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Information storage, reflecting the capability of a dynamical system to keep predictable information during its evolution over time, is a key element of intrinsic distributed computation, useful for the description of the dynamical complexity of several physical and biological processes. Here we introduce a parametric framework which allows to compute information storage across multiple time scales in stochastic processes displaying both short-term dynamics and long-range correlations (LRC). The framework exploits the theory of state space models to provide the multiscale representation of linear fractionally integrated autoregressive (ARFI) processes, from which information storage is computed at any given time scale relating the process variance to the prediction error variance. This enables the theoretical assessment and a computationally reliable quantification of a complexity measure which incorporates the effects of LRC together with that of short-term dynamics. The proposed measure is first assessed in simulated ARFI processes reproducing different types of autoregressive (AR) dynamics and different degrees of LRC, studying both the theoretical values and the finite sample performance. We find that LRC alter substantially the complexity of ARFI processes even at short time scales, and that reliable estimation of complexity can be achieved at longer time scales only when LRC are properly modeled. Then, we assess multiscale information storage in physiological time series measured in humans during resting state and postural stress, revealing unprecedented responses to stress of the complexity of heart period and systolic arterial pressure variability, which are related to the different role played by LRC in the two conditions.

Frequency conversion by means of Kerr-nonlinearity is one of the most common and exploited nonlinear optical processes in the UV, visible, IR and Mid-IR spectral regions. Here we show that wave mixing of an optical field and a Terahertz wave can be achieved in diamond, resulting in the frequency conversion of the THz radiation either by sum- or difference-frequency generation. In the latter case, we show that this process is phase-matched and most efficient in a counter-propagating geometry.

We describe a technique for surface domain engineering in congruent lithium niobate single crystals. The method is based on conventional electric-field poling, but involves an intentional overpoling step that inverts all the material apart from a thin surface region directly below the patterned photoresist. The surface poled structures show good domain uniformity, and the technique has so far been applied to produce domain periods as small as 1 \mu m. The technique is fully compatible with nonlinear optical integrated devices based on waveguide structures.

We observe second harmonic generation via random quasi-phase-matching in a 2.0 \mu m periodically poled, 1-cm-long, z-cut lithium tantalate. Away from resonance, the harmonic output profiles exhibit a characteristic pattern stemming from a stochastic domain distribution and a quadratic growth with the fundamental excitation, as well as a broadband spectral response. The results are in good agreement with a simple model and numerical simulations in the undepleted regime, assuming an anisotropic spread of the random nonlinear component.

We implement a simple and powerful approach to characterize the domain distribution in the bulk of quadratic ferroelectric crystals via far-field second-harmonic spectroscopy. The approach is demonstrated in a lithium tantalate sample with periodic electric field poling and random mark-to-space ratio.

We carried out second-harmonic generation in quasi-phase-matched \alpha-phase lithium niobate channel waveguides realized by proton exchange and surface periodic poling. Owing to a limited ferroelectric domain depth, we could observe the interplay between second-harmonic generation and self-phase modulation due to cascading and cubic effects, resulting in a nonlinear resonance shift. Data reduction allowed us to evaluate both the quadratic nonlinearity in the near infrared as well as the depth of the uninverted domains.

Domain engineering technology in lithium tantalate is a well studied approach for nonlinear optical applications. However, for several cases of interest, the realization of short period structures (< 2 \mu m) is required, which make their characterization difficult with standard techniques. In this work, we show that high resolution x-ray diffraction is a convenient approach for the characterization of such structures, allowing us to obtain in a nondestructive fashion information such as the average domain period, the domain wall inclination, and the overall structure quality.

We demonstrate efficient first-order quasi-phase-matched second-harmonic generation in a surface periodically poled Ti:indiffused lithium niobate waveguide; 6 mW of continuous-wave blue radiation (wavelength = 412.6 nm) was produced showing the potential of surface domain inversion for efficient nonlinear waveguide interactions.

We report on bulk and guided-wave second-harmonic generation via random Quasi-Phase-Matching in Lithium Tantalate. By acquiring the far-field profiles at several wavelengths, we extract statistical information on the distribution of the quadratic nonlinearity as well as its average period, both at the surface and in the bulk of the sample. By investigating the distribution in the two regions we demonstrate a non-invasive approach to the study of poling dynamics.

We report on backward second-harmonic-generation in bulk periodically poled congruent lithium niobate with a 3.2 microns period. A tunable continuous-wave Ti:sapphire laser allowed us exciting two resonant quasi-phase-matching orders in the backward configuration. The resonances were also resolved by temperature tuning and interpolated with standard theory to extract relevant information on the sample.

We present a general analysis of the influence of nonlinear optical absorption on terahertz generation via optical difference frequency generation, when reaching for the quantum conversion efficiency limit. By casting the equations governing the process in a suitably normalized form, including either two-photon- or three-photon-absorption terms, we have been able to plot universal charts for phase matched optical-to-terahertz conversion for different values of the nonlinear absorption coefficients. We apply our analysis to some experiments reported to date, in order to understand to what extent multiphoton absorption could have played a role and also to predict the maximum achievable conversion efficiency at higher peak pump intensities., Comment: 16 pages, 2 figures. Some correction and some explanation added

We present a universal and rigorous approach to study difference frequency generation in the terahertz domain, keeping the number of degrees of freedom to a minimum, through the definition of a suitable figure of merit. The proposed method relies on suitably normalized charts, that enable to predict the optical-to-terahertz conversion efficiency of any system based on wave propagation in quadratic nonlinear materials. The predictions of our approach are found to be in good agreement with the best experimental results reported to date, enabling also to estimate the d22 nonlinear coefficient of high quality GaSe., Comment: 3 pages in 2 columns format, 3 figures. GaSe analysis has been corrected. Fig. 3 has been replaced

We present a detailed analysis and comparison of dielectric waveguides made of CdTe, GaP, GaAs and InP for modal phase matched optical difference frequency generation (DFG) in the terahertz domain. From the form of the DFG equations, we derived the definition of a very general figure of merit (FOM). In turn, this FOM enabled us to compare different configurations, by taking into account linear and nonlinear susceptibility dispersion, terahertz absorption, and a rigorous evaluation of the waveguide modes properties. The most efficient waveguides found with this procedure are predicted to approach the quantum efficiency limit with input optical power in the order of kWs., Comment: 8 pages in two columns format, 6 figures, 2 Tables