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

Abstract

The effects of small relativistic corrections to the off-resonant polarizability, hyperpolarizability, and second hyperpolarizability are investigated. Corrections to linear and nonlinear optical coefficients are demonstrated in the three-level ansatz, which includes corrections to the Kuzyk limits when scaled to semi-relativistic energies. It is also shown that the maximum value of the hyperpolarizability is more sensitive than the maximum polarizability or second hyperpolarizability to lowest-order relativistic corrections. These corrections illustrate how the intrinsic nonlinear-optical response is affected at semi-relativistic energies.

Role of Donor and Acceptor Substituents on the Nonlinear Optical Properties of Gold Nanoclusters

“…While gold is an element with strong relativistic effects, 113,114 we ignore these at this point due to lack of information on how many electrons to consider in relativistic systems. 115 Furthermore, thiolate-protected gold clusters would require including both non-relativistic and relativistic electron masses for the electrons, leading to additional complexity. Also, an 'apparent gap' between the measured first hyperpolarizability and the maximum first hyperpolarizability was noted.…”

Polynomial potentials determined from the energy spectrum and transition dipole moments that give the largest hyperpolarizabilities

“…This notion has led researchers to recently consider more exotic Hamiltonians in search of the limit. [27][28][29][30] In an attempt to understand the gap between the previously-reported largest hyperpolarizability from optimized scale-invariant potentials and the fundamental limit, we search for potentials that might yield the largest response. Our approach, which is independent of the others tried to date, seeks to find an approximate solution to the inverse problem of finding the potential that gives the largest values from the energy spectrum and transition dipole matrix.…”

Using excited states and degeneracies to enhance the electric polarizability and first hyperpolarizability

“…Note that the above calculations only hold for nonrelativistic systems. It has been predicted that the fundamental ground state limits decrease with first order relativistic corrections [34]. This is largely due to the relativistic transition moments being smaller than their nonrelativistic counterparts.…”