: This supplemental document contains further details about the numerical simulations of the optical propagation, both in the linear and in the nonlinear regime. In accordance with the experiments, on the incident Gaussian beam a conical phase angle modulation is imparted by a spatial light modulator (SLM); the beam is then focused into the glass.

Manipulating geometric and optical properties of laser-inscribed nanogratings with a conical phase front: supplement

: We report on the experimental realization and a systematic study of optical frequency comb generation in doubly resonant intracavity second harmonic generation (SHG). The efficiency of intracavity nonlinear processes usually benefits from the increasing number of resonating fields. Yet, achieving the simultaneous resonance of different fields may be technically complicated, all the more when a phase matching condition must be fulfilled as well. In our cavity we can separately control the resonance condition for the fundamental and its second harmonic, by simultaneously acting on an intracavity dispersive element and on a piezo-mounted cavity mirror, without affecting the quasi-phase matching condition. In addition, by finely adjusting the laser-to-cavity detuning, we are able to observe steady comb emission across the whole resonance profile, revealing the multiplicity of comb structures, and the substantial role of thermal effects on their dynamics. Lastly, we report the results of numerical simulations of comb dynamics, which include photothermal effects, finding a good agreement with the experimental observations. Our system provides a framework for exploring the richness of comb dynamics in doubly resonant SHG systems, assisting the design of chip-scale quadratic comb generators

Optical frequency combs in dispersion-controlled doubly resonant second-harmonic generation

: Burning forests, petrochemical installations and material warehouses generate very large ﬁelds and thermal gradients, which means human intervention to extinguish the ﬁre is greatly limited. For that reason, the use of robots is recommended, but because of high temperature, they have to be equipped with protective thermal shields. This article is an analytical, numerical, and experimental study on how a double-wall, stainless steel heat shield inﬂuenced the thermal gradients acting on a ﬁreﬁghting robot. Following the analytical analysis at a maximum temperature of 350 ◦ C, it was possible to identify the parameters that must be measured to be correlated with those from ﬁnite element analysis (FEM) analysis. Experimental tests showed a decrease in temperature behind the shield due to the stainless steel and the double-walled. The main conclusions and contributions of this paper consist of the realization of a ﬁnite difference model with FEM that takes into account conduction, convection, and radiation. It also highlights the beneﬁts of using a multilayer shield.

Research on Heat Transfer through a Double-Walled Heat Shield of a Fireﬁghting Robot

We derive an anomalous, sub-diffusive scaling limit for a one-dimensional version of the Mott random walk. The limiting process can be viewed heuristically as a one-dimensional diffusion with an absolutely continuous speed measure and a discontinuous scale function, as given by a two-sided stable subordinator. Corresponding to intervals of low conductance in the discrete model, the discontinuities in the scale function act as barriers off which the limiting process reflects for some time before crossing. We also discuss how, by incorporating a Bouchaud trap model element into the setting, it is possible to combine this ‘blocking’ mechanism with one of ‘trapping’. Our proof relies on a recently developed theory that relates the convergence of processes to that of associated resistance metric measure spaces.

Anomalous scaling regime for one-dimensional mott variable-range hopping

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Papers

Manipulating geometric and optical properties of laser-inscribed nanogratings with a conical phase front: supplement

Optical frequency combs in dispersion-controlled doubly resonant second-harmonic generation

Research on Heat Transfer through a Double-Walled Heat Shield of a Fireﬁghting Robot

Anomalous scaling regime for one-dimensional mott variable-range hopping