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.     

Quantum chemical investigation on the structure and first hyperpolarizability for N‐substituted [n]cyclacene

Six N‐substituted [n]cyclacene (n = 5, 6, 7,…,10) molecules were designed to study the relationship between the structure and first hyperpolarizability. Their static first hyperpolarizabilities (β₀) were obtained by MP2/6‐31 + g(d) level. Two interesting relationships between the β₀ value and the structure have been found: (1) The β₀ value increases with the increase of the number n when n is odd: 3155 ([5]cyclacene) < 48,905 ([7]cyclacene) < < 393,444 ([9]cyclacene), and when n is even: 357,620 ([6]cyclacene) < 618,608 ([8]cyclacene) < 3,513,644 a.u. ([10]cyclacene). (2) The β₀ values (in the range of 357,620 ~ 3,513,644 a.u.) of the N‐substituted [n]cyclacene (when n is odd) are much larger (in the range of 3155~393,444 a.u.) than that of the N‐substituted [n]cyclacene (when n is even). Furthermore, their frequency‐dependent β (?2ω; ω, ω) and β (?ω; ω, 0) (ω = 0.005, 0.01, and 0.0239 a.u.) were also estimated by Møller–Plesset perturbation/6‐31 + g(d) level. Among the frequency‐dependent β (ω), [10]cyclacene has the largest β (?ω; ω, 0) and β (?2ω; ω, ω) to be 1.2 × 10⁸ (ω = 0.01) and 2.9 × 10⁷ a.u. (ω = 0.005 a.u.), which are much larger than the static β₀ = 3.5 × 10⁶ a.u. by 34 and 8 times. Our present work may offer a new idea in the design of high‐performance tubiform nonlinear optical materials. Copyright © 2011 John Wiley & Sons, Ltd.     

在高频区存在巨带隙的长方晶格二维光子晶体

本文利用降低光子晶体的对称性来提高绝对禁带宽度, 提出两种长方结构长方介质柱二维光子晶体, 用快速平面波展开法研究其高频区的带结构.经参数优化发现, 长方晶格包含一套介质柱时, 最大绝对禁带宽度Δω为0.1265ωe（ωe=2πc/a, a为晶格常数, c为光速）, 绝对禁带中心频率ωmid为1.9256ωe, Δω/ωmid=6.6%; 当长方晶格包含两套介质柱时, 最大绝对禁带宽度为0.203ωe, 绝对禁带中心频率为1.8597ωe, Δω/ωmid=10.9%.     

Change in the shape of a symmetric light pulse passing through a quantum well

A theory for the response of a 2D two-level system to irradiation by a symmetric light pulse is developed. Under certain conditions, such an electron system approximates an ideal solitary quantum well in a zero field or a strong magnetic field H perpendicular to the plane of the well. One of the energy levels is the ground state of the system, while the other is a discrete excited state with energy ?ω₀, which may be an exciton level for H=0 or any level in a strong magnetic field. It is assumed that the effect of other energy levels and the interaction of light with the lattice can be ignored. General formulas are derived for the time dependence of the dimensionless “coefficients” of the reflection ?(t), absorption A(t), and transmission ?(t) for a symmetric light pulse. It is shown that the ?(t), A(t), and ?(t) time dependences have singular points of three types. At points t ₀ of the first type, A(t ₀)=T(t ₀)=0 and total reflection takes place. It is shown that for γ_r?γ, where γ_r and γ are the radiative and nonradiative reciprocal lifetimes, respectively, for the upper energy level of the two-level system, the amplitude and shape of the transmitted pulse can change significantly under the resonance ω_l=ω₀. In the case of a long pulse, when γ_l<γ_r, the pulse is reflected almost completely. (The quantity γ_l characterizes the duration of the exciting pulse.) In the case of an intermediate pulse duration γ_l?γ_r, the reflection, absorption, and transmission are comparable in value and the shape of the transmitted pulse differs considerably from the shape of the exciting pulse: the transmitted pulse has two peaks due to the existence of the point t ₀ of total reflection, at which the transmission is zero. If the carrier frequency ω_l of light differs from the resonance frequency ω₀, the oscillating ?(t), A(t), and ?(t) time dependences are observed at the frequency Δω=ωl?ω₀. Oscillations can be observed most conveniently for Δω?γ_l. The position of the singular points of total absorption, reflection, and transparency is studied for the case when ω_l differs from the resonance frequency.     

Stimulated Raman spectra of a strong bichromatic field interacting with a three-level atom

We have studied the stimulated Raman spectra arising from the interaction of a three-level atom with two strong electromagnetic fields whose initially populated modes ω _a and ω _b are in resonance with the two atomic transition frequencies. The Green's function formalism has been used in the limit of high photon densities to calculate the excitation spectra near the frequencies ω = ± ω _ab = ± (ω _a - ω _b ). Expressions are derived for the relative intensities, which describe, apart from the usual Raman peak at the frequency ω = ω _ab , four pairs of lorentzian lines peaked at the frequencies ω - ω _ab = ± Ω _a /√2, ± Ω _b /√2, ± Ω and ± 2Ω, respectively, and having spectra widths of the order of 3γ₀/4. The parameter Ω is defined as Ω² = (Ω _a ² + Ω _b ²)/2, where Ω _a and Ω _b are the Rabi frequencies of the two laser fields and γ₀ is the spontaneous emission probability. Numerical calculations for selected values of the Rabi frequencies are graphically presented and discussed. Conditions have been established for which Raman gain processes are anticipated to take place.     

Low-frequency dispersion of the effective transverse conductivity in inhomogeneous media in strong magnetic field

On crystalline silicon specimens with a nonuniform carrier concentration distribution produced by an optical method, a dispersion of the effective transverse conductivity σ _⊥ ^eff (ω) is observed near the frequency ω≈ω_c=τ _⊥ ^?1 ≡ε/4πσ _⊥ ^eff . At ω<ω_c, an anomalous transverse effective conductivity is observed: σ _⊥ ^eff (ω) is greater than the transverse conductivity of a homogeneous specimen σ _⊥ ^h (ω) (in the frequency range studied in the experiment σ _⊥ ^h (ω) = const). Near ω≈ω_c, the conductivity σ _⊥ ^eff decreases, and, at ω>ω_c it coincides with σ _⊥ ^h .     

On the dynamic conductivity for an electron-impurity system

The correlation function formula for the dynamic conductivity of a system of non-interacting electrons in the field of impurities is analyzed in terms of proper connected diagrams. By selecting those diagrams appropriate in the region of weak coupling and low impurity concentration, a set of coupled equations for the energy broadening γ (ω, ε, n_s) and the energy shift Δ(ω, ε, n_s) is derived, where both γ and Δ depend on the frequency ω of a probing field, the energy ε of the electron, and the concentration, n_g, of impurities. With the assumption of a finite range potential, these equations are solved. It is found that γ (ω, n_s) is smaller than that extrapolated value which the conventional expression γ₀ for the low-concentration collision frequency would predict, in the entire region studied, that the difference γ₀-γ becomes appreciable when the ratio of the average time between scatterings, τ_c, to the average duration of a scattering, τ_d, is 100 or less, that γ (ω, n_s) decreases monotonically from its static value γ (0, n_s), and becomes vanishingly small in the region ω≈1/τ_d, and that in the static limit (ω=0), γ=γ₀[1?(2/π) (γ₀τ_d)+…], that the energy shift Δ is positive, and increases from 0 and reach a peak of magnitude γ₀ as ω is raised from 0. By using the γ and Δ obtained, the dynamic conductivity σ(ω, n_s) for degenerated electrons is calculated. The deviation, σ-σ₀, from the conventional expression σ₀=(?i) (n_ee²/M) [ω-iΓ₀]^?1, (n_e]=number density of electrons), for 0°K, is appreciable when the ratio τ_c/τ_d is 100 or less. The field-term correction, which arises from the modification of the scattering due to the probing field, is found to be negligible in the entire region studied.     

Estimation of the influence of ionic dielectricity on the dynamic superconducting order parameter

We consider the influence of an ω-dependent ionic dielectric constant ?(ω) on the properties of a superconductor. Assuming that the pairing interaction is proportional to ?² we have solved the Eliashberg equations for this case, both for imaginary and real frequencies. The interaction potential depends on a coupling constant λ and on a longitudinal phonon frequency Ω. The dielectric constant is assumed to be independent of wavevector q, and to depend on frequency through the expression: ?(ω) = (ω² - ω²_long)/(ω² - ω²_trans), where ω_long, ω_trans are the frequencies of optical phonons of the dielectric. We find that along the imaginary frequency axis (but not for real frequencies) the weighted phonon propagator can be modeled by an appropriate choice of a cutoff frequency and an effective coupling constant. The influence of ?(ω) on T_c, the gap δ(ω), and the renormalization function Z(ω) are studied and it is found that these quantities increase significantly with the dielectric constant.     

Nonlinear susceptibilities of vapors and solutions of organic dyes

Results of theoretical studies of laser and Kerr nonlinear susceptibilities of vapors and solutions of organic dyes using a series of polycyclic arenes as an example are presented. Nonlinear susceptibilities of the third χ⁽³⁾ (?3ω; ω, ω, ω) and the fifth χ⁽⁵⁾ (?3ω; ω, ω, ω, ω, ?ω) orders of a series of organic dyes responsible for third harmonic generation of Nd:YAG laser radiation are calculated within the context of the free electron model. Results of calculations of their Kerr third-order nonlinear susceptibilities χ⁽³⁾ (?ω; ω, ?ω, ω) and non-linear refractive indices n ₂ are presented. The calculation results are compared with experimental data on third harmonic generation in naphthalene vapors and with χ⁽³⁾ (?ω; ω, ?ω, ω) as well as n ₂ of paraterphenyl and naphthalene solutions.     

The determination of hopping rates and carrier concentrations in ionic conductors by a new analysis of ac conductivity

The a.c. conductivity σ(ω) of ionic materials takes the form, σ(ω) = σ(0) + Aωⁿ. The carrier hopping rate, ω_p, is obtained from the new expression σ(0) = A ω_pⁿ and the carrier concentration is estimated from σ(0). The contribution of creation and migration terms to the activation energy for conduction may be determined from the thermal activation of σ(0) and ω_p and the corresponding entropy terms quantified. Data have been analyzed for four widely different ionic materials: single crystal Na β-alumina, polycrystalline Li₄SiO₄, Ag₇l₄AsO₄ glass and Ca(NO₃)₂/KNO₃ glass and melt. For each, the carrier concentration and hopping rates have been obtained.     

Effective field and the Bloch-Siegert shift at bichromatic excitation of multiphoton EPR

The dynamics of multiphoton transitions in a two-level spin system excited by transverse microwave and longitudinal RF fields with the frequencies ω_mw and ω_rf, respectively, is analyzed. The effective time-independent Hamiltonian describing the “dressed” spin states of the “spin + bichromatic field” system is obtained by using the Krylov-Bogoliubov-Mitropolsky averaging method. The direct detection of the time behavior of the spin system by the method of nonstationary nutations makes it possible to identify the multiphoton transitions for resonances ω₀ = ω_mw + rω_rf (ω₀ is the central frequency of the EPR line, r = 1, 2), to measure the amplitudes of the effective fields of these transitions, and to determine the features generated by the inhomogeneous broadening of the EPR line. It is shown that the Bloch-Siegert shifts for multiphoton resonances at the inhomogeneous broadening of spectral lines reduce only the nutation amplitude but do not change their frequencies.     

Frequency Dependence of the Dielectric Loss Angle in Disordered Semiconductors in the Terahertz Frequency Range

Frequency dependence of the real part of the conductivity σ₁(ω) in the region of the transition from almost linear (s < 1) to quadratic (s ≈ 2) can indicate a change in the conduction mechanism (the transition from the variable-range to the fixed-range hopping with increasing frequency); in this case, the sharpness of the change in the slope of the frequency characteristic is related to the dependence of the preexponential factor of the resonance integral on the intercenter distance in the pair. The frequency dependence of the imaginary part of the conductivity σ₂(ω) has no kink in the vicinity of the transition frequency ωcr, remaining almost linear. A large dielectric loss angle |cotγ| = |σ₂|/σ₁ can indicate that the imaginary part of the conductivity at ω < ω_cr is defined by the larger zero-phonon contribution in σ₂^res the region of weak variation in the loss angle γ(ω), which significantly exceeds the relaxation contribution σ₂^res.     

Parametric Excitation of Plasma instabilities by two Monochromatic Pump waves

The dispersion characteristics of a plasma in a pump field ??(t) = ?? sub ω₀t + ??₁ sin ω₁t are considered. Firstly we assume, that the second wave is weak (|??₁| ? |??₀|) and the frequency ω₁ is near sω₀(ω₁ = sω₀ + Ω,Ω ? ω₀). We obtain the dispersion equation, describing the parametric coupling of the waves driven by the strong field ??₀ sin ω₀t under the resonance condition ω₀ ≈ ω_Le/P and derive the expressions for the growth rates (ω_Le is the electron LANGMUIR frequency; s, p are integers). In the second part it is shown, that a strong field ??₁ with a frequency ω₁ much larger than ω _Le(ω _Le ≈ pω₀) stabilizes the plasma; the growth rates are reduced and the frequency region of the parametric instability is contracted.     

Far-infrared reflection spectra of HgSe

Reflectivity of HgSe (N = 2.0 × 10¹⁸-4.2 × 10¹⁷ cm^-3) was measured in the spectral region from 2–100 μm at temperatures between 95 and 300 K. The frequency of the transverse optical phonon ω_t = 132 ± 2 cm^-1 was determined from Kramers-Kronig analysis. The ω+ mode of the plasmon-LO phonon coupled modes is shown to depend anomalously on temperature. Two extra bands of unknown origin were also observed at about 110 and 120 cm^-1.     

Stationary Propagation of Coupled Nonlinear High Frequency Waves and Ion-Acoustic Waves in a Plasma

Stationary solutions of the coupled equations for high frequency transverse waves in a plasma and for the low frequency ion motion (T_e?T_i) are investigated numerically. The use of the nonlinear hydrodynamic equations instead of the linear wave equation for ion acoustic waves allows to look for solutions without restrictions of the Mach number M = V/c_s (V group velocity, c_s ion acoustic velocity) and the ratio ω/ω_pe (ω frequency of the HF-field, ω_pe electron plasma frequency at the undisturbed region). In particular, supersonic soliton-like solutions with n/n_o > 1 were found. Dispersion effects due to charge separation are not included.     

Two-photon echo method to determine the transverse relaxation time of excitonic molecules

A nonlinear optical method to determine the transverse relaxation time of excitonic molecules by means of two-photon echo is proposed. In the case of two-photon transition such as excitonic molecule one needs three pulses to obtain an echo signal. When the wave-vector and frequency of the three successive pulses are denoted by k₁,ω₁, k₂,ω₂ and k₃,ω₃, the two-photon echo can be observed in the direction of 4k₂-2k₁-k₃ with frequency 4ω₂-2ω₁-ω₃. Tuning both ω₁ and ω₂ to be two-photon resonant with excitonic molecule, we can satisfy the phase-matching condition rather easily for appropriate values of ω₃ due to the large dispersion of excitonic polaritons. From the correlation trace of the two-photon echo we can determine directly the transverse relaxation time of excitonic molecules.     

Singular Resonance in Fluctuation-Induced Electromagnetic Phenomena at the Rotation of a Nanoparticle near the Surface of a Condensed Medium

It has been shown that the rotation of a spherical nanoparticle with the radius R near the surface of a semi-infinite homogeneous medium can result in singular resonance in fluctuation-induced electromagnetic phenomena (Casimir force, Casimir friction, and radiative heat generation). Fluctuation electromagnetic effects increase strongly near this resonance even in the presence of dissipation in the system. The resonance occurs at distances of the particle from the surface d < d₀R(3/4ε″₁(ω₁)ε″₂ (ω₂))^1/3 (where ε″_i(ω_i) is the imaginary part of the dielectric function of the particle or the medium at the frequency of a surface phonon or plasmon polariton ω_i), when the rotation frequency coincides with poles in the photon generation rate at Ω ≈ ω₁ + ω₂. These poles are due to the multiple scattering of electromagnetic waves between the particle and surface under conditions of the anomalous Doppler effect. These poles exist even in the presence of dissipation. At d < d₀, depending on the particle rotation frequency, the Casimir force can change sign; i.e., the attraction of the particle to the surface changes to repulsion. The results can be important for the development of experimental methods for the detection of quantum friction.     

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.     

The permittivity of a monatomic gas with spatial dispersion

The longitudinal, ε^l(ω, k), and transverse, ε^tr(ω, k), permittivities of a monatomic gas were calculated. The frequency ranges in which the permittivity ε(ω) and permeability μ(ω) of a gas without spatial dispersion have a physical meaning were determined. The limiting magnetic susceptibility χ(ω) at ω=0 and the static magnetic susceptibility were found. The question of whether an electromagnetic wave with antiparallel group and phase velocities can propagate through a monatomic gas is discussed.