## 1 Introduction  
There are two different applications of gratings in general. First is a diffraction tool with a period larger than the wavelength, and second is as an engineered film with controlled material parameters. The second type of application requires substantially subwavelength gratings, so that in some ranges of wavelengths and angles they can be described by the effective parameters of a uniform film. For those ranges of wavelengths and angles there are no detectable non-zero diffraction orders. One-dimensional gratings consisting of stacked metal-dielectric strips are investigated for their ability to provide magnetic as well as electric resonances [1; 2; 3; 4]. Such resonances are located in the visible spectrum due to the size of the unit cell--less than 0.5 \(\upmu\)m. Effective magnetic permeability appears due to circular currents in the stacked structure. It follows from [PERSON]'s equations that the transmission and reflection coefficients for the effective film depend on both the product and the ratio of permittivity and permeability, i.e., on the refractive index and the impedance [5; 6]. As for any nonlocal effect, the magnetic response increases with the size-to-wavelength ratio. That is why, in the case of metamaterial applications, we are often at the borderline of applicability of the effective parameter approach [7; 8]. Often, the grating can be treated as an effective film at normal incidence but it cannot be at inclined incidence. The boundary angle at a specific wavelength is defined by appearance of the first diffraction order, which is the Wood's anomaly [9; 10; 11].  
Here we characterize such a grating consisting of a stacked vertical substructure by an effective permittivity and permeability of the strips instead of by a continuous effective layer. The approach captures both the effect of the substructure resulting in an artificial permeability, and the diffraction of a grating, by employing a set of effective parameters for the geometrically defined strips. It should be clear that, as is the case with any effective medium approximation, the model works best in the long wavelength limit compared to the strip dimensions. Note, that the effective layer approach can be applicable only in the spectral range of the zero-order diffraction. Any high-order diffraction would result in a wrong retrieval. The experiments presented here show first diffraction order at 450 nm making effective layer approximation not applicable. It is important to note that a grating with the structured strips can be of great interest for the first type of application, especially as an input/output tool for waveguides. Indeed, the structured strips introduce anisotropy in the effective parameters, which makes it possible to realize different polarization and angular dependences, and this behavior is captured by the proposed model.  
For similar grating structures, the permeability and permittivity retrieval process has been previously demonstrated for normal-incidence illumination using rigorous coupled wave (RCW) methods [5; 6; 12] and using complex transmission and reflection coefficients [3; 4]. The retrieval for the effective films, however, cannot be verified conclusively for inclined illumination. This is in large part due to the difficulty arising from the effect of diffraction [8; 9]. While diffraction occurs at normal incidence, its higher order effects in the range from 400 nm to 1000 nm are typically masked in the effective layer scheme. Under inclined illumination, the Wood's anomaly is red-shifted into the visible, higher diffraction orders are no longer hidden, and the effective layer method breaks down.