New materials and technologies, such as metamaterials^[1–3], plasmonics^[4–6], graphene^[7–9], metasurface^[10,11], and nanomaterials^[12,13], are constantly emerging in order to manipulate electromagnetic waves and make new progress. Mid-infrared lasers have important applications in communications and medical treatments. The effective transmission control of polarization states on the mid-infrared lasers is an important factor, which is indispensable for their better applications. Chiral metamaterials, a new kind of artificial electromagnetic materials, have been intensively studied and show strong abilities in polarization state controls^[14–21]. Such abilities generally only occur near the oscillation wavelengths of the metamaterials. At present, the proven responses of the chiral metamaterials are mainly distributed in the microwave^[22], terahertz^[23], visible, or near-infrared regions^[24–32]. Only a few researchers reported the responses distributing in the mid-infrared band^[33–36]. In these works, the conventional metals such as copper, silver (Ag), and gold (Au) were used as plasmonic materials. The metal materials have large real parts of permittivities, low chemical stability, and poor compatibility with the standard silicon manufacturing processes. These shortcomings affect the polarization control performances of the mid-infrared chiral metamaterials composed of conventional metals. Metal oxides^[37] were found to be good alternative plasmonic materials in the mid-infrared band due to their low losses. Our group previously selected indium tin oxide (ITO) as a plasmonic material to fabricate an L-shaped mid-infrared chiral structure^[36]. The structure exhibited circular dichroism (CD) responses stronger than those of the structure consisting of Ag in the mid-infrared band.

In this paper, ITO is selected to design a periodic helix structure. Each helix unit cell consists of four helices with different radii. The simulation results show that the structure has flat-topped broadband CD, which is unattainable for the Au or Ag helix structures.

A periodic helix array structure was designed in this paper. Each unit cell consists of four subunits, each of which is composed of a helix, and the different helices have different radii, as shown in Fig. 1. The helix radii of the four subunits are R1=0.3µm, R2=0.35µm, R3=0.4µm, and R4=0.45µm, respectively. The materials of the helix and substrate are set to ITO and silicon, respectively. The radius of the wire is r=0.2µm, the pitch of the helix is p=1µm, the number of helix turns is N=1, and the period of the unit cell is a=3.4µm. The coordinate origin is located on the upper surface of the substrate and set at the center of the unit cell. Each subunit is located in the middle of every quarter unit cell. The helix structure we proposed can be manufactured by laser direct writing similar to the production processes in Refs. [33,38,39]. The process goes through four steps: coating photoresist, laser direct writing to form helix air gaps with different radii, depositing ITO in the helix air gaps, and removing photoresist.

A finite-difference time-domain (FDTD) method software was employed to simulate chiral properties of the structure. Due to the periodicity of the structure, we therefore considered a single unit cell with periodic boundary conditions in both x and y directions in simulations. It is assumed that a right-handed circularly polarized (RCP) wave and a left-handed circularly polarized (LCP) wave are incident along the z direction, respectively. In addition, perfect matched layer (PML) boundary conditions are set in the z direction. The permittivity of the silicon substrate is derived from experimental data^[40], and the permittivity of ITO is determined by the Drude–Lorentz model^[37].

By FDTD simulations, the transmission spectra of RCP and LCP waves were calculated and substituted into the CD formula below: CD=|T+−T−|,(1)where T+, T− are the transmittances for the RCP and LCP incident waves, respectively. The resulting CD spectrum at 3–10 µm was obtained, as shown in Fig. 2. From this figure, we can see that evident differences exist between T+ and T− in this band, leading to an obvious CD response of the structure. At about the wavelength of 6.44 µm, the value of CD reaches a maximum of 0.298. If the full width at half-maximum (FWHM) of CD is defined as such a wavelength range in which the CD drops to half of the maximum value, the FWHM is 5.06 µm ranging from 3.65 µm to 8.71 µm. The transmittance for the LCP wave is greater than that for the RCP wave in the 3.1–10 µm band. The reason is that the handedness of the circular polarization electromagnetic wave is identical to that of the helices of the structure. The selected model is a right-handed helix structure. When the RCP wave is incident, the helix structure composed of the ITO plasmonic material has a strong plasmon resonance, and the oscillation absorption is enhanced. In contrast, when the LCP wave is incident, the helix structure has a weak plasmon resonance due to their different handedness, and therefore the absorption is also weak.

We also simulated the distributions of electric field intensities in different cross sections vertical to the incident direction for the RCP and LCP waves at the wavelength of 6.44 µm, which is shown in Fig. 3. The cross sections were selected at 0.2 µm intervals from the incident end to the exit end. It can be seen from the figure that the field intensity at the upper end of the structure for the RCP wave incidence is the strongest, the plasmon resonance in ITO is also the strongest, and the field intensity gradually decreases from top to bottom. However, for the LCP wave incidence, the field intensity as well as the plasmon resonance is the strongest in the middle of the structure, and the plasmon resonances at the two ends weaken. These fields occur mainly on the surfaces of the helices, indicating that surface plasmon polaritons (SPPs) are induced. The couplings of the SPPs between different helices also appear, inflencing the CD responses of structures. By comparing them, the plasmon resonance caused by the RCP wave is stronger than the one for the LCP wave incidence. Therefore, the structure absorbs the RCP wave more strongly than the LCP wave, resulting in an obvious CD response. This is the same as the results shown in Fig. 2.

It is assumed that the structure is illuminated by a plane wave propagating in the positive z direction, E→i(r→,t)=(ixiy)ei(kz−ωt),(2)where ω is the frequency, k=ω/cε(ω) is the wave vector, and the complex amplitudes ix and iy describe the state of polarization. The transmitted field is then given by E→t(r→,t)=(txty)ei(kz−ωt).(3)

A complex Jones matrix T connects the generally complex amplitudes of the incident and the transmitted fields: (txty)=(TxxTxyTyxTyy)(ixiy)=(ABCD)(ixiy)=T(ixiy).(4)

For circular states, the T matrix is given by^[41]$$\begin{gathered} Tcirc=(T++T+−T−+T−−) \\ =12(A+D+i(B−C)A−D−i(B+C)A−D+i(B+C)A+D−i(B−C)), \end{gathered}$$(5)connecting the amplitudes of circularly polarized incident and transmitted waves: (t+t−)=Tcirc(i+i−),(6)where “+” and “−” denote RCP and LCP waves, respectively. A, B, C, and D are influenced by the parameters, shapes, and components of the structure. Additionally, the couplings between different helices also affect their values, leading to the changes of CD.

The unit cell of the model proposed is composed of four subunits with different helix radii. In order to compare easily, four subunits were simulated separately, and the period remained the same as that of the original unit cell. Each subunit is in the middle of the unit cell. Their CD curves are shown in Fig. 4. The chirality of metamaterial structures usually occurs near the resonance frequencies of the structures. The resonance frequencies are closely related to the sizes of the structures. From this figure, it can be seen that for one of the subunits, corresponding resonance frequencies exist. With the increasing radius of the helix, the resonance of the subunit shifts towards the longer wavelengths. Their CD bandwidths are all narrower than that of the unit cell. The reason lies in that the unit cell is composed of four subunits with different helix sizes. Multiple resonance peaks caused by different subunits work together, leading to CD broadening.

We change the number of turns of each subunit helix to keep them different. The simulated CD curves for two different cases are shown in Fig. 5, in which the original CD curve for the one turn helix is also plotted. Case one: the number of turns of the helix with the smallest radius is set to 1.07, the number of turns of the helix with the largest radius is set to 0.93, and those of the other two subunits remain at one. Case two: the number of turns of the helix with the second smallest radius is set to 1.04, and other parameters are the same as those of case one. It is found that for the adjusted structure, their CD values from 4.5 µm to 7 µm change between 0.265 and 0.274, while the CD values for the same number of turns change between 0.251 and 0.288. It means that the CD distributions with the adjusted structure are flatter, which provides a design idea for the flat-topped broadband CD.

To investigate the influences of structural materials on CD responses, we change the component of helices and replace ITO with Au and Ag. The other parameters remain unchanged. The dielectric constants of Au and Ag come from experimental data^[40]. The simulated CD results are shown in Fig. 6. From this figure, we can see that the CD curves of the two material structures oscillate more than that of the ITO structure, which leads to narrower CD bandwidths. Therefore, to obtain the broadband CD responses in the mid-infrared band, ITO as a component is more advantageous. The figure also shows that the CD curves for the Au and Ag components are almost coincident. The reason is that their dielectric constants have slight changes in the band, leading to almost the same plasmon resonance behaviors.

Optical activity refers to the rotation ability of a polarized wave passing through the chiral structure, which can be expressed as θ=12[arg(tL)−arg(tR)],(7)where tR and tL stand for the transmission coefficients of RCP and LCP waves, respectively. Utilizing Eq. (7), we calculated optical activity corresponding to ITO, Ag, and Au structures with geometric parameters the same as those in Fig. 1. The results are shown in Fig. 7. For the ITO structure, its optical activity θ varies between 85° and 95° in the range of 4.5–10 µm. For the metallic (Ag and Au) structures, however, the optical activity shows strong oscillation with the change of wavelength. That is to say, the ITO helix structure shows relatively stable optical activity in the mid-infrared band, which provides a new idea for the design of mid-infrared broadband rotatory devices.

In this paper, we proposed a periodic chiral structure, in which each unit cell consisting of four ITO helix subunits with different radii realized flat-topped broadband CD and optical activity in the mid-infrared band. The simulation results show that by optimizing parameters of the helix structure, flat-topped broadband CD distributions with their values from 4.5 µm to 7 µm can be obtained. The comparisons between the ITO helix structures and metallic (Ag and Au) helix structures show that the CD and the optical activity of the former have broader bands, which provides a new idea for the design of broadband polarization state control devices in the mid-infrared band. Future work will be to further research the mechanism of chirality and explore improvement to the design of broadband chiral devices.