Concept

Our approach is based on the fact that nanoparticles with sharp resonances can selectively scatter light of a particular wavelength, while being almost transparent at other wavelengths. By embedding wavelength-selective nanoparticles in a transparent medium and by projecting images at the resonant wavelength λ 0 , we can create a screen that scatters most of the projected light while being almost transparent to the broadband ambient light. This is illustrated in Fig. 1. To implement a full-color display, one could use three types of nanoparticles, each selectively scattering light at one of the three desired colors: red, green and blue; alternatively, one could use a designed nanoparticle with multiple resonances, each lying at one of the three desired wavelengths. The challenge of a good implementation lies in making the resonances sharp while maintaining high transparency away from the resonances.

Figure 1: Working principle for a transparent display based on wavelength-selective scattering from nanoparticles. The desired nanoparticles have the scattering cross-section sharply peaked at wavelength λ 0 , and the absorption cross-section uniformly zero. A transparent medium embedded with such nanoparticles is transparent except for light at wavelength λ 0 , as sketched in the inset. As an example, here we show the cross-sections for a metallic sphere in air, where the sphere has radius r=15 nm, and the metal is described by the Drude model with plasma wavelength 260 nm and negligible dissipation; the absorption cross-section is negligible in this case. Full size image

Theoretical design

One way to achieve wavelength selectivity is using the localized surface plasmon resonances in metallic nanoparticles10,11,12,13,14. We first provide a rough estimate to determine which metal is optimal to use. For a small particle (particle size << wavelength) with dielectric function ∈(λ), one can show that the ratio between on-resonance (at λ 0 ) and off-resonance (at λ 0 + Δλ, for a small Δλ of interest) scattering cross-sections is

for particles of arbitrary shapes. The derivation is given in Methods. Equation (1) reveals that, for optimal wavelength-selective scattering, the desired material should have a small Im(∈) and a fast-changing Re(∈) near the resonance wavelength λ 0 . A metal with negligible loss would be ideal (Fig. 1 provides one example; also see ref. Tribelsky and Luk'yanchuk), but most metals are quite lossy in the visible spectrum. Figure 2a shows the metals with large η≡|Re(d∈/dλ)/Im(∈)|2 in the visible spectrum (refractive index from ref. Palik). Silver has the highest value of η for most of the visible spectrum, so we choose to work with silver-based nanoparticles.

Figure 2: Theory design for metallic nanoparticles suitable for displaying three different colors. (a) A performance estimator for the wavelength selectivity of small plasmonic particles. See text for the definition of η. (b–d) Scattering and absorption cross-sections for silica-core silver-shell nanoparticles (embedded in an n=1.44 medium) optimized to scatter monochromatic light at λ 0 =458 nm (blue, b), 532 nm (green, c), and 640 nm (red, d). Insets show the relative sizes of the structures; r is the outer radius of the particle. Full size image

For more detailed optimization, we define a figure of merit (FOM)

that captures the desired properties: a uniformly low absorption cross-section σ abs , a high scattering cross-section σ sca at λ 0 , and low σ sca elsewhere. The overline and the symbol max{…} denote the mean and the maximum in the visible spectrum (from 390 nm to 750 nm). The number 2 is a weighing factor chosen to balance sharp scattering and low absorption. The absolute value of the cross-section per particle is less important here because one can adjust the areal density of the nanoparticles on the screen; thus, the FOM is defined as a ratio. Also, in order to have a colorless transparent screen, we prefer a flat absorption spectrum, so we use max{σ abs } rather than . One can also consider imposing a wavelength-dependent weight on the cross-sections to account for the spectral sensitivity of human eyes15, but we omit this weight for simplicity. With this FOM, we perform numerical optimizations on spherical core-shell nanoparticles with a silver shell and silica core, embedded in a transparent medium with refractive index n=1.44. Scattering and absorption cross-sections are calculated with the transfer matrix method16, using n=1.45 for silica and experimental values of the dielectric function for silver17. Particle size distribution is assumed to be a Gaussian with the standard deviation being 10% of the mean. We choose the core radius and shell thickness that maximize the FOM by performing a global optimization via the multi-level single-linkage algorithm18 implemented within the free nonlinear optimization package NLopt19. The resonance wavelength λ 0 can be tuned to arbitrary colors. Figure 2b–d show the cross-sections of structures optimized to scatter monochromatic light at λ 0 =458 nm (blue), 532 nm (green), and 640 nm (red); the corresponding particle sizes and FOMs are listed in Table 1.

Table 1 Optimal particle sizes and FOM for silica-core silver-shell nanoparticles. Full size table

According to the example in Fig. 1, one would prefer σ sca to be even more narrow in wavelength; nevertheless, as we will see, one can obtain fairly good transparent display properties even with cross-sections comparable with those shown in Fig. 2. Therefore, we leave it to future work to further improve the design. Dielectric nanoparticles may be a promising direction, as their resonance line widths are not as limited by absorption loss compared with metals20; Supplementary Fig. 1 provides such examples. Utilizing higher-order resonances21,22,23,24 is also a possible direction, provided that one can keep the lower-order broadband resonances out of the visible spectrum. The same FOM and optimization procedure can be applied in these explorations.

Experimental realization

As a proof of principle, we experimentally realize a blue-color-only transparent display. Simple spherical silver nanoparticles are used, since the structure optimized to scatter blue light has a negligible silica core (Table 1). A transmission electron microscopy image of these particles (nanoComposix) is shown in the inset of Fig. 3a; their diameter of 62±4 nm is chosen to match the optimized structure. To host the nanoparticles in a transparent polymer matrix, we mix 10% weight of polyvinyl alcohol (PVA, 80% hydrolyzed, Sigma-Aldrich) into an aqueous solution of silver nanoparticles (concentration 0.01 mg ml−1). We pour 480 ml of this liquid onto a framed square glass plate that is 25 cm in width, remove air bubbles from the liquid with a vacuum chamber and let the liquid dry out in the hood at room temperature. Over a course of 40 h, the liquid solidifies into a transparent polymer film of thickness 0.46 mm. This transparent thin film is the screen of our display. Its average transmittance is 60% in the visible spectrum (averaged from 390–750 nm).

Figure 3: Characterization of the fabricated film that is used as a transparent screen. (a) Transmittance spectrum of the film; width of the experimental curve indicates plus/minus one s.d. across different spots on the film. Inset shows a TEM image of the nanoparticles; the diameter is 62±4 nm. Scale bar, 200 nm. (b) Same data plotted as extinction, together with theory-predicted contributions from scattering and absorption. (c) Angular distribution of scattered light at 458 nm, when normally incident light has electric field polarized perpendicular (s) and parallel (p) to the scattering plane. The radial axis is in arbitrary units. Full size image

Figure 3a shows the transmittance spectrum of this film. For a direct comparison with theory, the measured data are normalized by the transmittance of a plain PVA film of the same thickness (which is higher than 90% in the visible spectrum). Theory prediction (solid line in Fig. 3a) from the calculated cross-sections and the Beer–Lambert law (no fitting variables) agrees well with the measured data; the slight discrepancy is due to a minor clustering of the nanoparticles (Supplementary Fig. 2). The calculated cross-sections indicate that the on-resonance scattering is significantly stronger than the on-resonance absorption (Fig. 3b), which is good for our purpose here. Figure 3c shows the angular distribution of scattered light at λ 0 . The distribution is close to the Lambertian distribution for an ideal diffusely reflecting surface, confirming that the scattered light can be viewed from a wide angle. The polarization dependence is weak, indicating that we may operate the screen with incident light of arbitrary polarization. A minimal model for the angular dependence (described in Methods) yields the lines in Fig. 3c.

In Fig. 4a, we show the transparent display at work, with a blue MIT logo projected onto the screen from a small laser projector (MicroVision SHOWWX+). This projector is suitable here since it functions by projecting monochromatic light from three laser diodes (red, green and blue)25; we measure the wavelength of its blue light to be 458±2 nm. The projected image shows up clearly on our screen, and is visible from all directions. In comparison, the same image projected onto regular glass (Fig. 4a, photo on the right) can barely be seen due to the lack of scattering. The transparency of our screen can be judged by comparing it with regular glass: Fig. 4a shows that objects behind the screen (three colored cups) remain visible, and their apparent color and brightness change only very slightly. A recording of the screen displaying animated images is shown in Supplementary Movie 1. We also compare an image projected onto this screen and onto a piece of white paper: Fig. 4b shows that on our screen, the projected image is slightly dimmer but the contrast is better due to less scattering of ambient light. Finally, we point out that high-resolution images can be projected onto this screen with clarity, because the screen has on average 6 × 109 nanoparticles per cm2 of area.