Wide-angle, broadband, and highly efficient holography

Computer-generated holography is a widely used technology for various applications, e.g., from authentication and optical data storage, to interferometry, particle trapping, and phase conjugation.^1–4 In these applications, complex waveforms are radiated efficiently at small angles from the holographic elements. Alternatively, simple grating lobes—with specific resonant conditions—can be used to project the waveforms at larger angles.^5–7 To achieve wide-angle projection of computer-generated holograms, a steep phase gradient between adjacent pixels is required. To attain such a gradient, however, a small number of pixels in each period is needed and the projected hologram is therefore inefficient.^8–10 Efficient projection of complex waveforms at large angles thus remains a challenge.^{11, 12}

An alternative approach for the generation of complex reflective patterns involves the use of nano-antenna-based metasurfaces. Nano-antennas, which are nanometer-sized metallic structures, resonate at optical frequencies and are essentially a scaled-down counterpart of conventional radio-frequency antennas.^13–16 In some recent studies, the use of nano-antennas for holography has been demonstrated.^17–21 These previous investigations, however, have mostly focused on optical transmission metasurfaces. This has limited the measured efficiency levels to below 10%.

In this work, we propose and demonstrate the use of a nano-antenna reflectarray for efficient, broadband, and wide-angle holography applications.²² We use our reflectarray, which is composed of optical nano-antenna elements in a coupled dipole-patch configuration, to control the phase of the scattered light. Before we are able to realize our nano-antenna-based hologram approach, we have to determine the phase map that corresponds to the desired output beam. We thus implement the Gerchberg-Saxton algorithm^{23, 24} for this purpose. We have chosen the logo of Tel Aviv University as the pattern for the demonstration of our technique. During the demonstration, we projected this logo at angles of 20 and 45°, relative to the incident beam. The required phase map and the corresponding optical output are shown in Figure 1, as well as an illustration of the holography concept.

Figure 1. Demonstration of the nano-antenna reflectarray holography approach.²⁰The (a) phase map and (b) simulated far-field image of the Tel Aviv University logo are shown. AU: Arbitrary units. (c) Illustration of the experimental concept. θ: Angle of projection.

The next step in our approach is to design nano-antennas that scatter light with the desired phase. The antennas are chosen so that the continuous phase is quantized into six discrete values between 0 and 300° (in 60° increments). To span the phase completely, we find that it is advantageous to use unit cells that comprise two antenna elements with different geometries. The combined spectral response of the two elements provides more degrees of freedom for the design and facilitates 2π-phase spanning. We used the technique of electron-beam lithography to fabricate our nano-antenna arrays (see Figure 2).

Figure 2. Optical microscope (a) and scanning electron microscope (b) images of a fabricated nano-antenna array. (c) A high-magnification scanning electron microscope image of the region indicated.²⁰The array consists of 256×256 unit cells, and each unit cell is a 720nm-side square. The final device therefore has dimensions of 184×184μm.

To achieve a high efficiency with our technique, the reflectivity of the individual elements should differ only in phase and a constant amplitude should be maintained. By properly selecting the dimensions of our antenna elements—see Figure 3(b)—it is possible to attain a scattered wave that possesses any required phase response, while retaining a uniform amplitude. By varying the dimensions of these elements, we can alter the combined antenna response, which in turn changes the phase of the reflected wave. We conduct the optimization of the nano-antennas over a supercell consisting of the six phase pixels, organized in sequence from 0 to 300°, as shown in Figure 3(a). We simulate the supercell in an infinite 2D array, which enables a computationally efficient optimization of the elements. It is also possible to modify the element dimensions in the supercell. We can thus optimize the phase response and obtain the final element dimensions.

Figure 3. Unit cell geometry of the supercell used for nano-antenna optimization.²⁰(a) Top view of the unit cells. Au: Gold. Cr: Chromium. Si: Silicon. SiO₂: Silica. L: Length. W: Width. (b) Phase response (top) and amplitude response (bottom) of the antenna elements. Stars in (b) indicate the dimensions of the dipole and patch nano-antennas, which are obtained during the supercell optimization.

The scattering efficiency of our resultant hologram is illustrated in Figure 4. These measurement results indicate that the efficiency remains high over a spectral range of 200nm. This broadband response is caused by the phase response of our designed nano-antennas, which is strongly wavelength independent. We also find that the image projected by the hologram remains unchanged. For comparison, the theoretical efficiencies of the phase-quantized hologram projected at 20 and 45° are 60 and 55%, respectively. Our measured efficiency is therefore only slightly lower than the theoretical predictions. This difference arises from fabrication errors and optimization tolerances.

Figure 4. Efficiency measurements for the 20^°(dashed red) and 45^° (solid blue) holograms. The inset is an image of the projected hologram.²⁰λ: Wavelength.

We have demonstrated a new wide-angle, highly efficient optical holography approach in which we use a reflectarray of optical nano-antenna elements to control the phase of the scattered light. In our methodology, we use the Gerchberg-Saxton algorithm to determine the phase map that is required to project our chosen pattern at angles of 20 and 45^°, relative to the surface normal. We found that the measured efficiency of the projected hologram is between 40 and 50% over a broad wavelength range. To further improve the efficiency of our holographic technique, we need to develop new methods to eliminate phase and fabrication errors. Moreover, by incorporating an active tuning mechanism, it may be possible to extend our approach and thus realize active holographic displays and communication devices.