Metamaterials-Inspired Software Engineering

This paper above is groundbreaking in the field of light/lasers amplification, allowing light to be amplified into harmonic fields of second and third order very efficiently up to frequencies of the spectrum that were supposed to be unreachable (6.4 to 9.6 TeraHertz). This can lead to the development of sensors for bands of the electromagnetic spectrum that we currently can’t scan. This inspired me to perform some science-driven software engineering in the scope of `arrowspace`, a graph and search library I have developed.

This experiment has been made possible by this tech: “Topological insulators (TIs) have attracted considerable interest owing to their peculiar characteristic of having an insulating bulk state and highly conductive, topologically protected surface states with a Dirac-like dispersion.”

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fig.2 as from the paper

The idea at the base of `arrowspace` numerical library has always aligned with experimental constructs used in super-conductors and metamaterials research (one of the original inspirations was the concept of metalenses).

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The current `arrowspace` algorithm already deals with topological surfaces and dispersion computation (interesting the difference between Dirac-like dispersion and Dirichlet dispersion used in `arrowspace`), so it can be extended to simulate this kind of signal amplification, let’s briefly see how:

* Graph Laplacian computation acts as the metamaterial (if the tweak below is applied as minimal implementation, additionally translating the entire algorithm to leverage complex numbers will make the current dispersion into a Dirac-like dispersion as in TIs)

* Eigenstructure describe the resonant modes

* With a tweak to the computation of the Graph Laplacian (extending the graph construction to compute Laplacian powers of second- and third-order), taumode can be viewed as a hyperharmonic signature — a higher-order synthetic index derived from the fundamental graph structure.

Just a sneak-peek of a potential implementation:

These improvements make possible to extend the search function to incorporate multi-order taumode (indices computed on Laplacian powers of L² and L³ instead of just L2 as it is now).

This interpretation can transform `arrowspace` from a single-frequency spectral index to a multi-harmonic nonlinear diffuser, directly analogous to the metamaterial’s ability to generate and detect multiple harmonic frequencies simultaneously.

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