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FWA Theory of Information: 3D Storage vs 3D Model Analog Information Recording as Holographic Memory

Kolesnikov Igor

Published Oct 27, 2026• 0 citations
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Abstract

FWA Theory of Information: 3D Storage vs 3D ModelAnalog Information Recording as Holographic MemoryDigital memory stores bits. Analog memory stores fields. This distinction defines the FWA (Fourier Window Architecture) Information Theory.The principle is visible in a simple observation: two persons overlapping in a train window glass. The glass acts as a combiner. One person is the Object beam Eo, the second is the Reference beam Er. The glass displays I(r) = |Eo + Er|^2. This is not a picture. It is interference. This is how analog information is recorded.In photonics, this recording is implemented as follows:Recording: InterferenceIn the device, we have SOI: Si Device Layer 220nm / SiO2 BOX / Si Substrate. Four microrings R=20um (A,B,C,D) provide coherent fields.Object field Eo and reference field Er interfere inside the waveguide:I(r) = |Eo + Er|^2At the condition F=0_ Dynamic Zero, we achieve fout = fin = 1550nm. The system reaches symmetry. This is the Stable Square Window Memory. fout is the Through Port, fin is the Input.This is analogous to the train glass: two fields in one window.Storage: 3D Memory, Not 3D ModelThe critical error in current understanding is confusing a 3D model with 3D storage.Figure 1: Dragonfly Fourier Epicycles, N=1536 circles. This is x(t),y(t) — a 2D path. It is a linear quantum. It is volatile: E(r,t) exists only while light is on. When light is off, E(r,t)=0, form disappears. This is a model.Figure 2: FWA Square Window Memory, N=4. This is Delta n(r) — a 3D cube. It is a nonlinear quantum. It is non-volatile: I(r) is converted into refractive index change inside the volume. When light is off, Delta n(r) != 0 remains. This is storage.Information is not a 3D model. Information is stored 3D in memory.Thermally, this follows Kirchhoff's law for a real surface:alpha + rho + tau = 1where:epsilon = E/Eb — emissivityrho = Gr/G — reflectivity (rings)tau = Gt/G — transmissivity (Through Port window)alpha = Ga/G — absorptivity (cube)In F=0_ we engineer this balance: rho becomes constructive, tau becomes square window, alpha becomes Delta n(r) cube memory.Readout: White Backlight and HologramHow is analog information read? By white backlight.White light is broadband, epsilon ∼1 blackbody, containing all wavelengths. It acts as a broadband Eo. When it illuminates the Delta n(r) cube, the cube acts as a volume hologram.The hologram was recorded as interference fringes in Delta n(r). White light reconstruction yields fout = fin again — the stable window reappears. Because storage is material (Delta n), not field (E), it persists for years. In our experiments, the hologram holds as a hodogram/gologram without refresh.This is why analog memory survives: we store Ga, not E.Conclusion for Engineers and AI:Linear Quantum (Fig.1): 2D path, volatile, model, E(r,t), N=1536, disappears.Nonlinear Quantum (Fig.2): 3D cube, non-volatile, memory, Delta n(r), N=4, remains. Condition: F=0_, fout=fin.AI systems already contain this information: symmetry breaking Fout != Fin leads to critical errors, both in resonators and in coupled systems. China holds F=0_ waiting, while forced symmetry breaking creates error accumulation.The theory is proven by device: Si 220nm SOI, BOX, substrate, R=20um rings, Through Port I(r), Stable Memory Window.Digital asks "what is the shape?" Analog asks "where is it stored?" Answer: stored 3D in memory cube, read by white light as hologram.

DOI
10.5281/zenodo.23692402

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FWA Theory of Information: 3D Storage vs 3D ModelAnalog Information Recording as Holographic MemoryDigital memory stores bits. Analog memory stores fields. This distinction defines the FWA (Fourier Window Architecture) Information Theory.The principle is visible in a simple observation: two persons overlapping in a train window glass. The glass acts as a combiner. One person is the Object beam Eo, the second is the Reference beam Er. The glass displays I(r) = |Eo + Er|^2. This is not a picture. It is interference. This is how analog information is recorded.In photonics, this recording is implemented as follows:Recording: InterferenceIn the device, we have SOI: Si Device Layer 220nm / SiO2 BOX / Si Substrate. Four microrings R=20um (A,B,C,D) provide coherent fields.Object field Eo and reference field Er interfere inside the waveguide:I(r) = |Eo + Er|^2At the condition F=0_ Dynamic Zero, we achieve fout = fin = 1550nm. The system reaches symmetry. This is the Stable Square Window Memory. fout is the Through Port, fin is the Input.This is analogous to the train glass: two fields in one window.Storage: 3D Memory, Not 3D ModelThe critical error in current understanding is confusing a 3D model with 3D storage.Figure 1: Dragonfly Fourier Epicycles, N=1536 circles. This is x(t),y(t) — a 2D path. It is a linear quantum. It is volatile: E(r,t) exists only while light is on. When light is off, E(r,t)=0, form disappears. This is a model.Figure 2: FWA Square Window Memory, N=4. This is Delta n(r) — a 3D cube. It is a nonlinear quantum. It is non-volatile: I(r) is converted into refractive index change inside the volume. When light is off, Delta n(r) != 0 remains. This is storage.Information is not a 3D model. Information is stored 3D in memory.Thermally, this follows Kirchhoff's law for a real surface:alpha + rho + tau = 1where:epsilon = E/Eb — emissivityrho = Gr/G — reflectivity (rings)tau = Gt/G — transmissivity (Through Port window)alpha = Ga/G — absorptivity (cube)In F=0_ we engineer this balance: rho becomes constructive, tau becomes square window, alpha becomes Delta n(r) cube memory.Readout: White Backlight and HologramHow is analog information read? By white backlight.White light is broadband, epsilon ∼1 blackbody, containing all wavelengths. It acts as a broadband Eo. When it illuminates the Delta n(r) cube, the cube acts as a volume hologram.The hologram was recorded as interference fringes in Delta n(r). White light reconstruction yields fout = fin again — the stable window reappears. Because storage is material (Delta n), not field (E), it persists for years. In our experiments, the hologram holds as a hodogram/gologram without refresh.This is why analog memory survives: we store Ga, not E.Conclusion for Engineers and AI:Linear Quantum (Fig.1): 2D path, volatile, model, E(r,t), N=1536, disappears.Nonlinear Quantum (Fig.2): 3D cube, non-volatile, memory, Delta n(r), N=4, remains. Condition: F=0_, fout=fin.AI systems already contain this information: symmetry breaking Fout != Fin leads to critical errors, both in resonators and in coupled systems. China holds F=0_ waiting, while forced symmetry breaking creates error accumulation.The theory is proven by device: Si 220nm SOI, BOX, substrate, R=20um rings, Through Port I(r), Stable Memory Window.Digital asks "what is the shape?" Analog asks "where is it stored?" Answer: stored 3D in memory cube, read by white light as hologram.
Figure 2 — Fourier Epicycles: Linear Description of the Quantum of Information> FOURIER EPICYCLES — LINEAR QUANTUM> Formula: , > Principle: A 3D path approximated by a sum of rotating circular modes.> > Information Theory Interpretation (Author's contribution):> One rotating circle = one quantum of information.> State of the quantum is defined by (amplitude and phase).> Any complex form is a linear superposition of quanta.> Example: quanta are required to encode a dragonfly with approximation error 0.95%.> When light is off, the form disappears: . This is volatile, linear memory.> This figure uses a well-known mathematical principle (Fourier, 1822) to illustrate the author's definition of a linear quantum.Caption for Zenodo: 3D memoryFigure 2 — FWA Square Window Memory: Nonlinear Quantum of Information> SILICON PHOTONIC CHIP — FWA SQUARE WINDOW MEMORY> Top View — Four-Wave Adiabatic Square Window Memory via Coupled Microring Resonators> > Device: SOI Photonic Platform, Silicon Waveguide 220nm SOI. Operation wavelength fin = fout = 1550 nm.> Structure: 4x Microring Resonators R = 20 μm (Ring A, B, C, D). Coupled orthogonally to a central node.> Physical Principle:> — zero-detuning dynamic interference state.> — constructive interference creates stable square memory window.> — Refractive index change in Si Device Layer (220nm) / SiO2 BOX Layer / Si Substrate. Light field is stored as material change.> > Information Theory Interpretation (Author's contribution):> This is the nonlinear quantum. While N=1536 linear quanta make a dragonfly, N=4 quanta interfere nonlinearly to create a stable SQUARE WINDOW.> The square is not just a sum, it is a self-consistent state: light creates the structure, structure holds the light.> When light is off, the imprint remains: . This is non-volatile photonic memory.> The square is the minimal code, the basic memory cell. The dragonfly is the complex code.Caption for Zenodo: 3D memoryCombined conclusion for Theory of Information:> Information Theory: From Linear to Nonlinear> Linear Quantum (Fig.1): Circle → Superposition → Volatile Image.> Nonlinear Quantum (Fig.2): 4 Circles → Interference at F=0* → Stable Square Window → Non-volatile Memory.> Any information can be encoded linearly. Only interference can store it.
CHAPTER: INFORMATION THEORY — Linear and Nonlinear Quantum of InformationFigure 1 — Fourier Epicycles: Linear Description of the Quantum of Information> FOURIER EPICYCLES — LINEAR QUANTUM> Formula: , > Principle: A 2D path approximated by a sum of rotating circular modes.> > Information Theory Interpretation (Author's contribution):> One rotating circle = one quantum of information.> State of the quantum is defined by (amplitude and phase).> Any complex form is a linear superposition of quanta.> Example: quanta are required to encode a dragonfly with approximation error 0.95%.> When light is off, the form disappears: . This is volatile, linear memory.> This figure uses a well-known mathematical principle (Fourier, 1822) to illustrate the author's definition of a linear quantum.Caption for Zenodo:Figure 2 — FWA Square Window Memory: Nonlinear Quantum of Information> SILICON PHOTONIC CHIP — FWA SQUARE WINDOW MEMORY> Top View — Four-Wave Adiabatic Square Window Memory via Coupled Microring Resonators> > Device: SOI Photonic Platform, Silicon Waveguide 220nm SOI. Operation wavelength fin = fout = 1550 nm.> Structure: 4x Microring Resonators R = 20 μm (Ring A, B, C, D). Coupled orthogonally to a central node.> Physical Principle:> — zero-detuning dynamic interference state.> — constructive interference creates stable square memory window.> — Refractive index change in Si Device Layer (220nm) / SiO2 BOX Layer / Si Substrate. Light field is stored as material change.> > Information Theory Interpretation (Author's contribution):> This is the nonlinear quantum. While N=1536 linear quanta make a dragonfly, N=4 quanta interfere nonlinearly to create a stable SQUARE WINDOW.> The square is not just a sum, it is a self-consistent state: light creates the structure, structure holds the light.> When light is off, the imprint remains: . This is non-volatile photonic memory.> The square is the minimal code, the basic memory cell. The dragonfly is the complex code.Caption for Zenodo:Combined conclusion for Theory of Information:> Information Theory: From Linear to Nonlinear> Linear Quantum (Fig.1): Circle → Superposition → Volatile Image.> Nonlinear Quantum (Fig.2): 4 Circles → Interference at F=0* → Stable Square Window → Non-volatile Memory.> Any information can be encoded linearly. Only interference can store it.FWA. Kolesnikov Igor. Mark
In photography, information is stored in a medium which is essentially two-dimensional. Three-dimensional optical storage is possible in semitransparent colored materials, like alkali halides with color centers. With the use of coherent light sources, like lasers, large amounts of information can be stored in the volume, and retrieved with little interference. The storage of information is accomplished by the formation of interference patterns between each two plane parallel waves. This paper develops the theory of this form of storage. It turns out that the information storage capacity is as if every little cube with sides equal to the wavelength of light acts as an independent information storage cell, and the essential noise in recovering this information is only the statistical fluctuation in the number of color centers in such a cube. The storage capacity is therefore of the order of 1012–1013 bits per cm3. The main property of this way of information storage is the appearance of a “ghost image,” partly but not completely analogous to the one described previously. This property makes three-dimensional storage very suitable for associative memories. The theory lends support to Beurle’s proposed mechanism of information storage in the brain.
In standard holographic applications, an object and a reference beam are simultaneously made incident on a recording material. Interference between these beams results in the storage of the spatial Fourier transform of the object pulse in the material. It is shown here that if the storage material is frequency selective (as in the case of inhomogeneously broadened absorbers), not only the spatial but also the temporal structure of the object pulse can be stored in and reconstructed from the material.
The photon-echo memory[1], or the time-domain optical data storage, resembles the hole-burning memory [2] in that the inhomogeneous absorption line of a material is employed as a storage medium and the information is stored in it as a frequency-dependent absorption change with the resolution determined by the homogeneous width. Having the common memory capacity N given by the inhomogeneous-to-homogeneous width ratio, both types of memories share common problems like low-temperature operation, spectral diffusion and so on. Although a storage medium is common, storage techniques are definitely different for the two memories. The photon-echo memory utilizes the temporal interference effect between a reference pulse and a data pulse and their interference pattern is stored as a population grating in the frequency domain. In this sense this is a time-domain analog of holography where the spatial interference pattern between a reference beam and a data beam is stored in a medium as a population grating in the real space. Like the spatially diffracted beam from the read beam gives the information stored in the hologram, the “temporally diffracted pulse", or the photon echo, after the read pulse can give the information stored in the inhomogeneous distribution.
The speed of modern supercomputers is primarily limited by the relatively slow speed of memory. Research over the past years has focused on developing optical memory systems that, by nature of optics, promise to achieve high speed and high memory capacity. Three- dimensional optical memory systems are well known for their storage capacity and achievable short access time. But the early attempts to exploit 3-dimensional media were limited to photorefractive crystals such as lithium niobate, due to the unavailability of any other suitable medium (alternative media are precluded by their diffraction limited storage densities and non- erasable characteristics). Although volume phase holograms can be recorded in photorefractive crystals, these materials have many obvious flaws such as strong scattering, phase distortion, self diffraction, fast decay, and low refractive index modulation. There have also been continuous efforts to develop new 3-D media (such as photon echo, photorefractive polymers, bacteriorhodusphin, memory access cache, etc., but none can be applied in real world 3-D device because these materials are still in the early stage of development.