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Abstract
In this paper, a novel compact quasi-optical mode converter based on anisotropic metasurfaces for high-order mode terahertz electronic devices is presented. To demonstrate the design model, a Ka-band metasurface quasi-optical mode converter that converts cylindrical waveguide TE01 mode to circularly polarized Gaussian beam is designed and fabricated. Both electromagnetic simulation and experiment results show that the Gaussian beam can be observed from 35 to 38 GHz, corresponding to over 8.5% of the bandwidth. The maximum scalar Gaussian mode content of 97.85% is observed in the experiment, and the output radiation from the metasurface quasi-optical mode converter is approximate circular polarization. This work unveils the potential of compact quasi-optical mode converter based on metasurfaces.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Terahertz (THz) waves, electromagnetic radiation between far infrared and millimeter wavelengths, have very important academic and application values. The characteristics of THz waves are used in a large and increasing number of applications [1,2]. For investigation and application, the radiation source is an important component in the system. Generating electromagnetic wave by extracting energy from electron beam in interaction circuit is general method in microwave electronic devices. However, as the frequency improves to millimeter wave and terahertz wave bands, the size of the conventional fundamental mode interaction circuit of the electronic devices shrinks, and the power capability is consequently reduced. Thus, operating at high-order mode is proposed and attempted in research works. Several novel over-mode interaction circuits are proposed and built [3–10]. The advantages of operating at high-order mode include enlarging the interaction circuit size, improving the power capability, and easing fabrication and assembly. However, in most cases, the high-order modes are not proper in terms of power delivery and transmission. Thus, mode conversion is necessary to transform the spatial distribution of electromagnetic energy to meet the application or transmission requirements [11–13].
As novel functional material, electromagnetic metamaterials have shown great promise in controlling the electromagnetic wave front by imparting local, gradient phase shifts to the incoming waves, which leads to a generalization of the ancient laws of reflection and refraction. In this way, a metamaterial can be used as a planar lens, vortex generator, beam deflector, axicon, and so on [14–18]. Metasurfaces are the two-dimensional equivalent of metamaterials and have received much attention recently, since they can offer reduced losses, are of lower profile, and are simpler to fabricate than bulk metamaterials. Meanwhile, they also showcase great promise in controlling the electromagnetic wave fronts [19–29]. Several mode converters based on metasurfaces for the transformation between free-space wave modes are proposed and presented, e.g., Pfeiffer et al. convert linearly and circularly polarized Gaussian beams into vector Bessel beams [30], and He et al. transform the Gaussian mode to Hermite-Gaussian and Laguerre-Gaussian modes [31].
Until now, few studies have explored mode converters based on metasurfaces for converting waveguide modes to free-space wave modes because these modes are sufficiently different. In this paper, a novel quasi-optical mode converter based on anisotropic metasurfaces that transforms the high-order waveguide mode to free space wave mode is proposed. In waveguide, the electromagnetic wave propagation is restricted by waveguide wall. There are two types of wave can be propagated in rectangular waveguide and circular waveguide: TE mode and TM mode. In this mode converter, the mode pattern changing is realized in free-space during the wave transportation. It is similar as light transportation and different from conventional waveguide transportation, and the output radiation is free space Gaussian beam. Thus, it can be classified in quasi-optical component [32]. The design principle of this proposed mode converter is adjusting the wave fronts at different positions as the differences between input and output modes by metasurfaces. A Ka-band metasurface quasi-optical mode converter that converts cylindrical waveguide TE01 mode to circularly polarized Gaussian beam is designed and fabricated to demonstrate this approach. Compared to conventional quasi-optical mode converter that consists of several mirrors [33–35], the metasurface quasi-optical mode converter (MQOC) can be compact and easy to fabricate. Meanwhile, the MQOC can convert the polarity without additionally component. This MQOC is better suited for use in high-order mode terahertz electronic devices which operate at high-order mode in high frequency terahertz region, such as gyrotron, overmoded backward wave oscillator.
2. Principle, theoretical model and experiment setup
2.1 Physical model and theory
The meta-unit of proposed anisotropic metasurface for the quasi-optical mode converter is shown in Fig. 1, in which cross-shaped apertures with two orthogonal slits are placed on the top of the dielectric layer. The cross-shaped apertures are set at a 45° angle to the incident wave Ei, as shown in Fig. 1. The incident wave Ei would be coupled to the two slits of meta-unit and can be decomposed to two orthogonal electric field vectors of Ei1 and Ei2 that are parallel to slits 1 and 2, respectively and equally. The transmitted wave Et is composed of two orthogonal electric field vectors Et1 and Et2, and they are parallel to Ei1 and Ei2, respectively. By choosing the appropriate slit width w, the transmitted wave electric field vectors Et1 and Et2 can be independently controlled by the lengths of ls1 and ls2. Then, the characteristics of the transmitted wave can be changed by the metasurfaces. Design each unit on the metasurface according to the incident wave vector direction and field distribution at this position, the whole metasurfaces for mode conversion can be designed.
Fig. 1. (a) Principle of meta-unit of the proposed anisotropic metasurface for a quasi-optical mode converter; (b) Scheme of cascaded cross-shaped apertures meta-unit in metal layers placed on dielectric layers for mode conversion.
To demonstrate the above proposition, a Ka-band millimeter wave MQOC that converts cylindrical waveguide TE01 mode to circularly polarized Gaussian beam is designed and presented. The TE01 mode is the fourth high-order mode in cylindrical waveguide that is higher than TE11, TE21, TM01 modes and cannot directly propagate in free space. According to the Maxwell equations and boundary conditions, the field distribution of TE01 mode in cylindrical waveguide is satisfied by
A Gaussian beam is characterized by Gaussian mode purity, which is usually described by the correlation coefficient between the output beams. The scalar Gaussian mode content of the Gaussian beam can be obtained by the following formula [34]:
As shown in Fig. 2(a) and Eq. (1), for the cylindrical waveguide TE01 mode, the E vector only has the Eϕ component. According to the principle described in Fig. (1), the anisotropic metasurface for TE01 mode is shown in Fig. 2(b). As shown in Fig. 2(c), the cylindrical waveguide TE01 mode is linearly polarized at each position, and the fields of TE01 mode on the same wave front that are perpendicular to transmission direction are at the same phase. At the same radius on a wave front, the $E({\rho ,\phi ,z} )={-} E({\rho ,\phi + \pi ,z} )$ when ϕ and ϕ + π, the field strength is the same, and the vector direction is positive. For a circularly polarized Gaussian beam, at each position, the E vector has both Ex and Ey components, and there is a 90° phase-shift between Ex and Ey. If the electric field at the same radius is directly reflected to the central position as same refraction angle, it will cause coherent destructive interference in the central axis and would not generate a circularly polarized wave. Thus, when the wave propagates through the anisotropic metasurface, at each position, not only the beam transmission direction must be changed, but the different phase delays at different ϕ must also be produced. Reference [25] shows that the beam-steering can be controlled by the difference in phase-shift between slits 1 and 2. The desired beam deflection angle can be predicted using the generalized Snell’s law of refraction as $\textrm{si}{\textrm{n}^{ - 1}}\left( {\frac{{{\lambda_0}}}{{2\pi }}\frac{{\mathrm{\Delta }\phi }}{{\mathrm{\Delta }x}}} \right)$, where λ0 is the vacuum wavelength and $\frac{{\mathrm{\Delta }\phi }}{{\mathrm{\Delta }x}}$ is the phase gradient in the desired direction for beam steering x [28]. Thus, the MOQC can be designed based on the differences between the TE01 mode and the Gaussian beam through the designed slits 1 and 2 on each meta unit at each position.
Fig. 2. (a) Vector diagram of cylindrical waveguide TE01 mode; (2) Designed MQOC for cylindrical waveguide TE01 mode; (c) The design principle of MQOC that converts cylindrical TE01 mode to circular Gaussian beam;
2.3 Methods in experiments
To verify the design, the Ka-band MOQC is fabricated using standard printed circuit board processes, and an experimental platform is built up as shown in Figs. 3(a) and 3(b). The signal generator (Ceyear AV1465) is used as a millimeter-wave source. A WR-28 to 2.4 mm Waveguide to Coaxial Adapter and a waveguide mode converter [36] are adopted to excite the circular TE01 mode. Considering that the waveguide detector can only receive one directional component of E field, a radiometer Room Temperature Optoacoustic Detector Golay Cell (Tydex) is used to measure the output power intensity. The Golay Cell is fitted on a programmable 2-D motorized translation stage controlled by LabVIEW code, and the signal is recorded by a high-resolution oscilloscope device (National Instruments PCI-5122). By scanning the power intensity at each position on the observing plan, the output radiation distribution can be obtained.
Fig. 3. (a) Fabricated sample; (b) Schematic diagram of the experimental setup. 1-signal generator, 2-coaxial cable, 3-WR-28 to 2.4 mm waveguide to coaxial adapter, 4-waveguide mode converter, 5-cylindrical waveguide launcher, 6-MQOC, 7-2-D motorized translation stage, 8-Golay Cell, and 9-computer installed oscilloscope device.
3. Results and discussion
3.1 Electromagnetic simulation
In this study, the electromagnetic simulation is done by a commercial finite element method solver High Frequency Structure Simulator (HFSS). Considering fabrication factors, the two-dimensional array of cross-shaped apertures is in a 105-µm-thick copper layer placed on a 0.7-mm-thick Teflon layer which permittivity ɛ = 2.1. In initial design, each unit size is about 4.28 mm × 4.28 mm (corresponding to 0.5λ of 35 GHz), and the initial values of ls1 and ls2 are both 3.6 mm which is little smaller than 0.5λ.The slit width w and lengths ls1, ls2 are optimized by meta-unit simulating. In simulation, the results show that if the w is too small, the transmission wave would be small; if the w is too large, the cross-coupling between the E fields in ls1 and ls2 directions would be happened. Thus, w = 0.6 mm is chosen in the design, the ls1 and ls2 are varied from 3.25 mm to 3.75 mm to change the phase delay separately, and the unit size is 3.9 mm × 3.9 mm which is little larger than the maximum slit size. From meta-unit simulation results, layer space 1.6 mm (corresponding to d = 2.405 mm) is chosen since the phase delay is not very sensitive to lengths ls1 and ls2, and the transmission loss is less than −1 dB. To cover the entire 360° phase delay, four layers are sufficient. In this investigation, five layers were adopted to operate wide bandwidth, which is benefit for wideband operation.
The magnitudes and phases of the S21-parameters of Et1 and Ei1 with different ls1 and ls2 at 35 GHz are presented in Figs. 4(a) and 4(b), respectively. The results show that the magnitudes and phases of the S21-parameters of Et1 and Ei1 are mainly dependent on ls1 and are barely affected by ls2. The magnitudes of S21-parameter are all larger than −1 dB when ls1 varies from 3.25 mm to 3.75 mm, as shown in Fig. 4(a). The phases of S21-parameters of Et1 and Ei1 can cover over 360° by changing the length ls1. To realize circularly polarization, the phase-shift between Et1 and Et2 at each point is 90°. The phase-shift between Et1 and Ei1 at each point is according to the desired beam deflection angle as the ϕ at each point.
Fig. 4. (a) The S21-parameter magnitudes of the meta-unit as a function of lengths ls1 and ls2, under the excitation of Ei1 at 35 GHz; (b) The S21-parameter phases of the meta-unit as a function of lengths ls1 and ls2, under the excitation of Ei1 at 35 GHz.
In the MOQC design, the incident wave is launched from a tapered waveguide with an output port of 24 mm diameter and 10 mm away from the MOQC. The observer plane is 22.6 mm away from the MOQC on the output side. The parameters of each meta-unit are based on the data in Figs. 4(a) and 4(b) The normalized simulated power intensity on the observer plane is shown in Fig. 5(a). The results show that the Gaussian profile is obtained on the observer plane, and the MOQC designed according to the above process can convert the TE01 mode to Gaussian beam. Through adjusting the frequency of the incident wave, it was found that the Gaussian beam was also observed at 35 GHz.
Fig. 5. (a) The normalized simulated power distribution on the observer plane with incident wave frequencies of 35, 36, 37, and 38 GHz; (b) Simulated radiation pattern at far field zones of 35, 36, 37, and 38 GHz.
In simulation, the output radiation with scalar Gaussian mode content up to 90% can be observed from 35 to 38 GHz, and the operating bandwidth is over 8.5%. The scalar Gaussian mode contents observed in the simulation are 91.86%, 92.57%, 94.41%, and 95.81% at 35, 36, 37, and 38 GHz, respectively. The axial ratios of far field in the axial line obtained in the simulation are 5.61, 3.93, 4.44, and 2.90 dB. The radiation pattern at the far field zone is presented in Fig. 5(b), which shows that at the far field zone the radiation power is still mainly concentrated and not divergent.
3.2 Experimental results
The experimental results of normalized power distributions of input and output wave are presented in Figs. 6(a) and 6(b). Figure 6(a) shows that the distributions of input wave are as circular ring, and Fig. 6(b) shows that the distributions of input wave are focused on the center. From 35 to 38 GHz, the output radiation with the scalar Gaussian mode content of up to 95% has been observed in this experiment. The scalar Gaussian mode contents observed in the experiment are 95.96%, 97.01%, 96.84%, and 97.85% at 35, 36, 37, and 38 GHz, respectively. The maximum scalar Gaussian mode content is also observed at 38 GHz in the experiment, which agrees with the simulation results. The Gaussian mode content observed in the experiment is closer to the theoretical prediction and higher than that in the simulation. The possible reason is that the metasurface is subwavelength structure and the mesh size in simulation is not small enough.
Fig. 6. (a) The normalized measured power distribution of input wave on the plane before metasurfaces with frequencies of 35, 36, 37, and 38 GHz. (b) The normalized measured power distribution on the observer plane with frequencies of 35, 36, 37, and 38 GHz. (c) Experimentally measured E field strength as a function of the rotation angle.
To measure the polarization characteristics of the output wave, a WR-28 waveguide detector is used instead in the Golay Cell and is placed at the center of the observed plane. The waveguide detector can only detect the E field parallel to the narrow side walls of the waveguide. Through rotating the waveguide detector along the wave propagation direction, the E field strengths at different rotation angles are measured, as shown in Fig. 6(c). The results show an approximate circular distribution in the polar coordinate system from 35 to 38 GHz, which indicates that the output radiation on the observer plane is approximate circularly polarized.
4. Conclusions
In summary, a novel quasi-optical mode converter based on a few layers of anisotropic metasurfaces for high-order mode terahertz electronic devices is presented in this paper. To verify the design principle, a Ka-band millimeter wave MQOC that converts cylindrical waveguide TE01 mode to circularly polarized Gaussian beam is designed and fabricated. The Gaussian beams were obtained from 35 to 38 GHz in the electromagnetic simulation and experiment, respectively, and the maximum scalar Gaussian mode content of 97.85% is observed in the experiment. The experiment results also demonstrate that the output radiation from the MQOC is approximate circularly polarized. This investigation shows that the metasurfaces can be used to build up a quasi-optical mode converter. Compared to conventional quasi-optical mode converters, the mode conversion in MQOC is realized within the distance of several wavelength, the size of the MQOC is sufficiently compact and it is easy to fabricate. Although dielectric metasurfaces restrict its power capability due to dielectric loss, the power capability could be improved by adopting full-metal metasurfaces [37]. This approach could promote the development and application of high-order mode terahertz electronic devices.
Funding
National Key Research and Development Program of China (2019YFA0210202); National Natural Science Foundation of China (61971097, 62111530054).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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