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Abstract
Dichroism, an important property for the manipulation and characterization of polarization states, has been widely studied. However, owing to the inherent relationship between linear and circular polarization, it is difficult to generate high linear dichroism (LD) and circular dichroism (CD) in the same structure. Previous study can only solve this problem in the condition of oblique incidence. Here, a method is proposed to generate high LD and CD under normal incidence without any structural changes. By the design of metamolecule composed of two pairs of twin nanopillars, the polarization-dependent interference from those twin nanopillars can be utilized to achieve giant dichroism. Meanwhile, the phase state of Sb2S3 is introduced as an additional degree of freedom to further control the polarization-dependent interference thus generating LD and CD in the same structure. Moreover, the proposed method can achieve both LD and CD in transmission as well as reflection modes. This full-space feature was not achieved before. Due to the compactness and excellent performance, we envision that this work will advance the development of tunable dichroic devices and flat polarization optical elements in the optical integrated system.
© 2021 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The manipulation and characterization of polarization states of light play an important role in many applications such as spectral measurement, chemical analysis, biomedical diagnosis and polarimetric imaging [1–4]. Dichroism refers to the differential transmission, reflection or absorption between the incident orthogonally polarized electromagnetic waves and thus is generally utilized to manipulate polarization. Dichroic materials are found in the nature and extensively employed. A representative example is the dichroic crystal which was used to make inchoate polaroid [5]. Some natural helical structures such as DNA and protein exhibit circular dichroism(CD) [6]. Linear dichroism(LD) and CD are both the natural mechanism of polarization control but they are weak in natural materials due to the weak light-matter interaction. Hence, the traditional dichroic devices are generally bulky in dimensions, which is far away from miniaturization and integration for modern photonic systems.
Recently, metasurfaces with strong light-matter interaction have been considered as the efficient alternatives. Metasurfaces have shown their unprecedented abilities in efficiently tailoring phase, amplitude and polarization [7–16]. For the polarization control and characterization, a variety of planar chiral metasurfaces have been investigated to achieve impressive CD [17–24], and the nanowire-grid grating as well as nanorod were generally employed to generate high LD [25–28]. However, one nanostructure with a given dimension can only achieve single functionality with either LD or CD, which strongly hinders its application. For instance, the Stokes polarization detection contains not only linearly polarized light detection but also circularly polarized light detection [29,30]. Therefore, researchers had to integrate several different structures on a single metasurface to accomplish full-Stokes polarization detection [31,32]. Besides, all of these previous dichroic metasurfaces usually work in either transmission space or reflection space. In the face of the increasingly complex modern integrated system, the flexible full-space modulation is obviously essential.
Researchers have tried to solve the problems mentioned above. A group innovatively proposed an inverted V-shaped metal structure and successfully achieved giant LD and CD performance [33]. However, the giant LD and CD were obtained under different oblique incidences in the orthogonally incident planes respectively and only worked in reflection mode, which further complicates its optical path system and limits its application. Therefore, there is still a need for a novel method to achieve giant LD and CD under normal incidence and work in full space.
In this paper, a novel approach based on the metamolecule design is proposed to generate high LD and CD under normal incidence. By using metamolecule composed of two pairs of twin nanopillars with properly tailored anisotropic phase responses and relative rotation angles [12,15,34,35], the collective interference of light through those twin nanopillars can be controlled to generate near unitary dichroism. Meanwhile, the phase state of Sb2S3 is introduced as an additional degree of freedom to further control the collective interference from those twin nanopillars, where Sb2S3 is a new family of ultralow loss reversible nonvalatile phase change material [36]. Therefore, both LD and CD can be achieved by changing the phase state of Sb2S3. To demonstrate the method, we choose the working wavelength of 1550 nm to exhibit the LD and CD performance for the reason that Sb2S3 features ultralow loss in the near-infrared region and the wavelength of 1550 nm is widely used in optical communication. When Sb2S3 is in the amorphous state, the designed metasurface is able to preferentially transmit y-linearly polarized (YLP) incident light while reflecting x-linearly polarized (XLP) incident light, manifesting LD of 81% at the designed wavelength of 1550 nm. After changing Sb2S3 into the crystalline state by optical pulse or heating, the designed metasurface preferentially transmits right-handed circularly polarized (RCP) light and converts it into left-handed circularly polarized (LCP) light while reflecting LCP incident light, thus generating CD of 86% at 1550 nm. It is worth noting that the designed metasurface performs as well in reflection mode as in transmission mode. Therefore, this method has great potential in tunable dichroic integration device with applications in polarimetric imaging and detecting.
2. Design and methods
Figure 1 depicts the working schematic diagram of the designed metasurface with dynamic dichroic response. The orthogonally polarized light incident on the proposed metasurface experiences distinct transmission and reflection, which mainly attributes to the polarization-dependent constructive and destructive interference. In this work, when Sb2S3 is in the amorphous state, YLP incident light is preferentially transmitted due to constructive interference while XLP incident light is preferentially reflected due to destructive interference. After converting Sb2S3 into the crystalline state, similar to linearly polarized incidence, RCP incident light undergoes constructive interference while LCP incident light experiences destructive interference.
Fig. 1. Schematic illustration of the designed dichroic metasurface. The metasurface exhibits high LD when the Sb2S3 nanopillars are in amorphous state. By heating to 543 K [36], the Sb2S3 nanopillars are transited into crystalline state and the metasurface generates high CD.
Figure 2 shows the 3D and top views of the metamolecule. In this configuration, the metamolecule is composed of two pairs of twin Sb2S3 nanopillars with different dimensions and orientation angles on the top of silicon dioxide (SiO2) substrate. The metamolecules are periodically arranged in both x- and y-directions with periodicity of P=1400 nm in this work. The period (P) of metamolecule is smaller than the operating wavelength in order to avoid higher order diffraction. Each nanopillar is placed at the centre of its meta-atom whose period is P/2. Here, nanopillars with different colors represent different nanopillars with same height (h) but different dimensions (l, w). Moreover, nanopillar 1 (P1) is tilted at an angle of θ1 with respect to the x-axis with the length l1 and the width w1, and the corresponding parameters of nanopillar 2 (P2) are θ2, l2 and w2.
Here, the dichroism in transmission is defined as the transmission difference in orthogonally polarized incident light, i.e., LD = Ty−Tx, CD = TRCP−TLCP. Tx and Ty can be expressed by
Then the transmission coefficients for circularly polarized light can be easily retrieved from the linear transmission coefficients by the following formula:
According to interferential principle and Jones matrix analysis, the conditions required to implement high LD and CD are discussed in the following. By means of polarization-dependent interference, giant LD can be easily achieved. When the orientation angles of P1 and P2 are both 0, i.e. ${{\theta }_1}$=${{\theta }_2}$=0, the anisotropy of nanopillars can be designed to meet that the propagation phase difference between P1 and P2 is 0 for YLP incidence but π for XLP incidence. Under the circumstances, x-linearly polarized incidence undergoes constructive interference while y-linearly polarized incidence undergoes destructive interference, thus near unitary LD generated.
In order to generate high CD and LD in the same structure, the orientation angles of P1 and P2 should be set as: ${{\theta }_1} \ne {{\theta }_2},{{\theta }_2} = 0$. Assuming the transmission close to 1, the Jones matrices of P1 and P2 can be expressed as follows:
It can be found from Eq. (5) that the transmitted light contains both cross-polarized component and co-polarized component for P1 but only co-polarized component for P2. To ensure complete interference of the transmitted light from P1 and P2, the polarization of the transmitted light should be consistent. Consequently, the transmitted light from P1 should also contains only co-polarized component, i.e., ${{\varphi }_{\textrm{f}1}} = {{\varphi }_{\textrm{s}1}} = {{\varphi }_1}$, which indicates that P1 behaves as a full-wave plate. Since the period P is smaller than the working wavelength, the transmitted light from metamolecule can be considered as the coherent superposition of the transmitted light from distinct twin nanopillars, i.e., $T = \frac{{{T_1} + {T_2}}}{2}$. Therefore, combining Eq. (1) and (5), the transmission of metamolecule for XLP and YLP incident light can be theoretically calculated as follows:
As a consequence, under the condition of ${{\varphi }_{\textrm{f}1}} = {{\varphi }_{\textrm{s}1}} = {{\varphi }_1}$, we can achieve arbitrary LD by only changing ${\Delta }{\phi _\textrm{x}}$ and ${\Delta }{\phi _\textrm{y}}$ which are related to the dimensions of nanopillars. For instance, unitary LD (i.e., ${\mathrm{{\rm T}}_\textrm{y}} = 1$ and ${\mathrm{{\rm T}}_\textrm{x}} = 0$) can be achieved at $\Delta {\phi _\textrm{y}} = 0$ and $\Delta {\phi _\textrm{x}} = \mathrm{\pi }$. Therefore, the phase retardations of P1 and P2 satisfy ${\mathrm{\varphi }_1} - {\mathrm{\varphi }_{\textrm{f}2}} = \mathrm{\pi }$ and ${\mathrm{\varphi }_1} - {\mathrm{\varphi }_{\textrm{s}2}} = 0$, and then ${\mathrm{\varphi }_{\textrm{f}2}} - {\mathrm{\varphi }_{\textrm{s}2}} = \mathrm{\pi }$ is obtained, which indicates that P2 behaves as a half-wave plate. Overall, to achieve unitary LD, the metamolecule should satisfy that P1 works as a full-wave plate while P2 works as a half-wave plate and the phase retardations along the slow axes of P1 and P2 are consistent.
By properly designing the anisotropy and relative rotation angles of twin nanopillars, circularly polarized light incident on the metasurface experiences polarization-dependent constructive or destructive interference. Combining Eq. (3) and (5), the Jones matrices of circular basis of P1 and P2 can be simply expressed by
It can be seen from Eq. (8) that the transmission ${\mathrm{{\rm T}}_{\textrm{LCP}}}$ and ${\textrm{T}_{\textrm{RCP}}}$ are determined by the phase difference $\mathrm{\Delta }{\phi _\textrm{L}}$ and $\mathrm{\Delta }{\phi _\textrm{R}}$, respectively. Moreover, the total phase difference includes the propagation phase difference and the geometric phase difference, where propagation phase difference is spin-independent while geometric phase difference is spin-dependent. Therefore, by adjusting the dimensions and relative rotation angle of nanopillars, we can achieve arbitrary CD. For example, to generate near unitary CD, i.e., ${\mathrm{{\rm T}}_{\textrm{RCP}}} = 1$ and ${\mathrm{{\rm T}}_{\textrm{LCP}}} = 0$, the total phase difference can be designed to satisfy the condition of $\mathrm{\Delta }{\phi _\textrm{R}} = 0$ and $\mathrm{\Delta }{\phi _\textrm{L}} = \mathrm{\pi }$. Hence, as long as the propagation phase difference between P1 and P2 satisfies ${{\mathrm{\varphi} }_{\textrm{f}1}} - {\mathrm{\varphi }_{\textrm{f}2}} = {\raise0.7ex\hbox{$\pi$} \!\mathord{\left/ {\vphantom {{\pi } 2}}\right.}\!\lower0.7ex\hbox{$2$}}$ and the relative orientation angle satisfies ${\mathrm{\theta }_1} = {\raise0.7ex\hbox{$\pi $} \!\mathord{\left/ {\vphantom {{\pi } 4}}\right.}\!\lower0.7ex\hbox{$4$}}$, near unitary CD can be systematically achieved at designed wavelength.
Hereinbefore, we have obtained the requirements for the realization of high LD and CD, but it is obviously impossible to simultaneously satisfy these requirements in the same condition. (e.g. P1 works as half-wave plate for generating unitary CD but full-wave plate for generating unitary LD). Here, the different states of phase change material are introduced as additional degree of freedom, i.e., achieving high LD and CD at different states, respectively. Among phase change materials, Sb2S3 is a new family of reversible phase change materials. The complex refractive index of Sb2S3 in the near-infrared region was experimentally measured by M. Delaney et al. [36]. It was demonstrated that Sb2S3 features ultralow loss at both crystalline and amorphous states and large refractive index difference between crystalline and amorphous states in the near-infrared region. These features ensure that the phase responses of Sb2S3 nanopillar at different states are quite distinct. Moreover, Sb2S3 can be reversibly switched between crystalline and amorphous states by heating. Therefore, Sb2S3 is chosen to assist in achieving giant LD and CD under the normal incidence in the same structure.
3. Results and discussions
According to the theoretical analysis, the proper parameters of nanopillars for achieving giant CD and LD in different states of Sb2S3 can be found out. With the commercial finite-difference time-domain software (Lumerical FDTD Solutions, Lumerical Inc., Vancouver, Canada), the transmission and phase modulation of nanopillars as well as the performance of metamolecule were simulated. The refractive index of Sb2S3 is adopted from Ref. [36], and the refractive index of SiO2 is set to 1.45. Based on the requirements obtained above, the transmission under XLP and YLP incidence in both amorphous and crystalline states should be near unity. Furthermore, for generating CD, the phase difference of π between XLP and YLP incidence for each nanopillar (i.e. $\mathrm{\Delta }\phi = {\mathrm{\varphi }_\textrm{f}} - {\mathrm{\varphi }_\textrm{s}} = \mathrm{\pi }$) should be mainly considered. For generating LD, the phase difference of 2π for P1 and π for P2 (i.e. $\mathrm{\Delta }{\phi _1} = 2\pi ,\; \mathrm{\Delta }{\phi _2} = \mathrm{\pi }$) are mainly considered. The height (h) of each nanopillar is fixed at 1.3 µm to ensure that many nanopillars with required $\mathrm{\Delta }\phi $ can be obtained in the results of scanning the length and width. Figure 3 shows the transmission and phase difference between XLP and YLP incidence varying with dimensions when Sb2S3 is in the amorphous and crystalline state. Considering the requirements of generating high LD and CD, the parameters of P1 are chosen as l1=390 nm, w1=240 nm and the parameters of P2 are chosen as l2=560 nm, w2=270 nm, which are marked in Fig. 3. The transmission and phase responses of P1 and P2 in amorphous states are close to the requirements for realizing high LD while those of P1 and P2 in the crystalline satisfy the requirements for generating high CD.
Fig. 3. The simulated transmission and phase responses of Sb2S3 nanopillars with varying dimensions at the designed wavelength 1550 nm. (a) The transmission under XLP incidence and (b) phase difference between XLP and YLP incidence for Sb2S3 in amorphous state. (c) The transmission under XLP incidence and (d) phase difference between XLP and YLP incidence for Sb2S3 in crystalline state.
Due to the slight mismatch with the ideal requirements, θ1 can be changed to further optimize the LD and CD performance of the metamolecule. Here the LD spectra in amorphous state and CD spectra in crystalline state are simulated with θ1 varying from 40° to 50°, which are shown in Fig. 4(a) and (b). To focus on the LD and CD performance at 1550 nm, the LD and CD performance varying with θ1 from 35° to 55° at 1550 nm is shown in Fig. 4(c). Figure 4(c) indicates that LD increases at first and then decreases as θ1 increases and reaches the largest value at θ1=40°. Similarly, it can be seen from Fig. 4(c) that CD increases at first and then decreases as θ1 increases and reaches the largest value at θ1=46°. As a consequence, we set θ1=42° as the optimum parameter so that both LD and CD are over 80% at 1550 nm.
Fig. 4. (a) LD and (b) CD spectra vary with θ1 from 40° to 50°. (c) LD and CD varies with θ1 from 35° to 55° at 1550 nm.
Figure 5(a) and (b) illustrate the transmission performance of the proposed metamolecule in amorphous state from 1500 nm to 1600 nm. It can be seen from Fig. 5(a) that the amplitude of complex transmission coefficient txx approaches 0, and the non-zero of txy and tyx may attribute to the imperfect full-wave plate. In addition, tyy close to 1 means that YLP light transmits through the metasurface and maintains the polarization state. Figure 5(b) shows the simulated transmission for linearly polarized light and the calculated LD which reaches 81% at 1550 nm. Transiting Sb2S3 into crystalline state, the transmission performance is shown in Fig. 5(c) and (d). At the designed wavelength, due to the imperfect half-wave plate and incomplete destructive interference of RCP, the amplitudes of tRR are slightly larger than 0, which is illustrated in Fig. 5(c). Even so, tLR is much larger than tRR and thus RCP light flips it’s handedness through the metasurface. As shown in Fig. 5(d), the transmissions for RCP and LCP light are 86% and 0 with CD reaching 86% at 1550 nm. These results indicate that the great performance of the metasurface is comparable with the previously reported works only achieving CD or LD.
Fig. 5. The performance of the proposed metasurface. (a) The complex transmission coefficient spectra and (b) transmission spectra under the linearly polarized incidence when Sb2S3 nanopillars are in amorphous states. (c) The complex transmission coefficient spectra and (d) transmission spectra under the circularly polarized incidence when Sb2S3 nanopillars are in crystalline states.
Most of previous works achieved dichroism (especially CD) by means of polarization-selective absorption, resulting in that they merely exhibited dichroism in transmission mode or reflection mode [18,21–23,33]. In this work, the orthogonally polarized light incident on the metasurface experiences polarization-dependent interference, which means that one polarized light experiences constructive interference leading to complete transmission while the orthogonally polarized light experiences destructive interference leading to complete reflection. Therefore, the designed metasurface can generate dichroism not only in transmission mode but also in reflection mode. The working modes can be chosen at will, which will offer great convenience for practical applications. The reflection for XLP, YLP, LCP and RCP incidence can be expressed by following formulas:
Moreover, to further explain that the dichroic performance is the same in reflection mode and transmission mode, we calculate the absorption for XLP, YLP, LCP and RCP incidence. The absorption can be calculated by:
Figure 6 illustrates the reflection and absorption of the metasurface. The performance of the metasurface in amorphous state under linearly polarized incidence is shown in Fig. 6(a), (b) and (c) and the performance of the metasurface in crystalline state under circularly polarized incidence is shown in Fig. 6(d), (e) and (f). As shown in Fig. 6(a) and (d), the co-polarized reflection coefficients have the quite different amplitude, while the cross-polarized reflection coefficients have the same amplitude. Therefore, dichroism in reflection is obtained. It can be seen from Fig. 6(b) and (e) that LD of 81% and CD of 86% are achieved at 1550 nm, respectively. It is obvious that the dichroic performance in transmission and reflection modes is almost consistent, which attributes to the ultralow loss of the designed metasurface. The absorption spectra shown in Fig. 6(c) and (f) confirm the ultralow loss feature of the designed metasurface.
Fig. 6. The reflection and absorption of the designed metasurface (a) The complex reflection coefficient spectra, (b) reflection spectra ($\textrm{LD} = {\textrm{R}_\textrm{x}} - {\textrm{R}_\textrm{y}}$) and (c) absorption spectra under the linearly polarized incidence when Sb2S3 nanopillars are in amorphous state. (d) The complex reflection coefficient spectra, (e) reflection spectra ($\textrm{CD} = {\textrm{R}_{\textrm{LCP}}} - {\textrm{R}_{\textrm{RCP}}}$) and (f) absorption spectra under the circularly polarized incidence when Sb2S3 nanopillars are in crystalline state.
4. Conclusion
In summary, we have proposed a strategy for generating high CD and LD in the same structure under normal incidence and implemented it in full space. The high dichroism stems from the fact that incident light undergoes polarization-dependent interference through adjacent nanopillars. According to the interferential condition and Jones matrix analysis, the requirements for generating CD and LD are theoretically derived in detail. Moreover, taking advantage of the phase transition property of Sb2S3, the metamolecule is designed to generate high CD and LD in the near-infrared region at different states of Sb2S3, respectively. This design strategy can be readily extended to other electromagnetic spectra by using other phase change materials. When Sb2S3 is in the amorphous state, the metasurface exhibits LD of 81% at 1550 nm in transmission mode. By heating Sb2S3 into crystalline state, the metasurface is changed to exhibit CD of 86%. With this design strategy, the metasurface can also work well in reflection mode. The high dichroism performance, tunability, full-space working modes and simple structure endow this work with great potential in polarization imaging, displaying and spectroscopy applications.
Funding
Science and Technology Program of Guangzhou (2019050001); National Natural Science Foundation of China (11674109, 61774062, 61875057); Natural Science Foundation of Guangdong Province (2019A1515011578, 2021A1515010352).
Disclosures
The authors declare no conflict of interest.
Data availability
All data and models generated or used during the study appear in the submitted article.
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