*Topological Sensors

 

**Topological Sensors:

From Linear Semiconductor Junctions to Flow-Sensitive Topological Perception**

Abstract

Classical sensor technologies are fundamentally based on linear response principles, where physical signals are reduced to scalar values such as intensity, voltage, or frequency. While this paradigm has proven highly effective for decades, it encounters intrinsic limitations when applied to complex, nonlinear, and structurally rich environments. This document introduces the concept of topological sensors — a new class of sensing systems designed to detect not merely signal magnitude, but structural, configurational, and topological changes in discretized flows. The proposed framework outlines a gradual transition from traditional p–n and n–p–n semiconductor architectures toward hybrid and fully topological sensing systems, preserving technological continuity while enabling fundamentally new modes of perception.

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1. Limitations of Linear Sensor Paradigms

Modern semiconductor sensors — including CMOS image sensors, photodiodes, and transistor-based detectors — operate on the principle of linear or quasi-linear response. In such systems:

• a physical stimulus is converted into an electrical signal,

• the response is proportional to the stimulus within a defined operating range,

• the sensing element itself remains passive and memoryless.

In p–n, p–n–p, and n–p–n junctions, detection is essentially binary or scalar: the system responds to the presence, absence, or intensity of an external influence. While this architecture excels in precision and reproducibility, it inherently discards structural information contained in complex physical processes.

As a result, conventional sensors struggle to represent:

• spatial morphology of signal propagation,

• topological rearrangements of fields or flows,

• multi-scale interactions across heterogeneous media,

• nonlinear, history-dependent phenomena.

These limitations motivate the search for alternative sensing paradigms.

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2. From Signals to Flows

The topological sensor framework replaces the notion of a “signal” with that of a flow — a discretized, structured process characterized by:

• local density variations,

• multiple internal states (λ-parameters),

• phase heterogeneity,

• dynamically evolving boundaries.

In this view, meaningful information is not carried by amplitude alone, but by changes in configuration, connectivity, and boundary geometry. Observation thus shifts from measuring values to detecting events — moments when the structure of the flow changes.

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3. Active Probing and Structural Readout

A defining feature of topological sensing is the introduction of an active probing agent. This agent may take the form of:

• a photon flux,

• a weak electromagnetic or acoustic wave,

• a quasi-particle-like excitation,

• or an artificial “beam” designed to minimally perturb the medium.

Crucially, the probe does not carry the information itself. Instead, it reveals information through the way the medium responds to its passage. Detection focuses on:

• boundary deformation,

• emergence or disappearance of closed regions,

• changes in curvature or connectivity,

• symmetry breaking at local scales.

This principle is conceptually similar to neutrino detection: the event is inferred not from the probe directly, but from rare or subtle interactions within the sensing medium.

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4. Elementary Topological Sensor Cell

The fundamental unit of the system is the Elementary Topological Sensor (ETS). Unlike a transistor, an ETS is not a simple switch. It is defined by:

• a local discretized domain,

• an internal multi-parameter state,

• a set of observable boundaries,

• a reaction rule linking structural change to memory.

The ETS responds only when a topological transition occurs. If no structural change is detected, the system remains silent — regardless of signal intensity. Each ETS retains a trace of its interaction history, introducing local memory and hysteresis into the sensing fabric.

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5. Transitional Architectures: From p–n Junctions to Topology

The proposed development path explicitly avoids abrupt technological discontinuity. Instead, it introduces a transitional phase, where classical semiconductor elements coexist with topological components.

Examples include:

• hybrid pixels combining RGB photodiodes with curvature-sensitive elements,

• p–n junctions augmented by memristive or hysteretic layers,

• sensor arrays where only a subset of cells operate in topological mode.

In this phase, linear electronics handle signal transport and power management, while topological elements provide higher-order structural sensitivity. This approach allows gradual integration into existing fabrication processes.

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6. Topological Pixels and Sensor Fields

At a higher level, ETS units combine into topological pixels. Unlike RGB pixels, which encode three scalar values, a topological pixel encodes a configuration of sensitivities. Such pixels can detect:

• angular structure of incoming radiation,

• phase discontinuities,

• spatial coherence,

• micro-fluctuations in flow density.

Arrays of topological pixels form sensor fields rather than images. These fields do not merely represent scenes; they respond to them. The sensing surface itself becomes a computational medium.

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7. Toward Non-Biological Neuromorphic Systems

Topological sensors naturally lead to neuromorphic architectures without biological substrates. Here, computation is not centralized, and perception is not separated from processing. The sensing medium:

• computes through its own structural dynamics,

• learns through persistent deformation,

• adapts without explicit training algorithms.

This opens pathways toward artificial perception systems capable of interacting with complex environments in ways that linear sensors cannot.

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8. Applications and Outlook

Potential applications include:

• advanced solar energy harvesting based on structural light perception,

• flow-sensitive environmental sensing,

• adaptive imaging under extreme conditions,

• artificial cognitive environments and embodied AI systems.

Topological sensors represent not a replacement of semiconductor technology, but its conceptual expansion — from value detection to structure perception, from signals to flows, and from linear response to topological awareness.

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