Longitudinal polarization manipulation based on all-dielectric terahertz metasurfaces

Susu Hu; Susu Hu; Li Wei; Li Wei; Yan Long; Shaoqi Huang; Bo Dai; Liang Qiu; Liang Qiu; Songlin Zhuang; Dawei Zhang; Dawei Zhang

doi:10.1364/OE.514410

1. Introduction

Polarization is one of the key parameters of electromagnetic wave and plays an important role in electromagnetic wave. Polarization has extensive applications in optics and optical devices [1–3], involving display technology [4], communication, microscopy and measurement, significantly contributing to the remarkable advancements in optics and photonics [5–7]. Polarized optical elements are often used for physical measurement, information recording and transmission [8–10]. Typical traditional polarized optical components include polarizers, wave plates, vortex wave plates, etc., which necessitate a long propagation distance to accumulate phase shift [11], and their functions are usually simple. Indeed, certain complex polarization conversion and processing even require simultaneous cascading of multiple polarization optical components, which inevitably brings certain obstacles to optical integration [12].

In recent years, the significant manipulation capability of electromagnetic waves based on the metasurfaces has aroused widespread attention among researchers [13,14]. As the two-dimensional form of metamaterial [15,16], metasurface is a planar optical element composed of artificially designed meta-atoms [17]. Well-designed metasurfaces can not only realize the polarization transformations [18,19], but also cope with other inherent characteristics of electromagnetic waves [20], including phase [21], frequency, and amplitude [22], providing great flexibility to control electromagnetic waves. The manipulation of polarization states and the integration of polarization with other properties based on the metasurface have not only spurred the development of various novel functional photonic devices, but also advanced the progress of physics research [23]. The capability to manipulate the polarization of electromagnetic waves in three-dimensional space is crucial for research advancements [24,25]. With this, H. Markovich et al. demonstrated a bifocal Fresnel lens based on the polarization-sensitive metasurface [26]. Sun et al. constructed metalenses with bifocal spots, which realizes the beam focusing with controllable intensity ratio and free deflection of the bifocal spots [27]. These works mainly focus on the manipulation of uniformly polarized waves in two-dimensional or three-dimensional space. Presently, the longitudinal polarization manipulation is still difficult, especially the generation of non-uniformly vector beams along the propagation direction.

In addition, vector beams have broad applications in fields such as laser processing, atomic cooling, and surface plasma excitation [28]. Due to the difficulty in synthesizing vector beams, the vortex beam coherent synthesis of vector beam is more commonly used [29]. Currently, the generation of vector beams based on metasurfaces has also been widely reported, such as independent generation of vector beams on multiple focal planes and the realization of vector beams with specific three-dimensional trajectories through non-iterative focal field shaping [30,31]. Fu et al. proposed a method to generate Bessel-type vector beams with spatial oscillating polarization along the propagation direction [32]. Ahmed H. Dorrah et al. introduced a method for generating polarization transformations along the optical path based on metasurface [33]. Furthermore, there are some applications using these metasurface structures for detecting optical path and refractive index. Ahmed H. Dorrah et al. proposed and experimentally demonstrated a novel mechanism for sensing the index of refraction of a medium by utilizing the orbital angular momentum (OAM) of structured light [34]. Qin et al. introduced an ultracompact biosensor based on a longitudinally structured vector beam [35]. Currently, by combining spin decoupling with multi-focus phase design or focal depth design, various vortex vector terahertz fields can be output along the propagation path [36,37]. However, previous studies have only proposed longitudinal terahertz polarization manipulation in limited locations [38]. Therefore, it is necessary to construct metasurfaces to achieve polarization evolution over long distances along the propagation direction.

Here, a concept for manipulating polarization along the propagation path is proposed in the field of terahertz using functional all-silicon metasurfaces, and we present two metasurfaces to demonstrate the proof-of-concept. The first one is a longitudinal bifocal metalens, under the incidence of left-handed circularly polarized (LCP) wave, the light focused at 3.8 mm along the transmission direction exhibits left-handed circular polarization, and focused again at 6.1 mm along the transmission direction with the y-polarized beam. The experimental findings closely align with the simulation results. The second is a versatile metalens. In addition to generate a focused beam with uniform polarization, it can also generate a vector beam with longitudinally variation of phase difference between the LCP and the right-handed circularly polarized (RCP) components. These metasurfaces integrate both the propagation phase and Pancharatnam-Berry (PB) phase, encoding complex amplitude information into the orthogonal polarization components of the output. This provides additional degrees of freedom for the longitudinal polarization manipulation. Our research broadens the utilization of polarization in the development of multifunctional metasurfaces, and may find application in tunable structured light, optical imaging and optically switchable devices.

2. Proof-of-principle and meta-atom design

2.1 Design of fully phase-modulated metasurface

When a circularly polarized (CP) wave is incident upon an artificially designed metasurface, both co-polarization and cross-polarization components are inevitably present in the output electromagnetic wave due to design and fabrication considerations [16]. Then, different wavefront manipulation can be achieved only when an independent phase function is applied to the CP component of the output wave. Assuming that the incident LCP light is represented by $\vec{\xi }$, then the relationship between the output wave and the incident wave is established by Jones matrix

(1)$${{\mathbf J}_1} = {\mathbf J} \cdot \vec{\xi } = {e^{i{\phi _1}}} \cdot \vec{\delta } + {e^{i{\phi _2}}} \cdot {\vec{\delta }^ \ast }$$

where, $\vec{\delta }$ represents the co-polarized component of the output wave, ${\vec{\delta }^ \ast }$ represents the cross-polarized component of the output wave. If the summation of propagation phase along the fast and slow axes defines the value of parameter Σφ=φ_xx+φ_yy, the phase difference between two mutually perpendicular linear polarizations is denoted as Δφ=φ_xx-φ_yy, Eq. (1) can be further expressed as:

(2)$${\mathbf J}_1 = \cos \left( {\displaystyle{1 \over 2}{\rm \Delta }\varphi } \right)e^{i\cdot \displaystyle{1 \over 2}\sum \varphi }\cdot \vec{\xi } + \sin \left( {\displaystyle{1 \over 2}{\rm \Delta }\varphi } \right)e^{i\cdot \displaystyle{1 \over 2}\left( {\sum \varphi + \pi } \right)}e^{-i2\alpha }\cdot \vec{\xi }^-$$

Associated the Eq. (2), it can be observed that two types of circularly polarized components would be generated with one CP incidence. One maintains the same polarization state as the incident light, while the other exhibits cross-polarization. Here, the phase and amplitude of the co-polarized component are Σφ/2 and cos(Δφ/2), while the phase and amplitude of cross-polarized component are (Σφ+π)/2-2α and sin(Δφ/2) respectively. It can be concluded that the phase of the co-polarized component solely depends on propagation phase, while the phase of the cross-polarized component depends not only on the propagation phase but also the geometric phase. Furthermore, it exists a strong correlation between energy ratios of co-polarized and cross-polarized components, as follows:

(3)$$\eta = {\rm E}_{{\rm co}}^2 /{\rm E}_{{\rm cross\; }}^2 = \sin ^2\left( {\displaystyle{1 \over 2}{\rm \Delta }\varphi } \right)/\cos ^2\left( {\displaystyle{1 \over 2}{\rm \Delta }\varphi } \right) = \tan ^2\left( {\displaystyle{1 \over 2}{\rm \Delta }\varphi } \right)$$

E_co and E_cross represent the amplitude of co-polarized wave component and cross-polarized wave component, respectively.

For the convenience of discussion, only the LCP incident case is considered here. Under the incidence of the LCP wave, Eq. (2) can be further transformed as follows:

(4)$$E_{{\rm out\; }} = {\mathbf J}\cdot |{\mathbf L}\left. {} \right\rangle = \cos \left( {\displaystyle{1 \over 2}{\rm \Delta }\varphi } \right){\rm e}^{i\cdot \displaystyle{1 \over 2}\sum \varphi }\cdot |{\mathbf L}\left. {} \right\rangle + \sin \left( {\displaystyle{1 \over 2}{\rm \Delta }\varphi } \right){\rm e}^{i\cdot \displaystyle{1 \over 2}\left( {\sum \varphi + \pi } \right)}\cdot {\rm e}^{-i2\alpha }\cdot |{\mathbf R}\left. {} \right\rangle$$

Supposing the phase difference between the x and y polarizations is Δφ=π/3. The energy ratio of the LCP and the RCP component in the output wave is 3:1 (η=tan²(Δφ/2 = 3:1), when LCP wave operates on the metasurfaces composed of meta-atoms with a phase difference of π/3. In this case, the original distribution of the energy of the output wave has been accomplished.

2.2 Meta-atom design

The meta-atoms of the designed metasurface consist of rectangular highly resistive silicon columns, as illustrated in Fig. 1(a). In terahertz band, the dielectric constant of highly resistive silicon is set to ε=11.9. Among them, the thickness of substrate is H₁= 300 µm, and period of lattice is P = 150 µm. The height of the rectangular pillar is H₂= 200 µm, and the lengths of which in the x and y directions are denoted as L_x and L_y, respectively. We employ the time domain solver of commercial software to explore different structural parameters of the meta-atoms. In perforation of parametric sweep, the x and y directions are both configured with periodic boundary conditions, while the z direction is configured with open boundary conditions. By adjusting the L_x and L_y, the phase responses can encompass a range of 2π under both x and y polarized illuminations. Based on deduction made in section 2.1, which shows that the selected meta-atoms should satisfy a phase difference of π/3. In order to regulate the wavefront effectively, the phase shifts during the transmission of selected meta-atoms are incremented by π/3. For the designed six structures, and detailed information regarding their structural parameters can be shown in Table 1. Simulation results for these six meta-atoms are presented in Fig. 1. These six silicon rectangular pillars enable the transmission of x- and y-polarized waves with equal amplitude and phase coverage ranging from 0 to 2π, which meets the required parameter range for metasurface design [39]. Additionally, the phase of the x-polarized component lags behind the y-polarized component by π/3, leading to simultaneous outputting of LCP and RCP waves.

Fig. 1. (a) Structural parameters of the meta-atoms. (b) The x- and y- polarized component amplitudes of the output wave. (c) The relative phase of the corresponding x-polarized component. (d) The phase difference between the y- and x- polarized components.

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Table 1. The structural parameters for six meta-atoms

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3. Longitudinal bifocal metalens

First, an amplitude-encoded metasurface was designed to demonstrate independent control of polarization states in two focal planes along the direction of transmission. The complex amplitude of the output wave can be expressed as:

(5)$$\begin{matrix}{\varphi _{\rm I} = \displaystyle{{2\pi } \over \lambda }\left( {\sqrt {x^2 + y^2 + f_1^2 } -f_1} \right)} \cr {\varphi _{{\rm II}} = \displaystyle{{2\pi } \over \lambda }\left( {\sqrt {x^2 + y^2 + f_2^2 } -f_2} \right)} \cr {E_L = \beta _1\exp \left( {i\varphi _{\rm I}} \right) + \beta _2\exp \left( {i\varphi _{{\rm II}}} \right)} \cr {\varphi _{LL} = {\rm abs}\left( {E_L} \right) \times {\rm angle}\left( {E_L} \right)} \end{matrix}$$

where λ is working wavelength corresponding to 0.95 THz, φ_I and φ_II are the phase profiles for the converging output wave of LCP components with focal lengths of f₁= 3.8 mm, f₂= 6.1 mm, β₁ and β₂ are the amplitude of the LCP component in the output wave at f₁ and f₂, respectively. When (β₁:β₂)²= 2:1, the secondary distribution of energy could be realized. E_L represents the designed complex amplitude distribution of output LCP components, φ_LL represents the phase distribution of the transmitted LCP component in response to LCP incident wave. Meanwhile, for the RCP component of the output wave, its phase distribution needs to satisfy the following formula:

(6)$$\varphi _{{\rm III\; }} = \displaystyle{{2\pi } \over \lambda }\left( {\sqrt {x^2 + y^2 + f_2^2 } -f_2} \right) + \pi$$

Thus, through elaborately design, there is only the focused LCP component at the first focal point under LCP incidence, while there are both co-polarized and cross-polarized components at the second focal point with equal amplitudes and a phase difference of π. Then, the y-polarized wave is obtained by superposition of the waves of two polarization states at the second focal point, the derivation process is as follows:

(7)$$E_{f_2} = {\rm A}\left[ {\begin{matrix} 1 \hfill \cr {-i} \end{matrix} } \right] + {\rm A}e^{i\pi }\left[ {\begin{matrix} 1 \hfill \cr i \end{matrix}} \right] = -2i{\rm A}\left[ {\begin{matrix} 0 \hfill \cr 1 \end{matrix} } \right]$$

where A represents the amplitudes of the LCP and RCP components, $E_{f_2}$ represents the complex amplitude distribution of a wave converged at the second focal point. The top view and functional diagram of the designed metasurface are illustrated in Fig. 2.

The simulated axial intensity profile is shown in Fig. 3. In the theoretical design, two foci are converged along the optical axis. Figure 3 shows the simulated intensity profiles of E_x, E_y, E_RCP and E_LCP along the propagation path, respectively. As shown in Fig. 3(c) and Fig. 3(d), the RCP component in the transmitted wave is sharply converged at 6.1 mm, while the LCP component in the transmitted wave is converged at 3.8 mm and 6.1 mm, respectively, with varying energy ratios. These results shown in Fig. 3(c) and Fig. 3(d) correspond exactly to Fig. 3(a) and Fig. 3(b). Figure 3(e) shows the intensity profile along the optical axis when illuminated with LCP light, the intensity profiles in these two focal planes are depicted in Fig. 3(d). These simulation results are in excellent agreement perfectly with the theoretical results.

Fig. 2. (a) Top view of the designed metasurface (Sample 1). (b) Diagram illustrating the function of the longitudinal bifocal metalens.

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Fig. 3. The simulated intensity profile when illuminated with LCP light. (a) The axial intensity profile for transmitted x component. (b) The axial intensity profile for transmitted y component. (c) The axial intensity profile for transmitted RCP component. (d) The axial intensity profile for transmitted LCP component. (e) The intensity distribution of RCP and LCP components along the z axis at the focal plane. (f) The intensity profiles of two focal planes.

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To further verify the reliability of the simulated results, the transverse electric field distributions of wave components with varying polarization states at the two foci are shown in Fig. 4. It is apparent from the analysis of Fig. 4(a) that the 3.8 mm focal point only exhibits the LCP component, on the other hand, Fig. 4(b) shows that there are both RCP component and the LCP at 6.1 mm of the transmission direction, and the superposition of the two components forms a y-polarized wave at 6.1 mm, as shown in Fig. 4(c). Such bottom plots represent the phase profiles, respectively.

Fig. 4. Transverse distribution of different polarized components at two focal points (a) Transverse light field distribution at 3.8 mm. (b) Transverse optical field distribution at 6.1 mm: The top is the optical field distribution of RCP component and LCP respectively, and the bottom is the corresponding phase distribution. (c) Transverse light field distribution at 6.1 mm: The diagram above shows the light field distribution of the x and y components, and the diagram below shows the corresponding phase distribution.

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To enhance the verification of the feasibility of the scheme, we proceed to fabricate the designed metasurface. Subsequently, the electric field intensity distributions of the fabricated metasurface was detected using a near-field scanning terahertz imaging system, as depicted schematically in Fig. 5(a). A femtosecond incident laser beam, with a central wavelength of 1560 nm, is directed into two separate optical paths. In the two optical paths, one laser beam is coupled with the photoconductive antenna transmitter to generate terahertz waves, simultaneously, the other laser beam is illuminated on the periodically polarized lithium niobate (PPLN) to excite a laser beam with a central wavelength of 780 nm. The laser beam (λ=780 nm) is then illuminated on the terahertz tip/detector to detect the electric field distribution. We used point-by-point scanning in the near-field terahertz imaging system. The terahertz tip is fixed on a three-dimensional (3D) translation platform, enabling to scan three-dimensional fields with a scanning step of 50 µm. To obtain the distribution of electric field intensity for the designed metasurface, the sample remains stationary while the THz tip is positioned within the focal region to scan the electric field distribution. The next step is sample processing. Inductively coupled plasma (ICP) etching technology is used to process the sample on a commercial high-resistance silicon wafer with a thickness of 500 µm. Figure 5(b) and Fig. 5(c) show the scanning electron microscope (SEM) images of the sample. Under the incidence of the LCP light, the measured intensity profiles along the x and y axis at focal plane are depicted in Fig. 5(d). It can be clearly seen that x and y polarization components with equal amplitudes are detected at the first focus, while only y polarization component is detected at the second focus, which is completely in agreement with the simulations. The maximum transmission efficiency of the bifocal metalens can reach 70% because of the high transmittance of silicon. In addition, the focusing efficiencies are 54.6% and 75.3% for the LCP and y-polarized beam, respectively. Here, the efficiency is defined as the ratio of the optical power in the focal area with a radius of three times of the full width at half maximum (FWHM) to the total power in focal plane. The diameter of the metalens is 12 mm. The numerical aperture of the lens is approximately NA = 0.84 for LCP and NA = 0.7 for y-polarized beam, respectively.

Fig. 5. (a) The near-field scanning terahertz microscopy. (b),(c) The SEM images of designed metasurface. (d) The measured intensity profile at the focal plane under the LCP illumination.

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4. Versatile metalens

4.1 Design and simulation of the versatile metalens

It is well-established that a vector beam with a vortex polarization distribution at the transverse interface can be mathematically represented by the Jones vector [32]:

(8)$$E(r,\varphi ) = {\rm A}(r)\left[ {\begin{matrix} {\cos \left( {p\varphi + \theta _0} \right)} \cr {\sin \left( {p\varphi + \theta _0} \right)} \end{matrix}} \right]$$

where A(r) is the amplitude distribution of the beam, p is the topological number of spatial polarization, which denotes the quantity of polarization state alterations occurring within the cross-sectional area of the beam, and θ₀ is the initial polarization direction at φ=0. A vector beam can be generated through the coherent superposition of mutually orthogonal polarized vortex beams. Supposing that the difference between orthogonal polarized vortex beams is ΔΦ, the coherent superposition can be mathematically expressed in a general form as follows:

(9)$$\displaystyle{{e^{i(p\varphi + {\rm \Delta \Phi })}} \over 2}\left[ {\begin{matrix} 1 \hfill \cr {-i} \hfill \end{matrix}} \right] + \displaystyle{{e^{-ip\varphi }} \over 2}\left[ {\begin{matrix} 1 \hfill \cr {-i} \end{matrix}} \right] = e^{i\displaystyle{{{\rm \Delta \Phi }} \over 2}}\left[ {\begin{matrix}{\cos \left( {p\varphi + \displaystyle{1 \over 2}{\rm \Delta \Phi }} \right)} \cr {\sin \left( {p\varphi + \displaystyle{1 \over 2}{\rm \Delta \Phi }} \right)} \end{matrix} } \right]$$

here, the initial polarization direction is θ₀=ΔΦ/2, which means that the initial polarization angle of the generated vector beam is determined by the phase difference (ΔΦ) between the two orthogonal circularly polarized vortex beams. This enables accurate manipulation of the polarization angle of the vector beam during the process of superposition. If ΔΦ varies along the direction of transmission, then

(10)$$\theta _0(z) = {\rm \Delta \Phi }(z)/2$$

A special metasurface was designed to show the function, which is characterized by the generation of vector beams that continuously vary along the propagation path, the top view and functional diagram of this specific functional metalens are shown in Fig. 6.

Fig. 6. (a) Top view of the designed metasurface (Sample 2). (b) A functional diagram: generation of vector beams continuously varying along the propagation direction.

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Similar to the bifocal metasurface discussed in Section 2, the partial LCP transmission components remain focused at a distance of 3.8 mm in the propagation direction. However, a vector beam with continuously changing direction is generated along the propagation direction, after transmitting a distance of 6.6 mm in the propagation direction. To facilitate this evolution, it is necessary for the phase distributions of the two CP components to satisfy the following criteria:

(11)$$\begin{matrix}{\phi _{\rm I} = k\cdot \left( {\sqrt {r^2 + f_1^2 } -f_1} \right)} \cr {\varphi {(r,\theta )}_{{\rm LCP}} = k\cdot r^2/\left( {f_{\rm L} + \left( {{\rm \Delta }f_{\rm L}\cdot r^2/R^2} \right)} \right)/2 + p\theta } \cr {\varphi {(r,\theta )}_{{\rm RCP}} = k\cdot r^2/\left( {f_{\rm R} + \left( {{\rm \Delta }f_{\rm R}\cdot r^2/R^2} \right)} \right)/2-p\theta } \cr {E_L = \beta _1\exp \left( {i\phi _{\rm I}} \right) + \beta _2\exp \left( {i\varphi {(r,\theta )}_{{\rm LCP}}} \right)} \cr {\phi _{LL} = abs\left( {{\rm E}_L} \right) \times angle\left( {E_L} \right)} \cr {E_R = \exp \left( {i\varphi {(r,\theta )}_{{\rm RCP}}} \right)}\end{matrix}$$

In this case, the phase distribution of the first part is identical to that of the first example, the variable “k”(k = 2π/λ) represents the wave number in free-space, where the “λ” denotes the wavelength corresponding to the designed frequency of 0.95THz. The rotation angle of the meta-atom is denoted by θ. R is radius of the metasurface. For the LCP component focused at length f₁, it still maintains a value of 3.8 mm. While the RCP component and the remaining LCP component are focused at the focal length f_R and f_L and the focal depth is Δf_R and Δf_L, respectively. The focal lengths were set to f_L= 7.0 mm and f_R= 9.0 mm, the focal depths were set to Δf_L= 2 mm, Δf_R= 1.5 mm, respectively. The “p” in Eq. (11) is the phase topological charge, set p_R= -1, p_L= 1, β₁and β₂ represent the amplitude of the LCP component in the output wave at focal length f₁ and f₂, respectively ($\left( {\beta _1^2 :\beta _2^2 = 2:1} \right)$).

The metasurface was simulated in CST Studio Suite, driven by MATLAB. The propagation of the transmitted field was monitored through a field monitor.

The simulated intensity profiles of LCP components at the focal length f₁ are shown in Fig. 6 (a), the phase profiles for the RCP and LCP components are shown in the insets below, respectively. From Fig. 7(a), it is evident that the focal length f₁ does not contain any RCP components, but only the LCP components. Figure 7(b) shows the simulated intensity profiles of the x component at different distances along z coordinates. In order to conduct a more detailed analysis of the evolution of the vector beam as it propagates, we have chosen 6 distinct positions to illustrate the electric field of the transverse component (E_x), as depicted in Fig. 7(b). The white dotted line is used as a reference, and the red arrow represents the intensity direction. As the distance of the monitoring point increases, the intensity direction of E_x rotates counterclockwise, which means that the intensity of the three-dimensional vector beam also gradually changes with the propagation direction.

Fig. 7. Under the LCP illumination (a) Simulated LCP transmitted field profiles on the focal plane (f₁= 3.8 mm). (b) Simulated intensity profiles of the x component at different distances along z coordinates.

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4.2 Application of the versatile metalens

The longitudinal polarization variable terahertz metasurface represents a new type of functional material with many potential applications, such as stealth and jamming techniques for radar systems. By manipulating the constituent components of the metasurface, it is possible to alter the polarization state of electromagnetic waves at each point along their propagation path, thereby enhancing the security of communication. The proposed metalens, which exhibits longitudinal polarization variable in the terahertz range, can serve as a potential alternative for a novel modulator capable of manipulating the longitudinal polarization of electromagnetic waves in space, this development addresses the increasing demand for systematization and integration. In addition, the variation of polarization state along the vertical direction implies that the polarization state at each point along the transmission direction of the transmitted wave is related to the effective optical path to that point. Therefore, an additional media in the propagation path can change the effective optical path of the transmitted wave to the destination point, thus changing the polarization state at each point, which can be used as a new scheme to detect the thickness of the additional media.

Assuming that an unknown thickness of medium is placed on the transmission path, the effective optical path length for the transmitted wave to reach the same monitoring position can be determined as follows:

(12)$$L = n_{\rm 1}z-d{\rm + }n_{\rm 2}d{\rm }$$

Here, n₁ is the refractive index of air, n₂ is the effective refractive index of the medium, z is the geometric distance from the monitored point to the center of the all-dielectric metassurface, d is the thickness of the measured medium slice. Given that the vector beam undergoes continuous changes in the vertical direction and the polarization state of each point along the propagation direction of the transmitted wave is dependent on the effective optical path length to this point, by detecting the polarization state of a certain point, the effective optical path can be determined. Based on Eq. (12), the thickness of the medium slice can be easily derived.

Therefore, as shown in Fig. 8(a), a silica plate was positioned at z = 5 mm, after the first focal point, to investigate the correlation between the variation of the transverse component x polarization angle at the observation point z = 7 mm and the thickness of the silicon medium film. The simulation results are shown in Fig. 8(b). As the thickness of the silica medium slice increases, the intensity direction of E_x rotates significantly clockwise, which indicates that the overall vector beam intensity direction changes with the increase of the thickness of measured medium slice. The correlation between the polarization angle of the vector beam and the thickness of the medium slice is described in Fig. 8(c). It can be observed that the polarization angle increases with the increasing thickness of the measured medium. Therefore, the thickness of the medium slice can be determined by analyzing the rotation angle of the vector beam polarization, and placing an unknown thickness medium slice in a certain region before the formation of the vector beam. The dynamic range of the sensor based on this lens is 0-1.5 mm limited by the focal depth. The limited focal depth also results in the ambiguous measurement after 180° rotation. The vertical incidence of light in the operating frequency of 0.95THz was considered in this work.

Fig. 8. (a) A schematic diagram of simulation. (b) Transverse polarization angle simulation of E_x at monitoring point z = 7 mm with thickness variation. (c) The relationship between the polarization angle of the vector beam and the thickness of the medium.

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4. Conclusion

In summary, we have proposed a scheme for manipulating polarization along the propagation path. Two novel all-dielectric metasurfaces with the purpose of manipulating the longitudinal polarization state were designed. Firstly, the bifocal polarization manipulation along the propagation path is achieved through encoding complex amplitude modulation. Then by introducing the continuous change of phase difference between the two circular polarization states in the longitudinal direction, the vector beam that undergoes constant changes along the propagation path is generated. Finally, we present an application that showcases the measurement of thickness using the characteristics of longitudinal polarization variation. This novel approach offers a fresh perspective for the generation and control of vector light fields utilizing metasurfaces. The two designed metasurfaces exhibit significant potential for applications in terahertz communication, terahertz generating devices, polarization multiplexing source signals, and high-sensitivity optical biosensors. Simultaneously, the scheme completes the candidate scheme of vector light field manipulation in full space, and provides a novel choice for the advancement of multifunctional photonic devices.

Funding

National Natural Science Foundation of China (62205017); Shanghai Science and Technology Commission (22xtcx00103, XTCX-KJ-2022-32).

Acknowledgments

We sincerely thank the editors and anonymous reviewers for their contributions to this paper, and Professor Xiaofei Zang for help implementing the experiment.

Disclosures

The authors declare that there are no conflicts of interest related to this article.

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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Longitudinal polarization manipulation based on all-dielectric terahertz metasurfaces

Abstract

1. Introduction

2. Proof-of-principle and meta-atom design

2.1 Design of fully phase-modulated metasurface

2.2 Meta-atom design

3. Longitudinal bifocal metalens

4. Versatile metalens

4.1 Design and simulation of the versatile metalens

4.2 Application of the versatile metalens

4. Conclusion

Funding

Acknowledgments

Disclosures

Data availability

References

Data availability

Cited By

Figures (8)

Tables (1)

Equations (12)

Optics Express

Unit cells	1	2	3	4	5	6
L_x (µm)	52	36	70	66	62	58
L_y (µm)	64	66	118	86	74	68