Paraxial Approximation of Modern Radiometry for Beamlike Wave Propagation

A new approach to the construction of a system of the generalized radiometric quantities expressed in terms of the cross-spectral density function of the wave field is proposed. The key distinction of this approach lies in the fact that the initial hypothesis of beamlike wave propagation allows to invoke the paraxial approximation when deducing the generalized radiant flux. Within the framework of this approach the new expressions for the generalized radiant emittance, the generalized radiant intensity and the generalized radiance are derived. All the proposed generalized radiometric characteristics represent physically measurable quantities and, hence, may be used in practical radiometry. The results obtained in this paper can be regarded as a particular case of the modern radiometry theory in paraxial approximation for beamlike wave propagation.On leave from Kiev Polytechnic Institute, Ukraine.     

Series representation of the Gaussian beam far-field diffracted by annular aperture

Accurate, analytical series expressions for the far-field diffraction of a Gaussian beam normally incident on a circular and central obscured aperture are derived with the help of the integration of parts method. With this expression, the far-field intensity distribution pattern can be obtained and the divergence angle is deduced too. Using the first five items of the series, the accuracy can satisfy most laser application fields. Compared with the conventional numerical integral method, the series representation is very convenient for understanding the physical meanings.     

Emergence of spatiotemporal chaos arising from far-field breakup of spiral waves in the plankton ecological systems

It has been reported that the minimal spatially extended phytoplankton--zooplankton system exhibits both temporal regular/chaotic behaviour, and spatiotemporal chaos in a patchy environment. As a further investigation by means of computer simulations and theoretical analysis, in this paper we observe that the spiral waves may exist and the spatiotemporal chaos emerge when the parameters are within the mixed Turing--Hopf bifurcation region, which arises from the far-field breakup of the spiral waves over a large range of diffusion coefficients of phytoplankton and zooplankton. Moreover, the spatiotemporal chaos arising from the far-field breakup of spiral waves does not gradually invade the whole space of that region. Our results are confirmed by nonlinear bifurcation of wave trains. We also discuss ecological implications of these spatially structured patterns.     

Ion cyclotron electrostatic waves in a low-temeprature low-density magnetized plasma

Summary The electrostatic dispersion relation for a low-temperature, low-density magnetized plasma has been studied in the range of the ion cyclotron frequency and its first harmonics. The presence of a forward wave and of an infinite number of backward waves has been shown. The characteristics of propagation of these modes and the possibility of conversion are analysed.

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Riassunto Viene studiata la relazione di dispersione elettrostatica relativa ad un plasma magnetizzato di bassa densità e di bassa temperatura nel campo della frequenza ciclotronica ionica e delle sue prime armoniche. Si mostra la presenza di un unico modo forward e di un insieme infinito di modi backward. Si analizzano le caratteristiche di propagazione di queste onde e la possibilità di conversioni tra di esse.

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Резюме Исследуется электростатическое дисперсионное соотношение для намагниченной плазмы с низкой температурой и низкой плотностью в области ионной циклотронной частоты и ее первой гармоники. Показывается наличие единственной моды в направлении вперед и бесконечного числа волн в обратном направлении. Анализируются характеристики распространения этих мод и возможность конверсии.

     

Stimulated brillouin scattering of electromagnetic waves in an-type InSb-filled rectangular waveguide

Summary This paper presents a theoretical investigation of the stimulated Brillouin scattering of a beam of electromagnetic radiation in a semiconductor-filled rectangular waveguide. The incident electromagnetic wave decays parametrically into a low-frequency electrostatic ion acoustic wave and a scattered electromagnetic sideband. For typical plasma parameters in an-InSb-filled rectangular waveguide and when the pump-induced drift velocity of electrons,v ₀, is comparable to the ion acoustic velocity,C _s , inn-InSb (i.e. |v ₀/C _s |≅1), the growth rate of the decay waves turns out to be ∼10³ rad s⁻¹ for a 3 cm microwave and ∼10⁷ rad s⁻¹ for a CO₂ laser radiation. The growth rate of the instability vanishes at the boundary of the waveguide.

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Riassunto Questo articolo presenta uno studio teorico dello scattering stimolato di Brillouin di un fascio di radiazione elettromagnetica, in una guida d’onda rettangolare riempita con un semiconduttore. L’onda elettromagnetica incidente decade parametricamente in un’onda elettrostatica a bassa frequenza di ioni e in una banda laterale elettromagnetica diffusa. Per parametri tipici del plasma in una guida d’onda rettangolare riempita conn-InSb e quando la velocità di deriva degli elettroni indotta dalla pompa,v ₀, è confrontabile con la velocità ionicaC _s inn-InSb (cioè |v ₀/C _s |≅1), la velocità di crescita delle onde di decadimento risulta di ∼10³ rad s⁻¹ per una microonda di 3 cm e ∼10⁷ rad s⁻¹ per una radiazione di laser a CO₂. La velocità di crescita dell’instabilità si annulla agli estremi delle guide d’onda.

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Резюме Эта статья представляет теоретическое исследование стимулированного бриллюэновского рассеяния пучка электромагнитного излучения в полупроводнике, заполняющем прямоугольный волновод. Падающая электромагнитная волна распадается параметрически на низкочастотную электростатическую ионную акустическую волну и рассеянную электромагнитную побочную полосу. Для типичных плазменных параметров вn-InSb, заполняющем прямоугольный волновод, и когда насос индуцирует дрейфовую скорость электронов,v ₀, сравнимую с ионной акустической скоростью,C _s , вn-InSb (т.е. |v ₀/C _s |≅1), интенсивность образования распадных волн составляет ∼10³ рал c⁻¹ для 3 см микроволнового излучения и ∼10⁷ рад c⁻¹ для излучения CO₂ лазера. Интенсивность образования неустойчивости обращается нуль на границе волновода.

     

Experimental study of solitary waves in a nonlinear transmission line

Several properties of solitary waves were measured on a nonlinear transmission line. These include the transition from a linear dispersive response into a solitary wave response as the amplitude of a narrow voltage impulse is increased, and an observation of the recurrence phenomena of solitary waves. Supported in part by the National Science Foundation.     

含气泡液体中的非线性声传播

考虑到分布在液体中的气泡是声波在含气泡液体中传播时引起非线性的一个很重要的因素,本文研究了声波在含气泡液体中的非线性传播.将气体含量的影响引入到声波在液体中传播的方程中,从而得到声波在气液混合物中传播的数学模型.通过对该模型进行数值模拟发现,气体含量、驱动声场声压幅值及驱动声场作用时间均会影响到气液混合物中的声场分布及声压幅值大小.液体中的气泡会"阻滞"液体中声场的传播并将能量"聚集"在声源附近.对于连续大功率的驱动声场来说,液体中的气泡会"阻滞"气液混合物中声场及其能量的传播.     

Paraxial propagation in disclinated amorphous media

We study paraxial beam propagation along the wedge axis of a disclinated amorphous medium. The defect-induced inhomogeneity results in Berry phase and curvature that are affected by the induced uniaxial anisotropy. The Berry phase manifests itself as a precession of the polarization vector. The Berry curvature is responsible for the optical spin Hall effect in the disclinated medium, where beam deflection varies sinusoidally along the paraxial direction. Its application in determining the birefringence and the magnitude of the Frank vector is explained.     

Propagation of electron cyclotron waves in a weakly relativistic plasma with steep density and temperature profiles

Summary A detailed analysis is made of the deduction of systems of differential equations describing the propagation of both ordinary and extraordinary waves in the electron cyclotron frequency range in a stratified plasma, perpendicularly to the magnetic field and across the electroncyclotron fundamental resonance layer. The equations are derived under conditions of not too large electron temperature (the so-called weakly relativistic condition) and of very weak nonuniformities of the confining magnetic field. The effects of the nonhomogeneities of the equilibrium plasma density and temperature are carefully examined. It is shown that the propagation equations derived previously in the literature can be extended with only a moderately larger effort in computations to take account also of very strong density and temperature gradients.     

Ordinary and extraordinary cyclotron waves in metals

Dispersion equations for the ordinary and extraordinary cyclotron waves propagating perpendicular to the magnetic field in metals in the critical region where the wavelength is comparable to the electron Larmor radius are derived as an infinite but rapidly converging power series expansion in δ( = Ω/Ω-M). Numerical studies for the cyclotron wave propagation near the first seven resonances are carried out. The non-local behaviour of those waves in the critical region 01 ⩽ kR ⩽ 3-0 is studied. For the ordinary waves the first few resonances show significant dispersion than those near higher resonances which are dispersion-free. Only one extraordinary wave propagates near the fundamental cyclotron frequency. For the higher resonances, two modes propagate near each of the resonant frequencies, of which one mode remains constant for all values ofkR whereas the second mode shows significant dispersion. But beyond the fifth resonance both the modes are dispersion free.     

Theoretical and experimental investigation of millimeter wave phase fluctuations in an absorption region

The differential phase scintillations between two neighbouring frequencies on the side of the oxygen absorption peak have been measured. The –8/3 slope of the asymptotes to the measured spectra at the lowest and highest scintillation frequencies and the spectral ratio between these asymptotes are in good agreement with the theoretical model proposed.     

Influence of water vapor pressure fluctuations on the spectral density of millimeter wave amplitude scintillations in an absorption region

Results are presented of scintillation spectra, measured at 54.5GHz on a 4.1 km line of sight path, when the variance of the water vapour pressure fluctuations (_e ²) is very much greater than the variance of the temperature fluctuations (_T ²). The effect of _e ² under these conditions is established both through the experimental results and the theoretical considerations which are also presented.     

Influence of atomic defect generation on the propagation of elastic waves in laser-excited solid layers

The mechanical behavior of solid layers subjected to laser irradiation is investigated by a dynamical model that is based on coupled evolution equations for the elastic displacement of the medium and lattice defect-density fields. The evolution of defect-density is governed by the (i) generation of defects by irradiation, (ii) their diffusion and recombination and (iii) diffusion induced by strain field. The strain field associated with lattice dilatation due to atomic defects is shown to couple with deformation fields of the layer. Frequency equations corresponding to the symmetric and anti-symmetric modes of vibration of the layer are obtained. It is found that coupling between diffusion and strain fields cause dispersion of the general waveform. Explicit expressions are defined for the wave velocity, and the attenuation (amplification) coefficients which characterize these waves.     

不同形状孔缝微波耦合的实验研究

探讨了椭圆、圆环、方环、十字交叉形、圆形、正方形、正三角形及双矩形孔缝在2～18GHz频率范围内的耦合系数，并与矩形孔缝的耦合特性进行了比较。结果表明: 各种不同形状孔缝微波耦合的共振特性与其纵横比有关, 纵横比较大的孔缝耦合共振现象比较明显，纵横比较小的孔缝耦合特性趋于高通；各种孔缝的共振频率与孔缝长度有密切关系。     

A note on Snell laws for electromagnetic plane waves in lossy media

Based on Maxwell's equations and Ohm's law, we rederived the Snell laws for reflection and transmission of harmonic inhomogeneous plane electromagnetic (EM) waves propagating through planar lossy interfaces. The present results are new, simple and exact and they recover the ordinary Snell laws in the case of lossless media. Besides, these results show that the wave propagation direction strongly depends on the polarization state of the EM wave and the lossy media can behave as a polarizing device. Moreover, we verify that in low frequency regime these traveling waves do not exhibit total internal reflection at interfaces between two adjacent lossy media.     

Extinction theorem and propagation of electromagnetic waves between two anisotropic materials

We systematically investigate the reflection and refraction of an electromagnetic wave between two semi-infinite anisotropic magnetoelectric materials. Using the integral formulation of Hertz vectors and the principle of superposition, we generalize the extinction theorem and derive the propagation characteristics of wave. Applying the results obtained, we find a general origin of Brewster effect. We also show that, through choosing appropriate material parameters, oblique or omnidirectional total transmission can occur to TE and TM waves. Compared to the traditional method, the method used here discloses the underlying mechanism of wave propagation between two arbitrary anisotropic materials and can be applied to other problems of propagation.     

Nonparaxial diffraction of vectorial plane waves at a small aperture

By using the vectorial Rayleigh diffraction integrals, a nonparaxial propagation equation of vectorial plane waves diffracted at a small rectangular aperture is derived analytically and some special cases are discussed. Numerical calculation results are given to illustrate the applicability and validity of our theoretical formulae. It is shown that for the apertured case the ratio of the aperture width and wavelength affects the beam nonparaxiality. The nonparaxial approach presented in this paper has to be used for diffracted plane waves if the aperture width is comparable with or less than the wavelength.     

流体/准饱和多孔介质中伪Scholte波的传播特性

研究流体/多孔介质界面Scholte波的传播特性对于水下勘探、地震工程等领域具有重要意义.本文基于Biot理论和等效流体模型,采用势函数方法,推导了描述有限厚度流体/准饱和多孔半空间远场界面波的特征方程和位移、孔压计算公式.在此基础上,分别以砂岩和松散沉积土为例,研究了流体/硬多孔介质和流体/软多孔介质两种情况下,可压缩流体层厚度和多孔介质饱和度对伪Scholte波传播特性的影响.结果表明：多孔介质软硬程度显著影响界面波的种类、相速度、位移和水压力分布;有限厚度流体/饱和多孔半空间界面处伪Scholte波相速度与界面波波长和流体厚度的比值有关;孔隙水中溶解的少量气体对剪切波的相速度的影响不大,对压缩波相速度、伪Scholte波相速度和孔隙水压力分布影响显著.     

A fresh outlook for Fresnel diffraction

Fresnel theory, with certain level of assumptions, explains satisfactorily observed diffraction patterns. It is a scalar theory and basically it deals special way of superposition of fields originated from several points of Huygens wave front. In the present paper a total new approach is proposed according to which the interacting electric fields are not originated from the secondary emitters of the same wave front, instead, they are originated from the successive Huygens wave fronts. The proposed approach is explained with the help of the circular aperture. This new view supports Fresnels theory without a set of assumptions.