The effect of extreme confinement on the nonlinear-optical response of quantum wires

This work focuses on understanding the nonlinear-optical response of a 1-D quantum wire embedded in 2-D space when quantum-size effects in the transverse direction are minimized using an extremely weighted delta function potential. Our aim is to establish the fundamental basis for understanding the effect of geometry on the nonlinear-optical response of quantum loops that are formed into a network of quantum wires. Using the concept of leaky quantum wires, it is shown that in the limit of full confinement, the sum rules are obeyed when the transverse infinite-energy continuum states are included. While the continuum states associated with the transverse wavefunction do not contribute to the nonlinear optical response, they are essential to preserving the validity of the sum rules. This work is a building block for future studies of nonlinear-optical enhancement of quantum graphs (which include loops and bent wires) based on their geometry. These properties are important in quantum mechanical modeling of any response function of quantum-confined systems, including the nonlinear-optical response of any system in which there is confinement in at leat one dimension, such as nanowires, which provide confinement in two dimensions

Monte Carlo Studies of the Intrinsic Second Hyperpolarizability

The hyperpolarizability has been extensively studied to identify universal properties when it is near the fundamental limit. Here, we employ the Monte Carlo method to study the fundamental limit of the second hyperpolarizability. As was found for the hyperpolarizability, the largest values of the second hyperpolarizability approaches the calculated fundamental limit. The character of transition moments and energies of the energy eigenstates are investigated near the second hyperpolarizability's upper bounds using the missing state analysis, which assesses the role of each pair of states in their contribution. In agreement with the three-level ansatz, our results indicate that only three states (ground and two excited states) dominate when the second hyperpolarizability is near the limit.Comment: 8 pages, 7 figure

Geometry-Controlled Nonlinear Optical Response of Quantum Graphs

We study for the first time the effect of the geometry of quantum wire networks on their nonlinear optical properties and show that for some geometries, the first hyperpolarizability is largely enhanced and the second hyperpolarizability is always negative or zero. We use a one-electron model with tight transverse confinement. In the limit of infinite transverse confinement, the transverse wavefunctions drop out of the hyperpolarizabilities, but their residual effects are essential to include in the sum rules. The effects of geometry are manifested in the projections of the transition moments of each wire segment onto the 2-D lab frame. Numerical optimization of the geometry of a loop leads to hyperpolarizabilities that rival the best chromophores. We suggest that a combination of geometry and quantum-confinement effects can lead to systems with ultralarge nonlinear response.Comment: To appear in J. Opt. Society of America

STUDYING THE ORIGIN OF THE NONLINEAR OPTICAL RESPONSE OF COMPLEX STRUCTURES USING MONTE CARLO SAMPLING

The field of nonlinear optics has been preoccupied with finding better materials that interact more efficiently with photons. Part of this effort has focused on understand- ing the fundamental concepts underlying light-matter interactions, the fruit of which has led to the theory of fundamental limits of the first and second hyperpolarizabil- ities. Based on this theory, the nonlinear optical response of materials is found to be bounded. The comparison of this limit with experimental values of molecules re- vealed a gap between the two. Attempts to overcome this gap have deepened our understanding about how quantum systems interact with light, the properties of ma- terials that optimize its response, and have led to new numerical and experimental approaches.In this dissertation, we will review the theory of fundamental limits, its underlying assumptions and the numerical approaches that have been used to investigate the gap. We will discuss the guidelines that the theory provides for making better nonlinearoptical materials and based on them, we propose quantum graphs as a new class of nonlinear optical molecules that can be used to make artificial materials. The quantum mechanical properties of graphs are discussed in detail and the sum rules are used to verify the solutions to the Schro ̈dinger Equation. Starting from the one- electron model, we show that confinement, topology and geometry of graphs can have profound effects on their nonlinear response. We identify star graphs as the best motifs for building more complex graphs with larger nonlinear response.We then generalize the one-electron model to many-electrons model and employ the jellium model and the Pauli exclusion principle to study the effects of geometry and topology on the nonlinear optical response of electrons inside one-dimensional graph embedded in two dimensional space that represent quantum wires which can be studied experimentally

From quantum wires to quantum loops: enhancement of nonlinear optical properties

We investigate a system of 1-D quantum wires confined to a plane, as building blocks of quantum loops, to study the role of geometry on their nonlinear optical (NLO) properties