Giant photonic spin Hall effect in momentum space in a structured metamaterial with spatially varying birefringence

Abstract

The photonic spin Hall effect (SHE) in the reflection and refraction at an interface is very weak because of the weak spin-orbit interaction. Here, we report the observation of a giant photonic SHE in a dielectric-based metamaterial. The metamaterial is structured to create a coordinate-dependent, geometric Pancharatnam-Berry phase that results in an SHE with a spin-dependent splitting in momentum space. It is unlike the SHE that occurs in real space in the reflection and refraction at an interface, which results from the momentum-dependent gradient of the geometric Rytov-Vladimirskii-Berry phase. We theorize a unified description of the photonic SHE based on the two types of geometric phase gradient, and we experimentally measure the giant spin-dependent shift of the beam centroid produced by the metamaterial at a visible wavelength. Our results suggest that the structured metamaterial offers a potential method of manipulating spin-polarized photons and the orbital angular momentum of light and thus enables applications in spin-controlled nanophotonics. Keywords: geometric phase; metamaterial; photonic spin Hall effect INTRODUCTION Metamaterials or metasurfaces are artificial materials that are engineered to produce nearly any imaginable optical properties that are not found in nature. 1,2 They are typically structured at the subwavelength scale with ultrathin metallic or dielectric micro/nanoparticles or with holes opened in metallic films. Metamaterials exhibit unprecedented degrees of freedom in the polarization and phase manipulation of light via the geometric structuring of their structural units, especially on the wavelength scale, 3-9 which leads to applications such as vortex beam generators, 3,7 metalenses 10,11 and optical holography. 12,13 These materials also offer considerable potential for the manipulation of the angular moment of light and the photonic spin Hall effect (SHE), thereby providing convenient opportunities for spin-polarized photonics and nanophotonics. [14][15][16][17] The photonic SHE describes the mutual influence of the photon spin (polarization) and the trajectory (orbital angular momentum) of light-beam propagation, i.e., the spin-orbit interaction (SOI), which results in two types of geometric phases: the Rytov-VladimirskiiBerry (RVB) phase and the Pancharatnam-Berry (PB) phase. [18][19][20][21][22] The RVB phase is associated with the evolution of the propagation direction of light. When a light beam reflects/refracts at a planar interface between different media, a SOI occurs, and the corresponding momentum-dependent RVB phase leads to a spin-dependent real-

Polarization State Manipulation of Electromagnetic Waves with Metamaterials and Its Applications in Nanophotonics

“…Spindependent geometric phase gradient in metamaterials provide an alternative method to realize a gain on spin-orbit interaction at nanoscale [40,[62][63][64]. Figure 8a-c shows an experimental demonstration of a giant photonic spin Hall efect at a visible wavelength in a dielectric-based metamaterial device with spin-dependent geometric phase gradient [65]. The spin-dependent shift induced by geometric phase gradient is suiciently large to be observed directly compared with traditional approaches.…”

Spin-selected focusing and imaging based on metasurface lens

“…A spin-dependent shift in the k-space can be induced by the PB phase and thus a giant photonic SHE in the real space can be obtained [25]. However, most spin-based metasurface devices have been restricted to the separation of photons with different spin states [17][18][19][20][21][22][23][24][25], without further manipulating photons based on the corresponding spin states. In [14] and [26], only either left circularly polarized (LCP) light or right circularly polarized (RCP) light can be focused, but both the LCP and RCP lights propagate in the same direction and are not separated.…”

“…Moreover, the polarization state of light can also be manipulated by the metasurface, which is closely related to the Pancharatnam-Berry (PB) phase [21][22][23][24]. A spin-dependent shift in the k-space can be induced by the PB phase and thus a giant photonic SHE in the real space can be obtained [25]. However, most spin-based metasurface devices have been restricted to the separation of photons with different spin states [17][18][19][20][21][22][23][24][25], without further manipulating photons based on the corresponding spin states.…”

Spin-dependent optics with metasurfaces

“…It is proposed and experimentally demonstrated as what we now commonly refer as the optical SHE (OSHE) in showing a transverse spin-split of light trajectory [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. These works can actually be traced back to the early works about the Berry phase for photons [22][23][24][25][26], which have triggered a series of developments to manipulate light and to study geometric phases using helical fibers [23][24][25][26], gratings [27][28][29], and liquid crystals [30][31][32]. More recently, the appearance of metamaterials allows us to have very flexible optical properties by building up artificial atoms with tailor-made responses at will, with the most prominent applications such as negative refraction [33,34] and invisibility cloaks [35,36] to practical applications such as flat lens [37,38] and polarization control [39,40].…”