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We present a simplification of the well-known Fourier Modal Method (FMM) equipped with Adaptive Spatial Resolution (ASR) concept for gratings with subwavelength heights. We show that in this case it is possible to compute the scattering matrix of the structure by solving only one eigenvalue problem (instead of three) which reduces the most expensive computational part of the FMMASR algorithm. This approach is very efficient and thus suitable for periodic metasurfaces.The Fourier Modal Method1 is one of the most versatile and efficient methods for modeling diffraction from gratings. This is why it is suitable for modeling metasurfaces based on binary gratings. The problem with this approach is that for metallic structures, it is necessary to truncate the Fourier series representing the fields to a high order implying the use of large matrices (especially in the case of crossed gratings). This situation can be improved by using the ASR concept2 to accelerate the convergence rate and thus reduce the size of the matrices in play. Still, this remains demanding from the computational point of view, for certain applications, because the heart of the FMM is based on the solution of an eigenvalue problem. This later has a cost scaling with the third power of the dimension of the matrices involved. This can be a severe limitation and hinder the use of the FMM.On the other hand, an interesting class of metasurfaces is made of gratings with subwavelength thicknesses. In this special case, it is possible (via a Taylor series expansion of the phase propagation matrix) to simplify the FMMASR is such a way that it is no longer needed to solve any eigenvalue problem3. This proves to be very efficient in reducing the computational cost.After recalling the principle of the FMMASR and the details of the corresponding algorithm, I will show how the assumption of subwavelength height leads to a simplified scattering matrix where it is sufficient to solve one eigenvalue problem. Numerical examples will be presented to support this new algorithm.References1. L. Li, “New formulation of the Fourier Modal Method for crossed surface-relief gratings,” J. Opt. Soc. Am. A 14, 2758-2767, 1997.2. B. Guizal, et al., “Reformulation of the eigenvalue problem in the Fourier modal method with spatial adaptive resolution,” Opt. Lett. 34, 2790-2792, 2009.3. J. Li, et al., “Efficient Rigorous Coupled-Wave Analysis Without Solving Eigenvalues for Analyzing One-Dimensional Ultrathin Periodic Structures,” IEEE Access, Vol. 8, 198131-198138, 2020.

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We present a dramatic simplification of the, well-known, Fourier Modal Method1 (FMM) equipped with the Adaptive Spatial Resolution2 (ASR) concept for gratings with subwavelength heights. We show that, in this case, it is possible to compute the scattering matrix of the grating by solving only one eigenvalue problem (instead of three or even more) which reduces the most expensive computational part of the FMM-ASR algorithm. This approach is very efficient and thus suitable for periodic metasurfaces.References1. G. Granet and B. Guizal, Efficient implementation of the coupled wave method for metallic lamellar gratings in TM polarization, J. Opt. Soc. Am. A, Vol 13, No 5, pp 1019-1023, May 1996.2. B. Guizal, et al., “Reformulation of the eigenvalue problem in the Fourier modal method with spatial adaptive resolution,” Opt. Lett. 34, N° 18, 2790-2792, 2009.

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In the context of fluctuational electrodynamics, an approach for the computation of the Casimir-Lifshitz force and the near field radiative heat transfer has been established under a unified formalism involving, as a main ingredient, the S matrices of the interacting objects [1]. Thus an important part of the computational effort relies on the efficient evaluation of these matrices. To show how crucial this step can be and how match it deserves attention, we will consider the simple example of graphene strips gratings. The S matrix of such a structure can be obtained through different approaches. The simplest one is the classical Fourier Modal Method (FMM) [2] where the graphene is taken into account through its surface conductivity. This method is very simple but suffers from a serious drawback for it doesn’t handle properly the singularity of the electric field at the level of the strips edges [2]. Another, commonly used, approach is the well-known Rigorous Coupled Wave Analysis (RCWA) in which the graphene strips are given finite thickness and their 2D conductivity is converted into a dielectric permittivity for the resulting rods. This method is more efficient but at a highest computational cost compared to the classical FMM. For this type of structures, we will show that the best approach is the FMM augmented by a set of Local Basis Functions [3] devised to account for the field singularities at the surface of the grating.Bibliography[1] R. Messina and M. Antezza, Scattering-matrix approach to Casimir-Lifshitz force and heat transfer out of thermal equilibrium between arbitrary bodies, Phys. Rev. A 84, 042102 (2011).[2] A. Khavasi, Fast convergent Fourier modal method for the analysis of periodic arrays of graphene ribbons, Opt. Lett. 38, 3009(2013).[3] Y. Jeyar, M. Antezza and B. Guizal, Electromagnetic scattering by a partially graphene-coated dielectric cylinder: Efficient computation and multiple plasmonic resonances, Phys. Rev. E 107, 025306 (2023).

Ref HAL: hal-05364352_v1
DOI: 10.1088/2058-9565/ae186c
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Abstract Open many-body quantum systems can exhibit intriguing nonequilibrium phases of matter, such as time crystals. In these phases, the state of the system spontaneously breaks the time-translation symmetry of the dynamical generator, which typically manifests through persistent oscillations of an order parameter. A paradigmatic model displaying such a symmetry breaking is the boundary time crystal (BTC), which has been extensively analyzed experimentally and theoretically. Despite the broad interest in these nonequilibrium phases, their thermodynamics and their fluctuating behavior remain largely unexplored, in particular for the case of coupled time crystals. In this work, we consider two interacting BTCs and derive a consistent interpretation of their thermodynamic behavior. We fully characterize their average dynamics and the behavior of their quantum fluctuations, which allows us to demonstrate the presence of quantum and classical correlations in both the stationary and the time-crystal phases displayed by the system. We furthermore exploit our theoretical derivation to explore possible applications of time crystals as quantum batteries, demonstrating their ability to efficiently store energy.

Ref HAL: hal-05349562_v1
DOI: 10.1180/clm.2025.10012
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This study investigates the influence of interlayer cations on the thermodynamics and sorption mechanisms of water in a reference Wyoming montmorillonite. The behaviour of the montmorillonite exchanged with monovalent cations (Li + , Na + , K + , Rb + , Cs + ) or divalent cations (Mg 2+ , Ca 2+ , Ba 2+ ) is compared. The analysis combines X-ray diffraction (XRD), water sorption isotherms at various temperatures and mid-infrared spectroscopy. Li + , Mg 2+ and Ca 2+ promote greater water uptake and swelling, whereas K + , Rb + and Cs + significantly limit these processes. The behaviour of Na + and Ba 2+ stands out, demonstrating intermediate water uptake and high swelling. Mid-infrared spectral analysis supports these observations. It is shown that a cation’s effect on water uptake and swelling correlates best with the product of its elementary charge and ionic radius rather than with other properties such as the electrostatic potential, solvation enthalpy or chemical hardness. However, differences in isotherm shapes, hysteresis between adsorption and desorption and the variation of isosteric heat with water content suggest the presence of two distinct sorption mechanisms: one involving Li + , Cs + , Mg 2+ , Ca 2+ and Ba 2+ , and another involving Na + , K + and Rb + . These findings indicate that isotherm shape and swelling alone do not directly reflect water uptake capacity. These findings thus outline that the chaotropic (structure-breaking) or kosmotropic (structure-making) nature of the cations, along with the complex interplay between cation hydration and TOT layer attraction, may explain the complex observed differences.

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Gravity affects the flow and the behavior at rest of complex fluids and flows by inducing sedimentation, drainage, and interfacial deformation, which can mask more fundamental physical processes. On Earth, standard countermeasures against gravity come with limitations in terms of possible formulations or the quality and homogeneity of the applied strain. Alternatively, one can run these experiments in free-fall or in orbit where the effects of gravity are canceled i.e., under microgravity conditions. In this short review, we present several European Space Agency-led projects of interest to rheologists that leverage microgravity environments: FAST/FASTER , which studies interfacial rheology using Capillary Pressure Tensiometers; SMD-FOAM, fundamental experiments on foam coarsening ; SMD-PASTA and SEEDS, aimed at understanding the dynamics of emulsion droplets, its evolution and microrheology using Diffusing Wave Spectroscopy; results associated with studies on granular materials in microgravity, including AstEx and CompGran; COLIS, which examines the thermally driven perturbation of soft colloidal glasses monitored by Dynamic Light Scattering; BIOMICS/KRABS, investigating the aggregation and migration of soft particles and red blood cells under flow. Microgravity experiments allowed for high-precision measurements of interfacial viscoelasticity, detailed studies of emulsion aging and drop coalescence, observed plastic rearrangements in colloidal glasses, characterized the dynamics under flow of red blood cell analogues, and rationalized the impact of gravity on convection and fluidization in agitated granular matter. Collectively, these experiments demonstrate the complementarity and the relevance of ESA's microgravity platforms in expanding the frontiers of soft matter rheology.

Commentaires: Submitted to Journal of Rheology (revised version)

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Ref Arxiv: 2501.16736
DOI: 10.1103/PhysRevMaterials.9.024001
Ref. & Cit.: NASA ADS
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