1. Introduction

Nanostructures with broken chiral symmetry, which offer an attractive approach for realizing strong interaction with circularly polarized light (CPL) [1–13], have enormous potential for applications such as ultracompact polarization components [1,14], enhanced enantiomeric sensing of biochemical substances [15–17], etc. Given the three-dimensional (3D) structure of CPL, 3D chiral nanostructures are in general required to achieve strong chiroptical responses. In contrast to the chiral metamaterials operating in the transmission mode, the recently reported chiral meta-mirrors can achieve strong chiral responses in the reflection mode [18,19]. In particular, a chiral meta-mirror strongly absorbs CPL of one handedness and highly reflects the other but preserves its initial polarization state. Therefore, chiral meta-mirrors can be considered as one-way reflection metadevices without relying on magneto-optical or nonlinear materials [20–23]. More importantly, requiring only a single nano-engineered layer, chiral meta-mirrors allow optical designers to circumvent the difficulties typically associated with 3D nano-fabrication, which can potentially lead to a series of practical chiral metadevices. For instance, chiral-selective nonlinear signal generation and optical imaging have been observed in plasmonic meta-mirrors [24]. Leveraging the carrier dynamics in α-Si under optical excitations, ultrafast switching of light polarization in a dielectric-plasmonic hybrid chiral meta-mirror has been reported [25]. A close inspection shows that the strong chiral response from most of the reported studies originates from spin-selective resonant cavities which, for fixed cavity geometries, is primarily determined by the structural and symmetry properties of the nano-patterned layer. These properties not only explain the narrowband chiroptical response in most of the reported studies (e.g. < 100 nm for a resonance around 900 nm [24]), but also shine new light on achieving broadband strong chirality [26].

For a chiral mirror with metal/dielectric/metal-backplane sandwich structures, the chiral resonance design shares similarity with the engineering of a metamaterial absorber which can be described by interference theory [27]. In contrast to the metamaterial absorbers for linear polarized waves, the overall reflection of a chiral meta-mirror when it interacts with CP waves can be written as ${r^{\textrm{CP}}} = r_{12}^{\textrm{CP}} - r_{23}^{\textrm{CP}}t_{12}^{\textrm{CP}}t_{21}^{\textrm{CP}}{e^{i2\mathrm{\beta }}}/({1 + r_{21}^{\textrm{CP}}{e^{i2\mathrm{\beta }}}} )$. Note that $r_{12}^{\textrm{CP}}$, $r_{21}^{\textrm{CP}}$, $t_{12}^{\textrm{CP}}$, and $t_{21}^{\textrm{CP}}$ are the handedness-dependent complex reflection and transmission coefficients at the air-structure and spacer-structure interfaces, β is a spacer-induced complex propagation phase, while $r_{23}^{\textrm{CP}}$ is the complex reflection coefficient at the spacer-backplane interface and $r_{23}^{\textrm{CP}} \approx{-} 1$ in the near-infrared regime. Accordingly, the key features of chiral meta-mirrors, i.e., the chiral-selective absorption and the polarization preservation upon reflection (e.g., $|{{r^{\textrm{LCP}}}} |\to 1$, and simultaneously $|{{r^{\textrm{RCP}}}} |\to 0$), stem from the handedness-dependent reflection and transmission behavior of the nano-engineered plasmonic layer. These requirements make the design of broadband chiral meta-mirrors a challenging engineering task for empirical methods. On the other hand, metadevices exhibiting strong chiroptical response over a broad bandwidth have numerous applications in biosensing, chiral photochemistry, pharmaceuticals, etc. Therefore, broadband chiral meta-mirrors based on an advanced inverse-design strategy are highly desired, but have so far remained unexplored.

Here in this work, by leveraging a genetic algorithm (GA) based optimization approach, we numerically validate a plasmonic chiral meta-mirror exhibiting handedness-selective reflection (absorption) over an octave bandwidth in the near-infrared spectrum. By performing a field analysis, we show that the observed broadband strong chiral response is attributed to the multiple chiral resonances across the wavelength range of interest. Beyond the linear regime, based on the Lorentz reciprocity theorem, we show that, under circularly polarized excitations, the chiral meta-mirror gives rise to broadband spin-dependent second harmonic generation (SHG). Note that our customized GA inverse-design method, which satisfies the potential fabrication restrictions (e.g., in e-beam lithography), can also be employed to facilitate the rapid exploration of chiral metadevices with other desired functionalities, such as enhanced optical chirality for chirality detection of enantiomers.

2. Device optimization and discussions

Global optimization algorithms based on evolutionary computation have been widely used in the design of electromagnetic devices due to their capability in effectively optimizing high-dimensional multi-modal problems [28]. Among the popular approaches, the GA, which can represent a wide range of unique designs using a binary bitstring, has been used to achieve metadevices exhibiting broadband optical response [14,29,30]. Figure 1 illustrates the chiral meta-mirror consisting of a GA optimized (50-nm-thick) gold layer, separated from an unpatterned gold backplane by a 150-nm-thick SiO₂ spacer. The unit cell of the optimized design is displayed on the bottom-right in Fig. 1, while the inference model of the chiral meta-mirror is shown on the top-right. The non-intuitive asymmetric structure of the optimized design offers the desired broadband handedness-dependent response and, on the other hand, indicates the potential of advanced inverse-design methods for meeting a challenging set of metadevice specifications. Importantly, recent studies have shown that deep-learning-assisted methods can be used in the design of chiral metadevices with optimal chiroptical responses [31].

 

Fig. 1. A GA optimized chiral meta-mirror for broadband strong chiroptical responses. The chiral meta-mirror strongly absorbs a CP wave of one spin state and reflects that of the opposite spin while preserving its polarization state. Bottom-right inset: Schematic of the unit cell that consists of a nano-engineered gold layer (50-nm-thick), a SiO₂ spacer (150-nm-thick), and an optically thick gold backplane. P_x = P_y = 500 nm. Top-right inset: Schematic of the interference analysis. $r_{12}^{\textrm{CP}}$, $r_{21}^{\textrm{CP}}$, $t_{12}^{\textrm{CP}}$, and $t_{21}^{\textrm{CP}}$ are the complex circular reflection and transmission coefficients at the air-structure and spacer-structure interfaces, while $r_{23}^{\textrm{CP}} \approx{-} 1$.

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Figure 2(a) illustrates the iterative design process of our GA optimization. In particular, the GA optimizer starts with a set of initial random designs. Note that, with the fixed periodicity (P_x = P_y = 500 nm) and spacer thickness (t_s = 150 nm), the top patterned layer was optimized by encoding a unit cell of the nanostructure as a 10 × 10 binary grid, where “1” denotes a discretized pixel with a gold material property and “0” represents a pixel without a gold feature. This binary representation was selected based on a balance between the optimization efficiency and the feature size satisfying the restrictions of the nano-fabrication approaches. In other words, using voxels that are too small would considerably slow down the optimization process and likely end up with designs that are impractical to fabricate, while, on the other hand, using voxels that are too big, the optimizer may not be able to find a good topology due to the limited parametric search space. Furthermore, a square lattice of 500 nm was selected based on the following two considerations. First, in the linear regime, a planar structure with this periodicity can support strong resonances in the wavelength range of interest. Second, in the nonlinear regime, no diffraction occurs when the SHG signal emits from the structure at the shortest wavelength of interest. Before running the evaluation (simulation), sharp connections between orthogonal neighboring pixels are improved as shown in Fig. S1 (Supplement 1). Following the evaluation, the optimizer ranks and selects outperforming designs which are used to create new ‘child’ designs based on the crossover and mutation processes. This procedure is iterated until the convergence criteria is met. The optimization objective was set to be the average absorption difference between the two circular polarizations, i.e., CD_avg = |A$_{\mathbb{RCP}}$-A$_{\mathbb{LCP}}$| across eleven equally spaced wavelengths from 1000 to 2000 nm. We note that the shape generation approach employed here, which allows the structure to connect to neighboring unit cells, is essential for achieving unit cell designs with broader bandwidth. The gray curve in Fig. 2(b) illustrates the objective value for the evaluated designs during the optimization process, while some typical designs over the course of the optimization indicate the design evolution. Note that our optimization process terminates when no improvement to the objective function was observed for multiple succeeding generations. Our simulations were performed using a frequency domain FEM commercial solver (Comsol Multiphysics v5.5). Periodic boundary conditions were imposed in all unit cell simulations, in which tetrahedral meshing was employed. The mesh elements were tetrahedrals and the largest element dimension was less than λ/6 or finer for the non-gold regions. For the gold regions, the mesh size was iteratively reduced until the solution results converged. Figure 2(c) shows the handedness-dependent total absorption spectra of the optimized design, in which an average CD greater than 0.65 is observed in the wavelength range from 1000 to 2000 nm. To investigate the robustness of the optimized design, a parametric study of the broadband chiroptical response of the optimized design has been performed and summarized as Fig. S3 (Supplement 1). In particular, the simulation results have shown that the overall performance of the proposed metamirror is robust to the thickness of the top Au layer, the thickness of the SiO₂ spacer, the rounding of corners, and structure incompletion. This study illustrates the fabrication-friendly nature of the design as well as the feasibility of the proposed chiral metamirrors for use in practical applications.

 

Fig. 2. Optimization of the chiral meta-mirror. (a) Flowchart of the optimization process. (b) The average absorption difference between the two circular polarizations. Some typical designs shown on the left illustrate the evolution of the design process. (c) The handedness-dependent absorption spectra of the optimized design based on COMSOL simulations.

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To provide a complete picture of the chiroptical properties of the optimized broadband chiral meta-mirror, an analysis of the reflection polarization, enantiomeric property, and anisotropy property is conducted and summarized in Fig. 3. In particular, Fig. 3(a) depicts the handedness-dependent reflection spectrum of the design obtained from the optimization which is referred to as enantiomer A in the following discussion. R$_{\mathbb{LL}}$ (R$_{\mathbb{LR}}$) denotes the power reflection coefficient, i.e., the ratio between the LCP (RCP) portion of the reflected power and that of the LCP incidence, while R$_{\mathbb{LR}}$ (R$_{\mathbb{RL}}$) corresponds to the cross conversion of circular polarization. Figure 3(a) shows that the cross conversion effect is weak (R$_{\mathbb{LR}}$ and R$_{\mathbb{RL}}$ are small) and, due to the symmetry of the unit cell, R$_{\mathbb{LR}}$ = R$_{\mathbb{RL}}$ [32]. More importantly, enantiomer A exhibits high reflectance under RCP illumination and the reflected light preserves its initial state of circular polarization. Simultaneously, enantiomer A shows low reflectance under LCP illumination. Given the zero transmissivity of the system (T = 0), this reflection behavior leads to handedness-dependent absorption (A = 1 - R). The schematic shown on the left of Fig. 3(a) depicts the mirror-image relationship between enantiomer A and B. Figure 3(b) illustrates the handedness-dependent reflection spectrum of enantiomer B, in which the handedness-flipped chiroptical response under CPL illumination reveals the enantiomeric characteristic of the optimized structure. Furthermore, it is important to note that the observed chiral reflection behavior originates from both the broken 2D-chiral symmetry of the nano-engineered layer and its optical anisotropy. To characterize the corresponding anisotropic property, we simulate the response of the optimized design (enantiomer A) under x- and y-polarized illumination at normal incidence. The reflectance (absorption) spectra shown in Fig. 3(c) and (d) clearly show the polarization-sensitive optical response to a linearly polarized wave, which is attributed to the lack of in-plane rotational symmetry of the optimized design.

 

Fig. 3. Chiroptical property analysis of the optimized design. Reflectance spectra of the co- and cross-polarization components when (a) enantiomer A and (b) enantiomer B is under LCP and RCP illumination, respectively. Inset: The corresponding handedness-dependent absorption spectra. The enantiomeric sketches of enantiomer A and enantiomer B are shown on the left of (a). Reflectance spectra of the co- and cross-polarization components when enantiomer A is under (c) x-polarized and (d) y-polarized illumination, respectively. Inset: The corresponding absorption spectra. The schematic of the linearly polarized excitation is shown on the left of (c).

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Beyond the linear regime, the observed broadband strong chiroptical response indicates the potential of the optimized chiral meta-mirror for spin-dependent enhanced nonlinearities in a wide frequency range. Here, we focus on the broadband chiral-selective SHG enabled by the optimized meta-mirror. Based on the enhanced light-matter interaction arising from the plasmonic resonance, plasmonic nanostructures have been widely used to demonstrate strong and controllable nonlinear generations using relatively low excitation power [33]. According to the nonlinear scattering theory, the nonlinear emission from the plasmonic nanostructures can be quantified using the Lorentz reciprocity theorem [34], i.e., ${E_{\textrm{nl}}}({2\omega } )\propto \mathrm{\int\!\!\!\int }{\chi _{\textrm{nnn}}}E_\textrm{n}^2(\omega )\cdot {E_\textrm{n}}({2\omega } )\textrm{dS}$, where ${E_{\textrm{nl}}}({2\omega } )$ and ${\chi _{\textrm{nnn}}}$ are the field of nonlinear emission and the local nonlinear susceptibility, whereas ${E_\textrm{n}}(\omega )$ and ${E_\textrm{n}}({2\omega } )$ are the local linear field normal to the surface of the nanostructure [35]. Establishing the relationship between the nonlinear field in the far-zone regime and the local linear fields, this approach has been widely used in the quantitative analysis of the nonlinear response of plasmonic nanostructures without involving nonlinear calculations (simulations) [35–38]. In particular, for circularly polarized SHG from chiral nanostructures, the spin-dependent field distribution at both fundamental ($E_\textrm{n}^{\textrm{CP}}(\omega )$) and second harmonic ($E_\textrm{n}^{\textrm{CP}}({2\omega } )$) frequencies are required [36,37]. Importantly, this method allows us to differentiate the co- and cross-polarization components of the circularly polarized SHG signal emitted from the chiral plasmonic nanostructures under CP excitation.

Figure 4(a) shows the simulated polarization-dependent SHG spectra for enantiomer A. The notation $\mathbb{L}$_ω$\mathbb{L}$_2ω ($\mathbb{L}$_ω$\mathbb{R}$_2ω) corresponds to the LCP excitation enabled LCP (RCP) SHG signal, while $\mathbb{R}$_ω$\mathbb{L}$_2ω ($\mathbb{R}$_ω$\mathbb{R}$_2ω) corresponds to the RCP excitation enabled LCP (RCP) SHG signal. A SHG peak is identified for both $\mathbb{R}$_ω$\mathbb{L}$_2ω and $\mathbb{R}$_ω$\mathbb{R}$_2ω spectra around 1710 nm wavelength. Furthermore, it is found that SHG for RCP excitation (red solid and dashed curves) is significantly greater than that for LCP excitation (blue solid and dashed curves) in the wavelength range of interest. This can be more clearly seen from the handedness-dependent total SHG intensity in a logarithmic scale shown in Fig. 4(b). These results unambiguously demonstrate the feasibility of the optimized chiral meta-mirror for broadband spin-dependent enhanced nonlinearities. It is important to note that although the observed enhanced SHG is based on our optimization at the fundamental wavelengths, as shown in the following discussion, co-optimization at both fundamental and harmonic wavelengths might be desired to achieve better control over the nonlinearities of the chiral metadevices.

 

Fig. 4. Handedness-dependent second harmonic generation (SHG) from the chiral meta-mirror. (a) Calculated circularly polarized SHG signal emitted from the optimized meta-mirror (Ent A) under circular polarization excitations. (b) The total SHG emitted from the system under circular polarization excitations.

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The observed spin-dependent SHG spectra shown in Fig. 4 embody the chiral-selective field enhancement in the optimized chiral meta-mirror. Note that, according to Lorentz reciprocity theorem, the nonlinear emission from chiral plasmonic nanostructures under CP excitation results from the contribution of $E_\textrm{n}^{\textrm{CP}}(\omega )E_\textrm{n}^{\textrm{CP}}(\omega )E_\textrm{n}^{\textrm{CP}}({2\omega } )$. Therefore, to better elucidate the CP-dependent SHG from the meta-mirror, electric field distributions at a series of fundamental wavelengths and their second-harmonic wavelengths, are presented in Fig. 5, along with the distributions corresponding the amplitude of $E_\textrm{n}^{\textrm{CP}}(\omega )E_\textrm{n}^{\textrm{CP}}(\omega )E_\textrm{n}^{\textrm{CP}}({2\omega } )$ at a fundamental wavelength of 1710 nm where the SHG peaks. Figure 5(a) shows that, compared with the LCP excitation scenarios, a significantly stronger field enhancement effect is identified when the chiral meta-mirror is under RCP excitation at the fundamental wavelengths. Furthermore, from Fig. 5(b) we can see that ${E^{\textrm{RCP}}}({2\omega } )$ shows overall stronger field concentration than ${E^{\textrm{LCP}}}({2\omega } )$ at the corresponding second-harmonic wavelengths. These handedness-dependent field concentration phenomena at both ω and 2ω frequencies give rise to the polarization-sensitive SHG spectra shown in Fig. 4. Note that only the normal components of the linear field ($E_\textrm{n}^{\textrm{CP}}(\omega )$ and $E_\textrm{n}^{\textrm{CP}}({2\omega } )$) on the surface of the plasmonic nanostructures makes a contribution to the SHG signal. Therefore, in Fig. 5(c) we show the polarization-dependent amplitude of $E_\textrm{n}^{\textrm{CP}}(\omega )E_\textrm{n}^{\textrm{CP}}(\omega )E_\textrm{n}^{\textrm{CP}}({2\omega } )$ on the surface of the gold layer cross-section that intersects with the mapping plane at a fundamental wavelength of 1710 nm, which unambiguously illustrates a stronger contribution in the $\mathbb{R}$_ω→ $\mathbb{R}$_2ω scenario, i.e., RCP SHG emission under a RCP excitation. Note that the SHG from a plasmonic nanostructure is determined by the near-field contribution from all of its plasmonic surfaces. To evaluate the contribution of the backplane in our design, a similar field analysis on a plane 1 nm above the backplane surface is presented in Fig. S3 (Supplement 1). Despite the handedness-dependent behavior, the field enhancement effect identified in Fig. S3 is much weaker than that seen in Fig. 5(a) and (b), indicating the less critical role of the backplane in determining the SHG emission from the meta-mirror.

 

Fig. 5. Field analysis. (a) The handedness-dependent electric field distributions cut from the middle of the top gold layer at wavelengths of 1400, 1600, 1710, 1800 and 1900 nm. (b) The handedness-dependent electric field distributions at wavelengths of 700, 800, 855, 900, 950 nm. The electric field magnitude is normalized to that of the incident field. (c) The amplitude distribution of $E_\textrm{n}^\textrm{L}(\omega )E_\textrm{n}^\textrm{L}(\omega )E_\textrm{n}^{\textrm{CP}}({2\omega } )$ representing the local field contribution to far-field SHG for a CP excitation at 1710 nm. The amplitude distributions in (c) were normalized to the maximum value in the panel of $\mathbb{R}$_ω→ $\mathbb{R}$_2ω, which corresponds to the RCP excitation enabled RCP SHG.

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3. Conclusions

In summary, leveraging a genetic algorithm (GA) based optimization method, we have numerically demonstrated a broadband chiral meta-mirror with octave bandwidth in the near-infrared region. The customized GA enables an efficient exploration of a wide range of unique designs, which leads to the optimized nanostructure supporting strong chiral resonances in a wavelength range from 1000 to 2000 nm. Our findings confirm the potential of advanced inverse-design approaches for the creation of chiral metadevices with customized properties, which can facilitate applications in biosensing, chiral photochemistry, pharmaceuticals, etc. Beyond the linear regime, the chiroptical response of the optimized chiral meta-mirror can facilitate handedness-dependent nonlinearities. Based on the Lorentz reciprocity theorem, we show that the chiral meta-mirror exhibits broadband spin-dependent SHG under CP excitations. The extraordinary chiroptical response of the proposed meta-mirror is attributed to the chiral-selective field enhancement effect arising from the multiple chiral resonances across the wavelength range of interest. We envision that a combination of advanced inverse-design approaches and the concept of chiral metasurfaces provides the key to unlocking the door to practical chiral metadevices with a potentially wide range of sophisticated functionalities.