Near Field Electromagnetics

Near-Field Electromagnetics

Audience

Difficulty	Intermediate

Notation on this page

Near-field electromagnetics is the branch of electromagnetic theory concerned with the fields near an antenna or radiating element — distances comparable to or smaller than a wavelength. In contrast to far-field (radiation-zone) behaviour, near-field fields exhibit:

• Strong stored (non-radiated) energy.
• E and H mutually out of phase.
• Faster than r⁻¹ spatial decay (r⁻², r⁻³ terms).
• Direct inductive/capacitive coupling to nearby matter.

These properties make the near field the operational regime for psionic devices such as HelmKit — devices that must couple strongly to nearby biological tissue (a few cm distant) while minimising far-field radiative exposure.

Field-zone boundaries

For an antenna of largest dimension D operating at wavelength λ = c / f, the EM field is conventionally divided into three zones:

| Zone | Range | Field character | Energy state | |---|---|---|---| | Reactive near-field | 0 < r < 0.62·√(D³/λ) | E and H ~90° out of phase; r⁻³ behavior | Stored | | Radiating near-field (Fresnel) | 0.62·√(D³/λ) ≤ r < 2D²/λ | E and H phase-aligning; r⁻² | Mix | | Far-field (Fraunhofer) | r ≥ 2D²/λ | E ⊥ H ⊥ propagation; plane wave; r⁻¹ | Radiated |

The transition wavelength-distance r = 2D²/λ defines the boundary at which the antenna's emitted wave can be treated as a plane wave — the standard far-field idealisation.

Worked examples at 2.45 GHz

The 2.45 GHz ISM band is the standard operating frequency for many HelmKit-class devices (chosen because of regulatory allowance and the availability of standard hardware).

At f = 2.45 GHz: λ = c/f = 0.1224 m = 12.24 cm.

D = 5 cm coil (HelmKit-typical)

• Reactive boundary: 0.62 · √(0.05³/0.1224) ≈ 6.3 cm.
• Fresnel boundary: 2 · 0.05²/0.1224 ≈ 4.1 cm.

The Fresnel boundary is smaller than the reactive boundary — a sign that the antenna is electrically small (D ≪ λ) and the standard boundary formulas no longer cleanly separate the zones. Essentially the entire local field is reactive.

D = 10 cm coil

• Reactive: ~ 5.6 cm.
• Fresnel: ~ 16.3 cm.
• Far-field begins at r ≈ 16 cm.

D = 50 cm dish

• Reactive: ~ 63 cm.
• Fresnel: ~ 4.1 m.
• Far-field begins at r ≈ 4 m — a real beam emerges at this scale.

Why the reactive zone matters

The reactive near-field is where:

1. Inductive/capacitive coupling to nearby matter is strongest. For a coil near a brain, the coil's stored magnetic energy couples directly into the brain tissue via mutual inductance.
2. EM energy is stored, not radiated. High field amplitudes can be achieved per unit input power. A 100 mW source can produce locally large E-fields without significant radiated power.
3. Field can be spatially shaped with higher precision than the diffraction-limited far-field. Sub-wavelength field structures are easily made in the reactive zone.

For psionic-device design, operate in the reactive zone to maximise coupling to biological tissue while minimising radiative loss and far-field exposure (which would otherwise expand the regulatory compliance burden).

Electrically small antennas

When D ≪ λ — the regime of compact wearable devices — the antenna is electrically small and obeys different scaling laws. See Antenna_Theory_for_Psionic_Devices for the Chu-Harrington bound, Wheeler radiation resistance, and related limits.

For a 5 cm coil at 2.45 GHz (ka ≈ 1.28), the antenna sits at the boundary between electrically small and resonant. For deeper near-field operation, lower the operating frequency to ~ 300-500 MHz (or larger coils at 2.45 GHz).

Coupling to ψ in the near field

In the framework:

• The ψ-source J_ψ = α F_μνF^μν is proportional to E² − c²B² locally.
• In the reactive near-field, both E and B are large; their product F_μνF^μν ≠ 0.
• Per-volume ψ-source density can exceed far-field by factors of 10²-10⁴ at typical near-field amplitudes.
• This is the rationale for near-field operation of psionic devices: high-efficiency ψ-source per watt of input power.

Safety

The reactive near-field is also the regime of highest biological exposure risk. See SAR_Calculation_for_Psionic_Devices for the ICNIRP/IEEE compliance framework: the localised SAR limit (2.0 W/kg over 10 g of head tissue) demands strict control of near-field E-amplitudes.

Sanity checks

• r ≫ 2D²/λ → recovers standard far-field plane-wave radiation. ✓
• Static limit (f → 0) → reactive near-field becomes pure inductive/electrostatic. ✓
• ψ → 0 (in framework) → standard near-field EM intact; no ψ-coupling. ✓ (Sanity_Check_Limits §6.)

See Also

• Reactive_Near_Field
• Antenna_Theory_for_Psionic_Devices
• Caduceus_Coil
• Bifilar_Coil
• Double-Helix_Antenna
• Psionic_Device_Overview
• HelmKit
• Psionic_Device_Safety

References

• Balanis, C. A. (2016). Antenna Theory: Analysis and Design. 4th ed., Wiley.
• Pozar, D. M. (2011). Microwave Engineering. 4th ed., Wiley.
• Kraus, J. D. (1988). Antennas. 2nd ed., McGraw-Hill.