Information multiplexing from optical holography to multi-channel metaholography

3.1.1 Orthogonal polarization multiplexing meta-holograms

In 2017, Capasso group demonstrated chiral holograms with independent phase control of arbitrary orthogonal states of polarization, pushing the holographic multiplexing from circular polarizations [34] to any desired orthogonal states on the Poincaré sphere [126]. Generally, metasurfaces impart polarization dependent phase profiles through two major principles: propagation phase design for linear polarizations and geometric phase design for circular polarizations carrying the spin angular momentum. For example, geometric phase from space-variant subwavelength dielectric gratings can lead to a spin angular momentum-dependent focusing lens [146]. Considering the case of more general elliptical polarizations, neither of the two mentioned principles alone can address the polarization selectivity. As shown in Figure 3(a) left, Capasso group combined the above two principles to manipulate the phase of any two orthogonal states of polarization independently and with high efficiency. Their metasurface consists of an array of dielectric nanopillars with elliptical cross-sections that act as birefringent meta-atoms. By tuning the orientation and aspect ratio of the nanopillars, they can achieve arbitrary phase profiles for any desired orthogonal states of polarization, including the linear and circular polarization states. Experimental results of the chiral holograms are shown in the Figure 3(a) right, where under the illumination of left- and right-handed circular polarizations, a cartoon dog and a cat can be reconstructed respectively.

Figure 3:

Metasurface multiplexing holography. (a) Arbitrary orthogonal polarization multiplexing meta-holograms. Left, the combined propagation (x–y orthogonal bricks) and geometric (rotated bricks) phase design. Right, experimental reconstruction of two independent image channels from an elliptical-polarization-multiplexed meta-hologram. Reproduced from Ref. [126] with permission from American Physical Society, copyright 2017. (b) High-dimension polarization-multiplexed meta-hologram. Top left, an example of unit cell and the responsive matrix. Bottom left, the design principle of polarization multiplexing through engineered correlated (step 1) and random (step 2) noise. Right, schematic of holographic display from a high-dimension polarization meta-hologram. Reproduced from Ref. [32] with permission from American Association for the Advancement of Science, copyright 2023. (c) Wavelength-multiplexed holographic color prints. The device displays as color images in white light (top) but three different holograms under RGB laser illumination (bottom). Reproduced from Ref. [30] with permission from Nature Publishing, copyright 2019. (d) Angle-multiplexed meta-hologram. Schematics illustrates those two images can be extracted out based on two different incidence angles. Reproduced from Ref. [36] with permission from American Physical Society, copyright 2017.

3.1.2 High-dimensional polarization multiplexing meta-holograms

The conventional design of polarization-multiplexed metasurfaces is limited by the dimensionality of the Jones matrix, which describes the polarization transformation of light by each metasurface element [147]. The upper limit of independent channels for polarization multiplexing was theoretically limited to 3 [147]. Wang group recently reported a high-dimensional polarization multiplexing metasurface hologram that breaks this limit and achieves unprecedented polarization multiplexing capacity, which was achieved from introducing controlled noise to the each polarization image channel [32]. As shown in Figure 3(b), correlated noises (step 1) were firstly added to polarization channels, while the random noises (step 2) were further added to approach the precise solutions of Jones matrix elements which shall wipe the crosstalk of holographic images (inset alphabet image). By doing so, multiple independent polarization channels carrying independent holographic images are created. Experimentally, they demonstrated that a single metasurface can generate up to 11 independent images for different polarizations of visible light, which is the highest number reported so far. Moreover, by combining polarization multiplexing with position multiplexing, they further generated 36 distinct images from a large piece of a metasurface hologram forming a holographic keyboard pattern. It shows that noise can be beneficial rather than detrimental in optical engineering if it is properly controlled and utilized.

3.1.3 Wavelength multiplexing meta-holograms

Color prints and holograms are used as two typical optical security means. Adding amplitude control to the phase holograms, one can achieve bifunctional device that displays color images under incoherent white light and different holograms under coherent laser illumination. Figure 3(c) shows a transmission-type holographic color print by Yang’s group in 2019 [30]. In this work, the encoding of phase and amplitude is realized at an individual pixel level, each pixel consists of a top-layer structural color element that modulates the amplitude of transmitted light and a middle-layer phase plate that modulates the phase of light. The structural color element is a dielectric nanopillar that transmits desired wavelength on-axis while the rest are diffracted with large angles. The wavelength selectivity stems from the nanopillar dimensions (i.e., height, diameter and pitch). The phase of transmitted light is then modified by the phase plate, following the equation ∅ λ = 2 π n − 1 t / λ , where λ is the incidence wavelength, t is the phase plate thickness and n is the medium refractive index. By arranging these pixels in an array, the device can display a colored image under white light illumination and project up to three different holograms under red, green, and blue laser illumination. This device enables good versatility and security by creating holographic color prints with various images that are readily verified but challenging to emulate. Moreover, the whole device was fabricated in a monolithic way that makes it more attractive for applications.

3.1.4 Angle-multiplexed meta-holograms

Angle is another physical dimension that has been used for traditional multiplexing holography. Conventional lenses, gratings and holograms have a highly correlated angle response, meaning that the same optical transformation is applied to different incident angles with possible distortions and efficiency reduction [148]. Faraon and co-workers introduced a novel concept of angle-multiplexed metasurfaces, which can encode independent wavefronts in a single meta-hologram under different illumination angles [36]. To achieve this, the authors applied high-contrast dielectric (a-Si) U-shaped meta-atoms on a reflective substrate, whose scattering properties depend strongly on the angle of incidence. By designing the meta-atoms to have different resonant modes under different incident angles, they can control the phase and amplitude of the reflected light independently for each angle (Figure 3(d)). This enables flat optical devices that can perform different and independent optical transformations when illuminated from different directions, such as angle-multiplexed gratings and holograms.

Metasurface multiplexing holography is a promising research field that has the potential to revolutionize the field of holography and optical information processing. However, there are still some challenges and limitations that need to be addressed, such as the fabrication complexity, reduced efficiency and pronounced crosstalk through multiplexing, limited bandwidth, and the compatibility with different light sources. We next introduce another promising platform for multiplexing holography based on the use of the orbital angular momentum (OAM) modes.

3.2.1 Principle of OAM holography

Unlike other physical properties of light, OAM of light has very recently been explored for optical holography, mainly due to the lack of OAM selectivity in the conventional hologram design. Typically, a conventional digital hologram has a quasi-continuous spatial frequency distribution, destroying the helical wavefront of an incident OAM beam and hence losing the OAM physical property in the holographic reconstruction process (Figure 4(a)). Mathematically, the OAM-reconstructed electric field in the image plane is a convolution between the electric field of a holographic image and the Fourier transform of a helical wavefront [38]. In this case, the Fourier transform of a helical wavefront, which acts as the kernel function of the convolution, is simply copied in each pixel of the holographic image. As such, to preserve the OAM property in each pixel of a reconstructed holographic image, it is necessary to spatially sample the holographic image by using an OAM-dependent 2D Dirac comb function to avoid spatial overlap of the helical wavefront kernel, i.e., creating OAM-pixelated images. As such, the constituent spatial frequencies (k _g in the momentum space) of an OAM-conserving hologram add discrete linear spatial frequency shifts to an incident OAM beam (k _in). The outgoing spatial frequencies leaving the hologram (k _out) possess a helical wavefront inherited from the incident OAM beam, implying that the OAM-conserving hologram could create OAM-pixelated holographic images (Figure 4(b)).

Figure 4:

Comparison of a conventional digital hologram with an OAM-conserving hologram. (a) A conventional digital hologram with a quasi-continuous spatial frequency distribution breaks down the helical wavefront carried by an incident OAM beam. The inset (left) shows a quasi-continuous spatial-frequency content of the hologram. The insets (right) show the phase and intensity distributions of an enlarged pixel in an OAM-reconstructed holographic image, respectively. (b) An OAM-conserving hologram with a discrete spatial frequency distribution, capable of preserving the helical wavefront from an incident OAM beam. The inset (left) shows a discrete spatial frequency distribution of an OAM-conserving hologram. The insets (right) show the phase and intensity distributions of an enlarged pixel in an OAM-reconstructed holographic image, respectively. Reproduced from Ref. [38] with permission from Nature Publishing, copyright 2019.

OAM-multiplexing holography can be represented as superposition of complex-amplitude fields of different image channels encoded with distinctive OAM modes in the hologram plane: E mul = ∑ j = 1 M A j e i ∅ j e i φ j , wherein A _j and ∅ _j stand for the amplitude and phase information of each image channel, respectively; φ _j = l _j φ where l _j ϵ Z and φ represent the helical mode index and azimuthal angle, respectively, and M denotes the total number of multiplexing channels. Since the complex-amplitude hologram is Fourier-based, its reconstructed optical fields in momentum space can be represented as F E mul = ∑ j = 1 M F A j ⊗ F e i ∅ j ⊗ F e i φ j , where F denotes the Fourier transform operator, expressing multiplexing results as the superposition of a convolution of the amplitude (A _j ), phase (∅ _j ), and encoded OAM (l _j ) information of each image channel. It is obvious to see that the amplitude of each image channel can be individually controlled, allowing the adjustment of image frame intensity essential for high-quality holographic video displays. On the other hand, a phase-only OAM-multiplexing hologram can be described as an argument result: P mul = arg ∑ j = 1 M e i ∅ j ′ e i φ j , wherein ∅ j ′ denotes an iteratively retrieved phase-only hologram for each image channel. The reconstructed optical fields in momentum space can thus be represented as F P mul = F arg ∑ j = 1 M e i ∅ j ′ e i l j φ , indicating that the amplitude information of each image channel is lost, which degrades the reconstruction quality by increasing the multiplexing crosstalk.

The design principle of a complex-amplitude hologram for OAM holography is illustrated in Figure 5. To achieve OAM holography, an OAM diffuser array that consists of an OAM-dependent sampling array and a random phase function was developed to perform the spatial-frequency sampling in momentum space (Figure 5(a)). As such, the inverse Fourier transformation of a sampled target image gives rise to a complex-amplitude hologram with a discrete spatial-frequency content. In each holographic image channel, a specific OAM helical phase and a Fourier transform lens were added to the phase information of the complex-amplitude hologram, leading to the OAM selectivity at a given image plane. According to diffraction theory, the size of OAM pixels in the image space can be determined from both the helical mode index (l) at a given wavelength and the effective numerical aperture of the Fourier hologram with respect to a specific image plane. As a result, there are fundamental limits on both the maximal multiplexing channel number and the upper resolution limit of an OAM-converted holographic image (Figure 5(b)). The trade-off between the highest OAM helical mode index and the resolution of the OAM-dependent holographic images sets up an upper limit of the maximum multiplexing channel number when a certain image resolution is specifically required [39]. In principle, enlarging the hologram size or reducing the reconstruction distance can help improve the image resolution, since the effective numerical aperture of the Fourier hologram can be increased.

Figure 5:

Design principle of a complex-amplitude hologram for OAM holography in momentum space. (a) Schematic illustration of OAM holography based on a complex-amplitude hologram that is sampled in its momentum space through an OAM diffuser array. OAM helical phase and a Fourier transform lens were added to the phase information of the complex-amplitude hologram, offering strong OAM selectivity at a given image plane. iFT represents inverse Fourier transform. (b) Numerical characterization of OAM pixel size and image resolution as a function of helical mode index |l| at different image planes, respectively. (c) The effect of an OAM diffuser array with random phase on the digitalization of a complex-amplitude Fourier hologram. (d) Numerical characterization of coefficient of variation (black lines) and normalized inner vector product (blue lines) of complex-amplitude Fourier holograms as a function of OAM-multiplexing channel number, with (solid lines) and without (dashed lines) the use of an OAM diffuser array, respectively. Reproduced from Ref. [39] with permission from Nature Publishing, copyright 2020.

Apart from the spatial-frequency sampling, the random phase of an OAM diffuser array also plays a key enabling role in the digitalization of a complex-amplitude hologram. Like the case of image processing with Fourier transform, the direct FT of an image usually gives rise to a complex-valued Fourier hologram with a large amplitude variation difficult to implement through a digital device (Figure 5(c)). The broad spatial-frequency content of a random phase function acts as a convolution kernel to diffuse the amplitude of a Fourier hologram, capable of flattening the large amplitude variation present in the Fourier hologram. To quantify the effect of the random phase on digitalization, the coefficient of amplitude variation as a function of OAM-multiplexing channel number was characterized in Figure 5(d). Without the OAM diffuser array, the coefficient of variation in the amplitude part of a Fourier hologram is nearly 300 % for a typical set of images and increases with the multiplexing channel number. This results in about 90 % area of the Fourier hologram having normalized amplitudes smaller than 0.05. This sets a fundamental barrier to digitalise a Fourier hologram due to the loss of phase information and low transmission efficiency (less than 2.5 %) in that area. After applying the OAM diffuser array, the coefficient of variation is reduced below 100 % and kept nearly constant by increasing the multiplexing channel number (Figure 5(d)). It was found that the random phase of an OAM diffuser array can also eliminate the coherence of image channels and further suppress multiplexing crosstalk in addition to the OAM orthogonality [149].

3.2.2 OAM-selective and -multiplexing holograms

The principle of OAM holography is illustrated in Figure 6, where an OAM-preserved hologram with a discrete spatial-frequency distribution is designed to maintain the OAM property of incident OAM beams in each pixel of reconstructed holographic images (Figure 6(a)), laying the physical foundation for using OAM as an independent information carrier [37]. To achieve the OAM selectivity in holography, the phase function of a spiral phase plate with a topological charge of l can be further added onto the design of an OAM-conserving hologram, leading to an OAM-selective hologram (Figure 6(b)). In this context, holographic images appear only when an OAM beam with an inverse topological charge of −l is incident on an OAM-selective hologram. Such strong OAM selectivity originates from both the spatial and intensity distinctions between a fundamental spatial mode and high-order OAM modes in the image plane. Each pixel in the selectively reconstructed holographic images features a fundamental spatial mode dictated by a solid-spot intensity distribution with higher intensity value. To further improve the OAM selectivity, a fundamental mode filtering aperture array in the detector plane was added to rule out high-order OAM modes with doughnut-shaped intensity distributions. To demonstrate the OAM selectivity, four OAM-selective holograms (labelled as “1”, “2”, “3”, and “4”) were designed to confirm strong OAM selectivity (Figure 6(c)). It was shown that four different holographic images can be selectively reconstructed from the OAM-multiplexing holograms based on the incident OAM beams with topological charges of −2, −1, 1, and 2, respectively.

Figure 6:

Schematic illustration of OAM-preserved, -selective, and -multiplexing holograms. Bottom (a, b): schematics of an OAM-preserved hologram (a) and an OAM-selective hologram (b) capable of transferring the OAM property from an OAM incident beam to a holographic image and of reconstructing given OAM channels, respectively. Top left (a, b): OAM transfer in conjunction with the linear spatial frequency shift (k-space). Top right (a, b): intensity (I) and phase (φ) distributions of single pixels selected from the reconstructed holographic images, where the holographic images highlight OAM pixels featuring a doughnut-shaped intensity distribution (a) and solid-spot pixels reconstructed from a given incident OAM beam (b), respectively. (c) Schematic of an OAM-multiplexing hologram capable of reconstructing OAM-dependent holographic images. Reproduced from Ref. [37] with permission from Nature Publishing, copyright 2019.

3.2.3 Machine-learning and superresolution OAM holography

Even though OAM holography can be achieved from a spatial-frequency-sampled hologram, this approach inevitably leads to a sparse image with a trade-off between the hologram bandwidth (the number of OAM multiplexing channels) and the image resolution, as represented in Figure 5(b). This bottleneck in OAM multiplexing holography reveals that a single-layer diffractive structure cannot realize complex structured light field conversion. To address this key challenge in OAM holography, the idea of using multiple diffractive phase plates was recently proposed [40]. Multiplane light conversion (MPLC), a commercial technology that uses cascaded phase plates, has recently offered a viable approach to performing arbitrary transformations on spatial modes with low intrinsic loss and low crosstalk [150]. The phase profiles of the multiple diffractive phase plates can be numerically designed by the optical diffractive neural network (ODNN), exhibiting an excellent information processing ability. Recently, OAM multiplexing holography was implemented by ODNN. By employing the MPLC and in-situ optical forward/backward propagation principles, unitary transformation and linear phase modulation were implemented to simultaneously modulate multiple OAM channels, where OAM modes are encoded independently with holograms and converted during optical propagations. Huang et al. [40] showed that a 5-layer ODNN can realize simultaneous conversion and evolution of 10 OAM multiplexing image channels at 5 spatial depths, where the mean square error and structural similarity index measure were 0.03 and 86 %, respectively. In the proposed OAM multiplexing holography, the OAM modes are mainly modulated by the MPLC principle that is composed by multiple amplitude-phase modulated diffractive layers. Figure 7(a) shows a schematic diagram of a five-layer ODNN. Huang et al. utilized Laguerre–Gaussian beams to generate the OAM modes at a wavelength of 1550 nm. They trained a five-layer ODNN to construct the light field conversion between the OAM modes and kinetic action (KA) holograms with binary grayscale values. They selected 10 OAM modes (l ∈ [−5, +5], l ≠ 0) as inputs to encode 10 KA holograms. By feeding these 10 samples into the ODNN for training to minimize the loss function, the amplitude and phase parameters inside the diffractive layers were simultaneously calculated and updated owing to the backward propagation of gradients. After 8000 iterations, the ODNN can accurately convert all 10 OAM modes to the corresponding KA holograms at an output plane, and the loss function converges at approximately 0.06.

Figure 7:

Principle of OAM holography based on an optical diffractive neural network (ODNN) and a pseudo incoherent approach. (a) Schematic illustration of OAM multiplexing holography based on a five-layer ODNN, wherein each incident OAM vortex mode can be converted to a kinetic action (KA)-based holographic image. Right column: calculated phase (left) and amplitude (right) distributions in the five layers ODNN model. Reproduced from Ref. [40] with permission from Optica, copyright 2022. (b–e) Schematic illustration of the OAM property transfer in the spatial frequency domain. Reconstructed images with two OAM channels are shown, where the enlarged areas (marked as i to p) are compared in the rightmost panel. (b) General coherent case. (c) General incoherent case. (d) Pseudo incoherent case. (e) Coherence suppression case with temporal multiplexing. (b–e) reproduced from Ref. [41] with permission from Nature Publishing, copyright 2023.

To reduce strong multiplexing crosstalk in OAM holography, the above introduced sampling criterion dictates that the image sampling distance should be no less than the diameter of largest addressable OAM mode, which severely hinders the increase in resolution and capacity. To mitigate this compelling challenge, an idea of multiplexing a range of OAM holograms in the time domain via a fast-switching digital mirror device was proposed [41], leading to a pseudo incoherent approach that largely relaxes the sampling constraint in OAM holography. Shi et al. [41] recently proposed a pseudo incoherent approach that is almost crosstalk-free, and demonstrated an analogous coherent solution by temporal multiplexing, which dramatically eliminates the crosstalk and largely relaxes the constraint upon sampling condition of OAM holography, exhibiting a remarkable resolution enhancement by several times, as well as a large scaling of OAM multiplexing capacity at fixed resolution. In principle, the ratio of the diameter of largest addressable OAM mode (dmax, denoting the OAM-multiplexing capacity) to the sampling distance (L, indicating the image resolution of OAM holography), γ = d _max/L, is a core factor termed as the sampling condition. It is greatly desirable to enlarge the value of γ as much as possible for OAM holography, since it corresponds to higher resolution with a certain number of OAM channels, or equivalently higher capacity at a certain resolution. However, for the general coherent OAM holography as previously reported, OAM property cannot be preserved in densely sampled high-resolution images due to interference, thereby imposing a fundamental resolution limit for a given OAM channel number by demanding γ ≤ 1. Specifically, for the general coherent case (Figure 7(b)) that uses a coherent illumination source, the constituent spatial frequencies (k _g in the momentum space) of an OAM-conserving hologram add a linear spatial frequency shift to an incident OAM beam (k _in). Considering a hologram that multiplexes two OAM channels as an example, a sparse sampling (γ = 0.56) can retain the OAM property of the incident beam (as denoted in the enlarged area i), however a denser sampling with γ = 1.75, which exceeds the sampling criterion limit, causes a complete loss of OAM property due to interference (see the enlarged area j). On the other hand, for the general incoherent case (Figure 7(c)) that uses an incoherent illumination source, the spatial frequencies of different incoherent wavefronts have deviated outgoing directions according to the diffractive grating formula, which brings serious undesired blurring to the reconstructed image (see the enlarged area of l).

Unlike the general incoherent case, a pseudo incoherent case (Figure 7(d)) assumes that the outgoing wave vectors leaving the hologram coincide perfectly for all incoherent incident vectors (k ₁ to k _n ), so that individual diffraction patterns can be superposed in an intensity manner (see the enlarged area of n) without introducing image blurring. However, this case is practically challenging to realize due to the violation of the dispersion of diffractive gratings; thus, a coherent analogy to that is alternatively carried out, by temporal multiplexing of a coherent beam, thereby suppressing the coherence. It is shown in Figure 7(e) that temporal multiplexing introduces time-varying phase delays to the incident vector, thereby creating multiple incoherent wavefronts within each modulating duration, which is akin to inherent multiple wavefronts in the pseudo incoherent case, and consequently enables high reconstruction quality at super-resolution condition as well (see the enlarged area of p). Therefore, temporal multiplexing, rather than a partially coherent light source, can be used to reduce the coherence of the reconstructed images, well-preventing damage in the structure of holographic images and OAM orthogonality. However, this temporal multiplexing method requires high-speed spatial light modulating devices such as digital micromirror device and ferro-electronic liquid crystal on silicon, thus restricting the available types of CGHs to amplitude binary holograms for digital micromirror device and phase binary holograms for ferro-electronic liquid crystal on silicon, respectively.

Figure 8(a) and (b) present the holographic imaging results of the ODNN approach based on five-layer MPLC holograms. The average mean square error (MSE) and structural similarity index measure (SSIM) for the two OAM modes of l = 1 and 2 at five spatial depths were 0.0107 and 87.01 %, respectively [40]. Even though this method allows the reconstruction of OAM-dependent holographic images with continuous image pixels not suffering from a sparse spatial sampling, there is huge room for improving the image quality and testing more complex gray scale image targets. Figure 8(c) and (d) present the experimental imaging results of densely sampled grayscale images for the temporal multiplexing OAM holography [41]. Figure 8(a) compares the results of two OAM pixels based on the coherent and pseudo incoherent approaches, with the sampling rate exceeding the size of diffraction-limited OAM pixels in the Fourier plane, as explained in Figure 4. For the coherent case, the two OAM pixels cause strong mode degradation due to interference. Five OAM-encoded holographic images with 256 gray levels of landmarks were faithfully reconstructed from 50 binary OAM-multiplexed holograms dynamically displayed on a digital micromirror device at 10 kHz (mid row in Figure 8(d). As a comparison, the experimental results obtained from a single coherent OAM-multiplexing hologram suffer from heavy noises that severely reduce the image quality.

Figure 8:

Holographic imaging results of the ODNN approach and of temporal multiplexing OAM holography. (a) and (b) Imaging reconstruction results of the ODNN approach based on five-layer MPLC holograms. (c) and (d) Pseudo incoherent approach based on temporal multiplexing of 50 binary OAM-multiplexed holograms on a digital micromirror device. MSE: mean square error. SSIM: structural similarity index measure. (b) Reproduced from Ref. [40] with permission from Optica, copyright 2022; (c) and (d) reproduced from Ref. [41] with permission from Nature Publishing, copyright 2023.

3.3.1 High-resolution lithographic techniques

Electron-beam lithography (EBL) system is similar to a scanning electron microscope, instead of scanning the full area for imaging purpose, electron beam is scanned in a controlled manner (via a blanker) so that computer-aided design patterns can be written to desired sample area with high accuracy. A more dedicated EBL working under high accelerating voltage (over 100 KV) enables the focal spot of a few nanometers leading to ultrahigh patterning resolution. EBL is likely to be one of the most frequently used nano fabrication methods in labs and research institutes due to its high resolution and flexibility of patterning. The EBL fabrication usually consists of three main steps, patterning, mask deposition and pattern transfer.

Patterning on the resist is the key step in EBL that dominants the resolution of fabrication. In this process, the chemical property of the polymer resist is modified by the secondary electrons and forming the designed structures after development. Specifically, first spin coats the e-beam polymer resists solution, poly (methyl methacrylate) for example, on a clean substrate. And remove the residual solvent by a short baking on a hotplate or an oven. Then the coated substrate is loaded to a high vacuum chamber for electron beam exposure. Predesigned patterns are drawn by the programed focused electron beam scanning across the resist. Note that the majority pristine high-energy electrons just pass through due to the high accelerating voltage and relative thin resist film. The secondary electrons and a few back-scattered electrons with a few electron-volts energy effectively interact with the polymer chemical bond and determine the resolution of the exposure [155]. The exposed resist area will either become soluble (positive resist) or become resistant (negative resist) to the developer. To achieve good defined patterns, not only these secondary electrons but also the near- and far-field back scattered electrons need to be considered into the effective total dosage. These can be corrected based on the beam and material parameters. After the development, we get our designed nanostructure pattern on the resist layer.

The pattern can be transferred to the target substrate by dry etching (chemically or physically). For good etching selectivity, a thin layer of metal (e.g., chromium, nickel, and tungsten) can be deposited as the hard mask. The unwanted metal and resist will be removed during the liftoff process. Specifically, metal deposited on the surface of the resist will be washed away while only metal that directly deposited in the pattern area (on the substrate) remains. The metal mask then goes through an etching process by reactive (or inert) gases plasma. Note that many parameters including ion species, plasma density and bias voltage and so on need to be optimized to get desired etch rate and geometry profile. After etching, the pattern is finally transferred to the substrate. The metal mask is then chemically removed by corresponding remover solution. For metasurface holograms in the visible range, one can also consider using the SiO₂, or negative resist hydrogen silsesquioxane (HSQ) as the mask, as the mask removal is less important in this scenario [156].

Like focused electron beam, focused ion beam (FIB) also can be used to do nanoscale precision fabrication. Unlike EBL, FIB is capable of material “deposition” and “milling”. For deposition, the gas precursor molecules are adsorbed on the surface, and then are decomposed by the ion-beam. Meanwhile, the high energy and large cross section property of the ions enable milling the substrate or target materials directly. FIB fabrication is based on the principle of ion-solid interactions, which causes sputtering, milling or deposition processes depending on the beam current and gas chemistry. There are a large range of ion species available for different purposes. Light ions such as helium, lithium, nitrogen can be used to achieve high lateral resolution and deep penetration while heavy ions like argon, gallium, and xenon are suitable for milling on hard materials.

Sub-10 nm resolution is easy to access for both EBL and FIB [157]. The high resolution mostly comes from the ultra-small beam spot size. Electron beams can be focused to sub-one nm, intrinsically smaller than the point spread function of extreme ultraviolet (UV) light source (13.5 nm wavelength) which is the most advanced and important light source for photolithography. Considering the meta-atom size, a beam spot of a few to 10 nm is sufficient for the visible and longer spectra range. The cost of high resolution and precision is low scalability and throughput, as the pattern must be written individually.

3.3.2 High-throughput lithographic techniques

It is the high throughput instead of high resolution that greatly impacts the manufacturing of metasurface holograms. Products like semiconductor chips and book presses are the well-known typical examples that benefit from mass production. Technologies behind these are photolithography and imprint lithography. As is known, in photolithography, wide-field illumination is applied to create the patterns with the help of predesigned photomasks. Therefore, the total resolution relies highly on light source and masks (molds for the imprinting). High-energy photons trigger the chemical reaction in photon sensitive resists (i.e., photoresist) just like the low-energy secondary electrons that trigger the chemical reaction of e-beam resists in EBL process. Short wavelength light (λ) in the UV range is desired source for photolithography due to lower diffraction limit, about λ/2n, where n is the real part refractive index of the medium. To increase the resolution, we either increase the n or decrease the λ. However, bright and short-wavelength light sources are expensive, plus the corresponding optical components that work in the deep and extreme UV range further increase the expense. For the photomasks, it is usually an opaque plate with transparent areas that allows light to pass through, it can be fabricated by EBL or FIB. Apart from the use of mask and the large-area exposure, photolithography follows the same work procedure as EBL, namely the development, lift-off, etch, etc.

Imprint lithography may be the oldest and simplest form of expression of human that our ancestors used to paint objects like hands, feet, and tools on soft surfaces. It evolved a lot as civilizations. For example, the use of metal stamps and seals enabled the creation of more durable and precise imprints on various media such as wax, paper, leather, or wood. The invention of movable type and printing press revolutionized the production and dissemination of written texts and images. Nowadays, it is even more useful and powerful. The developed nanoimprint lithography (NIL) has emerged as a promising candidate to fabricate metasurfaces. Specifically, it is potentially of high resolution, high-throughputs, scalable and low cost at the same time. NIL can be classified into two main types: thermal imprint and UV imprint. Thermal imprint uses heat and pressure to deform a thermoplastic polymer film, while UV imprint uses a UV-curable resin and UV light exposure to harden the pattern [158]. Since both methods need the master molds to transfer the structures or pattern. Sub-10 nm feature sizes and high throughput can be achieved only if molds are prefabricated properly. Rho’s group and their collaborators remarkably demonstrate wafer-scale metasurfaces fabricated via nanoimprint lithography with a critical dimension of ∼40 nm [159]. It is potentially a desired next generation affordable high-throughput technique. However, at this stage, it also faces some challenges, such as mold fabrication and alignment, defect control and demolding.

3.3.3 Highly scalable fabrication techniques

Self-assembly nanofabrication is a bottom-up approach that uses chemical or physical forces at the nanoscale to assemble basic units into larger structures or patterns with desired properties and functions. It is inspired by biological systems that create complex structures through self-organization of molecular components. One of the methods for creating nanostructures on various substrates is colloidal lithography, which uses self-assembled spherical monolayers as masks for etching and deposition [160]. Polymer spheres such as polystyrene, which can form large-scale and nearly defect-free monolayer hexagonal close-packed arrangements on the water−air interface or by using a Langmuir−Blodgett trough [161]. Colloidal lithography is a simple and efficient technique that does not require expensive equipment or clean-room facilities. The spacing and density of the particles in a monolayer can be tuned by varying the length of polymer chains on the nano-particle surface and the particle concentration, respectively. The assembled nanoparticles can transfer the pattern to the substrate by direct etch or further combine vacuum deposition to transfer the pattern to a hard mask and followed by dry etch [161].

Some examples of self-assembly nanofabrication methods are inverse micelles [29], quantum dots [162], carbon nanotubes [163], and DNA-assisted assembly [163, 164]. These methods can produce nanoparticles, nanowires, nanotubes, and nanodevices for various applications in electronics, optics, magnetism, biotechnology, and medicine. Self-assembly nanofabrication offers several apparent advantages over top–down techniques, such as low cost, high throughput, and precise control over size, shape, and composition of the nanostructures.

3.3.4 3D laser nanoprinting technique

The above techniques are broadly and effectively used to determine the lateral features of nanostructures. To shape structures in 3D in these technologies, processes like layer-by-layer approach are needed. Given the fabrication process and nanoscale dimensions, the alignment precision between layers is challenging and the complexity is increased inevitably. 3D laser printing in transparent materials has becoming popular, especially multiphoton lithography (MPL) that allows the fabrication of 100-nm features. MPL uses ultrafast (femtosecond) laser pulses to create small three-dimensional structures. The principle of MPL is based on the nonlinear absorption of photons by a photosensitive material, such as a photoresist (usually polymers). It is originally predicted by Maria-Gőppert-Mayer in 1931 [165]. The photon energy of the light source is lower than the materials bandgap (e.g., an infrared laser), so it is transparent to the pristine light source, no spontaneous absorption. However, when the laser is confined into a small volume (i.e., voxel, the 3D analogy to 2D pixel), the photon density increase greatly, two or more photons can be simultaneously absorbed by the material, initiating a chemical reaction that changes the resist properties. Since the laser intensity maxima is located solely at the focal volume, direct writing in the material at arbitrary depth is achieved. By scanning the laser focus in a controlled manner, computer designed complex 3D patterns can be written in the material with sub-diffraction-limited resolution. Post processes like annealing and etching may further reduce the structure size hence increase the resolution [166, 167]. Another straightforward way of higher resolution is to increase the photons in the nonlinear process, like three-photon polymerization [168]. At present, two-photon polymerization (2 PP) is the main MPL, where near infrared (780 nm–800 nm) femtosecond lasers are used. The simplest 2 PP setup consists of a laser source, a focusing objective, a translational stage (or scanning mirror), a laser power control system, and a shutter. It is very similar to a conventional confocal system.

MPL has several advantages over conventional lithography methods, such as noncontact and maskless fabrication, high spatial resolution, and low environmental impact MPL has facilitated fields like nanophotonics [30, 169], microfluidics [170] and bioengineering [171, 172]. In addition, it allows direct printing of refractive and diffractive optical elements, and recently ultrathin metasurfaces on optical fibres and camera pixels [173–180] However, limitations exist as well. One of the main limitations is the trade-off between resolution and fabrication speed. In addition, limitation in the choice of suitable materials and photo-initiators that can support multi-photon absorption and polymerization, while being compatible with the desired properties and functionalities of the 3D structures. A third limitation of MPL is the difficulty of integrating other components or devices into the 3D structures. Therefore, developing new materials, photoinitiators and integration techniques that can overcome these limitations are important research directions for MPL.

Metasurface is a versatile platform that can be applied to any solid material. Up to date, numerous materials have been investigated, including both metals and dielectrics. High-quality single crystals may be required in some circumstances, for example, to achieve less loss. In most times, amorphous materials are expected, due to the more controllable and flexible in both thickness and dimensions. Table 2 lists some of the frequently used materials for metasurface devices. We note the size of the metasurface varies dramatically, as it is mainly restricted to the material growth methods and the patterning technologies as we introduced above. For example, wafer-scale single crystals could be a challenge for most materials, but their amorphous phases are usually not an issue. Additionally, when time cost is considered, up to a few millimeter or centimeter scale is reasonable for EBL and FIB, while photolithography and nanoimprint can easily reach wafer scale [207].