Significance The ability to perfectly absorb light with optically thin materials poses a significant challenge for many applications such as camouflage, light detection, and energy harvesting. Current designs require planar reflectors that crack and delaminate after heating or flexing. Moreover, they cannot be transferred to more desirable substrates for mechanically flexible and low-cost applications. Although particulate-based materials overcome these challenges, broadband absorption from standalone systems has not been demonstrated. Here, a class of materials, transferrable hyperbolic metamaterial particles (THMMP), is introduced. When closely packed, these materials show broadband, selective, omnidirectional, perfect absorption. This is demonstrated with nanotubes made on a silicon substrate that exhibit near-perfect absorption at telecommunication wavelengths even after being transferred to a mechanically flexible, visibly transparent polymer.

Abstract Broadband absorbers are essential components of many light detection, energy harvesting, and camouflage schemes. Current designs are either bulky or use planar films that cause problems in cracking and delamination during flexing or heating. In addition, transferring planar materials to flexible, thin, or low-cost substrates poses a significant challenge. On the other hand, particle-based materials are highly flexible and can be transferred and assembled onto a more desirable substrate but have not shown high performance as an absorber in a standalone system. Here, we introduce a class of particle absorbers called transferable hyperbolic metamaterial particles (THMMP) that display selective, omnidirectional, tunable, broadband absorption when closely packed. This is demonstrated with vertically aligned hyperbolic nanotube (HNT) arrays composed of alternating layers of aluminum-doped zinc oxide and zinc oxide. The broadband absorption measures >87% from 1,200 nm to over 2,200 nm with a maximum absorption of 98.1% at 1,550 nm and remains large for high angles. Furthermore, we show the advantages of particle-based absorbers by transferring the HNTs to a polymer substrate that shows excellent mechanical flexibility and visible transparency while maintaining near-perfect absorption in the telecommunications region. In addition, other material systems and geometries are proposed for a wider range of applications.

Selective and broadband perfect absorbers generally consist of plasmonic cavities coupled to metallic reflectors separated by dielectric spacers. These geometries have led to many exciting applications such as thermophotovoltaics (TPV) (1, 2), thermal emitters (3, 4), camouflage (5), and thermal detectors (6). However, the ability to be scaled up to larger surface area devices and transferred to more desirable substrates is a major limitation of absorbers that rely on planar reflectors. Here, we introduce a class of standalone particles, transferrable hyperbolic metamaterial particles (THMMP), that display broadband, selective, omnidirectional absorption and can be transferred to secondary substrates, allowing enhanced flexibility and selective transmission. This is demonstrated using vertically aligned hyperbolic metamaterial nanotube (HNT) arrays. We first realize the concept by fabricating the HNTs on silicon substrates and then transfer the arrays to a thin elastomer to create a mechanically flexible, visibly transparent material that maintains near-perfect absorption at telecommunication wavelengths (∼1,550 nm). In addition, different materials systems and geometries are discussed, leading to a broader range of applications.

Currently, carbon nanotubes (CNTs) provide perfect ultrabroadband absorption (7). However, CNT films are relatively thick and do not allow any control over the operating wavelengths of the absorber, which is critical for creating visibly transparent IR absorbers and materials for many other applications including TPV that require selective yet broadband absorption (8). Hyperbolic metamaterials (HMMs) can provide an alternative to creating selective and broadband absorption. HMMs are materials engineered to possess extreme optical anisotropy that is typically observed and studied in two structures: (i) alternating layers of metal and dielectrics and (ii) metallic nanowires embedded in a dielectric medium (9, 10). In each case, the characteristic dimensions (layer thickness or nanowire diameter and separation distance) must be deeply subwavelength such that the bulk material properties can be described under an effective medium approximation (EMA), where the permittivity is defined in terms of a tensor with one unique axis (optical axis) and two similar axes. When the optical axis has an opposing sign to the other two axes, the material dispersion is hyperbolic, arising from a hyperboloidal isofrequency surface (9). This stands in contrast to the ellipsoidal isofrequency surface of conventional materials. The hyperbolic dispersion results in an extremely large optical density of states that supports large wavevector modes. This property has been used to exploit negative refraction (11⇓–13), enhanced spontaneous emission (14), and hyperlensing (15).

Due to the large optical density of states, layered HMMs have been shown to be excellent absorbers within narrowbands (16, 17). It has also been shown that the absorption bandwidth could be increased yet still remain selective by structuring the HMMs into pyramids (18⇓–20); however, these materials have shown limited absorption at telecommunication wavelengths (∼85%), have not yet shown large-angle absorption, and have only been demonstrated on metallic back reflectors, making simultaneous broadband absorbance and visible transparency challenging. Furthermore, the recently demonstrated HMM pyramids are made with low–melting-point metals that are not compatible with the high temperatures required for applications such as thermal emitters. Perfect absorbing metamaterials have also been used to demonstrate broadband absorption by the convolution of multiple loss mechanisms (8). However, these materials require dielectric spacers and metallic back reflectors, and use advanced nanostructured geometries, making it difficult to scale up the fabrication for larger area applications and/or transfer the materials to more desirable substrates. More favorable architectures include nanoparticle monolayers and vertically aligned nanowires that can be assembled and transferred via inexpensive techniques to different substrates while maintaining mechanical flexibility due to the gaps between the independent structures (21, 22). In addition, the substrate/nanoparticle interfacial surface area is reduced, mitigating problems that arise due to lattice mismatch. This is particularly important for high-temperature applications such as heat-generating absorbers and thermal emitters, which put extreme stresses on the interfaces within the device.

Hyperbolic Nanotubes As shown in Fig. 1A, an HNT is defined in terms of its length, L; total diameter, D t ; and air core diameter, D c . The shell is comprised of n HMM periods with alternating aluminum-doped zinc oxide (AZO) and ZnO concentric layers of thicknesses t m and t d , respectively. Therefore, one period has a thickness, p, equal to t m + t d , and the total shell thickness is given as the product of n and p. When oriented in an array, the lattice period, a, and HNT gap, g, are also defined, where a = g + D t . To engineer such an array, we leveraged high-quality, ultraconformal AZO/ZnO HMM multilayers afforded by atomic layer deposition (ALD), which have been shown to display negative refraction due to hyperbolic dispersion (23). The HNT array fabrication starts with a silicon hole array template made by nanosphere lithography. The hole arrays are then filled with the HMM multilayers by exploiting the ultraconformal properties of ALD. Next, reactive ion etching (RIE) is used to remove the top layers and expose the underlying silicon. The silicon surrounding the HNTs is then removed by RIE, leaving a vertically aligned triangular array of closely packed HNTs (Fig. S1, Supporting Information, for the complete fabrication flow). The air core is an artifact of the conformality limit of ALD and/or bowing effects due to imperfect etching profiles in the nanohole template. This can be mitigated by adjusting the ALD and etching parameters; however, the air core has little consequence on the absorption when D c is ∼220 nm (Supporting Information). Fig. 1 B and C shows the resulting vertically aligned HNTs with D c , a, and L equal to 235, 770, and 1,730 nm, respectively. D t varies from 770 nm at the top to 650 nm at the bottom. Fig. 1. (A) Schematic of coupled HNTs. SEM images of the HNT arrays as viewed in the plane (B) parallel and (C) perpendicular to the nanotube axis. Fig. S1. Fabrication scheme of vertically aligned HNT arrays.

Absorption Measurements It is well documented that the carrier concentration of AZO is dependent on the ALD deposition temperature, T d , allowing for the absorption of the HNT array to be tuned (24⇓⇓–27). Using an integrating sphere, Fig. 2A captures the true absorption spectrum [absorption(%) = 100% – transmission(%) – reflection(%)] of HNT arrays deposited at a T d of 200 and 185 °C. Broadband absorption of >87% from 1,200 nm to over 2,200 nm is demonstrated with a maximum absorption of 98.1% at 1,550 nm for a T d of 200 °C. For a T d of 185 °C, broadband absorption of >87% is observed from 1,500 nm to over 2,200 nm with a maximum absorption of 96.3% at 1,700 nm. As a control, pure AZO nanotubes are also plotted, which exhibit only a modest absorption maximum of 82.5% at 1,400 nm with a narrow spectral width. The HNTs show excellent selectivity by displaying increased reflection at longer wavelengths (Fig. S2A). This is due to an increased impedance mismatch as the real permittivity of AZO becomes increasingly negative at longer wavelengths (23). The angular dependence was also studied by sputtering a 100-nm gold film on the back of the silicon. This allowed only the specular reflectance to be considered when calculating the absorption [absorption(%) = 100% – reflectance(%)]. This method was found to be valid within 1% from 1,500 to 2,400 nm and within 6% from 1,400 to 1,500 nm. However, at wavelengths shorter than 1,400 nm, we found that this method was not accurate due to photon scattering (Fig. S2B). As shown in Fig. 2 C and D, HNTs possess omnidirectional absorption for both transverse-magnetic (TM) and transverse-electric (TE) polarizations. For TM polarization, the absorption is maintained above 85% at all angles and wavelengths measured. For TE polarization, the absorption is diminished at higher angles and longer wavelengths; however, an absorption of >70% is maintained across the measured wavelengths and angles smaller than 50°. Fig. 2. (A) Absorption spectra of HNT arrays deposited at a temperature of 185 and 200 °C along with a spectrum of a pure AZO nanotube array deposited at 200 °C. (B) Schematic of the incident radiation at angle θ showing TM polarization. Wide-angle absorption spectra for (C) TM and (D) TE polarizations of an HNT array deposited at 200 °C. The color corresponds to the percent absorption. Fig. S2. (A) IR reflection spectrum of an HNT array. (B) Absorption spectrum of HNT arrays measured by an integrating sphere (A = 1 − T − R) and specularly (A = 1 − R). Using the complex permittivity values previously published (23), simulated absorption of over 90% from 1,400 to 2,000 nm agrees well with the experimental data (Fig. S3A). Our simulations suggest that the broadband absorption arises from the coalescence of bulk/surface plasmons and lossy modes due to the hyperbolic dispersion of the HNT arrays (Fig. S4, Supporting Information). In addition, we find that the absorption of the array does not decrease linearly with the HNT filling fraction, indicating that HNT coupling, and therefore g, plays an important role in the absorption. When a periodic dielectric gap is placed within an HMM, the photonic band structure of the system is expected to be altered due to Bragg scattering, even if the gap is deeply subwavelength. This is known as a photonic hypercrystal (28). Because strong coupling provided by periodic dielectric spacing is expected in a THMMP array, the structure can be classified as a photonic hypercrystal. Using a qualitative analytical approach, we observe an alteration in the band structure when adjusting the air gaps for a similar 1D structure in the lossless limit (Figs. S5 and S6, Supporting Information). Based on these results, it is clear that the absorption spectrum depends upon both the wavelength-scale periodicity of the hypercrystal and the deeply subwavelength scale of the HMM. The simultaneous control of these structural parameters enables a tailorable absorption and emission spectrum unachievable in other systems, such as self-aligned carbon nanotubes. However, the emission spectrum of quantum emitters has been enhanced recently by embedding them within a photonic hypercrystal where the enhancement is attributed to tailoring the band structure of the high photonic density of state HMM and allowing more efficient coupling into free space (29). Consequently, given the high sensitivity of high wavevector modes to small changes in dielectric spacing, this also suggests that the disorder of the HNT array will likely impact the band structure and thus the absorption properties. However, the incident light from free space typically has small wavevectors, unless a strong scattering effect is present. Therefore, the relationship between disorder-induced high wavevector mode modification and absorption becomes nontrivial. The quantitative analysis of this effect needs further investigation. Fig. S3. Simulated absorption of (A) the exact structure and EMA to describe the HNT shell and (B) EMA HNT arrays with air cores and solid hyperbolic metamaterial nanowires. Fig. S4. Simulated absorption of (A) exact structure HNTs with increasing n from 1 to 8 (blue to yellow) and 13 (black) with constant g, (B) exact structure HNT arrays with varying a and constant D t , and (C) EMA solid hyperbolic nanowire arrays of varying diameter. Fig. S5. Effective material dispersion, Eqs. S4 and S5 of AZO-ZnO uniaxial multilayer HMM with ff m = 0.5. Upper Inset shows the structure we consider with the definition of parallel and normal directions with respect to the optical axis of the multilayer that is homogenized. Lower Inset is a magnified plot of the transition between type I and type II hyperbolic dispersion for the TM modes. Fig. S6. Dispersion of an AZO/ZnO/air 1D photonic hypercrystal with a constant d H = 740 nm. The dark blue and red regions correspond to stop bands where propagating modes are forbidden. Lines separating these regions correspond to narrow bands where propagating modes are supported. Outside of the 1,400- to 2,000-nm spectral range, the experimental absorption is larger than the simulated absorption. The larger observed experimental absorption at wavelengths shorter than 1,400 nm is due to the silicon substrate, as discussed later. At longer wavelengths, this discrepancy is attributed to surface roughness, which is verified both experimentally and by simulation (Fig. S7). It should be noted that, although high absorption has been obtained for planar HMMs (30, 31), our simulations show that the absorption occurs within a narrower band when similar length scales (1.5 µm) are used for both the planar and embedded nanowire HMM geometries (Fig. S8C). Furthermore, planar HMMs do not have the many benefits of nanoparticle films as mentioned above. Fig. S7. (A) Exact structure simulations of HNT arrays with smooth and roughened tops (RMS = 200 nm). (B) Experimental absorption spectra of an as-processed HNT array and an array that was further roughened with RIE (deposition temperature was 200 °C). The Inset shows a SEM image of a roughened HNT array. Fig. S8. Simulated absorption using the exact structure of HNTs with varying (A) lengths and (B) ff m in the shell. (C) Simulated absorption using the exact structure of common HMMs compared with the HNTs.

HNT Substrate Transfer To investigate whether the HNT arrays could operate as a standalone material after being removed from the growth substrate, we transferred the arrays to a thin, flexible, and visibly transparent substrate by spin coating 60 µm of polydimethylsiloxane (PDMS) onto the top of the arrays and removing the silicon via RIE. This was carried out for three different arrays with various parameters as described in Table 1 and observed from direct imaging (Fig. S9). The absorption spectra of sample A and a simulated exact structure (with a similar structure to sample A, but with a rounded top to replicate experimental conditions) have excellent agreement (Fig. 3A). This suggests that the shorter wavelength discrepancy between the simulated and experimental absorption described earlier is due to the silicon substrate either from reflection back into the HNTs or absorption of the textured surface created during the HNT fabrication. The transmission and absorption spectra of the three samples (Fig. 3 B and C) illustrate that a large transmission window is observed from 500 to 1,300 nm, with the broadest IR absorption band belonging to sample A at the expense of a narrower and weaker transmission window. The transmission can be slightly increased by lowering T d and keeping the geometry constant, but the largest gain in transmission is observed when L is decreased and g is increased (sample C). Because all of the constituent materials (AZO, ZnO, and PDMS) in the free-standing HNT array have large optical transparencies throughout the visible, and reflection accounts for <12% of the decreased transparency, we believe the additional absorption stems from silicon contaminates left over from the transfer process and/or subband levels (defects states) in the ZnO/AZO layers. With further refinement in the synthesis, etching, and transferring steps, we anticipate a significant improvement in the visible transparency. After transferring the HNT array to the PDMS film, they can be reproducibly flexed while still maintaining their excellent broadband absorption in the near IR (NIR), and transmission in visible, as well as their physical interface with the polymer (Fig. 3 D–F). Table 1. Parameters of samples A–C Fig. 3. (A) Comparison of experimental and simulated absorption spectra for sample A. (B) Transmission and (C) absorption spectra for samples A–C with parameters as described in Table 1 after flexing several times as shown in E. Photograph of sample A showing (D) visible transparency and (E) mechanical flexibility. (F) SEM image of an HNT array (sample B) after transferring to a flexible PDMS substrate and flexing several times as shown in E. Fig. S9. SEM image of sample B as viewed in the plane (A) perpendicular and (B) parallel to the nanotube axis and sample C as viewed from the plane (C) perpendicular and (D) parallel to the nanotube axis.

Other THMMP Systems Beyond the AZO/ZnO HNT system, selective and broadband absorption can be applied to many other material systems and geometries. For example, the TiN/(Al,Sc)N material system has been shown to produce high-quality epitaxial HMMs with refractory qualities (32). THMMP arrays with these materials could be advantageous for applications such as TPV and visible emitters that require many cycles at elevated temperatures (>1,000 °C). Current research in this area focuses on nonselective absorbers (1) and plasmonic metamaterials (8); however, these planar materials either lose efficiency due to parasitic radiation at higher temperatures or can crack and delaminate due to thermal expansion mismatch between the absorber layer and substrate. A major advantage of a THMMP array is that it has a reduced substrate contact area that minimizes the impact of thermal expansion mismatches and would allow for a wider selection of substrates to be used while promoting the use of facile transfer techniques. Simulations reveal that TiN/(Al,Sc)N-based HNT arrays (L = 750 nm, D t = 500 nm, D c = 30 nm, n = 11, t m = t d = 10 nm, a = 530 nm) have absorption values of >93% throughout the entire visible spectrum while suppressing absorption at longer wavelengths (Fig. S10A). In comparison with the HNT geometry, closely packed hyperbolic nanospheres could be particularly useful because they are expected to have less angular dependence and can be deposited onto substrates via low-cost/scalable processes such as nanoparticle self-assembly and spray-on techniques. Simulations also reveal that these types of arrays made from a TiN/(Al,Sc)N material system have a large absorption (>89% throughout the entire visible spectrum) while suppressing absorption in the NIR with only a 540-nm-thick single monolayer (Fig. S10B). Fig. S10. Exact structure simulated absorption spectra of a closely packed TiN/(Al,Sc)N-based (A) HNT array and (B) hyperbolic nanosphere array. The HNT array parameters L, D t , D c , g, a, n, t m , and t d used in the simulation were 750 nm, 500 nm, 60 nm, 30 nm, 530 nm, 11, 10 nm, and 10 nm, respectively. The D t , D c, g, a, n, t m , and t d used for the hyperbolic nanosphere simulation were 540 nm, 60 nm, 30 nm, 570 nm, 12, 10 nm, and 10 nm, respectively. Optical constants were retrieved from ref. 32.

Conclusions In conclusion, we have demonstrated a class of metamaterials, THMMP, that have tunable, selective, and broadband near-perfect, omnidirectional absorption. The broad absorption bandwidth is a result of the coalescence of absorption peaks due to bulk or surface plasmon-polaritons in the AZO and lossy modes that exist due to the hyperbolic dispersion of the arrays. With the ability to remove these particles from their growth substrates, we were able to demonstrate that the arrays could be transferred to visibly transparent and mechanically flexible substrates while maintaining their broadband absorption in the NIR. We believe the synthetic strategies presented here are universal and can be applied to other nanoparticle systems. Not only would this enable a host of different materials that operate at distinct parts of the electromagnetic spectrum, but it is anticipated that novel light–matter interactions that have yet to be explored would be uncovered.

Materials and Methods HNT Array Fabrication. HNT arrays were fabricated using silicon nanohole templates created by nanosphere lithography. Stöber particles (770-nm diameter) were grown from standard processes (33) and used as the nanosphere mask. Next, the Stöber particles were functionalized with 3-aminopropylmethyldiethoxysilane (APMDES), cleaned, and deposited onto p-type, double-sided polished, prime silicon using a Langmuir Blodgett trough. The silica particles were then shrunk using RIE with CHF 3 and Ar gases in an Oxford P80 (34). A 45-nm-thick nickel film was then deposited on the sample using a Temescal BJD 1800 electron beam evaporator. The Stöber particles were then mechanically removed with a Cleanroom Q-tip and sonication. Next, using an Oxford P100 with SF 6 and C 4 F 8 gases, the exposed silicon was etched creating the nanohole template. After removing the nickel mask using TFB nickel etchant, the ZnO/AZO HMM was deposited into the nanoholes with a Beneq TFS200 ALD system operating at a reactor temperature of 185 or 200 °C. Diethylzinc, trimethylaluminum, and deionized water were used as the zinc, aluminum, and oxygen sources, respectively. The Zn:Al pulse ratio for the AZO films was kept constant at 20:1 for all experiments. The film thicknesses were first determined for each material on planar silicon substrates by ellipsometry using a Rudolph Auto EL ellipsometer at each deposition temperature. A total HMM thickness of ∼350 nm (each individual ZnO and AZO layer was 10 nm) was deposited on the nanohole template such that the nanoholes were completely sealed. Next, a 20-nm protection layer of HfO 2 was deposited via ALD by using tetrakis(dimethylamido)hafnium(IV) and water as the hafnium and oxygen sources, respectively. After depositing the HMM and protection layer, rapid thermal processing was carried out to activate the aluminum dopants (23) using an AG Associates Heat Pulse 610 with a 1.5 L⋅min−1 nitrogen flow rate. The top layers of HfO 2 and ZnO/AZO were then removed using RIE with CHF 3 and Ar gases using an Oxford P80 until the top silicon was exposed. The exposed silicon was removed using an Oxford P100 with SF 6 and C 4 F 8 gases, leaving behind the HNT array (Fig. S1). The roughened HNTs were created by additional etching of the HNTs (deposited at a temperature of 200 °C) using RIE with CHF 3 and Ar gases. Before measurements, dilute HCl was applied to the back of the samples to remove any contaminates that may have been generated during the ALD process. Numerical Simulations. Simulations of the exact structure were carried out using finite-difference time-domain (FDTD) methods (Lumerical), and EMA simulations were implemented with COMSOL using the finite-element method (FEM). All simulations used plane wave excitation with periodic boundary conditions at normal incidence. The optical constants used for AZO and ZnO were experimentally determined via ellipsometry as previously reported (23). TiN and (Al,Sc)N optical constants were obtained from literature (32). All structures were simulated in a vacuum without any substrate. HNT Transfer Process. The HNT arrays were transferred to a flexible polymer film by depositing a ∼60-µm film of PDMS and etching away the silicon substrate. First, the PDMS film was coated on the top of the HNT array by spin coating at 8.5 × g for 45 s and curing at 125 °C for 8 min. The back silicon was then cleaned with O 2 plasma (Oxford P100) and removed using a Xactix XeF 2 Etcher. Optical Measurements and Imaging. All experimental absorption measurements between 1,200 and 2,400 nm were taken using a PerkinElmer Lambda 1050 UV/Vis/NIR spectrometer. For non–angle-dependent data, a 150-mm Spectralon-coated integrating sphere with a photomultiplier tube (visible wavelengths) and InGaAs (NIR wavelengths) detector was used. For angle-dependent measurements, a universal reflectance accessory was used with an InGaAs detector. IR reflectance was determined using a Bruker LUMOS Fourier transform IR (FTIR). All SEM imaging was carried out on a FEI XL30 ultrahigh-resolution microscope.

SI Note I: Numerically Simulated Results Using the complex permittivity values previously published (23), the simulated absorption of a closely packed HNT array is shown in Fig. S3A. Unless otherwise specified, the parameters used in the simulations were L = 1.5 μm, D t = 740 nm, D c = 220 nm, g = 30 nm, a = 770 nm, n = 13, and t m = t d = 10 nm. The data show absorption values greater than 90% from 1,400 to 2,000 nm. In addition to simulations that explicitly compute for a structure described by each individual ZnO and AZO layer (exact structure), simulations were carried out where the permittivity of the shell material is replaced with the permittivity tensor derived from EMA for curved multilayer structures. This is accomplished by describing the electrical response of the system in terms of a diagonal effective permittivity tensor: ε e f f = [ ε x x 0 0 0 ε y y 0 0 0 ε z z ] , [S1]where the elements ε xx , ε yy , and ε zz describe the permittivity along the three principal directions of a Cartesian (rectangular) coordinate system. Hyperbolic dispersion arises when one of the elements is unique and of opposite sign to the remaining two that are of equal value: ε x x = ε ∥ > 0 ; ε y y = ε z z = ε ⊥ < 0 , [S2]or ε x x = ε ∥ < 0 ; ε y y = ε z z = ε ⊥ > 0 , [S3]where the parallel and perpendicular directions are referenced with respect to the interfaces between constituent materials. For a planar multilayer HMM made up of oscillating layers of metal and dielectric materials, the tensor elements can be given as follows: ε ⊥ = f f m ε m + ( 1 − f f m ) ε d , [S4] ε ∥ = ( f f m ε m + 1 − f f m ε d ) − 1 , [S5]where ff m is the filling fraction of the metallic component, and ε m and ε d are the permittivities of the metal and dielectric, respectively. Following methods from the literature, a cylindrical multilayer, with alternating layers forming concentric circles, can be accurately described using a coordinate transformation (35). In Cartesian coordinates, the effective permittivity tensor of the cylindrical multilayer is as follows: ε e f f = [ ε ∥ c o s 2 ( ϕ ) + ε ⊥ s i n 2 ( ϕ ) ( ε ∥ − ε ⊥ ) sin ( ϕ ) cos ( ϕ ) 0 ( ε ∥ − ε ⊥ ) sin ( ϕ ) cos ( ϕ ) ε ∥ s i n 2 ( ϕ ) + ε ⊥ c o s 2 ( ϕ ) 0 0 0 ε ⊥ ] , [S6]where the angle ϕ describes rotation about the axis of symmetry. As shown in Fig. S3A, the exact structure agrees well with EMA. This allowed us to simulate the structure with less computational expense and study the effects of adjusting D t and D c without changing n and p. Importantly, the simulations also showed that the existence of the core has little effect on the absorption (Fig. S3B). Through the simulations, we find that the broadband absorption is due to the coalescence of multiple absorption peaks (Fig. S4). This is accomplished by varying some of the parameters described in Fig. 1A of the main text. As shown in Fig. S4A, as n decreases from 8 to 1 with constant g, the broadband absorption separates into two peaks at 1.45 and ∼2–3 µm. Moreover, when n and D t are held constant, but a is increased from 770 to 3,500 nm, we observe a deconvolution of the peaks (Fig. S4B). To study the effects of varying D t , we first use the EMA to eliminate the effect of n and replace the air core with the effective medium. Using solid HMM nanowires, no significant effect on the absorption band is observed when D t is varied from 740 to 260 nm with constant g (Fig. S4C). Simulations also show that the length of the HNTs does not contribute much to the absorption when greater than 1.5 µm. However, at lengths smaller than 1.0 µm, the absorption decreases due to increased transmission (Fig. S8A). Broadband absorption is achieved when there is a sufficient number of periods and when the HNTs are packed close enough to allow strong resonance coupling. Physically, g is responsible for the intercoupling of the HNTs and n is responsible for the number of higher-order plasmon-polaritions modes supported by the HMM (36). The bandwidth of high-wavevector modes supported by the HMM depends upon p but not n. However, as n increases, the discrete modes supported by the HMM are expected to coalesce. If there were no losses, each mode would have a sharp profile, but due to the high losses the discreteness vanishes and a single absorption band appears. The shorter wavelength peak located at 1,450 nm corresponds to the zero point (crossover wavelength) in the real permittivity of AZO and shows little tunability. Therefore, we conclude that the short wavelength peak arises due to excitation of bulk and/or surface plasmon-polaritons in the AZO. Conversely, the longer wavelength peak intensifies and blueshifts as n gets larger (Fig. S4A). Importantly, the accuracy of EMA increases with a larger number of periods and only the long wavelength peak changes with the AZO filling fraction, ff m (Fig. S8B). Additionally, as will be described in the following section, an analytical model reveals that as air gaps are introduced into the HMM the system evolves into a photonic hypercrystal which supports additional modes and allows for additional absorption band tailoring.

SI Note II: Analytical Description of Photonic Hypercrystal The mechanism for absorption can be better appreciated by examining the dispersion of the AZO/ZnO/air system analytically. We hypothesize that absorption occurs through the excitation of bulk plasmon polaritions (36) that are supported by the periodic AZO/ZnO/air system. Due to the high losses, we assume that all excited modes eventually dissipate, contributing to absorption. Therefore, absorption occurs at frequencies for which the system supports modes. Because our material system is highly dispersive, traditional methods for computing the entire 2D band structure, such as the plane wave expansion method or FDTD (37), are unreliable and inefficient. To address this complication, we make a number of simplifying assumptions. Namely, we ignore losses and approximate the entire structure as a 1D photonic hypercrystal (28) with variable air gap, g. Although ignoring the center air hole and excitation of modes traveling along the length of the HNT, our assumptions provide a first-order description of the actual system and yields results qualitatively consistent with the experimental absorption spectra. Propagation of electromagnetic waves through periodic media is conveniently described using Bloch’s theorem (38⇓–40). Because the layer thicknesses of the AZO/ZnO HMM are deeply subwavelength, we use effective medium theory (41, 42) to treat the HMM as a homogeneous uniaxial layer. The general formalism for wave propagation through periodic anisotropic layers for arbitrary angles of incidence and arbitrary orientation of optical axes is rather complex and necessitates numerical solution of a 4 × 4 matrix problem with complex coefficients (38). However, Boucher et al. (40) showed that for the case of a periodic system consisting of one uniaxial and one isotropic layer, with the optical axis of the uniaxial layer aligned with the optical axis of the bilayer, the problem resembles an isotropic–isotropic periodic system with an angle-dependent permittivity included in the dispersion relation for TM waves. Using previously reported optical data (23), we first determine the wavevector component parallel to the optical axis of the system, k || , for both TM and TE polarizations, as a function of the transverse wavevector component, k ┴ , and vacuum wavelength, λ 0 . The dispersion relations of a 1D infinitely periodic uniaxial-isotropic system, with period length, a, are as follows (40): k ∥ , TE ( λ 0 , k ⊥ ) = 1 a cos − 1 ( A TE + D TE 2 ) , [S7] k ∥ , TM ( λ 0 , k ⊥ ) = 1 a cos − 1 ( A TM + D TM 2 ) , [S8]where A T E = exp ( i k ∥ , T E ( H ) d H ) [ cos ( k ∥ , 0 d 0 ) + i 2 ( k ∥ , 0 k ∥ , T E ( H ) + k ∥ , T E ( H ) k ∥ , 0 ) sin ( k ∥ , 0 d 0 ) ] , [S9] D T E = exp ( i k ∥ , T E ( H ) d H ) [ cos ( k ∥ , 0 d 0 ) − i 2 ( k ∥ , 0 k ∥ , T E ( H ) + k ∥ , T E ( H ) k ∥ , 0 ) sin ( k ∥ , 0 d 0 ) ] , [S10] A T M = exp ( i k ∥ , T M ( H ) d H ) [ cos ( k ∥ , 0 d 0 ) + i 2 ( ε T M ( H ) ( θ ) k ∥ , 0 ε a i r k ∥ , T M ( H ) + ε a i r k ∥ , T M ( H ) ε T M ( H ) ( θ ) k ∥ , 0 ) sin ( k ∥ , 0 d 0 ) ] , [S11] D T M = exp ( − i k ∥ , T M ( H ) d H ) [ cos ( k ∥ , 0 d 0 ) − i 2 ( ε T M ( H ) ( θ ) k ∥ , 0 ε a i r k ∥ , T M ( H ) + ε a i r k ∥ , T M ( H ) ε T M ( H ) ( θ ) k ∥ , 0 ) sin ( k ∥ , 0 d 0 ) ] . [S12]In Eqs. S9–S12, the longitudinal wavevector components are as follows (42): k ∥ ,TE ( H ) = ε ⊥ k 0 2 − k ⊥ 2 , [S13] k ∥ ,TM ( H ) = ε ⊥ ( k 0 2 − k ⊥ 2 ε ∥ ) , [S14]with k 0 = 2π/λ 0 . The effective permittivity elements, ε ⊥ and ε ∥ , are given by Eqs. S4 and S5, and k ┴ is an independent, purely real-valued variable. Also, ε air = 1 is the permittivity of air; d H and d 0 are the lengths of the uniaxial HMM and isotropic air layers, respectively; and k ∥ , 0 = ( k 0 2 − k ⊥ 2 ) 1 / 2 . The photonic hypercrystal (PhHC) described in this section then has a period of a = d H + d 0 . Finally, the angle-dependent permittivity element of Eqs. S11 and S12 is defined as follows: ε TM ( H ) ( θ ) = ε ∥ 2 ⁡ cos 2 ⁡ θ + ε ⊥ 2 ⁡ sin 2 ⁡ θ , [S15]where θ ≡ cot − 1 ( k ∥ ,TM ( H ) k ⊥ ) . [S16]We note that, for waves propagating normal to the layer interfaces, θ = 90°, the TM and TE modes are degenerate. The structure we consider is shown schematically in Fig. S5. Also shown is the effective permittivity elements of the AZO/ZnO HMM parallel and normal to optical axis of the system, which is normal to the layer interfaces. All calculations in this section use a constant metallic filling fraction, ff m = 0.5. From effective medium theory, the HMM exhibits type I hyperbolic dispersion for 1,450 nm < λ 0 < 1,720 nm and type II hyperbolic dispersion for λ 0 > 1,750 nm for TM modes, that is, modes with an electric field component normal to the layer interfaces. Dispersion is elliptical for λ 0 < 1,450 nm for both TM and TE modes. In the type I and type II hyperbolic regimes, TE modes are elliptical and not supported, respectively. As a increases with a fixed d H , the fill fraction of the HMM in the PhHC becomes smaller. This corresponds to the experimental situation of a decreasing hyperbolic nanotube fill fraction, ff HNT , which we define as follows: f f HNT = π 6 3 D t 2 a 2 . [S17]Compared with PhHCs with a = 1,500 nm, a = 2,500 nm, and a = 3,500 nm, a PhHC with a = 770 nm has a ff HNT 4×, 11×, and 21× greater, respectively. Therefore, a naive prediction would assume that the close-packed PhHC with a = 770 nm has 4×, 11×, and 21× greater absorption at a given wavelength, which is not observed in the numerical simulations displayed in Fig. S4B. Fig. S6 compares a PhHC of constant d H = 740 nm and a increasing from 740 to 3,500 nm as a function of both λ 0 and k ┴ . Key observations are (i) the existence of type I and type II hyperbolic dispersion, denoted by regions where modes exist in the spatial frequency bandwidth |k ┴ /k 0 | → inf for 1.45 μm > λ 0 > 1.72 μm and k ┴,min < |k ┴ /k 0 | → inf for λ 0 > 1.75 μm, respectively; (ii) appearance of stop bands in the PhHC as a increases in the type I regime for k ┴ /k 0 < 1 and in the type II regime for k ┴ /k 0 > 1; and (iii) appearance of pass bands in the PhHC as a increases in the type II regime for k ┴ /k 0 < 1. Despite the appearance of bandgaps during the formation of the PhHC, additional modes also appear. These modes are responsible for the larger-than-expected absorption of the PhHC with large a, particularly in the type II regime. The naive prediction based on HNT density fails because it does not account for the appearance of additional modes as the HMM evolves in the PhHC. These features correlate well with the numerical simulation presented in Fig. S4B. Based on these results, it is clear that the absorption spectrum depends upon both the wavelength-scale periodicity of the hypercrystal and the deeply subwavelength scale of the HMM. The simultaneous control of these structural parameters enables a tailorable absorption spectrum unachievable in other systems, such as self-aligned carbon nanotubes. Therefore, the near-perfectly absorbing photonic hypercrystal represents a platform for tailor-made manipulation of light. Although we have demonstrated this effect using AZO, ZnO, and air in the NIR, we stress that our methodology is general and may be applied to myriad material systems across the electromagnetic spectrum.

SI Note III: Effects of Surface Roughness The experimental values are in good agreement with the simulated values from 1,400 to 2,000 nm. However, out of this spectral range, the simulated absorption is significantly lower. At shorter wavelengths, this is due to the silicon substrate (as explained in the main text), whereas at longer wavelengths the higher absorption can be attributed to scattering by the roughened surface. The effects due to roughening can be observed in the absorption profile from both the numerical simulations and experiments. It is clear from the simulations (Fig. S7A) that the shorter wavelengths are unaffected by the increased surface roughness, but at longer wavelengths (>2,000 nm) there is a much higher absorption for a roughened surface. To validate this experimentally, the as-processed arrays were further roughened by overetching during the RIE process (Fig. S7B). Although the HNTs are shorter by 260 nm after etching, the absorption is much higher at longer wavelengths compared with the smoother and longer HNTs. However, at shorter wavelengths, the absorption of the roughened HNTs is diminished due to the shorter length of the HNTs. Increased sensitivity to the HNT length at shorter wavelengths is expected because it is closer to the crossover wavelength where the polarization response and loss are lower. The absorption of photons by scattering into modes of the HMMs has been previously studied and, following Fermi’s golden rule, is attributed to the high photonic density of states in these materials (31, 43).

Acknowledgments We acknowledge Dr. Bernd Fruhberger, Larry Grissom, Ivan Harris, and Dr. Xuekun Lu of Calit2 at University of California, San Diego, for their support in installing and calibrating the necessary precursor lines in the ALD system and assistance. We also acknowledge the Basov Laboratory for allowing us to use their Bruker LUMOS FTIR. Funding for shared facilities used in this research was provided by the National Science Foundation (Award NSF CBET1236155).