Nonresonant Third-order Susceptibility Research Articles

Measurement of field-free alignment of jet-cooled molecules by nonresonant femtosecond degenerate four-wave mixing

A femtosecond degenerate four-wave mixing (fs-DFWM) technique for probing the alignment of molecules is described. The rotational wave packet generated by a strong pump beam modulates the nonresonant third-order susceptibility of the gas and this modulation is observed using a noncollinear background-free setup. As a demonstration of the technique, we measure the alignment of a linear molecule (nitrogen), a symmetric top (benzene), and an asymmetric top (iodobenzene) in a supersonic jet. The measured signal is shown to agree well with calculations of the nonresonant third-order susceptibility from the solution of the time-dependent Schr\"odinger equation. The pump-DFWM measurement scheme can be used with dilute jet-cooled targets, allows arbitrary pump pulses to be used, and is rapid enough to be incorporated into a feedback optimization loop. The scheme can easily be made polarization-sensitive, indicating the possibility of measuring and optimizing three-dimensional alignment of asymmetric-top molecules.

Circumferences Lead to Enhancements of Nonresonant Third-Order Susceptibilities for Carbon Nanotube Bundles

Nonresonant enhancements of third-order susceptibility χ(3)(-ω; ω, ω, -ω) have been investigated for zigzag carbon nanotube (n,0) bundles (n = 5, 7, 11, 13, 8, 10, 14, 16) based on the energy band theory combined with the classic anharmonic oscillator model. The obtained results show that the (3) values increase as circumference of tube varies in the order of 5<7<11<13 and 8<10<14<16 for (n,0) tube bundles, respectively. The origination of the large third-order susceptibility is ascribed to the circumference effect of individual tube. The nonresonant third-order susceptibility is estimated to be about 10-6 esu in the axial direction of (16,0) tube bundles, and it is possible for a good candidate to make optical phase conjugate device.

Optical Properties of Cu Nanocrystalline-OPAA Composite Film

Optically transparent Cu nanocrystalline/OPAA composite film was successfully prepared by electrodepositing Cu into ordered porous anodic alumina (OPAA) template using constant voltage direct current technique. The morphology, structure, linear optical absorption, third-order optical nonlinearity and ultrafast dynamics of the Cu/OPAA composite were characterized by field emission scanning electron microscope (FESEM), transmission electron microscope (TEM). UV-Vis spectrophotometer, Z-scan technique and femtosecond pump-probe experiment. The results show that Cu nanoparicles have diameters of 40–50nm with face center cubic structure and disperse in the branched pores of the OPAA template, which induce a surface plasmon resonance (SPR) absorption at 584 nm. When the probe optical wavelength is far away from the SPR wavelength, Cu nanocrystalline/OPAA composite film possesses a character of light-induced absorption. When the probe optical wavelength is near the SPR wavelength, it possesses a photo-bleaching character. The composite film has a non-resonant third-order nonlinear susceptibility of 0.73×10 esu and a response time of 1.3 ps.

Highly efficient, thermally stable and optically transparent third-order nonlinear optical copolymers consisting of fluorene and quinoxaline/quinoline units

New fluorene-linked conjugated polyquinoxaline and polyquinoline possess adequate optical transparency, excellent thermal stability and good processability. Degenerate four-wave-mixing measurements on these polymers yield nonresonant third-order susceptibilities as high as 1.1×10-10 esu and nonresonant second-order hyperpolarizabilities per repeated unit as high as 2.0×10-31 esu. The large nonlinearity originates from the high electron delocalization due to the planar rigid structure of the fluorene ring and the imine nitrogen of quinoxaline and quinoline.

Enhanced third-order nonlinear optical properties of C60–silane compounds

The nonlinear optical properties of C60[NH2–(CH2)3–Si(OC2H5)3]3 sol and gel were investigated by femtosecond optical Kerr gate technique at 820 nm. The nonresonant third-order optical susceptibilities were measured to be 1.4×10−13 and 1.6×10−13 esu for the C60[NH2–(CH2)3–Si(OC2H5)3]3 sol and gel, respectively, which are two orders larger than that of C60 molecule.

Large third-order nonlinear optical response of a conjugated copolymer consisting of 2,5-diethynylthiophene and carbazole units

The third-order nonlinear optical (NLO) properties of a novel π-conjugated copolymer constituted of electron-rich carbazole and 2,5-diethynylthiophene have been studied using degenerate four-wave mixing (DFWM) at 1064 nm. The off-resonance second-order hyperpolarizability γ per repeated unit is estimated to be 2.2×10 −31 esu; the nonresonant third-order susceptibility χ (3) approaches (8.6±1.7)×10 −10 esu. The large ultrafast nonlinearity originates from an instantaneous electronic polarization.

Effect of the Solid State Structure on the Third-Order Nonlinear Optical Response of Poly(2,5-dialkoxy-p-phenyleneethynylene)s

The third-order nonlinear optical (NLO) properties of a series of poly(2,5-dialkoxy-p-phenyleneethynylene)s (PPEs) have been investigated in solution and in the solid state. In these PPEs, different alkoxy side chains are attached to the rigid-rod polymer main chain, leading to a series of polymers having an identical conjugated backbone but different supramolecular structures in the solid state. The nonresonant third-order NLO susceptibilities χ(3)(−3ω;ω,ω,ω) were measured by third-harmonic generation experiments. χ(3) values of up to 7.5 x 10-20 m2/V2 in solution and 14 × 10-20 m2/V2 in the solid state were determined. In solution, the NLO susceptibilities were found to be proportional to the content of polymer backbone, which depends on the functionalization of the PPEs. The solid state NLO susceptibilities were found to be related to the degree of long-range order in the samples, increasing with increasing order. In samples which adopt only a small extent of long-range order, the rigid-rod conjugated polymer backbones behave if they were “dissolved” in a hydrocarbon solvent, and consequently the nonlinear optical susceptibilities are comparable to those determined for solutions of these polymers. In films in which the polymer chains were found to adopt lamellar type supramolecular structures, the coplanar orientation of the conjugated polymer backbones is assumed to lead to intermolecular electronic interactions which give rise to extended conjugation lengths and hence lead to an increase of the nonlinear optical response.

Measurement of nonresonant third-order susceptibilities of various gases by the nonlinear interferometric technique

We applied nonlinear interferometry of coherent anti-Stokes Raman spectroscopy (CARS) to measure the nonresonant third-order susceptibilities of various gases. Using argon as an internal calibration standard, we determined the effective nonresonant susceptibilities of acetylene, carbon dioxide, methane, nitrogen, oxygen, propane, carbon monoxide, Freon, and hydrogen from the amplitudes of the interference fringes of the CARS signals generated in the two gas cells. The electronic susceptibility was calculated by subtracting the off-resonant term of each molecule from the measured effective nonresonant susceptibility, and the results of this work are compared with the published data. The overall uncertainty is estimated to be less than 5%.

Measurement method of nonresonant third-order susceptibility by using off-resonant coherent anti-Stokes Raman spectroscopy

Nonresonant third-order susceptibilities (χ(nr)) of N(2) and Ar gases by using an off-resonant coherent anti-Stokes Raman spectroscopy of the N(2) Q branch, whose spectral profile is highly sensitive to the value of χ(nr), have been measured to demonstrate the possibility of the present method. The χ(nr) of N(2) and Ar using the off-resonant coherent anti-Stokes Raman spectroscopy were 8.4 ± 0.2 and 9.7 ± 0.8 (× 10(-18)cm(3) /erg/amagat), respectively. These values are in good agreement with those of previous studies. The off-resonant spectra were theoretically calculated by using the Raman linewidth given by a modified exponential gap model, and they were compared with the experimental ones to determine χ(nr). The effects of uncertainties of the Raman linewidth of the N(2) Q branch on the determination of χ(nr) were investigated by changing the parameters in the modified exponential gap model. The determined χ(nr) value changed by only 0.05% with 50% change of the Raman linewidth. The potential advantages of this method are no requirements of high spectral resolution measurements, no accurate Raman linewidth data for each experimental condition, and no optical delay between pump beams.

Nonresonant Third-Order Susceptibility Measurements in 4'-(Pentyloxy)-4-Biphenyl Carbonitrile (5OCB)

This paper reports, for the first time, the determination of the real part of the third-order nonlinear susceptibility χ(3) (-ω; ω, 0, 0) in the isotropic phase of a nematic liquid crystal 4'-(pentyloxy)-4-biphenyl carbonitrile (5OCB), based on electrooptic Kerr effect experiments. The highest value of χ(3) observed near the nematic to isotropic transition temperature at 632.8 nm is found to be 8.02×10-19 m2 v-2. The observed value of χ(3) in this medium is about 113 times higher than that of CS2.

Nonresonant third-order susceptibility measurements in the nematic liquid crystal K18

We have observed a large nonresonant third-order nonlinear susceptibility, X(3) (-ω; ω, 0, 0) in the isotropic phase of a nematic liquid crystal 4′-n-hexyl-4-cyanobiphenyl (K18). The highest value of X(3) obtained at 632.8 nm is 1.16274×10-18 m2V-2 corresponding to a temperature 29.3°C. The observed second-order pretransitional temperature T* from our measurements is 1.2°C below the first-order nematic to isotropic transition temperature. The dependence of the Kerr constant on (T-T*)-1 is found to be in good agreement with the predictions of the Landau-de Gennes model.

The impact of laser field statistics in determination of temperature and concentration by multiplex USED CARS

Experiments have been performed which demonstrate that the ratio of resonant to nonresonant third-order susceptibilities measured in multiplex USED CARS are affected by the time correlation of the pump fields. Comparing the resonant to nonresonant signal ratio obtained with decorrelated fields to the ratio obtained with correlated fields, a relative increase of 2.5 was measured for the nitrogen Q-branch, whereas a corresponding increase of 1.9 was observed for the hydrogen Q(1)-line. To compare our experimental results with theoretical calculations of the spectral shapes, the nonresonant third-order susceptibilities of a number of gases were re-evaluated by calibrating to the nonresonant susceptibility of argon.

Measurements of the nonresonant third-order susceptibilities of gases using coherent anti-Stokes Raman spectroscopy

We report on measurements of the nonresonant third-order susceptibilities of the gases water vapor, n-butane, and propane. The susceptibilities were obtained from scanned coherent anti-Stokes Raman spectroscopy (CARS) spectra of binary gas mixtures containing N2 and each species of interest. The resonant susceptibility of N2, which served as a calibration standard for the measurements, was calculated using a modified exponential-gap model. Raman transition linewidths for the model were based on separate measurements by inverse Raman spectroscopy. We separately measured the nonresonant contributions from distant Raman transitions, predominantly C–H stretch modes. For parallel-polarized CARS configurations, the total effective nonresonant susceptibilities for propane, n-butane, and water vapor, respectively, were found to be 11.5 ± 1.4, 14.4 ± 1.8, and 2.2 ± 0.3 times that of N2 [using 8.5 × 10−18 (cm3/erg)/amagat].

Excited-state dynamics and temporally resolved nonresonant nonlinear-optical processes in polydiacetylenes

Degenerate four-wave mixing experiments (along with saturated absorption experiments) were carried out in and below the excitonic-state resonance in polydiacetylenes. A self-consistent analysis of the data was obtained with a two (electronic) level molecularlike model. The excitonic-state lifetime was determined to be 1.8 psec, and an initial excited-state process with a 100-fsec time constant was resolved. The time constant of the nonresonant third-order nonlinear-optical susceptibility was determined to be less than the resolution of the four-wave mixing experiment, -300 fsec, which was limited by the optical pulse duration.

Non-resonant third-order susceptibilities measured for ethane, propane and n-butane

Third-order non-linear susceptibilities have been measured for ethane, propane and n-butane at three wavelengths in the visible region by means of gas-phase electric-field-induced second-harmonic generation (ESHG). The susceptibilities are found to be large and strongly frequency dependent. The possible application of these results to the calibration of the non-resonant background in coherent anti-Stokes Raman scattering (CARS) measurements is discussed.

Quadratic Electro-Optical Characterization of Molecular Nonlinear optical Materials

ABSTRACTA convenient method of measuring the nonlinear optical properties of molecular compounds is described. The method involves measuring the quadratic electro-optical coefficient of a polymer composite containing a variable concentration of the candidate NLO material. The X(3) (ω) value obtained by this low-frequency Kerr measurement, after local-field corrections, can be compared to the nonresonant third-order susceptibility measured by degenerate-four-wave-mixing technique on selective samples. We find that the choice of the polymer matrix dictates the contribution of second-order susceptibility to the Kerr coefficient. Therefore, our method can also be extended to the measurement of second-order susceptibility, analogous to the technique of field-induced second-harmonic-generation.

Measurement of resonant and nonresonant third-order nonlinear susceptibilities by coherent Raman spectroscopy.

A phase-modulation technique for coherent Raman spectroscopy is used to measure both the real and imaginary parts of the third-order nonlinear susceptibility of gases. The Raman Q-branch resonance of ${\mathrm{D}}_{2}$ is calibrated by comparison to the Q-branch resonance of ${\mathrm{N}}_{2}$. By using ${\mathrm{D}}_{2}$ as an internal standard, the nonresonant electronic susceptibility of Ar and the sum of the electronic and molecular reorientation contributions to the nonresonant susceptibility of ${\mathrm{N}}_{2}$ are determined. The results of these measurements are compared to published data on the Q-branch Raman cross section of ${\mathrm{H}}_{2}$, to predictions from the theory of the optical (ac) Kerr effect, and to measurements of electronic hyperpolarizabilities. For the last-mentioned quantity, measurements from three-wave mixing, from field-induced second-harmonic generation, from third-harmonic generation, and from the electro-optic (dc) Kerr effect are intercompared and agreement at the 10% level is established. Formulas interrelating a number of different definitions of third-order susceptibilities found in the literature are presented.

Measurement of the third-order nonlinear susceptibility ratio by the CARS Maker fringe technique

Using the CARS Maker fringe technique, the nonresonant third-order nonlinear susceptibility was measured in several liquids.