Sum-Frequency Generation from a Thin Cylindrical Layer

In the Rayleigh–Gans–Debye approximation, we have solved the problem of the sum-frequency generation by two plane elliptically polarized electromagnetic waves from the surface of a dielectric particle of a cylindrical shape that is coated by a thin layer possessing nonlinear optical properties. The formulas that describe the sum-frequency field have been presented in the tensor and vector forms for the second-order nonlinear dielectric susceptibility tensor, which was chosen in the general form, containing chiral components. Expressions describing the sum-frequency field from the cylindrical particle ends have been obtained for the case of a nonlinear layer possessing chiral properties. Three-dimensional directivity patterns of the sum-frequency radiation have been analyzed for different combinations of parameters (angles of incidence, degrees of ellipticity, orientations of polarization ellipses, cylindrical particle dimensions). The mathematical properties of the spatial distribution functions of the sum-frequency field, which characterize the symmetry of directivity patterns, have been revealed.     

Sum-Frequency Generation from a Thin Spherical Layer: II. Analysis of Solution

We have analyzed the influence of the angle between the wave vectors of two incident waves (the opening angle) and of the type of the anisotropy of a nonlinear layer on the shape of the directivity pattern of a sum-frequency harmonic generated by the two plane elliptically polarized electromagnetic waves from a thin spherical optically nonlinear layer deposited on the surface of a dielectric spherical particle placed in a dielectric. Our analysis has shown that, if the radius of the thin spherical nonlinear layer is small, the shape of the directivity pattern will change significantly with increasing opening angle only for some types of anisotropy: the main lobes shift toward the direction that is opposite to the direction of the sum of the wave vectors of the incident waves. For three types of anisotropy, the directivity patterns have similar shapes. We have also found that, for one of the types of the anisotropy, the shape of the directivity pattern remains unchanged upon a change in the opening angle. The mathematical properties of functions describing the spatial distribution of the generated harmonic have been determined. In particular, it has been found that, upon incidence of linearly polarized waves on a thin nonlinear spherical layer that possesses either solely chiral or solely nonchiral nonlinear properties, linearly polarized radiation of the sum-frequency harmonic is generated.     

Classical theory of non-degenerate sum-frequency generation by incoherent nonlinear optical mixing of coherent and chaotic radiations II. Coherent and chaotic input radiations — Efficiency and spectral distribution

Sum-frequency generation by incoherent nonlinear optical mixing of one coherent and one chaotic, mutually uncorrelated input radiations in a dispersive medium is treated in this paper. The efficiency of the process is calculated in the second approximation of the iterative method. It is shown that for perfect phase matching or small phase mismatch of interacting waves and small spectral width of chaotic input radiation the efficiency of incoherent sum-frequency generation can be enhanced compared with the coherent interaction due to the difference between group velocities of sub-frequency radiations. On the other hand, for greater spectral width the efficiency of the process decreases with increasing spectral width of chaotic input radiation. In the case of considerable phase mismatch the efficiency of sum-frequency generation first decreases, but then increases with increasing spectral width of chaotic input radiation. The spectral distribution of the resulting sum-frequency radiation is calculated in the first approximation of the iterative method. There is a general tendency to narrowing the spectral distribution of generated radiation in the course of the process. Moreover, when there is phase mismatch present, a spectral shift of the maximum of generated radiation towards blue or red region, according to the signs of the phase mismatch and the typical dispersion coefficient, appears in the later phases of the sum-frequency generation.This work was partially supported by Research Project C.P.B.P. 01. 07.     

Classical theory of non-degenerate sum-frequency generation by incoherent nonlinear optical mixing of coherent and chaotic radiations

The incoherent nonlinear optical sum-frequency generation with non-monochromatic initially uncorrelated sub-frequency input radiations in a dispersive medium is studied in this paper. The efficiency of the process is calculated in the second approximation, whilst the spectral distribution of generated radiation is merely described in terms of the first approximation of the iterative method. The calculations of the efficiency of nonlinear process and the spectral distribution of sum-frequency radiation are performed for one coherent and the other chaotic input radiations, and for both chaotic input radiations, respectively.This work was partially supported by Research Project C.P.B.P. 01. 07.     

Classical theory of sum-frequency generation by coherent nonlinear optical mixing of coherent and chaotic radiations II. Conserved statistics solution

The problem of nonlinear optical sum-frequency generation and second harmonic generation is solved by a method neglecting changes of statistics of generating radiations. It is shown here that the increase of fluctuation levels in subfrequency radiations reduces the total efficiency of the sum-frequency generation, whilst in the degenerate case the second harmonic generation is accelerated with an increasing fluctuation level in the fundamental radiation. Total efficiencies of real nonlinear processes are estimated at the end of the paper.     

Molecular QED of coherent and incoherent sum-frequency and second-harmonic generation in chiral liquids in the presence of a static electric field

Coherent second-order nonlinear optical processes are symmetry forbidden in centrosymmetric environments in the electric-dipole approximation. In liquids that contain chiral molecules, however, and which therefore lack mirror image symmetry, coherent sum-frequency generation is possible, whereas second-harmonic generation remains forbidden. Here we apply the theory of molecular quantum electrodynamics to the calculation of the matrix element, transition rate, and integrated signal intensity for sum-frequency and second-harmonic generation taking place in a chiral liquid in the presence and absence of a static electric field, to examine which coherent and incoherent processes exist in the electric-dipole approximation in liquids. Third- and fourth-order time-dependent perturbation theory is employed in combination with single-sided Feynman diagrams to evaluate two contributions arising from static field-free and field-induced processes. It is found that, in addition to the coherent term, an incoherent process exists for sum-frequency generation in liquids. Surprisingly, in the case of dc-field-induced second-harmonic generation, the incoherent contribution is found to always vanish for isotropic chiral liquids even though hyper-Rayleigh second-harmonic generation and electric-field-induced second-harmonic generation are both independently symmetry allowed in any liquid.     

Three-wave mixing in chiral liquids

Second-order nonlinear optical frequency conversion in isotropic systems is only dipole allowed for sum- and difference-frequency generation in chiral media. We develop a single-center chiral model of the three-wave mixing (sum-frequency generation) nonlinearity and estimate its magnitude. We also report results from ab initio calculations and from three- and four-wave mixing experiments in support of the theoretical estimates. We show that the second-order susceptibility in chiral liquids is much smaller than previously thought.     

耦合双振子模型手性分子的微观参量对和频过程的影响

用经典理论方法推出了适合于耦合双振子模型的手性分子的超极化率,给出了分子超极化率与分子微观参量的关系式.由微观与宏观极化率的关系,具体讨论了分子微观参量对宏观介质极化与和频过程产生效率的影响,本模型得到的理论结果与已有的实验结果很好地符合. 关键词： 手性分子介质 和频产生 超极化率 二阶极化率     

双轴晶体LiB3O5和频与倍频转换特性的研究

本文在光学主轴坐标系下,对双轴晶体LiB3O5共线和频与倍频特性进行了计算与分析.给出了xy面应用tyyeⅠ相位匹配及yz面应用typeⅡ相位匹配情况下,基波波长与相位匹配角、有效非线性系数、离散角、容承角及基波频谱带宽的关系曲线,对LiB3O5晶体的实验与应用提供了有指导意义的理论结果.     

Improving the resolution in quantum and classical temporal imaging

The point-spread function of an optical system determines its optical resolution for both spatial and temporal imaging. For spatial imaging, it is given by a Fourier transform of the pupil function of the system. For temporal imaging based on nonlinear optical processes, such as sum-frequency generation or four-wave mixing, the pointspread function is related to the waveform of the pump wave by a nonlinear transformation. We compare the point-spread functions of three temporal imaging schemes: sum-frequency generation, co-propagating four-wave mixing, and counter-propagating four-wave mixing, and demonstrate that the last scheme provides the best temporal resolution. Our results are valid for both quantum and classical temporal imaging.     

The fluorescence rate of a single molecule close to a spherical metallic nanoparticle

The theoretical study of fluorescence rate of a single molecule close to a spherical metallic nanoparticle is presented. The dielectric function of the metallic nanoparticle and its polarizability is analyzed when the radii of the nanoparticle is rather small. Based on dipole–dipole model, the distance dependence of the excitation rate, radiation rate, nonradiation rate and quantum yield of the emitter molecule are derived out. The results show that the quantum yield is rather small at the vicinity of the metallic nanoparticle surface.     

Optical extinction for determining the size distribution of gold nanoparticles fabricated by ultra-short pulsed laser ablation

This work presents a method, based on measurements of the optical extinction spectra, to determine the size of spherical gold nanoparticles produced using the femtosecond laser ablation process in deionized water. By using an improved theoretical model that modifies the contribution of the free electrons to the dielectric function introducing a size-dependent term, it is possible to fit the full experimental extinction spectrum considering a certain size distribution. Additionally, in order to obtain complementary measurements of the size distribution, TEM analysis was performed. The results obtained showed that the predominant nanoparticle size distribution ranges from 1 to 11 nm in terms of radii. An optical extinction measurement together with an appropriate theoretical model based on Mie’s theory represents a simple, low-cost, fast and easy method to describe a multimodal size distribution of spherical gold nanoparticles.     

Thin-film narrowband tunable dye laser

We report a relatively simple system for obtaining a smoothly frequency tunable narrowband laser radiation. The action of the system is based on the possibility of quasiwaveguide generation of the amplifying layer inserted between two passive dielectric media. The retunable radiation in the wavelength range 570–610 nm was obtained and the generation line width was 0.01 nm.     

Natural Electromagnetic Waves in a Circular Waveguide with a Chiral and a Dielectric Layer

Based on particular solutions of a system of wave equations which describe electromagnetic processes in an unbounded biisotropic medium and are represented in the form of generalized power series, a dispersion equation is obtained for a two-layer circular waveguide with a chiral and a dielectric layer. The solution of the dispersion equation is analyzed for some types of natural waves.     

Orbiting naked singularities in large-$$\omega $$ Brans–Dicke gravity

Brans–Dicke gravity admits spherical solutions describing naked singularities rather than black holes. Depending on some parameters entering such a solution, stable circular orbits exist for all radii. One shows that, despite the fact a naked singularity is an infinite redshift location, the far observed orbital motion frequency is unbounded for an adiabatically decreasing radius. We then argue that this feature remains true in a wide set of scalar(s)–tensor theories if gravity. This is a salient difference with general relativity, and the repercussion on the gravitational radiation by EMRI systems is stressed. Since this behaviour survives the \(\omega \longrightarrow \infty \) limit, the possibility of such solutions is of utmost interest in the new gravitational wave astronomy context, despite the current constraints on scalar–tensor gravity.     

A kinetic model for droplet growth in the transition regime

A variant of the moment expansion method, used in an earlier paper to describe the flow of a gas toward an absorbing sphere, is applied to a more realistic model of a droplet condensing from a supersaturated vapor. In the simplest version a spherical droplet absorbs all incoming vapor molecules, but spontaneously emits molecules with a Maxwellian distribution at the droplet temperature and with the corresponding saturated vapor density. From a solution of the stationary linearized Boltzmann equation with these boundary conditions we obtain expressions for the heat and mass currents toward the sphere as a function of the supersaturation and the temperature difference between the droplet and the vapor at infinity. For small droplet radii the known free flow limit is obtained in a natural way. From the calculated expressions for the heat and mass current we derive evolution equations for the radius and temperature of the droplet. The temperature evolves more rapidly and can thus be eliminated adiabatically; the resulting growth curve for the radius shows a sharp transition from a kinetically controlled regime for small radii to a regime dominated by heat conduction for large radii. The effect of incomplete absorption at the surface is also studied. The actual calculations are carried out for Maxwell molecules, with parameters corresponding to argon at 0.65T _c and 100% supersaturation.     

Quasi-phase-matched sum-frequency generation in layered structures

A theory has been developed for quasi-phase-matched generation of a wave at a sum-frequency within a constant-intensity approximation. In contrast to a constant-field approximation, the constant-intensity approach has been found to give an optimum pump intensity value at which the conversion efficiency reaches its maximum. Analytical expressions have been derived for optimal values of the problem’s parameters. Ways to enhance the power of the coherent optical radiation are shown and analyzed. This will make it possible, in particular, to increase the power in an RGB-source color for which the sum-frequency generation is responsible.     

Theoretical model of phase exclusion conditions for the sum-frequency wave produced by a nonlinear acoustic source

A theoretical model of the sum-frequency wave field produced by a nonlinear acoustic source with three-frequency pumping is reported. The model allows for the dissipation and diffraction of the Gaussian beam. The sum-frequency wave is represented within the second-order approximation as a superposition of two synchronous copropagating waves with equal frequencies. It is shown that the spatial and amplitude-phase characteristics of the sum-frequency wave are affected not only by the amplitude-phase relations in the pumping spectrum, but also by the diffraction-caused variations in amplitudes and phases of the primary waves. This dependence is most clearly seen under the phase exclusion conditions, when the generation of the sum-frequency wave is actually suppressed (excluded) owing to the appropriate choice of the amplitude and phase pumping spectra. The theoretical results are found to agree well with experimental data. The possible practical applications of the phase exclusion conditions are as follows: inspection of inhomogeneous media, detection of objects near interfaces, reduction of nonlinear attenuation, acoustic measurements, etc.     

负性介电各向异性向列相液晶中空间光孤子的理论研究

对非局域非线性介质向列相液晶中介电各向异性为负时的情况进行了研究.理论研究表明,负性介电各向异性的向列相液晶具有负的非线性系数.文中给出了其空间非局域响应特征宽度和非线性系数的表达式,并求出了其非局域响应函数;其次,用数值计算的方法给出了其空间孤子的传输结果.最后,研究了光束功率和偏置电压的改变对负性介电各向异性向列相液晶中光束传输的影响,发现偏置电压的改变会导致光束在负性介电各向异性液晶中形成孤子所需的临界功率发生改变.     

Nanophotonics of isolated spherical particles

The problem of extreme focusing of an optical beam into the spatial region with wavelength dimensions is considered with the use of the special features of radiation interaction with isolated spherical particles. Results of numerical computations of the optical field intensity at the surface of silver particles of different radii upon exposure to laser radiation with different wavelengths are presented. It is demonstrated that the relative intensity of the plasmon optical field on the nanoparticle surface increases and the field focusing region decreases with increasing particle radius. Results of numerical computations illustrating the influence of the shell of composite nanoparticles comprising a dielectric core and a metal shell on the optical field intensity in the vicinity of the particle are presented. The problem of local optical foci of a transparent microparticle (photonic nanojets) is investigated. It is established that variation of the micron particle size, its optical properties, and laser radiation parameters allows the amplitude and spatial characteristics of the photonic nanojet region to be controlled efficiently.