A metasurface, as a two-dimensional artificial material, can achieve unique physical properties by changing the geometric size and periodic arrangement of structural units [1–3]. Metasurfaces offer more compact platforms for the investigation of light-matter interaction, as well as a wide range of practical applications [4,5]. The electromagnetic wave’s amplitude, phase, polarization, and nonlinearity could be precisely controlled by the metasurface [6–8], notably the phase modulation, which plays an important role in fields such as metalenses [9], holograms [10], and beam steering [11]. Since its creation, the idea of programmable metasurfaces and digital coding has been extensively researched [12], offering a fresh viewpoint on the real-time control of electromagnetic wave propagation [13–15]. For coding a metasurface, the binary codes “0” and “1,” which stand for the discretized reflection phase, have recently been presented as an alternate method of realizing electromagnetic wave manipulation [16–18]. However, the independent control of circularly polarized light based on a phase coding metasurface is still lacking, especially for cross-polarization conversion [16,17]. It is relatively simple to manage linear polarization light by altering the geometric parameters of the metasurface unit structure, while circular polarization (CP) is more challenging. Currently, the mainstream method is to regulate CP through the Pancharatnam-Berry (PB) phase, which has one clear drawback. It is challenging to accomplish independent control of CP light since the phase modulation of the PB phase is the opposite for right-handed circularly polarized (RCP) light and left-handed circularly polarized (LCP) light. Therefore, the composite phase is introduced to achieve multi-dimensional optical field control of multifunctional surface devices [19–21]. The arbitrary phase modification for LCP and RCP light has been accomplished by integrating the propagation phase and PB phase [19]. Even though this approach can produce positive outcomes, an extra simple and straightforward approach is still required to decouple and independently regulate the CP light [21]. Non-Hermitian systems based on parity-time (PT) symmetric transformations have real eigenvalues as well, which were discovered by Bander and Boettcher in 1998 [22]. The exceptional point (EP), as the phase transition point of open systems, manifests unique characteristics that greatly enrich the research and development in the field of open systems [23–26]. Based on the advantages of flexible construction and the unconstrained regulation of the equivalent permittivity, the research on the non-Hermitian metasurfaces is also highly fascinating, especially in the polarization space [27–31]. There has been a substantial advancement in the fields of chiral detection, polarization imaging, and high sensitivity sensing based on a PT symmetric metasurface. Interestingly, it has been discovered that the surrounding of an EP may produce unique mode selection features and generate a topological phase. This is a new phase formation mechanism to distinguish from the previous propagation phase and PB phase [28]. Exceptional topological phase (ETP) enriches the method of phase regulation and can be combined with traditional phase control, which greatly enriches the design and application of metasurfaces [32–34].

In this work, by designing a PT symmetric metasurface, it is found that the polarization eigenstates have degeneracy at EP, which is related to the chirality of the system, and the $2\pi$-phase accumulation occurs through any path around EP. The independent polarization control of CP light is realized. This novel approach utilizes the phase accumulation generated around the EP, which is plainly distinct from the conventional geometric phase. The potential of phase coding is confirmed based on the ETP, while combined with the conventional PB phase, a composite phase coding metasurface is created to accomplish the independent regulation of RCP and LCP light. This work not only simplifies the structure design and phase distribution of CP regulation but also promotes the development of multifunctional coding metasurfaces.

As schematically shown in Fig. 1, the metasurface consists of three layers, consisting of two lossy aluminum [35] spaced by silica with permittivity 2.31. The metal background resists all transmission so that the metasurface works in the reflective regime. The structured layer is formed by a chiral structure array and can be excited by $x$-polarized and $y$-polarized waves, respectively (see Appendix A). For describing the coupling between two resonators, coupled-mode theory is a popular and efficient method. To create the Hamiltonian matrix for the PT symmetric system, the reflection matrix and coupled-mode equation are combined (see Appendix B). Considering that the reflection matrix $\widehat{r}$ and the system Hamiltonian $H$ have the same eigenvector, it is more straightforward to re-express the reflection matrix in the circular polarization basis as [29] $$\widehat{r}=\left(\begin{array}{ll}{r}_{++}\hfill & r_{+-}\hfill \\ r_{-+}\hfill & r_{--}\hfill \end{array}\right),$$(1)where subscripts $+$ and $-$ represent RCP and LCP, respectively. It can be seen from the reflection matrix that $r_{++}=r_{--}$, and the eigenvalues are $r_{\mathrm{1,2}}=r_{++}\pm \sqrt{r_{+-}{r}_{-+}}$. The condition required to achieve EP is $r_{+-}{r}_{-+}=0$. Since the $x$- and $y$- polarized resonances occur in the metasurface, we can adjust the resonances concerning each other by a variation of the structural parameters, and in consequence, allow for engineering the reflection behavior with $r_{+-}=0$ or $r_{-+}=0$, which means EP occurs. Through CST simulation, it can be seen that cross-polarized reflection curve $r_{-+}$ (red curve) suddenly drops nearly to zero at 667 nm in Fig. 2(a), while $r_{+-}$ (blue curve) does not change. This is due to the degeneracy of the eigenpolarization state of the system at the EP, where there is only RCP; therefore no cross-polarization conversion $r_{-+}$ occurs. The emergence of EP can be proved more clearly by solving the system eigenvalues. As shown in Fig. 2(b), it is obvious that the real and imaginary parts of the eigenvalues coalesced at 667 nm, which is consistent with the phenomenon in Fig. 2(a).

The degeneracy of eigenvalues is one of the key distinctions between non-Hermitian and Hermitian systems. In a non-Hermitian system, two or more intersecting Riemann surfaces centered around an EP are formed. As shown in Fig. 3, we reveal the evolution of system eigenvalues in parameter space ($L_1$, $L_3$). The existence of an EP is demonstrated by the spectrum of $r_{-+}$ and the degeneracy of its eigenvalues and eigenstates at $\lambda =667\mathrm{nm}$. The intersecting double Riemann surface that corresponds to the eigenvalues of the reflection matrix further supported this pattern. It is very evident that the eigenvalues will be switched rather than the recurrence of their original values under a single full loop around the EP, and they will only do so under two full loops. This provides clear and convincing evidence that the EP exists in our system [28,31,36].

To observe the exceptional topologic phase of the eigenvalues’ surface, two parameters need to be varied, as shown in Fig. 4. $L_1$ and $L_3$ were chosen because they play important roles in the $y$- and $x$-polarized resonances [28]. As expected, the reflection matrix from the metasurface can be tailored with varying parameters. By changing the geometric parameters of the structures, it can be clearly seen that EP appears only when a single circular polarization is incident, and there is a significant $2\pi$ phase accumulation around EP. As long as the reflected phase encircles one EP in parameter space, the $2\pi$ phase accumulation is preserved regardless of the closed path. In contrast to the classical PB phase, this type of phase accumulation caused by circling a singularity exhibits a clear topological robustness.

Compared to the conventional coding metasurface, the ETP metasurfaces require no complicated phase independent CP control [16]. Choosing the “0” and “1” elements, as shown in Fig. 5, the parameters of the two elements are as follows: $(L_1,L_3)=(81,102)$ (nm) and $(L_1,L_3)=(48,135)$ (nm). With the RCP, due to the existence of an EP, there is a $\pi$ phase delay between the two elements, and the reflective amplitudes are almost the same as shown in Figs. 5(b) and 5(d). On the contrary, since there is no EP under the LCP incidence, their phase values are the same. Thus, it is possible to achieve CP coding independently. It is worth noting that both elements “0” and “1” have no phase differences when rotation occurs. This is merely due to differences in geometric parameters, which are also distinct from the conventional use of PB phase for CP encoding.

Since ETP is a topological phase generated around a singularity, it can be combined with PB phase to achieve more complex phase coding (see Appendix C). In Fig. 6, we chose the previous “0” and “1” elements, represented in green and blue, to satisfy the phase delay $\pi$ for RCP incidence. We implement the new coding unit at LCP incidence by rotating the “0” and “1” elements that exist only at the ETP for RCP incidence, shown in red and indigo. To verify the feasibility of its encoding, a 1-bit encoded metasurface based on ETP was proposed. Two types of elements are arranged in the pattern of “0101,” represented by green and blue colors, respectively. As mentioned earlier, these two elements exhibit a phase difference of $\pi$ for RCP incidence, while they have the same phase for LCP incidence. Due to this feature, there is a significant difference in the reflected waves for different polarizations. Specifically, the reflected RCP waves are split and deflected in the $\pm 45°$ direction, while the reflected LCP waves are emitted vertically, as shown in Figs. 7(a) and 7(b). It is worth mentioning that the far-field scattering patterns here are all cross-polarized reflections. This polarization-selective characteristic is a result of the ETP. Compared to conventional phase coding metasurface that requires independent control of CP, the novel coding scheme based on the ETP greatly simplifies the design of metasurface structures and eliminates the need for complex phase calculations (see Appendix D).

In order to further explore the advantages of ET phase coding, we try to combine ETP with PB phase to design a compound phase coding metasurface to realize more complex CP beam modulation. Using the result of the ETP coding in the previous step, the “0” and “1” elements are both rotated 90° to achieve PB phase. A 2-bit compound phase coded metasurface is finally obtained through the convolution operation, as shown in Fig. 8. In fact, we still choose only “0” and “1” as two elements, but the rotation of the elements is increased. When RCP is incident, four-beam reflection is generated, while two-beam reflection corresponds to LCP incidence. When RCP is incident, the metasurface is 2-bit encoded due to the presence of EP. When LCP light is incident, the metasurface is equivalent to a 1-bit PB phase coded metasurface. The two designs can be in superposition since in contrast to the PB phase, the ETP is generated by circling a singularity and is topologically robust [28,37].

In a reflection regime, we have shown that a planar chiral plasmonic metasurface achieves $2\pi$ exceptional topological phase accumulation. It is demonstrated that only one of the circular polarization conversion beams, as specified by the chirality of the encircling exceptional point, is subject to $2\pi$ phase accumulation. By choosing two elements around an exceptional point, a coding metasurface can be realized based on exceptional topological phase and achieve the independent control of circular polarization. More importantly, exceptional topological phase can be combined with Pancharatnam-Berry phase to accomplish 2-bit coding metasurface designs. The $2\pi$ topological phase coding design based on the surrounding of an exceptional point is a new method in polarization control and extends the platform for nanophotonics applications by utilizing the nontrivial characteristics.