# Ultra-Thin Metamaterial Beam Splitters
## 1 Introduction  
A beam splitter is an important optical component used to split a beam of incident light at a desired ratio into two separate beams. The beam splitters can be typically classified into three kinds according to the input and output polarizations: polarizing beam splitter (PBS), partially polarizing beam splitter (PPBS) and non-polarizing beam splitter (NPBS). In the recent works, NPBS based on phase gradient dielectric metasurfaces was theoretically proposed at visible and near-infrared spectra with TiO\({}_{2}\) nanopillars on a glass substrate and LiNbO\({}_{3}\) nanocylinders on a fused quartz substrate [1, 2], and experimentally realized with a 1-bit coding scheme [3] and tested with variable splitting ratios and broadband response [4] at THz frequencies using Si pillars on a Si substrate fabricated by combined photolithography and deep reactive ion etching. A PBS for circularly polarized light mimicking a Rochon prism was realized with a dielectric metasurface at near-infrared wavelengths using Si nanoblocks on a fused silica substrate fabricated by series of processes including chemical vapor deposition, electron-beam evaporation, electron-beam lithography and plasma etching [5, 6]. Spatially dispersive hyperbolic metamaterials were theoretically proposed to realize a PBS for white light with a wide angular range. However, the theoretical analysis therein does not consider the optical losses and discrete unit cells in the metamaterials [7]. Hyperbolic metamaterials are typically fabricated as either layered metal-dielectric structures or metallic nanowire arrays [8]. In earlier works, PBS designs based on an Ag mirror embedded in silica grating [9] and perforated GaAs photonic crystal [10] were theoretically proposed and experimentally realized with gratings etched in a TiO\({}_{2}\) layer on a glass substrate fabricated by electron-beam writing and reactive ion etching [11]. Other interesting designs that were demonstrated include a PBS cube for arbitrary orthogonal polarizations based on liquid crystal polymer layers [12] and electrically tunable beam splitters employing polymer dispersed liquid crystals [13]. One can design a PBS to split light into reflected transverse electric (TE)/transverse magnetic (TM) polarization and transmitted TM/TE-polarization. Here TE-polarized means electric field is perpendicular to the plane of incidence, and TM-polarized means electric field is parallel with the plane of incidence. PBS can split unpolarized light at a 50/50 ratio, which makes it an essential element in applications, such as polarization based imaging system [14], free-space optical switching networks [15], and read-write magneto-optical data storage systems [16]. NPBS can split the light at a specific reflectance (R)/transmittance (T) ratio, at the same time, the original polarization state of the incident light is still maintained. NPBS is widely used in interferometers. Between polarizing and non-polarizing is PPBS. For example, an important application of PPBS is in quantum information processing in that it is a key component to realize the quantum controlled-NOT (CNOT) gate [17], an essential gate in the construction of a photonic quantum computer. By using a combination of the CNOT gate and single qubit rotations, one can build any quantum circuit to an arbitrary degree of accuracy [18]. NPBS can also be used in quantum entanglement distillation tasks [19; 20]. Inspired by the sub-wavelength unit cell size and arbitrarily controlled electromagnetic response, metamaterial-based beam splitters are promising to form compact and functional photonic devices. Here, we present three types of ultra-thin beam splitters under different geometries of fishnet metamaterial structures (see Figure 1). These beam splitters are all designed to operate at the 1.55 \(\upmu\)m wavelength, relevant to optical communication systems, where the absorption of glass material used in fiber is small.