Nonlinear optical polarization effects in quantum-dot materials

The amplitude and dispersion of the cubic susceptibility-tensor components χ _ijkl ⁽³⁾ (?Ω; Ω, ω, ?ω) and of their combinations responsible for the Kerr and Faraday optical effects, as well as for the self-rotation of the polarization ellipse, are calculated within a simple model of a material with semiconducting spherical quantum dots without the inclusion of the excitonic effects and of processes of higher orders in field. It is shown that the susceptibilities increase smoothly in amplitude below the two-photon absorption threshold while remaining negative. Above the threshold, the susceptibilities exhibit sharp maxima associated with two-photon resonances. The regions with positive and negative real parts of the χ⁽³⁾ tensor components alternate. The magnitude of the induced linear or circular birefringence obtained suggest the possibility of using the nonlinear optical polarization effects in these materials to control light with short, high-intensity light pulses.     

Third harmonic generation in copolymer films with optically nonlinear N-substituted 4-nitroazobenzene in the side and main polymer chains

The third-order nonlinear optical susceptibility χ⁽³⁾(3ω; ω, ω, ω) of two types of copolymer films containing optically nonlinear N-substituted nitroazobenzene in the side (methacrylic series copolymers) and main (copolyimidoamido esters) polymer chains is investigated using the third harmonic generation method at a wavelength of 1.064 μm. __________ Translated from Fizika Tverdogo Tela, Vol. 44, No. 2, 2002, pp. 379–382. Original Russian Text Copyright ? 2002 by Lebedeva, Loretsyan, Ivanova, Romashkova, Lukoshkin, Kudryavtsev.     

Nonlinear susceptibility x;(3) in a direct gap semiconductor derived from coupled inter-and intraband equations of motion

A set of generalized Maxwell Bloch Equations describing a two band semiconductor as a system of interacting two level atoms is used to calculate the nonlinear dielectric susceptibility x;⁽³⁾ (ω, ? ω, ω). For near resonance conditions (ω ≈ ω_g) we find a simplified expression for χ⁽³⁾ that is compared with other theories. A fit using parameters relevant for InSb leads to good agreement with experimental results.     

Nonlinear optical properties of polyamidine complexes of a series of modified oligomeric ω,ω′-diaminopropylene oxides

The third-order nonlinear optical susceptibility χ⁽³⁾ in poly(octamethylene acetamidine) complexes of a series of modified oligomeric ω,ω′-diaminopropylene oxides is investigated by the third-harmonic generation technique at a wavelength of 1064 nm. It is demonstrated using UV spectroscopy that the interaction of the aforementioned chromophore-terminated polymers with polyamidine leads to the formation of network structures in which the polymer network is formed as a result of the ionic interaction. The ionic intermolecular complexes formed in this case are capable of generating the third harmonic. An increase in the length of the polymer chain in the series of modified ω,ω′-diaminopropylene oxides leads to a decrease in the absorption coefficient of the chromophore fragment and a considerable decrease in the nonlinear optical response χ⁽³⁾     

Detection of a new SRS‐promoting phonon mode and cross‐cascaded χ(3)‐nonlinear lasing in single crystals of calcite (trigonal CaCO3)

For calcite (CaCO₃), one of the pioneer crystals in nonlinear optics, new results of stimulated Raman scattering (SRS) spectroscopy are presented. Among them are the discovery of a new SRS‐promoting vibration mode with ω_SRS2 ≈︁ 282 cm^‐1 and its participation, together with the main SRS mode ω_SRS1 ≈︁ 1086.5 cm^‐1, in cross‐cascaded (χ⁽³⁾ ↔ χ⁽³⁾) nonlinear‐lasing generation, as well as the observation of efficient self‐upconversion via cascaded parametric four‐wave processes of one‐micron Stokes and anti‐Stokes χ⁽³⁾‐lasing into the UV‐region of third harmonic generation. The investigations show that calcite is able to generate a χ⁽³⁾‐lasing comb of more than two octaves bandwidth. The article also gives a brief review on the discovery and study of the SRS‐effect in natural crystals (minerals), which have expanded our ability to study the photon‐phonon nonlinear‐laser interactions in crystalline materials. A short summary of information about χ⁽³⁾‐lasing properties of the triangular planar structure units in SRS‐active crystals is included.     

On the analysis of factors limiting third harmonic generation of Nd:YAlO<Subscript>3</Subscript> laser radiation in barium vapor

The efficiency of generation of the third harmonic (THG) of Nd:YAlO³ laser radiation in barium vapor is analyzed. The influence of the following factors is taken into consideration: the interference of transformed radiation in the case of THG via two channels ω+ω+ω→3ω and 2ω+2ω?ω →3ω, the Kerr effect, two-photon absorption, and the relationship between the energies of the first and second harmonics of radiation. It is shown that the Kerr effect, on the one hand, violates the phase matching conditions in the direct channel but, on the other hand, increases the conversion efficiency due to a defocusing action of the medium, which reduces the influence of the phase detuning between the pumping waves on the process of harmonic generation in the case of generation of difference frequencies. At the same time, the two-photon absorption leads to the depletion of one of the interacting waves (in this case, the second harmonic) and to the prevalence of third harmonic generation through the direct channel.     

Double resonance interference in third-order light mixing

The first observation of interference effects between two sharp resonant contributions to the third-order nonlinear susceptibility χ₍₃₎ (ω₃=ω₀+ω₁?ω₂) is reported. Using two tunable near ir frequencies, ω₀=ω₁ and ω₂, the was seen in crystalline CuCl when 2ω₁ and ω₁?ω₂ were close to the sharp Z₃ exciton at 3.21 eV and the 210 cm^-1 Raman line, respectively. Three different tunable visible frequencies were used to observe similar interference effects in a benzene-cyclohexane mixture when ω₀?ω₂ and ω₁?ω₂ were close to the 992 cm^-1 Raman line of benzene and the 801 cm^-1 Raman line of cyclohexane, respectively.     

On the enhancement of the nonlinear frequency transformation in periodic media

It is theoretically shown that an enhancement of the nonlinear frequency transformation in a periodic medium occurs under definite conditions if it is accompanied by light diffraction in this medium. The enhancement of the phase-matched frequency transformation occurs if the harmonic frequency ω approaches the stop band frequency ω_e. In the nondepleted pump approximation the corresponding increase of the harmonic intensity is proportional to ω_e(ω?ω_e)^?1 and is restricted by a quantity proportional to the fourth power of the sample thickness. The formulas for the enhancement of second harmonic generation are presented.     

Measurement of third-order nonlinear susceptibilities by non-phase matched third-harmonic generation

The third-order susceptibilities χ _xxxx ⁽³⁾ (?ω₃;ω₁,ω₁,ω₁) of some liquids, solids and air are determined by third-harmonic generation. The samples are placed behind the focal region of a laser beam in an evacuated environment to avoid third-harmonic generation of the surroundings. For fluid media the sample cell is made out of two thin fused quartz plates and oriented to an angle of zero net third-harmonic production in each window (minimum Maker fringe position).     

Anomalous behavior of linear and nonlinear longitudinal susceptibilities below T c in a weakly anisotropic CdCr2Se4 ferromagnet

Frequency dependences of the linear and nonlinear longitudinal dynamic susceptibilities of an almost isotropic cubic CdCr₂Se₄ ferromagnet were studied experimentally in the ordered phase. It was found that at frequencies above the two-magnon creation threshold the linear susceptibility decreases as χ₁∝ω^?0.28 with increasing frequency and the nonlinear susceptibility decreases as χ_n∝ω^?0.73, irrespective of n, where n is an odd number. The observed susceptibility anomalies are due to the dipolar forces that violate the conservation of total spin.     

Four-wave mixing and hyper-Raman scattering in CuCl

Non-degenerate four-wave mixing using two non-collinear laser beams with frequencies (wavevectors) ω_p, ω_t (k_p, k_t) respectively is studied in CuCl. Two emission lines at frequencies ω⁽¹⁾=2ω_t-ω_p, and ω⁽²⁾=2ω_p-ω_t are observed. Their excitation spectrum is sharply peaked if the phase-match condition k⁽¹⁾=2k_t-k_p is fulfilled. This is the case, if ω_p coincides with the hyper-Raman lines (R⁺_T, R^-_T) of the laser labelled (t) in a well-defined geometrical configuration.     

Feldgleichungen der TREDERschen Gravitationstheorie,die aus einem Variationsprinzip ableitbar sind. I

In the frame work of TREDER 's gravitational theory we consider two classes of field equations which are derivable from two classes of LAGRANGE ian densities Ω⁽¹⁾(ω₁, ω₂), Ω⁽²⁾(s?₁, s?₂). ω₁, ω₂; s?₁, s?₂ are parameters. Ω⁽²⁾(ω₁, ω₂) gives us field equations which are up to the post-NEWTON ian approximation in the sense of NORDTVEDT , THORNE and WILL equivalent to the field equations given by BRANS and DICKE . For ω₂ = ?1 ?2ω₁ field equations follow from Ω⁽¹⁾(ω₁, ?1 ?2ω₁) which are in the above mentioned sense of post-NEWTON ian approximation equivalent to EINSTEIN 's equations. The field equations following from Ω⁽¹⁾(ω₁, ω₂) have a cosmological model with the well known cosmological singularities for T → ± ∞ in case that ω₁/(1 +3ω₁ +ω₂) ? γ > 0. For ω₁/(1 +3ω₁ +ω₂) ≤ 0 cosmological models with no cosmological singularities exist. From Ω⁽²⁾(s?₁, s?₂) we obtain field equations which at the best give us perihelion rotation 7% above EINSTEIN 's value and light deflection 7% below the corresponding EINSTEIN 's value. But in that case we are able to show the existence of a cosmological model without any cosmological singularity.     

Third-harmonic generation in polyvinylpirrolidone-based metallic complexes

The third-order nonlinear susceptibilities of the aqueous solutions of polyvinylpirrolidone doped with iron and zinc were studied by the method of third-harmonic generation with 1064-nm Nd:YAG laser radiation. The efficiencies of transformation into the third harmonic in these metallic complexes were 8×10^?7 and 5×10^?7, respectively. To determine the role of the Kerr effect in the transformation process, the nonlinear refractive index of the iron-doped polyvinylpirrolidone solution was measured by the Z-scan method and a value of n ₂=?6.7×10^?13 cgs unit was obtained.     

Giant nonlinear refraction in gold island films

Giant nonlinear refraction has been experimentally observed in gold island films. The real part of the third-order nonlinear susceptibility χ⁽³⁾(ω: ω,-ω, ω) reaches a value of about 10^?4 CGS units. The mechanism of nonlinearity of the refractive index can be associated with the resonance enhancement of the factor of the local optical field at the pump wavelength due to the excitation of surface plasmons, as well as with the contribution of the heating of conduction electrons in an ensemble of metal particles.     

Nonresonant third order hyperpolarizability of rare gases and N2 determined by third harmonic generation

The third order hyperpolarizabikity γ⁽³⁾₁₁₁₁(-ω₃;ω₁,ω₁,ω₁) of the rare gases He, Ne, Ar, Kr, Xe and of N₂ are determined by third harmonic generation involving picosecond light pulses of a Nd-glass laser. The results are compared with reported experimental and theoretical values.     

Third harmonic generation of laser radiation in Fe- and Zn-doped polyvinylpyrrolidone

The results of third-order nonlinear susceptibilities studies of Fe- and Zn-doped polyvinylpyrrolidone (PVP) aqueous solution in processes of third harmonic generation of Nd:YAG laser radiation are presented. Nonlinear susceptibilities of PVP:Fe and PVP:Zn were calculated to be 5×10^-13 esu and 3×10^-13 esu respectively. Third harmonic conversion efficiencies in these metallocomplexes were measured to be 8×10^-7 and 5×10^-7 respectively. The Z-scan method was applied to determine Kerr effect influence on frequency conversion process. The value of nonlinear refractive index of PVP:Fe at the wavelength of λ = 1064 nm was measured to be n ₂ = - 6.7×10^-13 esu. Received 30 November 2001 / Received in final form 27 March 2002 Published online 28 June 2002     

The nonlinear optical susceptibilities of polydiacetylenes

We present a general formalism of the NLO susceptibilities by using the Genkin-Mednis approach for a one-dimensional electron-lattice system. Based on the SSH model, we obtained an analytic expression for the third-order nonlinear optical susceptibilities χ⁽³⁾(ω) for polydiacetylenes (PDAs) after considering the case of conjugated chains, in which there is no adjustable parameter. The results are in good agreement with experiments on PDAs. Furthermore, the origin of the second peak in the χ⁽³⁾(ω) spectrum of PDAs is discussed, and a transition mechanism is proposed. It is believed that when the external light field is applied along the centrosymmetric polymer backbone, the parity symmetry of the system is broken, there occurs a mixing between the even- and odd-parity exciton states, leading to the transition from the ground state to the A_g excited state, and accordingly a second sharp peak appears in the χ⁽³⁾(ω) spectrum which could be attributed to the three-photon resonance with the A_g exciton generation process at around 2.2 eV.     

High resolution nonlinear spectroscopy. Dicke narrowing and dispersion of the third-order nonlinear susceptibility of H2 near the Q01 (1) vibrational resonance

The forward scattering process of motional narrowing in hydrogen gas has been investigated by an original method of nl spectroscopy of general application. The method has allowed a detailed study of the dispersion of the nl susceptibility χ⁽³⁾(ω) showing an unexpected behavior of χ⁽³⁾(ω)' near the Q₀₁ (1) molecular eigenfrequency.     

Spin susceptibility of cuprates in the model of a 2D frustrated antiferromagnet: Role of renormalization of spin fluctuations in describing neutron experiments

Experimental data on the spin susceptibility of HTSC cuprates are reproduced on the basis of a spherically symmetric approach in the frustrated Heisenberg model. The inclusion of real and imaginary renormalizations in spin Green’s functions makes it possible to explain the evolution of spin excitation spectrum ω(q) and susceptibility spectrum χ(q, ω) in the range from insulator to optimal doping. In the low-frustration limit corresponding to the weakly doped mode, the saddle singularity of ω(q) and scaling of χ_2D(ω) =∫d q Im χ(q, ω) are reproduced and an analytic expression is derived for the scaling function. In the strong frustration (optimal doping) mode, the stripe scenario is demonstrated; this leads to a peak of χ_2D (ω) in the region of ω～60 meV.