Approach to equilibrium for the stochastic NLS

We study the approach to equilibrium, described by a Gibbs measure, for a system on a $d$-dimensional torus evolving according to a stochastic nonlinear Schr\"odinger equation (SNLS) with a high frequency truncation. We prove exponential approach to the truncated Gibbs measure both for the focusing and defocusing cases when the dynamics is constrained via suitable boundary conditions to regions of the Fourier space where the Hamiltonian is convex. Our method is based on establishing a spectral gap for the non self-adjoint Fokker-Planck operator governing the time evolution of the measure, which is {\it uniform} in the frequency truncation $N$. The limit $N\to\infty$ is discussed.Comment: 15 p

Terahertz imaging of sub-wavelength particles with Zenneck surface waves

Impact of sub-wavelength-size dielectric particles on Zenneck surface waves on planar metallic antennas is investigated at terahertz (THz) frequencies with THz near-field probe microscopy. Perturbations of the surface waves show the particle presence, despite its sub-wavelength size. The experimental configuration, which utilizes excitation of surface waves at metallic edges, is suitable for THz imaging of dielectric sub-wavelength size objects. As a proof of concept, the effects of a small strontium titanate rectangular particle and a titanium dioxide sphere on the surface field of a bow-tie antenna are experimentally detected and verified using full-wave simulations

Spatiotemporal Coherent Control of Light through a Multiple Scattering Medium with the Multispectral Transmission Matrix

We report the broadband characterization of the propagation of light through a multiple scattering medium by means of its multispectral transmission matrix. Using a single spatial light modulator, our approach enables the full control of both the spatial and spectral properties of an ultrashort pulse transmitted through the medium. We demonstrate spatiotemporal focusing of the pulse at any arbitrary position and time with any desired spectral shape. Our approach opens new perspectives for fundamental studies of light-matter interaction in disordered media, and has potential applications in sensing, coherent control, and imaging

Bose-Einstein Condensation of a Gaussian Random Field in the Thermodynamic Limit

We derive the criterion for the Bose-Einstein condensation (BEC) of a Gaussian field $\phi$ (real or complex) in the thermodynamic limit. The field is characterized by its covariance function and the control parameter is the intensity $u=\|\phi\|_2^2/V$, where $V$ is the volume of the box containing the field. We show that for any dimension $d$ (including $d=1$), there is a class of covariance functions for which $\phi$ exhibits a BEC as $u$ is increased through a critical value $u_c$. In this case, we investigate the probability distribution of the part of $u$ contained in the condensate. We show that depending on the parameters characterizing the covariance function and the dimension $d$, there can be two distinct types of condensate: a Gaussian distributed "normal" condensate with fluctuations scaling as $1/\sqrt{V}$, and a non Gaussian distributed "anomalous" condensate. A detailed analysis of the anomalous condensate is performed for a one-dimensional system ($d=1$). Extending this one-dimensional analysis to exactly the point of transition between normal and anomalous condensations, we find that the condensate at the transition point is still Gaussian distributed but with anomalously large fluctuations scaling as $\sqrt{\ln(L)/L}$, where $L$ is the system length. The conditional spectral density of $\phi$, knowing $u$, is given for all the regimes (with and without BEC).Comment: REVTeX file, 32 pages, 2 figures, submitted to J. Phys. A: Math. Theo

Efficient compact modelling of UTC-photodiode towards terahertz communication system design

Monolithic optoelectronic integrated circuits, OEICs are seen as key enabling technologies to minimal power loss criteria. Monolithic OEICs combine, on the same die, cutting-edge optical devices and high speed III-V electronics able to generate terahertz signal targeting beyond-5G networks. Computationally efficient compact models compatible with existing software tool and design flow are essential for timely and cost-effective OEIC achievement. The analog nature of photonic devices wholly justifies the use of methodologies alike the ones employed in electronic design automation, through implementation of accurate (and SPICE-compatible) compact models. This multidisciplinary work, describes an efficient compact model for Uni-Traveling Carrier photodiodes (UTC PD) which is a key component for OEICs. Its equations feature the UTC PD electronic transport and frequency response along with its photocurrent under applied optical power. It also dynamically takes into account the device junction temperature, accounting for the self-heating effect. Excellent agreement between model and measurements as well as model scalability (several geometries have been validated) has been achieved that marks the first demonstration of a multi-physics, computationally efficient and versatile compact model for UTC-PDs

Decaying shock studies of phase transitions in MgOSiO2 systems: implications for the Super-Earths interiors

We report an experimental study of the phase diagrams of periclase (MgO), enstatite (MgSiO3) and forsterite (Mg2SiO4) at high pressures. We investigated with laser driven decaying shocks the pressure/temperature curves of MgO, MgSiO3 and Mg2SiO4 between 0.2-1.2 TPa, 0.12-0.5 TPa and 0.2-0.85 TPa respectively. A melting signature has been observed in MgO at 0.47 TPa and 9860 K, while no phase changes were observed neither in MgSiO3 nor in Mg2SiO4. An increasing of reflectivity of MgO, MgSiO3 and Mg2SiO4 liquids have been detected at 0.55 TPa -12 760 K, 0.15 TPa - 7540 K, 0.2 TPa - 5800 K, respectively. In contrast to SiO2, melting and metallization of these compounds do not coincide implying the presence of poor electrically conducting liquids close to the melting lines. This has important implications for the generation of dynamos in Super-earths mantles

Wideband THz time domain spectroscopy based on optical rectification and electro-optic sampling

We present an analytical model describing the full electromagnetic propagation in a THz time-domain spectroscopy (THz-TDS) system, from the THz pulses via Optical Rectification to the detection via Electro Optic-Sampling. While several investigations deal singularly with the many elements that constitute a THz-TDS, in our work we pay particular attention to the modelling of the time-frequency behaviour of all the stages which compose the experimental set-up. Therefore, our model considers the following main aspects: (i) pump beam focusing into the generation crystal; (ii) phase-matching inside both the generation and detection crystals; (iii) chromatic dispersion and absorption inside the crystals; (iv) Fabry-Perot effect; (v) diffraction outside, i.e. along the propagation, (vi) focalization and overlapping between THz and probe beams, (vii) electro-optic sampling. In order to validate our model, we report on the comparison between the simulations and the experimental data obtained from the same set-up, showing their good agreement

Coherent spatio-temporal control of pulsed light through multiple scattering media

We report broadband characterization of the propagation of light through a multiply scattering medium by means of its Multi-Spectral Transmission Matrix. Using a single spatial light modulator, our approach enables the full control of both spatial and spectral properties of an ultrashort pulse transmitted through the medium. We demonstrate spatiotemporal focusing of the pulse at any arbitrary position and time with any desired spectral shape. Our approach opens new perspectives for fundamental studies of lightmatter interaction in disordered media, and has potential applications in coherent control and imaging