QM4E.1.pdf CLEO:2013 Technical Digest © OSA 2013 Dispersion of the Electronic Third-Order Nonlinearity of Symmetric Molecules Honghua Hu 1 , Trenton R. Ensley 1 , Marcus Seidel 1 , Manuel R. Ferdinandus 1 , Matthew Reichert 1 , Olga V. Przhonska 1,2 , David J. Hagan 1,3 , Eric W. Van Stryland 1,3 1 CREOL & FPCE, The College of Optics and Photonics, University of Central Florida, Orlando, FL 32816 2 Institute of Physics, National Academy of Sciences, Prospect Nauki 46, Kiev, 03028, Ukraine 3 Department of Physics, University of Central Florida, Orlando, FL 32816 Email address: ewvs@creol.ucf.edu Abstract: Using a dual-arm Z-scan to increase the signal-to-noise, we measure the dispersion of the electronic third-order nonlinearity of symmetric polymethines and squaraines and find good agreement with the essential-state model including CS 2 . OCIS codes: (190.0190) Nonlinear optics; (190.4400) Nonlinear optics, materials; (300.6420) Spectroscopy, nonlinear. 1. Introduction Understanding the dispersion of nonlinear refraction (NLR) and two-photon absorption (2PA) is the key factor in our ability to tailor molecules for applications [1]. In molecular level, these two aspects of the nonlinearity can be characterized by the NLR and 2PA cross section (δ NLR [2] and δ 2PA ), in Göppert-Mayer (GM, i.e. 10 -50 cm 4 ∙s∙molecule -1 ∙photon -1 ), corresponding to the real and imaginary part of the second hyperpolarizability γ respectively. γ can be converted from δ NLR and δ 2PA via the equation Re(γ) = 2.0×10 -23 n 0 2 δ NLR Ȝ 2 /f 4 and Im(γ) = 1.0×10 -23 n 0 2 δ NLR Ȝ 2 /f 4 , where n 0 is the linear refractive index, Ȝ is the wavelength in m, and f is the local field correction defined as (n 0 2 +2)/3. The most widely-adopted theory to describe the electronic nonlinearity of organic molecules, is the “sum over states” model [3], which takes into account the ground state and all possible excited states and their corresponding transition dipole moments. Centro-symmetric molecules possess zero permanent dipole moment and have ground and excited states of relatively “pure” even (gerade, g) or odd (ungerade, u) spatial symmetry, labeled as A g and B u , respectively. Due to the selection rules, the two-photon transition is only allowed between the ground state and a 2PA final state of the same even symmetry, with an excited state of odd symmetry as an intermediate state. Hence, to describe the third-order nonlinearity of centro-symmetric molecules, a minimum of three states (so called essential-state model) needs to be considered [4,5]. Using a dual-arm Z-scan technique, we measured the 2PA spectrum and the dispersion of the electronic nonlinear refractive index (n 2 ) of several symmetric molecules, and used the essential-state model to fit the spectra and obtain their molecular parameters. 2. Essential-State Model The frequency () dependence of γ of a symmetric molecule, is mainly determined by the following resonant terms         (   )  ቀ    ቁ     (   )  (1) where    is the transition energy and linewidth between the ground (g) to the intermediate state (e), or to the 2PA final state (e’), while ȝ ge and ȝ ee’ are the ground and excited-state transition dipole moments, respectively. The first term is usually called the two-photon term (T-term), and the second term is called the negative term (N- term) due to its negative contribution to the overall γ, corresponding to the 1PA resonance term between the ground and intermediate state. For a molecule with multiple 2PA final states sharing the same intermediate state, each 2PA state has a T-term, and γ is the summation of these T-terms minus the N-term. Based on Eq. (1), the magnitude and sign of γ, more especially its real part connecting to NLR, is the competing result of T- and N- terms, related to the magnitude of the transition dipole moments and detuning energies, determined by the relative positions between the intermediate state and 2PA final states. 3. Results and Discussion Polymethine and squaraine molecules have large resonant nonlinearities due to strong delocalization of the π- electrons along their conjugated chain leading to large ȝ ge ; however, for low molarity solutions, the n 2 at photon energies below the 2PA resonance is small, making it difficult to distinguish the n 2 of the solute molecule from the dominating background n 2 of the solvent. To overcome this difficulty, we recently developed a dual-arm (DA) Z- scan [6], which simultaneously scans solution and pure solvent on two equalized Z-scan arms to discriminate their nonlinear signal difference. This technique greatly suppresses the measurement uncertainty induced by fluctuations of the excitation source (i.e. pulse energy, beam pointing instabilities, beam size and pulsewidth changes, etc), leading to nearly an order of magnitude increase in sensitivity. We were able to measure the n 2 of solutes of -