Beyond the Rozanov bound on electromagnetic absorption via periodic temporal modulations

Zeki Hayran and Francesco Monticone

Phys. Rev. Applied 21, 044007 – Published 2 April 2024

Abstract

Incorporating time-varying elements into electromagnetic systems has been shown to be a powerful approach to challenge well-established performance limits, for example, bounds on absorption and impedance matching. So far, most of these studies have concentrated on time-switched systems, where the material undergoes instantaneous modulation in time while the input field is entirely contained within it. This approach, however, necessitates accurate timing of the switching event and limits how thin the system can ultimately be because of the spatial width of the impinging pulse. To address these challenges, here we investigate the periodic temporal modulation of highly lossy materials, focusing on their relatively unexplored parametric absorption aspects. Our results reveal that, by appropriate selection of the modulation parameters, the absorption performance of a periodically modulated absorber can be greatly improved compared with that of its time-invariant counterpart, and can even exceed the theoretical bound for conventional electromagnetic absorbers, namely, the “Rozanov bound.” Our findings thus demonstrate the potential of periodic temporal modulations to enable significant improvements in absorber performance while circumventing the limitations imposed by precise timing and material thickness in time-switched schemes, opening up new opportunities for the design and optimization of advanced electromagnetic absorber systems for various applications.

Received 13 July 2023
Revised 26 December 2023
Accepted 21 February 2024

DOI:https://doi.org/10.1103/PhysRevApplied.21.044007

Physics Subject Headings (PhySH)

Electromagnetic waves & oscillations Light propagation, transmission & absorption Metamaterials Parametric resonance Time crystals

Bloch-Floquet theorem Classical electromagnetism

Atomic, Molecular & OpticalCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Zeki Hayran and Francesco Monticone ^*

School of Electrical and Computer Engineering, Cornell University, Ithaca, New York 14853, USA

^*francesco.monticone@cornell.edu

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Vol. 21, Iss. 4 — April 2024

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Figure 1
(a) An electromagnetic pulse impinging on a nonmagnetic absorber with thickness $d$ backed by a metallic mirror. (b) Illustrative reflection-coefficient spectrum, with the absorption bandwidth determined by the maximum tolerable reflection magnitude ( $Γ_{0}$ ) from the absorber. (c) Practical example demonstrating the constraint on the integral $I_{R}$ imposed by the Rozanov bound for passive, linear, and time-invariant absorbers. (d) Implications of the Rozanov bound for electromagnetic absorption, highlighting the typical necessity for increased absorber thickness to improve the absorption performance, for a given bandwidth. The normalized absorption bandwidth in this case is assumed to be $10 d$ . In (c),(d), the considered material has a lossy Drude-type dispersion with a normalized damping coefficient equal to $γ d / 2 π c_{0} = 330$ . In (d), the plasma frequency is equal to $ω_{p} d / 2 π c_{0} = 6$ , where $c_{0}$ is the speed of light in a vacuum.
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Figure 2
(a) An incident pulse interacting with an electromagnetic absorber with periodically modulated permittivity. (b) Band structure of the time-modulated material, calculated through the Floquet theorem. The emergence of a momentum band gap in the band structure due to the periodic temporal modulation (upper panel) results in the imaginary part of the eigenfrequency splitting into two distinct values within the gap (lower panel). Triangular markers denote results obtained with the theoretical approach outlined in Sec. 2. Material and modulation parameters are as follows: $ω_{p0} = 10 ω_{\mod}$ , $γ = 1000 ω_{\mod}$ , and $M = 1$ . (c) Spatiotemporal characteristics of the considered incoming pulse. (d) Rozanov-integral $I_{R}$ values for a range of modulation parameters. Absorber properties are as follows: $ω_{p0} d / 2 π c_{0} = 6$ , $γ d / 2 π c_{0} = 330$ , and $M = 0.4$ . Color-bar arrows in (d) indicate the Rozanov limit.
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Figure 3
(a) Computed Rozanov integral $I_{R}$ as a function of the modulation amplitude. (b) Superimposed reflection-coefficient spectra for $M = 0$ (time invariant), and $M = 0.96$ [denoted with red and blue arrows, respectively, in (a)]. Absorber properties are the same as for Fig. 2, with $φ_{\mod} / π = 0.60$ and $ω_{\mod} d / 2 π c_{0} = 0.133$ . (c),(d) Same as (a) and (b) but with a multiharmonic modulation function with modulation frequencies $ω_{\mod_{1}} d / 2 π c_{0} = 0.100$ , $ω_{\mod_{2}} d / 2 π c_{0} = 0.133$ , and $ω_{\mod_{3}} d / 2 π c_{0} = 0.166$ , modulation phases $φ_{\mod_{1}} / 2 π = 0.90$ , $φ_{\mod_{2}} / 2 π = 0.60$ , and $φ_{\mod_{3}} / 2 π = 0.25$ , and the same modulation amplitude $M$ for each individual modulation harmonic. The upper-left insets in (a),(b) show the periodic temporal modulations given by Eqs. (4) and (18), respectively.
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Figure 4
(a) Calculated absorption efficiency (upper panel), as defined in the main text, and absorbed energy (lower panel), normalized to incident energy, both plotted as a function of the modulation amplitude. The upper-left inset shows the periodic temporal modulation. (b) Superimposed spectra of the reflected electric field for $M = 0$ (time invariant) and $M = 1.0$ [denoted with red and blue arrows, respectively, in (a)]. Absorber properties are as follows: $ω_{p0} d / 2 π c_{0} = 5.5$ , $γ d / 2 π c_{0} = 100$ , $φ_{\mod} / π = 0.45$ , and $ω_{\mod} d / 2 π c_{0} = 0.1$ .
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