1. Introduction

Computer-generated holograms (CGHs) use computers to produce designs that are then produced by printing or microfabrication. Illumination of the resultant structure with an appropriate coherent light source then results in the desired holographic image being reconstructed at the image plane. CGHs can be grouped into two categories according to the desired holographic image field. In the first, the desired holographic field is the Fourier transform of the object field. In the second category, the desired holographic field is the Fresnel transform of the object field [1,2].

The first detour phase Fourier-type CGH was introduced by Brown and Lohmann in 1966 and soon followed by related work by Lohmann and Paris in 1967 [3,4]. In a detour phase hologram, the sizes and the positions of structures, such as apertures in an opaque film, are chosen to modulate the amplitude and phase of the transmitted light, which in turn results in the desired holographic image being produced in the image plane. Since their inception, there has been much interest in adding new capabilities to detour phase holograms. Some examples include holograms that control the polarization of transmitted light [5,6], holograms with nonlinearity [7,8] and multicolor holograms that also function as printed color images [9].

There has recently been much interest in multicolor holography because images are rendered in a more realistic fashion than monochromatic holography. This is advantageous for applications such as displays and optical document security. The basis of multicolor holography is that three interference patterns at three different wavelengths (i.e. red, green, and blue) are recorded from an object. After reconstruction, these three patterns will be merged, and a colorful image of the desired scene will be obtained [10]. As noted in [10], metasurface-based multicolor holograms can be classified into four different classes on the basis of the color-separation mechanisms employed. The metasurface holograms that do not perform color filtering are classified into the first class [11,12]. This type of hologram does not have a meaningful image under incoherent light. Under coherent illumination at the design wavelengths, however, a colourful image is produced [13]. In the second class, the nanostructures that constitute the metasurface both control the phase of the illuminated light and perform color filtering [9,14]. The metasurface serves as a color printed image when viewed under incoherent light while producing a different holographic image with coherent light [15,16]. The third class comprises monolithically integrated-metasurfaces [17], e.g. two layer devices. Like the previous class, the metasurface shows a colorful image under incoherent light, and another image under coherent light but the holographic image is produced by a certain layer of the metasurface while the white light image is produced by another layer. In the fourth class, unlike the aforementioned classes, amplitude modulation by the metasurface produces multicolor hologram images [18,19]. While these previous works demonstrated impressive results, these were often achieved using sophisticated nanofabrication techniques, e.g. lithography and inductively coupled reactive ion etching (ICP-RIE) to control nanoparticle size and shape. Ideally, one would achieve the multicolor hologram functionality using as simple a fabrication process as possible. That is the topic of this work. We present a method for multicolor holography that is based on common and low cost materials (i.e. aluminum and silicon dioxide) that are standard in CMOS processes and that does not require etching [20]. Our method would of course be significantly cheaper than the use of spatial light modulators (SLMs). In addition, we present an idea for fabricating of our metasurface using nanoimprint lithography (NIL). Our metasurface, which was briefly explained in [21], uses detour phase to achieve the holographic functionality and aluminum nanoholes that function as plasmonic color filters (PCFs) to provide the red, green and blue channels. Our metasurface achieves low cross talk between color channels, which is a key performance metric of multicolor holograms. PCFs [22,23] have been the topic of much interest recently, due to color filter and related applications [24,25,26,27].

Our paper is organized as follows. In the Methods section, we first discuss the proposed structure and simulations of the unit cell. We discuss a simple method that could be used for fabrication of the metasurface. We discuss details concerning the simulations of the holograms using the commercial software package MATLAB. In the Results section, we present simulations of the transmission spectra of nanohole arrays designed for use with red/green/blue illumination. In order to demonstrate the intended application, we design two Fourier-type detour phase holograms based on the proposed structure and simulate their performance. The reconstructed images show very good similarity to the target images. In the Discussion section, we discuss the performance of the engineered hologram using quantitative estimators, namely the signal to noise ratio (SNR) and peak signal to noise ratio (PSNR).

2. Methods

The proposed detour phase hologram is schematically illustrated as Fig. 1(a). As shown, the intended illumination scheme consists of three laser beams at different incident angles. The holographic image would be reconstructed on the transmission side of the metasurface from the first diffraction order (which is transmitted normal to the substrate). Figure 1(b) depicts a z-axis exploded view of the hologram. It consists of three different layers, namely a glass substrate, an Al film (150 nm thick) in which the nanoholes are formed, and an SiO₂ coating layer (200 nm thick). The plasmonic nanoholes have two resonances in the visible spectrum (one at a short wavelength and the other at a longer wavelength). Increasing the thickness of the SiO₂ coating layer results in the peak transmission of longer wavelength resonance increasing. This improves the efficiency of the transmission but also increases the cross talk. To strike an appropriate balance between transmission and cross talk, we choose the SiO₂ coating to be 200 nm thick.

 

Fig. 1. (a). 3D schematic of proposed multicolor hologram and illuminating laser beams. The latter are incident on the hologram from the glass substrate side and at different angles. (b). Exploded-view schematic of pixel of hologram. (c). Top-down schematic of pixel. Nanoholes are arranged in triangular lattices with hole-to-space spacings of a_b, a_g and a_r for the blue, green and red channels, respectively. Nanoholes have diameters of R_b, R_g and R_r for the blue, green and red channels, respectively. Each pixel has an overall extent of L_x× L_y. As illustrated, by changing the nanohole group position in the x-direction, the detour phase can be varied. In this work, we choose { a_b, a_g, a_r }={255 nm,320 nm,415nm}, { R_b, R_g, R_r }={145 nm,175 nm,210 nm}, and { L_x, L_y. }={3000 nm,4350 nm}.

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Our holograms are made up of pixels. As illustrated in Fig. 1(c), each pixel contains three types of nanohole groups for the red, green, and blue channels. The design wavelengths we employ are 635 nm, 532 nm, and 450 nm. The diameter of the nanoholes determines the transmission spectrum, and the position of a nanohole group in the x direction determines the detour phase that the transmitted light carries. To illustrate this, in Fig. 1(c) we show the position of the red channel nanohole group that gives a phase of $- \pi $ for the transmitted light. If we were to move the nanohole group to the new position denoted by the white dotted line, then the phase would be $\pi $. It can be seen from Fig. 1(c) that the red, green, and blue channels have nanohole groups that are 4 × 5, 4 × 6, and 4 × 7 nanoholes, respectively. This ensures that the different channels have similar transmission efficiencies, as discussed later.

The parameters we use to denote the geometry of the proposed structure are given in the caption of Fig. 1(c). As our device is based on detour phase, it operates on a diffraction order. The incident angle of the illumination beam is thus given by:

Here $\theta $ is the angle that the incident beam makes with the normal to the metasurface. The plane of incidence is the xz plane. Here n is the diffraction order (and is therefore an integer) and ${k_0}$ is the wavenumber in free space. From this equation, assuming that we are operating on the first order (n = 1), and using ${L_x} = 3\; \mu m$, the illumination angles for the blue, green, and red laser beams are ${8.6^o}$, ${10.2^o}$, and ${12.2^o}$, respectively. By shining three lasers at these angles, the (outgoing) first order diffraction of the laser beams would be normal to the metasurface.

We next describe the process we used to design the nanoholes for the hologram. We start by considering periodic arrangements of unit cells. i.e. the nanohole are in triangular lattices, rather than being in the 4 × 5, etc. groups of the hologram pixels. Simulations are performed using a commercial FDTD solver (Lumerical) with a laptop, whose specifications are as follows: six core CPU (core i7-9750 H) and 16 GByte RAM. A schematic of a unit cell is shown in Fig. 2(a). The simulated transmission spectra (Fig. 2(b)) show that the proposed structure achieves good transmission efficiency and low cross talk at the intended wavelengths of operation (∼450 nm, ∼532 nm, and ∼635 nm). The process by which the nanoholes are optimized by parameter sweeps is discussed more in the Supplement 1.

 

Fig. 2. a). Schematic of unit cell. Periodic boundary (PB) conditions are used at x- and y-direction boundaries. Perfectly matched layers (PMLs) are used at z-direction boundaries. b). Transmission spectra of blue, green, and red color filters that each comprise periodic arrangements of unit cells. Filter transmissions at wavelengths representative of intended laser sources are shown. It can be seen that the cross-talk values of the blue, green and red channels are ∼6%, ∼17% and ∼16%, respectively. Here the cross-talk value is defined as the out of band transmission (e.g. blue channel has transmission of 0.07124 at green channel wavelength of ∼532 nm) divided by the in-band transmission (e.g. green channel has transmission of 0.4189 at green channel wavelength of ∼532 nm).

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We next consider the pixel configuration, i.e. containing the three nanohole groups whose x-position can be varied to achieve the necessary phase, with the extent of the nanohole pattern in the y direction determining the amplitude of the transmitted light. The relationship between phase and the distance in x direction can be understood as follows. Let us denote the distance of the center of the nanohole group to the center of the pixel in x-direction by δx. In the image field, the phase of the Fourier component associated with the $i,{j^{th}}$ pixel is then given as follows [1]:

From Fig. 2(b), it can be seen that the in-band transmission of the blue filter is the greatest, followed by the green and red filters. In the pixel configuration, we mitigate this by having the blue channel nanohole group (i.e. 4 × 7, with ${a_b}$=255 nm) occupy a smaller area than the green (i.e. 4 × 6, with ${a_g}$=320 nm) and red (i.e. 4 × 5, with ${a_r}$=415 nm) channel nanohole groups. Simulations of the pixel are again performed by the FDTD method, but with PMLs at all (i.e. x,y,z) boundaries to consider the case of an isolated pixel. We use the unit cell size designed in the previous part as the starting design, and then adjust dimensions to optimize the transmission and cross talk of the pixel. The geometric parameters of the pixel that results from this optimization are shown in the next section. To make the simulations computationally tractable, they are performed at normal incidence. To characterize the response of each channel, we use a field and power monitor at 100 nm above each nanohole group. Simulations are performed for a pixel in which the x-positions of the nanohole groups are chosen so that the phases of the blue, green and red nanohole groups are $- \pi $, 0, and $\pi $, respectively. For each channel, we find the power passing through a rectangle (in the xy plane at 100 nm above the nanohole surface). The results are through a rectangle (in the xy plane at 100 nm above the nanohole surface). The results are plotted in Fig. 3(a). The rectangles are shown in Fig. 3(b)–(d). From Fig. 3(a), it can be seen that the transmissions of the channels are very similar (i.e. between 0.05188 and 0.05519) at the intended wavelengths of operation. This confirms that the strategy of making the red/green/blue nanohole groups comprise different numbers of nanoholes has been successful. We also note that the transmission of each channel (in the pixel configuration) is approximately one tenth of its transmission in the unit cell configuration. This originates from the fact that each aperture (i.e. rectangles of Fig. 3(b)) occupies an area of ∼15% of the pixel. This modest efficiency, which is mainly due to the size of area occupied by each nanohole group with respect to the area of the entire pixel, can be increased by increasing the diameter of the nanoholes in each nanohole group and by adding more nanoholes in y direction. But increasing the nanohole diameter also increases the cross talk. By increasing the size of the pixel, we will increase the number of diffraction orders. The power that passes through the hologram is divided into these diffraction orders. The power in the first order diffraction will therefore reduce, thereby lowering the SNR of the image. In Fig. 3 (b-d) we show the electric field intensity of the transmitted light (${|E |^2}\left[ {{{\left( {\frac{V}{m}} \right)}^2}} \right]$) through the pixel at the intended wavelengths, namely 450 nm (Fig. 3(b)), 532 nm (Fig. 3(c)), and 635 nm (Fig. 3(d)). At each of these wavelengths, the intensity of the electric field for the corresponding nanohole group is maximized. It can also be seen from Fig. 3(a) that low cross talk values (of ∼10% to ∼20%) are achieved.

 

Fig. 3. (a) Transmission spectra of blue, green, and red nanohole groups from pixel. (b)-(d) Intensity of electric field (${|E |^2}\left[ {{{\left( {\frac{V}{m}} \right)}^2}} \right]$) at 100 nm above the filter at λ= 450 nm, 532 nm and 635 nm, respectively. Dashed white rectangles show regions over which power flows are integrated for blue, green and red channels.

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As discussed, an advantage of our approach is that it uses materials that are standard in CMOS technology. For the fabrication of the metallic nanoholes, one could use a variety of techniques, such as focused ion beam lithography (FIB), electron beam lithography (EBL), direct laser writing, interference lithography, dip pen nanolithography, self-assembly, and nano imprint lithography (NIL). NIL has the benefits of being simple, fast, and cost-effective and could therefore be suitable for our device. In [28], for example, Lu et al. used NIL to manufacture subwavelength Al, Ag, and Au nanoholes to demonstrate transmissive plasmonic structural color. A simple one-step method for fabricating subwavelength metallic nanoholes using NIL without additional etching is presented in [29]. Here, we propose an idea for fabrication of our metasurface using NIL (Fig. 4(a)-(e)). NIL is an embossing process in which a stamp is made from an ultraviolet-transparent material like quartz. In the first step (Fig. 4(a)), we would spin coat the photoresist (e.g. SU-8) on to the glass substrate. In the second step (Fig. 4(b)), the stamp would be pushed into the photoresist with a low contact force, e.g. 1-100 N, and ultraviolet (UV) illumination (e.g. in the wavelength range 350 to 450 nm) would be applied. In the next step (Fig. 4(c)), we would separate the stamp and photoresist (in which the patterns of holes are formed). It is known that the vapor deposition of an anti-stiction layer like Teflon onto the stamp can facilitate this. In the next step (Fig. 4(d)), we would evaporate the Al layer (150 nm). In the final step (Fig. 4(e)), we would lift-off the photoresist and coat the chip with SiO2 (200 nm thick).

 

Fig. 4. (a-e). The proposed fabrication process for Al nanohole array using NIL. (f) Schematic illustration of pixel model used in simulating hologram performance. Pixel is divided into $16\; \times 16$ sub-units. Here we illustrate pixel performance for the green band. For each sub-unit, amplitude and phase of transmitted field are calculated. If sub-unit corresponds to non-nanohole region, transmission field is assumed zero (here denoted with dark blue shading). As this example schematically illustrates green channel, transmission through green nanohole group will be high (as denoted by yellow shading). (g). Schematic of simulated hologram mask (for green channel), which contains ${({16 \times 512} )^2}$ sub-units.

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3. Results

We next design two Fourier-type detour phase holograms using our nanohole pixels. The first is the logo of a research center with which some of the authors are affiliated. The second is a rainbow-colored rose.

We perform the hologram simulations using the commercial software package MATLAB. The design process can be summarized as follows. In the first step, we read the target image with MATLAB and write it into a matrix with size 512*512*3. Here, the last index (3) represents the number of color channels. We then separate the matrix into color channels (red, green, and blue), with each saved as a 512*512 matrix. In the second step, we use the Gerchberg-Saxton algorithm [30] to design three holograms (for RGB) that would produce holographic images with equal sizes. By using the GS algorithm with 50 iterations, we calculate the hologram phase needed for the three channels. We round the phase values to eight phase levels. In the third step, we design the 16*16 subpixel array that encodes the eight phase levels for each of the 512*512 pixels (Fig. 4(f)). The subpixel array is illustrated in Fig. 4 g. Each subpixel array is divided into three rows for the three color channels (red/green/blue). As can be seen in Fig. 4 g, each color channel filter is eight pixels wide along the in x direction, with an eight additional pixels on either side to allow the phase to be encoded. We assign the amplitude of these regions by the transmission of the pixels we simulated in Fig. 3(a). Consider for example, the illumination of the structure of Fig. 4 g with a green laser. From Fig,. 4 g, it can be seen that the transmission of the green channel (denoted by yellow shading) is 0.0552. In this way, we model hologram performance in a realistic manner. Note that for a sub-unit in a non-nanohole region, the amplitude of the transmitted field is assumed to be zero. In the fourth step, we set the position of each rectangle (color filter) so that it yields the appropriate detour phase value (determined in the third step). In the fifth step, by taking the fast Fourier transform we determine the image field of the designed hologram. In the final step, we combine these three channels to yield the reconstructed image.

4. Discussion

We next simulate the performance of our holograms by modelling them as aforementioned. It can be seen that the holographic images predicted to be produced by our nanohole devices (bottom panels of Fig. 5 and Fig. 6) are in good agreement with the intended designs (top panels of Fig. 5 and Fig. 6). The reconstructed images for red, green, and blue channels are shown as the right panels of Fig. 5 and Fig. 6. The reconstructed images (i.e. combination of RGB channels) are shown as the bottom left panels of Fig. 5 and Fig. 6.

 

Fig. 5. Target image (top left panel), comprising the logo of a research center with which some of authors are affiliated. Reconstructed images for red, green, and blue channels (right panels). Reconstructed image (combination of RGB channels, bottom left panel). The reconstructed image has a SNR about 2.64 dB.

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Fig. 6. Target image (top left panel), comprising photo of a multi-colored rose. Reconstructed images for red, green, and blue channels (right panels). Reconstructed image (combination of RGB channels, bottom left panel) [33]. The reconstructed image has an SNR of ∼7 dB.

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To quantify the performance of the holograms, we find the SNR for the RGB image using the formula below:

To find the PSNR of the reconstructed images, we use an in-built function of MATLAB that is called “PSNR”. For the case of calculating PSNR for a single color channel, it is given as follows:

In which the MSE is the mean-square error of two images (target image, and achieved image) and is calculated as follows:

For the TMOS logo, the SNR and PSNR of RGB images are about 2.64 dB and 16.91 dB, respectively. For the multicolored rose, the SNR and PSNR of RGB images are about 7 dB and 15.97 dB, respectively. The SNR for the red, green, and blue channels for the TMOS logo are ∼ 3.2 dB, 2.35 dB, and 3.64 dB, respectively. The PSNR for them are ∼22.3 dB, 21 dB, and 21.9 dB, respectively. The SNR of red, green, and blue channel for the multicolored rose are ∼ 8 dB, 7.2 dB, and 6.4 dB, respectively. The PSNR for them are ∼ 19.5 dB, 21.2 dB, and 24.6 dB, respectively.

In our approach, the desired holographic field is the Fourier transform of the object field. Our hologram should therefore be used with a Fourier lens (e.g. see [1,2]), i.e. a lens would be placed at one focal length from the hologram to collect the light in the first diffraction order. The results shown in this paper are indeed from the first diffraction order. Some speckle is predicted but could be mitigated by filtering the high frequencies and other techniques mentioned in [34].

5. Conclusions

In conclusion, to best of our knowledge for the first time, nanohole arrays are used for detour phase multicolor holograms. Simulation results of the structure in the unit cell and pixel level configurations are shown. These predict good transmission efficiency and low cross talk. We design two multicolor holograms based on this approach and simulate their performance. The results demonstrate good fidelity to the desired holographic images. Due to the simplicity and CMOS compatibility of the fabrication process and the design process, we anticipate that our approach will be advantageous for many applications of multi-color holography.