Executive summary: You can shape real, energy-bearing fields into a torus without coils by pairing two counter-rotating optical vortex beams and converting their structured light into audible sound via the photoacoustic effect. Each beam carries orbital angular momentum. Their superposition forms a standing or slowly rotating donut of optical energy. When the beams are amplitude-modulated, air itself becomes the emitter and a co-registered toroidal sound field appears in free space. Drive the two beams with two mono streams, one clockwise and one anticlockwise, clocked from the same source. This approach does not create low-frequency magnetic flux like a PEMF coil. It is a coil-free light-and-sound holography path that is physically testable today.
1) The physics behind counter-rotating holographic tori
Optical vortices and orbital angular momentum: Vortex beams possess a helical phase labeled by a topological charge ℓ. They exhibit a dark axial core and ring intensity where the electromagnetic energy flows azimuthally, carried by the Poynting vector. The per-photon orbital angular momentum equals ℓħ.
Standing and rotating donuts: Superpose two co-axial vortex beams with equal amplitude and opposite helicity (+ℓ and −ℓ) to form a standing vortex. Add a small amplitude bias or a tiny carrier detune to make the donut precess slowly. This counter-rotation control gives precise handles on the geometry of energy flow.
Why this does not make PEMF: Low-frequency magnetic fields in tissue arise from currents described by Ampère–Maxwell and Faraday induction. A purely optical hologram cannot substitute for a current loop in the magneto-quasistatic regime, so it will not induce the same electric fields as PEMF.
2) From light to sound – converting the vortex into a toroidal acoustic field
Photoacoustic bridge: When modulated light is absorbed, rapid micro-heating causes pressure oscillations that launch sound. In air, using wavelengths near water-vapor absorption lines around one point nine micrometers improves efficiency at conservative power densities. Demonstrations show targeted audible messages in free space using photoacoustics, with no loudspeaker present in the volume.
Acoustic holography validation: Independent of optics, acoustic holography and phased-array work show that complex three-dimensional pressure fields, vortices and torus-like shapes can be synthesized and steered with high precision. This confirms that a toroidal sound map in free space is achievable and measurable.
3) The two-mono control law
Treat the azimuthal angle φ around the torus as your channel index. Render two phase-conjugate holograms and encode two mono streams on the two beams:
E(φ, t) = A_cw · s1(t) · e^{i(ωt + ℓφ)} + A_ccw · s2(t) · e^{i(ωt − ℓφ + θ)}
- s1 drives the clockwise beam. s2 drives the anticlockwise beam.
- Acw and Accw set balance. θ trims phase. ℓ sets ring tightness.
- Balanced amplitudes give a standing torus with stationary nodes. A small amplitude bias or tiny detune creates slow rotation.
4) A coil-free reference architecture
- Light engine: Continuous-wave source near one point nine micrometers aligned to a water-vapor line. Spatial light modulator or a high-efficiency diffractive optic to generate +ℓ and −ℓ beams.
- Audio buses: Two mono WAV streams from a common clock. One maps to clockwise, one to anticlockwise. Start with pink noise and chirps, then explore full-spectrum or binaural content.
- Optional scanning: A MEMS mirror or acousto-optic modulator can sweep beam segments at acoustic rates to boost local pressure while preserving the torus envelope.
- Sensing: Camera plus phase retrieval for ℓ verification. A small microphone ring confirms standing nodes and controlled precession. Simple grid scans reconstruct three-dimensional pressure maps.
5) Coils vs coil-free holographic torus – comparison at a glance
| Aspect | Actual coils – PEMF and related | Counter-rotating holographic torus with light and sound |
|---|---|---|
| Primary field type | Low-frequency magnetic flux density B from driven currents | Optical Poynting flow plus photoacoustically generated pressure field |
| Governing physics | Ampère–Maxwell and Faraday induction in the magneto-quasistatic regime | Orbital angular momentum of light and photoacoustic conversion in air |
| Ability to produce PEMF-like induced E in tissue | Yes – controlled by dB/dt and geometry | No – pure holograms do not replace current loops at low frequency |
| Topology control | Limited unless using multi-coil arrays with precise phasing | High – standing or rotating tori, multi-lobe ℓ modes, programmable in software |
| Transducer presence in the volume | Yes – coils or conductors near the body | No physical speaker in the volume – air becomes the emitter |
| Penetration into tissue | Magnetic fields penetrate non-conductive tissue with low attenuation | Air-borne sound couples at surface and via cavities. Near-IR is line-of-sight and safety limited |
| Uniformity and steering | Good with calibrated arrays and beamforming | Excellent spatial sculpting through holograms. Rapid preset switching |
| Hardware complexity | Power drivers, thermal management, current sensing | Laser source, SLM or diffractive optic, modulation and safety interlocks |
| Safety focus | dB/dt limits and coil heating | Laser eye safety near one point nine micrometers and comfortable long-session SPL |
| Best use | Applications that require low-frequency magnetic flux in depth | Coil-free immersive sound fields, energetic topologies, exploratory light-sound coupling |
6) Practical validation protocol
- Render +ℓ and −ℓ beams on the SLM. Verify ring radius and topological charge with camera-based diagnostics.
- Encode two mono streams on the two beams with a shared sample clock.
- Map the torus with 3 to 6 microphones on a circle. Balanced drives yield stationary nodes. A small amplitude bias or tiny detune creates controlled precession you can time and log.
- Estimate energy by measuring optical intensity for Poynting flux and acoustic pressure for acoustic intensity. Compare across settings to quantify geometric gains.
PEMF Healing App – recommended programs for content buses
- 528 Hertz – The Love Frequency: restorative and heart-centered themes. Open program
- 432 Hertz – Harmony of Nature: calming and grounding aesthetics. Open program
- Solfeggio Frequencies: a family of tones used for meditative sound design. Open programs
Use the two-mono scheme – one bus clockwise, one bus anticlockwise – and add a very slow breathing envelope at one quarter to one half Hertz while the program plays. These associations are experiential and cultural, not medical claims.
References – linked
- Allen, L., Beijersbergen, M. W., Spreeuw, R. J. C., & Woerdman, J. P. (1992). Orbital angular momentum of light and the transformation of Laguerre–Gaussian modes. Phys. Rev. A, 45, 8185–8189. https://link.aps.org/doi/10.1103/PhysRevA.45.8185
- Yao, A. M., & Padgett, M. J. (2011). Orbital angular momentum: origins, behavior and applications. Adv. Opt. Photon., 3(2), 161–204. https://doi.org/10.1364/AOP.3.000161 | Optica page
- Ostrovsky, A. S., Rickenstorff-Parrao, C., & Arrizón, V. (2013). Generation of the “perfect” optical vortex using a liquid-crystal spatial light modulator. Opt. Lett., 38(4), 534–536. https://doi.org/10.1364/OL.38.000534 | Full text
- Sullenberger, R. M., Bush, E., & Michael, J. (2019). Photoacoustic communications: delivering audible signals via absorption of light by atmospheric H2O. Opt. Lett., 44(3), 622–625. PubMed | Optica PDF
- MIT Lincoln Laboratory (2019). A laser can deliver messages directly to your ear across a room. https://www.ll.mit.edu/news/laser-can-deliver-messages-directly-your-ear-across-room | Optica news
- Hirayama, R., Christopoulos, C., Plasencia, D. M., & Subramanian, S. (2022). High-speed acoustic holography with arbitrary scattering objects. Nat. Commun., 13, 3696. Open access (PMC)
- Cox, L., Melde, K., Croxford, A., Fischer, P., & Drinkwater, B. (2019). Acoustic hologram enhanced phased arrays for ultrasonic particle manipulation. Phys. Rev. Applied, 12, 064055. https://link.aps.org/doi/10.1103/PhysRevApplied.12.064055
- Science Advances news link for compact holographic sound fields (2023). https://www.science.org/doi/10.1126/sciadv.adf6182
Disclaimer
This article is educational and experimental. It does not provide medical advice. Always follow laser and acoustic safety guidelines, verify exposure limits locally, and validate fields with measurement before any human use.
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