Three dimensional metafilms with dual channel unit cells

Man-made, structured electromagnetic materials offer enticing next-generation functionalities which are unattainable in naturally occurring materials. Metamaterials research¹ has spurred efforts to create perfect lensing,^2,3 electromagnetic cloaking,^4,5 and transformation optics,^6,7 while plasmonic-based nanophotonic research has offered energy harvesting approaches,^8,9 lasing spasers,^10,11 and chemical sensors.¹² The recent emergence of planar metasurfaces,¹³ where the thickness t is significantly thinner than the design wavelength λ_d (i.e., t ≪ λ_d), is further evidence of the potential power of structured materials. Despite this success, planar configurations are limited in the possible spatial orientations, packing density, and interaction mechanisms with incident light. Furthermore, some behaviors such as circular polarization control,¹⁴ chirality,^15,16 and electromagnetic toroidal dipole excitation¹⁷ specifically require that the structured electromagnetic material possess 3-dimensional spatial variation in the direction of propagation.

The vast majority of nano/microfabrication approaches are only capable of creating 2-dimensional (2D) structures, which are limited in the manner in which they can achieve coupling to incident electromagnetic fields as well as mutual coupling between neighboring inclusions. Three-dimensional fabrication approaches for structures with length scales in the micrometer and sub-micrometer regimes are much less common than their two-dimensional brethren. Layer-by-layer approaches¹⁵ can be used to create stacked versions of planar inclusions. Direct laser write¹⁴ and nano-origami^18,19 approaches can be used to create fully three dimensional structures; however, the structures that can be realized by these fabrication approaches may be limited in either form factor or areal packing density of inclusions. Recently, Tsai et al.^20,21 have demonstrated vertical split ring resonators (VSRRs) with their gaps oriented on the top of the SRR, fabricated by a two-write e-beam fabrication sequence, and measured enhancement of the magnetic field. While this two-write e-beam approach is capable of fabricating high resolution VSRRs resonant in the optical regime, it would be difficult to create VSRRs with other orientations, such as having the gap to the side.

Combining the powerful apparatus and design insight of planar metasurfaces with more conventional 3D thin film concepts has the potential to add new degrees of freedom in the construction of next generational optical components, provided we possess adequate understanding of the added complexities of the 3D nature of the metafilm. In this paper, we demonstrate that transitioning to 3D unit cells allows us to pack the volume of the unit cell with multiple scattering behaviors, or channels, which can be independently accessed by changing the linear polarization state of the incident plane wave.

Metafilms were created using membrane projection lithography.^22–24 The fabrication was carried out on a 150 mm silicon CMOS fabrication line with a 248 nm optical scanner. Square cavities (2 μm × 2 μm) in a 2.3 μm period (a = 2.3 μm) square array (1 cm × 1 cm) were etched into silicon wafers to a depth of 3 μm using a photoresist/silicon nitride etch mask. The wafer was oxidized to thin the silicon walls to ∼100 nm. The cavities were backfilled with polysilicon and polished back to planarize, stopping on the nitride. 100 nm of aluminum nitride (AlN) was deposited and an SRR pattern was etched through the AlN, centered in each unit cell. A chemical downstream etch was used to remove the polysilicon backfill material and a hydrofluoric acid etch removed the wall-thinning oxide through the patterned AlN membrane. The SRRs were deposited via non-rotated oblique e-beam evaporation consisting of a Chromium/Gold stack (10 nm/50 nm) at 2 Å/s through the membrane resulting in deposition of an SRR on a vertical sidewall. 2-SRR basis films, with two SRRs per unit cell, were created by performing two successive evaporations through the membrane with a substrate rotation of 90° between depositions. The metal-coated AlN was removed via SC1 clean (pH ∼10-H₂O:NH₄OH: H₂O₂, 5:1:1 at 70 °C), yielding the metafilm array.

In conventional optics, a thin film is typically a homogeneous layer of material with a thickness on the order of large fractions of the incident wavelength. For instance, the ubiquitous quarter wave stack has alternating layers of high and low indexes, each with an optical thickness equal to a quarter of the design wavelength, λ_d in the medium. In the 3D metafilms considered here, the material is inhomogeneous, containing metallic inclusions which can be oriented along any plane in the material in a dielectric host. Consider the SEM images of the metafilms in Fig. 1. The unit cells were decorated with a single SRR basis (Fig. 1(a) gap down, Fig. 1(b) gap right, and Fig. 1(c) gap up) on the X-Z face of the unit cell. Fig. 1(d) shows a sample with a 2-SRR basis: a gap-right SRR positioned on the X-Z face and a gap-up SRR positioned on the Y-Z face. We will indicate the cavities with single SRR basis as 1-SRR, the ones with two SRR basis as 2-SRR, etc. The arrays cover a 1 cm X 1 cm area, and except for occasion defects, are uniform. The layer apparent at the top of the cavities is a silicon nitride layer used as the etch mask and polish stop during fabrication.

The far-field scattered light was examined using a hemispherical directional reflectometer (HDR). The backs of the 1-cm² samples were bead blasted to prevent specular reflection from the back surface, mounted on glass slides, and placed in an SOC-100 Hemispherical Directional Reflectometer, interfaced to a Nicolet-760 FTIR. The samples were measured at 10° angle of incidence. The specular reflection spectra are all measured relative to a gold reference sample and have been normalized so that the maximum signal for each spectrum is unity. No further normalization or smoothing has been performed. At normal incidence, light below a certain frequency (∼75 THz, determined by numerical simulation) lacks sufficient momentum to resolve and diffract from the periodic array of boxes. Above this frequency, diffracted orders exist, first in the high index substrate and finally in the low index air above the array (indicated by the grey region in the plots in Fig. 2 and subsequent plots).

For 1-SRR basis films under linearly polarized light with the E-field oriented perpendicular to the X-Z plane containing the SRR (off-polarization), the presence of the SRR has a vanishing effect on the reflected signal. Under this polarization, the E-field is perpendicular to the SRR gap, while the B-field is parallel to the plane of the loop, so that neither field can excite the fundamental LC resonance of the SRR. Fig. 2 contains a plot of the measured normalized specular reflectance versus frequency for this polarization, for each of the three possible orientations of the SRR observed in Figs. 1(a)–1(c). Commercial rigorous coupled wave analysis (RCWA) code was used to model the far-field reflected signal from the samples and for plots of the magnetic field for visualization purposes (GD-Calc, KJinnovations Inc.), retaining the first 19 modes. The off-polarization spectra for each of the three orientations of SRR show virtually no dependence on SRR orientation. The black dotted curve in Fig. 2 is an RCWA simulation of a 2D array of undecorated unit cells. The magnitude and width of the oscillations are captured very well by the scattering response of the naked array, indicating that for this linear polarization, the SRRs appear to be transparent. In the low frequency region, large intensity oscillations reminiscent of thin film interference fringes (see supplementary material, Fig. S1) are apparent as the long wavelength incident light experiences an effective medium resulting from a mixing of the indices of air, silicon, silicon nitride, and metal. The structured material forms an effective antireflection coating at the air-silicon interface, but is otherwise insensitive to the orientation of the SRRs, yielding nearly identical reflectance spectra for all three samples.

In Figs. 3(a)–3(c), the incident polarization is rotated such that the E-field is parallel to the X-Z plane containing the SRR (on-polarization), with the B-field normal to the SRR loop. For the gap-up and gap-down SRRs, the E-field can directly drive the gap of the SRR while the B-field flux cuts through the loop of the SRRs, providing both electric and magnetic excitation of the fundamental RC resonance. For the gap-right SRR, the E-field is perpendicular to the gap and cannot excite the LC resonance; however, the B-field flux cuts through the loop, providing a purely magnetic excitation of the fundamental LC resonance.²⁵ These normalized specular reflection curves are significantly different than the curves of Fig. 2 due to the resonant excitation of the SRRs and now also deviate from one another.

A variable angle spectroscopic ellipsometer (IR-VASE, J. A. Woollam) was used to measure dispersive optical constants for the gold, silicon, and silicon nitride materials in our fabrication process. These optical constants were used in the RCWA simulations. The dimensions of the SRR and cavity were adjusted to fit the measured data, accounting for sample-to-sample variability in wall thickness, evaporation angle, and linewidth. Identical SRR dimensions for both SRRs were used for 2-SRR basis modeling, even though the second SRR linewidths will be slightly affected by metal accumulation during the first evaporation through the membrane pattern. The results of the RCWA modeling were confirmed with finite difference time domain simulations using commercial code (Lumerical). Good qualitative agreement is achieved between measured and modeled curves in the low-frequency region of the plots, deviating somewhat as diffractive modes emerge in the higher frequency region depicted by the grey boxes.

The reflection spectra in Fig. 3 demonstrate some of the additional complexity of 3D films. The SRRs decorating the unit cells in each of these samples have nominally the same physical dimensions; however, their reflection spectra are quite orientation-dependent. The presence of a substrate is known to break the translational symmetry of planar SRRs placed on a planar substrate,²⁶ inducing bianisotropy. In the 3D metafilms considered here, the relative orientation of the SRR on the vertical face provides an additional degree of complexity as the proximity of the SRR gap to the high index substrate is different for the gap up, gap down, and gap right versions, further altering the scattering response of the SRR.

Fig. 4 contains the reflection spectra for a unit cell with 2-SRR basis, composed of a gap up and a gap right SRR on adjacent faces inside the unit cell. In this case, both possible linear polarization states result in resonant coupling to either the gap-up SRR or the gap-right SRR, so that the thin film fringes from Fig. 2 are no longer apparent. In Fig. 4(a), the measured and modeled reflectance spectra of the 2-SRR basis array are plotted along with the reflection spectrum of the 1-SRR gap-up response under resonant polarization. Similarly, in Fig. 4(b), the measured and modeled response of the 2-SRR basis array is plotted along with the reflection spectrum for the 1-SRR gap-right response for its resonant polarization. Both 2-SRR-basis spectra bear a strong resemblance to the 1-SRR spectra for the corresponding resonant polarization. It is well known that SRRs placed in such close proximity to one another can couple either electrically or magnetically.²⁷ In this case, coupling between the neighboring SRRs causes a slight shift to lower frequency in the dominant peak (highlighted by a dashed circle). Plots of the magnetic field (insets of Fig. 4) indicate that even though only one SRR is driven by the incident field in either configuration, intra-unit cell coupling between the SRRs results in induced current flow and localized field enhancement on the non-driven SRR. Nevertheless, the far-field reflection behavior remains largely that of the individual driven SRRs, exhibiting a dual-channel optical behavior derived from the microscopic make-up of the unit cell.

Here, we have shown measured and modeled reflection data demonstrating several unique properties of 3D metafilms, and how the optical behavior of the film is modified by using multi-SRR basis unit cells. For 1-SRR unit cells, a strong degree of anisotropy is present for linear polarization, with one polarization experiencing resonant scattering from the SRR while for the other polarization, the SRR is transparent. In the transparent linear polarization, the finite thickness of the unit cells allows for classical thin film interference fringes in the long wavelength limit, a behavior which is not present in thin, planar 2D, and stacked-planar samples with thickness ≪ λ_d.

For 2-SRR-basis unit cells with inclusions on adjacent faces, the film can operate in a two channel mode, where inclusions on adjacent faces respond relatively independently from each other for each polarization. For the unit cells shown here, the 2 SRRs are created from the same template with similar physical dimensions and hence interact due to near field coupling. In a 3D unit cell with drastically different sized inclusions, or inclusions specifically engineered to suppress near-field coupling, the independence of the scattering response can be expected to be even more dramatic, further enabling the unit cell to be packed with independent channels of operation. 3D unit cells with 2-SRR-basis films possess excitation mechanisms and polarization behaviors which cannot be attained in planar, or stacked planar configurations, and hint at even richer electromagnetic behaviors for metafilms composed of 3-SRR and higher bases. In this way, we have gained multiple degrees of freedom to manipulate the effective behavior of 3D metafilms.

See supplementary material for the analysis of the non-resonant polarization in terms of classical thin film interference fringes.

This work was supported by the Laboratory Directed Research and Development program at Sandia National Laboratories, a multi-mission laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under Contract No. DE-AC04-94AL85000. Partially supported by the Defense Advanced Research Projects Agency Defense Sciences Office (DSO) Program: DARPA/DSO EXTREME; Agreement No. HR0011726711.