# Multiple Reflections and the Near-Field Effects on a Metamaterial Quarter-Wave Plate
## 4 Discussion  
In this paper, we designed a broadband transmission-based QWP optimized for use around 800 nm. Our QWP stands out for its ultra-thin, broad bandwidth, and transmission-based features, further bolstered by its simple 2D design. A study of its near-field behavior gave rise to an effective length of the device. This notion is significant, as it suggests that a metamaterial's dimensions should not only be determined by the device's physical parameters but also by the length required to achieve the desired output. A further analysis was conducted of the designed QWP as part of a cascaded system, highlighting how multiple reflections dramatically increased the loss of the Z component. This had an important effect on the output angle of the cascaded system to never be able to fully achieve the 90-degree rotation expected from cascaded QWPs.  
While metamaterials and metadevices have shown to have potential to miniaturize and revolutionize optical systems, the increased complexity of electromagnetic field interactions  
Figure 8: The simulation results for the physical design in Figure 7 at 800 nm with an input of a normally incident uniform plane wave with a 45-degree polarization angle. Displayed are the (**a**) transmittance, reflectance, and absorbance of the 45-degree input, (**b**) the phase difference between the Z and Y polarizations, (**c**) degree of linear polarization, and (**d**) polarization conversion ratio with respect to separation distance.  
Figure 7: 2D cascaded grating separation simulation schematic following the same design in Figure 4, with varying separation distance between the gratings. Both the input and output ports are 150 nm away from the grating surfaces.  
as these structures approach the near-field region poses a limitation that must be considered. We explored how this can lead to unwanted energy transfer, causing alterations to the transmittance and phase response of the cascaded QWP. Near-field effects are inherent to many metamaterial designs, yet the extent and implications of these effects often go unaddressed in standard design considerations. In the realm of high-density optical assemblies with components separated by sub-wavelength distances, it becomes paramount to grasp the potential interactions between these components. While simulations remain indispensable for every optical system, a prior understanding of device constraints within compact configurations can streamline the design process similar to large scale electronic circuit design. Such comprehension enhances the contributions of individual devices, facilitating the evolution of practical, high-density metamaterial optics. Comprehensive insight into metamaterial properties, inter-device interactions, and near-field dynamics will be pivotal for the advancement of future optical system designs and applications. A promising avenue for future research may involve leveraging auxiliary fields [80, 81] to modulate these inter-device interactions and near-field effects, paving the way for dynamic and reconfigurable metadevices.  
Conceptualization, J.D. and D.G.; methodology, J.D. and D.G.; software, J.D.; validation, J.D. and D.G.; formal analysis, J.D.; investigation, J.D.; resources, D.G.; data curation, J.D.; writing--original draft preparation, J.D.; writing--review and editing, J.D. and D.G.; visualization, J.D.; supervision, D.G.; project administration, D.G.; funding acquisition, D.G. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
All data are presented in this paper.  
The authors declare no conflict of interest.