# Enhancing Absorption Bandwidth through Vertically Oriented Metamaterials
## 1 Introduction  
Metamaterials play a crucial role in the development of micrometer-scale devices for a wide variety of applications, including electromagnetic cloaking [1], perfect absorption ranging from microwave to optical frequencies [2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14], and ultrasensitive terahertz sensing [15]. Among the numerous resonator geometries that have been explored, the split-ring resonator (SRR) is frequently used [10; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24].  
For this investigation, SRRs were studied based on their straight-forward fabrication, simple geometry, and strong absorption features. The infrared regime is of particular interest, based on the abundance of vibrational modes supported by the resonators, as well as the breadth of applications, such as sensing [25; 26], detection [27], tunable devices [28], and imaging [29].  
While a planar SRR (PSRR) can be fabricated using conventional lithography, fabrication of a vertical SRR (VSRR) is challenging, often requiring the combination of lithography and plating [10; 18; 30], deposition, or metal-stress driven self-folding [31]. However, these techniques require that the SRRs be bound to the top surface of the substrate, preventing any vertical displacement. Moreover, fabrication and design of VSRRs become increasingly difficult as the application wavelength, and therefore SRR dimensions, decreases.  
Membrane Projection Lithography (MPL), an alternative fabrication technique, alleviates the need to bind the vertical SRR to the substrate surface [32; 33]. Using this method, additional degrees offreedom are unlocked for the VSRRs, including rotation of the VSRR about the axis orthogonal to the broad face of the SRR--a parameter crucial to intra-cell coupling between the VSRR and PSRR. Additionally, MPL allows multiple resonators to be placed in a given unit cell in a dense array [34]. While the dimensions and distance between SRRs in neighboring unit cells undoubtedly impacts inter-cell electromagnetic coupling between SRRs, it is not discussed in detail here.  
Motivated by the applicability of vertically-oriented metamaterials to sensing and filtering, this study explored electromagnetic coupling between multiple SRRs in a single unit cell. In doing so, we demonstrate the role intra-cell coupling plays in enhancing the spectral response from a periodic metamaterial layer. Specifically, SRRs on orthogonal surfaces inside a unit cell were utilized to widen the bandwidth of the device's spectral absorption under plane wave illumination, without increasing the area occupied by the resonators. In contrast, previous investigations to widen absorption bandwidth examine purely planar resonant structures, including multiple crosses [35; 36], dual band absorbers [37], planar I-shaped resonators [38], and double split-ring resonators [39]. Similarly, much work has been done to understand coupling between planar split ring resonators [39; 40; 41; 42], but no attention has been given to vertical SRRs as we do here. Opening up designs to the vertical dimension enables new optical devices, such as lenses and polarizers, to be compact and introduce fewer aberrations.