Nonlinear Optical Properties of Bacteriorhodopsin: Assignment of Second Order Hyperpolarizabilities of Randomly Oriented Systems Using Two-Photon Spectroscopy

Abstract We demonstrate that the second order hyperpolarizability of a randomly oriented molecule can be determined directly from two-photon spectroscopic measurements on the low-lying excited state manifold. Equations are derived which allow not only a determination of β, but also a determination of the error associated with the numerical method. We apply our two-photon technique to an analysis of the second order hyperpolarizability of light adapted bacteriorhodopsin. Our analysis of this protein in D2O at ambient temperature yields a value of β (= βxxx + (1/3)[βxyy + 2βyyx + βxzz + 2βzzx]) of (2250 ± 240) × 10−30 cm5/esu for a laser wavelength of 1.06μ (Nd:YAG fundamental). The large second-order nonlinear properties of bacteriorhodopsin are due primarily to the large change in dipole moment associated with excitation into the lowest-lying strongly allowed “1Bu +” π, π* state (Δμ = 13.5 ± 0.8 D). We derive an equation which estimates Ωβδ, the ratio of the number of second harmonic photons generated by ...