Nonlinear optical components for all-optical probabilistic graphical model.

The probabilistic graphical models (PGMs) are tools that are used to compute probability distributions over large and complex interacting variables. They have applications in social networks, speech recognition, artificial intelligence, machine learning, and many more areas. Here, we present an all-optical implementation of a PGM through the sum-product message passing algorithm (SPMPA) governed by a wavelength multiplexing architecture. As a proof-of-concept, we demonstrate the use of optics to solve a two node graphical model governed by SPMPA and successfully map the message passing algorithm onto photonics operations. The essential mathematical functions required for this algorithm, including multiplication and division, are implemented using nonlinear optics in thin film materials. The multiplication and division are demonstrated through a logarithm-summation-exponentiation operation and a pump-probe saturation process, respectively. The fundamental bottlenecks for the scalability of the presented scheme are discussed as well.

Intramolecular vibrational coupling contribution to temperature dependence of vibrational mode frequencies.

High-frequency vibrational modes in molecules in solution are sensitive to temperature and shift either to lower or higher frequencies with the temperature increase. These frequency shifts are often attributed to specific interactions of the molecule and to the solvent polarization effect. We found that a substantial and often dominant contribution to sensitivity of vibrational high-frequency modes to temperature originates from anharmonic interactions with other modes in the molecule. The temperature dependencies were measured for several modes in ortho-, meta-, and para-isomers of acetylbenzonitrile in solution and in a solid matrix and compared to the theoretical predictions originated from the intramolecular vibrational coupling (IVC) evaluated using anharmonic density functional theory calculations. It is found that the IVC contribution is essential for temperature dependencies of all high-frequency vibrational modes and is dominant for many modes. As such, the IVC contribution alone permits predicting the main trend in the temperature dependencies, especially for vibrational modes with smaller transition dipoles. In addition, an Onsager reaction field theory was used to describe the solvent contribution to the temperature dependencies.

A method for determining small anharmonicity values from 2DIR spectra using thermally induced shifts of frequencies of high-frequency modes.

The off-diagonal anharmonicity for a pair of vibrational modes, determined as a shift of their combination level, Δ(12), can be linked to the molecular structure via modeling. The anharmonicity, Δ(12), also determines the amplitude and shape of the cross-peak between modes 1 and 2 measured using 2DIR spectroscopy. For large anharmonicities, the anharmonicity value can be readily obtained from the shape of the cross peak. In practice, however, the anharmonicities are often small (≪1 cm(-1)). In this case, the amplitude of the cross peak rather than its shape is sensitive to the anharmonicity value, and determination of the anharmonicity requires absolute cross-peak measurements. We proposed and tested a new approach of determining anharmonicities, which is based on sensitivity of high-frequency vibrational modes to temperature. The approach permits calibrating the cross-peak amplitude in terms of the effective anharmonicity resulting from the thermal excitation of lower-frequency vibrational modes. It relies on a series of relative 2DIR measurements. While the sensitivity of the method depends on various specific parameters of the molecular system, such as transition dipoles and temperature sensitivity of the high-frequency modes involved, we have estimated that the anharmonicities as small as 0.02 cm(-1) can be determined for the cross peaks between -N(3) and C═O stretching modes using this approach.