A Unified Mathematical Formalism for First to Third Order Dielectric Response of Matter: Application to Surface-Specific Two-Colour Vibrational Optical Spectroscopy

Abstract

To take advantage of the singular properties of matter, as well as to characterize it, we need to interact with it. The role of optical spectroscopies is to enable us to demonstrate the existence of physical objects by observing their response to light excitation. The ability of spectroscopy to reveal the structure and properties of matter then relies on mathematical functions called optical (or dielectric) response functions. Technically, these are tensor Green’s functions, and not scalar functions. The complexity of this tensor formalism sometimes leads to confusion within some articles and books. Here, we do clarify this formalism by introducing the physical foundations of linear and non-linear spectroscopies as simple and rigorous as possible. We dwell on both the mathematical and experimental aspects, examining extinction, infrared, Raman and sum-frequency generation spectroscopies. In this review, we thus give a personal presentation with the aim of offering the reader a coherent vision of linear and non-linear optics, and to remove the ambiguities that we have encountered in reference books and articles.

Two-Colour Sum-Frequency Generation Spectroscopy Coupled to Plasmonics with the CLIO Free Electron Laser

“…It is worth noting that the complex value a n is a combination of the IR transition dipole moments and Raman polarisability tensors of the molecule. The physical meaning and role of those fundamental parameters are exhaustively detailed in recent publications covering both a classical point of view [27] and advanced quantum formalism [50]. For the fitting of the set of SFG data, we used, for all spectra fitting procedure, the known fixed fit parameters for the SFG spectrum at 523.5 nm.…”

“…In a general way, whatever the probed scale, 2C-SFG spectroscopy gives access to intramolecular vibronic couplings [10][11][12], molecule/substrate interactions [13][14][15][16] and molecule/nanostructure interactions [17][18][19][20][21][22][23][24][25][26]. Similar to most of the spectroscopy techniques from the nonlinear optics family [27], 2C-SFG spectroscopy works only with high-intensity laser sources. Here we need two high-intensity laser sources in the infrared (IR) and in the visible spectral ranges.…”

Spatial Dependence of the Dipolar Interaction between Quantum Dots and Organic Molecules Probed by Two-Color Sum-Frequency Generation Spectroscopy

“…ijk (ω vis , ω IR ), with {i, j, k} = {x, y, z}. Taking into account the planar geometry of the Prism/PhTES/QD interface, it is possible to reduce this tensor to only four components (zzz, xxz, xzx, zxx), which combine themselves into an effective second-order susceptibility [31,37,38]. Indeed, as calculated in Ref.…”

“…To evidence such a vibroelectronic correlation, we performed 2C-SFG spectroscopy on thick layers of QDs deposited on CaF 2 prisms. From the symmetry rules proper to second-order optical processes [31], 2C-SFG spectroscopy is actually surface-specific and then constitutes an ideal tool to study the interactions occurring at the interface between QDs and molecules, both immobilized on a solid substrate. Besides, CaF 2 prisms benefit from favorable Local Field correction factors (reflectivity) in ATR configuration (Figure 1a) as explained in Section 3.1.…”

Special Issue of Symmetry: “Recent Advances in Linear and Nonlinear Optics”

“…The symmetry sensitivity and the subsequent surface specificity of (non)linear optical techniques arise from the tensor structure of the dielectric response functions which relate the excitation electric field(s) with the polarization of matter [1]. Contrary to scalar functions describing isotropic phenomena, the mathematics of tensors conceptually enables the description of the response of matter in any direction (in 3D space) as a combination of different electric field contributions associated with different light beams and light polarization states.…”