Recent advances in optical metasurfaces for polarization detection and engineered polarization profiles

2.1 Background

Polarization detection has been used for a wide variety of applications. Based on the measurement and interpretation of the polarization of light waves, polarimetry has been applied in many areas of science and technology [117], ranging from ellipsometry [118], [119], remote sensing [120] to polarization light scattering [121] and ophthalmic polarimetry [122]. For example, in defense and security, polarization information can be used to pick out artificial materials against natural surfaces. In atmospheric monitoring, it can be used to track the size and distribution of particles in the atmosphere, which can be used to monitor air quality. To measure the polarization state of a light beam, many polarization elements (e.g. polarizers, wave-plates, polarization modulators) are usually employed and placed in a beam of light in front of a power meter. The traditional measurement systems have advantages in measuring speed and accuracy, but their applications are still limited due to the various polarization elements and complicated data processing system adopted, leading to a large volume and high cost. The metasurface approach differs from previous approaches in that the phase change occurs abruptly at the interface rather than slowly evolving in, for example, a birefringent material commonly used in bulky polarization optics. Consequently, this can lead to further miniaturization and a greater potential for system integration. The ultrathin circular polarizers [123], [124], [125] and polarization rotators [126], [127] based on metamaterials have been developed recently. As planar metamaterials, metasurfaces [128], [129], [130] do not require complicated 3D nanofabrication techniques, but can convert the linearly polarized incident light to its cross polarization [116], or convert a circularly polarized light to its opposite handedness [14], [15], [131], [132], [133]. Metasurfaces have been used in circular polarization detection [94], [95], [96], [97], [98], [99], full polarization measurement [47], [100], [101], [102], [103], [104], [105], [106], [107], [108], [109] and polarimetric imaging [90], [91], [92], [93].

2.2 Circular polarization detection

Figure 1A shows the schematic of circular polarization detection based on a phase gradient metasurface consisting of spatially variant metallic nanorods [94]. All gold nanorods on indium tin oxide-coated glass substrate have identical geometric parameters with spatially variant orientations. The angular orientation of each nanorod varies along the x-direction with an increment of π/8 in a clockwise rotation, but remains invariant in the y-direction. Hence, each period in the x-direction contains eight nanorods, the orientations of which change from 0 to π, which generate the additional Pancharatnam-Berry phase shifts ranging from 0 to 2π. When an incident light beam passes through the metasurface, the refracted light emerging from the metasurface is the sum of three terms with separate amplitudes: the regularly refracted light with the same polarization of the incident light, the anomalously refracted left circular polarization (LCP) light and the right circular polarization (RCP) light. The ellipticity and the handedness of the incident light can be deduced from the relative intensities of the last two terms. Interestingly, since the refracted LCP and RCP light diverge naturally from each other, the metasurface can also be used as a circular polarization beam splitter, the split angle of which is determined by controlling the spatial distribution of the nanorods in the metasurface.

Figure 1:

Optical metasurfaces for polarization measurement.

(A) Left: schematic to show the polarization of the refracted light after a completely polarized light beam passing through the metasurface. Right: experimental results of the refracted light spots on the transmission side of the metasurface for incident light with different polarization states [94]. (B) Schematic of the experimental setup to demonstrate the polarization measurement based on the reconstructed holographic images [98]. (C) Illustration of the full polarization measurement based on a reflective metasurface consisting of triple layers: nanorods on the top, metal film at the bottom and the dielectric layer sandwiched between them. (D) Experimental results in (C) for an incoming beam with an unknown polarization state can allow one to determine the Stokes parameters [100]. (E) Three-dimensional illustration of a superpixel that can focus different polarizations to different spots [107]. Reprint permission obtained from [94], [98], [100], [107].

The low conversion efficiency can be dramatically improved by using a dielectric metasurface [95]. To develop such a planar chirality-distinguishing beam splitter with a large extinction ratio, a dielectric metasurface consisting of amorphous silicon nanofins on a glass substrate was used. Each nanofin thus acts like a wave-plate with phase retardation of ϕ and its transmission can be modeled by Jones matrix. Birefringence of the wave-plate originates from the asymmetric cross-section (length>width) of the nanofin. In this design, there are only three possible diffracted orders (m=0, ±1). The power in the m=0 diffracted order does not depend on the phase difference between incident electric field components. By contrast, the powers of the m=±1 orders are sensitive to the phase difference. This characteristic enables us to identify the handedness of the incident light through observation of the m=±1 orders. Furthermore, the fraction of power that is in the m=±1 orders vs. the m=0 order can be varied from zero to 100% by the appropriate choice of phase retardation ϕ. The latter can be achieved by adjusting the nanofin dimensions or changing the surrounding refractive index. If ϕ is an odd multiple of π, the output is entirely first order (m=±1), while if ϕ is an even multiple of π, the output is entirely zero-th order (m=0).

Recently, a polarization-sensitive hologram approach was also used to measure the polarization state of a light beam [98]. This approach is based on the reconstructed holographic images upon the illumination of the light beam. When the light beam with pure LCP is incident on the metasurface, a clear holographic image (graphene pattern) is seen. A holographic image of the same graphene pattern with a rotated angle is observed when the polarization state of the light is changed from LCP to RCP. The two holographic images overlap upon the illumination of the light beam with linear polarization, since it can be decomposed into LCP and RCP beams with equal components. For a light beam with elliptical polarizations, the intensities of the two holographic images for LCP and RCP are different, because the two components for LCP and RCP beams are different. Due to the unique pattern of the graphene structures, the polarization state of the incident light can be determined by measuring the intensities of the two neighboring light spots in the overlap area of holographic images. The dynamic polarization change of a light beam can be quickly estimated based on the rise and fall of intensities of the reconstructed holographic images, providing a fast and elegant polarization measurement method based on polarization-sensitive metasurface holograms.

2.3 Full polarization measurement

To completely characterize the polarization state of light, three metasurfaces constituting the metagratings were used. They can work independently due to different supercell periodicities (different diffraction angles) [100]. This point was validated by considering the diffraction spots of the metagrating. For the six polarizations, one diffraction order is in turn suppressed whereas the remaining two pairs of diffraction spots show (approximately) equal splitting. In addition, considering a multitude of polarization states along the main axes of the Poincaré sphere, the associated diffraction contrasts (each obtained by averaging three successive measurements) can replicate reasonably well the unit sphere, with points covering all octants of the 3D parameter space. A metagrating allows the determination of the polarization state of the incident light in one measurement without the need of additional polarizers. This is very attractive approach since the metagrating constitutes a fast, simple, and compact way to determine a probe signal’s unknown polarization state.

However, reflective metasurfaces are not compatible with most transmission type optical elements. To solve this issue, a metasurface consisting of dielectric birefringent nanopost structures are used [107]. The device was designed to split and focus light to six different pixels on an image sensor for three different polarization bases. This allows for complete characterization of polarization by measuring the four Stokes parameters over the area of each superpixel, which corresponds to the area of six pixels on an image sensor. There are several representations for polarization of light. Among them, the Stokes vector formalism has some conceptual and experimental advantages, since it can be used to represent light with various degrees of polarization and can be directly determined by measuring the power in certain polarization bases. This group experimentally demonstrated the ability of the metasurface masks to correctly measure the polarization state for different input polarizations. In addition, the division of a focal plane metasurface mask was used to form an image of a complicated polarization object, showing the ability to make a polarization camera. An optical metasurface with the ability to fully control the phase and polarization of light can perform the full polarization measurement over a much smaller volume.

2.4 Polarimetric imaging

Polarimetric imaging is the measurement of the polarization state of light over a scene of interest [90]. While spectral and hyperspectral imaging techniques provide information about the molecular and material composition of a scene, polarimetric imaging contains valuable information about the shape and texture of reflecting surfaces, the orientation of light emitters, or the optical activity of various materials.

Figure 2A shows the schematic for chiral imaging. Chiral materials, which are common in biological compounds, can be classified from consequential analysis of circular polarizations. The vast majority of biologically active compounds, ranging from amino acids to essential nutrients such as glucose, possess intrinsic handedness. This in turn gives rise to chiral optical properties, providing a basis for detecting and quantifying enantiospecific concentrations of these molecules. Harvard University experimentally demonstrated the chiral imaging capabilities and spatially resolved chiral spectroscopy with a single planar lens. Conventionally, this cannot be achieved using single optical components unless multiples of them are stacked together into a bulky system. The building blocks of a multispectral chiral lens are comprised of two nanofins shown in blue and green. The required phase for focusing light is imparted based on the Pancharatnam-Berry phase via rotation of nanofins. The focusing efficiency is maximized when each nanofin acts as a half-wave plate, which converts circularly polarized input light into transmitted light with opposite helicity.

Figure 2:

Optical metasurfaces for polarimetric imaging and wavefront sensors.

(A) Top: schematic diagram illustrating the imaging principle of the multispectral chiral lens (MCHL) where left circular polarization (LCP) and right circular polarization (RCP) light from the same object at coordinates (x_ob=0, y_ob=0, z_ob=−18 cm) are focused into two spots, (x_imL, y_imL, z_imL) and (x_imR, y_imR, z_imR), respectively. Bottom left: scanning electron microscopy image of the fabricated MCHL. Scale bar: 600 nm. The two interlaced arrays of nanofins are false-colored. Bottom right: experimental results from [90]. (B) Schematic illustration of the on-chip polarimetry with integrated metasurfaces that can work at visible light [91]. (C) Scheme of the generalized Hartmann–Shack beam profiler. Each pixel of the array shown on the left consists of six different polarization-sensitive metalenses and (D) measured images of the resulting focal spots for incident horizontal or vertical linear polarization (“x” and “y”), diagonal linear polarization (“a” and “b”), and circular polarization (“l” and “r”) [93]. Reprint permission obtained from [90], [91], [93].

Figure 2B shows a metasurface chip that can assist in detecting the intensity of one specific polarization state, therefore, one can attain a set of Stokes parameters simultaneously with the absence of optical components in front of the detector (a COMS camera) [91]. Samples with chiral properties were measured using both on-chip polarimetry and commercial ellipsometry.

Very recently, matrix Fourier optics was proposed for treating polarization in paraxial diffractive optics [92]. This formalism is a powerful generalization of a large body of past work on optical elements in which polarization may vary spatially. Moreover, it suggests a path to realizing many polarization devices in parallel using a single optical element. It can be used to design diffraction gratings, the orders of which behave as polarizers for an arbitrarily selected set of polarization states, a new class of optical element. Polarized light from a photographic scene is incident on the grating inside of a camera. The polarization is “sorted” by the specially designed subwavelength metasurface grating. When combined with imaging optics (a lens) and a sensor, four copies of the image corresponding to four diffraction orders are formed on the imaging sensor. These copies have each, effectively, passed through a different polarizer, the functions of which are embedded in the metasurface. The four images can be analyzed pixel-wise to reconstruct the four element Stokes vector across the scene. Several examples were demonstrated at 532 nm, both indoors and outdoors.

Figure 2C and D show a dielectric metalens system which can be used not only to measure phase and phase-gradient profiles of optical beams (as a conventional Hartmann-Shack array), but also to measure the spatial polarization profiles at the same time [93].

3.1 Background

We can not only measure the polarization state of light, but also can generate a light beam with an engineered polarization profile. A light beam usually has a homogeneous polarization profile after passing through a polarizer, but a vector beam has an inhomogeneous distribution of polarization in the transverse plane perpendicular to the propagation direction. Metasufaces have been demonstrated to generate vector beams, such as radially or azimuthally polarized cylindrical beams, and arbitrary spatial polarization profiles. Recently, metasurfaces have been demonstrated to encode images in the polarization profiles [110], [111], [112], [113], [114], [115], [116]. In order to overcome the present technical limitation of resolution and fundamental challenge of arbitrary polarization manipulation, high capacity information can be encoded by a light beam by precisely manipulating the spatially variant polarization states of a laser beam with an ultrathin metasurface. A metasurface platform for the arbitrary polarization manipulation has been used to encode various types of images, including a high-resolution grayscale image [111], a QR code [112] and a color image [113], which has been recently extended to nonlinear metasurfaces [116].

3.2 Image hidden in the polarization profile of a light beam

The structured beam that can be used to hide an image was created by a metasurface illuminated by the laser light at normal incidence [111]. According to the Malus’ Law, when a linearly polarized light beam (generated by a polarizer) with an intensity I₀ passes through an analyzer (linear polarizer), the transmitted light intensity is proportional to the square of the cosine of angle θ between the transmission axes of the analyzer and the polarizer, i.e. I=I₀cos²θ. Thus, the required linear polarization profile for a hidden image is determined by its intensity profile. The predesigned linear polarization topology can be generated by a coherent superposition of two planar circularly polarized beams with opposite handedness, which can be realized by a reflective metasurface.

To hide a portrait of James Clark Maxwell, a single reflective metasurface was used to continuously manipulate the superposition of two beams with opposite circular polarization states. The reflective metasurface consists of a gold ground layer, a silicon dioxide spacer layer, and a top layer of gold nanorods. The generated structured light has a very specific polarization in the light beam, thus the light field oscillates differently for different parts of the beam. In order to visualize the hidden image in the polarization topology of the laser beam, the grayscale of the image was revealed by using an analyzer (linear polarizer). In doing so, the spatially-variant polarization profile of the laser beam cannot be observed directly, but its existence can be indirectly confirmed through the intensity profile (grayscale image) behind the analyzer. Figure 3A shows the simulation and experiment results. Because the theoretical amplitudes of the two beams are exactly the same, no image is observed in the beam without the aid of the analyzer. The experimental result indicates that the image-hidden functionality is unambiguously realized. QR codes are 2D barcodes usually consisting of black white patterns with a spatially varying intensity profile, which can be processed by a QR reading machine such as a smart phone. QR codes have been widely used in many fields, including product identification, item tracking, and document management. To keep pace with the continued miniaturization of devices and the daunting increase in the volume of information, new approaches to generate QR codes are desirable. Figure 3B shows the experimental result of a QR code, which is hidden in the polarization profile of a light beam [112].

Figure 3:

Optical metasurfaces for engineered polarization profiles.

(A) Schematic for hiding a high-resolution grayscale image. Under the illumination of linearly polarized light, a grayscale image is hidden in the polarization profile of a reflected beam from the metasurface and revealed by a linear polarizer (analyser) [111]. (B) Generation of quick response (QR) code for anticounterfeiting [112]. (C) Top: schematic for the polarization encoded color image. Bottom: experimental results for incident light with red, green and two colors [113]. (D) Schematic of the multichannel metadevice for anticounterfeiting and encryption [115]. (E) Schematic of nonlinear vectorial metasurface for optical encryption [116]. Reprint permission obtained from [111], [112], [113], [115], [116].

3.3 Color image embedded in a metasurface

A metasurface platform has been demonstrated to simultaneously encode color and intensity information into the wavelength-dependent polarization profile of a light beam [113]. Unlike typical metasurface devices in which images are encoded by phase or amplitude modulation, the color image here is multiplexed into several sets of polarization profiles, each corresponding to a distinct color, which further allows polarization-modulation-induced additive color mixing. This unique approach features the combination of wavelength selectivity and arbitrary polarization control down to a single subwavelength pixel level. Upon the illumination of a linearly polarized light beam with multiple wavelengths, a color image is revealed after the light beam passes through a dielectric metasurface and a linear optical polarizer. The dielectric metasurface consists of silicon nanoblocks “meta-atoms” with different in-plane orientations and sizes on a fused silica substrate, which can be used to generate the desired polarization profile for two different colors, with a locally controlled intensity profile. Two wavelength-selective polarization profiles were designed to produce the polarization-encoded color images based on additive color mixing. Each supercell responds to a specific wavelength upon the illumination of a light beam containing red and green colors. The supercell represents a pixel of a mixed-color image with the brightness of each color being individually controlled. Figure 3C shows the schematic and the experimental results upon the illumination of linearly polarized red, green and dual-color light. This approach provides a novel route to hide a high-resolution grayscale image in the polarization topology of a laser beam. The dielectric metasurface having the ability to encode a spatially-varying and wavelength-selective polarization profile may provide a viable route for generating structured beams that unveil high-resolution color images with well-defined brightness and contrast.

3.4 Polarization-sensitive hologram with a hidden image

Driven by high profits, the potential harm and risks from the production and sale of fraudulent goods are big issues in our world. Much effort has been devoted to anticounterfeiting technologies. However, conventional methods for anticounterfeiting, such as commonly used holograms, are not very effective since they are outdated and easy to duplicate. Researchers have been looking for alternative holograms with unique properties that are not easy to design and are difficult to copy. Figure 3D shows a multichannel device that can realize an image-switchable hologram and nonuniform polarization profile for anticounterfeiting in different channels [115]. By integrating different functionalities (helicity multiplexed holograms and arbitrary polarization manipulation) onto the same metasurface device, a highly versatile ultracompact multichannel device with minimal spatial footprint can be achieved. Two separate holographic images are observed when the device is illuminated by a circularly polarized light beam (RCP or LCP). The holographic images will overlap when a light beam with elliptical polarization impinges on the device, since any polarized light beam can be decomposed into two beams with opposite circular polarization states. The rise and fall of intensities of two overlapping images is determined by the ellipticity of polarized light. The intensities of two overlapping images are the same for the linearly polarized light, since it contains an LCP light beam and a RCP light beam with the same components. When the incident light is linearly polarized and the analyzer is applied, the overlapped images will still exist, but the brightness is decreased. The intensity of the “QR code” dominates for the right-hand elliptically polarized light. Finally, two separate images are obtained again, but they are swapped and flipped. The second functionality of the developed device is an arbitrary polarization profile for the hidden image. Upon the illumination of linear polarization light along the horizontal direction, no image is obtained without the analyzer due to the uniform intensity distribution. The hidden image is decoded correctly only when the transmission axis of the analyzer is along the vertical direction. Hence, the transmission axis of the analyzer plays an important role in the decryption process.

3.5 Nonlinear vectorial metasurface

Nonlinear optical processes, such as second, third, and high harmonic generation, and broadband optical frequency mixers are extensively investigated by using both plasmonic and dielectric metasurfaces. A nonlinear optical metasurface was demonstrated to locally manipulate the polarization states of the SHG wave and encode a high-resolution image in the polarization profile accordingly [116]. To encrypt image information into nonlinear optical devices, the nonlinear plasmonic meta-atoms with threefold rotational (C3) symmetry were utilized to construct the nonlinear metasurface. For a meta-atom with m-fold rotational symmetry, upon illumination along its rotational axis by circularly polarized fundamental waves (FWs), the allowed orders of nonlinear harmonic generation are restricted by the selection rule to n=lm ± 1, where l is an integer and the “+” and “−” signs indicate that the harmonic waves and the FWs possess the same and opposite spin states, respectively. Detailed explanation is available in the references [80], [83], [84]. Therefore, the C3 meta-atom can selectively produce SHGs with opposite handedness to that of the incident circularly polarized FW. More significantly, the nonlinear polarizability of the meta-atoms can be continuously manipulated by varying their orientations. As a result, a nonlinear geometric phase, −3σθ, is simultaneously imparted to the SHG wave, where σ=±1 is the handedness of the incident FW and θ is the angle by which the C3 meta-atom is rotated with respect to the laboratory frame. By using this characteristic, image information can be encrypted into a polarization profile of the SHG waves. With such an encoding process, one can effectively control the polarization states of the SHG wave in the transverse plane. Using a linear polarizer, the polarization profile can be converted into an intensity profile, which allows for easier observation.