Mark G. Kuzyk

Using fundamental principles to understand and optimize nonlinear-optical materials

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.

Modulated conjugation as a means for attaining a record high intrinsic hyperpolarizability

We report on a series of chromophores that have been synthesized with a modulated conjugation path between donor and acceptor. Hyper-Rayleigh scattering measurements of the best molecule show an enhanced intrinsic hyperpolarizability that breaches the apparent limit of all previously studied molecules.

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. Furthermore, we posit that the two-photon absorption cross section near the limit must have only three dominant states, so by default, the three-level model is appropriate. This ansatz 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 nonexplicitly resonant terms cannot 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 todays 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.

Guest‐host polymer fibers for nonlinear optics

We report on the fabrication of poly(methyl methacrylate) (PMMA) nonlinear optical fibers with dye‐doped cores. The dye‐doped cores have an elevated refractive index that defines a waveguiding region with a large third‐order susceptibility and with single‐mode dimensions. The measured third‐order susceptibility of a squarylium‐doped PMMA film material and the measured optical loss of the dye‐doped fiber core results in a figure of merit that is suitable for all‐optical device applications at λ=1.3 μm. The impact of further improvements in PMMA loss and chromophore nonlinearity are also discussed.

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 wave functions 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.

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.

Single-mode nonlinear-optical polymer fibers

We report on the successful demonstration of a single-mode polymer-optical fiber with an 8-µm-diameter nonlinear-optical core composed of a dye-chromophore-doped polymer. Both solid-solution cores and copolymer cores were successfully fabricated. Using an imaging system, we show that the far-field transverse light pattern is that of a single-mode guide. We find that the loss at 1064 nm for the single-mode fiber is approximately 0.2 dB/cm and that it preserves polarization to better than 99.8%/cm.

Fabrication and mechanical behavior of dye-doped polymer optical fiber

The purpose of this article is to study the materials physics behind dye-doped polymethyl metharcylate (PMMA) that is important for the optical fiber drawing process. We report effects of the fabrication process on the mechanical properties of the final fiber. The qualitative degree of polymer chain alignment is found to increase with the drawing force, which in turn decreases with the drawing temperature and increases with the drawing ratio. The chain alignment relaxes when the fibers are annealed at 95 °C with a commensurate decrease in fiber length and increase in diameter. The annealed fiber has higher ductility but lower strength than the unannealed fiber. Both the yield and tensile strengths are dependent on the strain rate. The relationship between tensile strength, σb, and fiber diameter, d, is found empirically to be σb∝d−0.5. The yield strength appears to be less sensitive to the fiber diameter than the tensile strength. For PMMA doped with disperse red 1 azo dye, the yield strength, tensile str...

Measurement of ultrafast optical nonlinearities using a modified Sagnac interferometer

A method for the measurement of fast, intensity-dependent refractive-index changes with the use of a modified Sagnac ring interferometer is presented. The measurement is not degraded by slowly responding background index changes. Nonlinear refractive-index changes in an undoped silicon wafer, and in poly-bis toluene sulfonate polydiacetylene and dye-doped polymethyl methacrylate waveguides, were measured with the use of a cw mode-locked Nd:YAG laser.

Modulated conjugation as a means of improving the intrinsic hyperpolarizability.

A new strategy for optimizing the first hyperpolarizability based on the concept of a modulated conjugated path in linear molecules is investigated. A series of seven novel chromophores with different types of conjugated paths were synthesized and characterized. Hyper-Rayleigh scattering experiments confirmed that modulated conjugation paths that include benzene, thiophene, and/or thiazole rings in combination with azo and/or ethenyl linkages between dihydroxyethylamino donor groups and various acceptor groups result in enhanced intrinsic hyperpolarizabilities that exceed the long-standing apparent limit for two of the chromophores. The experimental results are analyzed and interpreted in the context of quantum limits, which show that conjugation modulation of the bridge in donor/acceptor molecules simultaneously optimizes the transition moments and the energy-level spacing.