Energy Absorption Interferometry

Energy Absorption Interferometry (EAI) is a technique for measuring the responsivities and complex-valued spatial polarimetric forms of the individual degrees of freedom through which a many-body system can absorb energy. It was originally formulated using the language of quantum correlation functions, making it applicable to different kinds of excitation (electromagnetic, elastic and acoustic fields). EAI has been applied in a variety of theoretical and experimental ways. It is particularly effective at characterising the multimode behaviour of ultra-low-noise far-infrared and optical devices, imaging arrays, and complete instruments, where it can be used to ensure that a system is maximally responsive to those partially coherent fields that carry signal whilst avoiding those that only carry noise. Despite its utility there is no comprehensive overview of electromagnetic EAI. In this paper we describe the theoretical foundations of the method, and present a range of new techniques in areas relating to sampling, phase referencing, mode reconstruction and noise. We present, for the first time, an analysis of how noise propagates through an experiment resulting in errors and artefacts on spectral and modal plots. A noise model is essential, because it determines the signal to noise ratio needed to ensure a given level of experimental fidelity.

💡 Research Summary

Energy Absorption Interferometry (EAI) is a powerful technique for directly probing the spatial and polarimetric degrees of freedom through which a many‑body system absorbs electromagnetic energy. The method uses two mutually coherent, phase‑locked sources that illuminate the system under test (SUT). By varying the relative phase ϕ between the sources and recording the total absorbed power as a function of ϕ, one obtains a complex fringe visibility. This visibility is proportional to the bilinear form ⟨E₁|χ_H|E₂⟩, where χ_H( r, r′, ω ) is the Hermitian part of the electromagnetic response tensor and E₁, E₂ are the complex field distributions generated by the two sources. Diagonalising the matrix of visibilities collected over many source positions and polarizations yields the natural absorption modes of the SUT together with their individual efficiencies (eigenvalues).

The paper first re‑derives the fundamental power‑absorption expression in both time‑domain and frequency‑domain forms. Starting from the instantaneous work rate P(t)=∫E·χ_EE·E + ∫H·χ_HH·H, the authors introduce an impulse response h(t) that models detector filtering and relaxation processes, and then move to the Fourier domain where the absorbed power at a single frequency ω₀ becomes P(ω₀)=∫E*(r,ω₀)·χ_H(r,r′,ω₀)·E(r′,ω₀) d³r d³r′. The Hermitian part χ_H yields the real, dissipative power, while the anti‑Hermitian part χ_A accounts for reactive energy exchange. This formalism clarifies why, for slowly responding read‑out electronics, only the real part of the complex power is experimentally accessible.

A major contribution of the work is the systematic treatment of practical experimental issues. The authors discuss (i) sampling strategies: dense, possibly oversampled grids of source locations and polarizations improve the conditioning of the visibility matrix; (ii) phase‑referencing: a dedicated reference arm removes systematic phase drifts and enables separate extraction of the real and imaginary components of the visibility; (iii) mode reconstruction: after forming the correlation matrix, a singular‑value or eigen‑decomposition provides the spatial‑polarimetric eigen‑fields, which can be back‑propagated to physical field patterns using Green’s functions; (iv) noise propagation: a comprehensive noise model is derived that includes thermal background, electronic read‑out noise, and source phase noise. By propagating the covariance matrices of these noise sources through the linear visibility extraction pipeline, the authors obtain analytical expressions for the uncertainties on both spectral power plots and modal amplitudes. This allows experimenters to set quantitative signal‑to‑noise ratio (SNR) targets before building the apparatus.

The paper also shows how the volume integrals in the theory can be reduced to surface integrals via Poynting’s theorem, which is especially useful when only tangential fields on a reference plane are measurable (e.g., for planar absorbers or detector arrays). In such cases the absorbed power can be expressed as a two‑dimensional surface integral over the measured electric and magnetic fields, greatly simplifying the experimental layout.

Several experimental demonstrations are reviewed to illustrate the breadth of EAI applications: early terahertz measurements (195–270 GHz), near‑infrared laser‑based experiments at 1500 nm, broadband THz photomixer systems (0.8–2.7 THz) for polarimetric studies, and free‑space measurements of biased LEDs. The technique has also been combined with rigorous electromagnetic simulation tools to study 3‑D plasmonic lattices, thermal emitters, and spin‑wave media. Moreover, the authors discuss the relationship of EAI to other interferometric methods such as phase‑shifting interferometry and pump‑probe sensing, emphasizing its unique ability to reveal correlations that are invisible in weak thermal radiation.

Finally, the authors outline future directions. Extending EAI to more than two sources would enable measurement of higher‑order spatial correlations, opening the door to characterising non‑linear or strongly driven systems. Implementing real‑time mode tracking algorithms could allow adaptive optimisation of detector arrays for specific partially coherent illumination conditions. The presented noise model provides a solid foundation for such advanced developments, ensuring that experimental fidelity can be quantitatively predicted and controlled.

In summary, this paper delivers a thorough theoretical foundation, practical guidance, and a pioneering noise analysis for electromagnetic Energy Absorption Interferometry, establishing it as an indispensable tool for characterising ultra‑low‑noise far‑infrared and optical devices, multimode metamaterials, and complex sensing instruments.