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Abstract
Focus-tunable metalenses play an indispensable role in the development of integrated optical systems. In this paper, the phase change material Sb2S3 is used in a thermally modulated varifocal metalens based on PB-phase for the first time. Sb2S3 not only has a real part of refractive index shift between the amorphous and crystalline state but also has low losses in both amorphous and crystalline states in the near-infrared region. By switching Sb2S3 between the two states, a metalens doublet with a variable focal length is proposed. Moreover, the full width at half maximum of each focal point is close to the diffraction limit. And the focusing efficiency can be over 50% for the two focal points. Together with the advantage of precise thermal control, the proposed metalens has great potential in the application of multi-functional devices, biomedical science, communication and imaging.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Metalens, as an emerging technology based on metasurface, has provided a platform for miniaturized optical lenses because of their small footprint and the unprecedented ability to control the wavefront of incident light for focusing [1–5]. Along with the fast development of metalens research, the limitations of the metalens in practical application gradually became apparent, i.e., limited working band-widths and fixed focal length [6]. As a result, many efforts have been devoted to the tunable metalenses. For tunable metalens, varifocal metalens is one of the most important parts. The varifocal metalens makes it possible to miniaturize the applications of conventional lenses such as vigilance [7], laser processing [8], mixed reality displays [9,10] and detections [11]. Varifocal strategies have been widely studied in recent years, such as microelectromechanical system(MEMS) [12,13], lateral actuation [14] and stretchable substrate [15,16]. However, the demands of accurate mechanical structures or high voltages may limit the practical applications. On the other hand, metalenses have achieved focusing x- and y- polarized light at different focal points, or focusing right-handed and left-handed circularly polarized light at different focal points [17–19]. But in practice, a varifocal metalens with an identical optical source is the most common situation.
Except to the above methods, phase change materials with characteristics of distinct phase change and fast switching speed are also good candidates for varifocal metalenses. Ge2Sb2Te5(GST) was the most commonly used phase change material [20–22] that has significant refractive index change between the amorphous state and crystalline state with a fast switching speed. Still, a non-negligible absorption in the crystalline phase always exists. For a metalens, GST is usually used to switch the focus on or off. By dividing a metalens into multiple areas that each area corresponds to one focal point and switching different focal points on or off, a varifocal metalens can be realized. But it will lead to a very low efficiency [23,24]. Vanadium dioxide(VO2) [25–27], another popular phase change material, whose reversible phase change is between insulating and metallic states, has been used to switch focus between transmission and reflection with the same focal length [28]. And VO2 needs constant energy to maintain the metallic state [29]. According to previous studies, phase change materials mentioned above exist limitation in the fabrication of a transmission-type varifocal metalens that is more convenient for practical application. Recently, an ultralow loss reversible phase change property of Sb2S3 was demonstrated [30–32]. After exploiting the phase change characteristics of Sb2S3, the methods of implementing Bragg gratings [33] and dynamical filter [34] with Sb2S3 appeared. As a phase change material, Sb2S3 is dielectric with low absorption in both amorphous and crystalline states. The real part of refractive index shift Δn is about 0.6 in the wavelength range of 800nm to 1600nm which provides a platform for designing a near-infrared transmission-type varifocal metalens. Besides, by employing thermal or optical pulse, its state can be switched precisely.
In this paper, we take advantage of phase change material Sb2S3 and multilayer Pancharatnam-Berry phase to design a thermally controlled varifocal metalens for the first time. The designed metalens is a doublet with Si nanofins and Sb2S3 nanofins placed on different layers. For amorphous Sb2S3, the Sb2S3 unit can act as a half-wave plate. The metalens focuses incident light with focal length F1. After changing Sb2S3 into the crystalline state, the Sb2S3 unit works as a full-wave plate. The focal length of the metalens is F2. Furthermore, the full width at half maximum (FWHM) of each focal point is close to the diffraction limit. The focusing efficiency of F1 and F2 can reach 55% and 50%, respectively. The results show that the metalens has high image quality that is important for practical applications. The proposed method with thermal control has no limitation of accurate mechanically moving structures and realizes a transmission-type varifocal metalens with high image quality. The novel approach for designing active compact nanophotonic devices has great potential in on-demand nanophotonic components, such as novel scanners combining beam switching and lensing, dual-functional devices and active holography.
2. Materials and methods
Figure 1 depicts the working schematic of the metalens. The metalens comprises elliptical Si nanofins and elliptical Sb2S3 nanofins placed on different layers. For amorphous Sb2S3, the metalens whose Sb2S3 unit works as a half-wave plate focuses light with focal length F1. By heating Sb2S3 to the crystalline state, the Sb2S3 unit functions as a full-wave plate and results in a focal length of F2.
Fig. 1. Schematic of the varifocal metalens based on Sb2S3. When Sb2S3 is in the amorphous state, the Sb2S3 unit works as a half-wave plate and leads to focal length of F1. After heating Sb2S3 to 573 K, the Sb2S3 unit changes to the crystalline state as a full-wave plate and causes the focal length of F2.
2.1. Material model analysis
Sb2S3 was demonstrated to be a family of ultralow loss phase-change materials for applications in electrically and laser tuned active photonics recently [30,31]. Its crystallization can be achieved when increasing the temperature of Sb2S3 higher than 573 K, while amorphization is realized by heating Sb2S3 to its 801 K ± 18 K melting point and then rapidly quenching [31,35,36]. The quenching rate of the phase change material can be set as 109–1010 K s−1 according to past researches [37,38]. It has been experimentally demonstrated that the Sb2S3 can be changed between the amorphous state and crystalline state reversibly [30,31], and the crystallization switching time is only 70 ns similar to GST. Furthermore, Sb2S3’s optical constants show a non-volatile change. And energy is only required during the conversion process that is more convenient than VO2 [31]. Figure 2 shows the complex refractive index of Sb2S3 from 800nm to 1600nm. As Sb2S3 switches from the amorphous state to the crystalline state, the shift in the real part of refractive index Δn is about 0.6, and the imaginary k component maintains close to 0 [30]. Based on the excellent properties, Sb2S3 suits a near-infrared transmission varifocal metalens with relatively high efficiency well. For the bottom layer material, Si was chosen with a refractive index about 3.4. Furthermore, the state of Sb2S3 can be switched by laser pulse, electrical or thermal energy. In our design, a 30 nm indium tin oxide (ITO) layer is employed. The refractive index was extracted from the Drude model [39]. In the past researches, as a transparent electrode, ITO layer can exert electrical Joule heating of GST due to the sufficient conductivity [40]. The electrical resistivity of ITO can be designed by controlling the growth conditions [41]. By applying an electrical current pulse through the conductive layer, the state of Sb2S3 can be switched reversibly. The manufacturing process of the metalens is illustrated below. One can fabricate Si nanofins first and then deposit filling material SiO2. After that, ITO layer and Sb2S3 nanofins are deposited in turn. Figure 3(a) shows the diagram of the unit cell according to the processes.
Fig. 2. Complex refractive index of Sb2S3 [30]. (a) The real part n varies with wavelength (b) The imagery part k varies with wavelength for both the amorphous state and crystalline state.
Fig. 3. (a) Diagram of the meta-atom with filling material (b) Side view of the unit cell with no rotation angle (c) Bottom view of the Si unit cell (d) Upper view of the Sb2S3 unit cell. The geometric parameters of the unit cell and the rotation angle can be seen from (b), (c) and (d)
2.2 Pancharatnam-Berry phase
Figure 3 shows the schematic diagram of the metalens’ unit. The bottom layer (from the direction of incident light) is composed of elliptical Si nanofins, and the upper layer is composed of elliptical Sb2S3 nanofins. As the incident wave transmits the nanofin, there's going to produce a phase shift difference between the polarized light along the major axes (a1, a2) and the minor axes (b1, b2). As the refractive index of the nanofin varies, the phase shift difference will change [42]. Thus, it has the possibility to find a parameter that can make the phase shift difference approaches π for the amorphous Sb2S3 unit and 2π for the crystalline Sb2S3 unit that means the function of Sb2S3 unit structure can be switched between a half-wave plate and a full-wave plate reversibly.
In the proposed design, the phase distribution is applied by PB phase method. When a circularly polarized light incidents on the nanofin whose rotation angle is θ concerning the major axes, the Jones matrix can be expressed by [43]
So, as the Sb2S3 unit remains in the crystalline state with a full-wave plate function, the Sb2S3 unit has no ability to affect the phase distribution of the incident light [44]. Therefore, the metalens works based on single-layer PB phase with Si nanofins layer. For a right-handed circularly incident light, as shown in Fig. 3(c), the Si unit whose rotation angle is θ1 can insert a phase distribution equal to 2θ1.
If Sb2S3 switches to the amorphous state, the Sb2S3 unit structure acts as a half-wave plate. At this time, the metalens becomes a metalens doublet. Both of the Sb2S3 unit and Si unit will provide phase distribution together. For a right-handed circularly polarized light through a two-layer P-B phase change element, the output light can be written as [45]:
3. Results and discussions
3.1 Confirmation of nanofins
Based on the above analysis, to construct the varifocal metalens, the geometric parameters of the nanofins are confirmed with the three-dimensional FDTD method (Lumerical Inc., Vancouver, BC, Canada). The mesh grids are set as 20nm×20nm×20nm. The periodic boundary condition is applied for the x- and y-axis, and the perfectly matched layer (PML) boundary condition is applied for the z-axis. The period of the nanofin is 700nm×700nm. The major axis, minor axis and height are a1, b1 and h1 for Si nanofins and a2, b2 and h2 for Sb2S3 nanofins. To eliminate the effect of resonance that can decrease the efficiency without affecting the phase distribution, the width of SiO2 between the two layers is 0.7µm (about half of the wavelength). For the operation wavelength, we choose 1310nm that is widely used in communication.
In order to optimize the desirable parameter of the Si nanofins, the lengths of major axes and minor axes are altered to find the parameter whose difference between phase shift of linearly polarized light along the major axes and the minor axes is π. As shown in Fig. 4(a), at the point A with a1=480nm, b1=140nm, h1=1µm, the phase shift difference approximates well to π indicating that the Si unit can work as a half-wave plate.
Fig. 4. The difference between the phase shift of linearly polarized light along major axis and minor axis with different lengths of major axis and minor axis for (a) Si nanofin, (b) the amorphous Sb2S3 nanofin and (c) the crystalline Sb2S3 nanofin
The same method is applied to get the appropriate phase shift difference when Sb2S3 is in the amorphous and crystalline state. After filtering the data in Figs. 4(b) and (c), it shows that the phase difference approaches π with n=2.767(amorphous) and 0 with n=3.343(crystalline) at the point B (a2 = 560nm, b2=188nm, h2=1.2µm). It means that the Sb2S3 unit can work as a half-wave-plate and a full-wave plate in different states.
Figures 5(a) and (b) illustrate the phase shift difference and the polarization conversion efficiency respectively at defined parameters with the wavelength range from 1200nm to 1400 nm. The results of the phase shift difference at 1310 nm corresponding to the swept results in Fig. 4 well. The conversion efficiency of Si nanofin, amorphous Sb2S3 nanofin and crystalline Sb2S3 nanofin can reach 99.8%, 95.4% (half-wave plate) and 9.28%(full-wave plate), respectively. The results further prove the Sb2S3 unit structure can work as a half-wave plate in the amorphous state and a full-wave plate in the crystalline state.
Fig. 5. (a) Phase shift difference of Si nanofin with A parameter and Sb2S3 nanofin with B parameter (b) Polarization conversion efficiency for Si nanofin, amorphous Sb2S3 nanofin and crystalline Sb2S3 nanofin
3.2 Design of varifocal metalens
To achieve the focus of incident light, the rotation angle of each nanofin should satisfy the spatial variation of the phase requirement as below:
The electric field intensity profiles in the x-y plane and x-z plane of F1 and F2 are illustrated in Figs. 6(a)-(d). The simulated focal lengths are about F1=15.41µm and F2=20.38µm which correspond to our designed focal lengths. According to the calculation of the numerical aperture $NA(\lambda ) = D/x\sqrt {f{{(\lambda )}^2} + {D^2}/4}$, NA of the two focal points are 0.714 and 0.608. Figures 6(e)–(f) show the normalized Intensity on the focal plane in the lateral direction for the focal points whose focal lengths are F1 and F2, the full-width at half-maximum (FWHM) of F1 and F2 can reach about 0.920 and 1.083 are close to the full-width at half-diffraction-limited values 0.917 for the first focal point and 1.078 for the second focal point calculated by $\frac{\lambda }{{2NA}}$. Besides, the focusing efficiency is calculated according to the fraction of incident light in a circular area whose radius is three times the FWHM spot size on the focal plane. The focusing efficiencies reach 60.08% for the focal point with F1 and 55.31% for the focal point with F2. It shows the focusing efficiency of F1 is a little higher than F2 that may be attributed to the polarization efficiency of amorphous Sb2S3 is more desirable than the polarization efficiency of crystalline Sb2S3.
Fig. 6. Schematics of far fields on the x-y and x-z planes (a) First focal point on the x-y plane. (b) First focal point on the x-z plane. (c) Second focal point on the x-y plane. (d) Second focal point on the x-z plane. (e) Normalized Intensity on the focal plane in the lateral direction for F1 = 15µm.(f) Normalized Intensity on the focal plane in the lateral direction for F2 = 20µm.
For a varifocal metalens, it is indispensable for practical applications that the separate distance can be designed at will between the two foci. So, we design another three distances between the two focal points. Figure 7 illustrates the intensity distribution in the x-z plane for the focal lengths are 15µm and 15µm, 15µm and 25µm, 15µm and 30µm. Besides, Table 1 shows the summary of focusing properties for different distances between the two focal points. It can be seen that the simulated focal lengths are in agreement with the designed focal lengths. The FWHM of each focal point is close to the theoretical diffraction limit. Furthermore, the efficiency of the first focal point can exceed 55%, and that of the second focal point can exceed 50%. It illustrates that the efficiency of the design is much higher than the metalens that realizes different focal lengths separately by dividing into multiple areas. The results significantly prove that the design can realize a varifocal metalens with high image quality. Furthermore, the phase distributions between the two states of the metalens have little effect on each other, so the method also can be used in other switchable devices such as tunable beam generators and dual-function devices that make the method more meaningful.
Fig. 7. (a)(b) The intensity distributions in the x-z plane of F1=15µm and F2=15µm. (c)(d) The intensity distributions in the x-z plane of F1=15µm and F2=25µm. (e)(f) The intensity distributions in the x-z plane of F1=15µm and F2=30µm.
Table 1. Focusing Properties of the varifocal metalens
4. Conclusion
This paper proposed a strategy of a near-infrared thermally controlled varifocal metalens based on phase change material Sb2S3 and PB phase. Sb2S3 was applied to a varifocal metalens in this paper for the first time. Through heating Sb2S3, it can be switched between the amorphous state and crystalline state reversibly. The main difference of Sb2S3 from the phase change material widely used is that, in the near-infrared region, Sb2S3 has low losses in both amorphous and crystalline states. And the refractive index difference between the amorphous and crystalline state can lead to different functions for the two states. By flexibly combining Sb2S3 with the concept of the half-wave plate and full-wave plate, the metalens doublet can focus incident light at different focal points separately by heating the phase change material. The focusing efficiencies for F1 and F2 are above 55% and 50%. And the FWHM of each focal point approaches to diffraction limit. The results reveal that the metalens has high image quality. Compared with previous studies, the thermally modulated metalens enables focus switching without mechanical compensation or incident light change. The proposed method has the potential to play an important role in optical technology, dual-functional devices, biomedical science, display technology, and virtual reality.
Funding
National Natural Science Foundation of China (NSFC) (61774062, 61875057, 11674109, 11674107); Science and Technology Program of Guangzhou (2019050001); Innovation Project of Graduate School of South China Normal University (2019LKXM026).
Disclosures
The authors declare no conflict of interest.
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