A schematic of the designed photonic crystal mirror is displayed in Fig. 1a. The photonic crystal membrane consists of a patterned layer of silicon nitride with a thickness of t ~ 309 nm that optimizes operation at the target wavelength of λ ~ 870 nm. The design can be adjusted for other wavelengths or dielectric materials. The Bravais lattice is square-shaped with a subwavelength lattice constant, which assures that upon free-space illumination only zeroth-order diffraction will contribute to the reflection and transmission in the far field. The photonic crystal membrane can thus be regarded as an effectively homogeneous boundary. The unit cell consists of a tripartite array of perforating holes with chiral symmetry in the xy-plane (see Fig. 1a). Here, chirality is achieved by engineering the detailed geometry of the unit cell, and the wavelength is adjusted by properly selecting the thickness of the slab.
Maximum electromagnetic chirality requires preservation of the light's handedness at normal incidence, which is imposed by time reversal symmetry34. In essence, the symmetry of the pattern of the unit cell dictates the basic relationship between the elements of the reflection tensor. Employing Jones calculus within the circular basis, the reflection and transmission properties of the slab are then described by the elements of the 2 × 2 matrices ${\bf{R}} = \left[{{\cal{R}}_{ij}} \right]$ and ${\bf{T}} = \left[{{\cal{T}}_{ij}} \right]$, respectively. Henceforth, the corresponding matrix elements are subscripted by + and −, designating the right-handed and left-handed circularly polarized modes, respectively. The desired reflection properties at the designed wavelength necessitate setting ${\cal{R}}_{ + + } = 1$ (or, for the opposite enantiomer, ${\cal{R}}_{ - - } = 1$), whereas the other three elements should be vanishingly small. This assures that the PC mirror reflects only one spin state of light without reversing the handedness, whereas the opposite spin is completely transmitted. It is also worth pointing out that due to its 2D nature, the structure should exhibit opposite chirality on both sides. In stark contrast to the properties of 3D chiral objects such as a helix, where the sense of twist associated with the object is independent of the observation direction, the perceived sense of twist of a planar chiral object is reversed upon reversal of the observation direction. This, in conjunction with time reversal symmetry, entails flipping the spin of the transmitted light (see Supplementary Material). Therefore, in an ideal scenario, the only nonzero element of the corresponding transmission matrix at the target wavelength is $\left| {{\cal{T}}_{ + - }} \right| = 1$ ($\left| {{\cal{T}}_{ - + }} \right| = 1$ for the opposite enantiomer). Figure 1b schematically illustrates the expected optical response of the PC slab at the designed wavelength.
The required structure of the reflection and transmission tensors defined above has several consequences and poses further limitations on the spatial symmetries of the perforating holes. As detailed in the Supplementary Material, only the onefold C1 and twofold C2 symmetry groups accompanied with broken mirror symmetry in the xy-plane will fundamentally allow preservation of the helicity (spin) upon reflection. In other words, the necessary condition to realize such spin-preserving mirrors is to simultaneously break the n-fold rotational symmetry (for n > 2) and any in-plane mirror symmetries9, 30. To also reduce the sensitivity of the structure with respect to the angle of incidence, we elected to design a unit cell with twofold rotational symmetry (see Fig. 1a). The dimensions were initially selected using band diagram analysis, and finely adjusted for a maximum extinction ratio and near-perfect reflection through a brute force-optimization technique. The optimization is constrained with the fabrication limitations, including the bridge sizes between adjacent holes and the smallest curvatures to be etched. An SEM image of the fabricated photonic crystal membrane is shown in Fig. 1c.
The structure was simulated with the finite difference time-domain (FDTD) method using a commercial solver (Lumerical Inc.). The power reflectivity of the slab for normal incidence of the RHCP and LHCP light and the corresponding field distributions are shown in Fig. 1d, e, respectively. The simulation results promise > 97% reflection for one spin state of light at the target wavelength, whereas the opposite spin state is almost completely transmitted. The extinction ratio can reach up to 1000, which is unprecedented among the relevant works30. This giant intrinsic chirality originates from the guided-mode resonance (GMR) mediated by two extremely leaky Bloch modes across the band edges of the PC slab. Due to bi-modal interference, the intensity profiles at the cross-section of the photonic crystal slab (shown in Fig. 1e) are asymmetric and symmetric for the reflected and transmitted helicities, respectively.
The simulated polarization-resolved reflection and transmission coefficients are displayed in Fig. 2. The power reflection and transmission coefficients, denoted by $r_{ij}$ and $t_{ij}$, respectively, are related to the elements of the Jones matrices as $r_{ij} = \left| {{\cal{R}}_{ij}} \right|^2$ and $t_{ij} = \left| {{\cal{T}}_{ij}} \right|^2$. The results confirm that over the operational frequency band (the shaded region in Fig. 2), the photonic crystal is maximally chiral34; at the target wavelength, the photonic crystal selectively reflects the light and retains its handedness and, in compliance with the symmetry constraints, transmits the opposite spin while flipping the helicity.
This realization of maximum intrinsic chirality in a monolithic structure is exceedingly surprising. As noted earlier, the origin of chiroptical effects can be traced back to the simultaneous excitation of effective in-plane magnetic and electric moments induced within the building blocks of the structure11, 36. Using the dipolar approximation, the optical response of the structure can be described on the basis of the net electric dipole per unit cell, i.e., ${\bf{p}} = {\frac{1}{i\omega}\int\!\int\!\int {\bf{J}}{\mathrm{d}}v}$, and the net magnetic dipole moment calculated as ${\bf{m}} = \frac{1}{{2c}}{\int\int\int} {{\bf{r}} \times {\bf{J}}{\mathrm{d}}v}$, where J, ω, and c are the polarization current, frequency, and speed of light in vacuum, respectively. Since both the electric and magnetic dipole modes radiate primarily along the directions normal to their axis, their cooperative action requires a co-planar and co-linear excitation of the moments so that ${\bf{p}}_\parallel \cdot {\bf{m}}_\parallel\; \ne\; 0$, where ${\bf{p}}_\parallel$ and ${\bf{m}}_\parallel$ refer to the components of the dipoles tangential to the plane of the slab36. For this to occur, the slab should be thick enough so the polarization/displacement current can be circulated within the vertical cross-section of the structure. In contrast to conventional wisdom, however, giant circular dichroism with maximum chirality occurs in a PC slab whose thickness is much less than the target operation wavelength.
The key to understanding the operational principles of our chiral PC mirror is guided-mode resonance. Here, maximum intrinsic chirality is achieved by engineering low-Q TE-like and TM-like modes within the radiation continuum. Since the Bloch modes across the band edges of the photonic crystal structure have a low lateral expansion velocity, the modes just radiate back into free space and thus effectively act similarly to the Mie and Fabry–Pérot resonant modes in dielectric metasurfaces and supercavities37. The details of the geometry of the unit cell allow us to adjust the radiation quality factor associated with each virtual resonant mode so that the modes become extremely leaky. Leaky modes provide an efficient way to channel light from within the slab to the external environment via radiation, and at the same time, the judicious design of the structure leads to the formation of TM modes that extend well outside of the slab. Thanks to the latter, desired magnetic moments can be excited. The TE-like modes can effectively generate the desired in-plane electric dipole moment, and the in-plane magnetic dipole is generated by the TM-like modes within the radiation continuum. If the slab dimensions are properly selected, the TE-like and TM-like modes acquire degenerate resonance frequencies, which allows their hybridization. This in turn gives rise to strong intrinsic chirality. Since the radiation channels associated with the TE-like and TM-like modes are not fully orthogonal, via-continuum coupling occurs, leading to a slight removal of the degeneracy37, 38. The relevant part of the band diagram around the band edge i.e., k = 0 (denoted by Γ) is displayed in Fig. 3a. The band diagram is obtained by a FDTD simulation with a Bloch boundary condition applied to a single unit cell. The simulation involves placing random dipole sources in the unit cell so that all possible modes are excited and recording the field in the time domain. High-Q modes are less leaky and therefore have longer lifetimes upon excitation. The color axis displays the spectral function obtained from the FDTD simulation; the modes with less radiation leakage exhibit stronger resonance and are thus brighter. Within the yellow-shaded frequency band, the desired low-Q TE and TM modes meet each other at the band edge, which enables their hybridization.
The anomalous reflection of photonic crystals occurs due to the interference of leaky Bloch modes and the continuum of unbounded modes and thus exhibits a Fano-shape spectral profile39. The electromagnetic dipole moments in the helical basis (which are commonly called σ-dipoles40) consist of parallel magnetic and electric dipole moments of equal amplitudes that are phase shifted by ±π/2. The presence of resonance based on σ-dipole gives rise to the chiroptical effects of interest. At the design wavelength, the reflection from our PC mirror is generated by a resonant coupling of circularly polarized light to σ-dipoles, which are essentially produced by the co-excitation of TE-like and TM-like modes and through the background reflection.
To reveal how mode hybridization leads to chirality, we performed parameter tuning to decouple the modes. The thickness of the slab was varied to observe the variations in the reflectively of the chosen helicity and the extinction ratio as the figures of merit. Figure 3b shows the investigated crossing region with the reflectivity results from finely sampled simulations. The spectral distributions of the associated TE and TM modes, calculated using the FEM method (ANSYS HFSS Inc.), are shown in Fig. 3c (the electric field profile for each mode is shown in the Supplementary Material, Fig. S2). The distributions are normalized and exhibit the resonance wavelength and linewidth associated with each Bloch mode. To confirm that mode crossing occurs, we applied a mode tracing scheme. As expected, the TE-TM-mode crossing occurs around the predicted thickness.
To more closely study the dipolar interpretation of our structure's predicted behavior, we studied the impact of dipole interactions. We calculated the in-plane components of the induced electric dipole p and the magnetic dipole m per unit cell for incident light of both circular polarizations. The toroidal dipoles and the higher-order multipoles were found to have negligible contributions. Figure 4a displays the spectral distribution of the induced dipole moments. The induced electric dipoles are identically excited for opposite helicities, whereas the strengths of the magnetic dipoles are different over the chiral bands. Around the design wavelength, where the modes are properly hybridized, the inner products of the resultant dipoles are distinctly different for the opposite helicities. Intriguingly, the circular dichroism upon reflection follows the magneto-electrical dipole interactions (see Fig. 4b).
The origin of the difference in the induced magnetic dipoles shown in Fig. 4a can be explained based on symmetry considerations. The induced polarization currents for circularly polarized incident fields can be naturally decomposed into a chiral component and an achiral component, namely, Jc and Ja, respectively. The chiral component Jc is induced differently for the opposite helicities and has in-plane chiral symmetry in its distribution. In addition, owing to the twofold rotational symmetry, Jc has a definite parity under in-plane space inversion. Specifically, it is observed that the chiral polarization vector is an odd-parity vector field i.e., ${\mathcal{P}}_{xy}${Jc} = −Jc, where ${\mathcal{P}}_{xy}$ is the in-plane parity operator. Since the electric dipole moment is obtained by a direct integration of the polarization current over the unit cell, the net electric dipole moment loses its in-plane chiral features. Therefore, the electric dipole moments are equally excited for both helicities of the incident light. In contrast, as the net magnetic dipole moment is calculated by a direct integration of r × J and ${\mathcal{P}}_{xy}${r × Jc} = + r × Jc, the chiral polarization components should have a nonvanishing contribution in the magnetic dipole moment, which in turn leads to the excitation contrast observed in Fig. 4a.
The magneto-electric dipole excitation described above is fundamentally different from the operational mechanism of lossless planar dielectric metasurfaces made of high refractive-index nanopillars. Analogous to high-contrast gratings that essentially operate in a dual-mode regime41, such all-dielectric metasurfaces support multiple-guided modes, and the formation of supermodes in a symmetry-broken geometry can result in asymmetric transmission for orthogonal polarizations. Therefore, the nanopillars need to be sufficiently tall to accommodate internal multimode propagation. It has been recently demonstrated that a judicious design of nanopillars with in-plane geometrical chirality can potentially result in different couplings of opposite helicities to the waveguide-array modes, which in turn leads to a differential response for left- and right-handed circularly polarized light42. Ye et al.43 showed that multimode interference can also arise in metasurfaces made of low-loss metallic nanostructures with finite thickness. Consequently, properly designed metallic nanoposts can support surface plasmon modes whose different interference schemes for the opposite helicities yield a giant chiroptical effect43.
The silicon nitride layer for our structures was grown on a silicon wafer using low-pressure chemical vapor deposition (LPCVD), producing a film with a refractive index of 2.26 at the designed wavelength. The structures were fabricated through soft-mask electron-beam lithography followed by plasma etching and a KOH undercut. This process results in a truly free-standing photonic crystal membrane, and the undercut area is sufficiently deep so that the impact of silicon substrate can be safely disregarded. A scanning electron microscopy (SEM) image of the fabricated device is displayed in Fig. 1c.
The experimental characterization of the photonic crystal mirror was carried out by free-space illumination with the beam of a supercontinuum white-light laser. The beam was focused onto the PC sample through a low-numerical-aperture objective lens to assure that the wavefront of the excitation remains similar to a plane wave. To obtain the reflection spectrum, we collected the reflected light into a spectrometer via a single-mode fibre. The focused beam at the sample was approximated by a Gaussian profile; the corresponding beam waist at the sample was estimated to be $w_0 \approx 18$ μm. To eliminate artefacts originating from unwanted rays, the reflected beam passed through a confocal reflectometry setup with appropriate polarimetric arrangements. The setup was designed to monitor the four components of the power reflection matrix in the circular basis: $r_{ + + }$, $r_{ - - }$, $r_{ + - }$, and $r_{ - + }$. The confocal configuration is necessary to compensate for the long depth of field associated with the loosely focused beam so that the rays reflecting off the undercut area are largely avoided. To further reduce the interference of the rays reflecting from the thick silicon layer underneath the PC membrane, the undercut region has a V-shaped cross-section in the silicon substrate; thus, the reflections from the undercut region are mainly off-normal. Additional details of the optical setup can be found in the Supplementary Material (see Supplementary Figs. S6 and S7).
Due to a slight astigmatism of the electron beam during the lithography process and imperfect etching, the fabricated samples exhibit some anisotropy that leads to a modest performance degradation of the PC mirror. Specifically, it was observed that the eigenpolarizations are not purely circular. To experimentally explore this effect, we carried out polarization-dependent reflectometry. The polarization of the incident light is adjusted by means of a broadband quarter-wave plate placed before the objective lens. This setup allows us to explore a wide range of elliptical polarizations for the incident light. The total reflectivity of the PC mirror for different states of polarization is shown in Fig. 5b. Note that all of the reflectivity measurements are calibrated based on the known reflectivity of the unpatterned silicon nitride on a silicon substrate. It is observed that around the target wavelength of ${\sim} 870\; {\mathrm{nm}}$, the sample exhibits extreme chirality. However, near-unity reflection occurs for right-handed elliptically polarized light with an axial ratio of $AR = \tan 32^\circ \approx 2:3$ (the dark red spot in Fig. 5b). We emphasize that due to the resonant nature of the chiral reflection mechanism, the sensitivity to structural deformations is expected to be pronounced. However, refinements to our fabrication procedure should allow us to make the eigenmodes purely circular. The observed deviation from circular to elliptical eigenpolarizations indicates a cross-coupling between the opposite spins. To inversely reconstruct the actual fabricated device, we carried out a diagnostic analysis based on the adjoint shape optimization technique44. The analysis revealed that due to the imperfect etching, the walls of the photonic crystal holes are not perfectly vertical, so the diameters of the holes at the bottom and top surfaces are slightly different. This small imperfection was observed in a zoomed SEM image of the device as two concentric boundaries appearing around the individual holes (see Supplementary Material, Fig. S6). In agreement with intuition, mirror symmetry breaking in the z-direction causes an additional cross-coupling between the associated TE-like and TM-like modes, which in turn leads to the presence of the off-diagonal elements ${\cal{R}}_{ + - }$ and ${\cal{R}}_{ - + }$ in the reflection matrix.
The measured spin-preserving components of the reflectivity tensor for circular and elliptical polarizations are shown in Fig. 5c, d, respectively. The off-diagonal elements are less pronounced within the chiral band and are presented in the Supplementary Material (see Supplementary Fig. S5). There are some discrepancies between the simulations and experimental results, including a few nanometers wavelength offset between the dominant features of the simulated and experimentally observed spectra. However, when overlaying the simulations and experimental results, we observe very good agreement overall, and the slight differences most likely arise from fabrication imperfections. The experimental results confirm the selective reflection of the incident light for two elliptically polarized eigenmodes with opposite helicity with an extinction ratio up to $r_{ + + }/r_{ - - }\, \, {\gtrsim}\!\, \, 30$. Such extreme chirality is unprecedented compared to the previously reported experimental results. The blue shaded reliability curves account for uncertainties in the calibration of the reflectivity measurement results, including a slight loss of coupling to the single-mode fibre when the illuminated spot is moved to the unpatterned area. It is also worth pointing out that the slightly smaller measured reflectivity compared with the simulation results can be partly attributed to the finite size of the focused beam at the sample. As is further evidenced by the plane-wave expansion analysis presented in the Supplementary Material, the Gaussian beam used in our experiment contains obliquely incident plane waves that have significantly lower reflection coefficients (see Supplementary Material, Fig. S8); thus, even in an ideal scenario, the reflectivity of such a Gaussian beam cannot exceed ${\sim} 85\%.$
To demonstrate the robust performance of the chiral mirrors, we performed two experiments involving polarization-resolved imaging. In the first experiment, two C-shaped photonic crystal membranes with opposite chiral patterns (two enantiomeric configurations) were fabricated. We identified the chiral operational band of the PC sample through polarization-resolved spectroscopy. An optical microscope image of the fabricated sample is displayed in Fig. 6a. The pattern was then illuminated by a monochromatic and spatially coherent laser beam from a tunable continuous-wave Ti:Sapph laser at 824 nm, the wavelength at which the PC sample exhibits extreme chirality. Polarization-resolved images are shown in Fig. 6b, c. The images are captured after a circular-polarization filter collecting only the spin-preserving (co-circularly polarized) reflection; thus, artefacts originating from the background are largely suppressed. Under purely circularly polarized illumination, only one of the photonic crystal structures appears bright, with the fringing in the image arising from the high level of spatial coherence of the illumination in this case.
We also created a pattern of letters (IQC) as shown in Fig. 6d. The interior and exterior of the letters are made of photonic crystal structures with opposite enantiomeric patterns. Following the experimental procedure outlined above, we again performed polarization-resolved imaging. This time, however, we illuminated the pattern with a monochromatic but spatially incoherent laser beam. To suppress the beam's spatial coherence but not its temporal coherence, the laser beam was first focused onto rotating ground glass diffusers and collimated again45. As can be seen in Fig. 6e, f, the letters appear bright with clear contrast with respect to the background under RHCP illumination, while for LHCP illumination, the exterior region appears bright and the letters are dark. Intriguingly, the contrast between complementary domains is relatively high, even around the sharp edges. Since the letters are ~10 μm wide, this result demonstrates that strong chirality can be achieved even for photonic crystal structures that are periodic over small scale areas. This observation is consistent with the results obtained from full-wave simulations of a number of finite-size photonic crystal slabs presented in Supplementary Material (see Supplementary Fig. S9).