Ultrathin flat diffractive optical devices with subwavelength thickness, such as metalenses, have emerged as promising alternatives to conventional diffractive devices, which offer new opportunities for myriads of miniaturization and interfacial applications, such as visual reality/augmented reality helmet-mounted display systems, miniaturized cameras
Nowadays, due to the increasing demands on integratable optical components, the thickness of flat lenses needs to be reduced significantly, which inevitably challenges the design and fabrication techniques. Therefore, it is desired to achieve ultrathin flat metalenses design, which modulates the phase and amplitude of the incident beam simultaneously for high focusing performance with subwavelength thickness. Although, focusing and holograms have been achieved using phase only modulation in previous works, considering practical applications and sampling theory, controlling both phase and amplitude of the electric field allows more flexibilities in the design, thus it is easier to achieve more accurate light intensity distributions for tighter focal spots and holograms of higher quality
Alternatively, flat lenses can be designed based on nanostructure engineering such as plasmonic nanostructures
Result and discussion
Recently, high index dielectric materials, like GaN, ZnO and TiO2, have been widely used in the field of metasurface and metalens, due to their sufficient wavefront modulation capability, small intrinsic loss in visible range and compatibility with Complementary Metal-Oxide-Semiconductor (CMOS) technology
A planewave incidents on a glass substrate with a refractive index n1 and passes through the GO metalens with a thickness of t and a complex refractive index of
The focusing schemes of the GO metalenses are shown in Figs. 1(a) and 1(b), in which a planewave incident light beam is focused by the GO metalenses into a super-resolved optical needle and an axial multifocal spot array, respectively. We choose these two cases because they require very accurate phase and amplitude modulations both in design and fabrication, in which the results are extremely sensitive to design/fabrication imperfections. Although the axicon for focusing an ultralong focal spot has been demonstrated by metalens before
The schematic demonstration of the GO metalenses is shown in Fig. 1(c), which is composed of concentric RGO rings and GO rings. The RGO rings are formed by direct femtosecond laser reduction on a uniform GO film, in which process the absorption and the refractive index increase while the thickness reduces
The phase-amplitude dependence is illustrated in Fig. 1(d). The blue line and brown line are the phase-amplitude relationships for the GO and RGO at the wavelength of 632.8 nm, respectively. Note that the maximum thickness change (
where, ϕ and Amp are the phase and amplitude of GO/RGO, respectively. C is the parametric equation of thickness
The position and the linewidth of each ring can be flexibly manipulated to optimize the light interference in the focal region of the incident beam. The linewidth of the rings is fixed at 400 nm, which is decided by the resolution of the laser fabrication system. Based on our quantitative phase-amplitude dependency, the optical needle lens and the multifocal lens are designed using an optimization process, in which the positions of the rings are input variables; the desired focal region optical field is the target function (see Methods).
The designed lenses (Supplementary information Table S2 and Table S3) are fabricated by reducing the GO film with direct laser writing (DLW), the optical setup of which is shown in Fig. S4. The optical image of the multifocal lens is shown in Fig. 2(a), which has a radius of around 180 µm composing of 100 rings. By magnifying the structure with a scanning electron microscope (SEM) (Fig. 2(b)), the 400 nm linewidth by laser reduction is verified. In order to visualize the morphology of the lens, a three-dimensional (3D) optical profiler (Bruker ContourGT InMotion) (Fig. 2(c)) and an AFM (Fig. 2(d)) were used. The results indicate that the thickness is reduced, and the Gaussian like profiles resulting from the laser reduction can be clearly identified (indicated by the cross-sectional plot in Fig. 2(d)), which is similar to our design in Fig. S3(a). The maximum
The focusing performance is characterized by a homemade imaging system (Fig. S5) consisting of a high NA objective (NA=0.8, 100×) mounted on a nanometric piezo stage and a tube lens (f = 200 mm). The intensity distribution in the focal region is captured by a high dynamic range (HDR) charge coupled device (CCD) camera. The lens is illuminated by the collimated planewave from a He-Ne laser at 632.8 nm.
The theoretical result of the optical needle in the x-z plane is shown in Fig. 3(a), in which a needle with a subwavelength full width at half maximum (FWHM) along the lateral direction (Fig. 3(d)) covering the axial range of 16.6λ (10.5 μm) in designed (Fig. 3(c)). The corresponding experimental intensity distributions in the x-z plane and lateral FWHM are shown in Figs. 3(b) and 3(d), which fit well with the simulation results. In Fig. 3(c), both theoretical and experimental normalized intensity along the optical axis are depicted with little discrepancy. Furthermore, normalized intensities at corresponding positions shown in Figs. 3(b) (marked by the white dash lines) are demonstrated in Figs. 3(e)-3(h), and the lateral FWHMs at these positions are 0.81λ, 0.74λ, 0.73λ, 0.70λ, respectively (Fig. 3(d)). The conventional diffraction-limited lateral resolution and axial resolution are
In addition, the theoretical and experimental results of the axial multifocal array in the x-z plane with four nearly identical focal spots along the optical axis are shown in Figs. 4(a) and 4(b). The lateral and axial resolutions of each spot are ~0.7λ and ~4λ, respectively. The experimentally measured normalized intensity distribution along the z-direction is shown in Fig. 4(c), which agrees well with the theoretical result in the same plot. The Figs. 4(d)-4(g) show that the four focal spot distributions are smooth and nearly identical at the positions marked by dashed lines in Fig. 4(b), with lateral FWHMs of 0.97λ, 0.94λ, 0.87λ, 0.91λ, respectively. It is worth mentioning that the well-separated focal spots with uniform intensity distributions can only be achieved by accurate phase and amplitude modulations, which can be attributed to the accurate control of the complex refractive index and the thickness with the laser reduction technique. Here, with quantitative phase-amplitude dependency guiding our design and laser fabrication, we demonstrate the generation of multifocal arrays with high qualities in the case of using GO metalenses. Although some discrepancy between simulation and experiments can be seen in Fig. 3 and Fig. 4 due to the surface roughness of the as-prepared GO films (the detailed analysis can be found in Supplementary information Section S1.3), the super-resolved optical needle and overall multiple foci distribution are still reasonably well matching the simulation to verify the accuracy of our amplitude and phase dependency and the design of our GO metalenses.
It is noteworthy that the GO metalenses are thicker than the metasurface designs based on metal structure. However, as metals are general lossy materials in visible range, the efficiency of the metal based design is limited to around 1%
In our previous work we have proved that by using the simultaneous phase and amplitude modulations provided by photo-reduction of GO materials
In conclusion, based on the unique optical properties of graphene-based materials (GO and RGO) under laser illumination, including the complex refractive index and the thickness change, we build up the quantitative phase-amplitude dependency, which provides a well-guided design process for photonic devices based on graphene-based materials with simultaneous amplitude and phase modulations at a single position. By understanding the phase-amplitude dependency, we are able to design photonic devices with a high accuracy. To validate the accuracy of our GO metalens design strategy, we experimentally demonstrated GO metalenses, which generate an ultra-long (~16λ) super-resolved optical needle and an axial multifocal array (4 focal spots) as examples. Although we have demonstrated only two designs in the study, the phase-amplitude dependency can be further applied to design other photonic devices such as optical chain, optical cage, optical bubble and optical tweezers for the applications in optical trapping, optical manipulating, optical delivering and optical staking
Due to the flexibility and mechanical robustness of graphene-based materials as well as the simple, low-cost, and scalable fabrication of GO metalenses, these ultrathin flat optical components enable great potential in applications and possess commercial value in integrated optical device
Preparation of GO film
The ~200 nm homogeneous GO film was prepared using the vacuum filtration method with high quality GO solution synthesized by the modified Hummer’s method
Lens design and optimization
The designs of the optical needle lens and the multifocal lens are based on the powerful interior-point optimization algorithm
The target function of multifoci is a summation of triangular function along the Z axis defined from 189.90 μm (300λ) to 227.88 μm (360λ).
where, amax is the radius of the largest ring, k is the wavenumber. AGO and φGO are the amplitude and phase modulations for GO in our design, respectively. Meanwhile, AT and φT are the amplitude and phase modulations of RGO zones, which obey our GO phase-amplitude dependency (chromatic transitional route 1 in Fig. 1(b)). The intensity at the focal point is the square of the absolute value of the electric field.
The constrains of the optimization are shown in Eq. (5):
Femtosecond laser fabrication
With a commercial laser 3D nanoprinting setup (Special Edition, Innofocus Nanoprint3D) (Fig. S4), the laser reduction process was performed on our as-prepared GO film according to the radii in supplementary information Tables 1 and 2. The femtosecond laser beam (100 fs pulse, 100 kHz, 800 nm) with a fabrication speed at 30 μm/s was calibrated at 12 μW for reducing the GO film, which is mounted on a 3D nanometric piezo stage (Physik Instrumente). A high NA oil objective (NA=1.4, 100×) is used in fabrication. The lateral resolution of laser fabrication on GO thin film is determined by the size of femtosecond laser focal spot and the laser interaction threshold with the GO material. The FWHM of the laser focal spot is determined by
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