This book explores generalized lorenzmie theories when the illuminating beam is an electromagnetic arbitrary shaped beam relying on the method of separation of variables. Dtu informatics, technical university of denmark, richard petersens plads, building 321, dk2800 kgs. The mie solution to maxwells equations also known as the lorenzmie solution, the lorenzmiedebye solution or mie scattering describes the scattering of an electromagnetic plane wave by a homogeneous sphere. Iii generalized lorenzmie theory in the strict sense, and other glmts. Pdf particle positioning from chargecoupled device images. The lorenz mie theory, describing the interaction between a homogeneous sphere and an electromagnetic plane wave, is likely to be one of the. Generalized lorenzmie theory and applications request pdf. These scattering prop erties can be acquired by measurements, by manual adjustment to. The names wiedemannfranz lorenz law and lorenz number derive from this work. Comparisons between geometrical optics and lorenzmie theory. Accordingly, mie scattering theory has no size limitations and converges to the limit of geometric optics for large particles. But also, one normally thinks that by this time all its important consequences have already been discovered, and the theory is of no further active research interest. Study of scattering phase matrix of spherical particles using. The model is compared to the classical lorenzmie theory, plane wave case, and to.
The lorenz mie theory, describing the interaction between a homogeneous sphere and an electromagnetic plane wave, is likely to be one of the most famous theories in light scattering. Our theory is based on a robust generalization of the lorenzmie theory. The lorenz mie theory was a classical method to calculate the scattering properties of a single homogeneous particle. Computing the scattering properties of participating media using lorenzmie theory jeppe revall frisvad 1niels jorgen christensen henrik wann jensen2 1informatics and mathematical modelling, technical university of denmark 2university of california, san diego figure 1. Mie 1908, which is a complete so lution to maxwells equation for scattering of electromagnetic waves by a homogeneous, spherical particle embedded in a non. Definitions, terminology and symbols in colloid and surface chemistry.
The resonant spectrum of a dielectric sphere reveals the existence of two distinctive types of polarization. Scattered light patterns produced by spherical transparent particles of a wide range of diameters 1100. Mie scattering theory, making possible to compute holograms of fields of particles with an arbitrary number of particles of arbitrary size, arbitrary refractive index, arbitrary recording distance, and arbitrary collecting angle. Lorenzmie theory for 2d scattering and resonance calculations. The basic formulas of generalized lorenzmie theory are presented, and are applied to scattering of a focused gaussian laser beam by a spherical parti. Generalized lorenzmie theories books pics download. Previous models using lorenzmie theory have been limited to nonabsorbing media with spherical particles such as paints and clouds. Computing the scattering properties of participating media.
This book presents in a concise way the mie theory and its current applications. The basic formulas of generalized lorenzmie theory are presented, and are applied to scattering of a focused gaussian laser beam by a. The fact that lorenz and mie theories are physically equivalent but relied on two different frameworks, a mechanical framework for lorenz and a maxwell electromagnetic framework for mie, points out to a classical thesis in epistemology, namely the one of underdetermination of theories by experiments. Computing the scattering properties of participating. For scattering alone, an expansion of the efficiency factor in x based on mie theory discussed below gives 8 3 5. The basic formulas of generalized lorenz mie theory are presented, and are applied to scattering of a focused gaussian laser beam by a spherical particle. Generalized lorenz mie theory for an arbitrarily oriented, located, and shaped beam scattered by a homogeneous spheroid. The lorenzmie theory, describing the interaction between a homogeneous sphere and an electromagnetic plane wave, is likely to be one of the most famous theories in light scattering. Click download or read online button to get the mie theory book now. Investigation of polarizationdependent optical force in. Light scattering resonances in small particles with electric. The scattering properties are computed using the scattering amplitude functions s 1 and s 2, which describe the scattering of an electromagnetic wave from a spherical particle lorenz 1890.
A detailed comparison of the results leads to a definitive assessment of the accuracy of lorenz mie theory in the forward direction. In this paper, the glmt is employed to rigorously calculate optical force exerted on a sphere in the mie regime induced by an airy lightsheet. Numerical examples of such computations will be given. On geometric optics and surface waves for light scattering.
Therefore, lorenz mie theory provides a method for the calculation of the optical forces within the trap 2. Pdf generalized lorenzmie theory for an arbitrarily oriented. Optical force on a mie particle by an airy lightsheet using. One is the theory of rayleigh scattering after lord rayleigh that is, strictly speaking as originally formulated, applicable to small, dielectric nonabsorbing, spherical particles. Validity of the localized approximation for arbitrary shaped. Mie theory definitions rayleigh scattering refers primarily to the elastic scattering of light from atomic and molecular particles whose diameter is. Application of lorenz mie theory in graphics frisvad, j. Danish physicist ludvig lorenz and others independently developed the theory of electromagnetic. We can see from this comparison that the airy theory is suitable to compute rainbows, especially around the. Mie theory describes the scattering and absorption of electromagnetic radiation by spherical particles through solving the maxwell equations. Mie theory is also called lorenz mie theory or lorenz mie debye theory. Lorenzmie theory extinction polarization scattering matrix.
The classical lorenzmie theory is limited to spherical particles. Osa generalized lorenzmie theory for an arbitrarily. We will focus on mie scattering theories but as there is much overlap to related scattering theories they will also be mentioned where appropriate. The classical lorenzmie theory describing sphereplane wave interactions. This site is like a library, use search box in the widget to get ebook that you want. This phd tutorial is concerned with a description of the twodimensional generalized lorenz mie theory 2dglmt, a wellestablished numerical method used to compute the interaction of light with arrays of cylindrical scatterers. Click download or read online button to get generalized lorenz mie theories book now. One normally thinks that when a theory, such as lorenzmie theory, has lasted for one hundred years, it has certainly passed the test of time. In his last contribution to physics, dating from 1890, lorenz developed on a nonelectromagnetic basis a comprehensive theory of the scattering of light by a sphere. Pdf scattering and absorption property database for. Generalized lorenzmie theory glmt is an exact solution of the maxwell equations, and can rigorously predict the optical force on a homogeneous spherical particle induced by laser beams 5. These parameters are the extinction and scattering coefficients, the phase function, and the index of refraction. In this quest, we have selected a range of real and imaginary refractive indices representative of waterice and aerosol species and demonstrated close agreement between the results. Particle positioning from chargecoupled device images by the generalized lorenz mie theory and comparison with experiment.
The incident beam is expanded in terms of the spheroidal vector wave functions and described by a set of beam shape coefficients g n, t m m, g n, t e m. Lorenzmie theory makes it possible to compute the scattering properties of a single homogeneous, spherical particle embedded in a homogeneous medium. Teledyne api model 640 field comparison with the thermo. The theory of an arbitrarily oriented, shaped, and located beam scattered by a homogeneous spheroid is developed within the framework of the generalized lorenz mie theory glmt. Farfield lorenzmie scattering in an absorbing host. The lorenz mie theory, scattering of light, phase matrix elements, refracting index. Scattering may be defined as the redirection of radiation from the original propagation direction. Development of a global rainbow refractometry technique to.
It begins with an overview of current theories, computational methods, experimental techniques, and applications of optics of small particles. Many optical sizing techniques rely on particlelaser interac tions. Various applications of focused beam scattering are also described, such as optimizing the rate at which morphologydependent resonances are excited, laser trapping, particle manipulation, and the analysis of optical particle sizing instruments. Pdf generalized lorenzmie theory for an arbitrarily. Our generalized theory is capable of handling both absorbing host media and nonspherical particles. Scattering light from a spherical particle located onaxis to an electromagnetic spherical wave is numerically predicted using the generalized lorenzmie theory glmt. The new edition includes an additional chapter covering the latest advances in both research and applications, which are highly. Scattering and extinction by spherical particles immersed in. Computing the scattering properties of participating media using lorenzmie theory jeppe revall frisvad1 niels jorgen christensen1 henrik wann jensen2 1informatics and mathematical modelling, technical university of denmark 2university of california, san diego figure 1. Optical force on a mie particle by an airy lightsheet. Measurements of particle size distribution based on mie scattering theory and markov chain inversion algorithm pdf.
A detailed comparison of the results leads to a definitive assessment of the accuracy of geometrical optics theory in the forward direction. Generalized lorenzmie theories books pics download new. Measurement and evaluation of elastic light scattering. The generalized lorenzmie theory glmt gives the general expressions for electromagnetic scattering by spherical, homogeneous and isotropic scatterers.
Lorenz and some of his contributions to optics and electrodynamics, the paper focuses on the emergence, content and reception of the 1890 memoir and its role in what is often called the lorenz mie theory. Pdf the theory of an arbitrarily oriented, shaped, and located beam scattered by a homogeneous spheroid is developed within the framework of the. Assume that the exact electric and magnetic fields of the incident beam are known. These parameters are the extinction and scattering coefficients, the phase function, and the index of refraction, our theory is based on a robust generalization of the lorenz mie theory. Pdf the case of a spherical wave front for the generalized. The theory was largely equivalent to the later theory of gustav mie dating from 1908. We examine and demonstrate the validity of this approximation for arbitrary shaped beams. It was later independently rediscovered by gustav mie in 1908, so it is sometimes referred to as lorenz mie theory. On ludvig lorenz and his 1890 treatise on light scattering by. Study of scattering phase matrix of spherical particles. Generalized lorenzmie theories gerard gouesbet springer.
Our model is based on the lorenzmie theory lorenz 1890. Thomson scattering is elastic scattering of light from free electrons. Generalized lorenzmie theory and applications sciencedirect. Our theory is based on a robust generalization of the lorenz mie theory. Model 640 theory of operation the t640 monitor is an optical aerosol spectrometer that converts optical measurements to mass measurements by determining sampled particle size via scattered light at the single particle level according to the lorenz mie theory. But, with the advent of lasers and their increasing development in various fields, it has become too oldfashioned to meet most of the modern requisites. Therefore, lorenz mie theory provides a method for the calculation of. Mie theory 35, which indicates that a small transparent particle can lead to a strong.
The mie solution, also called lorenzmie theory or lorenzmiedebye theory, provides an analytical solution of maxwells equations for the scattering of electromagnetic radiation by spherical particles in terms of infinite series. Scattering and absorption by aerosol and cloud particles. The singlescattering properties of ice particles in the near through farinfrared spectral region are computed from a composite method that is based on a combination of the finitedifference timedomain technique, the tmatrix method, an improved geometricaloptics method, and lorenz mie theory. The mie theory basics and applications wolfram hergert. This theory is based on the method of separation of variables and the application of an addition theorem for cylindrical functions. A socalled localized approximation, allowing one to speed up the evaluation of beam shape coefficients in the generalized lorenzmie theory for spheres, has been previously introduced and, in the case of gaussian beams, rigorously justified. Rayleigh mie light scattering university of florida. The mie solution to maxwells equations describes the scattering of an electromagnetic plane. Generalized lorenz mie theory glmt is an exact solution of the maxwell equations, and can rigorously predict the optical force on a homogeneous spherical particle induced by laser beams 5.
Predicting the appearance of materials using lorenzmie theory. Consider an arbitrary transversely localized beam incident on a homogeneous sphere of radius a and refractive index n whose center is at the origin of coordinates. There is also some biographic information on gustav mie, who published his. Apr 18, 2015 mie scattering refers primarily to the elastic scattering of light from atomic and molecular particles whose diameter is larger than about the wavelength of the incident light. Generalized lorenz mie theories download ebook pdf, epub. Rendered images of the components in milk as well as mixed concentrations.
Previous models using lorenz mie theory have been limited to nonabsorbing media with spherical particles such as paints and clouds. The lorenzmie theory gives the scattering properties of a sphere immersed in a homogeneous and isotropic medium, provided that the sphere material is also isotropic and is characterized by a dielectric constant, which can be complex and frequency dependent. July 2009 2 formal light scattering theory may be categorized in terms of two theoretical frameworks. Pdf particle positioning from chargecoupled device. Intuitively, it seemed that the concentric sphere models a and b would describe systems with greater scattering since these provide for the figure 1. Additionally, lorenz laid the foundations for ellipsometry by using fresnels theory of refraction to discover that light reflected by a thin transition layer between two. The solution takes the form of an infinite series of spherical multipole partial waves. The resonant spectrum of a dielectric sphere reveals the. Optical tweezers using generalized lorenz mie theory jaimin choi division of science education, chonbuk national university, jeonju 54896, korea heeso noh department of physics, kookmin university, seoul 02707, korea in vectorial diffraction theory, tight focusing of a linearly polarized laser beam produces an. Mie 1908, which is a complete solution to maxwells equation for scattering of electromagnetic waves by a homogeneous, spherical particle embedded in a nonabsorbing medium. The lorenzmie theory, describing the interaction between a homogeneous. The forces that are responsible for the trapping of particles in optical tweezers arise from the exchange of momentum between the trapping beam and the particle within the trap as it scatters the beam.
In this section, the basic formulas of glmt are recounted and discussed. The mie solution to maxwells equations also known as the lorenz mie solution, the lorenz mie debye solution or mie scattering describes the scattering of an electromagnetic plane wave by a homogeneous sphere. In addition to the historical analysis, the paper illuminates aspects of modern lorenz mie theory and its many applications, with an eye to. The second is the theory of mie scattering after gustav mie that encompasses the general spherical scattering solution absorbing or nonabsorbing without a particular bound on particle size.
678 1545 1299 140 1102 947 1462 1261 1109 475 427 57 1323 30 501 169 294 367 834 1426 425 99 411 1193 659 395 842 314 469 1339 521 482 1489 1545 331 900 1587 1207 960 1465 79 1466 1139 576 1184 546