1. Introduction

In recent years, there has been extensive research on metasurfaces composed of artificially designed metasurface units due to their unique capabilities in manipulating beams, including amplitude [1,2], phase [3,4], polarization [5,6], absorber [7], and orbital angular momentum (OAM) [8–11]. These powerful functions are closely related to the degrees of freedom in the metasurface design and the various wavefront modulation mechanisms employed. Metasurfaces can be broadly categorized into cross-polarized conversion (PC) (i.e., line-to-line PC) and line-to-circular PC metasurfaces. This categorization is based on their PC function and reflection/transmission characteristics, which stem from the propagation behavior of electromagnetic waves (EMWs). The transmission-based metasurfaces perform better than the reflection-based ones, especially when it comes to interference with incident waves and how that affects the device's radiation performance. As a result, research into transmission-type devices holds greater practical significance [12]. Conventional design methods for metasurfaces involve the construction of multi-layer resonant structures to establish Fabry-Perot (F-P) cavity resonance [13].

However, due to the inherent limitations in the beam control capabilities of two-dimensional metasurfaces composed of a single unit, the design of gradient metasurfaces with phase manipulation typically employs methods involving transmission phase [14] or Pancharatnam-Berry (PB) phase techniques (known as the PB phase method) [15,16]. This set of gradient metasurfaces facilitates the manipulation of beam phase, allowing for tailored control over EMWs by means of precisely arranged phase distributions. This capability has led to the development of various applications in the realm of light field regulation, encompassing phenomena such as Airy beams [17,18], OAM holography [19,20], achromatic metalenses [21,22], and more. In the domain of OAM research, emerging investigations into OAM with phase jump factors [23,24] and modulation OAM with modulation factors [25,26] have demonstrated significant applicability in diverse areas such as optical manipulation, optical encryption, optical communication, and optical imaging. Among these pioneering studies, Avayu O et al. innovatively employed nanoscale independent metasurfaces that were tightly stacked, leading to a reduction in individual diffraction element chromaticity. The stacking approach entailed multiple layers composed of distinct materials, each optimized for specific spectral bands. This meticulous optimization achieved an achromatic performance across the visible spectrum, effectively minimizing color variations in red, green, and blue light [27]. Conversely, Yan C. et al. leveraged an all-dielectric metasurface to generate polarization-sensitive modulated vortex beams (MOVs). By introducing tangential modulation factors to the phase distribution, they successfully extracted the intensity mode of MOVs [28]. These innovative results emphasize the importance of metasurface generation and application in OAM and provide a new way to advance various optical applications.

While these techniques hold significant promise, their widespread application is currently impeded by certain limitations. For instance, in the case of achromatic metalenses, although numerous studies have explored aspects such as achromatic focusing for vertically incident beams, encompassing features like high numerical aperture, multi-spectral achromatism, and broadband achromaticity, their practical integration presents considerable challenges due to the demanding real-world operating environments. While some hurdles can be surmounted, the inevitable future trajectory points toward multifunctional integrated devices. Considering these considerations, this paper introduces a metasurface featuring a complete spatial achromatic metalense, offering a novel research approach to address this challenge. Furthermore, we have designed a metasurface enabling modulation of MOAM in multiple dimensions, substantially augmenting the control capabilities over OAM and effectively tackling concerns related to communication capacity, encryption, and other pertinent issues. This innovative metasurface incorporates multiplexing across MOAM modes, frequencies, and angles, thereby presenting a fresh avenue for achieving more efficient OAM manipulation.

In summary, this paper demonstrates the application of the F-P interference model to the design of a metasurface capable of thermally-induced reconfiguration, offering ultra-broadband polarization conversion (PCR), and dynamic tuning. The design process involves three distinct sets of gradient matrices, which are crafted using the transmission phase method. The phase distribution for achieving both full-space achromatic metalenses and MOAM multidimensional multiplexing is theoretically derived. The outcomes of this research encompass the successful realization of full spatial achromatic metalenses, marked by focal length stabilization, and a 12-channel MOAM mode, incorporating frequency and angle reuse. Additionally, the exploration of full-space achromatic metalenses and MOAM multidimensional multiplexing was undertaken following a phase transition at a frequency of 5.6 THz. To sum up, the thermally reconfigurable metasurfaces described in this research show great promise for a variety of applications, including particle categorization, beam control studies, optical communication, and optical encryption.

2. Design and theory of metasurface structures

As shown in Fig. 1(a), the cross-line polarized thermal-reconfigurable metasurface designed in this paper can convert incident TM waves into transmitted TE waves, and the PCR is above 0.98, which can realize efficient polarization conversion. In addition, the incident TE linearly polarized wave will be fully reflected. The F-P interference model explains this phenomenon by stating that electromagnetic waves reflect and transmit many times in the multilayer structure of the metasurface, with the sum of all the reflections and transmissions being the result. This theory states that for a monolayer metal structure, the transmittance of an electromagnetic wave is generally no higher than 0.5. Therefore, multilayer structures are often designed to achieve efficient PCR. The metasurface designed in this paper has 6 layers composed of polyimide and gold. The relative permittivity of polyimide is 3.5, the electric tand is 0.0027 [29], and the conductivity of gold is $4.56 \times {10^7}\textrm{ }{S / m}$ [30]. A layer of vanadium dioxide (VO₂) film grating with a thickness of 0.1 um, a length of P, a width of ${w_2}$, and a width of $(P - \textrm{5}{w_1} - \textrm{4}{w_2})/2$ is added to the bottom layer of metal grating at the bottom of the metasurface. VO₂ is a type of thermal phase-change material (PCM) with superior performance that has been widely used in the construction of reconfigurable devices [31,32]. It can transform from a dielectric state to a metallic state at approximately 340 K, and its relative dielectric constant can be described by the generalized Drude model [33,34].

 

Fig. 1. (a) a schematic diagram of the reconfigurable metasurface structure and its local structure and function; and (b) the F-P interference model.

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The metasurface intermediate metal resonator is formed from inside to outside by a metal ring with a radius of ${r_1}$, a thickness of ${t_{4 - {r_1}}}\textrm{ = 0}\textrm{.5 }um$, and a width of ${d_1}$, and a metal ring with a radius of ${r_2}$, a thickness of ${t_{4 - {r_2}}} = \textrm{0}\textrm{.1 }um$, and a width of ${d_2}$. The opening sizes are 25° and 45°, respectively. The outermost part is a metal rectangle with a thickness of ${t_4}$, a width of ${d_3}$, and a length of $l + 2{d_3}$. The opening length is ${d_4}$, and all three components are composed of mixed metal resonators with an opening direction of ${\theta _{os}} = 45^\circ $. Table S1 in Supplement 1 shows all its parameters in depth.

The top metal grating structure is arranged along the x-direction, while the bottom metal grating is arranged along the y-direction, resulting in a strong reflection effect on TE waves (as shown by ${R_{yy}}$ in Fig. 2(a)). Meanwhile, TM waves are absorbed in large numbers (as shown by ${R_{xx}}$ in Fig. 2(a)) and converted into transmitted TE waves (as shown by ${T_{yx}}$ in Fig. 2(a)). In the band of 2.87∼7.65 THz, the ${T_{yx}}$ transmittance is maintained above 0.8, exhibiting the characteristics of high transmittance, ultra-broadband, and efficient PCR. Figure 2(a) shows the ${T_{yx}}$ transmittance, ${R_{xx}}$ and ${R_{yy}}$ reflectance, and ${T_{yx}}$ transmission phase when the underlying VO₂ film grating conductivity is ${\sigma _{V{O_2}}} = 2\textrm{e2 S/m}$ (i.e., in a dielectric state), and the transmission phase perfectly covers $2\pi $. When the VO₂ film grating conductivity is ${\sigma _{V{O_2}}} = 2\textrm{e}5\textrm{ S/m}$ (i.e., metallic state as depicted in Fig. 2(b)), the transmissibility of ${T_{yx}}$ reconstructed the reflection-type metasurface, and a large amount of ${T_{yx}}$ transmissibility was reflected, which greatly increased the reflectivity of ${R_{xx}}$ by about 0.6. This enables the designed metric to manipulate not only the transmitted wave but also the amplitude of the reflected wave. Moreover, the F-P interference model (Ref. [34]) was used for fitting, as shown in Figs. 2(c) and 2(d). The transmission spectrum and reflection spectrum of the medium state and the metal state were fitted, respectively. The fitting results demonstrate the correctness and feasibility of this work.

 

Fig. 2. In the dielectric state and metallic state, (a)-(b) reflectance (${R_{xx}}$ and ${R_{yy}}$), transmittance (${T_{yx}}$), and transmission phase (${T_{yx}}\textrm{ - Phase}$) were obtained by simulation, while (c)-(d) transmission coefficient and reflection coefficient were fitted according to the F-P interference model.

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The metasurface $PCR\textrm{ = }T_{yx}^2/(T_{yx}^2 + T_{xx}^2 + R_{yy}^2 + R_{xy}^2)$ needs to be studied, as it is an important index for characterizing the PCR of the designed metasurface. By changing the incident wave angles $\varphi $ and $\theta $ impact on PCR, it was observed that when $\theta $ was changed, PCR was not significantly affected at the frequencies of 2.8 THz, 7.8 THz, and 5∼6 THz (as shown in Fig. 3(a)), maintaining a super-high PCR. However, when $\varphi $ is changed, the PCR values remain symmetric, with high PCR values mainly observed at $\varphi \textrm{ = 0}^\circ \mathrm{\ \sim 20}^\circ $ and $\textrm{160}^\circ{\sim} \textrm{180}^\circ $. This is caused by the ${\theta _{os}} = 45^\circ $ symmetry of the metasurface mixed metal resonator along the opening direction as well as the metasurface's anisotropy. Figure 3(c) shows the change in PCR during the transition process of VO₂ film grating from the medium state to the metallic state. PCR mainly maintains high PCR at low conductivity because the metasurface transport capacity decreases in the metallic state. The increased reflexes resulted in a decrease in PCR. In summary, the designed reconfigurable metasurface exhibits broadband, efficient PCR capability. The asymmetric transmission characteristics of this high cross-polarization transformation can be described by the AT parameter, which is defined as $\Delta _{lin}^y = {|{{t_{xy}}} |^2} - {|{{t_{yx}}} |^2} ={-} \Delta _{lin}^x$. When the absolute value of AT is 1, the structure exhibits completely asymmetric transport properties. In turn, when it is zero, the structure exhibits fully symmetric transport properties. Figure 4 shows the AT parameters in the dielectric and metallic states. In the medium state, the absolute value of AT at the 5∼6 THz frequency is about 0.9 (as shown in Fig. 4(a)), exhibiting good asymmetric transmission characteristics. However, in the metal state, the absolute value of the AT parameter is about 0.01, which is very close to 0 (as shown in Fig. 4(b)). This indicates fully symmetric transport properties, which verifies the PCR results shown in Fig. 3.

 

Fig. 3. PCR changes with $\varphi $, $\theta $, and VO₂ conductivity $\sigma (\textrm{V}{\textrm{O}_2})$.

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Fig. 4. AT parameters in the dielectric and metallic states.

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Using the properties of the transmission phase, the geometric parameters of the metal resonator were changed to get the required phase mutation. As shown in Fig. 5(a), 10 metasurface units were designed at the frequency of 5 THz by changing the two parameters ${\theta _{os}}$ and ${d_4}$. The transmission phase ${T_{yx}}\textrm{ - Phase}$, of 10 units just covered $2\pi $, and the phase difference between each unit was $36^\circ{\pm} \Delta \varphi $. Here, $\Delta \varphi = 0.5^\circ $ is the slight disturbance caused by the design of the metasurface element parameters, which is negligible. The transmittance and transmission phase of the VO₂ film grating at the bottom of the 10 metasurface units were analyzed when the VO₂ film grating was in the medium state. Then, when the VO₂ film grating was in the metal state, as shown in Fig. 5(c), it was observed that the transmittance ${T_{yx}}$ was absorbed in a large amount, which indicates that it was converted into a TM wave (${R_{xx}}$) by a significant amount of reflection. This is also complementary to the results in Fig. 2(b). In addition, two sets of metasurfaces were designed at frequencies of 5.6 THz and 6 THz, whose specific parameters are detailed in Table S2. The unusual transmission effect is depicted in Fig. S1 in Supplement 1. A comparison of the metasurface performance of the proposed metasurface with other published metasurfaces is given in Table S3 in Supplement 1. This means that the wave amplitude of the TE transmission can be changed dynamically, and different structured optical fields can be created with the right phase distribution. These include vortex beams, zero-order Bessel non-diffracting beams, and OAM multidimensional multiplexing.

 

Fig. 5. (a) The designed metasurface unit of 10; (b) the metasurface transmission amplitude and corresponding phase at the frequency of 5 THz when operating in the medium state; (c) the metasurface transmission amplitude and corresponding phase at the frequency of 5 THz when operating in the metal state.

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3. Results and analysis

3.1 Full-space achromatic metalenses design concept and result analysis

Research on wide-band achromatic metalenses has matured, especially in the long-wavelength infrared, where the focal length or focus is independent of frequency compared to single-frequency metalenses in the designed frequency range. The proposal of achromatic metalenses is important for promoting applications such as miniaturized vision systems and broadband microscopes. However, the achromatic metalenses proposed so far mainly focus on vertical electromagnetic waves, and there are few achromatic metalenses designed for oblique incidence, especially in the THz band. This is also a limiting factor for its wide range of applications. Despite advances, errors and instabilities remain, making it necessary to design fully spatially achromatic metalenses in the THz band. For conventional single-frequency focusing metalenses, the phase distribution that needs to be satisfied is as follows:

Next, ${\varphi _{dm}}(x) ={\pm} ({{{2\pi } / D}} )\cdot x$ or ${\varphi _{dm}}(y) ={\pm} ({{{2\pi } / D}} )\cdot y$ is derived based on generalized Snell's law, so that within the working wavelength range of $[{{\lambda_{\min }},{\lambda_{\max }}} ]$, when the incident is along the ${\pm} x$ or ${\pm} y$ direction and the incident angle ${\theta _i}({f_\textrm{n}})$ satisfies Formula (5), where $D = M \cdot P$ and M represents the number of metasurface elements required for a $2\pi $ phase gradient. Here, $M = 5$, and P is designed as the period of the metasurface elements. When the designed achromatic metalenses satisfy the phase ${\phi _3}(x,y,\lambda ) = {\phi _2}(x,y,\lambda ) + {\varphi _{dm}}(x)(\textrm{or }{\varphi _{dm}}(y))$, it realizes the full-space achromatic focusing function.

The thermally reconfigurable metasurfaces designed in this paper can operate in the frequency range of 2.6 to 8 THz. However, the focal length $f = 490\textrm{ }um$ of the designed full-space achromatic metalenses is set at and the operating frequency is 4.9∼6.1 THz. This is because the metasurface can work with high cross-transmittance ${T_{yx}}$ and PCR in this frequency range, as shown in Figs. 2(a), (c), and Fig. 3(a), (b), thus achieving optimal focusing effects. Figure 6 shows that when the TM wave with frequency ${f_2} = 5.6\textrm{ }THz$ and incident angle ${\theta _i}({f_2}) = 53.03^\circ $ is incident along the ${\pm} x$ and ${\pm} y\textrm{ }$ directions, respectively, the focal length of ${f_z} = 495.01\textrm{ }um$ is obtained in the -z plane, and the full-width at half-maximum (FWHM) focal length effect in the x, y, -x, and -y directions is 92.40 um, 91.29 um, 90.94 um, and 90.94 um, respectively. Furthermore, when the frequency of the incident wave is ${f_1} = 5\textrm{ }THz$ and ${f_3} = 6\textrm{ }THz$, respectively, the focal length effect of the incident angle is ${\theta _i}({f_1}) = 63.5^\circ $ and ${\theta _i}({f_3}) = 48.22^\circ $, respectively, obtained by formula (5), as shown in Fig. 7(a). When the frequency and incident direction are consistent, the fluctuation of the focal length is very small. Therefore, the focal length change rate (FLFC) is introduced to describe the degree of focal length fluctuation with the formula $FLFC = ({f_{\max }} - {f_{\min }})/mean(f) \times 100\%$, where ${f_{\max }}$, ${f_{\min }}$, and $mean(f)$ are the maximum, minimum, and average values of the resulting focal length, respectively. Figure 7(b) shows the changes in focal length and FWHM, with the maximum deviation from the preset focal length $f = 490\textrm{ }um$ being only 5.13 um, indicating the feasibility of the work. In addition, the fluctuation of the FWHM can be reduced by improving the scale and process of the metasurface. In summary, the designed full-space achromatic metalenses address the problem of invariant incidence angle in the THz band. Moreover, this method is not limited to the THz band, opening up the possibility of its wide application in scientific research fields such as imaging systems, material detection, and light processing.

 

Fig. 6. This is a schematic of the full-space chromatic aberration metalense. When the TM wave is in the wavelength range of $[{{\lambda_{\min }},{\lambda_{\max }}} ]$, for example, with frequencies ${f_1}$, ${f_2}$, …, ${f_n}$, and the incident angles are ${\theta _i}({f_1})$, ${\theta _i}({f_2})$, …, ${\theta _i}({f_n})$, a focal point with focal length ${f_z}$ will be produced in the -z direction when the incident wave is incident along the -x, -y, x, and y directions, respectively.

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Fig. 7. If the frequencies of the TM waves are ${f_1} = 5\textrm{ THz}$, ${f_2} = 5.6\textrm{ THz}$, and ${f_3} = 6\textrm{ THz}$, respectively, and the incident angles are ${\theta _i}({f_1}) = 63.5^\circ $, ${\theta _i}({f_2}) = 53.03^\circ $, and ${\theta _i}({f_3}) = 48.22^\circ $, respectively, for the incident directions of x, y, -x, and -y, the electric field density, focal length ${f_z}$ position, and FHWM on the xoy plane and zox plane are to be determined.

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3.2 MOAM multidimensional multiplexing design concept and result analysis

Another aspect of this work is the implementation of MOAM multidimensional multiplexing. In 1992, Allen proposed that an OAM beam is a structured light field with a spiral phase factor of $\textrm{exp(}jl\varphi \textrm{)}$ and a spiral wavefront [35], where l is the mode term, $\varphi $ is the mode phase distribution, and j is the imaginary unit. The OAM beam is a structured light field with a unique toroidal light field and the presence of a phase singularity, which makes it widely used in optical tweezers, optical communication, holographic imaging, holographic encryption, and other fields. However, traditional OAM only allows for independent control of the l term, such as asymmetric OAM [36,37], conical spiral beam [38,39], Airy vortex beam [40,41], Pearcey vortex beam [42,43], fractional OAM [44,45], etc. These specially designed OAMs can produce unique optical field manipulation phenomena, and many related studies have been reported. However, control freedom is still limited, which is the main factor limiting the security of encryption, information capacity, and beam control freedom. Therefore, finding more controllable degrees of freedom for OAM is an area of significant research interest. Metasurface studies have combined physical quantities in electromagnetic waves with aspects of information science, which can be applied to signal modulation and demodulation in the field of communications. For example, the modulation quantity $\cos (n\varphi + {\varphi _i})$ is introduced, and MOAM satisfies the phase distribution (6):

Then, using Eq. (5) to determine that the frequency of the incident wave ${E_i} = exp (jk\sin {\theta _i}x)$ is ${f_1}$ and the incidence angle is ${\theta _i}({f_1})$, when the incident is along the -x direction, beams of MOAM mode $({l_1},{n_1},{\varphi _{i1}})$ with frequency ${f_1}$ and coaxial with the -z axis will be generated. For the distribution of other MOAM modes, the scattered field is further derived, as shown in Eq. (9).

Equation (10) reveals that the distribution coordinates of MOAM$({l_1},{n_1},{\varphi _{i1}})$ are $(0,0)$, while the distribution coordinates of the other modes are $(\frac{{2\pi }}{D}, - \frac{{2\pi }}{D})$, $(\frac{{4\pi }}{D},0)$, and $(\frac{{2\pi }}{D},\frac{{2\pi }}{D})$, respectively. These modes form sidelobes and grating lobes.

Based on the above theoretical derivation, the MOAM multidimensional multiplexing metasurface (Fig. 8 depicts the multidimensional multiplexing principle of MOAM.) is designed to operate at a frequency of 5 to 6 THz, which is consistent with the operating frequency design of the full-space achromatic metalenses at 4.9 to 6.1 THz. ${l_2}$ when TM waves with frequencies ${f_1} = 5\textrm{ THz}$, ${f_2} = 5.6\textrm{ THz}$, and ${f_\textrm{3}}\textrm{ = 6 THz}$ and incident angles ${\theta _i}({f_1}) = 48.22^\circ $, ${\theta _i}({f_2}) = 41.75^\circ $, and ${\theta _i}({f_3}) = 38.42^\circ $, respectively, are incident along the -x, -y, x, and y directions, they generate MOAM$({l_1},{n_1},{\varphi _{i1}})$, MOAM$({l_2},{n_1},{\varphi _{i1}})$, MOAM$({l_3},{n_2},{\varphi _{i2}})$, and MOAM$({l_4},{n_2},{\varphi _{i2}})$ patterns that are coaxial and orthogonal to the -z-axis, respectively. Here, ${l_1}$, ${l_2}$, ${l_3}$, and ${l_4}$ are 1, −2, 3, and −4, while ${n_1}$ and ${n_2}$ are 1 and 2, ${\varphi _{i1}}$ and ${\varphi _{i2}}$ are $\pi /6$ and $\pi /3$, respectively. These patterns can generate $(1,1,\pi /6)$, $( - 2,1,\pi /6)$, $(3,2,\pi /3)$, and $( - 4,2,\pi /3)$ MOAM patterns with coaxial orthogonal frequencies ${f_1} = 5\textrm{ THz}$, ${f_2} = 5.6\textrm{ THz}$, and ${f_\textrm{3}}\textrm{ = 6 THz}$ in the -z direction. As shown in Fig. 9, the far-field amplitude and phase of all MOAM multiplexing modes are simulated. When the incidence angle and frequency are consistent, the observation produces $(3,2,\pi /3)$ and $( - 4,2,\pi /3)$ MOAM modes. The far-field amplitude produces two splits, marked by ① and ②, respectively, and the deflection angle is $\pi /6$. The corresponding phases change by $\textrm{6}\pi $ clockwise and $\textrm{ - 16}\pi $ counterclockwise, respectively, indicating that the resulting OAM is modulated and consistent with the expected results. The far-field amplitude of $(1,1,\pi /6)$ and $( - 2,1,\pi /6)$ modes produces a split marked by ①, and the deflection angle is $\pi /6$. The other two data sets show that the designed MOAM multidimensional multiplexing is feasible, enabling 12-channel multiplexing. It is worth noting that since the different OAM modes are coaxially orthogonal, an infinite number of channels can be realized in theory. However, the upper limit of multiplexing is limited by the scale of the metasurface, the fabrication process, and the finite angle and frequency. These technical limitations are expected to be overcome in the future. Nevertheless, the MOAM multidimensional multiplexing technique designed in this paper has potential applications in optical communication, optical encryption, beam manipulation, and other fields.

 

Fig. 8. The multidimensional multiplexing principle of the designed MOAM is demonstrated when TM waves with frequencies ${f_1}$, ${f_2}$,…, ${f_n}$, incident from angles ${\theta _i}({f_1})$, ${\theta _i}({f_2})$,…, ${\theta _i}({f_n})$ and along the -x, -y, x, and y directions, respectively. This generates a coaxial orthogonal pattern MOAM$({l_m},{n_m},{\varphi _{im}})$ in the -z direction.

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Fig. 9. MOAM multi-dimensional multiplexing has resulted in 12 sets of multiplexed data.

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3.3 Dynamic amplitude modulation

The F-P interference model has previously described and fitted the transmittance and phase of VO₂ thin film gratings in thermally reconfigurable metasurfaces (Fig. 2(b), 2(d)). When combined with the ${T_{yx}}$ and phase of a set of gradient metasurfaces designed at the frequency of 5 THz (Fig. 5(c)), a problem has been illustrated. That is, the transformation of the VO₂ thin film grating into a metallic state basically only affects the amplitude of the TE transmitted wave but has little effect on its phase, which is also illustrated when observing its abnormal reflection (as shown in Fig. S1(d)-S1(f)). Fig. S2 shows the change in ${T_{yx}}$ transmittance as the VO₂ film grating changes from the dielectric state to the metallic state. The transmittance of ${T_{yx}}$ is reduced by more than 80% when it changes to the metallic state, for reasons described above. This leads to the important conclusion that the designed metasurface structure can dynamically regulate the amplitude of the TE transmitted wave without affecting its function. Figure 10 shows the realization of the full spatial achromatic metalenses and the MOAM multiplexing function when the VO₂ thin-film grating is converted to the metallic state at an operating frequency of 5.6 THz. For the full spatial achromatic metalenses, the focus is still around the preset 490 um. The mode, the number of main lobes splittings, and the deflection angle of the MOAM multidimensional multiplexing are all the same as those of the medium state. Note, however, that their amplitudes are reduced by more than 80%. In short, dynamic control of the transmitted wave amplitude can be achieved while ensuring the integrity of the function. This makes it possible to dynamically control the focal spot intensity of a full spatial achromatic metalense and the mode intensity of a MOAM multidimensional multiplexer, which is of great importance in wireless communications and optical processing.

 

Fig. 10. When a VO₂ thin-film grating is in a metallic state, full spatial achromatic metalenses and MOAM multidimensional multiplexing can be used to display the focusing and MOAM multiplexing at an operating frequency of 5.6 THz.

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4. Potential fabrication process

Figure 11 shows the manufacturing process of the proposed thermally reconfigurable F-P cavity. The structure proposed in this paper is completely feasible and realizable against the background of existing manufacturing technology. The device is mostly used by electron beam lithography (EBL), focused ion beam (FIB), ion beam lithography (IBM), electron beam evaporation (EBE) coating technology, and nano-imprint and lift-off technology. The relevant technologies are quite mature and play an increasingly important role in the metasurface manufacturing of different structures [46–48]. Please refer to Supplement 1 for a detailed manufacturing process description. Additionally, nanoimprint lithography followed by mass production using EBL or FIB lithography can significantly lower manufacturing costs. Furthermore, it is worth mentioning that current metasurface manufacturing still faces issues such as manufacturing scale, efficiency, material costs, stability, and integration, which means that metasurface technology can only be prepared, measured, and characterized on a small scale in the laboratory and cannot be widely applied in practical environments. Therefore, this is a problem that urgently needs to be addressed in the future, but it cannot be denied that it is guiding and important for cutting-edge research. THz time-domain spectroscopy, near-field scanning THz microscopy systems, or THz imaging systems can be used to characterize and measure manufactured metasurface samples.

 

Fig. 11. Potential manufacturing processes and processes for the designed multilayer thermally reconfigurable F-P cavity metasurface.

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5. Conclusion

In brief, a fully spatial achromatic metalense is designed to achieve achromatic focusing of the incident TM wave at any angle. The theoretical deduction of the distributional positions of the MOAM modes complements the simulation results. To sum up, the fully space achromatic metalenses and MOAM multidimensional multiplexing are a scientific answer to the problems of achromatic metalenses having vertically invariant incidence angles, OAM manipulation having only one degree of freedom, and modes that can't be combined. Moreover, dynamic control of the amplitude has been achieved, which is expected to play an essential role in research fields such as beam manipulation, optical encryption, optical communication, and particle classification. In the future, research will gradually shift from studying basic ideas to doing experiments and finding uses for them. This includes making samples, measuring, and characterizing them, and working together to find uses for them like miniature vision systems, broadband microscopy, optical communication, particle manipulation, and more. This will lead to more new research directions and uses in the fields of optics, medicine, and other things. It has a wide range of application fields and potential.