Quadratic electro-optic effects in bacteriorhodopsin: Measurement of γ(−ω;0,0,ω) in dried gelatin thin films

Abstract

Quadratic electro-optic effects (dc or low frequency Kerr effect) of bacteriorhodopsin dispersed in dried gelatin thin films are examined in the near resonance region at three wavelengths: 633, 647, and 676 nm. The films show relatively large quadratic electro-optic effects compared to other molecular dispersed systems. The purple membrane is fixed within the polymerized gelatin matrix, and we show that the electronic contribution to γ dominates over possible orientational contributions. At 676 nm, the quadratic electro-optic coefficient s1133(−ω;0,0,ω) is 6.7×10−20 m2/V2 and the third order nonlinear susceptibility χ1133(3)(−ω;0,0,ω) is 7.0×10−13 cm4 statCoulomb−2, with both values obtained for a protein concentration of 6.9×1018 cm−3. The orientationally averaged second molecular hyperpolarizability 〈γ(−ω;0,0,ω)〉 determined from the quadratic electro-optic coefficients at 676 nm assuming an Onsager ellipsoidal local field factor is (10.8±5.1)×10−32 cm7 statCoulomb−2 [(1.34±0.63)×10−56 F3 m4 C−2]. The 〈γ(−ω;0,0,ω)〉 value increases roughly tenfold when the probe wavelength is decreased to 633 nm. The behavior of γ(−ω;0,0,ω), when fit to a two-state model, predicts that γ(−ω;0,0,ω) is strongly enhanced via type III processes. Thus, the magnitude of γ(−ω;0,0,ω) is dominated by a term (Δμ102×μ102)/(ω10−ω)3, where Δμ10 is the change in dipole moment, μ10 is the transition moment, and ω10 is the transition energy of the lowest-lying allowed 1Bu*+-like π,π* state. We calculate that Δμ10 is 12.8±1.2 D, in good agreement with previous Stark and two-photon experimental values. Time-dependent Hartree–Fock methods based on the MNDO Hamiltonian yield reasonable agreement with experiment, underestimating γ(−ω;0,0,ω) by factors of only 2–4, with the error increasing as the frequency approaches resonance.