1. Introduction

Introduced by Gabor, a hologram is the recorded interference pattern between a known illumination pattern, called the reference wave, and the scattered fields from an illuminated object; when the hologram is illuminated by the original reference wave, the wave front that would have been scattered off of the original object is reconstructed [1]. The original Gabor holograms and subsequent early adaptations [2] sampled only the intensity distribution of the interference pattern (i.e., forming a real-valued hologram). As a consequence, when illuminated by a reference wave, these holograms generated an unwanted conjugate image and a zeroth order mode, in addition to the primary image [3]. In contrast, pioneering methods such as Detour-Phase [4], Kinoform [5], and ROACH [6] allowed researchers to fabricate complex-valued holograms, in which both the phase and the magnitude of the interference pattern could be sampled, mitigating the zeroth order and conjugate image problems.

Traditional holograms require the recording of actual fields scattered from a physical object, exposing photosensitive plates to produce a spatial transparency distribution that subsequently modulates the intensity of the reference wave. In a generalization of the concept, computer generated holograms can be designed using analytical expressions or computational simulations of the interference between reference and scattered waves [5,6]. Rather than producing interferograms by photographic techniques, computer generated holograms can be directly fabricated by a variety of lithographic methods. For example, phase holograms—as opposed to the original intensity-based amplitude holograms—can be created using dielectric materials to form arrays of pixels. The phase advance of each pixel can be adjusted by changing the length [5] or index-of-refraction [6] of the material. Alternative approaches include varying the density of a dielectric material by subwavelength patterning, such that the effective index can be controlled spatially [7]. These approaches provide approximate control over the phase, which is typically quantized into a small number of phase levels, but no independent control over the amplitude.

Because of their flexibility in design, artificially structured metamaterials provide potential advantages for holographic media. In experiments similar to that depicted in Fig. 1, metamaterial phase holograms have been demonstrated using arrays of patterned gold “I-beam” elements at 10.6 and 1.5$\text{μm}$wavelengths [8,9]. In this context, the non-resonant metamaterial elements are polarizable inclusions that behave similarly to artificial dielectrics, allowing the effective index at a point to be defined by the metamaterial geometry (I-beam size and shape). The metamaterial holograms displayed as many as 61 independent phase levels, much larger than typical dielectric holograms, limited only by fabrication tolerances.

 

Fig. 1 Experimental setup. A W-band, Fraunhofer, metamaterial hologram is excited using an off-axis, free- space illumination scheme. A planar near-field scanner measures the radiated near-fields across a plane parallel to the hologram; the far-field pattern is computed by propagating the near-fields to the far-field region. The inset depicts a section of the aperiodic metamaterial array forming the hologram.

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To achieve sufficient phase advance for optimal efficiency, however, these effective index holograms required six or more metamaterial layers in the propagation direction, implemented by a difficult multilayer fabrication approach. As an alternative, patterned metasurfaces have been used to create electrically thin holograms and other unusual diffractive optical elements [10–20]. Formed from single layer, two dimensional metamaterial arrays, metasurfaces have been investigated for applications in the fields of perfect absorbers [21,22]; computational imaging [23–25]; plasmonics [26]; and wireless power transfer enhancement [27] and shielding [28], among others. In the context of holography, metasurfaces comprising subwavelength, resonant metamaterials are used to couple to an incident reference wave and structure the resulting scattered fields. Relying on resonant structures, however, means the polarizabilities of the metasurface elements have a frequency-dispersive form that resembles a Lorentzian, with a phase response that is limited to $180°$, as shown in Fig. 2. In order to form holograms with the full $360°$ phase range, despite this Lorentzian limitation, researchers have developed three possible methods. The first manipulates the polarization of the scattered fields relative to the incident wave [10–12]. In a recent striking example [12], asymmetric metamaterial elements convert part of the incident light to the cross-polarized state, by an amount that is proportional to the element’s orientation. A single layer metasurface operating in this fashion can thus produce a well-defined holographic image, but the efficiency is often low since only a small portion of the incident light is converted. In the second method, a reflective surface is positioned behind the resonant array [13,14]. Using this method, Pors and Bozhevolnyi demonstrated a reflective metasurface able to reflect two orthogonal polarizations into different diffraction orders with an efficiency of about 80%. While this approach can clearly yield high efficiencies, it also limits the user to reflection-mode holography. Lastly, a third method introduced by Pfeiffer and Grbic utilizes metasurfaces that combine both electric and magnetic response [15,16]. By controlling both the phase advance as well as wave impedance, the Huygens’ surface can provide complete freedom for tailoring wave fronts, while simultaneously minimizing reflection. In general, though, it is very difficult to design matched electric and magnetic resonators that simultaneously control impedance for all phase shifts.

 

Fig. 2 Complex Lorentzian polarizability. (a) A resonator with Lorentzian polarizability exhibits the normalized magnitude (blue) and phase (red, degrees), plotted as a function of ${\omega }_0/\omega$. We define the phase at resonance to be zero degrees. (b) The coupled relationship between magnitude and phase. In this example the resonator’s quality factor was arbitrarily chosen as Q = 10.

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Motivated by the prospect of a single layer holographic metasurface, we present the use of resonant metamaterial elements that can impart a continuously tunable phase response and a variable, non-uniform magnitude to the generated wave front at every point on the surface. While similar to the concept applied in [15,16], our holographic metasurface is populated only with magnetic metamaterial elements. Because this design provides control over only the effective magnetic component of the field, the impedance is not directly controlled and the full $360°$ phase range is not reached by the elements’ polarizabilities. However, using only magnetic (or electric) resonators simplifies the metasurface design process; furthermore, with choice of an appropriate reference wave, our holographic metasurface can in fact form pixels with phases greater than the range subtended by the resonators’ polarizabilities alone.

The manuscript is organized as follows. In Section 2, we describe how the phase of each pixel in a hologram can be tuned using resonant metamaterial elements, which we model as magnetic dipoles with Lorentzian-like polarizabilities. Because the pixels are implemented using only magnetic resonators and not a pair of electric and magnetic resonators, their phases can span a maximum range of $180°$, with their magnitude coupled to the phase. In Section 3, we discuss how, despite these limitations, we can nevertheless design the hologram’s radiation pattern by treating the resonant (and coupled) phase and magnitude responses as constraints in the iterative Gerchberg-Saxton (GS) algorithm. In Section 4, we provide an experimental example of an off-axis, free-space illuminated W-band hologram designed using the method discussed in Sections 2 and 3. We also describe how, prior to designing the hologram, we characterize our metamaterial’s response as well as the reference wave used to excite the hologram (with further details pertaining to the hologram design, fabrication, and measurements are discussed in the accompanying appendices). In Section 5, we describe how an alternative realization of the constrained metasurface holograms can mitigate the undesired zeroth order mode: while the phase range of the metamaterials’ polarizabilities is still limited to $180°$, an appropriate choice of the hologram’s reference wave – such as the fields of a parallel-plate waveguide – can relax the demands on the polarizabilies’ phase range. Lastly, in Section 6, we summarize and conclude our findings.

2. Magnetic, holographic metasurface

The system we consider is a metallic screen with complementary meander line elements forming the metamaterial pixels, as depicted in Fig. 1. The resonant metamaterial elements that form the holographic pixels behave as polarizable magnetic dipoles, excited by the magnetic field of the reference wave, and radiate as magnetic dipoles [29]. The magnetic polarizability $\overline{m}$ of the metamaterial element is approximately

The complex response of a Lorentzian resonator is illustrated in Fig. 2, where we have normalized the polarizability such that at $\omega ={\omega }_0$ the phase is zero and the magnitude is unity. Based on a single magnetic resonator, $\overline{\overline{\alpha }}$ is limited in phase to a range of $180°$ centered around ${\omega }_{0,k}$ with magnitude that is coupled to the phase as indicated in Eq. (2).

We observe that the amplitude of the polarizability, $\left|\alpha \right|$, peaks at the resonance frequency, corresponding to a strongly radiating dipole, while far from resonance $\left|\alpha \right|$ approaches zero and the phase, ${\Phi }_{\alpha }$, approaches $\pm 90°$. Practically, we are limited to a range of ${\Phi }_{\alpha }$ that spans less than $\pm 90°$, because in these extremes the dipole radiation drops to negligible values. As we discuss below in Section 3, by constraining the hologram to ensure its elements obey the coupled amplitude and phase relationship of Eq. (2), the radiation pattern of a metamaterial hologram can be successfully optimized. Furthermore, despite the limits imposed by the Lorentzian response on the phase range of $\alpha$, we note that when the reference wave exhibits a large phase variation—for instance, by using a guided reference mode [23–25]—the phase of the holographic pixels can span a range greater than $\pm 90°$. This is possible because the phase of the dipole’s polarizability is added to the phase of the reference wave exciting it. To highlight the effect of this interference on the behavior of a hologram, $H$, it is convenient to represent its pixels with the phasor notation

Using this notation, we see that, when the reference wave exhibits a non-uniform phase distribution, the hologram’s pixels can exhibit phases beyond ${\Phi }_{\alpha }$, the polarizability’s Lorentzian-constrained phase response. This concept is addressed again and in Section 5.

3. Enforcing the Lorentzian constraints

To apply the constraints imposed by the resonant form of the polarizabilities, we use the well-known Gerchberg-Saxton (GS) algorithm, which iteratively computes the field patterns on two planes related via a propagating function, with both patterns satisfying user-defined constraints [34]. Here, the two planes are the hologram plane and the image plane. For simplicity, we choose to operate in the Fraunhofer regime, allowing use of the Fourier transform (FT) as the propagator.

We begin the iterative process with a desired field pattern $E$ to be generated by the hologram at the image plane; it is common to use a magnitude-only target image, and we do the same in the experiment as discussed below in Section 4. Then, at each iteration, the resonance constraints are applied according to the steps outlined below, where we use the tilde mark $\left(\tilde{\cdot }\right)$ to denote unconstrained quantities (we note that the reference wave, $U$, as well as the relationship governing the magnitude and phase response of the dipoles must first be characterized or otherwise modeled):

We can constrain the hologram’s pixels (step III and IV) in several ways. For example, transmission through any pixels exhibiting ${\tilde{\Phi }}_{\alpha }>{\Phi }_{\max }$ or ${\tilde{\Phi }}_{\alpha }<{\Phi }_{\min }$ can be prevented (implemented in the algorithm by setting $\left|\alpha \right|=0$ at these locations and realized experimentally with an opaque pixel). However, such a hologram would suffer from reduced efficiency. Instead, we choose to snap the phases of $\alpha$ to a pre-determined value, according to

4. Experimental example of an off-axis, free-space, W-band hologram

As an illustrative example, we present the design and fabrication of a W-band (75-110 GHz) Fraunhofer hologram with a far-field pattern forming the word ‘DUKE’ when illuminated by a horn antenna, as illustrated in Fig. 1. In the sections that follow, we discuss the details of our metamaterial elements design, fabrication, and characterization, as well as the experimental measurements and results.

4.1 Metamaterial fabrication and characterization

Each pixel in our hologram is realized using a complementary meander line metamaterial element [35] with the geometry shown in the inset of Fig. 3(a). Lithography is a common way to fabricate such metamaterial surfaces, but it suffers from various drawbacks, some of which are especially evident at the W-band frequency regime. Across all frequencies, due to their reliance on masks, lithographic techniques suffer from added costs associated with the mask materials; time delays due to mask fabrication and shipping; performance deterioration following successive uses; over- or under-exposure due to refraction through the transparent layer; and alignment difficulties. In-house lithography on copper-clad printed circuit boards (PCBs) is relatively easy, because it is possible to print large masks on inexpensive transparencies and develop the negatives in a dark room. However, due to aspect ratio limitations imposed by the PCB copper’s thickness, this technique cannot be leveraged to prepare elements with features small enough for W-band and is usually reserved for fabrication of metamaterials used in S-, C-, and X-bands. Cleanroom lithography, of course, is able to yield elements with very small feature sizes and has been used in fabrication of metamaterials for terahertz (THz) frequencies [9]. Cleanroom techniques, however, are significantly costlier and time consuming. Additionally, the cleanroom mask size—while large enough for THz applications—is too small for operation in the W-band regime where wavelengths are longer. For these reasons, we fabricated our metamaterial elements using an LPKF U3 laser system, etching the meander line structures onto the top plate of a 20 mil $\left(\text{508}\text{μm}\right)$ thick, low-loss, Rogers 4003 dielectric clad with 1.0 oz ($\text{35}\text{μm}$thick) copper. This method allowed us to fabricate an electrically large hologram comprising elements with features as thin as $\text{25}\text{μm}$. Specific details and challenges pertaining to this fabrication procedure, as well as images of the fabricated samples, can be found in Appendix A.

 

Fig. 3 Metamaterial characterization. (a) Illustration of the experimental setup, with the element design shown in the inset; here $\tau =\text{25}\text{μm}$and the unit cell size is 1 mm. Measured $S_{21}$ magnitude (b) and phase (c) for elements of various lengths. Interpolated (and normalized) magnitude (d) and phase (e) of $S_{21}$vs. $L$ at 92.5 GHz. Circles mark measured data points.

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The meander line’s resonance frequency is tailored by selecting its length parameter $L$ (see Fig. 3). To determine the value of $L$ required for an element to resonate at a desired frequency, we experimentally characterize the transmission through a sequence of fabricated metamaterial samples rather than relying solely on simulated values. The samples consisted of 1600 identical meander line elements forming a 4 cm x 4 cm array; each sample utilized a different meander line length $L$, ranging from $\text{363}\text{to}\text{500}\text{μm}$. We then positioned each sample between a pair of collimated lens antennas (Quinstar QLA-W00Y03S), measured the complex $S_{21}$values as a function of frequency using an Agilent PNA-X N5247A Vector Network Analyzer (VNA) with VDI WR10 + millimeter wave extenders, and normalized the measured S-parameters using a pre-recorded, air-only measurement. The free-space characterization setup is illustrated in Fig. 3(a). We note that the extenders, rated to have amplitude and phase stabilities of $\pm 0.15\text{dB}$ and $\pm 2°$, respectively, were warmed up for over an hour to ensure our source was stable. To reduce noise arising from multiple reflections, we gated the measurements inthe time-domain around the main transmission peak for a given sample. The measured (and normalized) magnitude and phase of the transmission for each of the samples are plotted in Figs. 3(b) and 3(c), respectively. We note that while the measured transmission is arguably low, our aim in this manuscript was to produce a proof-of-concept demonstration of a single-layer solely-magnetic hologram designed using our method, and no attempt was made in the design to optimize the elements’ transmission levels. Using these measurements, we interpolated the metamaterial elements’ complex response as a function of $L$ at an operation frequency $\omega =92.5\text{GHz}$, allowing us to design holograms with continuous phase levels (limited only by the fabrication method’s resolution). The interpolated transmission values are plotted in Figs. 3(d) and 3(e).

4.2 Hologram design and measurements

Before the iterative hologram design process could begin, accurate knowledge of the hologram’s reference wave was needed. In order to spatially separate the desired image from the hologram’s zeroth order, our reference wave was transmitted from a corrugated horn oriented $26.5°$ off the hologram’s normal, as shown in Fig. 1. We characterized the reference wave by sampling the fields transmitted from the horn over a grid of points on a plane parallel to the hologram plane, and using the known plane-to-plane field propagator to back-propagate the measured horn fields to the hologram plane [3,36]. To measure the transmitted fields we scanned a tapered rectangular waveguide probe in increments of 1.3 mm along $\widehat{y}$ (slightly smaller than ${\lambda }_0/2$) using a planar, microwave, near-field scanning device (model NSI-100V-1X1 by Nearfield System Inc., or NSI). The fields were measured at z = 16.5 mm, a distance corresponding to over five wavelengths at our operation frequency, in order to avoid any reactive near-field interactions between the probe and the hologram that was eventually placed in front of the horn. The phase and amplitude of the measured reference wave (when back-propagated to the hologram plane) are shown in Fig. 4(a) and 4(b), respectively. A figure of the actual experimental setup, as well as additional details regarding the hardware we used, is found in Appendix B.

 

Fig. 4 Fields at the hologram plane and far-field images. Phase (a) and magnitude (b) of the reference wave illuminating the hologram. Desired field pattern used in the GS algorithm (c). Phase (d), magnitude (e), and far-field pattern (f) of the simulated hologram generated by the GS algorithm. Measured and back-propagated phase (g) and magnitude (h) of the fabricated hologram and its experimental far-field pattern (i). Far-fields were computed as the Fourier transformed hologram fields. Simulations and measurements shown are reported at 92.5 GHz and 94.75 GHz, respectively.

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With the measured reference wave and metamaterial response, it was now possible to design a constrained hologram using the iterative GS algorithm. To satisfy the Fraunhofer approximation, we design the magnitude of the hologram’s far-field pattern to form the word ‘DUKE’ within a ${30}^o$field of view around the optical axis $(\widehat{z})$ and leave all other image pixels blank (the far-field phases were left unconstrained), as shown in Fig. 4(c). The hologram that we designed and fabricated was $\text{7}\text{.6}\text{cm}\text{×}\text{7}\text{.6}\text{cm}$ in size and populated by elements with polarizabilities constrained to phases between $\pm {60}^{°}$ (chosen empirically) and amplitudes matching the measured response shown in Figs. 3(d) and 3(e). We continued to iterate until a satisfactory convergence was reached in the hologram’s error level, which we computed as the mean-squared difference between the target image pixels and the simulated far-fields in the region surrounding the word ‘DUKE’ (excluding the region of the zeroth order mode). In our experience, convergence occurred within 20 iterations. The phase and magnitude of the analytical, constrained hologram generated by the GS algorithm is shown in Fig. 4(d) and 4(e), respectively. We observe that the hologram’s pixels span a phase range significantly greater than that of the resonant elements’ polarizabilities, because the (limited) phase of the dipole’s polarizability is added to that of the reference wave exciting it. The analytical hologram’s far-field pattern, computed by taking the Fourier transform of the hologram-plane fields, is shown in Fig. 4(f) in log scale (and normalized to its maximum value). We note that, at each iteration, our model assumes the reference wave is not perturbed by scattering from the dipoles, and that interactions between dipoles are negligible. Interaction effects can be modeled using more sophisticated tools such as the discrete-dipole approximation (DDA) [37,38], which are beyond the scope of this discussion.

To experimentally measure the hologram fields, we inserted the fabricated hologram between the horn and the probe, repeated the measurement procedure described above, and again back-propagated the measured fields to the hologram plane. The phase and magnitude of the experimentally computed hologram are shown in Figs. 4(g) and 4(h), respectively, and the experimental hologram’s far-field pattern is shown in Figs. 4(i), where we observe that the fields clearly form the word ‘DUKE’ away from the zeroth order mode.

The experimental results shown in Figs. 4(g-i) (i.e. the complex hologram and its far-field pattern) were measured at 94.75 GHz, corresponding to a shift of about 2.5% from the intended operation frequency. We attribute this blue shift to the fact that we characterized our metamaterial response using uniform, periodic, samples, while neighboring elements in the hologram are not necessarily identical. However, we believe this discrepancy can be accounted for using DDA tools, and can serve as the topic of future research. Lastly, we note that while our hologram was designed to operate in W-band using the off-axis, free-space illumination setup depicted in Fig. 1 — and the Fraunhofer regime allowed us to use the simple Fourier transform as the propagator in the GS algorithm — the techniques we describe here can be readily applied to holograms operating at higher or lower frequencies, to Fresnel holograms [10], and to reconfigurable apertures [39–41].

5. Analytical example of a hologram excited by a guided mode

While the transmitted fields of the hologram discussed in Section 4 were successfully structured to form the word ‘DUKE,’ the limited phase range of the element polarizabilities allows a significant portion of the incident reference wave to propagate into the undesired zeroth order mode (a theoretical study of the hologram’s zeroth order transmission as a function of the limits imposed on its resonant elements’ phase is discussed in Appendix C). Free-space illumination, however, is the only way to excite the metasurface elements. Alternatively, we can use guided fields to couple to the resonant elements. The benefit of using a guided reference mode is twofold: first, it can yield a larger phase variation and reduce or altogether eliminate the zeroth order mode; and secondly, a hologram excited by a guided mode can be significantly more compact than one operating in transmission or reflection. In fact, the compact form factor is a particularly desirable feature because it allows the hologram to be used in an antenna format, a concept recently explored and implemented at frequencies below W-band. In one particular example, Sievenpiper et al. demonstrated a flat antenna that supports a surface wave on top of a patterned surface [18]. By implementing a holographic design for the patterned surface, the authors were able to control the antenna’s surface impedance and form a beam pointing in a desired direction. In subsequent work, guided structures were used to form reconfigurable, holographic, metamaterial antennas [39–41]. The ability to form dynamically reconfigurable, inexpensive, flat antennas has been a ‘holy grail’ in the field of holographic apertures, and relying on a guided reference wave makes it possible to populate the antenna with the many bias lines needed to modulate its elements.

In several recent examples of dynamic apertures based on waveguide fed metasurfaces, amplitude holograms have been generated through selective damping of the metamaterial resonators [41]. The guided mode structures can be used in conjunction with the phase-modulating technique we described earlier (in the context of a free-space illuminated hologram) to produce a guided-mode phase hologram. As an example, we simulate a guided-mode metasurface hologram, and analytically model its reference wave, metamaterial response, and resulting radiated field pattern.

The guided-mode metasurface geometry we consider for this example is that of two parallel plates with a probe at their center launching a guided mode with cylindrical phase fronts, as shown in Fig. 5(a). The guided fields radiate from the structure by coupling to resonant, complementary, metamaterial elements patterned into the top plate of the waveguide. While the concept we discuss is applicable to other varieties of aperture configurations, we choose this particular configuration as an example because it is similar to existing holographic metasurface implementations used for computational imaging [22–24] and beam-forming [39–41].

 

Fig. 5 Simulated guided-mode hologram. (a) One possible embodiment of a hologram excited by a guided reference wave utilizes a parallel-plate waveguide excited by a source at the center. The guide mode’s magnitude (b) decays away from the excitation point while the phase (c) propagates with cylindrical phase fronts (assuming no reflections from the edges or perturbations due to the metamaterial elements). The magnitude (d) and phase (e) distribution of the hologram. (f) The resulting (normalized and log-scale) far-field pattern, computed as the aperture fields’ Fourier transform.

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For the scope of this discussion, we assume the guided mode experiences no reflections from the hologram’s edges, and that it is not perturbed by the metamaterial elements’ presence. While we recognize such assumptions make this theoretical hologram significantly simpler to design than would otherwise be possible, in this discussion we are merely interested in a qualitative demonstration of the image-forming abilities such holograms can exhibit. Treating the probe as a line source along $\widehat{z}$ and assuming the distance between the plates does not support higher-order modes, we model the guided magnetic field by [42],

Next, using the modeled guided fields as our hologram’s reference wave, and, assuming this hologram’s metamaterial elements behave as those measured and discussed previously, we again use the GS algorithm to design a constrained hologram forming the word ‘DUKE’ in the far-field. The magnitude and phase of the resulting hologram are plotted in Figs. 5(d) and 5(e), respectively. We again computed the far-field pattern by taking the Fourier transform of the hologram fields, and plot the results (normalized and in dB scale) in Fig. 5(f). When comparing the far-field pattern of the free-space illuminated hologram (simulated or experimental) to that of the guided-mode hologram, we can clearly see that the latter produces no observable zeroth order.

6. Conclusion

Holography is a powerful tool for imaging and beam formation. Due to their inherent design flexibility, metamaterials and metasurfaces have distinct advantages in the formation of computer generated holograms. Here, we have introduced a metasurface hologram with pixels solely consisting of magnetic metamaterial resonators. While the resonant polarizabilities of these elements limit the phase range to $180°$ or less, by accounting for their resonant response, it is possible to design holograms with a continuous phase variation and non-uniform (albeit coupled) magnitude distribution. To enforce the resonant phase constraints (and coupled magnitude response) of the holographic pixels, we apply the iterative Gerchberg-Saxton algorithm. As a demonstration, we designed, fabricated, and measured an off-axis, free-space illuminated hologram with a co-polarized far-field pattern that forms the word ‘DUKE’ at W-band frequencies. While such a hologram suffers from a transmitted zeroth order mode, we have shown that a metasurface hologram excited by a guided reference wave can mitigate this problem and simulated such a structure at 92.5 GHz. Lastly, the approach we described in this manuscript can be leveraged in the design of holograms at higher or lower frequencies; for Fresnel holograms; and for reconfigurable holographic apertures.

Appendix A Hologram fabrication

The metasurface hologram was fabricated from a single layer of 20 mil thick$\text{(508}\text{μm)}$low-loss Rogers 4003 dielectric, clad on both sides with 1 oz. $\text{(35}\text{μm)}$thick copper. To fabricate the hologram, we used an LPKF U3 laser system operating at a wavelength of 355 nm to etch the metamaterial elements into the copper layer on one side of the substrate. Then, since our hologram operates in transmission mode, we formed an aperture on the opposing side by removing all copper in an area just larger than the metamaterial array. The laser system’s default settings have it cycle through several steps, known as phases, in the process of etching copper away from the circuit board; an illustration of the beam paths associated with the various phases is shown in Fig. 6(a). The first phase, called contouring, outlines a desired polygon using a focused beam $\text{15}\text{μm}$in diameter; only the metal along the polygon’s outline is removed at this stage. In the following phase, called hatching, the metal within the outlined polygon is divided into thin stripes. By default, these stripes are $\text{120}\text{μm}$wide and up to 20 mm in length. In the final phase, called heating, the laser beam is defocused to increase its area, and the metallic stripes are separated from the substrate. Unlike the focused beam used in the first two phases, which melts and vaporizes the copper, the defocused beam used in the last phase provides enough heat to delaminate the copper from the substrate’s surface and an air knife blows the delaminated copper away.

 

Fig. 6 Laser phases and etching. (a) Our laser’s default phases are contour (red), hatch (blue), and heat (green) – shown her along paths computed by the laser’s software to etch a larger, conventional metamaterial element. (b) For our thin W-band elements, we utilized only the contour (red) phase. Initial unit cell simulations assumed only the copper layer was removed by the laser’s beam (c), these simulations were later revised to account for the fact that the laser penetrates beyond the copper layer and etches into the substrate as well (d).

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We have found that these steps and their associated default settings provide an effective way to remove large metallic areas. For small features, however, the hatching and heating phases can create undesired variations in the amounts of copper removed. For this reason, we designed our W-band elements using very fine traces, such that the hatching and heating phases were not needed and our metamaterial elements were instead fabricated using the contour phase alone, as shown in Fig. 6(b). In this fashion, we were able to use the laser’s focused beam to ablate meander line structures in a repeatable and accurate way with features as thin as $\text{25}\text{μm}$ – smaller than LPKF’s advertised minimum feature size.

Lastly, as illustrated in Figs. 6(c) and 6(d), we observed that in addition to etching the copper layer, the laser’s beam also etched away a non-negligible amount of the dielectric substrate lying underneath the copper – resulting in a significant frequency shift of our elements’ resonance. Using a Bruker Dektak 150 Profilometer and Zygo NewView 5000 3D Optical Profiler, we determined that, on average, this over-etching removed around $\text{80-90}\text{μm}$ of the substrate along the contour paths. To account for the effects of this substrate etching in the design process and mitigate the undesired frequency shift, we modified our unit cell simulations by removing this depth from the substrate.

The fabricated hologram, shown in Figs. 7(a)–7(c), was a 7.6 cm x 7.6 cm array populated by complementary meander line elements with a lattice constant of 1 mm, for a total of 5,776 elements. The entire array was etched in about 15 minutes, at a rate of almost 400 elements per minute. Such speed, and the relatively automated fabrication process, offers a significant advantage when compared to alternative fabrication methods in academic settings such as lithographic techniques, which could be expensive or require at least several hours (and likely days) and involve many manual steps.

 

Fig. 7 Fabricated sample. (a) The hologram covers a 7.6 cm x 7.6 cm square of 1 mm x 1 mm elements. (b) A confined view of approximately 7% of the total hologram area. (c) Zoomed view of 25 elements, which covers less than 0.5% of the total hologram.

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Appendix B Experimental setup and measurements

Before the hologram could be designed, we needed an accurate measurement of the reference wave used for illumination. We conducted this measurement using an NSI planar near-field scanner, (NSI-100V-1X1 by Nearfield System Inc.). This scanner was installed on site to work with a pair of OML V10VNA2-T/R millimeter wave extenders, controlled by an Agilent N5261A controller that was connected to an Agilent PNA N5222A Network Analyzer.

The experimental setup with the hologram in place is pictured in Fig. 8. The reference wave was transmitted from a 24.5 dBi scalar-feed, corrugated horn (Quinstar QSH-W1000), pointing at the hologram’s center at an angle of $26.5°$ in the xz-plane relative to the optical axis (aligned using laser diode sight). To measure the reference wave, we removed the hologram from its mounts while keeping the rest of the experimental setup intact, in order to include in our measurements reflections from objects used in the experiment. We then used the scanner to move a rectangular, tapered, open-ended waveguide (OEWG) probe and measure the fields at z=16.5 mm across a plane parallel to the hologram plane (defined as the xy-plane) in increments of 1.3 mm along y. To measure the hologram’s fields, we repeated the same procedure after the hologram was inserted between the horn and the probe. We note that we measured the fields radiating from the hologram across an area larger than the hologram itself, in order to be able to propagate them to a field-of-view spanning $\pm 45°$ around the optical axis. We also note that the measurement planes used when characterizing the reference wave and hologram fields were z=16.5 mm and z=17 mm, respectively. This difference was accounted for during the back-propagation step.

 

Fig. 8 Experimental setup. The hologram is illuminated by an off-axis transmitting (Tx) horn. Near-fields are measured by a receiver (Rx) probe across a plane parallel to the hologram plane.

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Appendix C The effect of the hologram’s phase range on the zeroth order

As discussed in Section 2 of the manuscript, our hologram was limited to a maximum phase range of $\pm 60°\left(\theta =26.5°\right)$, with its amplitude distribution coupled to the phase, due to the resonant nature of its element’s polarizabilities. As a result of this phase constraint, our hologram was not able to direct all of the incident reference wave fields towards the formation of the word ‘DUKE,’ and a zeroth order mode was formed along the same direction in which the reference wave was propagating from the transmitting horn. With a greater range of phases, however, a hologram can form an image without the undesired zeroth order.

To demonstrate the effects of a hologram’s phase range on the quality of the image it can form, we use the iterative GS algorithm to design a phase-constrained hologram forming the word ‘DUKE’ in the far-field. Unlike our experimental hologram’s resonant (and coupled) phase and magnitude relationships, for this study the only constraint we apply is to cap the phase of the hologram’s pixels at each iteration of the GS algorithm, and enforce a uniform amplitude distribution. For simplicity, we assumed the hologram is excited by a normally-incident plane wave, such that the reference wave is uniform across the hologram. Figs. 9(a) – 9(f) show the resulting far-field images, computed as the Fourier transform of the hologram, when the hologram’s phases were limited to spans ranging from $\pm 30°$ to the full $\pm 180°$. In Fig. 9(a), we observe how the fields radiating from hologram constrained to a narrow range of phases $(\pm 30°)$ are directed almost entirely to the zeroth order mode; the desired image is much weaker and cannot be observed when plotted on the illustrated scale. Figs. 9(b)–9(d) illustration how, as the phase range increases, a greater portion of the fields’ energy is directed toward the primary image and away from the zeroth order mode and conjugate image. When a sufficiently wide range of phases is used, only the hologram’s primary image is observable, as is the case in Figs. 9(e) and 9(f). We point out that the quality of the far-field images produced in this study, which utilized a phase-only hologram with uniform amplitude, is expected to be better than these of the metamaterial hologram described in Section 4, which had a non-uniform magnitude response and pixels that radiated less strongly when their phases deviated from zero degrees.

 

Fig. 9 The effect of a hologram’s phase constraints on the quality of its image. The resulting far-field patterns from theoretical phase holograms with uniform amplitude and varying phase ranges (a-f). The hologram is illuminated by a normally-incident plane wave, and its pixel’s phases are constrained to lie in a limited range, starting at $\pm 30°$ (a) and increasing in steps of $\pm 30°$(b-f) until a full range of $\pm 180°$ (f) is reached.

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Acknowledgments

This work was supported by the Army Research Office through a Multidisciplinary University Research Initiative (Grant No. W911NF-09-1-0539).

References and links

1. D. Gabor, “A new microscopic principle,” Nature 161(4098), 777–778 (1948). [CrossRef]   [PubMed]  

2. E. N. Leith and J. Upatnieks, “Reconstructed wavefronts and communication theory,” J. Opt. Soc. Am. 52(10), 1123–1128 (1962). [CrossRef]  

3. J. W. Goodman, Introduction to Fourier Optics (Roberts & Co., 2005).

4. B. R. Brown and A. W. Lohmann, “Complex spatial filtering with binary masks,” Appl. Opt. 5(6), 967–969 (1966). [CrossRef]   [PubMed]  

5. L. B. Lesem, P. M. Hirsch, and J. A. Jordan, “The kinoform: a new wavefront reconstruction device,” IBM J. Res. Develop. 13(2), 150–155 (1969). [CrossRef]  

6. D. C. Chu, J. R. Fienup, and J. W. Goodman, “Multiemulsion on-axis computer generated hologram,” Appl. Opt. 12(7), 1386–1388 (1973). [CrossRef]   [PubMed]  

7. W. Freese, T. Kämpfe, E.-B. Kley, and A. Tünnermann, “Design of binary subwavelength multiphase level computer generated holograms,” Opt. Lett. 35(5), 676–678 (2010). [CrossRef]   [PubMed]  

8. Y.-J. Tsai, S. Larouche, T. Tyler, G. Lipworth, N. M. Jokerst, and D. R. Smith, “Design and fabrication of a metamaterial gradient index diffraction grating at infrared wavelengths,” Opt. Express 19(24), 24411–24423 (2011). [CrossRef]   [PubMed]  

9. S. Larouche, Y.-J. Tsai, T. Tyler, N. M. Jokerst, and D. R. Smith, “Infrared metamaterial phase holograms,” Nat. Mater. 11(5), 450–454 (2012). [CrossRef]   [PubMed]  

10. U. Levy, H.-C. Kim, C.-H. Tsai, and Y. Fainman, “Near-infrared demonstration of computer-generated holograms implemented by using subwavelength gratings with space-variant orientation,” Opt. Lett. 30(16), 2089–2091 (2005). [CrossRef]   [PubMed]  

11. L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K.-W. Cheah, C.-W. Qiu, J. Li, T. Zentgraf, and S. Zhang, “Three dimensional Optical Holography using a plasmonic metasurface,” Nat. Commun. 4, 2808 (2013). [CrossRef]  

12. X. Ni, A. V. Kildishev, and V. M. Shalaev, “Metasurface holograms for visible light,” Nat. Commun. 4, 2807 (2013). [CrossRef]  

13. X. Li, S. Xiao, B. Cai, Q. He, T. J. Cui, and L. Zhou, “Flat metasurfaces to focus electromagnetic waves in reflection geometry,” Opt. Lett. 37(23), 4940–4942 (2012). [CrossRef]   [PubMed]  

14. A. Pors and S. I. Bozhevolnyi, “Plasmonic metasurfaces for efficient phase control in reflection,” Opt. Express 21(22), 27438–27451 (2013). [CrossRef]   [PubMed]  

15. C. Pfeiffer and A. Grbic, “Metamaterial Huygens’ surfaces: tailoring wave fronts with reflectionless sheets,” Phys. Rev. Lett. 110(19), 197401 (2013). [CrossRef]   [PubMed]  

16. A. Epstein and V. Eleftheriades, “Huygens’ metasurfaces via the equivalence principle: design and applications,” J. Opt. Soc. Am. B 33(2), A31–A50 (2016). [CrossRef]  

17. P. Genevet and F. Capasso, “Holographic optical metasurfaces: a review of current progress,” Rep. Prog. Phys. 78(2), 024401 (2015). [CrossRef]   [PubMed]  

18. B. H. Fong, J. S. Colburn, J. J. Ottusch, J. L. Visher, and D. F. Sievenpiper, “Scalar and tensor holographic artificial impedance surfaces,” IEEE Trans. Antenn. Propag. 58(10), 3212–3221 (2010). [CrossRef]  

19. N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014). [CrossRef]   [PubMed]  

20. F. Aieta, M. A. Kats, P. Genevet, and F. Capasso, “Multiwavelength achromatic metasurfaces by dispersive phase compensation,” Science 347(6228), 1342–1345 (2015). [CrossRef]   [PubMed]  

21. N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect metamaterial absorber,” Phys. Rev. Lett. 100(20), 207402 (2008). [CrossRef]   [PubMed]  

22. S. Zhong and S. He, “Ultrathin and lightweight microwave absorbers made of mu-near-zero metamaterials,” Sci. Rep. 3, 2083 (2013). [CrossRef]   [PubMed]  

23. J. Hunt, J. Gollub, T. Driscoll, G. Lipworth, A. Mrozack, M. S. Reynolds, D. J. Brady, D. R. Smith, and D. R. Smith, “Metamaterial microwave holographic imaging system,” J. Opt. Soc. Am. A 31(10), 2109–2119 (2014). [CrossRef]   [PubMed]  

24. G. Lipworth, A. Mrozack, J. Hunt, D. L. Marks, T. Driscoll, D. Brady, and D. R. Smith, “Metamaterial apertures for coherent computational imaging on the physical layer,” J. Opt. Soc. Am. A 30(8), 1603–1612 (2013). [CrossRef]   [PubMed]  

25. G. Lipworth, A. Rose, O. Yurduseven, V. R. Gowda, M. F. Imani, H. Odabasi, P. Trofatter, J. Gollub, and D. R. Smith, “Comprehensive simulation platform for a metamaterial imaging system,” Appl. Opt. 54(31), 9343–9353 (2015). [CrossRef]   [PubMed]  

26. A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science 339(6125), 1232009 (2013). [CrossRef]   [PubMed]  

27. G. Lipworth, J. Ensworth, K. Seetharam, J. S. Da Huang, J. S. Lee, P. Schmalenberg, T. Nomura, M. S. Reynolds, D. R. Smith, and Y. Urzhumov, “Magnetic metamaterial superlens for increased range wireless power transfer,” Sci. Rep. 4, 8–13 (2014). [CrossRef]  

28. G. Lipworth, J. Ensworth, K. Seetharam, J. S. Lee, P. Schmalenberg, T. Nomura, M. S. Reynolds, D. R. Smith, and Y. Urzhumov, “Quasi-static magnetic field shielding using longitudinal mu-near-zero metamaterials,” Sci. Rep. 5, 12764 (2015). [CrossRef]   [PubMed]  

29. T. H. Hand, J. Gollub, S. Sajuyigbe, D. R. Smith, and S. A. Cummer, “Characterization of complementary electric field coupled resonant surfaces,” Appl. Phys. Lett. 93(21), 1–3 (2008). [CrossRef]  

30. J. B. Pendry, J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999). [CrossRef]  

31. J. D. Jackson, Classical electrodynamics (Vol. 3) (Wiley, 1998).

32. B. J. Arritt, D. R. Smith, and T. Khraishi, “Equivalent circuit analysis of metamaterial strain-dependent effective medium parameters,” J. Appl. Phys. 109(7), 1–5 (2011). [CrossRef]  

33. G. Dolling, C. Enkrich, M. Wegener, J. F. Zhou, C. M. Soukoulis, and S. Linden, “Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials,” Opt. Lett. 30(23), 3198–3200 (2005). [CrossRef]   [PubMed]  

34. R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35(2), 237–246 (1972).

35. W. Tang and H. Zhao, “A meander line resonator to realize negative index materials,” in Proceedings of IEEE Conference on Antennas and Propagation Society International Symposium (IEEE, 2008), pp. 1–4.

36. S. Gregson, J. McCormick, and C. Parini, Principles of Planar Near-Field Antenna Measurements, Vol. 53 (IET, 2007).

37. M. Johnson, P. Bowen, N. Kundtz, and A. Bily, “Discrete-dipole approximation model for control and optimization of a holographic metamaterial antenna,” Appl. Opt. 53(25), 5791–5799 (2014). [CrossRef]   [PubMed]  

38. P. T. Bowern, T. Driscoll, N. B. Kundtz, and D. R. Smith, “Using a discrete dipole approximation to predict complete scattering of complicated metamaterials,” New J. Phys. 14(3), 033038 (2012). [CrossRef]  

39. M. C. Johnson, S. L. Brunton, N. B. Kundtz, and N. J. Kutz, “Sidelobe canceling for reconfigurable holographic metamaterial antenna,” IEEE Trans. Antenn. Propag. 63(1), 1881–1886 (2015). [CrossRef]  

40. M. C. Johnson, S. L. Brunton, N. B. Kundtz, and N. J. Kutz, “Extremum-seeking control of the beam pattern of a reconfigurable holographic metamaterial antenna,” J. Opt. Soc. Am. A 33(1), 59–68 (2016). [CrossRef]   [PubMed]  

41. T. Sleasman, M. F. Imani, J. N. Gollub, and D. R. Smith, “Dynamic metamaterial aperture for microwave imaging,” Appl. Phys. Lett. 107(20), 204104 (2015). [CrossRef]  

42. C. A. Balanis, Advanced Engineering Electromagnetics (Wiley, 1989).