## 2 Materials and Methods
Diffraction effects can be described by the well-known grating equation  
\[n\ sin(\theta_{m})=n_{inc}sin(\theta_{inc})-\frac{m\lambda}{p}, \tag{2}\]  
where the subscript-free \(n\) refers to the transmitted region's refractive index, \(n_{inc}\) is the refractive index in the incident medium, \(p\) is the period of the grating, \(\lambda\) is the wavelength in vacuum, and \(m\) is the  
Figure 1: Sample geometry and experimental setup. Panel **(a)** shows the vertical substructure of the strip; **(b)** portrays the replacement of the real structure with an effective strip; **(c)** depicts the inclined illumination setup, in addition to usual far-field transmission spectroscopy, necessary for retrieving the optical parameters. diffraction order. For the grating under study, our substrate also serves as a waveguide. We wish to simulate the diffraction that occurs due to a periodic grating structure, and the MIST suits our needs for this. MIST includes RCW analysis to simulate the interaction of arbitrarily polarized light with a grating structure of interest. More detail regarding MIST will be given in the subsequent simulation subsection. The strips of the diffraction grating consist of a total of six layers, essentially forming a metal-insulator-metal (MIM) configuration, which includes adhesion and oxide protection layers. As depicted in Figure 1, each layer of silver lays atop a thin titanium layer, with the metal layers separated by a spacer dielectric, and finally a top protective oxide layer. The die size is 500 \(\upmu\)m \(\times\) 500 \(\upmu\)m, with a period of 305 nm and a total height of 130 nm. The bottom and top widths are 155 nm and 80 nm, respectively, which causes an asymmetry to the shape of the two metal strips such that the bottom silver layer is wider than the top silver layer. The metal strips themselves have a thickness of 35 nm, with a 40 nm layer of alumina separating them. Silver is the selected metal due to its low losses at optical frequencies, while alumina has been chosen as the spacer dielectric for its high dielectric constant. It has been shown that the higher dielectric constant spacer is more suitable for magnetic grating metamaterials because it provides better field confinement [17]. Samples have been fabricated on a 15-nm indium-tin-oxide- (ITO) coated fused silica substrate using conventional electron beam lithography (EBL) techniques. The ITO layer is used primarily to provide conduction during EBL. Note that a trapezoidal shape of the cross-section is due to the applied fabrication protocol [6]. After development of the exposed resist, titanium, silver, and alumina layers are deposited by electron beam evaporation. A 3-nm layer of titanium is evaporated before each silver layer to provide good adhesion, making the samples more robust, but lowering the quality of the plasmonic resonances. It is worth mentioning that the roughness and grating quality have been found to be significantly affected by deposition rate [18]. This in turn can affect the optical characteristics of the sample. Specifically, lower deposition rates for gratings and other finer features tend to yield smoother and better-quality nanostructures, as opposed to higher deposition rates giving better quality continuous films. As such, a low deposition rate of 0.1 nm/s has been used. A final liftoff process in acetone is performed revealing the intended grating structure. Figure 2 shows a scanning electron microscopy (SEM) micrograph of the top view of the sample. Upon successful fabrication, the sample is used in conjunction with the optical scheme described in Figure 1c. Under normal incidence illumination, diffraction does occur for shorter wavelengths; however, the nonzero orders are trapped in the glass substrate by total internal reflection, and as a result, the detector only detects zero-order diffraction.