We demonstrate an effective microspectroscopy technique by tracing the dispersion of second order nonlinear optical susceptibility chi((2)) in single atomic layer materials. The experimental method relies on the detection of single-shot second harmonic (SH) spectra from the materials and the subsequent data normalization. The key point in our study is that we used a broadband (350 nm) near-infrared femtosecond continuum pulses generated at high repetition rates in a photonic crystal fiber with superior spatial quality and stable spectral power density. This is opposite to the point-by-point laser tuning method in SH generation spectroscopy that was applied extensively in the past and has shown limited precision in obtaining chi((2)) dispersion. The continuum pulse technique produces spectral resolution better than 2 meV (<0.3 nm at 450 nm) and shows low (<5-6% rms) signal detection noise allowing the detection of subtle features in the chi((2)) spectrum at room temperatures. Fine substructure features within the main peak of chi((2)) spectra indicate the impact of broadened resonances due to exciton transitions in the single layer materials. Tailored continuum pulses are used to generate second harmonic signal in non-centrosymmetric semiconductors. SHG spectrum carries fingerprints of the bandstructure around the direct gap states. The technique produces fine spectral resolution and much better signal-to-noise ratio compared to point-by-point wavelength tuning methods. Published by Elsevier B.V.

We demonstrate and analyze a series of experiments in traditional and soft condensed matter using coherent optical spectroscopy and microscopy with ultrafast time resolution. We show the capabilities of resolving both real and imaginary parts of the third-order nonlinearity in the vicinity of Raman resonances from a medium probed within microscopic volumes with an equivalent spectral resolution of better than 0.1 cm−1. We can differentiate between vibrations of various types within unit cells of crystals, as well as perform targeted probes of areas within biological tissue. Vibrations within the TiO6 octahedron and the ones for the Ti-O-P intergroup were studied in potassium titanyl phosphate crystal to reveal a multiline structure within targeted phonon modes with closely spaced vibrations having distinctly different damping rates (~0.5 ps−1 versus ~1.1 ps−1). We also detected a 1.7–2.6 ps−1 decay of C-C stretching vibrations in fat tissue and compared that with the corresponding vibration in oil.

We have studied tungsten diselenide (WSe2) and tungsten disulfide (WS2) monolayer materials in second harmonic generation spectroscopy and microscopy experiments. Ultra-broadband continuum pulses served as the fundamental beam while its second harmonic spectrum in the visible and ultraviolet (UV) range was detected and analyzed with a better than 0.3 nm spectral resolution (< 2 meV). We provide dispersion data and absolute values for chi((2)) for the materials within a photon energy range of 2.3-3.2 eV. Fine spectral features that were detected within the dispersion data for the optical nonlinearities indicate the impact of near bandgap exciton transitions. The fundamental bandgap of 2.35 eV and exciton binding energy of 0.38 eV were determined from the measurements for WS2 monolayers while the corresponding values in WSe2 monolayers were 2.22 eV and 0.71 eV. Ranges for the absolute values of the sheet nonlinearity for WS2 and WSe2 are shown to be 0.58-1.65 x 10(-18) m(2)/V and 0.21-0.92 x 10(-18) m(2)/V, correspondingly.

We demonstrate an effective microspectroscopy technique by tracing the dispersion of second order nonlinear susceptibility (χ(2)) in a monolayer tungsten diselenide (WSe2). The χ(2) dispersion obtained with better than 3 meV photon energy resolution showed peak value being within 6.3-8.4×10-19 m2/V range. We estimate the fundamental bandgap to be at 2.2 eV. Sub-structure in the χ(2) dispersion reveals a contribution to the nonlinearity due to exciton transitions with exciton binding energy estimated to be at 0.7 eV.

We demonstrate the quantitative spectroscopic characterization and imaging of biological tissue using coherent time-domain microscopy with a femtosecond resolution. We identify tissue constituents and perform dephasing time (T2) measurements of characteristic Raman active vibrations. This was shown in subcutaneous mouse fat embedded within collagen rich areas of the dermis and the muscle connective tissue. The demonstrated equivalent spectral resolution (<0.3 cm−1) is an order of magnitude better compared to commonly used frequency-domain methods for characterization of biological media. This provides with the important dimensions and parameters in biological media characterization and can become an effective tool in detecting minute changes in the bio-molecular composition and environment that is critical for molecular level diagnosis.

We show resolution of fine spectral features within several Raman active vibrational modes in potassium titanyl phosphate (KTP) crystal. Measurements are performed using a femtosecond time-domain coherent anti-Stokes Raman scattering spectroscopy technique that is capable of delivering equivalent spectral resolution of 0.1 cm−1. The Raman spectra retrieved from our measurements show several spectral components corresponding to vibrations of different symmetry with distinctly different damping rates. In particular, linewidths for unassigned optical phonon mode triplet centered at around 820 cm−1 are found to be 7.5 ± 0.2 cm−1, 9.1 ± 0.3 cm−1, and 11.2 ± 0.3 cm−1. Results of our experiments will ultimately help to design an all-solid-state source for sub-optical-wavelength waveform generation that is based on stimulated Raman scattering.

The equilibrium statistical mechanics of one-dimensional lattice gases with interactions of arbitrary range and shape between first-neighbor atoms is solved exactly on the basis of statistically interacting vacancy particles. Two sets of vacancy particles are considered. In one set all vacancies are of one-cell size. In the other set the sizes of vacancy particles match the separation between atoms. Explicit expressions are obtained for the Gibbs free energy and the distribution of spaces between atoms at thermal equilibrium. Applications to various types of interaction potentials are discussed, including long-range potentials that give rise to phase transitions. Extensions to hard rod systems are straightforward and are shown to agree with existing results for lattice models and their continuum limits.