Individually tunable array reflector for amplitude and phase modulation

Gongli Xiao; Jiapeng Su; Hongyan Yang; Jiayu Chen; Haiou Li; Xingpeng Liu; Zanhui Chen; Tangyou Sun; Peihua Wangyang; Jianqing Li

doi:10.1364/OE.472671

1. Introduction

For conventional optoelectronic devices, the production process is relatively complex, and they can achieve relatively fixed functions; therefore, they do not change with the external requirements; to acquire new functions or adapt to new working requirements, it is necessary to replace them, which significantly increases the research workload and expense [1,2]. The in-depth study of materials has revealed that some materials are affected by external effects, and their properties change, providing a solid foundation for devices that can be tuned [3–6]. Researchers have admired adjustable or reconfigurable optoelectronic devices in recent years due to their excellent tuning properties [7–10]. Q. Wang et al. presented a graphene absorber with two-sided coupling cavities by adding dielectric rings on both sides of graphene to generate two almost complete absorption peaks, with the control of the absorber being accomplished by the chemical formula of graphene [11]. Y. Chen et al. proposed a metasurface structure based on the composition of graphene and metal to achieve a tunable converter of bound states in the continuum [12]. This structure achieves a tunable transition between bound and quasi-bound states in the continuum by modifying the properties of graphene and metal. These modulation-capable gadgets provide valuable insight for the next phase of modulation investigation. However, their tuning is typically global and does not necessitate more precise local adjustment. It can be modified locally or independently to achieve a more accurate adjustment based on the situation [13].

Lenses are typical light-wave modulation devices in optical systems, and they play a crucial role in optical microscopy [14], high-definition imaging [15], and optical lithography [16]. However, conventional curved lenses with bulky material layers and complex geometry cannot meet the trend of shrinking and integrating optical systems. In recent years, the rapid development of metamaterials and metasurfaces has allowed a new generation of zoom systems to arise [17,18]. H. Guo et al. proposed that an ultraviolet-reflective metal body can focus the light band regardless of polarization. Adjusting the structural parameters enables good focussing in the ultraviolet to the visible spectrum. The reflective metal network is made of aluminum [19]. Y. Gao et al. examine the achromatic meta-lens at terahertz frequencies, which has a symmetrical structure and efficiently minimizes the susceptibility to polarization with an excellent achromatic effect; also, the focal point travels incoherently from the distribution of amplitudes [20]. These unique lens designs have significantly improved the ability of lenses to focus and contributed considerably to the study of high-performance lenses, although they are not perfect. The inability to dynamically alter lenses, whether conventional or metasurface, will limit their functionality [21].

In recent years, with the improvement of manufacturing processes and the intersection of different fields, multifunctional devices (lasers [22], anomalously reflector [23], photo-detector [24], imaging [25], etc.) composed of tunable or high-performance materials (graphene [26], Dirac semimetal [27], β-InSe [28], etc.) and metasurface structures are being investigated by researchers. J. Li et al. proposed a structure based on an all-silicon metasurface to achieve multi-channel polarization conversion. The design is based on the birefringence effect in spatially staggered anisotropic meta-atoms of linear shapes, with measured deflection conversion efficiencies higher than 70% [29]. T. Wang et al. propose a hybrid metamaterial absorber based on graphene and VO₂, which can achieve dual-controllable switchable bandwidth absorption in the terahertz band. The design enables switching between absorption and reflection by tuning the properties of the material, and the absorption can be adjusted from 0% to 65% [30]. L. Gao et al. observed the good physicochemical properties of niobium carbide (Nb₂C) and designed photodetectors and femtosecond mode-locked fiber lasers. They have successfully demonstrated the excellent modulation and ultra-stable pulse properties of Nb₂C through theoretical calculations, further expanding the application prospects of two-dimensional materials in the field of optoelectronics [22]. J. Huang et al. proposed a switchable coding metasurface, which is used to achieve dynamic beam steering in the terahertz band by modulating the Dirac semimetal. The control of the Dirac semimetal is achieved by changing the Fermi level to achieve beam modulation [31]. In conclusion, the proposed devices provide a good idea for the development of optoelectronic modulation as well as high performance devices.

In this paper, an individually tunable array structure is designed as a reflector, and the Fermi level (${E_F}$) of graphene and conductivity of vanadium dioxide (VO₂) is controlled by adjusting the external voltage and temperature, respectively, so that the reflected light can be focused by adjusting the phase and amplitude of the reflected light. The amount of control required for each graphene and VO₂ in the array structure is theoretically calculated. The position, intensity, and dispersion of the focal point are simulated and investigated, and the phase compensation method is used to concentrate the oblique incident light. The array structure enables variable focusing, providing a novel concept for variable devices and lens focusing. Based on our proposed individually tunable array reflector, it may be applicable to higher-order modulation of light, special beam generators (airy beam, swirl beam, etc.), imaging devices in the future.

2. Theoretical analysis

2.1 Structural design and mechanism analysis

Figure 1(a) depicts the structure of the adjustable array, which consists of multiple single forms grouped and merged. Each array of graphene is connected via wires, and each wire includes a tunable resistor ${R_x}$ that may be used to regulate the amount of voltage associated with each piece of graphene; all wires share a common voltage source. Each VO₂ array is also connected to an instrument ${T_x}$ that can control the temperature. By varying the temperature, the conductivity of VO₂ may be altered, enabling the regulation of VO₂. Figure 1(b) depicts the monolithic structure of the array. The width of the monolithic structure is ${W_2} = 8\textrm{ um}$, which contains a layer of SiO₂ with a thickness of ${H_1} = 8\textrm{ um}$, a layer of graphene with a width of ${W_1} = 3\textrm{ um}$, a layer of VO₂ with a thickness of ${H_2} = 2\textrm{ um}$ and a width of ${W_3} = 1.6\textrm{ um}$ in the center, and a layer of gold with a width of ${W_4} = 3.2\textrm{ um}$ on both sides of the SiO₂ layer. The size of each material in a single array has an effect on the reflected light characteristics, while the number and arrangement of arrays have an effect on the focusing characteristics. The fabrication procedure is straightforward, whether a single structure or an array. The mechanism of focussing the reflected light of the adjustable array is illustrated in Fig. 1(c). Traditional focusing lenses establish focus when incident light passes through varying surface angles through concave lenses. On the other hand, our array structure modifies the phase and amplitude of the reflected light by changing the characteristics of graphene and VO₂, so attaining the same degree of light concentration and the adjustable array offers a broader range of applications. Figure 1(d) illustrates the principle of light modulation. Graphene possesses capacitance and inductance capabilities to control the signal's phase, whereas VO₂ has resistance properties to modulate the signal's amplitude.

Fig. 1. (a) Structure of graphene-VO₂ tunable arrays. (b) One cell structure in the array. (c) Focusing principle of adjustable array structure and conventional lenses. (d) Analysis of modulation principles of a tunable array with traditional circuit modulation.

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2.2 Material properties and selection

The material's tuning properties are the most critical aspect of the overall tunable device. We utilize SiO₂ as the substrate because it is generally stable and easy to fix graphene, VO₂, and gold layers; SiO₂ has a refractive index of 1.45. The gold layer can reflect incident light effectively, and gold's conductivity in the terahertz range is 4.09 × 10⁷ S/m [32]. Graphene is one of the most promising materials for building tunable terahertz, and sheet graphene can be tuned to its Fermi level by dynamically changing the chemical doping or applying a bias voltage [30]. It has been demonstrated that graphene has a capacitive effect. Therefore, it is possible to use it to adjust the phase [33,34]. In the terahertz band, the graphene conductivity ${\sigma _G}$ is simulated by the intra-band conductivity ${\sigma _{\textrm{intra}}}$ and the inter-band conductivity ${\sigma _{\textrm{inter}}}$:[35]

(1)$${\sigma _G} = {\sigma _{{\mathop{\rm int}} ra}} + {\sigma _{{\mathop{\rm int}} er}},$$

(2)$${\sigma _{{\mathop{\rm int}} ra}} ={-} j\frac{{{e^2}{k_B}T}}{{\pi {h^2}(\omega - j2\Gamma )}}(\frac{{{\mu _c}}}{{{k_B}T}} + 2\ln ({e^{ - \frac{{{\mu _c}}}{{{k_B}T}}}} + 1)),$$

(3)$${\sigma _{{\mathop{\rm int}} er}} = \frac{{j{e^2}}}{{4\pi \hbar }}\ln (\frac{{2|{{\mu_c}} |- (\omega - j2\Gamma )\hbar }}{{2|{{\mu_c}} |+ (\omega - j2\Gamma )\hbar }}),$$

where e is the electronic charge, ${k_B} = 1.381 \times {10^{ - 23}}\textrm{ J/K}$ is the Boltzmann constant, $\hbar = 1.055 \times {10^{ - 23}}\textrm{ S}\cdot \textrm{m}$ is reduced Planck constant, $\tau$ is the relaxation time, $\Gamma = \mathrm{\hbar /2}\tau$ is the phenomenology scattering rate, T is the ambient temperature, ${\mu _c}$ is chemical potential, which is the same as the ${E_F}$, they are related to the applied bias voltage, $\omega$ is the angular frequency. Graphene is at standard temperature and terahertz frequency. The Drude model can be considered according to the Pauli exclusion principle [36,37].

(4)$${\sigma _G} \approx \frac{{{e^2}{\mu _c}}}{{\pi \mathrm{\hbar }}}\frac{j}{{\omega + j/\pi }},$$

Although the relaxation time $\tau$ is frequency and ${E_F}$ dependent, this dependence is not strong, and to get a more intuitive understanding of the nature ${E_F}$ of graphene, we set $\tau = 1\textrm{ ps}$.

Figure 2(a) depicts the band gap structure of graphene; monolayer graphene has a system with zero band gap; hence the ${E_F}$ value is 0. When the voltage is applied, ${E_F}$ at the Dirac point rises, and graphene's characteristics are changed [38]. Figure 2(c) and 2(d) depict the real and imaginary components of graphene's conductivity in the terahertz band.

Fig. 2. (a) Graphene energy band and Fermi level analysis. (b) Study of properties in different states of VO₂ crystal. (c) Real and (d) imaginary parts of ${\sigma _G}$ at different frequencies and Fermi level. (e) Real and (f) imaginary parts of ${\varepsilon _{V{O_2}}}$ at different frequencies and conductivity. (g) Real and (h) imaginary parts of ${\sigma _{V{O_2}}}$ at different temperatures in the terahertz band range.

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VO₂, a metal oxide, undergoes an insulator-to-metal transition via electrical, thermal, and optical pathways. via electrical, thermal and optical pathways has been used in metamaterial in functional devices [30]. As shown in Fig. 2(b), VO₂ changes from the insulating state to the metallic state as the temperature changes. This is because, as the temperature rises, changes occur in the VO₂ crystal, the chemical bonds that bound electrons in the low-temperature state are broken, and the number of carriers in the crystal increases, thereby transforming to a metallic state [39,40]. Similar to graphene, VO₂ can be modeled at terahertz frequencies by the Drude model [41].

(5)$${\varepsilon _{V{O_2}}} = {\varepsilon _\infty } - \frac{{\omega _P^2({\sigma _{V{O_2}}})}}{{{\omega ^2} + i\gamma \omega }},$$

(6)$$\omega _p^2({\sigma _{V{O_2}}}) = \frac{{{\sigma _{V{O_2}}}}}{{{\sigma _0}\omega _P^2({\sigma _0})}},$$

where ${\varepsilon _{V{O_2}}}$ is the relative permittivity of VO₂, ${\varepsilon _\infty } = 12$ is the permittivity at infinite frequency, $\gamma = 5.75 \times {10^{13}}\textrm{ rad/s}$ is the collision frequency, ${\sigma _{V{O_2}}}$ is the conductivity of VO₂, ${\sigma _0} = 3 \times {10^5}\textrm{ S/m}$ and $\omega _{_P}^2({\sigma _0}) = 1.4 \times {10^{15}}\textrm{ rad/s}$ [27]. Figure 2(e) and 2(f) depict the real and imaginary components of relative permittivity of VO₂ in the terahertz band. The reflector we have designed controls the conductivity of VO₂ by temperature, so it is indispensable to relate the temperature to the conductivity of VO₂, as shown in Fig. 2(g) and 2(h), which demonstrate the performance of the real and imaginary parts of ${\sigma _{V{O_2}}}$ at different temperatures in the terahertz band range [42].

3. Results and discussion

The preparation and manipulation of our proposed reflector are achievable. The preparation of Au and SiO₂ are already easy to achieve. The preparation of VO₂ arrays requires first etching the corresponding grating in the Au layer, then filling the bottom of the device with VO₂, and finally polishing off the excess VO₂ [43,44]. Graphene arrays can be grown first as a complete piece and then cut into the desired array structure according to the requirements of the device and finally transferred to SiO₂ [45]. The operation can be simplified. It is bound to be difficult for staff to regulate so many arrays, but it becomes very convenient if a chip is used to do so [46]. By connecting the voltage and temperature regulation devices to the associated chip, the chip can quickly and accurately regulate each array based on the parameters designed by the staff. To more correctly simulate the focus of the reflected light on the tunable array, we analyze the model using the finite element method and simulate the model using COMSOL Multiphysics. The specified frequency range for the simulation is 1 to 10 THz, the control ${E_F}$ of graphene is 0.1 to 1 eV, and the controlled conductivity of VO₂ is 500 to 50000 S/m. The above range is provided to help check the array's structure, not because the array can only be tuned within this range.

3.1 Analysis of graphene and VO₂ modulation properties

As demonstrated in Fig. 3, a single structure in the array is more likely to show the effect of graphene and VO₂ on the modulation. Initially, the modulation properties of graphene are simulated for VO₂ with a conductivity of 500 S/m. The variable ${E_F}$ of graphene and the observed variations in the reflected light phase and amplitude are depicted in Fig. 3(a) and 3(b). To ensure that the phase change can meet 2π and to keep the amplitude change of graphene to a minimum, the simulation frequency is set to 4.9 THz. Figure 3(c) depicts this frequency's modulated phase and amplitude values. According to the numerical study, the control of ${E_F}$ on graphene can be achieved by modulating the phase of the reflected light between 0 and 2π. At the same time, the amplitude fluctuates by no more than 15%. Next, the modulation properties of VO₂ are simulated, with the ${E_F}$ of graphene set at 0.1 eV. From Fig. 3(d), it can be seen that the phase does not change with the change of conductivity of VO₂ when the frequency is constant. In contrast, the amplitude varies more in Fig. 3(e), and Fig. 3(f) can better prove this point. From the simulation data, the phase basically does not change. In contrast, the amplitude varies a more extensive range of approximately 29%, and finally, when the frequency is 4.9 THz, let the ${E_F}$ of graphene and conductivity of VO₂ modulate together. Figure 3(g) and 3(h) show the phase and amplitude change graphs. When the ${E_F}$ of graphene is unchanged, the difference in conductivity of VO₂ does not result in a phase shift, but the amplitude shifts. Based on the simulation above, we can assume that the ${E_F}$ of graphene regulates just the phase of the reflected light, and the conductivity of VO₂ modifies only the amplitude of the reflected light.

Fig. 3. (a) Phase shift, (b) amplitude shift, and (c) their numerical analysis at 4.9 THz when ${E_F}$ of graphene ranges from 0.1 to 1 eV and conductivity of VO₂ is 500 S/m. (d) Phase shift,(e) amplitude shift, and (f) their numerical analysis at 4.9 THz when the conductivity of VO₂ ranges from 500 to 50000 S/m and ${E_F}$ of graphene being 0.1 eV. (g) Phase shift and (h) amplitude shift when ${E_F}$ of graphene and conductivity of VO₂ shift simultaneously.

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3.2 Graphene regulated focus position

After verifying the single structure's adjustable properties, the monolithic graphene-VO₂ array is simulated. The entire array is composed of 123 individual columns. The placement of the focal point is crucial to the study of the focussing of reflected light. To ensure that the reflected light at different places of the array may be gathered into a point, which requires the phase at different positions to meet focusing requirements, Eq. (7) expresses the relationship between phase and array at different places.

(7)$$\varphi (x) ={-} 2\pi /\lambda (\sqrt {{{(x - {x_c})}^2} + {f^2}} - f),$$

where $\varphi (x)$ is the desired phase of the array somewhere, x is the position of the array somewhere, ${x_c}$ is the horizontal coordinate at the focal point, f is the focal length, which is also the vertical coordinate of the focal point, $\lambda$ is the wavelength of the incident light.

Figure 2(c) depicts the relationship between the phase and the graphene ${E_F}$ at a frequency of 4.9 THz. Using the phase as the intermediate variable, the relationship between the position on the array structure and the graphene ${E_F}$ is created, allowing the value of the phase at each place on the array to be regulated by manipulating the graphene ${E_F}$ to achieve focused reflected light. The relationship among the three is depicted in Fig. 4(a), where the focal point coordinates are X = 0 um and Y = 500 um, Fig. 4(b) simulates the focusing of the reflected light, and Fig. 4(c) examines the cross-section and longitudinal section at the focal point tangent. We can see from these numbers that the reflected light is gathered to the point we specified, and the impact of focusing is also improved. The benefit of the adjustable array structure is that it can be tuned easily. Changing the value of graphene ${E_F}$ enables us to alter the position of the focal point. Figure 4(d)–4(f) illustrate the simulation and data of the focus when the focus is adjusted to X = 0 um, Y = 300 um, and Fig. 4(g)–4(i) illustrate the simulation and data of the focus when the focus is shifted to X = 300 um, Y = 500 um. Based on these graphs, it is evident that the focus point may be precisely positioned and that the focus effect is satisfactory. Consequently, the adjustable array can effectively regulate the position of the light's focal point.

Fig. 4. When the focus in X = 0um, Y = 500um, (a) the relationship between the graphene array position and the ${E_F}$ of graphene, (b) simulated light focus and (c) focus intensity analysis. When the focus in X = 0um, Y = 300um, (d) the relationship between the graphene array position and the ${E_F}$ of graphene, (e) simulated light focus and (f) focus intensity analysis. When the focus in X = 300um, Y = 500um, (g) the relationship between the graphene array position and the ${E_F}$ of graphene, (h) simulated light focus, and (i) focus intensity analysis.

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3.3 VO₂ uniformly regulates the focus intensity

In this model, the amplitude modulation is separated into two types: uniform modulation and non-uniform modulation. Amplitude modulation is a crucial component of reflected light focusing. So that the intensity of the reflected light can be manipulated uniformly, uniform modulation requires that only the conductivity in the VO₂ of the modulable array is identical. As seen in Fig. 5, the intensity varies when VO₂ is varied uniformly. When the conductivity of VO₂ changes from 500 to 50000 S/m, the intensity at the focal point changes in magnitude while the focal point's position remains unchanged. The modulation range of intensity is approximately 12.2% of the median value, indicating that VO₂ can achieve good modulation of the reflected light amplitude.

Fig. 5. (a) Simulated strength analysis in Y = 500 um. (b) Simulated strength analysis in X = 0 um. (c) Range of peak variation.

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3.4 VO₂ non-uniform modulated focal scattering

Uniform modulation of amplitude can only modulate the intensity of the focus. However, non-uniform modulation is theoretically estimated to determine the conductivity of VO₂ at different points of the array, resulting in improved focusing. The theoretical calculation is comparable to the graphene modulated phase. The amplitude intensity is employed as an intermediary variable to establish the link between the conductivity of VO₂ and the position of the array. First, we take a portion of the monotonically altered simulated intensity from Fig. 5(c), the conductivity of VO₂ from 4000 to 50000 S/m, and normalize it to get Fig. 6(a). We create the relational equation based the intensity of all reflected light at the focal point is the same, which allows us to obtain a prominent focus and eliminate interference in the vicinity of the focus. By finishing, Eq. (8) is obtained:

(8)$$A(x) = \frac{{\sqrt {{f^2} + {{(x - {x_c})}^2}} }}{f}{A_C},$$

where $A(x)$ represents the intensity of the reflected light needed somewhere on the array, ${A_C}$ represents the intensity of the reflected light from the focal point downmost hair array, $\sqrt {{f^2} + {{(x - {x_c})}^2}} /f$ is scale factor. We have a focal point X = 0 um, and Y = 650 um as an example. Figure 6(b) illustrates the relationship between the array position, scale factor, and conductivity of VO₂. Comparing our calculated non-uniform modulation with the uniform modulation of VO₂ with conductivities of 4000 and 45000 S/m, as depicted in Fig. 6(c)–6(g), reveals that the focal point of non-uniform modulation is more aggregated than that of uniform modulation, the full width at half maxima (FWHM) is narrower. The intensity of interference spots near the focal point is also lower. Therefore, according to theoretical calculations and simulation, non-uniform modulation has superior focusing and interference reduction properties.

Fig. 6. (a) The relationship between the normalized intensity and conductivity of VO₂. (b) The relationship between VO₂ array position and its conductivity. Reflection focus of VO₂ when their conductivity being (c) 4000 S/m, (d) 45000 S/m, and (e) after non-uniform modulation. Simulation intensity analysis in (f) Y = 650um and (g) X = 0um.

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3.5 Wide angle incident light modulation

Typically, the focal length of a conventional lens and the angle of incidence of the beam are fixed, whereas the angle of incidence with adjustable arrays is variable. As depicted in Fig. 7(a) and 7(b), we tune the phase of the graphene such that the incidence angle and reflection angle are identical, and the incident route of the light is similar to the reflected path. No focal point can be produced, whether the incidence is vertical or oblique. The graphene in Fig. 7(c) is the same ${E_F}$ as that in Fig. 4(b), and the same focus cannot be achieved when the incident light is incident at an angle. To achieve oblique incidence focusing, phase compensation is used to achieve focusing. Phase compensation is that we first adjust the phase of the reflected light by adjusting the voltage on the graphene, and the phase of the reflected light is offset from the phase of the obliquely incident light, so that the obliquely incident light can be considered as the vertically incident light. Then, based on this, the normal focus adjustment of the vertical incident light can be performed. Finally, the focusing of the obliquely incident light is realized by phase compensation. Based on the ${E_F}$ of graphene in Fig. 7(c), the phase is changed on each array after calculation, and this adjustment amount may exactly counteract the phase deviation caused by oblique incidence, thereby achieving focusing, as depicted in Fig. 7(d). The ${E_F}$ of graphene after phase compensation can well gather the light to the specified position and achieve the modulation and focusing of the wide-angle incident light is achieved.

Fig. 7. Light (a) vertical and (b) oblique incident, while the angle of incidence being equal to the angle of reflection. (c) Normal ${E_F}$ and (d) phase-compensated ${E_F}$ in X = 0 um, Y = 500 um.

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4. Conclusion

In this study, we present a graphene and VO₂ array reflector that can change the phase of reflected light by varying the ${E_F}$ of graphene and the amplitude of reflected light by varying the conductivity of VO₂, so creating a tunable reflected light focus. Through theoretical calculations, the ${E_F}$ of graphene is linked to the array position by employing the phase as an intermediate variable, the conductivity of VO₂ is connected to the array position by using the amplitude as an intermediate variable, and the control of the reflected light focusing position, intensity, and scattering degree is achieved through simulation, and the focusing of obliquely incident light is achieved through phase compensation. The design can be utilized not only as a focus but also as a reflected light modulator or customized beam generator, providing a valuable concept for future adjustable devices.

Funding

National Natural Science Foundation of China (62165004, 61765004, 61805053); the Open Fund of Foshan University, Research Fund of Guangdong Hong Kong-Macao Joint Laboratory for Intelligent Micro-Nano Optoelectronic Technology (2020B1212030010); the Innovation Project of GUET Graduate Education (2021YCXS131, 2021YCXS040, 2022YCXS047).

Acknowledgments

We thank the National Natural Science Foundation of China and the GUET Graduate Education Innovation Project for partial funding.

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available but may be obtained from the authors upon reasonable request.

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Individually tunable array reflector for amplitude and phase modulation

Abstract

1. Introduction