Band-tunable achromatic metalens based on phase change material

Yuhang Zhang; Zuyu Li; Shuai Qin; Hui Huang; Kaiqian Jie; Jianping Guo; Hongzhan Liu; Hongyun Meng; Faqiang Wang; Xiangbo Yang; Zhongchao Wei

doi:10.1364/OE.456752

1. Introduction

Optical dispersion is a key characteristic of optical materials, which also plays an important role in full-color imaging devices. Researchers seek to manipulate the dispersion, since the manipulation of dispersion means numerous potential applications where information can be multiplexed. Enhanced dispersion can be utilized to separate the electromagnetic wave of different wavelength in the field of spectrometry and tomography. Similarly, eliminating the dispersion is widely needed for achromatic imaging. To properly control the optical dispersion will always cost a lot either in design or experimental work.

Recently, metalens, a kind of artificial period arranged sub-wavelength nanostructure, have shown unprecedented abilities in tailoring amplitude and phase. Like the conventional refractive optical lenses, metalens also suffer from chromatic aberration [1]. Over the past few years, a large variety of achromatic metalens have been demonstrated [2–12]. Especially for the achromatic bandwidth, the improvement from discrete wavelength [13–17] to continuous band [18–21] greatly enriches the color information density of imaging. After that, researchers have tried to broaden the achromatic bandwidth as much as possible. Broader bandwidth leads to the requirement of higher dispersion value difference. To satisfy the need for a large dispersion value difference, researchers have explored many approaches. A simple and effective way for dielectric metasurfaces is to increase the range of effective refractive index such as employing high refractive index materials and increasing the height of metaunit, but the resonance effect (nonlinearity of the phase curve) [22–25] may lead to low efficiency and focal length shift [26]. Reducing the NA of the metalens is another way but cannot fundamentally solve the problem. A feasible exploration direction is to increase the structural complexity or the freedom degree to obtain greater difference of dispersion values [27–29]. A group innovatively proposed a hybrid 3D architecture combining nanoholes with a phase plate [30], and another group proposed a fishnet-achromatic metalens [31]. By properly designing the shape and stereo structure, both groups proposed a metalens with an ultrabroad achromatic bandwidth over 650 nm in visible and near-infrared spectrum, which open up a new way to broaden the achromatic bandwidth.

Actually, changing the refractive index of the material can be equivalent to increasing the freedom degree [32–36]. To modulate the refractive index and achieve different functions, there are a lot of methods, such as combining metasurfaces with digital coding or phase change materials to provide dynamic reconfigurability. Phase change materials usually refer to materials whose optical properties experience significant change after phase transition, which is widely used in reconfigurable photonic devices. However, few researchers have paid attention to broaden the achromatic bandwidth with phase change material. If we apply the phase change material properly, not only can the operation band being broader, but it can also be modulated actively. For the latter, in previous studies, one structural design corresponds to only one operation band, which strongly hinders its application. Realizing band-tunable functionality means we can switch the achromatic band without any structural change which is of great significance for imaging system with multi band imaging requirements. For instance, combining general infrared thermal imager and visible camera, we can switch the operation band without any inconvenient replacement of optical instrument or extra cost of other optical instrument.

In this work, we proposed a bilayer dielectric metasurfaces that can achieve achromatic focusing in a broad continuous bandwidth from 650 nm to 1100 nm under the incidence of circularly polarized light. The achromatic region consists of two bands, including Band A (650-830 nm) and Band B (830-1100 nm). By changing the state of Sb₂S₃ metaunits, the achromatic band can be switched between Band A and Band B without any structural change. This design method can be used to solve the problem that achromatic focusing in an ultrabroad band by splitting one band into two which avoids the inherent disadvantage of a single large band. What’s more, the average efficiencies of Band A and Band B are over 35% and 55% respectively with a peak efficiency of 70% at wavelength 1000 nm, and the average focal shift percentages are both below 3%. In addition, these two bands can be designed differently including the focal length and dispersion state within a certain range owing to the bilayer structure which successfully separates the requirements of dispersion value and focusing phase. Due to its flexible manipulation ability, it has great potential in dual-functional devices such as combining achromatic metalens with diffractive metalens. Our design propose a method to broaden the achromatic bandwidth while keeping a high image quality. The tunable bandwidth for achromatic metalens is a novel function for multifunctional metasurfaces, which is of great significance to the broadband applications of meta-devices.

2. Principle and design

Figure 1 depicts the working schematic of the metalens. The achromatic band of metalens can be switched reversibly based on phase change material Sb₂S₃. For amorphous Sb₂S₃, it can satisfy the required dispersion values in Band A (650-830 nm). By applying pulse voltage to indium tin oxide (ITO) layer to heat up Sb₂S₃ to the crystalline state, it can satisfy the required dispersion values in Band B (830-1100 nm).

Fig. 1. Schematic of the band-tunable bilayer achromatic metalens based on phase change material Sb₂S₃. Two Continuous bandwidth regions (650-830 nm and 830-1100 nm) can be achromatic focused with designed focal lengths at the incident of circularly polarized light. When Sb₂S₃ is in amorphous state, the achromatic metalens work in Band A (650-830 nm). After Sb₂S₃ units change to crystalline state, the achromatic metalens work in Band B (830-1100 nm).

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To achieve achromatic focusing in a broad bandwidth, each metaunit must be designed to satisfy the phase requirement at all design wavelengths. Assuming that the metalens deflect light by a position($r$) dependent angle($\theta $), then according to the generalized Snell’s law [37], we can give this relation [31]:

(1)$$\begin{array}{l} \sin (\theta ) = \frac{r}{{\sqrt {{r^2} + {f^2}} }} = \frac{1}{{k0}}\frac{{d\phi ({r,\omega } )}}{{dr}},i.e.,\\ \phi ({r,\omega } )= \int {dr{k_0}} \frac{r}{{\sqrt {{r^2} + {f^2}} }} ={-} \frac{\omega }{c}\left( {\sqrt {{r^2} + {f^2}} - f} \right) + g(\omega )\end{array}$$

where $\phi ({r,\omega } )$, $\omega $, $f$, r, $c$, $\textrm{g}(\mathrm{\omega } )$ are phase profile required, angular frequency, focal length, radial position, speed of light and reference phase function independent of $\textrm{r}$, which contribute no effect on the deflect angle but on dispersion values [38]. In the previous theory, $\textrm{g}(\mathrm{\omega } )$ has been proposed of generalized choice of [21]:

(2)$$g(\omega )= \frac{\omega }{c}\sqrt {r_0^2 + {f^2}} + {C_0}$$

which makes the required phase $\,\phi ({{r_0},\omega } )= {C_0}$ for all frequencies at the reference position $r = {r_0}$. Equation (1) indicates that, for a specific radius, phase is a simple linear function with respect to angular frequency. For conveniently describing, Eq. (1) can be expanded by Taylor expansion of a spatially dependent and frequency-dependent phase profile around an angular frequency ${\omega _r}$ [39]:

(3)$$\phi ({r,\omega } )= {\phi _0}({r,{\omega_r}} )+ \frac{{\partial \phi }}{{\partial \omega }}|{_{\omega = {\omega_r}}} ({\omega - {\omega_r}} )+ \cdots$$

where ${\phi _0}$ is the phase at a reference angular frequency ${\omega _\textrm{r}}$ and $\frac{{\partial \phi }}{{\partial \omega }}(r ){|_{{\omega _r}}}$ is the dispersion value (group delay) required. In other words, the required value of a given metaunit to be placed at position r can be described by two parameters: phase value ${\phi _0}$ and group delay $\frac{{\partial \phi }}{{\partial \omega }}(r ){|_{{\omega _r}}}$.

As a proof-of-concept, we design and simulate an achromatic metalens with focal length ${f_A} = 14{\mu}m$ in Band A and focal length ${f_B} = 11{\mu}m$ in Band B. To improve the manipulation ability of focusing phase, the bilayer structure is proposed to improve the degree of phase regulation which separates the requirements of focusing phase and dispersion values. This design aims to allow the metalens to simultaneously satisfy the dispersion and focusing phase distribution at the reference wavelength. Figure 2 shows the schematic diagram of a metaunit. In this configuration, the bottom layer composed of Sb₂S₃ annular pillars surrounded by silica. Here, the dimension value of Sb₂S₃ annular pillars $({R1,R2} )$ were adjusted to achieve the required dispersion values. The upper layer composed of rectangular Si metaunit with a fixed dimension ($L = 295\; nm$, $W = 120\; nm$) produces a phase (based on the Pancharatnam-Berry phase) by rotating different angles ($\alpha $) for all frequency light. A thin layer of ITO is placed between the SiO₂ substrate and Sb₂S₃ metaunits to heat up and realize the phase transition of Sb₂S₃. By properly selecting the $\textrm{g}(\mathrm{\omega } )$ function, the upper layer metaunits with identical dispersion will not affect the required dispersion [21]. In other words, we can almost ignore the constant dispersion acting on the whole metasurfaces. It’s worth noting that the layer distance $\textrm{h} = 400\,\textrm{nm}$ is designed to be close to minimize the effect of wavefront divergence after the first layer, bur far enough to avoid layer coupling [17].

Fig. 2. (a) Schematic of the metaunit. (b) Side view of the metaunit. The interval between two layers is $\textrm{h} = 400\,\textrm{nm}$ and the heights of upper and bottom layer are $\textrm{H}1 = 510\,\textrm{nm}$, $\textrm{H}2 = 800\,\textrm{nm}$. The lattice constant $\textrm{P} = 350\,\textrm{nm}$. (c) Upper view of the Si rectangle. The long and short axis of Si rectangle are $\textrm{L} = 295\,\textrm{nm}$ and $\textrm{W} = 120\,\textrm{nm}$, and alpha is the angle between long axis and horizontal direction. (d) Upper view of the Sb₂S₃ unit. The inner radius $\textrm{R}2$ and outer radius $\textrm{R}1$ both affect the value of dispersion.

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To realize the switching function, here phase change material Sb₂S₃ is used which is a new kind of ultralow loss non-volatile reversible phase change material. Its extinction coefficient k is close to zero from 650 nm to 1100 nm in both amorphous and crystalline states as shown in Fig. 3(b) [40]. By increasing the temperature higher than 573 K, the crystallization of Sb₂S₃ can be achieved and by heating Sb₂S₃ to its 801 K ${\pm} $ 18 K melting point and then rapidly quenching, the amorphization can be achieved [40]. And all these process can be realized by applying specific voltage pulse to ITO layer for a predefined time duration [40,41]. There is a contrast of refractive index of $\Delta n = 0.3 - 0.5$ between Band A and Band B which helps realize different dispersion values. Figure 3(c) shows simulated phase values for amorphous Sb₂S₃ element (black dotted curve) and crystalline Sb₂S₃ element (red dotted curve) in wavelength region 650-1100 nm. For a particular position and focal length of metalens, the required phase was plotted as linear functions (blue and green area). As is clearly shown in Fig. 3(c), the slope of the red dotted curve keep stable in Band B, but increase significantly in Band A. Similarly, the black dotted curve has a better fit than red one in Band A. Therefore, crystalline and amorphous Sb₂S₃ can meet the required value in Band B and Band A, respectively. The expanded phase formula in two bands can be written as follows:

(4)$${\phi _A}({r,\omega } )= {\phi _{A0}}({r,{\omega_r}} )+ \left.\frac{{\partial {\phi _A}({r,\omega } )}}{{\partial \omega }}\right|{_{\omega = {\omega_r}}} ({\omega - {\omega_r}} )+ \cdots$$

(5)$${\phi _B}({r,\omega } )= {\phi _{B0}}({r,{\omega_r}} )+ \left.\frac{{\partial {\phi _B}({r,\omega } )}}{{\partial \omega }}\right|{_{\omega = {\omega_r}}} ({\omega - {\omega_r}} )+ \cdots$$

where ${\phi _{A0}}(r )$ and ${\phi _{B0}}(\textrm{r} )$ are the required reference frequency phase profile, $\frac{{\partial {\phi _A}}}{{\partial \omega }}(r ){|_{{\omega _r}}}$ and $\frac{{\partial {\phi _B}}}{{\partial \omega }}(r ){|_{{\omega _r}}}$ are the required group delay values depending on r. For the convenience of phase profile design, ${\omega _r} = \; 2\pi c/830\; nm$ is selected as the reference frequency of both two bands. Based on the discussion of Si metaunits above, the effective group delay values are produced only by Sb₂S₃ metaunits in bottom layer since the Si metaunits share the same dispersion value. The reference frequency phase profile is affected by both upper and bottom layers. The reference frequency phase profile consists of two parts, the upper layer part and bottom layer part, written as:

(6)$${\varphi _{A0}}({r,{\omega_r}} )\textrm{ = 2}\alpha \textrm{ + }{\varphi _B}({{\omega_r}} )+ \Delta \varphi$$

(7)$${\varphi _{B0}}({r,{\omega_r}} )\textrm{ = 2}\alpha \textrm{ + }{\varphi _B}({{\omega_r}} )$$

Where $\Delta \varphi $ is defined as ${\varphi _A}({{\omega_r}} )- {\varphi _B}({{\omega_r}} )$ as shown in Fig. 3(c). With different rotating angle $\,\alpha $, ${\varphi _{B0}}(r )$ can be added with a compensatory phase which is independent of wavelength. To gain higher efficiency, the structure of upper layer has been optimized into half-wave plate. As shown in Fig. 4(a), the calculated cross-polarization conversion efficiency is mostly higher than 70% except for two resonant positions. Actually, $\Delta \varphi $ becomes an important factor evaluating metaunits, since $\Delta \varphi $ represents the difference of reference phase between two bands, limiting the regulation of phase profile of two bands. We scan the outer radius (40-140 nm) and inner radius (10-60 nm) of Sb2S3 unit and create a “library” of metalens elements. Each element has its corresponding set of group delay values and $\Delta \varphi $:

(8)$$\left( {\frac{{\partial {\varphi_A}}}{{\partial \omega }},\frac{{\partial {\varphi_B}}}{{\partial \omega }},\Delta \varphi } \right)$$

Fig. 3. The refractive index (a) and extinction coefficient (b) of Sb₂S₃ for amorphous and crystalline states. (c) The curve of phase with respect to frequency for a particular Sb₂S₃ element ($R1 = 90\; nm$,$R2 = 25\; nm$) at amorphous and crystalline state. The blue and green region represent the required phase curve for a specific position of metalens.

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To visualize the required phase and library, Fig. 4(c) plot the group delay for all simulated elements as red circles, with the group delay in Band B on the x-axis and with the group delay in Band A on the y-axis. In order to implement our designed metalens, we compared the group delay and $\Delta \varphi $ values for each library element (Eq. (8)) to those of the target values obtained from Eqs. (4) and (5) to select the best element for each lens position. The element selecting process can be regarded as minimizing an error function written as:

(9)$$error = \sum\limits_i {\left. {\left\{ {{\beta_\textrm{1}}\left( {\frac{{\partial \varphi_A^i}}{{\partial \omega }}|{_{{\omega_r}}} - \frac{{\partial \phi_A^i}}{{\partial \omega }}|{_{{\omega_r}}} } \right) + {\beta_\textrm{2}}\left( {\frac{{\partial \varphi_B^i}}{{\partial \omega }}|{_{{\omega_r}}} - \frac{{\partial \phi_B^i}}{{\partial \omega }}|{_{{\omega_r}}} } \right)} \right. + {\beta_\textrm{3}}({\Delta {\varphi^i} - \Delta {\phi^i}} )} \right\}}$$

where i represents specific position (radius) of metalens, $\beta $ represent weight coefficient. As shown in Fig. 4(b), there is a negative correlation between $\Delta \varphi $ and group delay. This can be explained by the effective refractive index. The metaunit with high effective refractive index (high group delay) tend to show more phase shift after phase change transition. Figure 4(d) plot the required phase for reference wavelength, required $\Delta \phi $ as black line and the red dots are the $\Delta \varphi $ of the selected elements which basically meet the needs.

Fig. 4. (a) The cross-polarization and co-polarization conversion efficiency of the Si nanopillar. (b) Each element with different group delay and $\Delta \varphi $ are plotted as 3D scatter figure. (c) The group delay of each element and required group delay are plotted in Band A and Band B. (d) The required phase at reference wavelength in both bands. By subtracting curve Band B from curve Band A, the required $\Delta \phi $ can be obtained and the red dots are $\Delta \varphi $ of the elements.

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3. Result and discussion

Based on the above analysis, we design and simulate an achromatic metalens with ${f_A} = 14\; {\mu}m$ and ${f_B} = 11\; {\mu}m$, and the corresponding numerical aperture (NA) are 0.39 and 0.47, which are calculated by $NA = \sin [{\tan ^{ - 1}}(D/2f)]$. Under the illumination of right-handed circularly polarized plane wave, the FDTD Solutions (Lumerical Inc., Vancouver, BC, Canada) simulation result of a full metalens is performed in Fig. 5. To reduce the simulation time and ensure accuracy, the mesh grids of the metalens and propagation space are set as 30nm×30nm×30 nm and 40nm×40nm×40 nm respectively. The perfectly matched layer (PML) boundary condition is applied for the three axis. When Sb₂S₃ is in crystalline stage, metalens only work in Band B, as shown in Fig. 5(b). By applying a voltage pulses to ITO layer to realize the switch from crystalline stage to amorphous stage of Sb₂S₃, metalens can work in Band A, as shown in Fig. 5(a). From the axial intensity distributions, the most obvious finding is that the chromatic aberration is apparently reduced across the entire operation bandwidth, with the focal planes for all wavelengths lying very close to one another. For both two bands, the focal shifts percentage, defined as the percentage of actual focal length deviating from the ideal focal length, are below 3%. Actually, FDTD simulations for a full metalens will calculate the coupling effect between metalens elements. However, since the period of element $P = 0.35\; \mu m$ satisfy the Nyquist sampling law, writing as $p \le {\lambda / {2NA}}$, the coupling effect is almost negligible and it will not affect the design process. For an imaging system, diffraction limit of the focal spots plays an important role for imaging quality. The full widths at half-maximum (FWHM) are shown in Fig. 5(f), and they are all close to the diffraction limit, calculated by $\lambda /2NA$. In addition, the depth of focus (DOF) keep stable for each achromatic band and parasitic focal spots is almost eliminated. DOF can be obtained by calculating the FWHM of the intensity field at z-axis in the propagation plane [42]. It is apparent that the uneven DOF will lead to image blur so maintaining the stability of DOF in a large operation band is also a key point of high-quality imaging. All these features could be attributed to the comprehensive coverage of group delay space provided by the element library. Figure 5(e) shows the focusing efficiencies for two wavelength region.

Fig. 5. Simulated result of band-tunable achromatic metalens. Normalized intensity distributions for propagation plane and focal plane in Band A (a) with a focal length 14$\mu m$ and distributions in Band B (b) with a focal length 11$\mu m$. The focal length value and focal length shift percentage with respect to wavelength in Band A (c) and in Band B (d), and the focusing efficiency was plotted in two bands (e). (f) The simulated and theoretical FWHM from 650 nm to 1100 nm. (g) The simulated DOF from 650 nm to 1100 nm. The dotted yellow is the dividing line between two operation bands.

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For Band A and Band B, the simulated average focusing efficiency are higher than 35% and 55% respectively. The focusing efficiency is defined as below [43]:

(10)$$\eta \textrm{ = }\frac{{\int\!\!\!\int {_{{S_f}}{{\overrightarrow E }_f} \times \overrightarrow H _f^\ast d{s_f}} }}{{\int\!\!\!\int {_{{S_i}}{{\overrightarrow E }_i} \times \overrightarrow H _i^\ast d{s_i}} }} \times 100\%$$

Where ${\vec{E}_f}$ and $\vec{H}_f^{\ast}$ are the electric and magnetic fields on the focal plane, similarly, ${\vec{E}_i}$ and $\vec{H}_i^{\ast}$ represent the incident light, ${S_f}$ is the area of circle whose diameter is three times the size of FWHM and ${S_i}$ is the same area as the designed metalens. There is a difference of focusing efficiency between two bands due to the higher absorptivity of Sb₂S₃ material in the Band A. The focusing efficiency may be relatively low but sufficient for imaging. For the visible wavelength region, the focusing efficiency reaches a low point at $\lambda = 650\; nm\; ,\; 725\; nm$, which can be ascribed to the low polarization conversion rate as shown in Fig. 4(a). Since we adopted the bilayer structure, the total efficiency will be limited by the polarization conversion rate of the upper structure. This kind of bilayer structure may lead to relatively low focusing efficiency. However, when considering the required complicated phase profile, the bilayer structure that can separate the group delay from focusing phase is necessary. In practical application, two achromatic bands may need to share the same focal length ${f_A} = {f_B}$. For the case of ${f_A} = {f_B} = 12\; {\mu}m$, the required $\Delta \varphi $ is the same value for all metalens elements, but it’s difficult to find elements with different values of group delay while keeping the same $\Delta \varphi $. However, $\Delta \varphi $ is only one of many factors that help determine the focal length. We select the metalens elements sharing small difference of $\Delta \varphi $, and simulate the propagation field to get the focal length as shown in Fig. 6(a). The focal shift percentages are both below 6% for two bands, which indicates that the two achromatic bands can basically work independently with our design method.

Fig. 6. (a) Simulated focal length for the case ${f_A} = {f_B} = 12\; um$. (b) The dispersion value coverage with respect to $N{A_A}$ and $N{A_B}$ in the case that the diameter of metalens is $12\; um$.

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Based on the manipulation ability of phase and dispersion, our design approach allows for one metasurfaces to exhibit different combinations of focal length and dispersion state as long as the required phase and dispersion values can be met. About the focal length, just like the example ${f_A} = {f_B} = 12\; {\mu}m$ discussed above, there is a numerical limiting relationship between ${f_A}$ and ${f_B}$. We outlined the distribution area of the group delay point map. Assuming that all the area can be met without considering the value of $\Delta \varphi $, we study how the required curve can lay down on this area. Actually, the designed focal length will significantly affect the maximum difference of required dispersion values. When the diameter of metalens D is $12\; {\mu}m$, the relationship of $N{A_A}$ and $N{A_B}$ is shown in Fig. 6(b). The value represented by the color is the coverage rate of the required dispersion. This figure implies that the value of $N{A_A}$ and $N{A_B}$ should not have great difference and both $N{A_A}$ and $N{A_B}$ should not be too large. In addition to the focal length, the dispersion state can also be adjusted. The dispersion state refers to achromatic focusing or diffractive focusing here. To realize this function, the required group delay in achromatic focusing band should meet a hyperbolic trend phase dispersion as before while the required group delay in the other band are all close to a fixed value. Here Band A and Band B correspond to diffractive focusing and achromatic focusing respectively. Unfortunately, the coverage area of group delay point map do not have enough span in the horizontal direction (in Band B). Therefore, we have to make a compromise in fulfilling the group delay by tilting the required line a bit as shown in Fig. 7(c).

Fig. 7. Simulated result of metalens that show achromatic focusing in Band B and diffractive focusing in Band A. Normalized intensity distributions of propagation plane and focal plane in Band A (a) and Band B (b). (c) The group delay of each element and required group delay are plotted with respect to two bands for above mentioned metalens. (d) The theoretical focal length calculated by $Fresnel$ approximation and the simulated focal length using FDTD in Band A. (e) The simulated focal lengths of metalens in Band B.

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The full lens simulation result using Lumerical FDTD is shown in Fig. 7(a) (b). The focal length shift in Band B is small enough for achromatic imaging while the focal length in Band A decrease with respect to wavelength. Under the $Fresnel$ approximation, the diffractive focal length of incident wavelength is:

(11)$$f(\lambda )= \frac{{{\lambda _0}}}{\lambda }{f_0}$$

As shown in Fig. 7(d), the theoretical focal length calculated by Eq. (10) fits well with the simulated focal length. By switching the state of Sb₂S₃, the function of metalens can be changed from achromatic imaging to tomography. The parasitic focal spots can be seen at wavelength $830\; nm$ in Band B, we attribute this to the sparse density of group delay point map at high group delays. Besides, the elements with higher group delay are always accompanied by low efficiency and poor phase match, which is unavoidable.

4. Conclusion

In conclusion, we have demonstrated a band-tunable achromatic metalens covering a bandwidth over 450 nm in near-infrared spectrum based on phase change material Sb₂S₃. By separating the requirement of dispersion value and focusing phase, the two layers metasurfaces composed of high efficiency and large difference of dispersion value elements have been designed. For both two bands, the average focusing efficiency is high enough for high quality imaging and the FWHM is near at diffraction limit. From another point of view, this design method proposed a new way to achieve broadband achromatic focusing by splitting one band into two. This design strategy can be readily extended to other spectrum by using other phase change material. Achieving the function of band-tunable for achromatic metalens is firstly proposed in infrared spectrum and this characteristic indicates the great potential in detecting, displaying and other multifunctional imaging applications.

Funding

National Natural Science Foundation of China (61774062, 61875057, 11674109, 11674107); Natural Science Foundation of Guangdong Province (2021A151501035); Science and Technology Program of Guangzhou (2019050001).

Disclosures

The authors declare no conflict of interest.

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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Band-tunable achromatic metalens based on phase change material

Abstract

1. Introduction

2. Principle and design

3. Result and discussion

4. Conclusion

Funding

Disclosures

Data availability

References

Data availability

Cited By

Figures (7)

Equations (11)

Optics Express