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Abstract
Metasurfaces provide a remarkable platform to manipulate over phase, amplitude, and polarization flexibly and precisely. Bifocal metalens draws great research interest due to its ability of converging wavefronts to different focal positions horizontally and longitudinally. However, as wavelength of incident light changes, chromatic aberration will cause the focal lengths reliance on the incident wavelength, which will affect the performance of metasurface, especially for longitudinal bifocal metalens. In this work, a broadband achromatic longitudinal bifocal metalens (BALBM) based on single nanofin unit cell is demonstrated. Pancharatnam-Berry (PB) phase is used to converge the incident light. Cross commixed sequence distribution (CCSD) is introduced to control the positions of focal points FLand FRwhen left-handed circularly polarized (LCP) and right-handed circularly polarized (RCP) incident. Propagation phase is used to compensate the phase difference caused by chromatic aberration. Simulation results show that in the continuous wavelength range from 500 nm to 700 nm, the focal point shifts caused by chromatic dispersion are reduced 81% for FL and 83% for FR, respectively. The focal length variations are stabilized to 6.21% for FLand 4.8% for FRcomparing with the focal lengths at the initial wavelength 500 nm. The proposed BALBM brings advances to bifocal metasurfaces in versatile application areas including machine vision, optical computed tomography and microimaging.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Metasurfaces which encompass carefully designed two-dimensional material with subwavelength nanofins has attracted great research interest for its excellent ability to control over phase, amplitude and polarization state of the incident electromagnetic wave. On the basis of abrupt phase change, phase profile discrete sampling and gradient phase, metasurface can be liberated from the dependence of the device thickness along the optical path to accomplish phase accumulation. Metasurface in dielectric also presents exceptional potential in integrated photonics [1,2]. With the advantages of thin thickness and easy engineering of the metasurface, metalens of varieties functions such as polarization control [3–5], beam splitter [6–8], vortex beam [9–12], hologram [13–15], waveguide crossings [1,2] have been investigated. Bifocal metalens, with its ability of concentrating incident light waves at different locations longitudinally/transversely, has been seen promising application prospect in fields like optical tomography technique [16,17], virtual reality (VR) [18,19] and microimaging [20].
Hitherto miscellaneous of bifocal metalenses have been realized by theories [21,22] and by experiments [23–26]. For instance, Chen et al. [25], designed a multifocal metalens consisting of three ring-bands of the nanofins, corresponding to left-handed circularly polarized (LCP) light, right-handed circularly polarized (RCP), and linear polarized (LP). Tian et al. [21] developed a longitudinal bifocal metalens with the hybrid phase consists of propagation phase and Pancharatnam-Berry (PB) phase, realized intensity control of the focal points. Zang et al. [26] proposed lateral bifocal metalens by introducing an extra phase gradient in x-axis direction of the phase profile function. However, the phase profile functions in the above works showed wavelength-dependent character since the working wavelengths remain unchanged. That is to say, when there is variation in the incident wavelength, the phase profiles of the above works will hence vary, similar to chromatic aberration in optical systems.
In optical systems, when the wavelength of incident light increase/decrease, chromatic aberration will emerge following the continuous change of the material’s refractive index. In spite of metasurface presenting great expectation of replacing traditional optical device, the existence of chromatic aberration will inhibit the metasurface from wider applications. Plenty of researches aiming at achromatism metalens have been developed [27–35]. Aieta et al. [27] proposed discrete wavelength achromatic metalens. Shrestha et al. [28] demonstrated broad waveband achromatic metalens, whereas the cross-section of the nanofins is complex and the achromatic ranges are of discrete wavelengths. Chen et al. [29] realized broadband achromatism of visible wavelength by using metal diatomic structure. Fan et al. [30] and Wang et al. [31] used multiple shapes of nanofin to compensate the chromatic aberration, realized achromatic metalens with high efficiency. All the above works are concentrated on single focal achromatism metalens. As for bifocal metalens, Li et al. [32] designed a broadband transverse bifocal metalens in mid-infrared wavelength. Ou et al. [33] demonstrated longitudinal metalens in mid infrared wavelength by using propagation phase in x- and y-axis. For a longitudinal bifocal metalens, chromatic dispersion in broadband wavelength will continuously change the focal lengths, leads to overlapping of the focal spots, resulting in low accuracy and weak performance of the metalens. Therefore, broadband achromatic in longitudinal metalens in visible range is urgently needed in practical fields, for example, machine vision [36].
Here, a transmissive broadband achromatic longitudinal bifocal metalens (BALBM) with polarization sensitivity has been proposed. The designed BALBM is of single layer and adopts single nanofin in each unit cell. TiO2 is employed for its low loss and high refractive index in the working wavelength. The BALBM is designed by combing PB phase with propagation phase. By changing the chirality of the incident beam, the focal points will appear at different focal length longitudinally. Simulation results show that, over the continuous wavelength 500-700 nm, the BALBM reduced 81% and 83% of the chromatic focal length shift for LCP and RCP incident, respectively. The proposed BALBM is expected to bring advances to bifocal metasurfaces in application areas including microimaging [32], VR [29], and optical storage [37].
2. Principle and design of BALBM
2.1 Principle of longitudinal bifocal metalens
The designed bifocal metalens consists of rectangular nanofins with different orientations on the substrate plane x-y, as shown in Fig. 1(a). The phase profile of an ideal mono-focal focusing spot can be expressed as follows [29,38–40]:
Fig. 1. (a) Schematic of the designed longitudinal bifocal metalens plane (a quarter of the metalens). The metalens consists of nanofins distributed with different orientations. (b) Schematic diagram of the working procedure of the designed longitudinal bifocal metalens. The metalens will excite RCP/LCP light which focus at ${\textrm{F}_\textrm{L}}$/${\textrm{F}_\textrm{R}}$, respectively for the incident LCP/RCP light.
To realize longitudinal bifocal metalens controlled by the polarization of incident light, we use PB phase for beam converging. When incident LCP light passes through the nanofin, the incident light will be divided into two parts with opposite helicity, one part is in the same polarization state with the incident light, and the other part is excited in cross-polarization state compared with the incident light carrying an additional phase shift $2\theta $. Therefore, the excited transmission light with additional phase shift $2\theta $ given by PB phase can be properly designed and controlled by the location $(x,y)$ and orientations $\theta $ of nanofins. Figure 1(b) illustrates the working procedure of the designed bifocal metalens. According to Eq. (1), for the designed longitudinal bifocal metalens, we introduced a cross commixed sequence distribution (CCSD) factor $\sigma $ into the phase profile function. The phase profile of designed longitudinal bifocal metalens can be written as [23]:
2.2 Principle of BALBM
It can be seen from Eq. (2) that ${f_\textrm{L}}$ and ${f_\textrm{R}}$ are wavelength-dependent. Assuming that the designed longitudinal bifocal metalens works in a broadband wavelength incident. For constant phase profile, when the incident wavelength increases, the focal lengths of the metalens will shift to shorter distance. Similarly, when the incident wavelength decreases, the focal lengths of the metalens will shift to longer distance. The reason is that interference makes the wavefronts of the longer wavelength electromagnetic waves more concentrate, demonstrated with a shorter focal length. Considering the application of longitudinal bifocal metalens, the metalens’ performance will be affected seriously when it is working in a broadband wavelength. Hence, achromatic study of longitudinal bifocal metalens is crucial. To achieve a BALBM, Eq. (2) should be modified by inducing a phase shift factor $\Delta \varphi (R,\lambda )$ and a phase compensation factor ${\varphi _{\textrm{comp}}}(R,\lambda )$.Take the achromatic aberration of focal point ${\textrm{F}_\textrm{L}}$ generated by LCP incident as example, here we assume that the incident wavelength is ${\lambda _{\max }}$ first. Figure 2(a) shows that when LCP incident, the $\sigma $ is even. The incident light passes through the arbitrarily point P$({x,y} )$ on a PB metalens and focused on the focal point ${\textrm{F}_\textrm{L}}$ by the phase function ${\varphi _\sigma }(R,{\lambda _{\max }})$. The focal length is ${f_\textrm{L}}$. Figures 2(b), 2(c) and 2(d) are schematics show the procedure of achromatic aberration. As shown in Fig. 2(b), when the incident light is of broadband range $[{\lambda _{\min }},{\lambda _{\max }}]$, chromatic aberration $\Delta \varphi (R,\lambda )$ will appear because of the continue phase profile change between ${\lambda _{\textrm{max}}}$ and ${\lambda _{\textrm{min}}}$. The $\Delta \varphi (R,\lambda )$ is represented by the gray shaded areas, which can be expressed by:
Fig. 2. Schematic of the principle of achromatic aberration when LCP incident. (a) Assume that the incident wavelength is ${\lambda _{\max }}$, the incident light passes through the point P$({x,y} )$ on a PB metalens and focused on the focal point ${\textrm{F}_\textrm{L}}$ by the phase function ${\varphi _\sigma }(R,{\lambda _{\max }})$. (b) Phase profile for the PB metalens in broadband wavelength, phase shift $\Delta \varphi (R,\lambda )$ is generated under broadband wavelength incident $[{\lambda _{\min }},{\lambda _{\max }}]$. (c) Phase compensation factor ${\varphi _{\textrm{comp}}}(R,\lambda )$ is induced to compensate the phase shift $\Delta \varphi (R,\lambda )$. (d) Schematic of ${\varphi _{\textrm{BALBM}}}(R,\lambda )$, which is phase profile of the BALBM, consists of ${\varphi _\sigma }(R,{\lambda _{\max }})$, $\Delta \varphi (R,\lambda )$ and ${\varphi _{\textrm{comp}}}(R,\lambda )$.
The procedure of achromatic aberration of ${\textrm{F}_\textrm{R}}$ is similar to that of ${\textrm{F}_\textrm{L}}$.
For ${\varphi _{\textrm{comp}}}(R,\lambda )$, we use propagation phase which provided by nanofins with the same height but different cross section. Different from using the nanofins with complex structure [28], multiple atoms [29,39] and unequal height [41], here, considering the convenience of fabrication, we use single nanofin in each unit cell, length L and width W are the only two parameters we use to modify in search of appropriate compensate phase in the given visible wavelength range.
Thus, the total phase profile of Eq. (4) is composed of the excited PB phase given by the distribution and the orientation of the nanofin, the phase shift caused by chromatic aberration, and the propagation phase provided by the geometric cross section variation of the nanofins.
2.3 Design of unit cells
TiO2 is selected as the material for nanofins owing to its high refractive index and low abortion loss in the visible wavelength. High refractive index of the nanofins helps confining the electromagnetic waves within the nanofins, so the coupling of electromagnetic wave between adjacent nanofins will be suppressed. Also, the incident light can get optical path extended when it passes through limited nanofin’s height. Moreover, the high refractive index supports more modes in the Fabry-Perot cavity, benefiting the expansion of the phase compensation value range [40]. SiO2 is chosen as the material for the substrate. SiO2’s low refractive index can help the substrate subdue the shutter/reflection of incident light, thereby enhance the efficiency of metalens. In this work, the anisotropic TiO2 nanofins stand on the SiO2 substrate square lattice, as shown in Fig. 3(a). The height of the nanofins H should be tall enough to provide sufficient phase accumulation. However, considering the actual fabrication situation that electron beam lithography technology is used to etch the nanofins, the nanofins with the same height can be fabricated more easily, the height H of the nanofins is set to be fixed. Further considering the actual fabrication capacity limitation, to avoid the high aspect ratio of the nanofin, the height value shouldn’t be too high. The height of nanofins and substrate are set as 800 nm and 480 nm, respectively. The PB phase for converging the light into two focal spots is modified by the orientations of the nanofins , as shown in Fig. 3(b). The propagation phase which provides phase compensation is tuned by the length L and width W of the nanofins, the period U is set to be 350 nm to meet with Nyquist sampling criterion, as shown in Fig. 3(c).
Fig. 3. Schematic illustration of the designed unit cell. (a) Perspective view of the unit cell, showing height $H$ of the nanofin. (b) Top view of the unit cell, showing the rotation angle $\theta $ of the nanofin that leads to PB phase. (c) Top view of the unit cell, showing the length L and width W of the nanofin, and the unit cell period.
The structure characteristics of the nanofins are scanned by finite difference time-domain (FDTD) method to calculate the dielectric nanofins’ amplitude, phase and polarization response to the electromagnetic wave. The nanofins can be considered as an intercept of the waveguide, and the energy oscillation in the nanofins can be regarded as multi-resonance of the electromagnetic field in Fabry-Perot cavity. To verify the nanofins’ ability of energy-constrain, the distribution of resonance energy in the nanofins is analyzed by the magnetic energy field amplitudes inside the nanofins. The x-z plane of magnetic energy field is monitored. Figure 4 illustrates the simulated normalized magnetic field amplitudes of resonant modes in two representative scanned nanofin geometric sizes (a)$L = 195\textrm{nm}$, $W = 125\textrm{nm}$ and (b)$L = 205\textrm{nm}$, $W = 95\textrm{nm}$. The gray dotted boxes represent the outlines of the TiO2 nanofins in L-H facade. It is shown in Fig. 4(a) that, in the visible wavelength range 500-700nm, the number of antinodes becomes stable as the increase of incident wavelength. The same trend can also be seen in Fig. 4(b) which means the normalized magnetic field distribution inside the nanofins gradually stabilized as wavelength increase, and the energy is strongly confined inside the nanofins. Thus, the energy coupling between the adjacent nanofins can be ignored, complied with the Fabry-Perot cavity multi-resonance model. Therefore, the largest aspect ratio of the nanofin in our design is set to be 20:1 to make sure the multi-resonance in the nanofins, so the length L and width W were scanned from 40nm to 295nm in steps of 5nm in wavelength range 500-700nm.
Fig. 4. Magnetic field amplitudes of two representative sizes. The gray dotted boxes represent the TiO2 nanofins with (a) $W$=125 nm, $L$=195 nm, (b) $W$=95 nm, $L$=205 nm.
In the scanning of nanofins geometric size, periodic conditions are applied in the x and y direction, the perfect matched layer (PML) condition is applied in the z direction in consistent with the light propagation direction. Broadband LCP from 500 nm to 700 nm is used as incident light. The meshing step is set as 18 nm. The propagation phase and polarization conversion efficiency of each nanofin’s geometric size were recorded. The polarization conversion efficiency is defined as the ratio of the RCP light output power over the total output light power. Figures 5(a) and 5(b) are phase spectra and polarization conversion efficiency of two selected nanofins. Here, the absolute compensate phase of each nanofin geometric size is calculated by the phase difference within the wavelength range 500-700 nm. Note that the phases in Fig. 5 changes linearly with the variation of frequency. Similarly, the absolute compensate phases are also in linear relationship with wavelength. Thus, the ${\varphi _{\textrm{comp}}}(R,\lambda )$ of each position in Fig. 2(c) can be met by the corresponding nanofin’s geometric size.
Fig. 5. Phase and polarization conversion efficiency responses to broadband wavelength of two representative nanofin sizes (a) $W$=125 nm, $L$=195 nm, (b) $W$=95 nm, $L$=205 nm.
When looking for the nanofin structures an evaluation function is used: the priority is to ensure that the compensating phase of the target is accurate to ensure achromatic, and then the polarization conversion efficiency should be more than 45%. Based on the phase and polarization conversion efficiency responses to the incident light in different nanofin sizes, 15 geometric parameters of nanofins are selected, as shown in Table 1. The absolute compensate phase range is 85-297°. The relative compensate phase is the value change relative to the starting absolute compensating phase 85°. The phase compensation value of each nanofin’s geometric size is 15°, so the maximum relative phase compensation provided by the nanofin’s geometric size is 225°. The nanofin sizes with corresponding relative compensate phase in Table 1 were adopted to match the ${\varphi _{\textrm{comp}}}(R,\lambda )$ in different positions. In this way, the designed BALBM’s maximum achromatic capacity is 0-225°.
Table 1. Phase and polarization responses to the nanofins’ sizes
Table 2. Comparation of the designed BALBM and other previous works
3. Simulation and discussions
3.1 Simulation and result discussions
Following the above rules, a BALBM for LCP and RCP incidences with different focal points ${\textrm{F}_\textrm{L}}$ and ${\textrm{F}_\textrm{R}}$ is designed. The BALBM tuned by the polarization state of the incident light is designed by putting the nanofins on two overlapped metalenses corresponds to ${\sigma _{\textrm{odd}}}$ or ${\sigma _{\textrm{even}}}$ positions in Eq. (2), so the two metalenses possess a same diameter of 17.85μm. The distance between the two foci is designed as 10μm. The Numerical Apertures (NAs) of ${\textrm{F}_\textrm{L}}$ and ${\textrm{F}_\textrm{R}}$ are set as 0.25 and 0.16, respectively. The required ${\varphi _{\textrm{comp}}}(R,\lambda )$ range of ${\textrm{F}_\textrm{L}}$ and ${\textrm{F}_\textrm{R}}$ are calculated to be 229$^\circ $ and 149$^\circ $. The nanofins are arranged to their positions with orientations given by the first part in Eq. (4). The nanofins geometric sizes are set according to Table 1 to provide relative compensate phase. Figures 6(a) and 6(b) show the layout and detail of the designed BALBM.
Fig. 6. (a)Layout of the designed BALBM, scale bar is 1μm. (b)Detail of the designed BALBM, scale bar is 1μm.
Figure 7 shows the simulation result of the designed metalens performed by FDTD method. In the simulation of the entire metalens, the perfect matched layer (PML) condition is applied in the x, y, and z direction. The maximum meshing step is 20 nm. We first simulated the BALBM when LCP incident. Broadband LCP from 500 nm to 700 nm is used as incident light. x-z and y-z monitors with multi-frequency and cover 1.3 times of ${f_\textrm{L}}$ are placed across the center of the BALBM O (0,0). Focal point is defined as the point at which the maximum power locates on the z-axis. After the first simulation, the locations of ${\textrm{F}_\textrm{L}}\textrm{s}$ in each frequency are recorded. Then we put monitors on x-y plane where the ${\textrm{F}_\textrm{L}}\textrm{s}$ located and run the simulation again. Note that the co-polarized part with the input light has been filtered to eliminate the influence of the co-polarized light in transmittance as background noise. The procedure of simulation when RCP incident is similar to that of LCP incident. For comparation, a PB metalens is designed in the same time. The designed PB metalens consists of identical nanofins with diverse orientations based on Eq. (2). The normalized intensity distribution in the x-z plane of PB metalens among selected wavelength range is shown in Fig. 7(a) and 7(b), revealing large chromatic dispersion within wavelength band 500 nm to 700 nm. Figure 7(a) shows the focal length shift of ${\textrm{F}_\textrm{L}}$ under wavelength range 500 nm to 700 nm, it can be observed that the focal point moves to -z direction as the wavelength increases. In Fig. 7(b), the focal point ${\textrm{F}_\textrm{R}}$ presents the same shift to -z direction while the change of focal length ${f_\textrm{R}}$ is more obvious than that of ${f_\textrm{L}}$, it is because the ${\varphi _{\textrm{comp}}}(R,\lambda )$ of ${\textrm{F}_\textrm{R}}$ is larger than that of the ${\textrm{F}_\textrm{L}}$’s in k-space. Figure 7(c) and 7(d) show the achromatic result of the designed BALBM in normalized intensity within the x-z plane. It can be observed that the focal lengths${f_\textrm{L}}$ of ${\textrm{F}_\textrm{L}}$ and ${f_\textrm{R}}$ of ${\textrm{F}_\textrm{R}}$ almost remain unchanged with the wavelength variation, indicating the achromatism function of the BALBM.
Fig. 7. The normalized intensity distribution in the x-z plane of PB metalens with focal spot (a) ${\textrm{F}_\textrm{L}}$ shift when LCP light incidence. (b)${\textrm{F}_\textrm{R}}$ shift dramatically when RCP light incidence. BALBM with focal spot (c) ${\textrm{F}_\textrm{L}}$ almost remain unchanged when LCP light incidence. (d) ${\textrm{F}_\textrm{R}}$ almost remain unchanged when RCP light incidence among the selected wavelength range.
The variances of the focal lengths in wavelength range 500-700nm are analyzed, as shown in Fig. 8. For PB metalens, it can be seen in Fig. 8(a) that the focal length of ${\textrm{F}_\textrm{L}}$ moves from 37.5μm to 28.17μm. The chromatic dispersion reached 9.33μm, which is 24.89% compared with the focal length at initial wavelength 500nm. The focal length shift of ${\textrm{F}_\textrm{R}}$ is even larger, decreases 11.41μm from 53.2nm to 39.46nm with a wavelength shift 21.45% compared with the initial focal length at wavelength 500nm. Note that the focal length of ${\textrm{F}_\textrm{L}}$ at 500nm is equivalent to that of ${\textrm{F}_\textrm{R}}$ at 700nm wavelength, showing the chromatic influence on the longitudinal bifocal metalens performance. The focal length shift for achromatic metalens are shown in Fig. 8(b), in the working waveband, the focal length of ${\textrm{F}_\textrm{L}}$ changes only 1.75μm from 27.81μm to 26.06μm while a 1.92μm change from 37.73μm to 35.8μm is recorded for ${\textrm{F}_\textrm{R}}$. The BALBM’s two focal lengths ${\textrm{F}_\textrm{L}}$ and ${\textrm{F}_\textrm{R}}$ shift only 6.21% and 4.8% compared to their initial focal lengths, respectively. No overlap of the focal points is observed, implying that the chromatic influence is eliminated by the BALBM to a great extent.
Fig. 8. Simulated focal length variation versus incident wavelength change of (a) PB metalens and (b) BALBM metalens.
The focusing efficiency and full width at half maximum (FWHM) of the BALBM’s ${\textrm{F}_\textrm{L}}$ and ${\textrm{F}_\textrm{R}}$ are shown in Fig. 9. The focusing efficiency is defined by the ratio of the power of focal point (3 times the FWHM range) to the total incident beam power. The maximum focusing efficiencies are 34.8% for ${\textrm{F}_\textrm{L}}$ and 42.85% for ${\textrm{F}_\textrm{R}}$, which are not as high as the metalenses employed polarization-insensitive methods [37]. The low focusing efficiency is caused by two reasons. On the one hand, the bifocal metalens split the incident power to each focus, so for each focus the focusing efficiency is no higher than 50%. The unfocused part of the incident beam becomes background noise which affects the focusing efficiency. On the other hand, the polarization conversion efficiencies of the nanofins change when the incident wavelength change, which means the nanofins are not perfect half wave plate at all the wavelengths. To increase the focusing efficiency, we can increase the polarization conversion efficiency of nanofins by improving the anisotropy of the nanofins, for example, use the nanofins with larger height while designing, or we can select the nanofins with higher polarization conversion efficiency at the cost of achromatic capability of the BALBM. However, the focusing efficiencies showed stable trends and the average focusing efficiencies are 26% for ${\textrm{F}_\textrm{L}}$ and 25.85% for ${\textrm{F}_\textrm{R}}$, higher than the average efficiency in Ref. [32].The FWHMs of the focal points ${\textrm{F}_\textrm{L}}$ and ${\textrm{F}_\textrm{R}}$ are calculated to be $1.78\lambda - 1.99\lambda $ and $2.26\lambda - 2.62\lambda $, showing the focal diameters are effectively controlled in the working wavelengths.
Fig. 9. Simulated focusing energy efficiencies and FWHMs for (a) ${\textrm{F}_\textrm{L}}$ and (b) ${\textrm{F}_\textrm{R}}$ of BALBM versus wavelength.
The imaging characteristic of the BALBM is illustrated in Fig. 10. Figures 10(a) and 10(b) show the focal plane parameters of ${\textrm{F}_\textrm{L}}$ and ${\textrm{F}_\textrm{R}}$ when LCP and RCP incidence. In Fig. 10, the upper part shows the point spread function (PSR) of the light beam and the lower part is the intensity profile comparation between the simulated BALBM focal point and ideal Airy spot in the working waveband. The upper part in Fig. 10(a) and 10(b) shows that the PSF maintains good symmetry. The lower part in Fig. 10(a) and 10(b) shows that in the working waveband, the intensity distributions of the BALBM are of highly similarity with that of ideal Airy disk, proving the high focusing performance of the proposed achromatic metalens. Furthermore, the background noise decreases as the wavelength increases, it is caused by the increasing of the nanofins’ effective refractive index which lead to the effective optical path grows closer to the height of the nanofin, thus the multi-resonance stability of the electromagnetic wave inside the nanofin is enhanced, in consistent with Fabry-Perot cavity model in Section 2.3.
Fig. 10. Horizontal cuts of the focal plane and the intensity curve compared with ideal Airy spot for (a) ${\textrm{F}_\textrm{L}}$ and (b) ${\textrm{F}_\textrm{R}}$. The solid blue line is the intensity profile of BALBM while the dashed black line is the intensity profile of ideal Airy spot representing the diffraction limit of given device diameter and wavelength.
3.2 Comparation with previous works
The characteristics of the proposed BALBM and the bifocal metalens in Refs. [6,32,42–46] are compared in Table. 2. The mechanism, nanofin material, working wavelength, polarization controllable, and achromatism are compared. Firstly, compared with metal material in Refs. [42,43], dielectric material, which Refs. [6,32,44–46] use, has advantages of high transmittance and integrability. In Ref. [44], bifocal metalens is realized by the propagation phase provided by cylindrical nanorods in holography application. On the other hand, Refs. [6,32,45,46] reported polarization controllable bifocal metalens, that is, the focal points can be tuned by changing the polarization state of the incident light. References [6,46] adopt the hybrid phase of PB and propagation phase, so they are of high focusing efficiency while possessing polarization controllability. However, Refs. [6,44,–46] are all based on single wavelength. When the incident light is broadband light, chromatic aberration will affect the devices’ performance by shifting the focal points. Reference [32] is a typical work of bifocal achromatic metalens. Similar to the proposed BALBM, Ref. [32] first use the PB phase to focus the incident light into two foci, and then use the propagation phase to compensate the chromatic phase shift of the foci which is cause by the broadband incident light. The foci in Ref. [32] are distributed transversely. Compared with Ref. [32], the designed BALBM has advantages of solving the focal points’ overlapping problem in longitudinal bifocal metalens caused by the broadband incident light. Also, as the CCSD factor $\sigma $ is introduced for tuning the focal point by the incident polarization state, the proposed bifocal metalens can be regarded as the coaxial overlap of two metalenses with the same diameter, each metalens corresponds to one focal point. Thus, the phase profiles of FL and FR are smooth and the sampling intervals are uniform, thereby the BALBM possesses higher average focusing efficiency. Furthermore, the wavelength range Ref. [32] uses is mid-infrared wavelength while the BALBM is realized in the visible range. The BALBM demonstrates potential in the applications like microscopic imaging, optical tweezers, AR and other imaging applications.
4. Conclusion
In this work, a dielectric broadband achromatic longitudinal bifocal metalens has been proposed in visible waveband. Single layer and single nanofin with fixed height in each unit cell are adopted for the convenience of fabrication. The designed metalens is realized through combining PB phase with propagation phase. When the incident beam’s polarization state change, the focal point will locate at different designed longitudinal focal lengths. By simultaneously adjusting the length and width of the nanofins, compensation phases are imparted to offset the phase difference between the minimum and maximum wavelength. The designed metalens’ focal length variations are stabilized compared with the comparative metalens. The overlap phenomenon of the foci has been corrected by the proposed metalens. The proposed metalens and the design method will greatly advance the application fields like machine vision, VR, microimaging, and optical computed tomography.
Funding
Shanghai Leading Academic Discipline Project (S30502); National Natural Science Foundation of China (61975125).
Disclosures
The authors declare no conflicts 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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