Using fundamental principles to understand and optimize nonlinear-optical materials

Abstract

Our approach to the problem of understanding the nonlinear-optical response of a material focuses on fundamental concepts, which are exact and lead to broad results that encompass all material systems. For example, one can calculate precisely and without approximation the fundamental limit of the efficiency of any optical phenomenon. Such limits, in turn, when built into a scale-invariant figure of merit can be used to determine what makes a material optimal for maximizing a desired property, such as its nonlinear-optical response. However, since the results are broad and general (for example, fundamental guidelines for making better quantum systems may demand a particular shape of an electron cloud or energy level spacing), the difficulty arises in implementing such fine tuning using the approaches available to the synthetic chemist or nanotechnologist. Undoubtedly, an intimate interplay of empirical and fundamental approaches will need to be applied to the problem of optimizing molecules and materials. Much of the work in the field of nonlinear optics has by necessity focused on empirical approaches. Our work focuses on the fundamental approach, which is beginning to bear fruit in providing practical guidelines for making new materials. This paper reviews progress made over the last decade.

Dressed Quantum Graphs With Optical Nonlinearities Approaching the Fundamental Limit

“…This effect appears to be related to the universal result that all graphs whose β are calculated by starting with a Hamiltonian and a potential of any kind have β xxx ≤ 0.7089, the potential optimization limit 29,33 . The sum rules do not constrain β xxx from equaling unity, as has been shown in a Monte Carlo calculation that starts with the energies and transition moments (top-down), rather than with a Hamiltonian and its energies and states (bottom-up) 52 . But the curve is a compelling reminder that there is some physical constraint at work for conservative, self-adjoint Hamiltonian The variation of βxxx with g is shown on the right axis.…”

Lowest-order relativistic corrections to the fundamental limits of nonlinear-optical coefficients

“…27-29 reduce to the off-resonant, three-level model calculated from the non-relativistic TRK sum rules. [17,19] The polarizability, hyperpolarizability and second hyperpolarizability in the non-relativistic limit are given by…”

“…The oscillator strength is limited by the nonrelativistic kinetic energy of a free particle, where field interactions from a four-potential do not contribute to the maximum oscillator strength. The intrinsic values of the hyperpolarizability and second hyperpolarizability in the non-relativistic limit have been studied in great detail, [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] where there is a looming gap between the measured/calculated values and the fundamental limits in the non-relativistic regime.…”

Classical model of the upper bounds of the cascading contribution to the second hyperpolarizability

“…[29][30][31] Here, E i0 = E i − E 0 is the energy difference between the i th excited state and the ground state, x ij is the transition moment between state i and state j, and e is the electron charge. The primed sums in Equations 22-24 exclude the ground state from the summation.…”

“…[30] Since we are interested in studying the limit when the direct and cascading contributions are large, we represent all of the susceptibilities using three states, i.e. the ground state and first two excited states.…”