Perturbation theory and the two-level approximation:A corollary and critique

This analysis addresses the use of a two-level approximation to simplify expressions derived from perturbation theory. It is shown that the limitations of validity for the emergent results are more stringent than is commonly understood, being equivalent in effect to the adoption of a more extensive approximation - one that significantly undermines the perturbative origin of those expressions. Effectively truncating the completeness relation, a series of interconnected operator relations comes into play, some with physically untenable consequences. A new theorem on the expectation values of operator functions highlights additional constraints upon any molecule modelled as a two-level system. © 2010 Elsevier B.V. All rights reserved

Limitations and improvements upon the two-level approximation for molecular nonlinear optics

When parametric nonlinear processes are employed in the cause of efficient optical frequency conversion, the media involved are generally subjected to substantially off-resonant input radiation. As such, it is usually only electronic ground states of the conversion material that are significantly populated; higher levels are engaged only in the capacity of virtual states, and it is frequently assumed that just one such state dominates in determining the response. Calculating the nonlinear optical susceptibilities of molecules on this basis, excluding all but the ground and one excited state in a sum-over-states formulation, signifies the adoption of a two-level model, a technique that is widely deployed in the calculation and analysis of nonlinear optical properties. The two-level model offers tractable and physically simple representations of molecular response, including wavelength dependence; it is also the origin of the widely applied 'push-pull' approach to designing optically nonlinear chromophores. By contrast, direct ab initio calculations of optical susceptibility are commonly frustrated by a complete failure to determine such dispersion features. However, caution is required; the two-level model can deliver potentially misleading results if it is applied without regard to the criteria for its validity, especially when molecular excited states are significantly populated. On the basis of a precise, quantum electrodynamical basis for the theory, we explore in detail why there are grounds for questioning the general validity of two-level calculations in nonlinear optics; we assess the criteria for high frequency conversion efficiency and provide a new graphical method to assist in determining the applicability of a two-level model for hyperpolarizability calculations. Lastly, this paper also explores the applicability and detailed conditions for the two-level model for electronically excited molecules, identifying problematic results and providing tractable methods for improving the accuracy of calculations on real molecule-photon interactions

Nonlinear Temporal Dynamics of Strongly Coupled Quantum Dot-Cavity System

We theoretically analyze and simulate the temporal dynamics of strongly coupled quantum dot-cavity system driven by a resonant laser pulse. We observe the signature of Rabi oscillation in the time resolved response of the system (i.e., in the numerically calculated cavity output), derive simplified linear and non-linear semi-classical models that approximate well the system's behavior in the limits of high and low power drive pulse, and describe the role of quantum coherence in the exact dynamics of the system. Finally, we also present experimental data showing the signature of the Rabi oscillation in time domain

Mobility of solitons in one-dimensional lattices with the cubic-quintic nonlinearity

We investigate mobility regimes for localized modes in the discrete nonlinear Schr\"{o}dinger (DNLS) equation with the cubic-quintic onsite terms. Using the variational approximation (VA), the largest soliton's total power admitting progressive motion of kicked discrete solitons is predicted, by comparing the effective kinetic energy with the respective Peierls-Nabarro (PN) potential barrier. The prediction is novel for the DNLS model with the cubic-only nonlinearity too, demonstrating a reasonable agreement with numerical findings. Small self-focusing quintic term quickly suppresses the mobility. In the case of the competition between the cubic self-focusing and quintic self-defocusing terms, we identify parameter regions where odd and even fundamental modes exchange their stability, involving intermediate asymmetric modes. In this case, stable solitons can be set in motion by kicking, so as to let them pass the PN barrier. Unstable solitons spontaneously start oscillatory or progressive motion, if they are located, respectively, below or above a mobility threshold. Collisions between moving discrete solitons, at the competing nonlinearities frame, are studied too.Comment: 12 pages, 15 figure

Higher-order triplet interaction in energy-level modeling of excited-state absorption for an expanded porphyrin cadmium complex

Recent measurements of transmission versus fluence for a methanol-solvated asymmetric pentaazadentate porphyrin-like (APPC) cadmium complex, [(C6H4-APPC)Cd]Cl, showed the limitations of current energy-level models in predicting the transmission behavior of organic reverse saturable absorbers at fluences greater than 1 J/cm². A new model has been developed that incorporates higher-order triplet processes and accurately fits both nanosecond and picosecond transmission-versus-fluence data. This model has provided the first known determination of a higher triplet excited-state absorption cross section and lifetime for an APPC complex and also described a previously unreported feature in the transmission-versus-fluence data. The intersystem crossing rate and the previously neglected higher triplet excited-state absorption cross section are shown to govern the excited-state population dynamics of methanol-solvated [(C6H4-APPC)Cd]Cl most strongly at more-practical device energies

Transverse Patterns in Nonlinear Optical Resonators

The book is devoted to the formation and dynamics of localized structures (vortices, solitons) and extended patterns (stripes, hexagons, tilted waves) in nonlinear optical resonators such as lasers, optical parametric oscillators, and photorefractive oscillators. The theoretical analysis is performed by deriving order parameter equations, and also through numerical integration of microscopic models of the systems under investigation. Experimental observations, and possible technological implementations of transverse optical patterns are also discussed. A comparison with patterns found in other nonlinear systems, i.e. chemical, biological, and hydrodynamical systems, is given. This article contains the table of contents and the introductory chapter of the book.Comment: 37 pages, 14 figures. Table of contents and introductory chapter of the boo