Controlling the polarization of light with efficient and ultra-thin devices is desirable for a myriad of optical systems. Bianisotropic metasurfaces offer a promising alternative to conventional optical components due to their ability to provide extreme wavefront and polarization control within a low profile. However, metasurfaces have typically suffered from poor efficiencies and extinction ratios due to the lack of systematic design procedures. Here, the first, to the best of our knowledge, impedance-matched polarization rotator with a subwavelength thickness that operates at optical frequencies is reported. The bianisotropic response needed for polarization rotation is systematically designed using cascaded plasmonic sheets. The metasurface is fabricated using straightforward nanolithography processes. Measurements demonstrate an efficiency of 45% and extinction ratio of 115 (20.6 dB) at the operating wavelength of 1.56 μm. This work experimentally demonstrates that a wide range of near-optimal bianisotropic responses can be designed and fabricated at optical frequencies. In the future, these surfaces could be utilized to develop high-performance, ultra-compact optical systems.
© 2016 Optical Society of America
Metamaterials exhibiting electric and magnetic responses can be used to control electromagnetic fields [1,2]. However, complete control of the amplitude, phase, and polarization of light requires a bianisotropic response: electric, magnetic, and magneto-electric responses . The bianisotropic responses of naturally occurring materials are typically extremely low, such that a large optical path length must be utilized to significantly affect the fields . Therefore, developing bianisotropic metasurfaces that allow extreme light control within a subwavelength thickness would be extremely useful for a myriad of optical applications. To date, numerous metasurfaces have demonstrated bianisotropic responses [5,6]. However, these metasurfaces are most commonly designed by simply taking a resonant geometry with the necessary mirror and rotational symmetry such that the desired response is simply possible, rather than optimal . The lack of a systematic design procedure has limited the performance of previous structures. In fact, the only bianisotropic metasurfaces that have demonstrated reasonable performance at optical frequencies are linear and circular polarizers [8–14].
More recently, it was shown that it is possible to design and fabricate a wide range of bianisotropic metasurfaces by simply cascading anisotropic plasmonic sheets in the direction of propagation . This implementation is particularly attractive because each sheet in the geometry can be sequentially designed using an iterative process, which enables the rapid realization of devices with near-optimal performance. Furthermore, the metasurface can be fabricated using straightforward 2D nanolithography processes. To date, only an asymmetric circular polarizer has been fabricated at optical frequencies using this design procedure . The goal here is to realize, to the best of our knowledge, the first impedance-matched polarization rotator that operates at optical frequencies, which provides further evidence that the same design procedure can create metasurfaces with arbitrary bianisotropic responses.
An ideal polarization rotator is reflectionless and rotates an arbitrary incident polarization by a specified angle upon transmission (an angle of 90° is chosen here), as shown in Fig. 1. This device is particularly interesting because it requires large magneto-electric coupling (specifically chirality) to achieve polarization rotation within a subwavelength overall thickness. Therefore, polarization rotation is one of the most extreme examples of polarization control since the electric, magnetic, and magneto-electric responses all need to be carefully tailored. Furthermore, polarization rotators composed of liquid crystals are commercially available. Therefore, the performance of the metasurface can be compared to a commercial product, which is insightful .
The most straightforward method of achieving a polarization rotation of 90° is cascading two dielectric half-wave plates with crystal axes rotated by 45° relative to each other. However, dielectric half-wave plates require thicknesses on the order of tens of micrometers when using naturally occurring materials, which are too bulky for integration in nanophotonic systems . More recently, it was demonstrated that polarization rotators can be realized by utilizing anisotropic beam refracting metasurfaces . However, any system employing these surfaces would also need to be quite large in order to separate the diffracted light. In addition, the efficiency is low since only 4% of the incident power is actually rotated by the metasurface. Furthermore, the design methodology cannot be extended to realize arbitrary polarization transformations.
Here, to the best of our knowledge, the first subwavelength thickness, impedance-matched polarization rotator that operates at optical frequencies is reported. The metasurface is designed using the systematic procedure outlined in Ref. , which provides further evidence that arbitrary bianisotropic metasurfaces can be realized using the same procedure. First, the design procedure is reviewed and the simulated performance is reported. Next, the metasurface is fabricated and experimentally characterized at operating wavelengths around 1.5 μm.
2. DESIGN AND SIMULATION
Let us first review the design procedure for realizing a metasurface with an arbitrary bianisotropic response. Consider the geometry shown in Fig. 2(a). Each sheet represents a metallic pattern on a dielectric substrate with intrinsic wavenumber and wave impedance . The cell size of the metallic pattern is subwavelength, and the sheets are not too close together such that evanescent coupling between the sheets can be neglected. This allows each sheet to be homogenized as an equivalent sheet admittance , such that , where is the tangential surface current flowing across the sheet, and is the tangential electric field at the sheet. In general, is a tensoral quantity that relates the - and -directed electric fields to the - and -directed surface currents. By homogenizing the surfaces as equivalent sheet admittances, the reflection and transmission coefficients for cascaded patterned metallic surfaces can be solved in closed form. Therefore, it is possible to stipulate desired transmission and reflection coefficients, which in general require a bianisotropic response, and then numerically solve for the necessary sheet admittances needed to realize them .
When designing a polarization rotator, the reflection coefficient is stipulated to be 0, and the transmission coefficient is stipulated to be3]. It should be noted that the sheet admittances can be approximated as purely imaginary at microwave frequencies because the structures are generally low loss. However, the permittivity of Au at near-infrared frequencies satisfies the Drude model: , where , (8.97 eV), and (0.1 eV) . Due to the notable loss of Au, both the real and imaginary parts of the sheet admittances must be considered when designing optical metasurfaces. In fact, full-wave simulations show that the quality factor of the sheets is generally around 10 (i.e., ) at the operating wavelength of 1.5 μm. Therefore, the required sheet admittances with are numerically solved first. Subsequently, the plasmonic geometries that approximate the numerical solutions are iteratively designed using well-known concepts from the field of frequency-selective surfaces . Note that the most straightforward method of designing an arbitrary tensoral admittance is to design the Au patterns in the rotated coordinate system that diagonalizes the admittance of each sheet. The dimensions of the four different sheets that make up the polarization rotator are shown in Figs. 2(c)–2(f), and their corresponding admittances at the wavelength of 1.5 μm are given by
Each sheet is inductive along one principal axis and capacitive along the other. By changing the dimensions of each layer, it is possible to arbitrarily control the sheet admittance along both principal axes. In addition, the progressively rotated principal axes provide a chiral response, which is necessary for polarization rotation.
The transmission and reflection coefficients of the cascaded sheets are calculated using the matrix approach. The matrix relates the electric and magnetic fields on either side of an arbitrary structure, which can in turn be related to the reflection and transmission coefficients . The matrix for four cascaded sheets is given by
The simulated transmittance () and reflectance () of the polarization rotator are shown in Fig. 3. At the wavelength of 1.5 μm, the metasurface provides high transmission of the incident power to the cross-polarization (, ), and the transmitted co-polarization (, ) is near 0, which is consistent with a polarization rotation of 90°. In addition, less than 2% of the incident power is reflected. The lossy plasmonic sheets absorb 55% of the incident power. It should be noted that it is not possible to simulate the periodic structure with many commercially available full-wave solvers since the principal axes of each sheet are rotated relative to each other. Instead, each sheet was simulated individually, and the overall response was calculated using the analytic model shown in Fig. 2(a).
It is important to note that the overall response of a polarization rotator should be isotropic even though the individual sheets composing it are anisotropic. To illustrate this, the metasurface is illuminated with an incident linear polarization that is oriented at an angle relative to the axis [see the inset of Fig. 4(a)]. As shown in Fig. 4(a), the cross-polarized transmittance is 45% and the co-polarized transmittance is less than 0.3% at the wavelength of 1.51 μm, independent of the angle between the incident electric field and the -axis axis. This fact illustrates that the metasurface exhibits a true isotropic chiral response that rotates an arbitrary polarization by 90° upon transmission. This analysis leads to the definition of an extinction ratio for the polarization rotator, which we define as the ratio of the minimum of the cross-polarized transmittance to the maximum of the co-polarized transmittance for all incident linear polarizations (i.e., for all ): Extinction . In other words, the extinction ratio represents a worst case scenario for the polarization purity transmitted by the metasurface. The simulated extinction ratio achieves a peak value of 240 (23.8 dB) at the wavelength of 1.52 μm, as shown in Fig. 4(b). The metasurface’s efficiency as a function of wavelength is plotted in Fig. 4(c), which is found by noting the cross-polarized transmittance averaged over all incident linear polarizations .
3. FABRICATION AND MEASUREMENTS
Next, the metasurface is fabricated on a 500 μm thick wafer using the same process that is detailed in Refs.  and . The bottom sheet () is fabricated first using e-beam lithography on 950 K A2 poly(methyl methacrylate) (PMMA) (MicroChem Corp., Boston, Massachusetts, USA) resist followed by metal deposition/liftoff. Alignment marks were employed to align all four layers. A water-soluble conductive polymer (ESPACER 300Z, SHOWA DENKO K.K. 13-9, Shiba Daimon 1-Chome Minato-Ku, Japan) was spun on the PMMA resist to minimize charging issues during the e-beam writing. To achieve uniform pattern features, proximity effect correction was implemented during the e-beam writing. Then a 200 nm thick SU-8 (MicroChem Corp., Boston, Massachusetts, USA) spacer layer is spin coated, which naturally planarizes the surface for the subsequent layer. During the fabrication, it is important that the SU-8 layer is thoroughly cured. Therefore, after being coated on the substrate, the SU-8 film underwent 30 s UV exposure (MJB3, Karl Suss), and then high-temperature hotplate baking (140°C for 10 min and then 180°C for 10 min). The process is repeated until all four layers are patterned. The patterned area of the metasurface is . SEM pictures of the four fabricated sheets can be seen in Fig. 5.
The transmission coefficient of the fabricated metasurface was experimentally characterized. The output of a 1.5 μm tunable laser (Hewlett Packard 8168F) was sent through a single-mode fiber (P3-1550A-FC-1, Thorlabs) whose end was fixed from the metasurface. The transmitted power was collected by an objective lens, sent through a linear polarizer (LPNIRA050-MP2, Thorlabs), and then received by an optical power meter (2835-C, Newport). The incident polarization was sequentially oriented at using a manual fiber polarization controller (FPC032, Thorlabs), and the co- and cross-polarized intensity were measured by appropriately orienting the linear polarizer, which resulted in a total of 16 measurements per wavelength. The Jones matrix that best fits the measured data was then found using a least squares fit. This simple procedure allows the Jones matrix of an arbitrary sample to be measured. Since the measurement procedure does not provide phase information, there is uncertainty in the overall transmitted phase and complex conjugate that is common to all elements of the Jones matrix. However, the overall phase and complex conjugate are not related to the efficiency and extinction ratio of the polarization rotator, which are the primary figures of merit. The transmission coefficient at the operating wavelength of 1.56 μm was measured to be6 and 7 show measurements of the fabricated polarization rotator. The measurements are red-shifted by 40 nm relative to the simulations due to fabrication tolerances, but otherwise there is good agreement between experiment and theory. Figure 6 plots the co- and cross-polarized transmittance in linear and logarithmic scales at the operating wavelength of 1.56 μm. The squares in these plots correspond to measured data, whereas the solid lines correspond to the transmittance of the Jones matrix that best fits the measured data [see Eq. (9)]. It can be seen that at the operating wavelength, the co-polarized transmittance is near 0 while the cross-polarized transmittance is 45%, independent of the orientation of the incident linear polarization. This fact clearly shows that the fabricated device operates as a near ideal polarization rotator. The peak extinction ratio was measured to be 115 (20.6 dB) at the wavelength of 1.56 μm. The efficiency of the fabricated metasurface is around 45%. The efficiency is determined by averaging the cross-polarized transmittance over all incident linear polarizations , which is plotted in Fig. 7(b).
Reflection from the metasurface was also experimentally characterized, and is shown in Fig. 7(c). A fiber optic circulator was inserted between the polarization controller and the fiber tip. This allowed light that was the reflected back into the fiber to be separated so that the total reflectance could be characterized with a power meter (sum of co- and cross-polarized reflectance). The reflection measurements were calibrated by measuring reflectance from a 200 nm thick Au sheet, which provides 98% reflectivity. The metasurface was illuminated with four different incident linear polarizations to demonstrate the isotropic response at the operating wavelength. The total reflectivity is below 10% for all incident liner polarizations at the operating wavelength of 1.56 μm. This reflectivity is larger than the 2% reflectance in simulations, which is likely due to a combination of measurement error and fabrication tolerance.
The performance of the metasurface is comparable with commercially available products based on liquid crystals, which achieve efficiencies of 90% and extinction ratios of 100 . However, liquid crystal based devices have thicknesses exceeding 3 μm. In addition, liquid crystal based devices are difficult to pattern on a subwavelength scale, which is necessary for controlling the shape of a wavefront in a compact manner .
In summary, the first, to the best of our knowledge, reflectionless polarization rotator that operates at optical frequencies is reported. The metasurface is realized by cascading four plasmonic sheets with rotated principal axes. In the future, additional sheets could be investigated, which may offer improved bandwidth, efficiency, and extinction ratio. Furthermore, the efficiency could potentially be improved by annealing the metal and/or using Ag to reduce plasmonic losses [21,22]. Polarization rotators can find many immediate applications from display technologies to identifying the spatial structure of molecules in analytical chemistry, biology, and crystallography [4,5]. More importantly though, this work provides evidence that a wide range of prescribed bianisotropic responses can be systematically designed and fabricated. For example, it was recently shown that perfect absorbers composed of chiral particles can be designed to provide high transmission, rather than reflection, when operating away from the resonant frequency . This concept can be extended from microwave to optical frequencies using the design procedure reported here, which would be particularly useful for photovoltaic applications. In particular, the efficiency of solar panels could be increased by using multilayer solar cells, where each layer absorbs an optimized wavelength while permitting other wavelengths to pass through to the following absorptive layers . Many other interesting physical processes could also be realized using the isotropic, chiral metasurface reported here. For instance, bianisotropic metasurfaces that simultaneously control the phase and amplitude of both the reflection and transmission coefficients could be designed . Alternatively, if several bianisotropic metasurfaces are cascaded together, a bulk chiral metamaterial could be realized that provides negative reflection or negative indices of refraction for circularly polarized light [26,27].
Office of Naval Research (ONR) (N00014-15-1-2390); National Science Foundation (NSF) (DMR 1120923).
We acknowledge technical support from the Lurie Nanofabrication Facility (LNF) at the University of Michigan.
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