Journal: Vestnik Inzhekon (Вестник инжэкона), 2007, Issue 6(19), pp. 199–
Institutions: Aires Foundation, St. Petersburg ITMO University, Herzen State Pedagogical University of Russia
Overview
Mathematical modeling of electromagnetic radiation interaction with the silicon self-affine surface of the Aires fractal-matrix resonator (FMR). Studies both stationary and non-stationary cases under varying boundary conditions that define the laws of change of incident EMR on the resonator surface. One of the earliest formal mathematical treatments of the FMR mechanism, predating the VGTU external testing series by nearly a decade.
Resonator Structure
The Aires resonator is manufactured on a silicon substrate with a surface of curvilinear slots (grooves) whose pattern obeys the laws of self-similarity and scale invariance, constructed via affine transformations — hence "self-affine." The resonator is produced on a silicon wafer with specific groove geometry forming a regular self-affine structure.
Modeling Approach
The authors investigated the interaction of the FMR with incident radiation for both the stationary and non-stationary (transient) cases, under different boundary conditions governing the incident EMF at the resonator surface. The study captures: diffraction and interference phenomena; polarization of the semiconductor material under incident radiation; spatial charge separation as the key physical mechanism producing the resonator's field-modification effect.
Physical Mechanism
Of particular interest is the interaction of radiation with surfaces of polar semiconductor materials (e.g., silicon). The combination of physical phenomena — diffraction, interference, and polarization — ultimately produces spatial charge separation. Objects whose surface is built on self-similarity and scale invariance laws (fractal or self-affine properties) are uniquely capable of producing structured electromagnetic field transformation.
Research Lineage
This 2007 paper extended earlier work (2002–2005 series: copper films, liquid crystals, resonance phenomena, long-range effects) into full mathematical modeling. It directly preceded the HOLOEXPO 2017 conference results, the Serov/Korshunov/Kopyltsov 2018 peer-reviewed paper (6 GHz → 6.85 & 5.38 GHz frequency conversion), and the Springer ICICT 2022 computer simulation series — establishing the complete mathematical physics lineage of the resonator mechanism.
Authors
I.N. Serov (Aires Foundation), G.N. Lukyanov (ITMO University), A.V. Kopyltsov (Herzen University)