📡 Antenna Radiation — Dipole Field Patterns

The time-averaged radiated power per unit solid angle from a Hertzian dipole of length dℓ and current I is dP/dΩ = (I² dℓ² / 8λ²) × Z⊂0; × sin²θ, where Z⊂0; ≈ 377 Ω is the impedance of free space and λ is the wavelength. The total radiated power is P = (I² dℓ² / 12) × Z⊂0; / λ². The far-field Poynting vector falls off as 1/r², so the electric field amplitude falls off as 1/r. These results follow directly from the retarded potentials of Maxwell's equations.

A phased array feeds each element a signal with a progressively shifted phase β relative to its neighbour. The combined array factor is AF = Σ exp(i(k d cosθ + β)n) for n = 0 to N-1, where k = 2π/λ and d is element spacing. The main beam peaks where k d cosθ + β = 0, giving a beam angle θ⊂0; = arccos(-β/(kd)). By electronically changing β in nanoseconds, modern radar and 5G systems scan the beam across the sky with no mechanical latency.

Yes. The reciprocity theorem of electromagnetics states that an antenna's gain pattern and impedance are identical whether it is transmitting or receiving. A half-wave dipole that radiates most strongly broadside is also most sensitive to incoming signals arriving from broadside. This is why the same antenna design (and even the same physical antenna, via a duplexer) can be used for both transmit and receive in radar systems and two-way radios.

Heinrich Hertz performed the decisive experiments in 1886-1888, producing and detecting radio waves with a spark-gap dipole transmitter and a resonant loop receiver. He measured the wavelength and showed the waves reflected, refracted, and polarised just as Maxwell's 1865 theory predicted — confirming that light and radio are the same phenomenon at different frequencies. Guglielmo Marconi subsequently extended Hertz's laboratory demonstration into practical long-range wireless telegraphy, sending the first transatlantic signal in 1901.

The near field (reactive zone, within roughly λ/2π of the antenna) stores oscillating energy that returns to the source each cycle rather than radiating away; fields fall off as 1/r² and 1/r³ and are highly reactive. The far field (radiation zone, beyond roughly 2D²/λ for aperture antennas) contains the propagating wave where fields fall off as 1/r and the ratio E/H = Z⊂0;. Practical impacts: near-field coupling is exploited in NFC, wireless charging, and MRI coils; far-field behaviour governs broadcast coverage, radar range, and satellite links.

Antenna gain, beamwidth, side-lobe levels, and front-to-back ratio are central figures of merit in every wireless link budget. Cellular base stations use sector antennas with roughly 120° horizontal beamwidth to cover cells without interfering with adjacent sectors. Satellite dishes use parabolic reflectors to focus a broadside beam to 0.5° or less, achieving gains of 40-50 dBi. Radio telescopes array hundreds of dishes coherently (e.g., the VLA) to synthesise apertures kilometres across, reaching milliarc秒-resolution maps of distant galaxies.

Active research areas include: reconfigurable intelligent surfaces (RIS) — passive arrays of electronically tunable reflectors that shape the wireless channel in 6G networks; orbital angular momentum (OAM) beams that multiplex independent data streams on coaxial vortex modes; terahertz (100 GHz - 10 THz) antennas for sub-millimetre imaging and beyond-5G links; and meta-material/metamaterial-inspired antennas that achieve sub-wavelength apertures and near-unity radiation efficiency. Quantum sensing using nitrogen-vacancy centres also enables antenna-free detection of oscillating magnetic fields at the nanoscale.