[Paper Review] Mechanical properties of the radio frequency field emitted by an antenna array

Holger Then, B. Thidé|ArXiv.org|Mar 3, 2008

Antenna Design and Optimization4 references3 citations

TL;DR

This paper analytically derives the mechanical properties—energy, linear momentum, and angular momentum—of radio frequency fields emitted by a circular antenna array, showing that angular momentum separates cleanly into spin and orbital components via helicity and vorticity. The key result is that orbital angular momentum density depends solely on vorticity, while spin angular momentum depends on both helicity and vorticity, enabling precise control and detection of these states via transverse field measurements without needing longitudinal components.

ABSTRACT

Angular momentum densities of electromagnetic beams are connected to helicity (circular polarization) and topological charge (azimuthal phase shift and vorticity). Computing the electromagnetic fields emitted by a circular antenna array, analytic expressions are found for the densities of energy, linear and angular momentum in terms of helicity and vorticity. It is found that the angular momentum density can be separated into spin and orbital parts, a result that is known to be true in a beam geometry. The results are of importance for information-rich radio astronomy and space physics as well as novel radio, radar, and wireless communication concepts.

Motivation & Objective

• To analytically determine the mechanical properties of electromagnetic fields radiated by a circular antenna array.
• To clarify the physical origin and separation of spin and orbital angular momentum in radio frequency beams.
• To demonstrate that angular momentum densities can be expressed explicitly in terms of helicity and vorticity.
• To enable practical detection and manipulation of orbital and spin angular momentum using only transverse field components.
• To establish the validity of the superposition principle for mechanical properties of interfering electromagnetic beams.

Proposed method

• Modeling the antenna array as a continuous distribution of N elemental dipoles with phase and amplitude control to generate helicity and vorticity.
• Using complex-valued vector potentials and harmonic time dependence to derive far-field expressions for electromagnetic fields.
• Computing energy, linear momentum, and angular momentum densities as homogeneous functions of distance to simplify expressions.
• Expressing angular momentum density in terms of helicity (h = ±1) and topological charge (l ∈ ℤ) to separate spin and orbital contributions.
• Applying Fourier convolution with a 'Pacman'-shaped mask to model discrete sources and introduce uncertainty in orbital angular momentum states.
• Using superposition principles to analyze interference terms and their non-vanishing contributions to transverse angular momentum components.

Experimental results

Research questions

• RQ1 Can the angular momentum of radio frequency beams from a circular antenna array be cleanly separated into spin and orbital components?
• RQ2 How do helicity and vorticity uniquely determine the spin and orbital angular momentum densities in the far field?
• RQ3 What is the role of interference terms in the mechanical properties of superposed electromagnetic beams?
• RQ4 How does the discrete nature of antenna elements affect the number of usable orbital angular momentum states?
• RQ5 Can spin and orbital angular momentum be detected and controlled using only transverse field components without measuring weak longitudinal components?

Key findings

• The angular momentum density separates cleanly into spin and orbital parts, with orbital angular momentum density depending only on vorticity and spin angular momentum density depending on both helicity and vorticity.
• The far-field expressions for energy, linear momentum, and angular momentum densities are homogeneous functions of distance, enabling simplification of complex terms.
• Interference terms in the superposition of beams do not fully vanish, leading to non-zero transverse components of orbital and spin angular momentum (L_x, L_y, S_x, S_y).
• The number of usable orbital angular momentum states in a discrete N-element array is approximately N, with corrections of order 1/N due to uncertainty principles from the discrete source distribution.
• The spin angular momentum density is directly linked to polarization (helicity), while its total value is independent of vorticity, confirming its identification with polarization.
• The method enables detection of spin and orbital angular momentum via transverse field triangulation, avoiding measurement of weak longitudinal components.