1. Introduction

The development of electromagnetic nanostructures has drawn considerable attention due to the broad applications in various fields with great opportunities. Among various functionalities, polarization control is of fundamental importance since many optical systems are operated based on polarization manipulation. The development of chiral photonic structures is particularly crucial for CD spectroscopy [1,2], biosensing [3], and imaging [4]. In those applications, the employment of circular polarization (CP)-dependent devices is essential to distinguish right-circularly polarized (RCP) and left-circularly polarized (LCP) light. Traditionally, organic chiral molecules, such as liquid crystals, are incorporated in the device to show CP-dependent responses [5,6]. Photonic crystals are also common alternatives to exhibit strong circular dichroism and CP stop bands [7–9]. However, stacks of alternating layers or multiple periods along light propagating direction are normally required for enhanced circular Bragg resonance [10,11]. Recent advances in nanotechnology enabled more compact designs based on metamaterials and metasurfaces. For example, nanostructures composed of 2D planar units arranged with broken symmetry or twisted stacks have been reported to show chiral properties [12–16]. There are also implementations based on 3D structures, such as spirals [17–20], gyroidal networks [21–24], or other 3D units [25–27]. In review of these studies, enhanced chiro-optical effects are primarily mediated by plasmons, which are intrinsically lossy and less efficient. Among the limited reports based on all-dielectric configurations, high-refractive-index dielectrics with a refractive index above $\sim$3 are essential in order to yield strong light-matter interactions. Owing to limited high-refractive-index dielectrics available at optical frequencies, such restriction has largely hindered the implementation horizon of materials and technology platforms.

In this study, we propose and numerically present the use of low-dielectric-index materials$(n\sim 1.5)$ for constructing a metasurface-like helical structure that can achieve strong chiral responses with dual circular polarization manipulation. We carry out comprehensive analysis to show that the scattering of dielectric helices is enhanced by tuning the wire radius and cross-sectional aspect ratio. As a result, the helical array exhibits strong chiral responses upon incident of CP light with a clear distinction between two CP states, where one is highly transmitted and the other is highly reflected. The electromagnetic induced transparency (EIT)-like response can be realized based on circular polarization and the induced slow light effect is also demonstrated. By virtue of the 3D helical arrangement, the present structure possesses unique mirror symmetry, where the arrangement of right-handed (RH) helices enables the emergence of effective left-handed (LH) motifs. The unique organization gives rise to dual circular polarization manipulation in an otherwise single handedness structure. Low-index materials have been utilized in chiral photonic structures in previous studies, yet with a photonic crystal configuration where multiple stacked layers or multiple periods are required [8,22]. For practical implementation, we further address the impact of a substrate with a similar low index on the device performance. We show that elevated helices with an elliptical cross-section can effectively preserve the mode fields and the optical properties are robust against the presence of the substrate. Our work presents general strategies to achieve dual CP light manipulation by 3D chiral structures, and demonstrates the feasibility of using low-dielectric-index dielectrics for achieving high-performance circular polarization-sensitive devices at optical frequencies. Toward experimental realization, several fabrication platforms can be employed based on photoresists. For example, photoresist structures with dual handedness have been realized by direct laser writing and interference lithography [28,29]. As a cost-effective approach, such low index chiral structures can be experimentally implemented by direct patterning on a photoresist coated substrate.

2. Methods

The helical structure under study is shown in Fig. 1(a). The array is comprised of an extended unit cell, as marked by the rectangular box, with four helices in a square lattice. The constituent helix is illustrated in Fig. 1(b), which consists of a single-pitched right-handed (RH) helix with pitch length $p$, connected with a rod of the same length. The helical structure has an elliptical cross-section. The wire radii along the transverse and z direction are $r$ and $r_z$, respectively, where the the aspect ratio (AR) is expressed by $r_{z}/r$. The unit cell of the array structure consists of four helices arranged with a phase shift of 180$^{\circ }$ with respect to the neighboring helices as shown Fig. 1(c). The spacing between adjacent helices is $a$ and the radius of the helix is $R$. The optical properties were calculated by the commercial 3D electromagnetic solver, FDTD Solutions (Lumerical Inc.) [30]. For calculating the scattering properties, the single helix was illuminated with the total-field scattered-field (TFSF) source of circularly polarized waves. At the boundary of the TFSF box, the scattered field was separated from the total field and collected by the frequency-domain field and power monitor enclosing the TFSF box. PML boundary condition was used to absorb the field to avoid reflection. For the reflection calculation, the boundary conditions were set to be periodic in x and y directions, and PML in z direction. Circularly polarized light was incident upon the structure along z direction. A representative refractive index of the dielectric is chosen to be 1.5 as a reference value taken from commercial photoresists [31]. The substrate is glass with the properties taken from Palik [32]. The spacing $a$ is 1.5$\mu m$ in all calculations.

 

Fig. 1. (a) The helical structure is depicted with the unit cell marked by the rectangular box. (b) The helix is right-handed (RH) with one pitch and a pitch length $p$, connected with a rod of the same length. The wire radii along the transverse and z direction are $r$ and $r_z$, respectively. (c) A unit cell consists of four RH helices with a 180$^{\circ }$ shift with respect to adjacent helices. The helix radius is $R$ and the spacing between helices is $a$.

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3. Results and discussions

3.1 Chiral properties of a single dielectric helix

We start our discussion by examining the scattering property of a dielectric helix. Light scattering ability of an object is known to be closely related to several properties of the object, including refractive index, dimension, and geometrical features [33]. In Fig. 2, we present the scattering properties of an RH single-pitched helix with $p=2.1 \mu m$ by different settings of refractive indices and geometries. The upper and lower panels are the scattering cross-sections with respect to wire radius $r$ ranging from $0.1 \mu$m to $0.3 \mu$m for RCP and LCP light, respectively. Figure 2(a) shows a scenario where the helix has a refractive index of $3.5$ and a circular cross-section ($\mathrm {AR}=1$). Due to the same sense of handedness, RCP scattering is more pronounced. Yet, multiple high scattering bands for LCP light are also displayed. The scattering behaviors of two CP states exhibit some differences in terms of scattering wavelength, intensity, and wavelength shift. As $r$ increases, both RCP and LCP scattering intensities are more enhanced, and spectra shift towards longer wavelengths. In Fig. 2(b), the same helix geometry is used while the refractive index decreases to 1.5. For both CP states, the number of high scattering band decreases along with a much weaker scattering intensity. In addition, the differences between the two CP states are less evident. The analysis shows even with a threefold increase of the wire radius, the scattering efficiency just undergoes limited increments. With the same refractive index of 1.5, we found that the scattering effect can be greatly enhanced by increasing the cross-sectional aspect ratio. Figure 2(c) shows the scattering intensity when the helical structure has an elliptical cross-section with an AR of 3. Compared to Fig. 2(b), increasing AR is very effective in enhancing the scattering intensity, and the corresponding wavelength range is also broadly extended. The enhanced scattering characteristic of a low-index, elliptical cross-sectional helix may imply stronger interactions for multiple helices positioned in close proximity.

 

Fig. 2. Scattering cross-section versus helical wire radius $r$ for RCP (upper panels) and LCP light (lower panels) of an RH single-pitched helix with different settings of refractive indices (n) and cross-sectional aspect ratio (AR): (a) $n=3.5$, $\mathrm {AR}=1$, (b) $n=1.5$, $\mathrm {AR}=1$, and $n=1.5$, $\mathrm {AR}=3$.

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To verify the effect, we characterize the optical property for the helical array based on two representative helix geometries. One is with a thin wire along with a circular cross-section, where the parameters are given as $r=0.15\mu m$, and $\mathrm {AR}=1$. The other is with a thick wire radius along with an elliptical cross-section, given the parameters as $r=0.25\mu m$, and $\mathrm {AR}=3.1$. Helices are arranged as the organization described in Fig. 1. We examine the RCP and LCP reflection spectra with respect to different pitch length $p$. Based on the first geometry, Fig. 3(a) is the RCP reflection, presented by the color gradient, versus wavelength while varying the pitch length from $1.5\sim 3.5\mu m$. The RCP color map shows one reflection peak around $2.17\mu m$. The maximum reflection stays below $55\%$ and the peak wavelength is almost invariant with respect to $p$. Figure 3(b) is the color map for LCP light. The response is similar to RCP light with an even smaller reflection level. This is in line with the weak scattering efficiency of helices as revealed in Fig. 2(b). With the second geometry, distinct color maps are shown in Figs. 3(c) and 3(d) for RCP and LCP light. In both CP states, multiple high reflection regions emerge. We can also observe narrower blue bands on the map, and some cross the high reflection regions. In addition, rather versatile optical properties are revealed for LCP light even in an otherwise RH helical structure. Due to low loss of the structure, the total power combining transmitted and reflected light for each CP state is close to unity. The handedness is maintained for the reflected and transmitted light without evident handedness conversion.

 

Fig. 3. The color maps represent the reflection versus pitch length of the helical array. (a) and (b) are based on the helical geometry with $r=0.15\mu m$, and $\mathrm {AR}=1$ for RCP and LCP light, respectively. (c) and (d) are based on the helical geometry with $r=0.25\mu m$, and $\mathrm {AR}=3.1$ for RCP and LCP light, respectively.

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3.2 Circular polarization-dependent properties in low-index dielectric helical structures

We feature one of the RCP region, as marked by the rectangle in Fig. 3(c), to exemplify the pronounced CP-dependent effects. Figure 4(a) is the 3D presentation of the region, featuring the red band interposed by a narrow blue band, denoted by the dashed lines. The corresponding RCP reflection spectra for different pitch lengths are shown on the right panel. The two bands are highlighted in blue and red to display relative wavelength shift. Of particularly interesting is the case when the spectral deep is located at the center of the high reflection band for $p=2.1\mu m$. The spectrum features a chiral electromagnetic-induced transparency (EIT)-like behavior, where RCP light is highly transmitted at the center of the high reflection band. We further analyze the fields of the two RCP modes involved in the process, where the fields on the transverse plane are depicted as shown in Fig. 4(b). The electric and magnetic field distributions of the broad and narrow bands are framed by the blue and red rectangles, respectively. The chiral character of the modes can be revealed by the spiral electric and magnetic fields. The chiral EIT-like response is attributed to the coupling between the two modes. From the evolution of spectra with respect to pitch length, we can observe the mode denoted by the red band undergoes a relative wavelength shift with respect to the broad blue band. The spectral deep is ascribed to the destructive effect due to mode coupling and can be explained by a classical two-coupled oscillator model, where the spectral profile can be fitted well by the equation of the coupled oscillator [34].

 

Fig. 4. (a) The featured region is illustrated in a 3D presentation with two dashed curves outlined the evolution of modes. The corresponding reflection spectra for different pitch lengths are depicted. (b) The electric and magnetic field distributions on the transverse plane of the broad and narrow RCP modes are framed by the blue and red rectangles, respectively.

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Around the EIT window, the corresponding LCP region is marked by the rectangle in Fig. 3(d), which displays a high LCP reflection band. We plot the RCP and LCP spectra in Fig. 5(a). The RCP spectrum exhibits a reflection minimum at $2.49\mu m$. Around the same wavelength, the LCP reflection reaches a maximum value of 98.2%. The two CP states can thus be separated, where RCP light is highly transmitted and LCP light is highly reflected, as depicted in the inset. The distinction between two CP states does not rely on the absorption of one state, and handedness of CP light can be distinguished with low loss. Figure 5(b) shows the energy distribution at the LCP reflection peak. The location of helices is outlined in the plot, and we can see most energy is confined in the region surrounded by helices. By further examining the 3D helical arrangement in Fig. 5(c), we can identify an effective LH motif as illustrated by the red helical structure. The effective LH structures are constructed by the four adjacent RH helices, and are the most interactive region under LCP incidence. Around the EIT window, another attractive implementation is the slow light effect, stemming from the extremely dispersive characteristics. Figure 5(d) shows the wavelength-dependent RCP transmission phase profile, plotted as the orange solid line. The phase undergoes a large variation with respect to wavelength, implying the dispersive character. The corresponding group index is shown as the green dotted line, calculated by $n_{g}=(c/L)(d\phi /d\omega )$, where $c$ is the speed of light in vacuum, $L$ is the length of the structure, $\phi$ is the phase of the transmitted wave, and $\omega$ is the angular frequency. Around the center of the transparent window, a larger group index is obtained derived from the enhanced dispersion, featuring the slow light effect for circular polarization.

 

Fig. 5. (a) The EIT window of RCP light is accompanied with a high reflection region of LCP light. Two CP states can be clearly distinguished, where one is highly transmitted and the other is highly reflected. (b) Upon incident of LCP light, the energy is mostly concentrated in the region surrounded by helices. (c) A 3D illustration shows the embedded LH helical motif is constructed by adjacent RH helices. (d) The wavelength-dependent RCP transmission phase profile is plotted by the solid line, and the corresponding group index is plotted by the dotted line around the EIT window.

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3.3 Dual circular polarization manipulation by structural mirror symmetry

Another appealing feature of the present structure is derived from the spatial organization of phase-shifted 3D helices. Figure 6(a) is the illustration of the RH helical array. Depending on the responsive regions, the structure can be decomposed into two highly identical structures with opposite chirality. One is the original RH helical array in cyan, and the other is the effective LH helical array in red. In spite of a relative lateral shift, the helical units in both sets are arranged in a square lattice, and possess the same 180$^{\circ }$ phase relation with adjacent units. Such organization gives rise to a unique configuration with mirror symmetry with an effective LH structure highly similar to the RH structure, which is only made possible by the 180$^{\circ }$ phase shift organization. With different phase shifts, different circular-dichroism resonances may emerge or be suppressed, depending on the specific design of helical dimension [35]. In the present design, we show a representative example by tailoring the helix radius $R$, as depicted in Fig. 6(b). With a fixed lattice constant, tuning the RH helix radius affects the lateral dimension for both RH and LH sets simultaneously, leading to corresponding changes for chiral responses. In Fig. 6(c), we show the RCP and LCP reflection spectra when the helix radii are $0.52, 0.57,$ and $0.61\mu m$ with $p=2.43 \mu m$, $r=0.25\mu m$, and $\mathrm {AR}=2.5$. For $R=0.52 \mu m$, the EIT spectral deep matches the LCP high reflection around the same wavelength. While $R=0.57\mu m$, the two spectra undergo a wavelength shift, moving toward each other. In spite of minor differences, the RCP and LCP spectra show an almost identical profile. It indicates the chiral structure responses equally to both CP states. This is the case when geometrical parameters are tailored in a way to yield a structure with an almost equal contribution from both handedness. At this radius, as depicted in Fig. 6(b), the corresponding helical radii denoted by $\mathrm {R_{RH}}$ and $\mathrm {R_{LH}}$ are around the same, leading to similar responsive regions for RCP and LCP light. Even though the LCP response is not directly ascribed to an ideal LH helical structure, the resulting LCP profile is still highly similar to the RCP profile. It manifests the feature resulting from a low-index-contrast scenario, where the field is less disturbed due to variations of the low-index structures. The identical spectral profiles further manifest the structural equivalence between the RH and LH sets. For $R=0.61\mu m$, the spectra experience further shifts. In this case, EIT-like profile is exhibited with LCP light. Similar to the case in $R=0.51 \mu m$ yet with handedness exchanged, LCP light is highly transmitted and RCP light is highly reflected. A more comprehensive analysis is shown in Fig. 6(d), where the RCP reflection (upper panel) and LCP reflection (lower panel) are plotted for $R=0.51\mu m\sim 0.61\mu m$. The two color maps display mirror symmetry, in which the patterns are mirror images with respect to the helix radius or wavelength. It means the same chiral responses can be realized in both CP states, despite the structure is constructed by chiral units of single handedness.

 

Fig. 6. (a) Illustrations are depicted to show the original RH and the effective LH structures. Both are arranged in a square lattice. (b) With a fixed lattice constant, tuning the RH helix radius affects the lateral dimension for both RH and LH sets simultaneously, leading to corresponding changes for chiral responses. (c) The RCP and LCP reflection spectra undergo a relative shift as $R$ varies from $0.52$, $0.57$, and $0.61\mu m$. (d) Color maps are the RCP and LCP reflection levels at different wavelengths while varying $R$. The RCP and LCP patterns exhibit mirror-image symmetry.

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3.4 Substrate effect on low-index-contrast structure

In practical implementation, functional structures are fabricated on a substrate but the desired performance may be degraded due to substrate interference. This is particularly challenging when the structure has a relatively low index contrast with the environment. We present several scenarios to examine the substrate effect in Fig. 7(a), where the structure consists of only the helical array, the helical array on the substrate, and the elevated helical array on the substrate. Figure 7(b) shows the RCP reflection spectra with structures of $\mathrm {AR}=1$ (left panel) and $\mathrm {AR}=3.1$ (right panel) with $r=0.25\mu m$. In both cases, the reflection spectra from simply the helical array are shown by the blue curves, displaying the ideal EIT profiles. While the helical array is in direct contact with the substrate, the spectra are shown by the black dotted lines. Both are feature-less with limited reflection variations. The impact of the substrate is quite severe, especially for such single-layered dielectric structures. To decouple from the substrate, we can separate the functional layer and the substrate by incorporating a rod in between. For example, the helical structure presented in this study is elevated using a rod of one pitch length. With the elevated geometry, the reflection profiles are shown by the magenta dashed lines in Fig. 7(b). With $\mathrm {AR}=1$, even though the structure is one pitch length away from the substrate, the EIT feature is still only partially retrieved. Using $\mathrm {AR}=3.1$, the EIT profile is almost completely restored, free from the substrate interference. We can see with a circular cross-section ($\mathrm {AR}=1$), the EIT response can still be obtained due to enhanced light-matter interaction with a larger structure size at a low index [33,36,37]. By further tailoring the aspect ratio, the field in the structure can be more spatially confined. The field distributions within the helical array of different ARs are shown in Fig. 7(c). Comparing the two, a large portion of the field is allocated between the helix and rod for $\mathrm {AR}=1$, whereas the field is mostly confined in the helical region for $\mathrm {AR}=3.1$. It shows the field confinement in the active region is closely associated with the cross-sectional geometry. With a better confinement, the desired performance is less disturbed. To examine the impact of cross-sectional geometry on the EIT performance, we record the maximum and minimum reflection of the EIT profile with respect to different rod lengths for $\mathrm {AR}=1$ and $\mathrm {AR}=3.1$. The rod length is expressed by the normalized value with one pitch length. The results of $\mathrm {AR}=1$ and $\mathrm {AR}=3.1$ are shown in Fig. 7(d) by the blue and red dots, respectively. For $\mathrm {AR}=1$, $\mathrm {EIT_{max}}$ gradually increases with rod length, which indicates restoring of the EIT response. However, even incorporating a rod of two pitch lengths, the $\mathrm {EIT_{max}}$ still has not reached the desired level. The oscillating behavior of $\mathrm {EIT_{min}}$ also implies on-going interference. For $\mathrm {AR}=3.1$, $\mathrm {EIT_{max}}$ increases more rapidly with rod length, and reaches above $90\%$ with 0.8$\times$(pitch length). $\mathrm {EIT_{min}}$ also drops to almost zero around the same length without the oscillating interference behavior. These results are in line with the AR-dependent field confinement, and also show cross-sectional aspect ratio of the wire plays a crucial role in determining the optical properties of low-index dielectric array structures. The strategies of tailoring the geometry to enhance the optical effect are quite general and can be applied to dielectrics with an even lower or higher refractive indices. For example, if the dielectric is taken to be the same as the glass substrate ($n\sim 1.43$), a similar optical response can be retrieved at the same wavelength range by enlarging the helical dimension with a larger $r$. For the dielectric with a higher refractive index ($\sim 1.7$), one can reduce the helical dimension to yield the optimized effect.

 

Fig. 7. (a) Three scenarios of the structure organization are depicted: the helical array, the helical array on the substrate, and the elevated helical array on the substrate. (b) RCP reflection spectra of the structures using $\mathrm {AR=1}$ (left panel) and $\mathrm {AR=3.1}$(right panel) (c) Energy distribution of the structures using $\mathrm {AR=1}$ (left panel) and $\mathrm {AR=3.1}$ (right panel) (d) The maximum and minimum reflectance values of the EIT profile with respect to different rod lengths

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4. Conclusion

We present an all-dielectric low-index helical structure that exhibits pronounced circular polarization-dependent properties. The helices are organized to possess mirror symmetry so that dual circular polarization manipulation can be achieved with high performance. In the present of the substrate, the desired chiral responses can be well-preserved by an elevated configuration with an elliptical cross-section. Our study presents general strategies of 3D chiral structure design to achieve CP light manipulation by low-index materials, broadening the application horizon of materials and fabrication platforms at optical frequencies.