz are also presented in Fig. 8. Although the radiating angular width is always 60 degree, it is obvious that the far-field radiating power realizes a tremendous enhancement under a moderate gain level. Nevertheless, it is important to note that the far-field radiation reduction above a certain critical gain coefficient, though in accordance with literatures33,34, should be attributed to an unrealistic consequence of the time-independent solution. That is to say, if one increases the gain coefficient to beyond certain threshold, the actual physical field will be increasing with time. This contradicts with our numerical calculation based on time-independent Maxwell equations. Therefore, physically there may be no way to obtain such overlarge value of gain coefficient in a steady state35.

Figure 7
figure 7

The far-field radiating powers at different gain coefficients for Δx = 80 nm.

Full size image
Figure 8: Under the geometric configuration of Δx = 80 nm, the two-dimension radiating patterns (Radiation unit: 109 ) under different gain coefficients at 235 THz.
figure 8

From (a) to (f), the gain coefficient α is 0, 762, 1526, 1756, 1909 and 2295 cm−1, respectively.

Full size image

Conclusion

In summary, the light radiating of a single emitter can be manipulated by the toroidal metastructure composed of double flat rings, from non- to super-radiating at 235 THz, rooting in hybridization interference between toroidal and electric dipoles due to an asymmetric configuration by shifting the dipole emitter along the radial direction. Gain medium is embedded in the gap layer between top and bottom metallic flat rings to vastly strengthen the far-field super-radiating power. The directive radiation intensity can reach orders of magnitude enhancement with a moderate gain level. It may provide a channel to manipulate the light-matter interaction.

Additional Information

How to cite this article: Li, J. et al. Super-radiating manipulation of a nano-emitter by active toroidal metamaterials. Sci. Rep. 7, 46609; doi: 10.1038/srep46609 (2017).

Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.