Open Access
Add to BibSonomy
Abstract
Multicolor two-photon endomicroscopy has become a highly competitive tool for functional imaging in biomedical researches. However, to make the imaging system miniature and applicable for freely behaving animal brain activity, metalenses have received much attention in compact imaging systems. For high resolution multicolor imaging and maximizing fluorescence collection, there is a challenge metalenses faced to achieve large numerical aperture (NA) and focus the NIR excitation and VIS emission lights of multiple fluorophores to the same distance simultaneously because of the limitation of the group delay range of the meta-units. In this paper, we proposed a high NA and polarization-insensitive ultra-broadband achromatic metalens specifically for achromatically focusing the excitation and emission light of multiple fluorophores commonly used in neuroscience studies. TiO2 and Si meta-unit libraries composed of heights, widths and the corresponding phase and group delay were constructed, and the optimal meta-units were selected by particle swarm optimization algorithm to engineer the dispersion of metalens in the VIS band and NIR band, respectively. Combining dispersion engineering with spatial multiplexing, the proposed metalens achieved the maximal effective NA up to 0.8 and large achromatic bandwidth ranging from 500 nm to 1050 nm, which exhibited the coefficient of variation of focal lengths was only 3.41%. The proposed achromatic metalens could successfully achromatically focus different fluorescence with any polarization, which was suitable for most fluorophores. Our results firmly establish that the proposed metalens can open the door to high resolution and minimally invasive multicolor two-photon functional imaging in intravital deep brain.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Multicolor two-photon endomicroscopy imaging has been the method of choice in functional imaging of morphology, physiology, and cell-to-cell interactions in deep tissue [1–3]. The prerequisite for two-photon excitation of multiple fluorophores with different emission spectra and fluorescence signal collection is the near-infrared (NIR) excitation and the visible (VIS) emission lights achromatically focusing [4]. However, current multicolor two-photon endoscopic systems usually use cascading compound lenses to correct chromatic aberration, which increase the complexity of the systems and limit the reachable depth in the tissue [5]. Therefore, there is an urgent need for a simple and miniaturized focusing element with chromatic aberration correction capability to make multicolor two-photon imaging system more integrated and universally applicable.
In recent years, metalenses have attracted much interest because of their ultrathin dimension and novel capabilities in precisely controlling light wavefront by adjusting the geometrical parameters of meta-units. Various promising applications have been proposed, such as light beam shaping devices [6], polarization modulation devices [7], and compact waveguide couplers [8,9]. Because of the flexible design of meta-unit and ultrathin compact integration, metalenses have been a competitive candidate to replace conventional optical components in compact imaging systems [10,11]. Nevertheless, metalenses exhibit large chromatic aberration due to structural and material dispersion, which causes that the focal planes of the excitation and emission lights of multiple fluorophores lie far apart from one another in multicolor two-photon imaging [12,13]. Therefore, the imaging performance (e.g., imaging blur), efficient excitation-collection of fluorescence and high-quality dynamic functional imaging will be affected [4,14]. How to eliminate chromatic aberration between the NIR excitation lights and the VIS emission lights is significant in metalens-based miniaturized multicolor two-photon endomicroscopy imaging. Some researchers have demonstrated achromatic metalens at discrete wavelengths by means of cascading or spatial multiplexing technology [7,15,16]. Up to now, there have been extensive researches undertaken on designing broadband achromatic metalenses due to their superior practical applications. Table 1 summarized the important metrics (such as NA, material, working bandwidth, working mode, and polarization) of different broadband achromatic metalenses in previous work. At present, most of broadband achromatic metlenses with slightly low NA were designed based on single material at the particular wavelength especially in the visible range [17–20]. In addition, recent studies have focused on developing metalenses with the broadband achromatic focusing capabilities in the near-infrared spectrum [11,21,22]. Among them, the NA of metalens working in the wavelength range from 1470 nm to 1590 nm is even up to 0.81. However, it can only focus light of a given circular polarization, which suffered from polarization sensitivity. Moreover, broadband achromatic metalenses have been demonstrated to work spanning the visible and near-infrared, which is consistent with the excitation and emission waveband for the two photon biological imaging [23,24]. However, constraints in the range of group delay provided by the meta-units result in significant decrease in NA that obscures high resolution imaging. Consequently, the currently reported achromatic metalenses suffered from either limited operational bandwidth or low NA, and either incident polarization dependence or reflective work mode, which makes them unable to fully meet the demanding requirements of multicolor two-photon fluorescence imaging. Besides, it remains a huge challenge to achieve high NA and large operational bandwidth simultaneously due to the provided finite group delay range by meta-units [25–27]. Therefore, how to design a high NA and polarization-insensitive ultra-broadband achromatic metalens across the VIS emission band and the NIR excitation band working in transmission mode is still a tricky problem, which is essential for high resolution functional imaging in multicolor two-photon endomicroscopy system.
Table 1. Summary of performance metrics for broadband achromatic metalenses
Here, we proposed a polarization-insensitive achromatic metalens with high NA working in the continuous bandwidth from 500 nm to 1050 nm. The phase and group delay of various meta-units with different heights and widths were calculated. Then diverse TiO2 meta-unit library and Si meta-unit library were constructed, which can be used to engineer the dispersion in the VIS emission band and the NIR excitation band, respectively. The optimal meta-units were selected by particle swarm optimization algorithm and arranged in 12-sectors interleaving to comprise the ultra-broadband metalens with dual-band modulation function. As a result, achromatic focusing for the incident light with any polarization was achieved in the wavelength range from 500 nm to 1050 nm. The focal lengths all converged to a narrow range and the coefficient of variation of focal lengths was only 3.41%. The maximal effective NA was up to 0.8 and the transverse sizes of focal spots were fairly close to the Abbe diffraction limit. Besides, the fluorescent spots of most common fluorophores were obtained according to the two-photon excitation theory. Consequently, the proposed achromatic metalens can become an optimal optical component choice for miniaturized multicolor two-photon imaging system, which can open a new window of long-time and minimally invasive functional imaging of awake or freely moving animals brain activity.
2. Design of ultra-broadband achromatic metalens
2.1 Principles for broadband achromatic focusing
For a metalens that focuses a normal incident plane light to a point, the required phase profile of the metalens can be expressed as [21]:
The required relative phase profile φ(r, ωd) at the design frequency ωd determines a spherical wavefront, which is given by:
The higher-order derivative terms ∂φ(r, ω)/∂ω and ∂2φ(r, ω)/(2(∂ω)2) control the focal length shift of the metalens [18]. The second term ∂φ(r, ω)/∂ω represents the phase dispersion which is called group delay and is related to r and β as:
The third term ∂2φ(r, ω)/(2(∂ω)2) represents group delay dispersion which is equal to zero.
Several studies have proved that controlling phase and group delay of meta-units on metalens is an effective method to engineer the dispersion of the metalens over continuous wavelength range [11,20,21,23,24,28]. However, the required group delay range of metalens monotonically increases with its NA, and the product of the required group delay range with the operational bandwidth depends on the upper bound of the group delay range provided by meta-unit library. Thus, there is a tradeoff between the NA and operational bandwidth of broadband achromatic metalens. The design of metalens with high NA and large achromatic bandwidth requires a more diverse meta-unit library with large group delay modulation range.
For meta-unit based on propagation phase principle, its group delay linearly increases with the effective refractive indices and the height of the meta-unit. Due to the requirements of large group delay modulation range and low loss in both design bands, we chose titanium dioxide (TiO2) and silicon (Si) meta-unit with square cross-section to manipulate the wavefront of the VIS band and the NIR band, respectively, which ensure polarization insensitive operation at the same time [21,28]. The electromagnetic field is strongly confined within the meta-unit with high refractive indices, which enhances phase modulation ability. Moreover, the degree of freedom in height (H) and width (W) were unleashed to largely extend the upper bound of the group delay range provided by meta-unit library. The double regulation functions of heights and widths as well as dual-material opened up the possibility to create a large modulation range of group delay. By space multiplexing principle, we set TiO2 meta-units modulated the VIS emission band and Si meta-units modulated the NIR excitation band achromatic focusing in staggered arrangement to integrate dual-band achromatic function onto the same metalens [16,29]. As shown in Fig. 1 (a), the structure of 12-sectors interleaving allows for the realization of dual-band achromatic focusing, and further extends achromatic bandwidth. The combination of dispersion engineering and spatial multiplexing technology provides a new opportunity for simultaneously achieving high NA and large operational bandwidth.
Fig. 1. (a) Schematic illustration of broadband achromatic focusing in the VIS and NIR band based on the spatial multiplexing metalens. (b) The layout of the ultra-broadband achromatic metalens. (c) The inset illustrates meta-unit distribution details: TiO2 and Si meta-units with different heights and widths arranged in quadrilateral lattices. Blue sectors: the VIS emission band modulation area composed of TiO2 meta-units; red sectors: the NIR excitation band modulation area composed of Si meta-units.
2.2 Design of the achromatic metalens
The design of the achromatic metalens is organized into three major parts. First, meta-unit libraries including heights, widths and its corresponding phase and group delay were constructed by the parameter sweeps of TiO2 and Si meta-unit. Second, the optimal meta-units for all positions were selected from meta-unit libraries by the particle swarm optimization algorithm. Third, the optimal TiO2 and Si meta-units were set in staggered arrangement to comprise the ultra-broadband achromatic metalens.
2.2.1 Construction of meta-unit libraries
Various subclasses of meta-units have emerged and allowed for diverse phase and dispersion responses and polarization independence, such as annular pillars [21], concentric pillars [28] and even free-form meta-units [30–32]. In comprehensive consideration of computation resources and fabrication, the simple fourfold symmetry TiO2 and Si nanopillars with square cross-section on a silicon dioxide (SiO2) substrate were selected as meta-unit to locally modulate the wavefront of the excitation and emission lights. Fourfold symmetry structure not only guarantees the polarization insensitive operation of the broadband achromatic metalens, but also maximizes the filling factor (γ) range from 0 (no nanopillar) to 1 (width equals center-to-center distance), which plays a key role in increasing the phase and group delay coverage of meta-units [17]. The three-dimensional schematic diagrams of meta-units were shown in Fig. 2(a) and Fig. 2(e). The phase response of the meta-unit depends on the lattice period U and square nanopillar dimensions (height H and width W). The lattice period U of the TiO2 and Si square nanopillars were set as 0.3 µm and 0.4 µm, respectively, which define the sampling rate of the phase profile and must satisfy the Nyquist sampling criterion (U<λ/(2 NA)). Additionally, the lattice period U should be smaller than all wavelengths (across the design bandwidth) in free space to suppress higher diffraction orders [17].
Fig. 2. Characteristics of meta-unit libraries. (a) and (e) Schematics of TiO2 and Si square nanopillar on SiO2 substrate. (b) and (f) Linear relationship of phase respect to angular frequency for different dimension TiO2 meta-units and Si meta-units. Circle: actual phase of the meta-unit; Solid line: fitted phase curve, the slope represents meta-unit group delay. (c) and (g) The goodness of fit (R2 value) of each meta-unit phase curve. (d) and (h) Phase-group delay libraries of TiO2 meta-units (blue dots) and Si meta-units (red dots).
The phase spectrum of meta-units was calculated by the finite difference time domain (FDTD) simulation. The X-polarized plane wave was incident on meta-units from the SiO2 substrate along z-axis. To avoid the occurrence of the reflected electromagnetic waves, perfectly matched layers (PML) were applied to the z-direction. Periodic boundary conditions were employed in the x- and y-directions to mimic a uniform array of meta-units with a given diameter and periodicity. The mesh grid size was set to 25 nm. A large number of parameters composed of different heights and widths of meta-units under different angular frequencies were swept to build a library including the values of phase and group delay. In the concerned wavelength range of 500 to 750 nm, the nested sweep was created by changing the width value of TiO2 meta-unit within the range of 50 to 300 nm and the height value within the range from 500 to 1700nm. In the concerned wavelength range of 800 to 1000 nm, the nested sweep was created by changing the width value of Si meta-unit within the range of 50 to 400 nm and the height value within the range from 500 to 1700nm. For each simulation under sweep parameter, the far-field electric field distribution of meta-units was normalized to the field with substrate only. The phase spectrum of meta-units was obtained from the recorded normalized electric field. Figure 2(b) and Fig. 2(f) show that the phase spectrums of TiO2 and Si meta-units with different parameters are almost linearly associated with the angular frequency over a continuous range, respectively. Based on least-squares regression analysis, the group delay of meta-units was calculated by linearly fitting the phase spectrum, which can be defined as the slope of the linear fitting curve. The goodness of fit (R2 value) of most meta-units is greater than 0.9 as shown in Fig. 2(c) and Fig. 2(g), which proves that the obtained group delay values are accurate. The meta-units with R2 value of less than 0.9 were dropped and a group of meta-units with high R2 value (>0.9) were collected for constructing meta-unit libraries, which were shown in Fig. 2(d) and Fig. 2(h). In Fig. 2(d) and Fig. 2(h), each dot represents a specific meta-unit with the corresponding phase and group delay. Then, the visualization of the available phase and group delay range of the TiO2 meta-unit library and the Si meta-unit library can be provided, which increases the group delay range of TiO2 meta-unit library and Si meta-unit library up to 17 fs and 30 fs. To make full use of the constructed libraries and reach limitation of the achievable parameters for achromatic metalens, the upper bound of the achievable parameters can be obtained when the required group delay range is equal to group delay range reached by the constructed meta-unit library. Thus, by calculating the required group delay range according to Eq. (3) and deriving the upper bound of the achievable parameters, the constructed meta-unit libraries allow basically realizing the required group delay of a metalens with a diameter of 21.6 µm when the designed NA is 0.8.
2.2.2 Selection of the optimal meta-units
In order to design the metalens with a diameter of 21.6 µm and NA of 0.8 based on the constructed meta-unit library, how to find the optimal meta-units from the meta-unit library to fulfil the required phase and group delay at each position of the metalens is intrinsically an optimization problem. Therefore, in this paper, the particle swarm optimization algorithm was utilized to find an optimal solution for C0 and β as well as select the optimal meta-units from the meta-unit library. To make the required phase response match with the phase response given by a meta-unit, C0 and β were optimized as the position vectors of the particle. The sum of absolute phase differences ($\Delta {\Phi _{\textrm{total}}}$) between the required phase (φrequired) and the actual phase (φactual) provided by the selected meta-units was taken as the fitness function to evaluate the fitness value of C0 and β [33]. The fitness function can be expressed as:
In each iteration process, a combination of C0 and β values was generated through learning and evolution operations. The required phase and group delay were calculated by putting the generated C0 and β values into Eq. (5) and Eq. (6). Then, the meta-units whose actual phase and group delay were closest to the required phase and group delay were chosen. The meta-units with filling factor of 1 were excluded to avoid coupling effect among adjacent meta-units. $\Delta {\Phi _{\textrm{total}}}$ was calculated and acted as the fitness value of a combination of C0 and β values in the current iteration. This iteration process would continue until the combination of C0 and β values with minimum fitness value $\Delta {\Phi _{\textrm{total}}}$ appeared and the change in $\Delta {\Phi _{\textrm{total}}}$ converged. Figure 3(a) and Fig. 3(c) show $\Delta {\Phi _{\textrm{total}}}$ as a function of number of iterations in the VIS band and NIR band, respectively. It can be seen that $\Delta {\Phi _{\textrm{total}}}$ changes with increasing number of iterations. and tends to converge to a constant after 1000 iterations. So the optimal solution for C0 and β with minimum fitness value and the optimal meta-units had been identified after 2000 iterations. The values of C0 and β and the finally selected meta-units in the last iteration were chosen as the optimal solution and the optimal meta-units. The combinations of C0 and β values were optimized to be 2.2981, 0.2220 and 3.5426, 1.5865 in the design of VIS and NIR band achromatic focusing, respectively, which can be used to calculate the final required phase and group delay by Eq. (5) and Eq. (6). The actual values of phase and group delay were provided by the optimal TiO2 and Si meta-units in the last iteration. Figure 3(b) and Fig. 3(d) illustrate the comparison of phase, group delay provided by TiO2 meta-unit and Si meta-unit libraries, required values and actual values. The results show that the optimal meta-units can basically realize the final required phase and group delay, which proves the effectiveness of the algorithm.
Fig. 3. (a) and (c) The sum of absolute phase differences as a function of the number of iterations in designing process of achromatic focusing the VIS band and the NIR band, respectively. (b) and (d) The comparison of the final required phase, group delay (black stars), the actual values (green dots) provided by the final selected TiO2 and Si meta-units, TiO2 meta-units (blue dots) and Si meta-units (red dots) libraries.
2.2.3 Arrangement of the optimal meta-units
We set the optimal TiO2 meta-units and Si meta-units in 12-sectors staggered arrangement to comprise the ultra-broadband achromatic metalens, which had a diameter of 21.6 µm, and the designed focal length of 10.4 µm. A schematic of the metalens composed of the optimal meta-units was shown in Fig. 1(b). The red sectors and the blue sectors could modulate the excitation and emission lights to focus achromatically on a tight spot, respectively. In the construction of the proposed metalens, the influence of coupling effect caused by the filling factor (γ) had been taken into account. The maximum width values of the optimal TiO2 and Si meta-units for constructing the proposed metalens were 280 nm (γ ≈ 0.933) and 290 nm (γ = 0.725), respectively. Figure 4(a) and Fig. 4(b) show the normalized magnetic field intensity profiles of TiO2 meta-units with width of 280 nm at λ = 500 nm and Si meta-units with width of 290 nm at λ = 1000 nm, respectively. The optical energy was confined inside the meta-units, which indicated the weak coupling between the adjacent meta-units. The dual-band achromatic focusing function was integrated onto the same metalens, which allowed for better implementation of large achromatic bandwidth.
Fig. 4. (a) The top and side views of the normalized magnetic field intensity at λ = 500 nm (width of 280 nm). The dashed white frames depict the boundaries of the TiO2 meta-unit. (b) The top and side views of the normalized magnetic field intensity at λ = 1000 nm (width of 290 nm). The dashed white frames depict the boundaries of the Si meta-unit.
To prove the validity of the actual phases realized by the optimal meta-unit, Fig. 5 shows the comparison between the actual phases provided by the optimal TiO2 and Si meta-units and the final required phases at sampled wavelengths of 550, 650, 750, 850, 950 and 1050 nm. The final required phases were gotten by taking the wavelength and the optimal values of C0 and β into Eq. (3). The actual phases of the optimal TiO2 and Si meta-units were obtained from the TiO2 and Si meta-unit libraries, respectively. Figure 5(a)-(c) and (g)-(i) show the comparison between the actual phases (top half) and the required ideal phases (bottom half) on half of the designed achromatic metalens at sampled wavelengths of 550 nm, 650 nm, 750 nm, 850 nm, 950 nm and 1050 nm, respectively. At the sampled wavelength, the actual phase distributions showed good agreement with the ideal phase distributions, which indicated the accuracy of the actual phases. Moreover, the actual and ideal phases were extracted along the radial direction across the metalens. Figure 5(d)-(f) and (j)-(l) depict the comparison between the actual phases (red circles) and the required ideal phases (blue curves) at each radial coordinate across the metalens at sampled wavelengths of 550 nm, 650 nm, 750 nm, 850 nm, 950 nm and 1050 nm, respectively. It can be seen that the actual phases are very close to the required phase curve, which further demonstrates the potential of the broadband achromatic focusing performance of metalens composed of these selected meta-units.
Fig. 5. (a)-(c) and (g)-(i) The comparison between the actual phases (top half) provided by the optimal meta-units and the final required ideal phases (bottom half) on half of the designed achromatic metalens at sampled wavelengths of 550 nm, 650 nm, 750 nm, 850 nm, 950 nm and 1050 nm respectively. (d)-(f) and (j)-(l) The comparison between the actual phases (red circles) and the required ideal phases (blue curves) at each radial coordinate across the metalens at sampled wavelengths of 550 nm, 650 nm, 750 nm, 850 nm, 950 nm and 1050 nm respectively.
We proposed the prospect for experimental fabrication processes of the proposed achromatic metalens based on the consideration of spatial multiplexing and difference of height. Firstly, according to the designed pattern of metalens, the photoresist is exposed by stimulated emission depletion inspired two-photon polymerization (STED-TPP). Through development, the photoresist mold with the complementary desired square holes is fabricated [34,35]. Secondly, the six-sector SiO2 sheet masks spaced 30° apart are processed to separate the deposition area and adjacent sectors. The Si material is deposited in the holes of the photoresist mold using the plasma enhanced chemical vapor deposition (PECVD) technique after one SiO2 sheet mask is placed on the TiO2 sectors to reveal Si deposition area. Then, the first SiO2 mask is removed. Subsequently, TiO2 material is deposited in the holes of the photoresist mold by atomic layer deposition (ALD) technique after another same SiO2 sheet is placed on the Si sectors to reveal TiO2 deposition area. The photoresist mold filled with TiO2 and Si material is obtained after removing the second mask. Thirdly, the SiO2 layer is attached to the top-side of the filled photoresist mold by using adhesive, which is used as the substrate of the meta-unit. Afterwards, the whole mold is flipped. Consequently, the preliminary model of the proposed achromatic metalens inside photoresist mold is achieved.
3. Performance characterizations and analysis
3.1 Performance of ultra-broadband achromatic focusing
The focusing characteristics of the proposed metalens were calculated by using the FDTD method at different incident wavelengths with X-polarized plane wave along z-axis. PML was employed as the boundary condition in the x-, y- and z- directions. The mesh grid size was set to 25 nm. We obtained point-spread functions of the proposed metalens in both transverse and longitudinal planes at wavelengths ranging from 500 to 1050 nm, respectively. Figure 6(a) shows the normalized intensity (|E|2) distribution of the proposed metalens in the axial plane (y–z cross section) at the selected wavelengths of 500, 550, 600, 700, 800, 900, 1000 and 1050 nm. It can be seen that the incident beams with different wavelengths in the range of 500–1050 nm were focused at almost the same position (z = 10.4 µm). Furthermore, we can see parasitic focal spots for wavelengths longer than 700 nm and an elongation of the depth of focus (DOF) for wavelengths longer than 1000 nm. This may be caused by the near-field coupling between adjacent meta-units and phase errors between the actual phase realized by the selected meta-units and the required one. The normalized intensity distributions in the focal planes (x–y cross section) at different wavelengths and their corresponding horizontal cuts of focal spots were plotted in Fig. 6(b) and Fig. 6(c). The focal intensity distribution results show nearly diffraction-limited focusing for all wavelengths with no obvious distortion. Besides, it can be seen that residual unwanted light spots regularly distributed near the focal spot, which was induced by the space multiplexing method. Nevertheless, there was no higher-order focal point whose intensity exceeded the main focal point in the axial plane. Therefore, the cross-talk among the two bands was weak, which had negligible effect on two-photon fluorescence imaging.
Fig. 6. (a) Normalized intensity distributions in the axial plane (y−z cross section) at selected wavelengths. (b) Normalized intensity distributions in the focal plane (x–y cross section) at selected wavelengths. (c) The intensity profile along with the horizontal cutting through the center of the focal spots at selected wavelengths.
The distance from zero point to the peak value of |E|2 at z-axis was regarded as the actual focal lengths of the proposed metalens at selected wavelengths, which is shown in Fig. 7(a). It can be seen that the actual focal lengths slightly shift with respect to the designed focal length (f = 10.4 µm). We attributed this phenomenon to the slight mismatch between the required group delay dispersion and the actual group delay dispersion realized by the selected meta-units. Since the relationships between phase and angular frequency were not completely linear for the meta-units in constructed libraries, a better match between the actual group delay dispersion and the required group delay dispersion cannot be implemented. The statistical concept of coefficient of variation is introduced to better evaluate the focal length fluctuation at different wavelengths [24]:
where MN is the average focal length, and SD is the standard deviation. The CV for the proposed metalens is derived to be 3.41%, which is within the allowed scope (5%) of the international standard of chromatic aberration. Therefore, focal length fluctuation of the proposed metalens over the entire continuous bandwidth can be allowed. The actual full-width at half-maximums (FWHMs) of the focal spots in Fig. 6(c) were plotted in Fig. 7(b). The actual FWHMs of the proposed metalens were 325, 375, 400, 475, 550, 575, 600 and 625 nm at the selected wavelengths of 500, 550, 600, 700, 800, 900, 1000 and 1050 nm, respectively. Figure 7(b) shows that the comparison between the actual FWHM of the focal spot and the theoretical limit FWHM. The focal spots were at or below the diffraction limit for the entire operational wavelength range, which resulted from the cross-talk impact introduced by spatial multiplexing segmentation. So the weak sidelobes near the main focal spot appeared and slightly dispersed the intensity of the main focal spot. The corresponding NAeffs (the effective NA and the FWHM are related as FWHM = 0.514λ/NAeff) were 0.79, 0.75, 0.77, 0.8, 0.75, 0.8, 0.85 and 0.86, respectively. Thus, continuous diffraction-limited focusing in the range of 500-1050 nm was achieved, which proved achromatic ability in ultra-broadband range. The focusing efficiency is defined as the ratio of the power passing through a 10-µm diameter circular aperture at the focal plane to the total power of incident light [36]. The focusing efficiency of the proposed metalens shown in Fig. 7(c) was 10.9%, 11.8%, 14.2%, 14.8%, 16.75%, 19.64%, 18.1% and 16.1% at the selected wavelengths of 500, 550, 600, 700, 800, 900, 1000 and 1050 nm, respectively. Since a single material can hardly maintain high refractive indices and high transmittance in both VIS and NIR bands, it is difficult to meet the requirement of dispersion engineering in a continuous and large wavelength range. TiO2 and Si have the high refractive indices and high transmittances in the VIS and NIR band respectively. Therefore, two types of materials are used to construct the meta-unit library with a large modulation range of phase and group delay. Due to spatial multiplexing segmentation, the focusing efficiency of the proposed metalens was limited to 50% of the theoretical value [15]. Moreover, the diffracted angle of light at the edge of metalens increases with NA and leads to decrease of diffracted efficiency at the edge due to the increasing phase gradient. So the high NA is another reason for limiting the focusing efficiency of the proposed metalens [27]. On the other hand, in order to fulfil the required phase and group delay over a continuous wavelength range, the sacrificed transmittance of chosen meta-units with height differences might affect the focusing efficiency. Nevertheless, according to the fluorescence collection theory, metalens with high NA provides a large collection angle for fluorescence, which can attenuate the unfavorable effect of low focusing efficiency on fluorescence collection efficiency to some extent [6]. The advantages of excitation and emission lights achromatic focusing and high NA play a pivotal role in maximizing the collection efficiency of fluorescence signal and promoted high resolution focusing [37].Fig. 7. (a) The comparison of the actual focal length (point-line) between the designed focal length (orange dotted-line) for the proposed metalens at selected wavelengths. (b) The actual FWHM (blue points) and the theoretical FWHM (red line) as the function of wavelength for the proposed metalens at selected wavelengths. (c) The focusing efficiency (orange point) for the proposed metalens at selected wavelengths.
3.2 Performance of two-photon fluorescence excitation
The proposed achromatic metalens with high NA works in the continuous bandwidth from 500 nm to 1050 nm, which almost spans the excitation and emission wavelengths range of most fluorophores that are commonly used in neuroscience studies in two-photon imaging. In order to prove the application of the proposed achromatic metalens in the multicolor two-photon fluorescence imaging, five fluorophores with different emission spectra were chosen including EGFP (excitation: 920, emission: 510), Rhodamine 6 G (excitation: 900, emission: 548), Dsred2 (excitation: 1050, emission: 582), Katushka (excitation: 1060, emission: 635) and ATTO 646N (excitation: 1060, emission: 664) [38]. The proposed metalens was illuminated by excitation beam with X-polarization. The intensity distributions for different excitation wavelengths were obtained by using the FDTD method and the corresponding effective fluorescence distributions were calculated according to two-photon fluorescence excitation theory. Figure 8(a) and Fig. 8(b) show the intensity distributions for excitation light with different wavelengths and the generated effective fluorescence intensity distributions in the axial and focal planes, respectively. Due to the intensity of parasitic focal spots failure to reach the threshold of the two-photon excitation, only fluorophores that lie in the focal position of excitation beam were excited, the generated spots were much smaller than the excitation spots. The selected fluorophores were excited by the excitation light passed through the proposed metalens and emitted fluorescence with different wavelengths at the same position, which demonstrated the possibility of simultaneous multicolor fluorescence imaging for the same biological structure. Therefore, the two-photon fluorescence excitation characteristic of the proposed metalens showed the potential application in studying dynamic functions in vivo.
Fig. 8. The excitation beam and the generated effective fluorescence intensity distributions in the axial (a) and the focal planes (b) for different fluorophores.
3.3 Characteristic of metalens polarization-insensitivity
Polarization insensitivity is an important characteristic of metalens for applications in fluorescence imaging, which affects the collection ability of metalens for fluorescence with different polarizations. The performance of the proposed metalens was simulated under the illuminations with four different polarizations, i.e., right-handed circular polarization (RCP), left-handed circular polarization (LCP), and X, Y polarizations (X-LP, Y-LP). Figure 9(a) shows the actual focal lengths of the proposed metalens at different fluorescent wavelengths for RCP, LCP, X-LP and Y-LP. Obviously, the axial focal positions remain close to identical at the selected fluorescent emission wavelengths with different polarizations. Figure 9(b) shows the normalization intensity distributions in focal plane for different polarizations. The results prove that the changes in the shape and size of the focal spots for different polarized inputs are very small. The FWHMs of focal spots weakly changed with polarization as shown in Fig. 9(c). The standard deviations of the FWHMs were 25, 12.5, 20, 25 and 12.5 nm at the selected fluorescent emission wavelengths of 510, 548, 582, 635 and 664 nm, respectively. They were within a generally acceptable range since all the standard deviations were less than ten percent of the average FWHM. Therefore, the proposed metalens maintained the achromatic focusing effect under any polarized incident light and had the same ability of collecting fluorescence signals with any polarization.
Fig. 9. Focus lengths (a) and FWHMs (c) of the proposed metalens as a function of the emission wavelengths for different polarizations. (b) Normalization intensity (|E|2) profiles in focal planes at the selected fluorescent wavelengths for different polarizations.
4. Conclusion
In summary, the performance of the polarization-insensitive ultra-broadband achromatic metalens with high NA working in the continuous wavelength range from 500 nm to 1050 nm had been demonstrated theoretically. We adopted TiO2 and Si square meta-units to manipulate the wavefront of the VIS emission band and the NIR excitation band, respectively. By the particle swarm optimization algorithm, the optimal meta-units were selected from TiO2 meta-unit library and Si meta-unit library to fulfil both the required phase and group delay of the emission and excitation lights achromatic focusing, respectively. We set the optimal TiO2 and Si meta-units in staggered arrangement to integrate dual-band modulation function. The unleashed height and width degree of freedom in a meta-unit largely increased the group delay range of meta-units and enriched meta-unit phase-group delay libraries as well as the dual-band regulation of dual-material opened up the possibility to achieve high NA and large achromatic bandwidth. Compared with existing broadband achromatic metalenses, the proposed metalens had the higher NAeff (0.8) and the largest achromatic operational bandwidth, which could work for incident light with any polarization. The coefficient of variation of the focal lengths was only 3.41% in the entire ultra-broadband range. “Therefore, we believe that the proposed achromatic metalens will have promising applications in multicolor two-photon endomicroscopy imaging system to obtain high resolution and functional imaging, which will offer a promising path for miniaturized imaging systems.
Funding
National Natural Science Foundation of China (62175186, 62027812).
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.
References
1. C. Stringari, L. Abdeladim, G. Malkinson, P. Mahou, X. Solinas, I. Lamarre, S. Brizion, J. B. Galey, W. Supatto, R. Legouis, A. M. Pena, and E. Beaurepaire, “Multicolor two-photon imaging of endogenous fluorophores in living tissues by wavelength mixing,” Sci. Rep. 7(1), 3792 (2017). [CrossRef]
2. W. Zong, R. Wu, S. Chen, J. Wu, and H. J. N. M. Cheng, “Miniature two-photon microscopy for enlarged field-of-view, multi-plane and long-term brain imaging,” Nat. Methods 18(1), 46–49 (2021). [CrossRef]
3. H. Guan, W. Liang, A. Li, Y. A. Gau, D. Chen, M.-J. Li, D. E. Bergles, X. J. O. l, and Xingde Li, “Multicolor fiber-optic two-photon endomicroscopy for brain imaging,” Opt. Lett. 46(5), 1093–1096 (2021). [CrossRef]
4. E. Arbabi, J. Li, R. J. Hutchins, S. M. Kamali, A. Arbabi, Y. Horie, P. Van Dorpe, V. Gradinaru, D. A. Wagenaar, and A. Faraon, “Two-Photon Microscopy with a Double-Wavelength Metasurface Objective Lens,” Nano Lett. 18(8), 4943–4948 (2018). [CrossRef]
5. V. Kučikas, M. P. Werner, T. Schmitz-Rode, F. Louradour, and M. A. M. J. van Zandvoort, “Two-Photon Endoscopy: State of the Art and Perspectives,” Mol. Imaging Biol. 25(1), 3–17 (2023). [CrossRef]
6. D. Sun, Y. Yang, S. Liu, Y. Li, M. Luo, X. Qi, and Z. Ma, “Excitation and emission dual-wavelength confocal metalens designed directly in the biological tissue environment for two-photon micro-endoscopy,” Biomed. Opt. Express 11(8), 4408–4418 (2020). [CrossRef]
7. Y. Li, S. Liu, D. Sun, M. Luo, X. Qi, S. Zhao, and Z. Ma, “Single-layer multitasking vortex-metalens for ultra-compact two-photon excitation STED endomicroscopy imaging,” Opt. Express 29(3), 3795–3807 (2021). [CrossRef]
8. S. H. Badri and M. M. Gilarlue, “Coupling Between Silicon Waveguide and Metal-Dielectric-Metal Plasmonic Waveguide with Lens-Funnel Structure,” Plasmonics 15(3), 821–827 (2020). [CrossRef]
9. S. H. Badri and M. M. Gilarlue, “Silicon nitride waveguide devices based on gradient-index lenses implemented by subwavelength silicon grating metamaterials,” Appl. Opt. 59(17), 5269–5275 (2020). [CrossRef]
10. M. Khorasaninejad, W. T. Chen, R. C. Devlin, J. Oh, A. Y. Zhu, and F. J. S. Capasso, “Metalenses at visible wavelengths: Diffraction-limited focusing and subwavelength resolution imaging,” Science 352(6290), 1190–1194 (2016). [CrossRef]
11. H. Ren, J. Jang, C. Li, A. Aigner, M. Plidschun, J. Kim, J. Rho, M. A. Schmidt, and S. A. Maier, “An achromatic metafiber for focusing and imaging across the entire telecommunication range,” Nat. Commun. 13(1), 4183 (2022). [CrossRef]
12. E. Arbabi, A. Arbabi, S. M. Kamali, Y. Horie, and A. Faraon, “Controlling the sign of chromatic dispersion in diffractive optics with dielectric metasurfaces,” Optica 4(6), 625–632 (2017). [CrossRef]
13. Z. Shi, M. Khorasaninejad, Y. W. Huang, C. Roques-Carmes, A. Y. Zhu, W. T. Chen, V. Sanjeev, Z. W. Ding, M. Tamagnone, K. Chaudhary, R. C. Devlin, C. W. Qiu, and F. Capasso, “Single-Layer Metasurface with Controllable Multiwavelength Functions,” Nano Lett. 18(4), 2420–2427 (2018). [CrossRef]
14. W. Li, J. Qi, and A. Sihvola, “Meta-Imaging: from Non-Computational to Computational,” Adv. Opt. Mater. 8(23), 2001000 (2020). [CrossRef]
15. E. Arbabi, A. Arbabi, S. M. Kamali, Y. Horie, and A. J. S. R. Faraon, “Multiwavelength metasurfaces through spatial multiplexing,” Sci. Rep. 6(1), 32803 (2016). [CrossRef]
16. O. Avayu, E. Almeida, Y. Prior, and T. Ellenbogen, “Composite Functional Metasurfaces for Multispectral Achromatic Optics,” Nat. Commun. 8(1), 14992 (2017). [CrossRef]
17. M. Khorasaninejad, Z. Shi, A. Y. Zhu, W. T. Chen, V. Sanjeev, A. Zaidi, and F. Capasso, “Achromatic Metalens over 60 nm Bandwidth in the Visible and Metalens with Reverse Chromatic Dispersion,” Nano Lett. 17(3), 1819–1824 (2017). [CrossRef]
18. W. T. Chen, A. Y. Zhu, V. Sanjeev, M. Khorasaninejad, Z. Shi, E. Lee, and F. Capasso, “A broadband achromatic metalens for focusing and imaging in the visible,” Nat. Nanotechnol. 13(3), 220–226 (2018). [CrossRef]
19. S. Wang, P. C. Wu, V. C. Su, Y. C. Lai, M. K. Chen, H. Y. Kuo, B. H. Chen, Y. H. Chen, T. T. Huang, J. H. Wang, R. M. Lin, C. H. Kuan, T. Li, Z. Wang, S. Zhu, and D. P. Tsai, “A broadband achromatic metalens in the visible,” Nat. Nanotechnol. 13(3), 227–232 (2018). [CrossRef]
20. W. T. Chen, A. Y. Zhu, J. Sisler, Z. Bharwani, and F. Capasso, “A broadband achromatic polarization-insensitive metalens consisting of anisotropic nanostructures,” Nat. Commun. 10(1), 355 (2019). [CrossRef]
21. S. Shrestha, A. C. Overvig, M. Lu, A. Stein, and N. Yu, “Broadband achromatic dielectric metalenses,” Light: Sci. Appl. 7(1), 85 (2018). [CrossRef]
22. F. Zhao, X. Jiang, S. Li, H. Chen, G. Liang, Z. Wen, Z. Zhang, and G. Chen, “Optimization-free approach for broadband achromatic metalens of high-numerical-aperture with high-index dielectric metasurface,” J. Phys. D: Appl. Phys. 52(50), 505110 (2019). [CrossRef]
23. A. Ndao, L. Hsu, J. Ha, J. H. Park, C. Chang-Hasnain, and B. Kante, “Octave bandwidth photonic fishnet-achromatic-metalens,” Nat. Commun. 11(1), 3205 (2020). [CrossRef]
24. P. Sun, M. Zhang, F. Dong, L. Feng, and W. Chu, “Broadband achromatic polarization insensitive metalens over 950 nm bandwidth in the visible and near-infrared,” Chin. Opt. Lett. 20(1), 013601 (2022). [CrossRef]
25. H. Liang, A. Martins, B. H. V. Borges, J. Zhou, E. R. Martins, J. Li, and T. F. Krauss, “High performance metalenses: numerical aperture, aberrations, chromaticity, and trade-offs,” Optica 6(12), 1461–1470 (2019). [CrossRef]
26. F. Presutti and F. Monticone, “Focusing on Bandwidth: Achromatic Metalens Limits,” Optica 7(6), 624–631 (2020). [CrossRef]
27. M. Pan, Y. Fu, M. Zheng, H. Chen, Y. Zang, H. Duan, Q. Li, M. Qiu, and Y. Hu, “Dielectric metalens for miniaturized imaging systems: progress and challenges,” Light: Sci. Appl. 11(1), 195 (2022). [CrossRef]
28. Y. Wang, Q. Chen, W. Yang, Z. Ji, L. Jin, X. Ma, Q. Song, A. Boltasseva, J. Han, V. M. Shalaev, and S. Xiao, “High-efficiency broadband achromatic metalens for near-IR biological imaging window,” Nat. Commun. 12(1), 5560 (2021). [CrossRef]
29. S. Baek, J. Kim, Y. Kim, W. S. Cho, T. Badloe, S. Moon, J. Rho, and J. Lee, “High numerical aperture RGB achromatic metalens in the visible,” Photonics Res. 10(12), B30–B39 (2022). [CrossRef]
30. S. An, B. Zheng, M. Y. Shalaginov, H. Tang, H. Li, L. Zhou, J. Ding, A. M. Agarwal, C. Rivero-Baleine, M. Kang, K. A. Richardson, T. Gu, J. Hu, C. Fowler, and H. Zhang, “Deep learning modeling approach for metasurfaces with high degrees of freedom,” Opt. Express 28(21), 31932–31942 (2020). [CrossRef]
31. F. Yang, S. An, M. Y. Shalaginov, H. Zhang, C. Rivero-Baleine, J. Hu, and T. Gu, “Design of broadband and wide-field-of-view metalenses,” Opt. Lett. 46(22), 5735–5738 (2021). [CrossRef]
32. L. Zhang, C. Wang, Y. Wei, Y. Lin, Y. Han, and Y. Deng, “High-Efficiency Achromatic Metalens Topologically Optimized in the Visible,” Nanomaterials 13(5), 890 (2023). [CrossRef]
33. W. Cheng, J. Feng, Y. Wang, Z. Peng, S. Zang, H. Cheng, X. Ren, Y. Shuai, H. Liu, J. Wu, and J. Yang, “Genetic algorithms designed ultra-broadband achromatic metalens in the visible,” Optik 258, 168868 (2022). [CrossRef]
34. C. Cao, Y. Qiu, L. Guan, Z. Wei, Z. Yang, L. Zhan, D. Zhu, C. Ding, X. Shen, X. Xia, C. Kuang, and X. Liu, “Dip-In Photoresist for Photoinhibited Two-Photon Lithography to Realize High-Precision Direct Laser Writing on Wafer,” ACS Appl. Mater. Interfaces 14(27), 31332–31342 (2022). [CrossRef]
35. M. Zou, C. Liao, Y. Chen, et al., “3D printed fiber-optic nanomechanical bioprobe,” Int. J. Extrem. Manuf. 5(1), 015005 (2023). [CrossRef]
36. Z. Zhou, J. Li, R. Su, B. Yao, H. Fang, K. Li, L. Zhou, J. Liu, D. Stellinga, and C. P. Reardon, “Efficient Silicon Metasurfaces for Visible Light,” ACS Photonics 4(3), 544–551 (2017). [CrossRef]
37. J.-C. Roulet, R. Voelkel, H.-P. Herzig, E. Verpoorte, F. de Rooij Nico, and R. Daendliker, “Microlens systems for fluorescence detection in chemical microsystems,” Opt. Eng. 40(5), 814–1378 (2001). [CrossRef]
38. M. Drobizhev, N. S. Makarov, S. E. Tillo, T. E. Hughes, and A. Rebane, “Two-photon absorption properties of fluorescent proteins,” Nat. Methods 8(5), 393–399 (2011). [CrossRef]
