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Mark G. Kuzyk

Publications and source records attributed to Mark G. Kuzyk.

69 records · Page 4Linked to original sources
arXiv2008

A general theory of inhomogeneous broadening for nonlinear susceptibilities: polarizability and hyperpolarizability

While nonlinear optical spectroscopy is becoming more commonly used to study the excited states of nonlinear-optical systems, a general theory of inhomogeneous broadening is rarely applied in lieu of either a simple Lorentzian or Gaussian model. In this work, we generalize all the important linear and second-order nonlinear susceptibility expressions obtained with sum-over state quantum calculations to include Gaussian and stretched Gaussian distributions of Lorentzians. We show that using the correct model to analyze experiments that probe a limited wavelength range can be critical and that this theory is better able to fit the subtle spectral features - such as the shoulder region of a resonance - when both models produce qualitatively similar responses.

physics.optics↗
arXiv2008

A general theory of inhomogeneous broadening for nonlinear susceptibilities: the second hyperpolarizability

A general theory of inhomogeneous broadening is rarely applied to nonlinear spectroscopy in lieu of either a simple Lorentzian or Gaussian model. In this work, we generalize all the important third-order nonlinear susceptibility expressions obtained with sum-over state quantum calculations to include Gaussian and stretched Gaussian distributions of Lorentzians. This theory gives a better fit to subtle spectral features - such as the shoulder of the electroabsorption peak, and is a more accurate tool for determining transition moments from spectroscopy experiments.

physics.optics↗
arXiv2007

Optical limiting using Laguerre-Gaussian beams

We demonstrate optical limiting using the self-lensing effect of a higher-order Laguerre-Gaussian beam in a thin dye-doped polymer sample, which we find is consistent with our model using Gaussian decomposition. The peak phase shift in the sample required for limiting is smaller than for a fundamental Gaussian beam with the added flexibility that the nonlinear medium can be placed either in front of or behind the beam focus.

physics.optics↗
arXiv2007

Effect of a thin optical Kerr medium on a Laguerre-Gaussian beam

Using a generalized Gaussian beam decomposition method we determine the propagation of a Laguerre-Gaussian beam that has passed through a thin nonlinear optical Kerr medium. The orbital angular momentum per photon of the beam is found to be conserved while the component beams change. As an illustration of applications, we propose and demonstrate a z-scan experiment using an $LG_0^1$ beam and a dye-doped polymer film.

physics.optics↗
arXiv2007

Monte Carlo Studies of the Fundamental Limits of the Intrinsic Hyperpolarizability

The off-resonant hyperpolarizability is calculated using the dipole-free sum-over-stats expression from a randomly chosen set of energies and transition dipole moments that are forced to be consistent with the sum rules. The process is repeated so that the distribution of hyperpolarizabilities can be determined. We find this distribution to be a cycloid-like function. In contrast to variational techniques that when applied to the potential energy function yield an intrinsic hyperpolarizability less than 0.71, our Monte Carlo method yields values that approach unity. While many transition dipole moments are large when the calculated hyperpolarizability is near the fundamental limit, only two excited states dominate the hyperpolarizability - consistent with the three-level ansatz.

physics.optics↗
arXiv2007

Studies on optimizing potential energy functions for maximal intrinsic hyperpolarizability

We use numerical optimization to study the properties of (1) the class of one-dimensional potential energy functions and (2) systems of point charges in two-dimensions that yield the largest hyperpolarizabilities, which we find to be within 30% of the fundamental limit. We investigate the character of the potential energy functions and resulting wavefunctions and find that a broad range of potentials yield the same intrinsic hyperpolarizability ceiling of 0.709.

physics.optics↗
arXiv2006

Pushing the hyperpolarizability to the limit

We use numerical optimization to find a one-dimensional potential energy function that yields the largest hyperpolarizability, which we find is within 30% of the fundamental limit. Our results reveal insights into the character of the potential energy functions and wavefunctions that lead to the largest hyperpolarizability. We suggest that donor-acceptor molecules with a conjugated bridge with many sites of reduced conjugation to impart conjugation modulation may be the best paradigm for making materials with huge hyperpolarizabilities that approach the fundamental limit.

physics.optics↗
arXiv2006

An optically activated cantilever using photomechanical effects in dye-doped polymer fibers

We report on what we believe is the first demonstration of an optically activated cantilever due to photomechanical effects in a dye-doped polymer optical fiber. The fiber is observed to bend when light is launched off-axis. The displacement angle monotonically increases as a function of the distance between the illumination point and the fiber axis, and is consistent with differential light-induced length changes. The photothermal and photo-reorientation mechanisms, each with its own distinct response time, are proposed to explain the observed time dependence. The measured degree of bending is consistent with a model that we have proposed which includes coupling between photoisomerization and heating. Most importantly, we have discovered that at high light intensity, a cooperative release of stress results in cis-to-trans isomerization that yields a large and abrupt length change.

physics.optics↗
arXiv2006

The Ultimate Fundamental Limits of Nonlinear-Optical Phenomena

Using sum rules and a new dipole-free sum-over-states expression, we calculate the fundamental limits of the dispersion of the real and imaginary parts of all electronic nonlinear-optical susceptibilities. As such, these general results can be used to study any nonlinear optical phenomena at any wavelength, making it possible to push both applications and our understanding of such processes to the limits. These results reveal the ultimate constraints imposed by nature on our ability to control and use light.

physics.optics↗
arXiv2006

The Effects of Geometry on the Hyperpolarizability

Extensive studies in the past have focused on precise calculations of the nonlinear-optical susceptibility of thousands of molecules. In this work, we use the broader approach of considering how geometry and symmetry alone play a role. We investigate the nonlinear optical response of potential energy functions that are given by a superposition of force centers (representing the nuclear charges) that lie in various planar geometrical arrangements. We find that for certain specific geometries, such as an octupolar-like molecule with donors and acceptors of varying strengths at the branches, the hyperpolarizability is near the {\em fundamental limit}. In these cases, the molecule is observed to be well approximated by a three-level model - consistent with the three-level ansatz previously used to calculate the {\em fundamental limits}. However, when the hyperpolarizability is below the {\em apparent limit} (about a factor of thirty below the {\em fundamental limit}) the system is no longer representable by a three-level model; where both two-level and a many-state models are found to be appropriate, depending on the symmetry.

physics.optics↗
arXiv2005

Compact Sum-Over-States Expression without Dipolar Terms for Calculating Nonlinear Susceptibilities

Using sum rules, the dipolar terms can be eliminated from the commonly-used sum-over-states (SOS) expression for nonlinear susceptibilities. This new dipole-free expression is more compact, converges to the same results as the common SOS equation, and is more appropriate for analyzing certain systems such as octupolar molecules. The dipole-free theory can be used as a tool for analyzing the uncertainties in quantum calculations of susceptibilities, can be applied to a broader set of quantum systems in the three-level model where the standard SOS expression fails, and more naturally leads to fundamental limits of the nonlinear susceptibilities.

physics.optics↗
arXiv2005

Fundamental Limits of the Dispersion of the Two-Photon Absorption Cross-Section

We rigorously apply the sum rules to the sum-over-states expression to calculate the fundamental limits of the dispersion of the two-photon absorption cross-section. A comparison of the theory with the data suggests that the truncated sum rules in the three-level model give a reasonable fundamental limit. Our ansatz that the two photon absorption cross-section near the limit must have only three dominant statesis is supported by a rigorous analytical calculation that the resonant term gets smaller as more states are added. We also find that the contributions of the non-explicitly resonant terms can not be neglected when analyzing real molecules with many excited states, even near resonance. However, puzzling as it may be, extrapolating an off-resonant result to resonance using only the resonant term of the three-level model is shown to be consistent with the exact result. In addition, the off-resonant approximation is shown to scale logarithmically when compared with the full three-level model. This scaling can be used to simplify the analysis of measurements. We find that existing molecules are still far from the fundamental limit; so, there is room for improvement. But, reaching the fundamental limit would require precise control of the energy-level spacing, independently of the transition dipole moments -- a task that does not appear possible using today's synthetic approaches. So, we present alternative methods that can still lead to substantial improvements which only require the control of the transition moment to the first excited state. While it is best to normalize measured two photon absorption cross-sections to the fundamental limits when comparing molecules, we show that simply dividing by the square of the number of electrons per molecule yields a good metric for comparison.

physics.optics↗
arXiv2005

Truncated Sum Rules and their use in Calculating Fundamental Limits of Nonlinear Susceptibilities

Truncated sum rules have been used to calculate the fundamental limits of the nonlinear susceptibilities; and, the results have been consistent with all measured molecules. However, given that finite-state models result in inconsistencies in the sum rules, it is not clear why the method works. In this paper, the assumptions inherent in the truncation process are discussed and arguments based on physical grounds are presented in support of using truncated sum rules in calculating fundamental limits. The clipped harmonic oscillator is used as an illustration of how the validity of truncation can be tested; and, several limiting cases are discussed as examples of the nuances inherent in the method.

physics.optics↗