Microwave Vortex Beam Launcher Design

A novel design for a vectorial vortex beam launcher in the microwave regime is devised. The beam is formed by launching a single guided transverse electric (TE) mode of a metallic circular waveguide into free-space. Excitation is achieved by the mean of an inserted coaxial loop antenna. Modal expansion coefficients are computed, and the resulting electric and magnetic fields are determined. The effect of the antenna location inside the waveguide on its effective input impedance is modelled using transmission-line relations and location for optimal matching is established. The analytical results are confirmed using multi-level fast multipole method full-wave simulations.

💡 Research Summary

The paper introduces a compact microwave vortex‑beam launcher that generates orbital‑angular‑momentum (OAM) carrying beams by exciting a single guided mode of a metallic circular waveguide with a coaxial loop antenna. The authors first review existing microwave OAM generators—Vivaldi arrays, leaky‑wave antennas, reflector‑based systems, and metasurface transmitarrays—highlighting their complexity and the need for multiple radiating elements. In contrast, the proposed architecture uses only one thin‑sheet loop antenna placed inside a finite circular waveguide whose radius is chosen so that the TE₁₁ (more generally TE_q1) mode is the only propagating mode at the operating frequency, while the next mode with the same azimuthal dependence (TM₁₁) remains below cutoff.

A rigorous modal analysis is performed. The loop current is modeled as a delta‑function sheet J(ρ,φ,z)=A δ(ρ−R_L) δ(z−z₀) ê_φ. Using Lorentz reciprocity and the orthogonality of circular‑waveguide eigenmodes, the excitation coefficients for each mode are derived. The analysis shows that only TE_q and TM_q modes are excited, and by selecting the waveguide radius according to k₀a=χ′₁₁ (the first zero of the derivative of the Bessel J₁ function) the TE_q mode alone propagates, guaranteeing single‑mode radiation.

The input impedance of the loop antenna inside the waveguide is then modeled with transmission‑line (TL) theory. The guided mode provides a propagation constant β=√(k₀²−k_c²) and a characteristic impedance Z₀=η₀ k₀/β. The structure is split into two TL sections: a short‑circuited section of length d₁ representing the closed end of the waveguide, and a terminated section of length d₂ representing the open end. The free‑space loop impedance Z_A and a series reactance jX_A (the loop’s inductive reactance in free space) are added in series. The resulting expression (equation 7) predicts that when d₁≈λ_g/4 the resistive part of the input impedance drops to near zero while an inductive reactance remains, making it easy to match with a small series capacitor.

The analytical model is validated with full‑wave simulations using the multi‑level fast multipole method (MLFMM) implemented in Altair FEKO. The design is demonstrated at 10 GHz (X‑band) with a waveguide radius a=13.5 mm, loop radius R_L≈λ₀/(2π), and waveguide length L=30 mm. The antenna position is swept from the closed end to the open end in 28 steps. Simulation results show excellent agreement with the TL model for the real part of Z_in (maximum deviation <0.2 Ω, RMS <0.05 Ω) and reasonable agreement for the imaginary part, especially near the waveguide ends. The optimal matching position is found at d₁≈0.23 λ_g, where both the model and simulation give Z_in≈50 Ω (purely resistive). Adding a 0.5 pF series capacitor achieves perfect matching.

Field plots from the simulation confirm that the aperture field at the waveguide opening exhibits a truncated Bessel‑function radial profile (first zero) and an azimuthal phase term e^{jℓφ} with ℓ=1, producing the characteristic doughnut‑shaped intensity distribution and helical phase front of an OAM beam. The Poynting vector’s z‑component further illustrates the hollow‑core power flow.

In conclusion, the authors present a simple yet powerful method for generating microwave vortex beams: a single large loop antenna encased in a circular waveguide. The waveguide not only enforces single‑mode operation but also provides a convenient degree of freedom (antenna position) to achieve impedance matching, overcoming the traditional difficulty of matching large loop antennas. The approach is suitable for high‑power applications because it relies only on metallic conductors and avoids dielectric or active electronic components. Future work is suggested on integrating a coaxial feed, extending the concept to multimode excitation for beam shaping, employing artificial dielectric fillings, and refining the TL impedance model to include higher‑order evanescent coupling. This research opens a practical pathway for OAM‑based microwave communication, radar, and sensing systems.