Nonlinear Optical Response Functions Research Articles

An Exact Expression for Multidimensional Spectroscopy of a Spin‐Boson Hamiltonian

AbstractMultidimensional coherent spectroscopy is a powerful tool to characterize nonlinear optical response functions. Typically, multidimensional spectra are interpreted via a perturbative framework that straightforwardly provides intuition into the density matrix dynamics that give rise to specific spectral features. When the goal is to characterize system coupling to a thermal bath however, the perturbative formalism becomes unwieldy and yields less intuition. Here, an approach developed by Vagov et al. is extended to provide an exact expression for multidimensional spectra of a spin‐boson Hamiltonian up to arbitrary order of electric field interaction. The utility of this expression is demonstrated by modeling polaron formation and coherent exciton‐phonon coupling in quantum dots, which strongly agree with experiment.

Intramolecular O-H⋯S hydrogen bonding in threefold symmetry: Line broadening dynamics from ultrafast 2DIR-spectroscopy and ab initio calculations.

The dynamics of intramolecular hydrogen-bonding involving sulfur atoms as acceptors is studied using two-dimensional infrared (2DIR) spectroscopy. The molecular system is a tertiary alcohol whose donating hydroxy group is embedded in a hydrogen-bond potential with torsional C3-symmetry about the carbon-oxygen bond. The linear and 2DIR-spectra recorded in the OH-stretching region of the alcohol can be simulated very well using Kubo's line shape theory based on the cumulant expansion for evaluating the linear and nonlinear optical response functions. The correlation function for OH-stretching frequency fluctuations reveals an ultrafast component decaying with a time constant of 700 fs, which is in line with the apparent decay of the center line slopes averaged over absorption and bleach/emission signals. In addition, a quasi-static inhomogeneity is detected, which prevents the 2DIR line shape to fully homogenize within the observation window of 4 ps. The experimental data were then analyzed in more detail using a full ab initio approach that merges time-dependent structural information from classical molecular dynamics (MD) simulations with an OH-stretching frequency map derived from density functional theory (DFT). The latter method was also used to obtain a complementary transition dipole map to account for non-Condon effects. The 2DIR-spectra obtained from the MD/DFT method are in good agreement with the experimental data at early waiting delays, thereby corroborating an assignment of the fast decay of the correlation function to the dynamics of hydrogen-bond breakage and formation.

Iterative approach to arbitrary nonlinear optical response functions of graphene

Two-dimensional materials constitute an exciting platform for nonlinear optics with large nonlinearities that are tunable by gating. Hence, gate-tunable harmonic generation and intensity-dependent refraction have been observed in e.g. graphene and transition-metal dichalcogenides, whose electronic structures are accurately modelled by the (massive) Dirac equation. We exploit on the simplicity of this model and demonstrate here that arbitrary nonlinear response functions follow from a simple iterative approach. The power of this approach is illustrated by analytical expressions for harmonic generation and intensity-dependent refraction, both computed up to ninth order in the pump field. Moreover, the results allow for arbitrary band gaps and gating potentials. As illustrative applications, we consider (i) gate-dependence of third- and fifth-harmonic generation in gapped and gapless graphene, (ii) intensity-dependent refractive index of graphene up to ninth order, and (iii) intensity-dependence of high-harmonic generation.

Semiclassical Path Integral Calculation of Nonlinear Optical Spectroscopy.

Computation of nonlinear optical response functions allows for an in-depth connection between theory and experiment. Experimentally recorded spectra provide a high density of information, but to objectively disentangle overlapping signals and to reach a detailed and reliable understanding of the system dynamics, measurements must be integrated with theoretical approaches. Here, we present a new, highly accurate and efficient trajectory-based semiclassical path integral method for computing higher order nonlinear optical response functions for non-Markovian open quantum systems. The approach is, in principle, applicable to general Hamiltonians and does not require any restrictions on the form of the intrasystem or system-bath couplings. This method is systematically improvable and is shown to be valid in parameter regimes where perturbation theory-based methods qualitatively breakdown. As a test of the methodology presented here, we study a system-bath model for a coupled dimer for which we compare against numerically exact results and standard approximate perturbation theory-based calculations. Additionally, we study a monomer with discrete vibronic states that serves as the starting point for future investigation of vibronic signatures in nonlinear electronic spectroscopy.

Derivation of complex cubic response function to guide development of nonlinear optical molecular materials

Fahleson and Norman derive nonlinear optical response function and provide numerical examples featuring para-nitroaniline and neon, with results relevant for future X-ray free electron laser molecular materials studies.

Dielectrics in a time-dependent electric field: A real-time approach based on density-polarization functional theory

In the presence of a (time-dependent) macroscopic electric field the electron dynamics of dielectrics cannot be described by the time-dependent density only. We present a real-time formalism that has the density and the macroscopic polarization P as key quantities. We show that a simple local function of P already captures long-range correlation in linear and nonlinear optical response functions. Specifically, after detailing the numerical implementation, we examine the optical absorption, the second- and third-harmonic generation of bulk Si, GaAs, AlAs and CdTe at different level of approximation. We highlight links with ultranonlocal exchange-correlation functional approximations proposed within linear response time-dependent density functional theory framework.

Examining resonant inelastic spontaneous scattering of classical Laguerre-Gauss beams from molecules

This paper theoretically treats the spontaneous resonant inelastic scattering of Laguerre-Gauss (LG) beams from the totally symmetric vibrations of complex polyatomic molecules within the semi-classical framework. We develop an interaction Hamiltonian that accounts for the position of the molecule within the excitation beam to derive the effective differential scattering cross-section of a classical LG beam from a molecule using the frequency domain third order nonlinear optical response function. To gain physical insight into this scattering process, we utilize a model vibronic molecule to study the changes to this scattering process. For specific molecular parameters including vibrational frequency and relative displacement of the involved electronic states, this investigation shows that an incident LG beam asymmetrically enhances one of two participating excitation transitions causing modulation of the interference present in the scattering process. This modulation allows a pathway to coherent control of resonant inelastic scattering from complex, poly-atomic molecules. We discuss the possible application of this control to the resonant x-ray inelastic scattering (RIXS) of small poly-atomic molecules central to applications ranging from single molecule electronics to solar energy science.

Advancing Hierarchical Equations of Motion for Efficient Evaluation of Coherent Two-dimensional Spectroscopy

To advance hierarchical equations of motion as a standard theory for quantum dissipative dynamics, we put forward a mixed Heisenberg-Schrödinger scheme with block-matrix implementation on efficient evaluation of nonlinear optical response function. The new approach is also integrated with optimized hierarchical theory and numerical filtering algorithm. Different configurations of coherent two-dimensional spectroscopy of model excitonic dimer systems are investigated, with focusing on the effects of intermolecular transfer coupling and bi-exciton interaction.

Hierarchical Dynamics of Correlated System−Environment Coherence and Optical Spectroscopy

We propose an efficient construction of the hierarchical equations of motion formalism of quantum dissipation on the basis of the Padé spectrum decomposition of the Bose function and the multiple brownian oscillators decomposition of the environment spectral density. The related hierarchical Liouville space algebra for quantum dissipative mechanics is outlined in relation to the evaluation of nonlinear optical response functions. With the simulated transient pump-probe spectroscopy of model exciton systems, we demonstrate the correlated system-environment coherence by the present nonperturbative and non-markovian quantum dissipation theory.

Nonlinear Optical Response Functions of Mott Insulators Based on Dynamical Mean Field Approximation

We investigate the nonlinear optical susceptibilities of Mott insulators with the dynamical mean field approximation. The two-photon absorption (TPA) and the third-harmonic generation (THG) spectra are calculated, and the classification by the types of coupling to external fields shows different behavior from conventional semiconductors. The direct transition terms are predominant both in the TPA and THG spectra, and the importance of taking all types of interaction with the external field into account is illustrated in connection with the THG spectrum and dc Kerr effect. The dependences of the TPA and THG spectra on the Coulomb interaction indicate a scaling relation. We apply this relation to the quantitative evaluation and obtain results comparable to those of experiments.

Anomalous continuous-time random-walk spectral diffusion in coherent third-order optical response

Recursive relations are derived for nonlinear optical response functions of a two-level chromophore with stochastic frequency fluctuations described by a continuous-time random walk. Stationary ensembles are constructed and signatures of anomalous relaxation in the photon echo signal are discussed for a two state jump modulation with a power law waiting time density function psi(t) approximately t(-alpha-1). Stretched exponential decay of the photon echo signal is predicted for 0<alpha<1 and power law asymptotics for 1<alpha<2.

Linear and nonlinear optical polarizabilities in supramolecular aggregates: Effects of hydrogen bonding and dipolar interactions

We consider linear hydrogen halide chains, (HX) n , X=F, Cl and Br, with varying chain length, n, to compare the role of hydrogen bonding strengths in controlling the optical response functions of linear aggregates. We find that while for weakly H-bonded linear chains, the 1st hyperpolarizabilities ( β) increase with the increase in the number of monomers in the aggregates, for strong H-bonding species like HF chains, the β shows a remarkable contrast with a maximum at the small chain limit with reduction thereafter with increase in chain length. This behavior is compared with that of a pure dipolar aggregate like (CO) n . The weak H-bonded species follow the trends similar to that of such dipolar aggregates. Additionally, we have considered the H-bonded linear chains as bridges between two terminal components for charge-transfer molecular one-dimensional devices, NH 2–(HF) n –NO 2. In contrast to the traditional π-conjugated species, NH 2–(CH CH) n –NO 2, we find that such linear H-bonded chains have very poor charge-transfer abilities. We report that strong H-bonding by itself is a negative parameter for nonlinear optical response functions at the supramolecular level, although, the directional properties of the H-bonds can be utilized for material integration. We show that it is the long-range supramolecular forces together with H-bonding at the intermediate energy scale at certain special geometries, which brings in a favorable situation for better optoelectronic applications.

Self-consistent density matrix algorithm for electronic structure and excitations of molecules and aggregates

An ab initio density matrix algorithm for electronic structure computations of many-electron systems is proposed. The reduced single-electron density matrices are derived by mapping the density functional theory nonlinear optical response functions onto an effective multilevel system. These density matrices are then used as a zeroth order iteration into self-consistent equations whose solution should yield the exact energies and the complete set of (transition and diagonal) single-electron density matrices. Higher order (n electron) density matrices are not computed explicitly. The linear and nonlinear optical response functions may be obtained at a low computational cost. Application is made to constructing an exciton Hamiltonian for molecular aggregates using density matrices of isolated molecules, avoiding electronic structure calculations of the entire aggregate.

First-principles calculations of second-order optical response functions in chalcopyrite semiconductors

The calculation of nonlinear optical response functions is reviewed. Results for II–IV–V 2 and I–III–VI 2 materials are compared. Some interesting and surprising results are highlighted. A related family of wurtzite based structures is briefly discussed.

A simple model for the calculation of nonlinear optical response functions and femtosecond time-resolved spectra

A simple model is developed for the calculation of optical response functions for electronically nonadiabatic systems coupled to a heat bath. A phenomenological dissipation ansatz is suggested which describes the major bath-induced relaxation processes, namely excited-state population decay, optical dephasing, and vibrational relaxation. The model is constructed in such a way that it allows one to express the nonlinear response functions for a dissipative system in terms of those for the corresponding bath-free system. The explicit formulas for the third order response functions are given. Several special cases are considered for which the evaluation of the response functions simplifies considerably. To illustrate the performance and validity of the theory, the response functions have been used for the calculation of time and frequency gated spontaneous emission spectra. The time-dependent spectra derived from the model have been compared with those calculated (i) for the standard damped harmonic oscillator model and (ii) for a model nonadiabatic electron-transfer system with Redfield theory. It is concluded that the present model provides qualitatively correct response functions and, therefore, may be useful for the interpretation of observed time-resolved spectra.

SiON films deposited on Si(111) substrates—new promising materials for nonlinear optics

Experimental measurements of the phototransparency stimulated by the YAG–Nd laser ( λ=1.06 μm) in the SiON films deposited on the Si<111> crystalline surfaces show essential dependence on the ratio between the nitrogen and oxygen (N/O) content. Dependencies of the phototransparency on the chemical content, delaying time, pressure and temperature demonstrate essential sensitivity to the N/O ratio. All of the data show that the photoinduced changes in the SiON–Si<111> are caused by both linear and nonlinear optical response function contributions and can be used for non-destructive diagnostic of the film content and thickness. To understand the physics of the observed phenomena, we perform detailed theoretical ab initio molecular dynamic simulations on the ground of the norm-conserving non-local pseudopotential method that give possibility to explain the observed dependencies and to predict the possible changes of the optical constants in the desired directions.

Linear and non-linear optical properties of periodic and antiperiodic dimers

The analytic expressions for the linear and non-linear optical response functions of a two-sites Holstein-Hubbard model with periodic and antiperiodic boundary conditions are obtained. They show that an antiperiodic dimer can be used to describe the main features of the linear optical spectrum of a half-filled dimerized mono-dimensional system. One also finds that the description of the non-linear optical properties are appropriate only for systems with the 2A g above the 1B u since only the ionic contribution to the A g state can be described.

Nonlinear optical response functions for a chromophore with linear and quadratic electron–vibration coupling

Two models for the third-order response function of a two-electronic level chromophore are investigated. The first assumes an excited state vibrational Hamiltonian whose phonon modes exhibit both linear and diagonal quadratic electron–phonon coupling. Impulsive stimulated photon echoes are calculated for this model. The second assumes linear electron–phonon coupling including vibrational relaxation and pure electronic dephasing. Impulsive two-pulse photon echo signals and their dependence on temperature and electron–phonon coupling strength are calculated for this model. The initial fast nonexponential (free-induction) decay due to all multiphonon transitions, quantum beats and the slow decay component due to the zero-phonon line (pure electronic dephasing) are identified and correlated with features of the single-site absorption spectrum whose relationship to the hole burned spectrum is well understood. Pure electronic dephasing associated with the zero-phonon line contributes to the decay of the quantum beats. This contribution may be non-negligible at high temperatures in certain systems. An application is made to the special pair absorption band of the bacterial reaction center.

First-Principles Calculations of Nonlinear Optical Response Functions in Semiconductors

ABSTRACTWe present our implementation of the length-gauge formalism of Sipe and coworkers (Phys. Rev. B 48, 11705 (1993); ibid 52, 14636 (1995)) using the linearized muffin-tin orbital (LMTO) method and discuss its application to the calculation of second order response functions. The importance of gap corrections beyond LDA is discussed. As primary application, we discuss the second harmonic generation (SHG) coefficients of the SiC polytypes and of the chalcopyrites of both the II-IV-V2 and I-III-VI2 families. These examples illustrate the relation of the second order response function to the modification of the crystal structure and chemical substitutions.

Heterodyne-detected stimulated photon echo: applications to optical dynamics in solution

Heterodyne detection of the stimulated photon echo (HSPE) is discussed and applied to explore molecular solvation dynamics. With this technique the in-phase and in-quadrature parts of the induced transient nonlinear polarization can be time-gated. A third-order perturbative description of the HSPE is presented, which shows that the transient polarization provides direct information on the real and imaginary components of the nonlinear optical response functions of the system. In the spectral diffusion limit and for impulsive excitation conditions, analytical expressions for the HSPE signal are derived and model calculations are presented. This novel technique is applied to a nonlinear optical study of the dye molecule DTTCI dissolved in ethylene glycol. Several effects are analyzed in detail as, for instance, the intriguing interference effect between the conventional and virtual echo contributions to the total HSPE signal. Furthermore, it is shown that from HSPE measurements the instantaneous frequency of the emitted (nonlinear polarization induced) signal can be derived and that its time-dependent shift projects directly onto the dynamical Stokes shift and the energy reorganization process of the coupled solute–solvent complex. It will also be shown that the experimental data can be simulated using the multimode Brownian oscillator model.