Leaky wave antenna

Leaky-Wave Antenna (LWA) belong to the more general class of Traveling wave antenna, that use a traveling wave on a guiding structure as the main radiating mechanism. Traveling-wave antenna fall into two general categories, slow-wave antennas and fast-wave antennas, which are usually referred to as leaky-wave antennas. Leaky-Wave Antenna (LWA) belong to the more general class of Traveling wave antenna, that use a traveling wave on a guiding structure as the main radiating mechanism. Traveling-wave antenna fall into two general categories, slow-wave antennas and fast-wave antennas, which are usually referred to as leaky-wave antennas. The traveling wave on a Leaky-Wave Antenna is a fast wave, with a phase velocity greater than the speed of light.This type of wave radiates continuously along its length, and hence the propagation wavenumber kz is complex, consisting of both a phase and an attenuation constant. Highly directive beams at an arbitrary specified angle can be achieved with this type of antenna, with a low sidelobe level. The phase constant β of the wave controls the beam angle (and this can be varied changing the frequency), while the attenuation constant α controls the beamwidth. The aperture distribution can also be easily tapered to control the sidelobe level or beam shape.Leaky-wave antennas can be divided into two important categories, uniform and periodic, depending on the type of guiding structure. A uniform structure has a cross section that is uniform (constant) along the length of the structure, usually in the form of a waveguide that has been partially opened to allow radiation to occur. The guided wave on the uniform structure is a fast wave, and thus radiates as it propagates. A periodic leaky-wave antenna structure is one that consists of a uniform structure that supports a slow (non radiating) wave that has been periodically modulated in some fashion. Since a slow wave radiates at discontinuities, the periodic modulations (discontinuities) cause the wave to radiate continuously along the length of the structure. From a more sophisticated point of view, the periodic modulation creates a guided wave that consists of an infinite number of space harmonics (Floquetmodes). Although the main (n = 0) space harmonic is a slow wave, one of the space harmonics (usually the n = −1) is designed to be a fast wave, and this harmonic wave is the radiating wave. A typical example of a uniform leaky-wave antenna is an air-filled rectangular waveguide with a longitudinal slot shown in Fig. 1. This simple structure illustrates the basic properties common to all uniform leaky-wave antennas.The fundamental TE10 waveguide mode is a fast wave, with β = k 0 2 − ( π a ) 2 < k 0 {displaystyle eta ={sqrt {k_{0}^{2}-left({frac {pi }{a}} ight)^{2}}}<k_{0}} , where k0 is the vacuum wavenumber. The radiation causes the wavenumber kz of the propagating mode within the open waveguide structure to become complex.By means of an application of the stationary-phase principle, it can be found in fact that: β k 0 = c v ph = λ 0 λ g ≃ sin ⁡ θ m {displaystyle {frac {eta }{k_{0}}}={frac {c}{v_{ ext{ph}}}}={frac {lambda _{0}}{lambda _{ ext{g}}}}simeq sin heta _{m}} where θm is the angle of maximum radiation taken from broadside (x direction), c {displaystyle c} and λ0 are the light velocity and the wavelength in vacuum, and λg is the guide wavelength. As is typical for a uniform LWA, the beam cannot be scanned too close to broadside (θm=0), since this corresponds to the cutoff frequency of the waveguide.In addition, the beam cannot be scanned too close to endfire (θm=90°,z direction) since this requires operation at frequencies significantly above cutoff, where higherorder modes can propagate, at least for an air-filled waveguide. Scanning is limited to the forward quadrant only (0<θm<Π/2), for a wave traveling in the positive z direction. This one-dimensional (1D) leaky-wave aperture distribution results in a 'fanbeam' having a narrow shape in the xz plane (H plane), and a broad shape in the cross-plane. A 'pencil beam' can be created by using an array of such 1D radiators.Unlike the slow-wave structure, a very narrow beam can be created at any angle by choosing a sufficiently small value of α. A simple formula for the beam width, measured between half-power points ( ≃ − 3 dB {displaystyle simeq -3,{ ext{dB}}} ), is: Δ θ ≃ 1 L λ 0   cos ⁡ θ m {displaystyle Delta heta simeq {frac {1}{{frac {L}{lambda _{0}}} cos heta _{m}}}}