Diagrammatic theory of linear and nonlinear optics for composite systems

Abstract

We present a general formalism to model and calculate linear and nonlinear optical processes in composite systems, based on a graphical representation of light-matter interactions by loop diagrams associated to Feynman rules. Through this formalism, we recover the usual second-order response of a simple system by drawing four times less loop diagrams than doubled-sided ones. For composite systems, we introduce coupling hamiltonians between subsystems (for example a molecule and a substrate), graphically represented by virtual bosons. In this way, we enumerate all the diagrams describing the second-order response of the system and show how to select those relevant for the calculation of the molecular second-order hyperpolarizabilities under the influence of the substrate, including effective second-order contributions from the molecular third-order response. As it applies to all nonlinear processes and an arbitrary number of interacting partners, this representation provides a general frame for the calculation of the nonlinear response of arbitrarily complex systems.

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.…”

Sum-frequency generation at molecule-nanostructure interfaces from diagrammatic theory of nonlinear optics

“…where p = (p h ) and µ = (µ l ) are the dipole moments of the nanoparticle and the molecule, respectively. This interaction process, associated to the coupling constant h,l W lh (ω, R) µ l ab p h mn , is in principle represented on the diagrams by a 4-particle vertex [21]. This interaction vertex is equivalently and conveniently represented by the exchange of a virtual boson (here, a virtual photon) from one loop to the other through two 3-particle vertices.…”

“…The ad hoc models developed to account for such mechanisms do not share any common theoretical foundation [9,[13][14][15][16][17][18][19][20]. In order to fill this gap, we have established in a previous paper [21] a general formalism to represent elementary linear and nonlinear optical response functions by loop diagrams connected to the incoming (i.e. visible and infrared) and generated (i.e.…”

“…molecules, substrate, nano-objects), this diagrammatic representation is very well suited to accounting for the interactions between the subsystems. Representing each subsystem by its own loop and defining their mutual interaction hamiltonian, it becomes possible to draw all the allowed diagrams involving new matter-matter vertices and to calculate them by following twelve Feynman rules [21] (recalled in Ref. [22], section 1.4).…”

“…It is hard a task to model or predict the amplitude of such an amplification since it depends on the optoelectronic response of the substrate. The resulting second-order hyperpolarizability is often described by (see [21], Appendix C):…”