Detailed derivation of the generalized Snell-Descartes laws from Fermat's principle.

Beginning with Fermat's principle, we provide a detailed derivation of the generalized laws of refraction and reflection for a geometry realizing a metasurface. We first solve the Euler-Lagrange equations for a light ray propagating across the metasurface. The ray-path equation is found analytically, and the results are supported by numerical calculations. We get generalized laws of refraction and reflection that have three main features: (i) They are relevant in gradient-index optics and in geometrical optics; (ii) A collection of rays emerges from the metasurface as a result of multiple reflections inside the metasurface; and (iii) The laws, although derived from Fermat's principle, differ from previously published results.

Properties of dentin, enamel and their junction, studied with Brillouin scattering and compared to Raman microscopy.

OBJECTIVE: Dentin, enamel and the transition zone, called the dentin-enamel junction (DEJ), have an organization and properties that play a critical role in tooth resilience and in stopping the propagation of cracks. Understanding their chemical and micro-biomechanical properties is then of foremost importance. The aim of this study is to apply Brillouin microscopy on a complex biological structure, that is, the DEJ, and to compare these results with those obtained with Raman microscopy. DESIGN: Both techniques allow noncontact measurements at the microscopic scale. Brillouin microscopy is based on the interaction between acoustic phonons and laser photons and gives a relation between the frequency shift of the scattered light and the stiffness of the sample. Raman spectra contain peaks related to specific chemical bonds. RESULTS: Comparison of the Brillouin and Raman cartographies reveals correlations between mechanical and chemical properties. Indeed, the shapes of the phosphate content and stiffness curves are similar. The two spectroscopies give compatible values for the mean distance between two tubules, i.e., 4-6 µm. Moreover, for the first time, the daily cross striations of enamel could be studied, indicating a relationship between the variation in the phosphate concentration and the variation in the rigidity within the enamel prisms. CONCLUSIONS: We demonstrate here the possibility of using Brillouin scattering microscopy to both study complex biological materials such as the enamel-dentin junction and visualize secondary structures. Correlations between the chemical composition and mechanical properties could help in better understanding the tissue histology.

Comment on the paper "Improving Poor Man's Kramers-Kronig analysis and Kramers-Kronig constrained variational analysis".

The title paper [Spectrochim. Acta A213 (2019): 391-396] reports an improvement of the "Poor Man's Kramers-Kronig analysis" and of the "Kramers-Kronig constrained variational analysis" thanks to an ad hoc modification of some analytical formulas existing in the literature. This ad hoc modification is not based on mathematical grounds. In this comment we show that no ad hoc modification is required but a correction of the analytical formula used by the authors of the title paper [Spectrochim. Acta A213 (2019): 391-396].

The quantum-optics Hamiltonian in the Multipolar gauge.

This article deals with the fundamental problem of light-matter interaction in the quantum theory. Although it is described through the vector potential in quantum electrodynamics, it is believed by some that a hamiltonian involving only the electric and the magnetic fields is preferable. In the literature this hamiltonian is known as the Power-Zienau-Woolley hamiltonian. We question its validity and show that it is not equivalent to the minimal-coupling hamiltonian. In this article, we show that these two hamiltonians are not connected through a gauge transformation. We find that the gauge is not fixed in the Power-Zienau-Woolley hamiltonian. The interaction term is written in one gauge whereas the rest of the hamiltonian is written in another gauge. The Power-Zienau-Woolley hamiltonian and the minimal-coupling one are related through a unitary transformation that does not fulfill the gauge fixing constraints. Consequently, they predict different physical results. In this letter, we provide the correct quantum theory in the multipolar gauge with a hamiltonian involving only the physical fields.

Broadband computation of the scattering coefficients of infinite arbitrary cylinders.

We employ a time-domain method to compute the near field on a contour enclosing infinitely long cylinders of arbitrary cross section and constitution. We therefore recover the cylindrical Hankel coefficients of the expansion of the field outside the circumscribed circle of the structure. The recovered coefficients enable the wideband analysis of complex systems, e.g., the determination of the radar cross section becomes straightforward. The prescription for constructing such a numerical tool is provided in great detail. The method is validated by computing the scattering coefficients for a homogeneous circular cylinder illuminated by a plane wave, a problem for which an analytical solution exists. Finally, some radiation properties of an optical antenna are examined by employing the proposed technique.

Fourier modal method with spatial adaptive resolution for structures comprising homogeneous layers.

A numerical improvement of the Fourier modal method with adaptive spatial resolution is obtained. It is shown that the solutions of all the eigenvalue problems corresponding to homogeneous regions can be deduced straightforwardly from the solution of one of these problems. Numerical examples demonstrate that computation time saving can be substantial.

What is the direction followed by a beam in a photonic medium?

The direction of propagation followed by a monochromatic beam in a periodic structure is generally deduced from the isofrequency diagram, which is related to the group velocity. However, the group velocity is the derivative of omega with respect to the wavenumber, while the behavior of the beam should depend on omega only. In the subwavelength regime, a method for choosing the relevant branch of the isofrequency diagram and relying on the behavior of the system at omega only is described.

All-angle phase matching condition and backward second-harmonic localization in nonlinear photonic crystals.

We demonstrate an isotropic phase matching in properly designed nonlinear two-dimensional photonic crystals. In addition, by combining left- and right-handed properties at the fundamental and second-harmonic frequencies, we obtain a backward second-harmonic generation. These two properties lead to an unusual second-harmonic localization effect in perfect lattice photonic crystals.

Bloch vector dependence of the plasma frequency in metallic photonic crystals.

In this paper, a wire mesh metallic photonic crystal is modelized as a stack of gratings of period d made of very thin infinitely metallic rods (the conductivity is assumed to be infinite) of radius a (a<>d) . We derive a very accurate formula for the cut wavelength and we show that the plasma frequency in wire photonic crystals depends upon the Bloch vector. This latest formula is checked numerically.

Left-handed media and homogenization of photonic crystals.

Using homogenization theory, we derive the effective permittivity and permeability of a wire-mesh photonic crystal from first principles. We show that this structure does not lead to a left-handed medium when it is embedded in a matrix with a negative mu, but that resonators in a medium with a negative epsilon do form a left-handed medium in the correct range of frequencies.

Theory of mesoscopic magnetism in photonic crystals.

We provide a rigorous theoretical basis for the artificial magnetic activity of metamaterials near resonances. Our approach is a renormalization-based scheme that authorizes a completely general theory. The major result is an explicit expression of the effective permeability, in terms of resonant frequencies. The theoretical results are checked numerically, and we give applications of our theory to left-handed media and to the solution of the Pokrovski-Efros paradox.

Multiple wavelengths filtering of light through inner resonances.

We show that by using the internal resonances of a grating, it is possible to design a filter working for multiple wavelengths. We study the characteristics of the device with respect to the constituting parameters and we propose a realization process.

BLOCH modes dressed by evanescent waves and the generalized Goos-Hänchen effect in photonic crystals.

It is common knowledge that in an infinite periodic medium, for instance, an infinite photonic crystal, the direction of propagation of a monochromatic wave packet is given by the normal to the isofrequency diagram. We show that this is no longer true in a finite size medium, due to the existence of evanescent waves near the interfaces of the photonic crystal. We derive a renormalized isofrequency diagram giving the correct direction. We give a physical interpretation, showing that this phenomenon can be considered as a generalized Goos-Hänchen effect.

Electromagnetic beam diffraction by a finite lamellar structure: an aperiodic coupled-wave method.

We have developed a new formulation of the coupled-wave method (CWM) to handle aperiodic lamellar structures, and it will be referred to as the aperiodic coupled-wave method (ACWM). The space is still divided into three regions, but the fields are written by use of their Fourier integrals instead of the Fourier series. In the modulated region the relative permittivity is represented by its Fourier transform, and then a set of integro-differential equations is derived. Discretizing the last system leads to a set of ordinary differential equations that is reduced to an eigenvalue problem, as is usually done in the CWM. To assess the method, we compare our results with three independent formalisms: the Rayleigh perturbation method for small samples, the volume integral method, and the finite-element method.

Goos-Hänchen effect in the gaps of photonic crystals.

We show the presence of the Goos-Hänchen effect when a monochromatic beam illuminates a photonic crystal inside a photonic bandgap.