On the limits of quasi-static theory in plasmonic nanostructures

The approximated analytical approach of Quasi-Static Theory (QST) is widely used in modelling the optical response of plasmonic nanoparticles. It is well known that its accuracy is remarkable provided that the particle is much smaller than the wavelength of the interacting radiation and that the field induced inside the structure is approximately uniform. Here, we investigate the limits of QST range of validity for gold nanostructures freestanding in air. First, we compare QST predictions of scattering spectra of nanospheres and cylindrical nanowires of various sizes with the exact results provided by Mie scattering theory. We observe a non-monotonic behaviour of the error of QST as a function of the characteristic length of the nanostructures, revealing a non-trivial scaling of its accuracy with the scatterer size. Second, we study nanowires with elliptical section upon different excitation conditions by performing finite element numerical analysis. Comparing simulation results with QST estimates of the extinction cross-section, we find that QST accuracy is strongly dependent on the excitation conditions, yielding good results even if the field is highly inhomogeneous inside the structure.

Ultrasonic Scattering Attenuation in Nodular Cast Iron: Experimental and Simulation Studies

This work evaluates the ultrasonic scattering attenuation of structures with complex scatterer distributions via experimental and simulation studies. The proposed approach uses experimental attenuation knowledge to infer the scatterer size and its concentration in the studied structures, which are important for the effective construction of simulated models. The MATLAB k-Wave toolbox has been used to implement the simulator. Several cast-iron samples have been used to demonstrate the importance of simulation in the characterization of such structures. First, the scattering attenuation was evaluated using the Truell and Papadakis models, and then the results were compared with experimental ones. Emphasis was given to the Papadakis approach because it takes into account the scatterer size distribution. It is demonstrated that both analytical models provide results that are far from the experimental ones. The developed simulator for the studied samples led to a predictive model, in which the attenuation was proportional to the fifth power of the scatterer size, and the corresponding formulation is close to the one proposed by the analytical models.

Influence of cancellous bone microstructure on ultrasonic attenuation: a theoretical prediction

Background Quantitative ultrasound has been used for the assessment of cancellous bone status. The attenuation mechanisms of cancellous bone, however, have not been well understood, because the microstructure of cancellous bone is significantly inhomogeneous and the interaction between ultrasound and the microstructure of cancellous bone is complex. In this study, a theoretical approach was applied to investigate the influence of the microstructure of cancellous bone on ultrasonic attenuation. Results The scattering from a trabecular cylinder was significantly angle dependent. The dependencies of the ultrasonic attenuation on frequency, scatterer size, and porosity were explored from the theoretical calculation. Prediction results showed that the ultrasonic attenuation increased with the increase of frequency and decreased linearly with the increase in porosity, and the broadband ultrasound attenuation decreased with the increase in porosity. All these predicted trends were consistent with published experimental data. In addition, our model successfully explained the principle of broadband ultrasound attenuation measurement (i.e., the attenuation over the frequency range 0.3–0.65 MHz was approximately linearly proportional to frequency) by considering the contributions of scattering and absorption to attenuation. Conclusion The proposed theoretical model may be a potentially valuable tool for understanding the interaction of ultrasound with cancellous bone.

A direct method for Bloch wave excitation by scattering at the edge of a lattice. Part II: Finite size effects

Summary A method for determining the reflection and transmission properties of a periodic structure occupying a half-space, previously developed for lattices formed from point scatterers, is generalized to allow for finite size effects. This facilitates the consideration of much higher frequencies (or more precisely, much higher scatterer size to wavelength ratios), and also a wider range of boundary conditions. The method is presented in a general context of linear wave theory, and physical interpretations are given for acoustics, elasticity, electromagnetism and water waves.