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Abstract
Metalens is an ultrathin flat optical device with a great potential for applications in spin-controlled nanophotonics. However, most advanced metalenses typically work at a single wavelength or one specific spin state of incident light, hindering their applications in practice. In the present work, we report three distinct spin-dependent metalenses based on the novel phase-change material of Ge2Sb2Se4Te1 (GSST), enabling multidimensional splitting and switchable manipulation capabilities. Such schemes are successfully realized due to synergizing propagation phase and specific PB phase together with deliberately selecting several anisotropic GSST nanofins that behave as half-wave plates for their constituent elements. In particular, the transverse spin-dependent splitting metalens (TSSM) is demonstrated to enable the left-circularly polarized (LCP) and right-circularly polarized (RCP) incidence to focus at opposite transverse offsets within a broadband width from 3750 to 4600 nm (20.2% of the bandwidth). The longitudinal spin-dependent splitting metalens (LSSM) realizes the longitudinal spin-dependent splitting performance along z-axis upon RCP and LCP incidence in a considerable bandwidth (from 3900 to 4900 nm, 23.8% of the bandwidth). While for the hybrid design, it is implemented to obtain transverse and longitudinal spin-dependent splitting simultaneously for LCP and RCP light. It should be emphasized that all of the proposed metalenses are proved to ensure continuous tunability and the switching of “ON” and “OFF” states in terms of focusing and splitting features upon λ0= 4200 nm by gradually converting Ge2Sb2Se4Te1 from the amorphous to crystalline state. Our results lay a solid basis for versatile potential applications such as optical imaging and communications, optical sensors, machine vision and so forth.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The photonic spin hall effect (abbreviated as PSHE) refers to the phenomenon that the photons with opposite spins split into separate trajectories when the incident light is reflected or refracted on the interface of the medium [1–5], which is considered to be the result of photonic spin-orbit interactions (SOIs) [6–8]. Commonly, the mechanism of SOIs is considered to be related to two geometric phases: Ryto-Vladimirskii-Berry (abbreviated as RVB) phase [9,10] and Pancharatnam-Berry (abbreviated as PB) phase [11,12]. The former is closely associated to the propagation direction of incidence, and thus, a spin-dependent shift is generated when the light propagates at an interface between different media. The latter is related to the polarization states of the light and it is yielded within inhomogeneous anisotropic media to generate PSHE. Unfortunately, by these approaches, the intensities of the spin-dependent splitting fields are quite weak, and the induced spin-dependent subwavelength shifts are exceedingly tiny (only on the order of a fraction of incident wavelength), which requires weak measurement techniques [13] or multiple reflections [1] to observe the PSHE, seriously hindering its further development and applications of photonic spin-related devices.
Metasurfaces, as one appealing platform to flexibly control over light at nanoscales, can provide unprecedented capabilities in manipulation of the polarization, phase and amplitude of light, enabling numerous extraordinary applications such as light beam shaping [14,15], electromagnetic virtual rendering [16], large field of view holographic display [17,18] and planar metalens [19–21]. Thanks to the flexible design, metasurfaces have been explored to realize huge manifestations of the PSHE by being carefully endowed with spin-dependent phase gradients. For instance, Shu et al. realized a radial PSHE-based multifocal metalens by constructing a super-structured surface with PB phase along the radial optical axis [22]. Jin et al. constructed three metalenses that are capable to focus light of different spins at designated positions along both transverse and longitudinal directions by combining the PB phase with the propagation phase [23]. Luo et al. fabricated a reflective meta-device that yielded a giant PSHE with efficiency close to 1 [2]. Even though metasurfaces with giant PSHEs and intense SOIs have made significant progress, the achievement of active control over the PSHE with high efficiency remains a huge challenge, since traditional metasurfaces lack the design flexibility and thus only valid for a static system once fabricated.
“Active metasurface” can actively/flexibly manipulate the optical response by integrating original metasurface and “active elements”. Currently, the “active elements” mainly include Micro-Electro-Mechanical System (MEMS) [24,25], graphene [26,27], liquid crystals [28,29], optical phase-change materials (O-PCMs) [30–32] and transparent conducting oxide [33]. Among them, O-PCMs, especially the germanium antimony selenium telluride alloy Ge2Sb2Se4Te1 provide an intriguing approach to obtain flexible reconfigurability owing to its conspicuous changes in optical properties in the mid-infrared regime (MIR) upon exposure to external stimuli. Compared with the prevailing Ge2Sb2Te5 (GST) phase-change alloy, the extremely wideband transparency, low loss and much larger switching volume in the MIR allows for optically thick GSST nanostructures to accelerate light-PCM interactions while maintaining multi-state operations and completely reversible switching capability [34,35]. Although the crystallization kinetics of GSST exhibits inferior ($\sim$microseconds) relative to that of GST ($ \sim $nanoseconds), it allows fully reversible switching of GSST films with thickness more than 1 µm, which is almost impossible for GST [36,37]. However, the study on GSST-based meta-devices is still imposed severe challenges, particularly etching GSST films into isolated nanopatterns with high aspect ratios.
Here, we report three different spin-decoupled metasurfaces, which are composed of anisotropic Ge2Sb2Se4Te1 nanofins sitting on the CaF2 substrate. These anisotropic nanofins with different geometries are imparted with different propogation phases and realize full 2π coverage fulfilled with the PB phases by rotating the nanofins’ rotation angles, which guarantees the three metasurfaces can elegantly achieve giant PSHE in distinct dimensions (transverse, longitudinal and hybrid dimensions) at the operation wavelength of λ0 = 4200 nm. In particular, the TSSM is demonstrated to enable the LCP and RCP incidence to focus at opposite transverse offsets within a broadband width from 3750 to 4600 nm (20.2% of the bandwidth). The LSSM realizes the longitudinal spin-dependent splitting performance along z-axis upon RCP and LCP incidence in a considerable bandwidth (from 3900 to 4900 nm, 23.8% of the bandwidth). While for the hybrid design, it is implemented to obtain transverse and longitudinal spin-dependent splitting simultaneously for LCP and RCP light. Moreover, the three designs are endowed with the continuous tunability and switching functions of “ON” and “OFF” states in terms of focusing and splitting performance at λ0 = 4200 nm due to the phase-transition characteristics of Ge2Sb2Se4Te1. With the above merits, the proposed schemes may provide potential applications in variety of spin-controlled nanophotonics, such as spin-dependent holographic imaging, spin selection, beam splitting and optical sensors.
2. Theory and design
To endow the metasurface design the helicity-dependent optical responses under the normally illumination of orthogonal spin-states polarized waves, the metasurface can be expressed by a Jones matrix J0(x) that simultaneously satisfy the following equations [38]:
where $|{LCP} \rangle = {1 / {\sqrt 2 }}[\begin{array}{c} 1\\ i \end{array}]$ and $|{RCP} \rangle = {1 / {\sqrt 2 }}[\begin{array}{c} 1\\ { - i} \end{array}]$ are Jones vectors, denoting LCP and RCP spin eigenstates. φ+(x) and φ−(x) respectively correspond to $|{LCP} \rangle$ and $|{RCP} \rangle$ states, keeping to the spatial hyperbolic phase profiles ${\varphi ^{_ \pm }}(x)$ for cylindrical metalenses. To be specific, for the TSSM, φ+(x) and φ−(x) obey the following form:While for the LSSM, φ+(x) and φ−(x) follow another form:
In Eq. (3) to Eq. (6), λ0 is the input wavelength, x is the position of the center of the meta-atoms, and Δx is the transverse offset of the focal spot from the center (x = 0), f0 is the focal length for the TSSM, ${f_\textrm{ + }} \ne {f_\textrm{ - }}$, representing the focal length for LSSM upon LCP and RCP incidence, respectively. Therefore, the Jones matrix J0(x) takes the form:
It satisfies the conditions ${J_0}(x) = T\Lambda {T^{ - 1}}$, in which T is a unitary matrix and Λ is a diagonal matrix. For the metasurface based on birefringent meta-atoms, the diagonal matrix Λ is responsible for the phase shifts PXX and PYY along the two orthogonal axes of nanofins, while the matrix T administers the in-plane rotation angle θ of the fast axes of nanofins relative to x axis. PXX and PYY, synergized with TXX and TYY denoting the absolute transmittance along the two orthogonal axes of nanofins, control the propagation phase of the output beam, while θ determines the geometric phase imposed on the transmitted light. For the given helicity-multiplexed phase contours φ+(x) and φ−(x), via solving Eq. (7), the phase shifts PXX and PYY and the in-plane rotation angle θ can be easily derived as follows:
To accomplish the Jones matrix J0(x), a phase library of Ge2Sb2Se4Te1 nanofins should be built to realize the desired phase shifts PXX and PYY that offer the 2π phase coverage and satisfy the orientation angle θ at any point (x). Meanwhile, to achieve high-definition, less chaotic focusing response, all selected nanofins constituting metasurface should behave as half wave plates or quasi-half wave plates, that is, the propagation phase shifts PXX and PYY, and the absolute transmittance TXX and TYY imparted by individual nanofin should be fulfilled the follows conditions:
Following this principle, we construct three different spin-dependent splitting metalenses composed of rectangular GSST nanofins setting on a 2 µm thick CaF2 substrate, as shown in Fig. 1(a). Due to the high-index contrast between GSST nanofins (ng≈ 3.19 + 0.001i) and CaF2 substrate (nc = 1.47) at the designed wavelength of λ0 = 4200 nm, the optical powers are all confined within individual nanofin and it can be deemed as a truncated waveguide, exhibiting birefringent optical response relying on the incident polarizations that is parallel to either axis of the nanofins. The constituent elements, i.e., the meta-atoms, possess a square lattice constant (p) of 3µm and a fixed height (h) of 2800 nm, while their in-plane dimensions (a, b) are spatially varied ranging from 300 to 2800 nm, and 50 nm increments of each geometric variable, to realize the desired 2π phase coverage.
Fig. 1. (a) Top: Schematic diagram of the metasurface consisting of GSST nanofins setting on the CaF2 substrate. Bottom: Schematic of the meta-atoms for the proposed multidimensional metasurface. (b) Optical properties of Ge2Sb2Se4Te1 films with amorphous and crystalline states. Transmittances TXX (c) and TYY (e), and phase shifts PXX (d) and PYY (f) as a function of GSST nanofin size parameters, a and b, at the illumination light wavelength λ0 = 4200 nm, respectively..
The performance of the proposed design is evaluated by the commercial software of COMSOL Multiphysics. For the meta-atoms, periodic boundary conditions (PBCs) are implemented at both x and y directions, whereas two periodic ports (in which the lower one is the excitation port) are set along the z axis. For the simulation of the designed metasurface, a perfectly matched layer (PML) is set around the model and a linealy or circularly polarized wave that is normally incident. The optical constants of GSST films show wavelength-sensitive features as depicted in Fig. 1(b), referring to the experimental data in Ref. [35], while the refractive index of CaF2 is set to 1.47. Figures 1(c)–1(f) illustrate the calculated TXX, PXX, TYY and PYY at the operation wavelength of 4200 nm versus the dimensions (a, b) varying from 300 to 2800 nm, respectively. I should note is that the polarized waves are input from the substrate side and propagate along the z direction, and the transmission spectra and propagation phase for the cross-polarized output light are collected from the other side of the structure. Three sets of multiple nanofins (25 for TSSM and LSSM, 50 for hybrid design) that satisfy Eqs. (8)–(12) are picked to cover the 2π phase range as shown in Fig. 2. From the simulation results, one can witness that high transmittance and absolute phase difference between PXX and PYY approaching π of the selected nanofins will ensure efficient generation for PSHEs of different splitting dimensions.
Fig. 2. Absolute phase difference between PXX and PYY (a, c, e), together with corresponding transmittances (b, d, f) of the selected nanofins for the TSSM, LSSM and the hybrid schemes, respectively.
3. Results and discussions
First, we use Ge2Sb2Se4Te1 anisotropic nanofins as building blocks to implement a transverse spin-dependent splitting metalens and simulate its focusing performance. Figure 3(a) shows its schematic diagram, from which one can observe that the TSSM converts the LCP (RCP) incidence into output RCP (LCP) light with an opposite spin state and focus them with opposite transverse offsets. Since any LP light can be regarded as the superposition of LCP and RCP lights, the TSSM can focus it at two separate focal spots with opposite transverse offsets simultaneously. To validate the TSSM scheme, the focal length f0, the transverse offset Δx and the illumination light wavelength λ0 are set to be 200 µm, 20 µm and 4200 nm, respectively. Figures 3(c)–3(e) show the simulated electric-field intensity distributions of the TSSM under the normal illumination of LCP, RCP and LP beams in the x–z plane, respectively. For LCP incident light, a bright focal spot at the position of + x can be observed, whose focal length f = 201 µm and the transverse offset Δx ≈ 20 µm. For RCP incident light, the generated bright spot is located in opposite positions, i.e., the transverse offset Δx ≈ −20 µm. For LP light, two separate focal spots with the same focal lengths (f = 201 µm) but opposite transverse offsets (Δx ≈ ±20 µm) are observed along the transverse direction simultaneously, agreeing well with the theoretical values. The negligible discrepancies in focal length between the simulated and theoretical values are mainly associated with the relatively small Fresnel number of diffractive lens [39,40]. Furthermore, at the focal plane (f = 201 um), the calculated E-field intensity profiles of the focal spot along the x- axis are shown in Fig. 3(b), from which one can see the central lobes stands symmetrically with respect to x = 0 and possess dazzlingly higher intensities than their sidelobes upon the normal illumination of LCP and RCP beams. While for LP beams, two central lobes that completely overlap with the above central lobes for LCP and RCP cases are generated, of which the maximum electric intensity is significantly reduced since the intensity of the incident electric field is declined to half of the original ones (LCP and RCP cases). Notably, the full width at half-maximum (FWHM) of the focal spots are about 1.09 λ0 and 1.08 λ0 for LCP and RCP incidences, respectively, lower than their corresponding diffraction limits of 1.42 λ0, manifesting the diffraction-limited focusing of the TSSM. Herein, the Abbe diffraction limit is calculated by the ratio of the incident wavelength λ0 and double the numerical aperture (NA) which is determined by the equation of $\textrm{NA = }\frac{r}{{\sqrt {{r^2} + {f^2}} }}$. Moreover, the corresponding focusing efficiencies of the TSSM are also investigated, which reach up to 73.1% and 69% under LCP and RCP light, respectively. The focusing efficiency is defined as the ratio of the transmitted optical power at the focal spot with a width of three times of the FWHM to the entire incident optical power [41]. All verifies that the TSSM can effectively split the incident beam along lateral direction, demonstrating its outstanding PSHE.
Fig. 3. (a) The schematic diagram of the TSSM. (b) The extracted E-field intensity profiles of the TSSM along the x-axis (white lines) at the focal plane upon different spin-polarized beams. Simulated E-field intensity profiles for the TSSM on the x-z plane (at y = 0 µm) upon normally illuminated LCP (c), RCP (d) and LP light (e) at λ0 = 4200 nm, reapectively.
Subsequently, we investigate the operation bandwidth of the TSSM. Figures 4(a)–4(l) show the corresponding simulated E-field intensity profiles on the x-z plane (at y = 0 µm) upon their respective wavelengths in the MIR. It can be observed that the TSSM enables the well-focusing and robust transverse spin-dependent splitting response across the wavelength range from 3750 to 4600 nm. To reveal the underlying physical mechanism of the broadband focusing and splitting performance, Figs. 4(m)–4(p) exhibit the corresponding phase profiles, in which the lines labelled by “Required” and “Realized” denote the theoretical and actualized phases, respectively. The cases for the TSSM at λ0= 4200 nm are also given for comparison, from which one can easily witness that the “Required” and “Realized” phase lines fit perfectly without any blemish. While for the cases with λ= 3750 nm, 4100 and 4600 nm, the “Realized” phases are more or less deviated from the target “Required” ones, but the overall phase trends remain good consistent, which is the foundation for the broadband and robust focusing and splitting performance of the TSSM in the MIR. The shift of the focal length originates from the chromatic aberration of the lenses.
Fig. 4. (a)-(l) Simulated E-field intensity profiles in the x-z plane for the TSSM upon normally incident LCP, RCP and LP beams corresponding to their respective wavelengths in the MIR (labelled to left side of plots). (m)-(p) The “Required” and “Realized” phase profiles for the TSSM corresponding to their respective wavelengths in the MIR, respectively.
Similar to GST, the phase transformation of GSST between amorphous and crystalline states is a step by step process rather than abrupt one, which imparts the GSST-based metasurface with unparalleled abilities and renders it a good avenue to multifunctional and versatile optics. For each intermediate phase of GSST, it can also be considered to be composed of different proportions of amorphous and crystalline molecules and its effective permittivity can be estimated as [42,43]
Fig. 5. Simulated E-field intensity profiles in the x-z plane for the TSSM with different crystallization levels of GSST, m = 0.2 (a), 0.4 (b), 0.5 (c), 0.6 (d), 0.8 (e) and 1.0 (f), respectively.
Subsequently, a longitudinal spin-dependent splitting metalens is proposed, in which we set λ0 = 4200 nm, f+ =200 µm and f_=120 µm, respectively. Figure 6(a) shows the schematic illustration of the designed LSSM, from which one could see that the LSSM can effectively transform the input LCP (RCP) light into the one with opposite helicity (RCP or LCP light) and focus them at different locations along z-axis. Similarly, the LSSM can focus it at two separate spots along z-axis for LP incident light. To verify the virtue of longitudinally split focusing manipulation of the LSSM design, Figs. 6(c)–6(e) depict the E-field intensity distributions of the LSSM in x-z plane. One can witness that the LSSM can efficiently focus LCP incidence into one spot at z ≈ 200 µm, focus RCP incidence into the other spot at z ≈ 120 µm and focus LP incidence into two separate spots at z ≈ 200 µm and z ≈ 120 µm, respectively, which agrees well with the theoretical analysis, confirming that the designed LSSM can realize the longitudinal split bifocusing performance. To quantitatively characterize the longitudinal bifocus performance, we show the calculated E-field intensity profiles of the focal spot along the x- axis for the cases of LCP and RCP incidence, as shown in Fig. 6(b). One can observe that a small difference in the peak E-field intensity of the two foci are generated due to the different NAs for the LSSM upon LCP (NA = 0.35) for and RCP (NA = 0.53) light. Moreover, the E-field intensity essentially concentrate on the central lobes located at x = 0 and the FWHM of the focal spots are about 0.86 λ0 and 0.66 λ0 for LCP and RCP incidences, lower than their corresponding diffraction limits of 1.42 λ0 and 0.94 λ0, respectively. The focusing efficiencies of the LSSM are also investigated, which are 72.1% for LCP and 66.2% RCP incidence, respectively.
Fig. 6. (a) Design principle of the LSSM design. (b) The extracted E-field intensity profiles of the LSSM along the x-axis (white lines) at the focal plane upon different circularly polarized incidence. Simulated E-field intensity profiles for the LSSM on the x-z plane (at y = 0 µm) upon normally incident LCP (c), RCP (d) and LP light (e) at λ0 = 4200 nm, respectively.
The working bandwidth of the LSSM is also investigated as illustrated in Fig. 7. One can witness from Figs. 7(a)–7(l) that the LSSM exhibits a broadband well-focusing and robust longitudinal spin-dependent splitting response across the wavelength range from 3900 to 4900 nm, 23.8% of the bandwidth. To reveal the underlying physical mechanism, Figs. 7(m)–7(p) show the corresponding “Required” and “Realized” phase profiles at the specific wavelengths of 3900, 4200, 4600 and 4900 nm, respectively. The overall trends of the “Required” and “Realized” phase lines keeping consistent, despite some tiny flaws, is the fundamental to achieve excellent broadband characteristics for the LSSM in the MIR. However, due to the existence of chromatic dispersion, the focal length are not identical for various incident wavelengths
Fig. 7. (a)-(l) Simulated E-field intensity profiles in the x-z plane for the LSSM upon normally incident LCP, RCP and LP beams corresponding to their respective wavelengths in the MIR (labelled to left side of plots). (m)-(p) The “Required” and “Realized” phase profiles for the LSSM corresponding to their respective wavelengths in the MIR, respectively.
Subjoining a transverse offset Δx = 20 µm on the LSSM scheme, we get a metalens called by TLSSM with transverse and longitudinal spin-dependent splitting simultaneously, whose principle diagram is depicted in Fig. 8(a). Likewise, we investigate the spin-dependent splitting focusing performance of the TLSSM, as shown in Figs. 8(b)–8(e). Evidently, the E-field intensity distributions of focusing spots (Figs. 8(c)–8(e)) and the calculated E-field intensity profiles of the focal spots along the x axis at their focal planes (Fig. 8(b)) for TLSSM combine the characteristics of the cases of TSSM and LSSM under LCP and RCP incidence, verifying again the feasibility of our proposed spin-dependent splitting scheme. The FWHM of the focal spots are about 1.1λ0 and 0.86λ0 under LCP and RCP incidences, below their corresponding Abbe diffraction limits of 1.42 λ0 and 0.94 λ0, respectively. It should be emphasized that the broadband and switchable focusing effect is not only suitable for the TSSM, but also valid for the LSSM and TLSSM, which is not shown herein for simplicity.
Fig. 8. (a) Schematic diagram of the TLSSM. (b) The extracted E-field intensity profiles of the TLSSM along the x-axis (white lines) at the focal plane upon different circularly polarized incidence. Simulated E-field intensity profiles for the TLSSM on the x-z plane (at y = 0 µm) upon normally incident LCP (c), RCP (d) and LP light (e) at λ0 = 4200 nm, respectively.
4. Conclusions
In conclusion, we proposed three distinct spin-dependent metalenses based on the novel phase-change material of Ge2Sb2Se4Te1, enabling multidimensional splitting and switchable manipulation capabilities. Such designs are assisted by synergizing propagation phase and specific PB phase on the premise of satisfying the quasi-half-wave plate for their constituent elements. For the designed TSSM, it can convert the LCP (RCP) incidence into output RCP (LCP) light with an opposite spin state and focus them at opposite transverse offsets within broadband width from 3750 to 4600 nm (20.2% of the bandwidth), verifying its giant and broadband transverse PSHE. Additionally, the designed TSSM can realize continuous tunability and the switching of “ON” and “OFF” states in terms of focusing and splitting features upon λ0= 4200 nm by gradually converting Ge2Sb2Se4Te1 from the amorphous to crystalline state. For the designed LSSM, it ensures LCP and RCP incidence to be focused on different longitudinal focal planes along z-axis in a considerable bandwidth (from 3900 to 4900 nm, 23.8% of the bandwidth), respectively. Hybriding the design features of TSSM and LSSM, TLSSM is implemented to realize transverse and longitudinal spin-dependent splitting for LCP and RCP light simultaneously, combining the focusing characteristics of the cases of TSSM and LSSM. It should be emphasized that the broadband and switchable focusing effect are also valid for the LSSM and TLSSM. Our proposed approach provides a flexible and robust avenue for controlling spin photonics and shows huge potential applications in the fields of spin-controlled nanophotonics, optical imaging and optical sensors.
Funding
National Natural Science Foundation of China (12004347); Henan Provincial Science and Technology Research Project (202102310535, 212102310255, 222102210063); Innovative Research Team (in Science and Technology) in University of Henan Province (22IRTSTHN004); Chinese Aeronautical Establishment (2019ZF055002, 2020Z073055002).
Acknowledgments
J. Xu thanks X. Tian and Prof. Y. DU for their kind guidance and constructive suggestions for this work.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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