Abstract:We derive the spectral dependence of the non-linear susceptibility of any order, generalizing the common form of Sellmeier equations. This dependence is fully defined by the knowledge of the linear dispersion of the medium. This finding generalizes the Miller formula to any order of non-linearity. In the frequency-degenerate case, it yields the spectral dependence of non-linear refractive indices of arbitrary order.

As a contribution to the ongoing controversy about the role of higher-order Kerr effect (HOKE) in laser filamentation, we first provide thorough details about the protocol that has been employed to infer the HOKE indices from the experiment. Next, we discuss potential sources of artifact in the experimental measurements of these terms and show that neither the value of the observed birefringence, nor its inversion, nor the intensity at which it is observed, appear to be flawed. Furthermore, we argue that, independently on our values, the principle of including HOKE is straightforward. Due to the different temporal and spectral dynamics, the respective efficiency of defocusing by the plasma and by the HOKE is expected to depend substantially on both incident wavelength and pulse duration. The discussion should therefore focus on defining the conditions where each filamentation regime dominates.

There is little consensus on the nature of the glass state and its relationship to other strain states in ferroelastic materials which show the shape memory effect and superelasticity. We provide a thermodynamic interpretation of the known strain states, including precursory tweed and strain glass, by mapping the problem onto a spin model and analytically obtaining the phase diagram using real-space renormalization group methods. We further predict a spontaneous transition from the glass state to the ordered martensite phase. We verify this prediction by mapping out the experimental phase diagram for the ternary ferroelastic alloy Ti50(Pd50−xCrx) and demonstrate the emergence of the spontaneous transition. Our work thus provides a consistent framework to understand the various experimental and theoretical studies on the glassy behavior associated with ferroelastic materials. PhaseOP characterization RG fixed point Austenite m = q = 0, p small ∆ * = +∞, J * = 0, σ * J = 0 Martensite m = 0, p = 0, q = 0 ∆ * = −∞, J * = ∞, σ * J J * = 0 Tweed m = q = 0, p large ∆ * = −∞, J * = 0, σ * J = 0 Strain glass m = 0, p = 0, q = 0 ∆ * = −∞, J * = 0, σ * J = ∞