**Abstract**

Orbital angular momentum (OAM) techniques are exploited for a wide range of potential radiofrequency (RF) and electromagnetic applications, including megahertz-through-terahertz wireless systems, fiber-based and free-space optical communications and sensing, just like acoustic and any other wave-based counterparts. In those RF and electromagnetic applications, OAM wave is set to enable the development of high-speed and high-capacity communications, radar imaging, and sensing systems, among many others. In this chapter, a comprehensive comparison between plane wave and OAM wave propagation using a patch antenna as a radiator at 2.45 GHz is presented and discussed. This comparison allows the appreciation of the fundamental properties of the OAM wave when compared against its plane wave counterpart. For simplified comparison and discussion, we will use two abbreviated terms: PWPA for plane-wave patch antenna and OWPA for OAM wave patch antenna. PWPA refers to as planar patch antenna that produces plane waves in farfield, whereas patch antenna that delivers OAM waves in far-field is termed as OWPA. In this context, all physical quantities for wave propagation such as electric field, magnetic field, wave impedance, wave vector, velocity, pitch, and propagation constant are theoretically studied for OAM waves and compared with plane waves. First, OAM wave generation is studied through widely used uniform circular antenna array (UCAA) in literature. Then, plane wave patch antenna (PWPA) and OAM wave patch antenna (OWPA) are designed and verified through simulation and measurement. OWPA is designed with characteristic mode analysis (CMA) based on a lossy substrate to excite a twisting wave at a determined patch location. With this in mind, a comparative investigation of PWPA and OWPA is conducted for different physical parameters. Cylindrical near-field scan clearly shows a helical wave motion for OWPA, whereas a normal plane wave motion for PWPA. Furthermore, the comparison of plane wave and OAM wave propagation is demonstrated using the combination of a Tx–Rx antenna pair. It is observed that the overall signal from OWPA can be received with two PWPAs at an angle as OWPA has a dispersive beam. Moreover, the receiving antenna with a large aperture and plane wave horn antenna (PWHA) in the line of sight (LOS) range can also be used to receive the overall signal from OWPA. The received signal in PWPA–PWPA, OWPA–OWPA, OWPA–PWPA–PWPA, OWPA–PWHA Tx–Rx pairs is thoroughly compared and studied. Measured and simulated results for transmission are 30 dB for 0 dB input signal in OWPA–PWPA– PWPA and OWPA–PWHA cases, which are reasonably justified within the sensitivity/dynamic range of short-distance communication and radar sensing receivers.

**Keywords:** plane wave patch antenna (PWPA), OAM wave patch antenna (OWPA), plane wave propagation, OAM wave propagation, Gaussian and Bessel beam, OAM impedance, OAM pitch, vortex wave, propagation constant
