
- Photonics Research
- Vol. 9, Issue 6, 1019 (2021)
Abstract
1. INTRODUCTION
Metasurfaces, which are the two-dimensional counterpart of metamaterials, have unprecedented capability to accurately control the amplitude, phase, and polarization of electromagnetic (EM) waves at subwavelength resolution [1,2]. Unlike conventional wavefront modulations based on the gradual phase accumulation along the propagation direction, the manipulation of wavefront based on metasurfaces is related to abrupt phase changes at planar antenna interfaces, opening a new window to design ultracompact (or ultrathin) devices that can outperform traditional bulky devices. Metasurfaces are divided into two categories: one is the resonant metasurfaces related to resonant phase (e.g., antenna resonance), while the other is the geometric metasurfaces associated with Pancharatnam–Berry phase (or geometric phase). Geometric metasurfaces consisting of anisotropic antennas with identical shapes and different in-plane orientations are usually applied to design flat components to manipulate the spin EM waves, e.g., left-/right-handed circularly polarized (LCP or RCP) EM waves. Benefiting from the local control of the wavefronts of spin EM waves, geometric metasurfaces enable a plethora of applications including generalized Snell’s law [3–5], metalenses [6–14], holograms [15–24], the spin Hall effect [25–28], polarization convertors [29–32], vortex beams [33–37], and nonlinear photonics [38–40].
The control of the wavefronts (e.g., amplitudes, phases, and polarizations) of spin EM waves is very important in optical communications [41,42]. With the increase of communication capacity, the independent manipulation of multiple spin beams with controllable energy allocation enables practical applications in multiple-target detection radar system and multiple-input multiple-output (MIMO) communications [43,44]. Additionally, miniaturization and integration are inevitable trends in the development of modern communication systems, and thus geometric metasurfaces provide a flexible platform to design the corresponding ultracompact devices/systems (for manipulating spin EM waves). Recently, great progress has been made on the independent manipulation of each spin state and energy distribution of spin EM waves [45–49]. For example, Liu
2. DESIGN AND METHOD
A terahertz (THz) spin-decoupled metalens is schematically shown in Fig. 1. This metalens consists of a variety of microrods with identical shape but different orientations sitting on a silicon substrate, and thus the manipulation of incident THz waves is dependent on pure geometric phase. For the incidence of LCP THz waves, such a metalens can generate two RCP focal points with the same focal distance (or different focal distance) that are transversely distributed (or longitudinally distributed) in the propagation direction (see Fig. 1). In contrast, there are two LCP focal points [that are transversely distributed (or longitudinally distributed) in the propagation direction] that can be observed under the illumination of RCP THz waves. In fact, our designed geometric metalens enables spin-decoupling functionality that can focus both LCP and RCP THz waves into helicity-dependent multiple focal points. It should be noted that all of the multiple RCP and LCP focal points are locked to the polarization state of incident THz waves. Therefore, the intensity of the helicity-dependent multiple focal points can be arbitrarily allocated by controlling the ellipticity of incident THz waves (see Fig. 1). For a geometric metalens that can focus LCP EM waves into a focal point, the required phase modulation can be governed by
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Figure 1.Schematic of the spin-decoupled metalens with intensity-tunable multiple focal points. Under the illumination of LCP THz waves, two RCP focal points are generated, while two LCP focal points can be observed for the incident RCP THz waves. The intensity between two RCP focal points and two LCP focal points can be arbitrarily modulated with different weights of LCP and RCP incident THz waves.
If a geometric metalens can focus the LCP incident EM waves into multiple focal points, the required geometric phase can be written as
In contrast, when a geometric metalens is applied to focus the RCP EM waves into multiple focal points, the phase profile for such a metalens can be expressed as
In fact, if a geometric metalens can simultaneously modulate LCP and RCP EM waves to generate both RCP and LCP multiple focal points, the total phase profile is given as follows:
It should be noted that the total phase requirements in Eq. (4) contain two independent phase profiles: one is the phase profile that can focus the LCP component into multiple RCP focal points, while the other is the phase profile that can focus the RCP component into multiple LCP focal points. Therefore, a spin-decoupled metalens with the aforementioned function [see Eq. (4)] is realized by embedding the functionalities of multiple convex lenses and concave lenses into a single metasurface, i.e., the LCP (RCP) EM waves will “see”
Figure 2(a) shows a schematic of the spin-decoupled metalens consisting of a variety of anisotropic silicon microrods with predesigned in-plane orientations. The unit cell is shown in Fig. 2(b), and the structure parameters are optimized as
Figure 2.Schematic, principle, and fabrication of the spin-decoupled metalens. (a) Schematic of the spin Hall metalens consisting of a variety of silicon microrods with identical shape but different orientations. (b) Unit cell of the microrod. (c) The transmission spectra of microrods under the illumination of TE and TM THz waves. (d) The corresponding phase difference between the transmitted TE and TM THz waves. (e) and (f) Optical images of the fabricated spin-decoupled metalenses that can generate transversely distributed and longitudinally distributed RCP and LCP multiple focal points, respectively.
3. RESULTS
As a feasibility study, we first discuss the spin-decoupled metalens that can generate helicity-dependent multiple focal points with the same focal distance. Numerical simulations and experimental demonstrations of such a metalens are shown in Fig. 3. To verify our proposed approach, a metalens consisting of
Figure 3.Electric-field intensity distributions (
Figure 4.Electric-field intensity distributions (
The proposed approach cannot only modulate the incident THz waves into transversely distributed multiple focal points but also enables the capability to steer the THz waves to form longitudinally distributed multiple focal points with intensity-tunable functionality. Figure 4 shows the calculated and measured results. The structure parameters of such a metalens for focusing longitudinally distributed multiple focal points are as follows:
4. DISCUSSION AND CONCLUSION
Geometric phase-based (or Pancharatnam–Berry phase-based) metasurfaces (named geometric metasurfaces) enable an unprecedented capability to control the phase, polarization, and amplitude of circularly polarized EM waves by arranging the orientation angle (
In summary, we have proposed an approach to design a spin-decoupled metalens that can independently modulate two orthogonal spin states of spin THz waves based on pure geometric phase. As a multifocus metalens, the incident LCP (or RCP) THz waves could be focused into helicity-dependent multiple focal points. The transversely distributed (or longitudinally distributed) helicity-dependent multiple focal points were experimentally demonstrated, and the intensity ratios between the RCP and LCP multiple focal points were arbitrarily allocated by selecting different weights of LCP and RCP THz waves. The robust and flexible approach in manipulating spin EM waves may have potential applications in designing multifunctional devices and integrated communication systems.
APPENDIX A: ELECTRIC-FIELD INTENSITY DISTRIBUTIONS (|E|2) OF A SPIN-DECOUPLED METALENS AT LINE y=?1.5??mm (z=3.75??mm)
Figure?
Figure 5.Calculated and measured electric-field intensity distributions at line
APPENDIX B: ELECTRIC-FIELD INTENSITY DISTRIBUTIONS (|E|2) AT THE x?z PLANE
Figure?
Figure 6.Electric-field intensity distributions (under the illumination of THz waves with polarization switched from LCP to RCP) at the
APPENDIX C: SIMULATED ELECTRIC-FIELD INTENSITIES (|E|2) AT THE FOCAL PLANE
Figure?
Figure 7.Simulated electric-field intensities (
APPENDIX D: SIZES OF FOCAL POINTS and FOCAL LENGTH
Sizes of the Focal Points of the Metalens for Generating Transversely Distributed Multiple Focal Points
Focal Position (mm) | LCP ( | LECP ( | LP ( | RECP ( | RCP ( | |
---|---|---|---|---|---|---|
Simulation | (1.5, 1.5, 3.75) | 310?μm | 320?μm | 320?μm | 320?μm | N/A |
(?1.5, 1.5, 3.75) | N/A | 320?μm | 320?μm | 320?μm | 310?μm | |
Experiment | (1.5, 1.5, 3.75) | 500?μm | 545?μm | 550?μm | 535?μm | N/A |
(?1.5, 1.5, 3.75) | N/A | 525?μm | 615?μm | 600?μm | 500?μm | |
Simulation | (1.5, ?1.5, 3.75) | 305?μm | 325?μm | 320?μm | 320?μm | N/A |
(?1.5, ?1.5, 3.75) | N/A | 320?μm | 320?μm | 320?μm | 305?μm | |
Experiment | (1.5, ?1.5, 3.75) | 485?μm | 560?μm | 550?μm | 535?μm | N/A |
(?1.5, ?1.5, 3.75) | N/A | 575?μm | 625?μm | 625?μm | 500?μm |
Focal Length of the Metalens for Generating Transversely Distributed Multiple Focal Points
Focal Position (mm) | LCP ( | LECP ( | LP ( | RECP ( | RCP ( | |
---|---|---|---|---|---|---|
Simulation | (1.5, 1.5, 3.75) | 905?μm | 910?μm | 910?μm | 915?μm | N/A |
(?1.5, 1.5, 3.75) | N/A | 905?μm | 910?μm | 910?μm | 900?μm | |
Experiment | (1.5, 1.5, 3.75) | 1355?μm | 1290?μm | 1290?μm | 1255?μm | N/A |
(?1.5, 1.5, 3.75) | N/A | 1300?μm | 1270?μm | 1185?μm | 1155?μm | |
Simulation | (1.5, ?1.5, 3.75) | 905?μm | 910?μm | 910?μm | 910?μm | N/A |
(?1.5, ?1.5, 3.75) | N/A | 900?μm | 910?μm | 915?μm | 905?μm | |
Experiment | (1.5, ?1.5, 3.75) | 1260?μm | 1255?μm | 1330?μm | 1305?μm | N/A |
(?1.5, ?1.5, 3.75) | N/A | 1285?μm | 1310?μm | 1225?μm | 1170?μm |
Sizes of the Focal Points of the Metalens for Generating Longitudinally Distributed Multiple Focal Points
Focal Position (mm) | LCP ( | LECP ( | LP ( | RECP ( | RCP ( | |
---|---|---|---|---|---|---|
Simulation | (0, 1.0, 3.75) | 305?μm | 280?μm | 280?μm | 275?μm | N/A |
(0, 1.5, 5.70) | 370?μm | 350?μm | 345?μm | 340?μm | N/A | |
Experiment | (0, 1.0, 3.75) | 480?μm | 635?μm | 605?μm | 680?μm | N/A |
(0, 1.5, 5.70) | 590?μm | 720?μm | 725?μm | 710?μm | N/A | |
Simulation | (0, ?1.0, 3.75) | N/A | 280?μm | 280?μm | 280?μm | 305?μm |
(0, ?1.5, 5.70) | N/A | 345?μm | 345?μm | 345?μm | 370?μm | |
Experiment | (0, ?1.0, 3.75) | N/A | 625?μm | 580?μm | 725?μm | 485?μm |
(0, ?1.5, 5.70) | N/A | 715?μm | 710?μm | 765?μm | 565?μm |
Focal Length of the Metalens for Generating Longitudinally Distributed Multiple Focal Points
Focal Position (mm) | LCP ( | LECP ( | LP ( | RECP ( | RCP ( | |
---|---|---|---|---|---|---|
Simulation | (0, 1.0, 3.75) | 895?μm | 900?μm | 890?μm | 895?μm | N/A |
(0, 1.5, 5.70) | 1250?μm | 1260?μm | 1260?μm | 1260?μm | N/A | |
Experiment | (0, 1.0, 3.75) | 1350?μm | 1375?μm | 1395?μm | 1450?μm | N/A |
(0, 1.5, 5.70) | 2505?μm | 2475?μm | 2550?μm | 2625?μm | N/A | |
Simulation | (0, ?1.0, 3.75) | N/A | 900?μm | 890?μm | 890?μm | 895?μm |
(0, ?1.5, 5.70) | N/A | 1260?μm | 1260?μm | 1265?μm | 1260?μm | |
Experiment | (0, ?1.0, 3.75) | N/A | 1270?μm | 1325?μm | 1330?μm | 1335?μm |
(0, ?1.5, 5.70) | N/A | 2355?μm | 2450?μm | 2525?μm | 2615?μm |
APPENDIX E: ELECTRIC-FIELD INTENSITY DISTRIBUTIONS (|E|2) OF A SPIN-DECOUPLED METALENS AT LINE z=5.75??mm (x=0??mm)
The simulated and experimentally measured electric-field intensity distributions at line
Figure 8.Calculated and measured electric-field intensity distributions at line
APPENDIX F: ELECTRIC-FIELD INTENSITY DISTRIBUTIONS (|E|2) AT THE x?y PLANE (z=3.75??mm)
Figure?
Figure 9.Electric-field intensity distributions (under the illumination of THz waves with polarization switched from LCP to RCP) at the
APPENDIX G: ELECTRIC-FIELD INTENSITY DISTRIBUTIONS (|E|2) AT THE x?y PLANE (z=5.7??mm)
For the spin-decoupled metalens that can generate longitudinally distributed multiple focal points, another one (or two) focal point(s) will be generated in the longitudinal direction as shown in Fig.?
Figure 10.Electric-field intensity distributions (under the illumination of THz waves with polarization switched from LCP to RCP) at the
APPENDIX H: SIMULATED ELECTRIC-FIELD INTENSITIES (|E|2) AT THE FOCAL PLANE
The calculated electric-field intensities of a spin-decoupled metalens (that can generate longitudinally distributed multiple focal points) at the focal plane are shown in Fig.?
Figure 11.Simulated electric-field intensities (
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