Millimeter-Wave Retro-Directive Frequency Coded Lens by Curved One-Dimensional Photonic Crystal Resonator

Innovating passive and chipless coded landmarks have recently emerged for high accuracy self-localization systems. Existing landmarks make use of the combination of retro-directive devices, corner reflectors and lenses, with a coding particle in order to give a high RCS response over a wide angle. In this paper, with a consideration of important practical parameters unappreciated in existing designs, we propose a wide-angle retro-directive frequency-coded lens based on a curved one-dimensional Photonic Crystal (PhC) resonator. The proposed frequency-coded lens is made of two parts: a homogenous lens and a curved PhC resonator where the resonator is located along the lens focal line. A frequency coding is used, where the presence or absence of a notch frequency in a specified information channel encodes an information bit. A PhC resonator provides unique advantages over existing coding particles due to its continuity along the lens focal line which creates a stable ID appearance over wide-angle. In addition, the potential of coding in its volume, rather than on the surface, allows for a high coding capacity. Two frequency-coded lenses with single and dual defect resonators are EM simulated, fabricated, and experimentally validated in the W-band (75 GHz-110 GHz). Simulated results show that a wide detection angle of 170° can be achieved where the tag ID is maintained over all angles. A wide retro-directivity of 80° and 60° is experimentally demonstrated for frequency-coded lenses by a single defect (single notch) and a dual defect (double notch) PhC resonator, respectively.


I. INTRODUCTION
Attaining fully automated and robotized systems in the industrial world entails the implementation of highly accurate self-localization, e.g., for flying robots. Indoor localization systems are growing up as a key element to overcome the shortcoming of existing satellite-based radio technology, such as GPS, in operating in indoor environments.
The associate editor coordinating the review of this manuscript and approving it for publication was Davide Comite .
Contemporary indoor positioning methods can instead operate with existing wireless infrastructure based on various radio technologies like Bluetooth, WiFi, and Radio Frequency IDentification (RFID) [1], [2]. Since these technologies use the lower microwave spectrum, limited localization accuracies in the cm range can only be achieved. Even with the high employed frequencies in 5G systems, below cm-accuracy is not approachable [3]. For low-cost infrastructures, [4], [5], localization based on asynchronous chipless RFID technology, rather than chipped, surpasses other radio technologies [6], [7]. On the other hand, high localization accuracy is allowed by exploiting high mm-Wave (e.g., W-band) or THz band since a superior time resolution can be achieved, thanks to exceptionally large bandwidths [8].
Substantially, a self-localization or device-based localization can be described by an object equipped with an RF reader which relies on coded landmarks to locate itself, see Figure 1. Coded landmarks (also called beacons or reference nodes) are distributed at fixed and known positions in an indoor area. Tags placement in terms of their positions and orientations is pre-optimized for a specific area in order to provide maximum coverage [9]. For a low-cost infrastructure, these landmarks should be passive, which operate without a power supply, and also chipless, which need no chip technology to be produced. Each tag should have a unique ID employing frequency coding where each tag should selectively react at a certain dedicated frequency by introducing a peak or a notch.
Innovative landmarks are required for a reliable operation of such a system. These landmarks should be designed to have a high coding capacity where several tags can be uniquely identified. High coding capacity is essential for achieving high accuracy and also increasing the coverage zone in which more tags can be reached by the reader [9]. Retro-directivity is a very important parameter since the reader may reach the tag under a wide range of incidence angles which have to be supported by the tags. Moreover, to allow long-range communication between the reader and tags, tags should have a sufficiently high Radar Cross Section (RCS). Furthermore, at high frequency, miniaturization of tag elements complicates the fabrication feasibility which should also be evaluated.
Therefore, several designs have been reported in the literature to support these factors [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22]. In [10], without the use of a retro-reflector, three Dielectric Resonator (DR) linear arrays were arranged to allow coding of 3-bits (i.e. 8 tags) where ±35 • retro-directivity is achieved. On the other hand, DR arrays of cylindrical and spherical shapes have been combined with dihedral reflector, trihedral reflector, Luneburg lens, and homogeneous lens [11], [12], [13], [14], [15], [16] and realized at different frequency ranges. Although DR-based retro-reflector provides good stability of ID over the operational angles, two main drawbacks are reported. First, the coding capacity is limited by the frequency separation between two consecutive modes. Therefore, for a specific resonance mode, the operational bandwidth within which we can codify is low in order to avoid the danger of misinterpretation with the next resonance mode. Second, DRs have a high relative permittivity which leads to small element sizes. As frequency increases, the realization of small elements of µm feature sizes becomes difficult, yet with a hardship of integration with a retro-reflector device.
Using a Frequency Selective Surface (FSS) as a coding structure has shown many drawbacks which are mainly the non-stability of tag ID over the operational angle [17], [18], [19]. In respective FSS designs, the angular response has been evaluated based on power consideration only where the RCS drops to 6 dB from its maximum without any consideration about the ability of the coded reflector to reflect its ID over all these incidence angles. ID stability over angle is an important practical limitation since, in case of the disappearance of ID or unidentifiable ID (for instance, due to a rippled response), this would simply deprive the tag of its main function (i.e. identification).
Photonic Crystal (PhC) resonators coupled to a dielectric waveguide have been also used as a coding structure in [20] and [21] with Luneburg lenses. Rod antennas were used to couple the energy from the lens focal area to 2-bit PhC resonator tags. Several PhC resonators were arranged around the lens periphery every 18 • [20] or 15 • [21]. Although the design can be realized at sub-terahertz frequencies, many drawbacks are seen. First, the coding capacity is limited to a few bits due to space limitation, where each rod antenna can couple the energy to a limited number of resonators. Second, the tag ID can be supported for only discrete angles where the rod antennas are integrated into the lens (multiple integers of 18 • [20] or 15 • [21]). Third, there is additional effort to design rod antennas as coupling elements between the lens and PhC resonators. A solution toward sparing the need of these rods is proposed in [22] by using quasi-conformal transformation optics to build a flattened lens. However, the lens has been tested with a metallic reflector instead of a coding particle.
In [23], we proposed a frequency-coded lens by a different coding structure than those reported in the literature which is a 1D PhC resonator. The coupling of a 1D PhC resonator with a homogeneous lens has been addressed where an increase in RCS by the square of the lens collimation gain was confirmed by measurements. However, the compatibility of a 1D PhC resonator with a lens has been found for an angle that relates to the axis between the resonator position behind the lens and the lens center. To address a wide-angle response, we extend the previous work by employing a curved 1D PhC resonator that covers a larger space around the lens. Contrary to other coding structures which employed discrete elements in the lens focal area, a curved 1D PhC resonator is a continuous structure that helps in maintaining the tag ID over the whole range without any discontinuity. In contrast, discrete coding elements cause some blind regions in the angle range where the tag can be identified. In other words, continuity in coding structure leads to continuity and stability in the tag ID over angles of operation. Another advantage related to coding capacity is that with a 1D PhC resonator the tag can be coded in the volume along the lens optical axis [24], instead of coding on the surface like in DR and FSS structures. This leads to a higher coding capacity compared to literature. Finally, the proposed solution in this paper can be easily fabricated at high mm-Wave or THz frequencies.
The paper is structured into six sections including this introduction section. In Section.II, we present the operation principle of the frequency-coded lens by a curved 1D PhC resonator including a design parametric study based on EM simulation. An analysis of the frequency coding of the proposed landmark is presented in Section.III. Section.IV describes the fabrication of the coded lens and presents the experimental validation. In Section.V, this work is compared to similar work in the literature. Finally, we close the paper with a summary.

II. RETRO-DIRECTIVE FREQUENCY CODED LENS
A Photonic Band Gap (PBG) where the light can be prohibited from propagating through a structure can be realized by the so-called photonic crystals. PhCs are periodic structures latticed with low-and high-index materials in one-(1D-), two-(2D-), or three-(3D-) dimensional configurations. The periodicity besides a sufficiently high index ratio can produce a PBG in the direction of propagation with a complete reflection in the backward direction similar to a mirror. A Bragg mirror is the simplest form of PhC where the low-and high-index materials are stacked in one dimension. To realize 1D PhC resonators, a defect layer should be inserted between two Bragg mirrors which act similar to a Fabry-Perot resonator. In Figure 2(a), a PhC resonator is designed by introducing a defect layer between two Bragg mirrors in the form of (LH) 2 D(HL) 2 where L, H, and D stand for lowindex, high-index, and defect layer. For our demonstration at mm-Wave frequency, a Bragg mirror is designed to provide a PBG in the frequency range (69 GHz-116 GHz) with a center frequency of 92.5 GHz [25]. A low index material of L r = 2.0 and a high index material of H r = 10.2 are selected for our investigation due to their availability with sufficiently low tangent loss. The symmetrical PBG is realized by selecting the layer thicknesses a quarter wavelength of the band gap center frequency inside the low and high index materials which are calculated as d L = 0.57 mm and d H = 0.254 mm, respectively. The resonator has a dimension of L × W and is excited by a plane wave whose direction of incidence is defined by the spherical coordinate θ inc and φ inc . The resonator generates a notch at the resonance frequency in the backward direction and a peak in the forward direction.
The main parameters that control the resonance position are the defect layer thickness (d def ) and permittivity ( def r ), while the quality factor of the resonance can be controlled by the layer stack and the number of layers; estimated formulas of defect resonance frequency can be found in [26]. Furthermore, figures and formulas showing the defect mode chart as a function of the optical thickness (n def d def ) can be found in [27], where n def is the defect refractive index.
In our investigation, we choose a defect thickness of 1.37 mm with low permittivity of 2.0. Figure 3 presents the simulated RCS of a planar PhC resonator of square shape for two different lengths (28 mm and 56 mm). For the resonator of 28 mm length, the mono-static RCS for different angles of incidence (0 • to 4 • in a step of 2 • ) is plotted. For the 28 mm-length cases, when the resonator is excited by a plane wave in a normal incidence (φ inc = 0 • ), a deep notch in the backscattered signal is observed at around 82.5 GHz which represents the frequency code of our landmark. Outside the notch, a large scattering magnitude is observed which is comparable to the scattering of a metal plate of the same size, see Figure 3. Therefore, the resonator acts as a notch-filter at its resonance frequency and a good reflector (i.e. mirror) outside the resonance. When the resonator is interrogated by an incidence angle different from the normal excitation, the scattering magnitude outside the notch starts to degrade where the notch ID is kept for angle 2 • and totally lost at 4 • . This can be explained by the Snell's law where most of the scattered power is re-directed to the specular direction and low RCS is observed in the retro-direction. Doubling the size of the resonator would increase the RCS by about 12 dB, compare the RCS of 28 mm-length and 56 mm-length in Figure 3, while the retro-directivity is kept low. Therefore, a square-shaped PhC resonator can be operated only when the reader interrogates the resonator by angles at or close to normal incidence.
In our system, as the reader may excite the tag under any angle of incidence, the planar design would not suit our application. A solution that may leap to minds is to structurally modify the resonator from planar to curved shape, as shown in Figure 2(b). However, even with changing the curvature radius, we find that the resonator properties changed since the incident divergent beam interacts with resonator parts differently which causes interference in the scattering response. Consequently, a rippled response is observed in the backscattering spectrum which overlays the notch.
A solution is to generate focused beams of high gain that can excite a semi-planar area of the curved resonator. Such beams should be flexibly steered through the PhC resonator curvature as the angle of incidence varies. This can be realized by locating the curved PhC resonator in the focal area of a spherical or cylindrical lens, as illustrated in Figure 4. The lens operates as a focusing device by collecting the incident wave across its aperture and concentrating it in a space behind its surface. A curved resonator in the lens focal area would be excited by a high-gain beam with a narrow  Figure 2(b). A cross-section of the biggest curved resonator has a semi-circular ring shape and completely covers a half circle around the lens with α = 180 • and β = 0 • . α and β represent the central angle and cut angle respectively. R l and R c are the lens radius and the location of the curved resonator measured from the lens center.
beamwidth confined to a semi-planar area of the resonator. The resonator couples a portion of the incident power back to the interrogator through the lens again. At resonance, the resonator would still create a notch at which less energy is coupled to the lens. Outside the resonance, the resonator acts as a metallic cap similar to those discussed in [28]. Since the wave travels twice in the lens, in both the transmission and the reflection channels, the expected RCS level is proportional to the square of the lens gain. For different incident directions, the lens is capable of focusing the beam to a focal area on the opposite side of the lens owing to its symmetry which should provide a wide-angle retro-directive response. In the coming sections, the RCS and resonance behavior of a curved 1D PhC resonator combined with a lens is compared to the case of a planar 1D PhC resonator as a reference structure.

A. LENS CHARACTERISTICS
In our investigations, we employed the homogeneous spherical type made of uniform material with a constant relative permittivity ( r ). The dependency of lens characteristics on lens parameters has been discussed in [29], [30], and [31]. In [23], it is found that the focal area of a spherical homogenous lens (R l = 20 mm and r = 2) calculated at f = 92.5 GHz is located 4.4 mm from the lens periphery. The same lens is used here where the lens is excited alone by vertically z-polarized plane wave in order to characterize its focal area. In Figure 5, the normalized electric-field (E z ) is plotted in both E-plane (xz plane) and H-plane (xy plane) over an arc 4.4 mm behind the lens. The 3 dB-width in both planes is approximately the same of around 4.2 • . At the same radius of 24.4 mm, this leads to a 3-dB focal spot area of about λ 2 /4 in both planes at f = 92.5 GHz which is equivalent to 2.6 mm 2 calculated by the equation π[x f tan( 3dB 2 )] 2 , where x f represents the focal area position along the optical axis x and 3dB represents the focal area 3-dB beam-width. Therefore, the curved PhC resonator should have a size greater than 2.6 mm 2 in the focal spot in order to be efficiently excited by the 3-dB power of the first main lobe of the beam. This can be only controllable by varying the curved PhC resonator height (W) indicated in Figure 2(b).

B. CODED LENS BY CURVED PHOTONIC CRYSTAL RESONATOR
Back to the combination of the lens with a curved PhC resonator depicted in Figure 4, the curved PhC resonator is designed to have a radius R c and is placed at the same radius around the lens. Full coverage of a circular half-plane around the lens can be achieved by a semi-circle ring shape of the resonator with a height (W), see also Figure 2(b). The resonator can be symmetrically clipped from both edges by the cut angle β to create a shape that makes a central angle of α. As a first guess of dimensions, we fixed the cut angle to β = 40 • , the resonator position to R c = 24.5 mm, resonator height to W = 11 mm, and PhC resonator parameters to a defect thickness of 1.37 mm and layer arrangement of (LH) 2 D(HL) 2 .
To clarify the operation of our landmark, the electric field distribution in the central cross-sectional plane of the lens and the resonator is plotted for two incident angles at the notch frequency, Figure 6. We observe that the lens in both cases effectively focuses the plane wave to a region exactly opposite to the incoming wave behind the lens where the resonator is placed. An internal reflection is also observed by the rippled distribution inside the lens. This causes some reflections that superimpose the coming reflection from the resonator and appears in the RCS spectrum as ripples. Since these reflections occur early in time and do not interfere with reflections that come afterward which importantly carry the resonator ID, the early reflections can be time-gated out to produce a less rippled RCS spectrum. At notch frequency, a strong electric field concentration in the defect layer is observed for both angles. This indicates that the resonator traps some energy at its resonance frequency and couples less energy back to the lens which preserves the tag ID in the backscattering to the same direction of the interrogator.  For frequencies outside the notch, the lens acts as an efficient mirror that couples high energy to the lens contributing to a high RCS response. Referring to Figure 7, the mono-static RCS for both angles shows a high RCS outside the notch with a little variation over the angle. Contrariwise, a deep notch is seen with a slight deviation in the notch position and a noticeable difference in the notch depth. The difference in the notch behavior as the angle changes can be explained by Figure 6 where we observe some low energy spots that are located in the resonator defect around the main focal spot. As the angle of incidence changes, these spots encounter different medium of posture causing the change in notch depth and position. In Figure 7, the mono-static RCS of a planar PhC resonator of square shape (28 mm length) is plotted for comparing the resonator characteristics with the case of a curved resonator combined with a lens. Originally, the planar PhC resonator resonates at a frequency of around 82.6 GHz. A noticeable shift in the resonance frequency is seen when the curved resonator is combined with the lens which can be attributed to a loading effect since the resonator is loaded by a lens with a permittivity of 2. In addition, the focal area hits a resonator with a semi-planar shape rather than a planar which seemingly reduces the optical thickness of the resonator causing a blue shift in the resonance. Also, it can be noted from Figure 7 that the mono-static RCS of the combination with a 20 mm radius lens has approximately the same RCS level of a squared planar resonator of length 28 mm, while the combination enjoys the high retro-directivity.
For a deep understanding of the landmark characteristics, several simulation setup scenarios have been investigated to study how the RCS spectrum changes with the incidence angle as we vary the cut angle (β) of the curved resonator and its height (W ). Figure 8 shows the simulated RCS results for four different cut-angles (0 • , 20 • , 40 • , and 80 • ). The incident plane wave elevation angle is fixed to θ = 90 • for all cases and its azimuthal angle varies in step of 2.5 • within a certain range for each individual case. For cut angle 0 • (Figure 8(a)), the resonance frequency (notch) appears clearly at almost all incident azimuthal angles (φ = 0 • to 90 • ). However, a reduction in the depth of the notches within the azimuthal angles (φ = 45 • to 65 • ) is observed due to seemingly an additional structural scattering from the resonator causes a fill in the notch at those angles. For a cut angle 20 • (Figure 8(b)), the resonance frequency (notch) appears clearly at incident azimuthal angles (φ = 0 • to 70 • ), then the RCS values dramatically decrease over the entire frequency range for higher incident angles which consequently causes an overlaid of the resonance frequency. A similar behavior is noticed for cut angle 40 • (Figure 8(c)) where the notch appears clearly at incident azimuthal angles (φ = 0 • to 50 • ) and then disappears beyond φ inc of about 50 • . For the last two cases, It is seen that the tag can not be reliably identified for incidence angles of about 90 • − β because of the increasing edge-diffraction effect. Furthermore, also beyond this angle most of the incoming energy is directed to the forward direction where the resonator is missed, leaving less RCS that is caused only by the reflection from the lens. For cut angle 80 • (Figure 8(d)), we approach the case where roughly a planar PhC resonator is located in the focal area. Therefore, the tag can be only identified within a narrow range of angles (φ = 0 • to 10 • ), but still with a better performance with respect to the identification angle compared to a planar resonator. Figure 9 shows the simulated RCS results when the resonator height (W ) varies from 5 mm to 15 mm in a step of 1 mm and the incident plane wave is fixed for all cases (θ = 90 • and φ = 0 • ). The notch frequency appears almost in all cases whereas its maximum value is confined when the height varies between the 9 mm and 11 mm. The effect of varying the layer arrangement around the defect layers for a finite-size PhC resonator on notch characteristics has been studied in [32]. It is found that increasing the number of layers around the defect improves the notch quality factor but also degrades the notch depth. In this paper, varying resonator lattice is not presented to avoid redundancy.
It is worth mentioning that the appearance of the notch is seen for a wide range of angles, where 170 • can be covered. Furthermore, as the incidence angle changes the notch remains undistorted when compared to existing works in the literature in which either the ID is astable over all angles [17], [18], [19], stable for only discrete angles [20], [21], or stable over narrower angular range like in [9], [10], [11], [13], [14], [15], and [16]. This is because all previous work that uses a lens as a retro-reflective device, replies by placing discrete coding particles in the focal region causing discontinues in the spectrum and missing the ID for angles in-between elements. In contrast, in this work, a curved PhC resonator, which is a symmetric and of a continuous structure, can provide approximately the same channel over wide-angle ranges.

III. FREQUENCY CODING OF LANDMARKS
The coding particle in our combination is the curved PhC resonator where different defect thicknesses or permittivities provide one or multiple notches with different spectral positions. The reader can easily identify the tag by detecting the number of notches and their positions in a specified number of information channels (N ). Information channels are determined by the reader bandwidth (BW r ), reader resolution ( f ), and the notch bandwidth (BW n ) where N = min( f , BW r )/BW n . Higher resolution allows the reader to discriminate between two codes with a low spectral spacing between their notches. On the other hand, lower notch bandwidth allows codifying more bits in the specified bandwidth. Interestingly, unlike other coding structures in the literature, the 1D PhC resonator can be frequency-coded in the volume rather than the surface of the tag. Since the axis of coding is along the lens optical axis, this allows the creation of multiple notches rather than one notch in the spectrum. The coding can be performed by varying the number of defects (K ) in order to produce a frequency code defined by the presence or absence of a notch in the pre-defined information channels. For each K , different sets of codes can be produced, therefore, the total coding capacity in bits can be calculated by summing the codes for each K as follows: C = k C(K ). In this section, the frequency coding of the combination is analyzed by considering one and two defect modes (K = 1, 2), however, the analysis can be extended for larger K .  (LH) 2 D(HL) 2 , the notch resonance has about 4.5 GHz of bandwidth BW n which provides 7 frequency codes (C(1)), each has a unique position. In Figure 10(a), the spectral signature of five codes is shown in the band 75 GHz to 95 GHz with their respective defect layer thickness.
In principle, a single resonance is not uniquely coded with a specified defect thickness, whereas different defect thicknesses can produce the same resonance frequency. This can be illustrated by plotting the mode chart of a single defect layer as a function of the defect thickness, shown in Figure 10(b). When the defect thickness is equal to 0, the resonator has a lattice LHLH 2 LHL where two hight-index layers stacked together would produce a defect layer that resonates at the central frequency of PBG. Increasing the defect thickness yields a decrease in the frequency. A further increase higher than 0.2 mm puts the resonator in the mirror region where no resonances are produced, up to a thickness of 0.9 mm. Beyond 0.9 mm, the resonance frequency drops up to about 1.7 mm to enter the second mirror region. The resonance starts to appear again when the thickness is greater than 1.8 mm with the same decaying effect in the resonance position. When the defect thickness reaches 2.8 mm, notch pairs start to emerge in the PBG whose spectral spacing is proportional to the defect thickness. As the defect thickness increases, higher order modes are excited which generates multiple notches to exist in the PBG. Although the mode chart is not an injective function; this is useful in finding the optimized defect layer for a specific frequency that provides the best notch characteristics; low bandwidth and high depth.
The coding results of the combination are compared to the Transfer Matrix Method (TMM) simulator, e.g. [33], which assumes an infinite size of the resonator without a lens and reflects the reference value of the notch position. A slight blue shift in the resonance position is observed with a maximum of about 4 GHz. The shift is caused by loading the curved PhC resonator by a lens, in addition to the curved shape of the resonator that alters the optical length.

B. DUAL DEFECT LAYER (K = 2)
Two methods to introduce two notches in the spectrum are either (1) by using one defect layer and increasing its thickness in order to excite dual mode, or (2) by using two defect layers located at a different position in the resonator structure. Back to Figure 10(c), employing the first method, a notch pair can be obtained with a defect layer of 2.8 mm and beyond seen by a notch pair in the mode chart. However, it is found that these modes are less coupled to the lens and provide deficient notches in the backscattering.
Using the second method, better performance is achieved where two defect layers having the same thickness are installed in the resonator structure creating the lattice HLHD (1) HLHD (2) HLH, where D (1) and D (2) are the first and second defect layers respectively, see Figure 11(a). Figure 11(b) shows the mono-static RCS spectrum of three frequency codes where each code has at least one unique notch position. Notably, an equal layer thickness for both defects gives the largest depth for both notches. The mode chart of the combination, shown in Figure 11(c), exhibits similar behavior to the TMM simulation where two notches are seen at the corresponding defect thickness except for a slight shift in their positions. As previously mentioned, the resonator acts as a mirror in the regions where no resonances exist in the chart. Considering the same notch bandwidth, we can add 7 frequency codes to those calculated for the single layer cases. Additional frequency codes can be obtained by extending the resonator to have multiple defect layers (K ≥ 3 ) in order to generate more than two notches in the spectrum.

IV. RESONATORS FABRICATION AND EXPERIMENTAL RESULTS
In this section, two frequency-coded lenses with single-and dual-defect PhC resonators are fabricated and experimentally examined.

A. FABRICATION PROCESS
Three main components were manufactured separately to compose and realize the designed landmark: the curved PhC resonator, the spherical dielectric lens, and the support structure. Figure 12(a) and Figure 12(b) present the fabricated single and dual-defect landmarks, respectively.
Low-index layers, as well as defect layers, were built as parts portions of half-cylindrical shells of 11 mm height with different radii that define their locations in the curved resonator and also their location from the lens surface. These layers were 3D printed from Cyclic Olefin Copolymer (COC) material with n L = √ 2. The thickness of the defect layers for the single defect and dual defect resonators has been chosen to be 1.55 mm and 1.2 mm, respectively, while low-index material layers were selected to be 0.57 mm thick. High-index material layers were obtained by etching a PTFE ceramic substrate (RT/duroid 6010.2LM) with n H = √ 10.2 and then VOLUME 10, 2022 creating planar sheets of 11 mm width. Taking advantage of the ceramic material plasticity, the high-index layers were easily inserted between the stiff COC layers. All the layers were then manually stacked without employing any extra adhesive material to form the curved PhC resonator. The focusing spherical dielectric lens was 3D printed of the same COC material with a lens radius of R l = 20 mm. Curved resonators have been trimmed with a cut angle of 30 • and 40 • for the single defect and dual defect resonators respectively, see Figure 12.
To ensure the PhC resonator alignment in the focal area of the lens, in addition to a well-established placement of the PhC's layers as well as minimizing the air gaps between them, a dedicated support structure was designed entailing a uniform combination of the landmark components. The support structure was 3D printed with a low infill density so that 90% of the structure is filled with air and only 10% was COC material. This guarantees a minimum effect of this structure on the resonator's behavior.

B. MEASUREMENT PROCEDURE
The measurement setup is exhibited in Figure 13. A vector network analyzer (VNA) based system was employed  as an interrogator where the ZC110 frequency conversion module extends the RF signal of the ZVA67 VNA with a multiplication factor of 8 to operate at a frequency range between 75 GHz and 110 GHz as a transceiver TRX. A 26 dBi horn antenna was attached to the flange of the extender's WR-10 rectangular waveguide. To verify the angular detection performance of the landmarks, a motorized turntable, which rotates in an azimuth plane with a 2 • angular step size was implemented. The landmark was fixed on a Styrofoam block on top of the rotation table to maintain alignment with the interrogator's horn antenna at a distance d ≈ 1.25m. Landmarks were placed in a way that the center of the lens is directly located at the rotation pivot of the turntable.
A control PC with a running MATLAB script directed the measurement procedure (sent control commands to the equipment) as follows: the angular movement range, as well as rotation step size, was first determined. Then, the rotation was commanded to the next intermediate angular sector by triggering the control unit of the turntable. The movement stopped at each step for a defined time duration to stabilize and allow the inerrogation. For each angle, measurement was initialized by the VNA and data acquisition was performed through the GPIB connection. For each angle, we extracted the scattering coefficient (S11), then we normalized it to the RCS of 15 mm diameter metallic sphere as a reference target [7]. To cancel out the surrounding channel as well as the antenna mismatch effect, time gating was applied to the time-domain response of the reflection coefficient, then the frequency response was calculated by applying Fast Fourier Transform (FFT) to the time-gated response.
First measurements results are presented along with the simulated results for both coded lenses, namely single defect and dual defect, in Figure 14 for normal incidence excitation (φ inc = 0 • ). A good agreement between the simulated and the measured results is observed with minor variation in the RCS values and behavior outside the notch which can be attributed to errors in normalization of the reflection coefficient to the RCS magnitudes and also a device noise arose from the limited dynamic range of the VNA of about 70 dB. Moreover, some variations in the notch bandwidth, position, and depth are observed, which are mostly related to fabrication inaccuracies; for instance, a slight error in the defect thickness in a resolution of less than 0.1 mm causes a noticeable shift in the resonance frequency.
In Figure 15, mono-static spectral signatures are plotted for the coded lens by single and dual defect resonators for angles of incidence in the range −40 • to 40 • and −30 • to 30 • , respectively. Measurements are compared to the EM simulated results plotted for only positive angles because of symmetry. In all plots, a notch line is characterized by a low RCS (RCS(f , φ inc ) ≤ χ) where χ define the notch line boundaries, see values of χ in Figure 15. The notch line clarifies the notch characteristics where line intensity denotes the notch depth and the line width is proportional to notch bandwidth. In a single defect resonator case, a deep notch at about 80 GHz appears in both simulation and measurements and covers a wide-angle range of 80 • . A better notch characteristic of more depth and less bandwidth is observed in the measured results. A slight variation in the notch position is observed in the measured results. This is explained by some variation in the curved crystal lattice along the focal line where layers have been stacked manually and small gaps between them can cause a shift in defect mode resonance. For the dual defect resonator, two notches are observed at around 96 GHz and 102 GHz with slight deviations between measurement and simulation subjected to errors in fabrication. However, both results indicate conservancy of notch characteristics over a wide angle of 60 • . Table.1 shows the comparison between related designs in the literature and this work. Due to the possibility of coding bits in the volume of the resonator, this landmark has TABLE 1. Selected coded retro-reflectors compared to this work. (x) indicates that the corresponding result has not been evaluated or is not evaluable. Coding capacity is the calculated value. Angular responses are the angle range at which the RCS reduces 6 dB from its maximum. The ID stability over the operational angle measures whether the tag can be identified by its ID over the whole range. the potential to provide high coding capacity. In this paper, we demonstrate single-and dual-defect resonators where each can provide 7 code combinations leading to 3.8 bits. Our proposed design can provide a high retro-directivity caused by the continuity of the 1D PhC resonator along the lens focal line. The simulated retro-directivity is the highest among reported works which can reach ±85 • by completely covering the focal area with a curved PhC resonator. We show by measurements a retro-directivity of 80 • and 60 • for singleand dual-defect resonators. Additionally, codes represented by a notch or notches in the RCS spectrum are stable and appear for all operational angles. This landmark is realized at the W-band which solves the difficulty of fabricating coding elements like DRs at those frequencies. In summary, our landmark gives the best code stability over a wide operational angle.

VI. CONCLUSION
In this paper, a wide-angle frequency-coded lens by a curved PhC resonator is proposed. Curved PhC resonators are placed in the focal line of a homogenous lens of low permittivity.
Due to the continuity of curved PhC resonators along the lens focal and the possibility of volume-coding along the lens optical axis, outstanding performance is achieved, surpassing existing coded retro-reflectors. Continuity allows a wide-angle retro-directivity where a high RCS spectrum that carries a deep notch is recognized for all angles. This is unlike coded lenses in the literature that offer a detected code for only discrete angles due to the discrete placement of coding structures in the lens focus.
On the other hand, volume-coding permits the integration of multiple defects that gives multiple notches in the spectrum, which significantly improves the coding capacity. In the state-of-the-art landmarks, no possible employment of different resonators for creating multiple peaks or notches in the spectrum. Although coding by two peaks were demonstrated in [20], the codes lose their characteristics for wide interrogation angles.
In a demonstrator design for the W-band, two coded lenses with single defect and dual defect resonators are fabricated and tested. Measured results demonstrate a reliable detection of single notch codes and dual notch codes over a wide angle of 80 • and 60 • , respectively. In all our investigations, a TE-polarized wave is used, however, a similar performance can be obtained for TM polarization where the structure is found to be nearly polarization independent.