Fifth-order Nonlinear Optical Susceptibility Research Articles

Fifth-order nonlinear optical response of Alq3 thin films

The fifth-order optical nonlinearity of Tris-(8-hydroxyquinoline) aluminium (Alq3) thin films deposited on quartz substrates when exposed to an intense laser excitation of mid-infrared femtosecond pulses is investigated. This property was examined by generating the fifth-harmonic frequency of the driving field whose signal strength as a function of laser intensity is well described by a power-law scaling. The perturbative nature of the underlying mechanism enabled the linking of the process directly to the fifth-order nonlinear optical susceptibility χ(5). We also utilized the open-aperture z-scan for studying the nonlinear absorption aspect of the third-order nonlinear optical properties of the sample. It was found that Alq3 thin-films inherit the same saturable absorption character reported in Alq3 solutions under continuous laser excitation in the visible range, with a comparable value of the nonlinear absorption coefficient βeff (in the order of 10−2 cm/W).

Enhanced third-order and fifth-order Kerr nonlinearities in a cold atomic system via Rydberg-Rydberg interaction

We investigate the optical Kerr nonlinearities of an ensemble of cold Rydberg atoms under the condition of electromagnetically induced transparency (EIT). By using an approach beyond mean-field theory, we show that the system possesses not only enhanced third-order nonlinear optical susceptibility, but also giant fifth-order nonlinear optical susceptibility, which has a cubic dependence on atomic density. Our results demonstrate that both the third-order and the fifth-order nonlinear optical susceptibilities consist of two parts, contributed respectively by photon-atom interaction and Rydberg-Rydberg interaction. The Kerr nonlinearity induced by the Rydberg-Rydberg interaction plays a leading role at high atomic density. We find that the fifth-order nonlinear optical susceptibility in the Rydberg-EIT system may be five orders of magnitude larger than that obtained in traditional EIT systems. The results obtained may have promising applications in light and quantum information processing and transmission at weak-light level.

Fifth-order nonlinear susceptibilities of sodium atomic vapor

This paper presents calculations of the fifth-order nonlinear optical susceptibilities of sodium vapor responsible for the third harmonic generation, degenerated six-wave mixing as well as for the fifth-order nonlinear Kerr effect. The values of the nonlinear susceptibilities were obtained applying the quantum-mechanical perturbation theory of the atomic wave function using values of the dipole matrix elements of 12 lowest atomic energy levels and are presented as functions of the wavelength within a wide spectral range from ionization wavelength of 241.3 nm to 2400 nm. Presented data can be used further for the theoretical modelling of various nonlinear optical processes.

High-order nonlinear optical response of a polymer nanocomposite film incorporating semiconducotor CdSe quantum dots

We report on observation of high-order optical nonlinearities in our recently developed photopolymerizable semiconductor CdSe quantum dot (QD)-polymer nanocomposite films at various volume fractions of CdSe QDs as high as 0.91 vol.% (3.6 wt.%). We performed Z-scan and degenerate multi-wave mixing (DMWM) measurements using a 532-nm picosecond laser delivering single 35 ps pulses at a repetition rate of 10 Hz. Using the uniformly cured polymer nanocomposite films, we observed the third- and fifth-order nonlinear optical effects in closed-aperture Z-scan measurements by which it was found that saturable nonlinear absorption (light-induced transparency) and large negative nonlinear refraction were induced. We also measured dependences of the effective third- and fifth-order nonlinear refraction constants on CdSe QD volume fraction. Based on the Maxwell-Garnett model, we estimated the third- and fifth-order nonlinear optical susceptibilities of CdSe QD and discussed a contribution of the third-order effect to the fifth-order one due to the cascaded (local-field) effect. Coexistence of the third- and fifth-order nonlinear refraction was also confirmed by DMWM.

Cascaded nonlinearity caused by local-field effects in the two-level atom

Contributions to the fifth-order nonlinear optical susceptibility {chi}{sup (5)} of a collection of homogeneously broadened two-level atoms that scale as N{sup 2}({gamma}{sub at}{sup (3)}){sup 2} and N{sup 2}|{gamma}{sub at}{sup (3)}|{sup 2}, where {gamma}{sub at}{sup (3)} is the lower-order atomic hyperpolarizability and N is the atomic number density, are predicted theoretically. These 'cascaded' contributions are a consequence of local-field effects. We determine them from a fifth-order solution of the Lorentz-Maxwell-Bloch equations. They are missing from a straightforward generalization of Bloembergen's result for the local field correction to the second order nonlinearity, but are recovered by a careful application of his general approach. We find that at high atomic densities (N>10{sup 15} cm{sup -3}) the value of the cascaded third-order contribution can be as large as the 'direct' fifth-order term in the expression for the fifth-order susceptibility.

Phonon-Assisted Second Harmonic Generation in As1-xBixTe3−CaBr2−PbBr2 Glasses

We have found experimentally the IR-induced second harmonic generation (SHG) in glasses possessing different degrees of electron-phonon interactions. For the investigations, we have chosen As(1)(-)(x)()Bi(x)Te(3)-CaBr(2)-PbBr(2) (0 < x <1) glasses. General formalism is based on consideration of fifth-order nonlinear optical susceptibility. The effect is observed in the middle IR region (spectral range 0.92-10.5 microm) where the value of the electronic energy gap is commensurable to the energies of actual quasi-phonons participating in the anharmonic (non-centrosymmetric) electron-phonon interactions. Varying the As/Bi ratio allows us to operate by the degree of electron-phonon anharmonicity in a wide spectral range. The second harmonic generation (SHG) output signal shows a correlation with IR-induced anharmonic phonon modes within the 1.5-4.8 microm spectral range. A maximum value of SHG is achieved at pump-probe delaying times of about 12.5-20 ps, which are typical for relaxation of the anharmonic electron-quasi-phonon subsystem. The maximally achieved value of the phonon-assisted optical susceptibility was about 6 x 10(-38) m(4)/V(4). The SHG signal was saturated for the IR pump power densities of about 1.73 GW/cm(2), corresponding to output SHG signals of about 9.8 x 10(-4) with respect to the fundamental ones. By varying the degree of electron-phonon anharmonicity and changing content of glasses, it was unambiguously shown that the IR-induced SHG signal correlates well with changes of oscillator strengths of IR-induced anharmonic phonon modes.

IR-stimulated second harmonic generation in Sb2Te2 Se-BaF2-PbCl2 glasses

Theoretically predicted and experimentally observed infraredinduced second-harmonic generation of glasses in the mid-infrared spectral region can be described by fifth-order nonlinear optical susceptibility. The effect is observed in the mid-IR region when the value of the electronic energy gap is comparable to the energies of actual phonons participating in the anharmonic (non-centrosymmetric) electron-phonon interactions. As subjects for investigation, chalcohalide Sb2Te2Se-BaF2-PbCl2 glasses were chosen. They are transparent, over a spectral range of 1.1–10.9 μm. The second-harmonic generation (SHG) output signal within the 1.5–4.8 μm spectral range has significant spectral dependence. Correlation of the SHG spectral maxima positions with spectral positions of anharmonic phonon frequencies confirms that the fifth-order steady-state process occurs due to cascading processes and IR-induced charge density non-centrosymmetry. A maximum value of the SHG is achieved at a pump-probe delay time of 18–36 ps, which is typical for anharmonic electron-phonon interactions. As temperature rises, the values of the photoinduced SHG signal susceptibility increases up to 3 × 10−39 m4/V4. The SHG signal reaches a saturation point for the IR-pump power densities of about 0.8 GW/cm2, which corresponds to the output SHG intensities of about 6 × 10−4 with respect to fundamental one. The values of the diagonal fifth-order tensor component χ(2ω) xxxxx are at least one order of magnitude larger than the off-diagonal tensor components.

Optically-induced second-order nonlinear optical effect in polyvinyl alcohol photopolymers

IR induced picosecond nonlinear optical effects in polyvinyl alcohol photopolymer is investigated. The second harmonic generation (SHG) is studied versus the pump power and delaying time between the pump and probing beam ( λ=1.55 and 1.32 μm, respectively). The phenomena are explained within a framework of fifth-order nonlinear optical susceptibilities. An explanation of the observed dependences is given within a framework of photostimulated vibrations, which enhance acentric electron–phonon anharmonicity. Temperature dependences of the observed phenomena fully confirm the electron–phonon anharmonic origin of the observed effect.

IR-Induced Second Harmonic Generation in Sb2Te3−BaF2−PbCl2 Glasses

Theoretically predicted and experimentally confirmed occurrence of infrared-induced second harmonic generation for glasses in the middle infrared spectral region is described by fifth-order nonlinear optical susceptibility. This effect is observed in the middle-IR region when the value of the electronic energy gap is comparable to the energies of actual phonons participating in the anharmonic (noncentrosymmetric) electron−phonon interactions. As a subject for the investigations, Sb2Te3−BaF2−PbCl2 glasses were chosen because they are transparent in the spectral range of 0.8−10.1 μm. The second harmonic generation (SHG) output signal within the 1.5−4.8 μm spectral range demonstrated a significant spectral dependence. Correlation of the SHG spectral dependences with spectral positions of the anharmonic phonon frequencies confirms that the fifth-order steady-state process occurs as a result of both the cascading processes and IR-induced charge density noncentrosymmetry. A maximum value of the SHG is achieved at a pump−probe delay time of about 20 ps, which is typical for the anharmonic electron−phonon interactions.

Mid-infrared light-induced second-harmonic generation in specific glasses

We have theoretically predicted and experimentally confirmed a possibility of optically induced second-harmonic generation (SHG) for glasses in the middle-infrared (IR) spectral region described by fifth-order nonlinear optical susceptibility. This effect may be observed in the middle-IR region when the value of the electronic energy gap is comparable to the energies of actual phonons participating in the anharmonic (non-centrosymmetric) electron–phonon interactions (EPIs). As a subject for the investigations we have chosen Sb2Te3–BaF2–SrBr2 glasses which are transparent in the range of 0.8–10.1 µm. The SHG output within the 1.5–4.8 µm spectral range demonstrates a crucial spectral dependence. Correlation of the SHG spectral dependences with spectral positions of the anharmonic phonon mode density confirms that a fifth-order steady-state process occurs from both the cascading processes and IR-induced charge density non-centrosymmetry. A maximal value of the photoinduced SHG is achieved at a pump–probe delaying time of about 20 ps which is typical for the anharmonic EPI.

Harmonic generation in organic dye vapors

Investigations of nonlinear optical frequency conversion of Nd:YAG laser radiation in naphthalene vapors are presented. The third harmonic generation (THG) caused by difference frequency generation in six-photon process has been studied. Phase-matching temperature for naphthalene vapor was found to be 170°C, at which synchronous conversion of pump radiation to the third harmonic was carried out. The THG conversion efficiency varied within 10 −10–10 −8 depending on pump intensity and cell temperature. Third- and fifth-order nonlinear optical susceptibilities were calculated and compared with the experimentally measured fifth-order susceptibility of naphthalene vapors.

Dispersion of the fifth-order nonlinear optical susceptibility χ^(5)_113333 (ω; ω, 0, 0, 0, 0) of a polydiacetylene film

The dispersion of the fifth-order nonlinear optical susceptibility χ113333(5)(ω; ω, 0, 0, 0, 0) of a spin-coated polydiacetylene film (poly(BPOD), i.e., poly{[[8-butoxy carbonyl] methyl urethanyl]1-(5-pyrimidyl)-octa-1, 3-diyne}) is determined through electroabsorption spectroscopy. The maximum values of the real and the imaginary parts of χ113333(5)(ω; ω, 0, 0, 0, 0) are 9.87×10-21 esu and 1.28×10-20 esu, respectively. A model is proposed to explain the spectral dispersion of the nonlinear optical susceptibility.