Metamaterials with anisotropic electromagnetic properties have the capability to manipulate the polarization states of electromagnetic waves. We describe a method to design a broadband, low-loss wave retarder with graded constitutive parameter distributions based on non-resonant metamaterial elements. A structured metamaterial half-wave retarder that converts one linear polarization to its cross polarization is designed and its performance is characterized experimentally.
©2009 Optical Society of America
Artificially engineered composites, termed metamaterials, have enabled precise control over the constitutive parameters of a medium and have made possible a range of parameter values not easily achievable in naturally occurring materials. Early and ongoing research efforts have focused on the investigation of phenomena associated with unusual constitutive parameters derived from resonant metamaterial elements. Among the interesting phenomena studied are negative refraction in negative index media , perfect-imaging by simultaneous negative permittivity and permeability , electromagnetic wave tunneling by zero-index material  and negative reflection by a strongly chiral material . However, many current research trajectories have focused on engineering applications of metamaterials and explored the diverse possibilities offered by the accurate design and flexible control that can be exercised over the effective constitutive parameters of metamaterials, including tunability , designable anisotropy and spatial gradients .
Recently, the manipulation of the polarization of electromagnetic waves has been reported using anisotropic metamaterials [7, 8, 9, 10]. The concept of negative refractive index was applied to create a distinct difference between the phase advances of two orthogonal polarizations [11, 7], as occurs in wave retarders . In an alternative approach, an engineered anisotropic metamaterial slab was used to manipulate polarizations of the reflected waves . Inspired by Ref. , wave retarders composed of periodic electrically resonant metamaterial elements with surface matched wave impedance were proposed [9, 10]. The metamaterial wave retarders have the ability to manipulate the polarization states in different ways and the merit of naturally well-separated incoming and outgoing waves.
Resonant metamaterial particles typically lead to highly dispersive constitutive parameters accompanied by considerable loss near the resonant frequency, which is not favorable for applications where broad bandwidth and low loss are required. Attempts have been made to broaden the frequency band of metamaterials [13, 14, 15]. The use of non-resonant metamaterial elements provides virtually non-dispersive effective constitutive parameters and negligible loss [14, 15] and offers a convenient approach to achieving broadband metamaterial devices [15, 16].
In this paper, we adopt the non-resonant metamaterial particle introduced in Ref.  to design a highly-efficient broadband wave retarder. The non-resonant metamaterial element exhibits little absorption and thus enables the wave retarder to have low loss. We also apply the concept of impedance matched layers (IMLs) [15, 16] such that the wave retarder has a gradient impedance distribution which minimizes the reflection of the incident and exiting waves. To confirm the approach, we design and fabricate a half-wave retarder, which demonstrates excellent performance in agreement with simulations.
Following the analogy with crystal optics , under certain conditions an anisotropic metamaterial slab is capable of controlling the polarization state of transmitted electromagnetic waves [9, 10]. In particular, the experimental results verified the conversion from linear polarization to circular polarization and that from linearly polarization to its cross polarization. Electric inductance-capacitance resonators (ELCs) were used to create an anisotropic effective refractive index and wave impedance, which yielded anisotropic transmission coefficients.
In this work, a metamaterial wave retarder is designed to operate on TEM (Transverse Electric-Magnetic) waves. The Cartesian coordinate system is defined such that the propagation wavenumber k lies along the z-axis and the TEM waves incident on the metamaterial with arbitrary polarization can therefore be resolved into two modes with the electric fields along the x- and y-axes, respectively. The principal axes of the anisotropic metamaterial lie along the x-and y-axes in order that the two wave modes maintain their polarizations as they propagate. A multi-layered metamaterial slab (see Fig. 1(a)) with a smoothly gradient impedance variation is virtually reflectionless, and when accompanied by a spatially gradient index distribution over the layers, can manipulate the polarization state by shifting the phase between the two wave modes travelling through it.
In order to convert the linear polarization p 1, which makes a 45 degree angle with the x-axis, to its cross polarization p 2 (p 1 and p 2 are depicted in Fig.1(a)) in the same fashion as demonstrated in Ref. , phase advances of the two modes need to satisfy the condition that
where p = ±1,±3,±5,…, i = 1,2,…,m indexes the different layers and θx (i) and θy (i) are phase advances over the layer numbered i for the two modes with electric field along x- and y-axis, respectively. m is the total number of the metamaterial layers.
To reduce the absorption by the metamaterial wave retarder and broaden its bandwidth, the I-shape metamaterial element shown in Fig. 2(a) is employed. Copper I-shapes patterned periodically on a substrate have a high frequency electric resonance and exhibit a non-dispersive parallel electric response to an external dynamic electric field along the x-axis at lower frequencies. Meanwhile, they show little electric response in the other two directions. The non-dispersive responses to the electric fields in different directions lead to a constant anisotropic effective permittivity. Therefore, an anisotropic non-dispersive refractive index n and an anisotropic wave impedance η are obtained from I-shape metamaterial over a broad bandwidth. The phase advances of the two different wave modes through a metamaterial slab with a certain thickness d are nxk 0 d and nyk 0 d, where is the wavenumber in free space. Hence, the difference between the two θx−θy = nxk 0 d−nyk 0 d changes linearly with the frequency and the dispersion is predictably small.
In order to make this broadband wave retarder reflectionless, we selected a series of I-shape metamaterial geometry elements such that the wave impedances of the two wave modes vary smoothly from that of the air η 0 to a smaller value. At the same time, the refractive indices vary over the layers while satisfying the relation indicated in Eq. (1).
The commercial software CST Microwave Studio was used to simulate the I-shape metamate-rial elements. The geometry of the I-shape is shown in Fig. 2(a). The FR4 substrate has a thickness of 0.2026mm and a relative permittivity of 3.84+i0.01. The family of I-shaped elements that we utilize is constructed from the initial design shown in Fig. 2(a) for which a = 3.333mm, l = 3.0833mm, w = 0.25mm, s = 1mm. Based on the standard retrieval technique , multiple simulations with different boundary conditions were conducted  to achieve the simulated effective constitutive parameters. As shown in Fig. 2(b), the effective refractive indices of the two wave modes nx and ny are almost non-dispersive from 0GHz to 12GHz and the difference between the two remains approximately constant. The imaginary parts of nx and ny are small enough so that the particle can be considered as lossless.
We then examined the variation of wave impedances and the anisotropic phase advances. Simulation results with the geometry variable s swept from 0.2mm to 3.0mm at 8.94GHz are shown in Figs. 3(a) and 3(b). We can see that as the value of s increases, the wave impedance of one mode, ηx, changes from 0.91η 0 to 0.67η 0 while that of the other ηy changes from 0.74η 0 to 0.32η 0. Meanwhile, the difference between the phase advances of the two modes increases from 8.61° to 41.14°.
To achieve the polarization conversion discussed in the previous section, we chose the half-wave retarder to be of 8 layers as shown in Fig. 1(a). Keeping the other geometry parameters fixed, we searched through the available range of s for the gradient difference between the phase advances of the two modes δθ to be δθ = −9°, −18°, −27°, −36°, −36°, −27°, −18° and −9° for the 8 layers, which adds to the required 180 degree phase shift. The corresponding values of the geometry parameter are s = 0.26mm, s = 1.03mm, s = 1.735mm, s = 2.56mm, s = 2.56mm, s = 1.735mm, s = 1.03mm and s = 0.26mm. The distribution of the wave impedance for one mode is 0.9124η 0, 0.8914η 0, 0.8520η 0, 0.7547η 0, 0.7547η 0, 0.8520η 0, 0.8914η 0 and 0.9124η 0, and that of the other mode is 0.7278η 0 to 0.5896η 0, 0.4834η 0, 0.3785η 0, 0.3785η 0, 0.4834η 0, 0.5896η 0, and 0.7278η 0 (see Fig. 1(b)). We then simulated the entire half-wave retarder with the 8 layers of I-shape, and analyzed the polarization properties of the outgoing waves. In Fig. 4, the simulated conversion factor from the original polarization p 1 to its cross polarization p2 is shown together with the polarization isolation over the frequency span from 6GHz to 12GHz. According to the simulation result, the outgoing waves are converted to the cross polarization state of the incoming wave around 8.8GHz, and the polarization isolation of the linearly-polarized waves is smaller than −20dB over the frequency band from 8.04GHz to 9.56GHz. The corresponding bandwidth of the half-wave retarder is therefore 1.52GHz and the relative bandwidth is 17%.
Using the structures designed in the last section, 8 sheets of 43 by 43 I-shapes patterned on FR4 were fabricated. Styrofoam with a thickness of 3mm was placed between each two I-shape layers as a spacer. The overall thickness of the half-wave retarder is 26.67mm, which is about 4/5 of the wavelength around the designed frequency. We first used a pair of horn antennas connected to a network analyzer with a 2m distance to measure the polarization property. The half-wave retarder was placed in the middle of the antennas, 1m away each of the antennas. The transmitting antenna was fixed with a 45 degree angle to the I-shape so that the incident electric field is directed along p 1 and Ex = Ey. The receiving antenna was attached to a gimbal which could rotate 360 degree to measure the polarization pattern. Figs. 5(a)–5(c) show the measured polarization patterns at 8.0GHz, 8.5GHz and 9GHz, respectively. Compared to Fig. 5(d) the polarization pattern without the sample, it is obvious that the linearly-polarized incident electric field is rotated by 90 degrees with a high efficiency.
In order to measure the dispersion property and the transmission coefficient of the half-wave retarder, a pair of X-band lens antennas with collimated beam connected to a network analyzer were set 1.3m apart. We first measured the transmission coefficient of the half-wave retarder for the two wave modes separately, with different electric field orientations along x- and y-axis. As we can observe from the results shown in Fig. 6(a), transmission coefficients of the two modes are identical from 6GHz to 10GHz, with the overall loss smaller than 2.5dB, which verifies the assumption of neglectable reflection and absorption. The existence of oscillation is due to multi-reflection between the lens antennas.
Another measurement of conversion efficiency and polarization isolation was carried out with the same antenna pair, with the transmitter antenna polarized as p 1 and the receiver antenna polarized as p 1 and p 2, respectively. The measured transmission coefficients (see Fig. 6(b)) prove a 90 degree rotation of the incident electric field around 8.56GHz and that over the frequency band from 7.935GHz to 8.94GHz the polarization isolation is less than −20dB, which agrees well with the simulation. Therefore, the measured relative bandwidth is about 12%.
We note that horn antennas have a better linear polarization but a divergent beam. They were therefore adopted in the first set of measurements concentrating on the polarization patterns. Lens antennas with collimated beams were used in cases when transmission coefficients were measured and convergence of the beam did not adversely affect the measurement results. Meanwhile, the experimental data in Fig. 6(b) is slightly different from the simulation result in Fig. 4 presumably because the radiation of the lens antenna is not perfect linear polarization.
In this paper, conversion between two cross linear polarizations without significant reflection or absorption of energy was realized by non-resonant I-shape metamaterial particles. Experiments demonstrate the small loss and the broadband property of the constructed half-wave retarder. More generally, a methodology has been described here to design a highly-efficient broadband metamaterial wave retarder which appears to be a promising candidate for device applications at optical frequencies. Specifically, by gradient anisotropic optical metamaterial particles, quarter- and half-wave retarders can be constructed with compact size and optimized efficiency. The low-cost method to manipulate polarization may find a wide range of applications, e.g. in telecommunication transmission and receiving systems and in various polarizing components for experimental use.
This work was supported in part by a key project of National Science Foundation of China, in part by the National Basic Research Program (973) of China under Grant No. 2004CB719802, in part by the Natural Science Foundation of Jiangsu Province under Grant No. BK2008031, in part by the 111 Project under Grant No. 111-2-05, and in part by the National Science Foundation of China under Grant Nos. 60871016, 60671015, and 60621002. J. Y. Chin acknowledges support from the foundation for Excellent Doctoral Dissertation of Southeast University under Grant 1104000133.
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