OAM Mode Order Conversion and Clutter Rejection With OAM-Coded RFID Tags

In this article, a uniform helically arranged dielectric resonator array can generate Orbital Angular Momentum waves (OAM) causing a conversion of OAM mode orders <inline-formula> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> from an incoming mode <inline-formula> <tex-math notation="LaTeX">${m}_{in}$ </tex-math></inline-formula> to an outgoing mode <inline-formula> <tex-math notation="LaTeX">${m}_{out}$ </tex-math></inline-formula>. The operating frequency is set as 10 GHz to facilitate the measuring process. This new approach provides additional OAM values per digit in the RFID technology according to the excited OAM modes <inline-formula> <tex-math notation="LaTeX">${m}_{n}\,\,\in \,\,\{\ldots,-2,-1,0,1,2,\ldots \}$ </tex-math></inline-formula> instead of the conventional binary values <inline-formula> <tex-math notation="LaTeX">${b}_{n}~\in ~\{0, 1\}$ </tex-math></inline-formula>. Thus, more information content is revealed. Through the OAM concept, a <inline-formula> <tex-math notation="LaTeX">${m}_{1} {m}_{2}~2$ </tex-math></inline-formula>-digits OAM coded tag is obtained upon the employment of two uniform helically arranged cylindrical dielectric resonator arrays operating at two different frequencies <inline-formula> <tex-math notation="LaTeX">${f}_{1} = 10\,\,\text {GHz}$ </tex-math></inline-formula>, and <inline-formula> <tex-math notation="LaTeX">${f}_{2} = 11\,\,\text {GHz}$ </tex-math></inline-formula>. Each array has 8 DRs but with different radius yielding a reduction of the mutual coupling between the varied circular arrays. The interaction between the phase delayed radiation of each DR element in the array generates different vortex waves with corresponding OAM mode orders. In order to achieve the correct phase delay, the elevation of each DR is specified by the desirable OAM mode order, the number of elements and the propagation wavelength. At first, the generation of OAM mode orders −1, 2, and −3 is carried out. Then, mode conversion from 0 to −1, +1 to −2, −1 to 0, +2 to −3, and −2 to +1 are depicted. After that, two simulated examples of 2-digits OAM coded tags with the code <inline-formula> <tex-math notation="LaTeX">$\{-1,1\}$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$\{-2,0\}$ </tex-math></inline-formula> are presented. A conversion of mode 0 to mode 1 has been simulated and also measured, where an additional metal sheet is used to evaluate the distortion in the OAM modes. As a result, this study demonstrates that the uniform helically arranged DR arrays can convert the incoming OAM mode order into another one, where the clutter from broadside direction is rejected due to the Butler matrix (BM), which interferes the clutter destructively.


Radio Frequency Identification Technology (RFID) offers a solution to the issue of the difficult distinction and
The associate editor coordinating the review of this manuscript and approving it for publication was Chinmoy Saha .
identification of many articles where it can detect, locate, identify and track these items using radio waves. An RFID system consists of an RFID reader and a transponder device (radio receiver and transmitter). When an electromagnetic (EM) interrogation pulse ejected from a nearby RFID reader triggers the transponder part, it responds back and sends out signals that are characterized by a specific code known to the reader. Furthermore, there are two kinds of RFID tags, namely passive and active. The active tags require an extra battery power to operate, as opposed to the passive tags which are powered by the electromagnetic field via the RFID reader having much lower production costs [1]. In addition, the passive dielectric resonators (DRs) designed in this study are composed of a dielectric material with a high permittivity. At certain resonance frequencies and corresponding EM field distribution (modes) which correspond to the eigen-frequencies, the passive DR shows the largest radar cross section (RCS). The corresponding quality factor and the mode's operating frequency depend mainly on the relative permittivity, the size and the loss tangent (tanδ) of the DR [2]. By illuminating a conventional RFID tag (1-bit tag) with plane waves, the backscattered signal may contain information in form of a sensed value [3]- [5] or frequency identification [6]. The modes of a DR can be frequency shifted by altering the dimensions of the DR. Through this manner, an N -digit coded tag can be formed with N differently sized DRs. Nevertheless, the number of digits is limited by the spectral mode spacing between the two adjacent modes thus avoiding the distortion between the different DRs resonating at different frequencies [7].
Electro-magnetic (EM) waves can carry an angular momentum, which can be divided into a spin angular momentum and an orbital angular momentum (OAM) in paraxial beams. The spin angular momentum is well known as the circular polarization that describes the intrinsic property of the spin characteristics of the EM rotational degrees of freedom. In contrast, the OAM of the EM wave is an extrinsic property that describes the orbital characteristics of its rotational degrees of freedom, which has a helical transverse phase structure of exp(−jϕm), where ϕ is the transverse azimuthal angle and m is an unbounded integer that indicates the OAM mode order [8]. Containing an infinite number of mutually orthogonal states m (i.e. the OAM mode order), the OAM waves present a new degree of freedom in signal coding, enabling a new spatial division multiplexing (SDM) procedure scheme with independent data streams at the same operating frequency [9]. Hence, an improvement of both capacity and spectral efficiency could be gained. The OAM mode division multiplexing (OAM-MDM) is a new physical transmission technology which can also be used in combination with the other multiplexing methods (time, frequency, polarization and code) yielding an enormous improvement in data transmission [10]. The OAM waves are characterized by a doughnut-shaped radiation pattern with the helical phase front and with a singularity, where the zero is centered in the doughnut-shaped radiation pattern. Concerning the generation of vortex waves, there are many available ways such as metasurfaces [11], spiral phase plates (SPP) [12], holographic plates (HP) [13], elliptical patch antennas which excite two at the same time orthogonally oriented resonant mode patterns [14], [15], reflectors [16] or uniform circular patch arrays (UCA) [17]. However, these approaches do not discuss the limitations compared to MIMO systems [18]. Furthermore, the vortex waves are advantageous for the field of imaging [19] and particularly for spinning objects, which can still be used even when the line of sight (LOS) is orthogonal to the object [20]. By means of tailored phased-array antenna concepts [21], the OAM beam is steered in which the typically large beam divergence inherent to the vortex waves can be reduced upon the usage of a lens [22]- [24], or a reflector [16], [25], [26].
In this work, not only the zeroth mode order is converted, but the rest of the modes also undergo certain conversion as introduced presenting its novelty. The initial idea is proposed in [27], whose RFID codes are increased by means of helically arranged DRs arrays in addition to the novelty of the clutter rejection's possibility. In contrast, the conventional arrangement of DRs suffers from the strong clutter leading to a loss in the transmitted data. This article is classified into the following sections. At first, Section II reveals the reflection coefficient and the far-field radiation pattern of a rectangular patch antenna in addition to the transmission coefficient of a cylindrical dielectric resonator. Then, the radiation pattern and the phase front of the converted OAM mode are depicted in proceeding Section III. Followed by Section IV, where the concept of N -digits coded tag enabling OAM coding of frequency tags with two digits with values {−3, −2, −1, 0, 1, 2, 3} according to the realized OAM mode order. Furthermore, in Section V, the measured transmission coefficient of an eight cylindrical dielectric resonator array with and without a metal plate is introduced. Finally, Section VI is presented as a conclusion of this study.

II. DESIGN OF RECTANGULAR PATCH ANTENNA AND CYLINDRICAL DIELECTRIC RESONATOR
With the aid of the MoM-solver FEKO, a rectangular patch antenna operating at 10 GHz is simulated to simplify the experimental studies. This y-polarized patch antenna is designed on a Rogers RO4003C substrate with a relative permittivity of 3.55 and a height of 1.524 mm. While the simulated patch antenna is specified by 7.53 mm length (about λ eff /2) and 10.8 mm width. In Fig. 1 (a, b, and c), the patch antenna and its radiation pattern are illustrated in 2D and 3D. When the directional antenna is matched to 50 , the gain is maximized through avoiding reflections at the antenna port hence yielding a gain of about 6.1 dBi (Fig. 1 (c)). Moreover, the simulated return loss S 11 is about −28 dB unlike the measured one which is about −12.7 dB at the operating frequency of 10 GHz ( Fig. 1 (d)). This is due to the changing of the antenna's characteristic impedance causing more reflections and a shift of the resonance frequency to 10.2 GHz. The underlying printed circuit board (PCB) board is characterized by a size of 30 mm × 30 mm. A cylindrical dielectric resonator reacts and resonates once illuminated by incident plane waves. This DR supports three kinds of mode (Transverse Electric (TE), Transverse Magnetic (TM) and Hybrid Modes (HE)) whose eigen frequency and corresponding quality factor depend mainly on the relative permittivity ε r , the size, the loss tangent (tanδ), and on the orientation of the DR. To be more specific, the 10 GHz operated DR has a 3.2 mm radius, a 3 mm height, and a relative permittivity ε r = 37 (ceramic) thus leading the DR to radiate with the mode HE 11 . In Fig. 2 (a, and b), the simulated and measured setup is shown with a separation of about 100 mm between the two horn antennas on one hand and between the horn antennas and the DR on the other hand. In Fig. 2 (c), the simulated and the measured insertion loss S 21 of the two horn antennas including and excluding DR are presented within 9.6 GHz and 10.4 GHz. However, an increased S 21 of about 5 dB appears specifically between 10 GHz and 10.3 GHz indicating the presence of the DR. The measured S 21 is in good agreement with the full-wave MoM simulation calculated with Feko.

III. OAM MODE CONVERSION
The cylindrical DR mentioned in the previous section is used to form a helically arranged cylindrical DR array in order to re-radiate vortex waves once illuminated by an antenna. These helically arranged DR array radiates into two opposite directions (forward and backward) based on the asymmetric doughnut radiation pattern of each DR. The forward transmitted OAM mode order propagates in the same direction of the incident OAM mode order thus having the same OAM mode order m in . Whereas, the backward reflected OAM mode order propagates in the opposite direction of the incident OAM mode order thus having a different OAM mode order m out depending on the DRs arrangement. The phase shift between each pair of the adjacent DRs, which is essential to OAM waves, is defined by the following equation: where N is the number of single DR, and m is the mode order of the vortex waves. Thus, the height h (cf. Fig. 3 (a, b, and c)) between each azimuthally adjacent DR, due to the twofold path length of the electromagnetic waves, is determined by If the DRs exceed the phase shift of 2π, the pitch p (cf. Fig. 3 (a, b, and c)), which is the total height between the lowest and the highest DR, can be shifted vertically downwards by λ/2 along the propagation-axis. In Fig. 3 (a, b, and c), three helically arranged cylindrical DRs array with three different OAM mode orders −1, +2, and −3 are illuminated by a rectangular patch antenna operating at 10 GHz, providing an incident OAM mode order of 0. Please note, that the different colors of the DRs are only to simplify the understand of the concept. Regarding equation (2), the height h between the adjacent DRs are 1.875 mm, 3.75 mm, and 5.625 mm with respect to the OAM mode orders −1, +2, and −3, respectively. The highest gain values of the backscattered direction of the DRs concerning the modes −1, +2, and −3 (cf. Fig. 3 (d)) are −17 dBi, −15.2 dBi, and −14.3 dBi at 154 • , 154 • , and 219 • , respectively. Note that the diagram actually does not depict true side lobes but rather cross sections of doughnut shaped radiation patterns. In addition, the orders of the backscattered OAM mode depend on the quantity of DRs, on the incident OAM mode order and on the spacing between each pair of adjacent DRs. Fig. 3 (e, f, and g) shows the conversion of the zeroth OAM mode order into the OAM mode orders of −1, 2, and −3, respectively, where the phase distribution is a distribution of one helix, two helices and three helices. Further, the positive OAM modes are specified by the right-handed thread whereby the rotation of the vortex waves is clockwise, in contrary to the negative OAM modes that rotate counterclockwise. Moving to Fig. 4, the conversion of vortex beams from different OAM mode orders [0 (a), +1 (b), −1 (c), +2 (d), and −2 (e)] is demonstrated. A lensed patch antenna array [22] emits towards the structured target that is configured according to the OAM mode order +1. The lens is crucial for the beam divergence compensation otherwise the OAM mode conversion will not be performed well. In case (a), the OAM mode order 0 is transmitted and converted to OAM mode −1.
While the cases (b) and (c) undergo OAM mode orders +1 and −1 conversion into the mode orders −2 and 0, respectively. Similar to the previous cases, the cases (d) and (e) transmit the mode orders +2 and −2 and convert them into the OAM mode orders −3 and +1. Moreover, the converted mode order m out is equal to the opposite sign of the sum of the incident OAM mode order m in and the DRs OAM mode order m DR .
However, the case (d) with the +2 mode exhibits slight distortion because of the strong divergence of the doughnut-shaped OAM beam with the mode order 2. In Fig. 4, all of the 5 cases are displayed with the forward (transmitted) and backward 218732 VOLUME 8, 2020 (reflected) scattered beam without taking into account the strong beam of the UCA antennas for reason of clarity.

IV. N-DIGITS CODED TAG
Converting the OAM mode order from mode 0 (plane waves) to another mode may have a new advantage with respect to the application of RFID. The conventional RFID application is based on the illumination of the DR with plane waves where the backscattered signal carries information in the form of frequency identification or a sensed value. The DR element's absence leads to understanding the value of 0, and its presence leads to understanding the value of 1. Upon the usage of N different DR elements in one tag, the number of codes increase to 2 N in which each DR is operating at a different frequency. However, the high demand of labeled products is greater than the limited capacity of the number of codes which encourages the search for new methods to increase the number of tags/codes. Two different cylindrical DRs with different radii and heights are simulated to operate at 10 GHz, and 11 GHz separately. The first DR is characterized with radius and height of 3.2 mm/3 mm value, while the second one 2.9 mm/2.72 mm. In Fig. 5, the radar cross section (RCS) of the two DRs is illustrated from 9 GHz to 12 GHz in which the maximum RCS is shown to be about −32 dBm 2 .
In addition, the difference between the DRs is about 20 dB which is enough to reduce the interference between the different DRs. The same helically DRs arrangement is applied as in Section (III) so that a 2-digits OAM coded tag is formed (cf. Fig. 6). A desirable enhancement of the isolation between the two helically arranged dielectric resonator arrays is accomplished through the usage of different radii for each helix. To be more specific, 20 mm, and 30 mm radii are applied for the frequencies 11 GHz, and 10 GHz, respectively. As noted, upon the usage of the same or closer frequencies, the sequence of codes is missing in a way that the receiver can not anymore distinguish between the codes, e.g. 12 or 21. Therefore, many codes become absent due to redundancy. The maximum number of values per digit D in one circular array is based on the number of the DRs N , which determines the number of possible mode orders [27]. This is defined by  Adding +1 in (4) considers the zeroth mode order, which can be reached if the pitch is zero. A helically arranged DR array composed of 8 elements can provide D = 7 values per digit {−3, −2, −1, 0, 1, 2, 3}. So, the equation (4) generates D k = 49 OAM codes in case of k = 2 and D = 7, where k is the number of DR helical arrays. While for k = 3 and D = 7, the number of codes will be increased to 343 codes, so it is better to use a spherical DR due to the more equidistant resonance frequencies. The initial idea has been presented in [27], where two examples {−1,1,0} and {−2,1,0} of 3-digits OAM-coded RFID Tags have been carried out by the aid of spherical dielectric resonator arrays. In Figs. 7 and 8 (a), the simulated radiation pattern of the

V. MEASUREMENT
In order to avoid undesirable reflections and distortions, the measurement is carried out in an anechoic chamber. A vector network analayzer (VNA) ZVA 40 from Rohde & Schwarz is utilized and calibrated with coaxial cables between 9 GHz till 11 GHz with 201 points. A transmit patch antenna is mounted in the middle of the UCA. The UCA task is to receive the reflected signal from the helically arranged DRs (cf. Figs. 9 and 10). The UCA has a radius of about 40 mm, so that the transmitting antenna can be placed easily. Variable receiving OAM mode orders are provided by a 8 × 8 Butler matrix (BM) which operates at 10 GHz and is connected to the UCA by eight coaxial cables of identical length (200 mm). Further, the whole system is suspended on a large piece of Rohacell with a permittivity of almost 1 in purpose to prevent the distortion and other undesirable side effects. Otherwise, the measurements would be manipulated if permittivity is higher. As a start, in Fig. 11 (a), the simulated and measured S 21 between the patch antenna and the UCA representing the mutual coupling, non-ideality of the BM, and reflections from the room are presented and taken as reference for the next scenarios yielding a transmission of −58.3 dB for simulation and −51.85 dB for measurement at 10 GHz. Moving on to Fig. 11 (b), the simulated and the measured S 21 with the existence of the helically arranged DRs assembled on cylindrical Rohacell is depicted, where the distance between each pair of adjacent DRs is about 15 mm (λ/2) in purpose to achieve the highest gain towards the UCA. The height h of the helically arranged DRs, which consist of 8 DRs, is adjusted according to equation (2) in order to convert the zeroth OAM mode order into the first OAM mode order. Consequently, the pitch equals seven times the height h, hence the pitch value of 13.125 mm. Due to the OAM divergence, the helically arranged DRs are separated from the UCA for a short distance, which is l = 100 mm. Increasing the number of the DRs can solve this divergence issue, and so can a lens. Very good agreement is shown between the simulated and the measured S 21 on one side and about a 20 dB gain enhancement at 10 GHz compared to the case without DRs on the other side. The gain enhancement starts from 9.6 GHz up to about 11 GHz, because the DRs work well within this bandwidth. In Fig. 11 (c, d, and e), the same configuration is applied but with a metal sheet for three varied distances d of 300 mm, 400 mm, and 500 mm, in order to reveal the influence as well as the distortion of a metal sheet on the S 21 . The S 21 results at 10 GHz show that the metal sheet has almost no effect on the transmission with the presence of the helically arranged DRs announcing a novel method to reject the clutter with the exception of the zeroth mode order. Such clutter rejection belonging to the BM is caused by different phase shifts resulting in destructive interference for the clutter, but constructive interference for the DR-coded OAM-signal. Table 1 summarizes the S 21 at 10 GHz according to the five different scenarios. One can notice, there are some notches in the measurement results, particularly two fixed notches and one movable notch. The two fixed notches (about 9.7 GHz, and 10.6 GHz) appear due to the mutual coupling between the transmitter and the receiver (UCA). While, the moving notch occurs as a result of the following issues. At first, the patch antenna is not accurately positioned in the middle of the UCA as well as the height between the DRs is not exactly accurate resulting in a non-ideal phase shift between the DRs. Then, the BM has shown phase shift errors of about ±5 • . Moreover, the distance between the DRs and the antennas is neither exactly 100 mm nor accurately oriented with the antennas. Finally, the metal sheet is not precisely parallel to the antennas. However, the measurement is well accomplished and agrees well with the simulation, noting that this clutter rejection works well, if the interferer is orthogonal to the main beam direction.

VI. CONCLUSION
In this article, a new approach concerning the generation and conversion of OAM mode orders through helically arranged cylindrical dielectric resonator arrays is introduced. The interaction of the phase delayed radiation of each DR element in the array submits different vortex wave modes. However, the proposed tag design is scalable to operate in the mm-wave/THz range yielding smaller structures with low radar cross-sections (RCS). This RCS can be mitigated with the aid of a larger number of DRs. Furthermore, the RFID tag technology can provide larger codes with new multi-valued digits instead of the two conventional binary codings (0 and 1). Three mode orders −1, 2 and −3 are exemplarity converted from the zeroth OAM mode order. Moreover, the OAM mode order conversions of 0 to −1, +1 to −2, −1 to 0, +2 to −3, and −2 to +1 are presented. Two examples of 2-digits OAM coded tags with the code {−1, 1} and {−2, 0} have been simulated. Furthermore, the simulated VOLUME 8, 2020 and measured S 21 of the mode conversion 0 to 1 are in good agreement demonstrating the very low efficacy and distortion of an orthogonal metal sheet on the receiving OAM antenna due to the different phase shifts in the Butler matrix. This article has shown that the OAM waves are very useful for the RFID application by increasing the RFID codes and by rejecting the clutter from broadside direction.