- Photonics Research
- Vol. 9, Issue 10, 1939 (2021)
Abstract
1. INTRODUCTION
Polarization is an important variable of electromagnetic waves, typical types of which include linear, circular, and elliptical ones. From the perspective of electromagnetic field, it refers to the trajectory of the electric field vibration, and from the perspective of the photons, it (circular polarization) can also be related to the spin angular momentum [1,2]. Therefore, polarization of light has been widely studied and applied in imaging, quantum optics, and other fields, and polarization manipulation has become an important research content of modern optics and photonics [3–5]. Traditional optical devices based on bulk crystals are used for polarization generation or conversion, such as polarizers and wave plates. The wave plate is based on the linear birefringence effect of the optical crystal, which produces a phase shift between the ordinary and the extraordinary components with an appropriate thickness, and then superimposes them into a new polarization. Such devices are large in size and require high processing accuracy, while only specific materials can be used in each electromagnetic band [6]. More importantly, these devices can hardly realize the simultaneous control of other optical parameters while performing polarization conversion, such as amplitude and phase. This is not conducive to the multi-functional and integrated development of modern optical devices.
Electromagnetic metasurfaces are planar functional devices composed of artificially designed sub-wavelength meta-atoms [7–10]. After more than 10 years of rapid development, significant progress of them has been made in the fields of information optics [11,12], quantum optics [4,5], non-linear optics, and terahertz photonics [13–17]. Electromagnetic functional devices based on metasurfaces are flexible in design and conducive for integration. They not only provide new ideas for the development of new optical devices, but also provide powerful tools for many basic physics researches [18–20]. In particular, metasurfaces also achieve optical linear birefringence and polarization conversion. Different from the material birefringence of traditional optical devices, the meta-atoms in metasurface utilize the shape birefringence [21], which has been realized from microwave to ultraviolet bands using a dielectric or metal [22,23]. For shape-induced linear birefringence, when the incident polarization is consistent with the symmetry axis of the anisotropic meta-atom, the output polarization state remains unchanged, and the incident polarization state is called the eigen-polarization state. When the other linearly polarized wave is incident, its projection in the eigen-polarization state will cause polarization transformation [21], and the output polarization state can be designed by changing the geometric parameters of the structure. The advantage of shape birefringence is that the working frequency can be designed, and other functions can be achieved with polarization conversion, such as non-linear effect [10], wavefront shaping [5,24,25], and polarization-dependent beam energy distribution [26,27]. In particular, researchers set the appropriate geometric dimensions to make the linear polarization conversion efficiency of the meta-atoms be about 50%, controlled the phase difference between the co- and cross-polarized components, and then obtained beam shaping with designed polarization [28–30]. This method is similar to the principle of a quarter-wave plate and can realize the polarization conversion with a simple structure, but the transformation channels are non-independent due to the symmetry of the meta-atoms. It is difficult to achieve independent polarization conversion between different channels. In addition to the linear polarization-based approach, the circular polarization-based one has also been reported, that is, the phase manipulation method of spin decoupling which combines geometric and dynamic phases, while the cross- and co-polarizations can be controlled at the same time [31–33]. However, the optical response of each unit needs to meet several conditions at the same time, which means that their design process is complicated. Therefore, metadevices for polarization conversion with a simple design and two or more independent channels are very necessary.
Here, we propose a new method for terahertz beam shaping with multiple polarization conversion channels. Two sets of spatially interleaved anisotropic units are used to obtain the linearly co- and cross-polarized components, which are superimposed to obtain a new polarization state in beam shaping. We take the focused beam as an example to improve the signal-to-noise ratio (SNR) of the measurement for terahertz electric field. We use two samples to demonstrate the high-efficiency, broadband polarization conversion and the multi-channel function brought about by the incident polarization and the sub-arrays. This method is not only suitable for design of linear polarization-based metasurfaces, but also can be extended to circular polarization-based devices.
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2. RESULTS AND DISCUSSION
The proposed scheme of beam shaping with polarization conversion is shown in Fig. 1, in which Fig. 1(a) is a schematic diagram of the metasurface. We take the incidence of two orthogonal linear polarization states as an example (such as and polarizations). In the transmitted wave, we can obtain two independent polarization states, such as different linear or circular polarizations. Here we define the polarization states with an angle of 45° or to the axis as “” or “” polarization, respectively [28]. The above-mentioned functions are realized by the spatially interleaved structure shown in Fig. 1(b), in which the two kinds of units differ by half a period () in both the and directions. When an - or -polarized wave is incident, the transmitted wave of the cross-ellipse cylinder [structure (i)] maintains its polarization state, which is called the eigen-polarization. Moreover, the transmission phases of the two polarization states can be independently controlled. For structure (ii), the long axis of the ellipse forms an angle of 45° or with respect to the axis, and its eigen-polarization states are and polarizations. The transmitted wave can be efficiently converted into cross-polarization when - or -polarized beam is incident. In this way, we have three polarization components to control, and then two independent polarization channels can be obtained after superposition. In addition, other incident polarization states can be regarded as vector superposition of and polarizations with a specific phase shift, so more transmission polarization states can also be obtained. For example, when -polarized waves are incident, the transmitted waves will be elliptically polarized.
Figure 1.Schematic diagram of the metasurface for beam shaping with dual-channel polarization conversion. (a) Taking the orthogonal linearly polarized terahertz waves as an example, a 45° polarized (
Here, we make a brief theoretical analysis of the working principle for the metasurface in Fig. 1. Without loss of generality, we consider the condition of or polarization incidence. Considering that there are two kinds of units in our metasurface, the operational relationship between the transmitted and incident electric field is
When the -polarized wave is incident, we have
Similarly, when the -polarized wave is incident, the transmitted electric field is
In order to obtain the above-mentioned metasurface, we use commercial numerical simulation software to obtain parameter libraries of the two kinds of meta-atoms. We choose high-resistance silicon as the constituent material, and process meta-atoms directly on the silicon wafer. High-resistance silicon () shows almost no absorption for terahertz wave, and its dielectric constant is set as during the simulation. The two structures are shown in Fig. 2(a), where the period is , the height of the silicon pillar is , and the thickness of the substrate is 300 μm. The major and minor axes of the ellipse in structure (ii) are and , respectively. The minor axes of the two ellipses in structure (i) are both , and the major axes are and , respectively.
Figure 2.Amplitudes and phases of the transmitted wave corresponding to meta-atoms with selected geometric parameters. (a) Geometric shape of the two kinds of meta-atoms. Amplitude and phase values for the (b) second and (c)–(f) first types of meta-atoms.
By scanning the parameters of the two structures (the original data can be seen in Appendix B, Fig. 6, the working frequency is ), we first obtained the parameter library of structure (ii), as shown in Fig. 2(b). Since the structure will generate - and -polarized waves that are equal in value when the and polarizations are incident, respectively, we use only one component to represent them uniformly ( and ). The phase shifts of the eight elements are changed from 135° to 180°, which is equivalent to covering the interval of [−180°, 180°] with a step of 45°. The first-order transmission coefficients of the eight elements are all around 0.6. The parameter library of structure (i) is shown in Figs. 2(c)–2(f); the values in the figure are obtained by probing the co-polarization components when - or -polarized waves are incident separately. Each unit in the library needs to consider the transmission phase shifts for both - and -polarized waves (eigen-polarizations) at the same time, and the amplitude remains the same. It can be seen from the figure that the selected phases show a good gradient with a step of 45°, and the first-order amplitudes of all units basically remain above 0.6. The transmission efficiency limitation of the two types of structures is mainly due to the reflection at the air/silicon interface.
Based on the above parameter library, we design two metasurfaces to verify the beam shaping with polarization conversion. The samples are processed from a 500 μm thick high-resistance silicon through inductively coupled plasma (ICP) etching technology. Each sample is a square with a side length of 1.4 cm. The specific processing steps can be seen in Appendix A. The scanning electron microscope (SEM) images of the first metasurface are shown in Fig. 3(a), which is called sample 1. Its effective area is a circular array composed of the two kinds of meta-atoms mentioned above. There are 80 units (1.12 cm) of each kind in the radial direction. It can be seen from the figure that the sidewalls of the meta-atoms are very steep, which means the processing error is not obvious. In order to illustrate the polarization conversion function of sample 1 intuitively, we use Poincaré spheres to show the incident and transmission polarization states, which are denoted by and , respectively, as shown in Fig. 3(b). To show the independence of the two polarization channels, we hope that when the - and -polarized waves are incident, the transmission waves are -polarized or right circularly polarized (RCP), respectively. In addition, we design the transmitted beam as a focused vortex beam, which can improve the SNR of the measurement results. Therefore, the expression of the phase profile of the three channels in the metasurface should be
Figure 3.Simulated and experimental results of sample 1 for the generation of focused vortex beam with polarization conversion. (a) SEM images of sample 1. (b) Demonstration of dual-channel polarization conversion on the Poincaré sphere. (c) Electric field intensity of the transmitted wave in the focal plane when the
It can be seen that the conversion efficiency at the design frequency of 1.1 THz is up to 89.2%, and it is greater than 60% in the entire survey frequency band. The simulated results show that the efficiency is higher than 80% in the range of 0.8–1.3 THz, with a peak value of 93.8% at 1.1 THz. The measured values are slightly smaller than the simulated ones; after all, there are some noise signals in the edge area of the focal plane in the measurement results.
In fact, we can obtain more channels in one metasurface via area division of the sample, which means designing different phase distributions in different areas [30]. For simplicity, we only consider the condition of dividing the effective area into two sub-arrays. When the - or -polarized wave is incident, the two areas produce different circularly polarized beams. To this end, we design and process the sample 2 shown in Fig. 4(a), where the phase functions of the left- and right-half regions are shown in Appendix B (Fig. 7). The focal length of sample 2 is , and the working wavelength is . The Poincaré sphere in Fig. 4(b) shows the polarization conversion function of sample 2. At this time, one input linear polarization state can generate two output circular polarization states at different positions. Figure 4(c) shows the polarization components of the transmitted electric field when the - or -polarized wave is incident. In addition to the electric field intensity and section curve similar to Fig. 3(c), here we also use the component (normalized) of Stokes parameters to intuitively show the circular polarization distribution of the transmitted wave. It can be seen that both left- and right-handed circular polarizations have been obtained efficiently, and the simulation results are in agreement with the experimental data. In addition, we show the electric field intensity and parameter distributions of the metasurface in the longitudinal section (-plane) in Fig. 4(d). It can be found that the division of the regions does not significantly affect the focusing efficiency of the metasurface.
Figure 4.Simulated and experimental results of sample 2 for the generation of focused vortex beam with polarization conversion. (a) SEM image and optical photo of sample 2. (b) Demonstration of the dual-channel polarization conversion on the Poincaré sphere. (c) Electric field intensity of the transmitted wave when the
Generally, in the case where linearly polarized waves are incident, all the polarization states we get are derived from the superposition of orthogonal linearly polarized components transmitted by the two types of meta-atoms. With different phase shifts, various states such as linear, elliptical, or circular polarization can be obtained. In particular, when the - or -polarized wave is incident, both of the polarization components appear in the transmitted beam. Assuming that the phase difference between the and polarization components in the transmission is , Fig. 5(a) shows the generated polarization states when takes different values. The corresponding positions on the Poincaré sphere are shown in Fig. 5(b). It should be noted that when only the - or -polarized wave is incident, we will never get a purely - or -polarized transmitted wave. However, as shown in Fig. 5(c), when the RCP or LCP wave is incident in sample 2, we can get - or -polarized beams. In this way, we have achieved the coverage of various typical polarizations of the transmitted wave.
Figure 5.General discussions on the available polarization states. (a), (b) The possible polarization realization of the transmitted wave when the linearly polarized wave is incident. (c) Transmitted electric field intensities under circularly polarized wave illumination.
3. CONCLUSION
In summary, we propose a new method for terahertz beam shaping with multi-channel polarization conversion based on all-silicon metasurfaces. We alternately arrange two kinds of meta-atoms in a single metasurface, eigen-polarizations of which are , , or polarizations, respectively. Therefore, when - or -polarized waves are incident, they will respectively generate co- or cross-polarized transmitted waves while achieving beam shaping. In this way, a new polarization state in transmission can be obtained after far-field interference, and there are two independent channels available. In addition, a single metasurface can be divided into two or even more sub-arrays to achieve more channels for polarization conversion or beam shaping. To this end, we designed and processed two samples to demonstrate the above functions. The simulated and experimental results of the first sample verify the dual-channel polarization conversion with linearly polarized incidence. The second one shows the multi-channel polarization conversion controlled by polarization incidence and region division. We use electric field intensities, Stokes parameters, and Poincaré spheres to show the working performance of the metasurface, which confirm our proposed scheme. The experimental results of the electric field are in agreement with the simulations. This design method is not only easier to implement and can provide independent polarization conversion channels, but can also be extended from a linear polarization base to a circular polarization base. The proposed metasurfaces are expected to be applied for polarization multiplexing imaging, holography, and detection of polarization state of terahertz wave.
APPENDIX A: EXPERIMENTAL SECTION
Numerical simulations: We simulate the meta-atoms and whole samples using the commercial software CST MICROWAVE STUDIO (2019, time domain solver). We first calculate the transmission amplitudes and phases of the units with different geometric dimensions. At this time, both and directions are set as periodic boundaries, and the open boundary is set along the direction, while a plane wave is used as the excitation source. Based on the parameter libraries, we use a MATLAB code to drive the CST MICROWAVE STUDIO to draw the whole structure of the sample. Then the , , and directions are set as open boundary conditions, and the calculation space in the direction is larger than the designed focal length. Finally, another MATLAB code is used to process the simulation results when needed.
Experimental setup: We measure the electric field intensity and phase distributions of the focused terahertz beam (Figs.
Sample fabrication: Ultraviolet lithography and ICP etching are used to process the samples. We use standard photolithography to form a 6.8 μm thick patterned positive photoresist (AZ4620) as a mask on a 500 μm thick silicon wafer with a diameter of 4 inch (1 inch = 2.54 cm). Then we use (ICP) etching technology (STS MULTIPLEX ASE-HRM ICP ETCHER, United Kingdom) to etch the sample, and finally the remaining photoresist is washed away to get the final sample. The etching depth is about 200 μm, and the remaining 300 μm thick silicon layer is used as the substrate.
APPENDIX B: GEOMETRIC SIZE SELECTION OF THE META-ATOMS
In order to obtain the parameter library of the two types of meta-atoms, we simulated the amplitudes and phases of the transmitted wave with their lateral dimensions as variables (the height of the silicon pillar is 200 μm, and thickness of the substrate is 300 μm). The results are shown in Fig.
Figure 6.Transmission amplitudes and phases of the meta-atoms with different geometric sizes.
APPENDIX C: PHASE DISTRIBUTION FUNCTIONS OF SAMPLE 2
As mentioned in the paper, the effective area of sample 2 is divided into two sub-arrays, in which the phase distribution functions of the two types of meta-atoms in the left half () and the right half () are as follows:
In order to show the near-field phase distributions of the metasurface more intuitively, we draw the phase profile of the two samples according to Eqs. (
Figure 7.Near-field phase distributions of the two samples.
Figure 8.Phase distributions in the focal plane of the generated vortex beam from sample 1.
Figure 9.THz imaging system based on two-dimensional electro-optical sampling.
APPENDIX D: TERAHERTZ IMAGING SYSTEM
We measure the electric field intensity and phase distributions of the focused terahertz beam (Figs.
APPENDIX E: MEASUREMENT OF THE POLARIZATION CONVERSION FOR TERAHERTZ WAVE
The imaging system we use can only generate a linearly polarized terahertz beam in the pump module, while the probe module can measure the linearly co- and cross-polarized components. Therefore, the transmitted circularly polarized wave can be obtained if we superimpose the measured and polarization components for sample 1, which is also applicable to the case of sample 2 when linearly polarized waves are incident:
For the condition where the circularly polarized wave is incident in sample 2, after measuring four linear polarization components, circularly polarized components in the transmitted beam can be obtained according to the following formula, and then the final polarization state can be judged:
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