Light Scattering by Systems of Particles: Null-FieldMethodwithDiscrete Sources: Theory and Programs PDF
Preview Light Scattering by Systems of Particles: Null-FieldMethodwithDiscrete Sources: Theory and Programs
SpringerSeriesin optical sciences 124 foundedbyH.K.V.Lotsch Editor-in-Chief: W.T.Rhodes,Atlanta EditorialBoard: A.Adibi,Atlanta T.Asakura,Sapporo T.W.Ha¨nsch,Garching T.Kamiya,Tokyo F.Krausz,Garching B.Monemar,Linko¨ping H.Venghaus,Berlin H.Weber,Berlin H.Weinfurter,Mu¨nchen SpringerSeriesin optical sciences TheSpringerSeriesinOpticalSciences,undertheleadershipofEditor-in-ChiefWilliamT.Rhodes,Georgia InstituteofTechnology,USA,providesanexpandingselectionofresearchmonographsinallmajorareasof optics:lasersandquantumoptics,ultrafastphenomena,opticalspectroscopytechniques,optoelectronics, quantuminformation,informationoptics,appliedlasertechnology,industrialapplications,andother topicsofcontemporaryinterest. Withthisbroadcoverageoftopics,theseriesisofusetoallresearchscientistsandengineerswhoneed up-to-datereferencebooks. 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Doicu T. Wriedt Y.A. Eremin Light Scattering by Systems of Particles Null-Field Method with Discrete Sources: Theory and Programs With 123 Figures , 4 in Col or a n d 9 Tables 123 AdrianDoicu Institutfu¨rMethodikderFernerkundung DeutschesInstitutfu¨rLuft-undRaumfahrte.V. D-82234O berpfaffenhofen,Germany E-mail:[email protected] ThomasWriedt UniversityofBremen,FB4,VT BadgasteinerStr.3,28359Bremen,Germany E-mail:[email protected] YuriA.Eremin AppliedMathematicsandComputerScienceFaculty MoscowStateUniversity 119899Moscow,Russia E-mail:[email protected] ISSN0342-4111 ISBN-103-540-33696-6SpringerBerlinHeidelbergNewYork ISBN-13978-3-540-33696-9SpringerBerlinHeidelbergNewYork LibraryofCongressControlNumber:2006929447 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broadcasting, reproductiononmicrofilmorinanyotherway,andstorageindatabanks.Duplicationofthispublicationor partsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9,1965,inits currentversion,andpermissionforusemustalwaysbeobtainedfromSpringer-Verlag.Violationsareliable toprosecutionundertheGermanCopyrightLaw. SpringerisapartofSpringerScience+BusinessMedia. springer.com ©Springer-VerlagBerlinHeidelberg2006 Theuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicationdoesnotimply, evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotectivelawsand regulationsandthereforefreeforgeneraluse. Typesetting by the Authors andSPiusingaSpringerLATEXmacropackage CoverconceptbyeStudioCalamarSteinenusingabackgroundpicturefromTheOpticsProject.Courtesyof JohnT.Foley,Professor,DepartmentofPhysicsandAstronomy,MississippiStateUniversity,USA. Coverproduction:design&productionGmbH,Heidelberg Printedonacid-freepaper SPIN:11554325 57/3100/SPi 543210 To our families: Aniela and Alexandru Ursula and Jannis Natalia, Elena and Oleg Preface Since the classic paper by Mie [159] or even the papers by Clebsch [37] and Lorenz[146]thereisapermanentpreoccupationinlightscatteringtheory.Mie was interested in the varied colors exhibited by colloidal suspensions of noble metalspheres,butnowadays,thetheoryoflightscatteringbyparticlescovers a much broader and diverse field. Particles encountered in practical applica- tions are no longer considered spherical; they are nonspherical, nonrotational symmetric, inhomogeneous, coated, chiral or anisotropic. Light scattering simulation is needed in optical particle characterization, to understand new physical phenomena or to design new particle diagnostics systems. Other examples of applications are climatology and remote sens- ing of Earth and planetary atmospheres, which rely on the analysis of the parameters of radiation scattered by aerosols, clouds, and precipitation. Sim- ilar electromagnetic modeling methods are needed to investigate microwave scattering by raindrops and ice crystals, while electromagnetic scattering is also encountered in astrophysics, ocean and biological optics, optical com- munications engineering, and photonics technology. Specifically, in near-field- or nano-optics and the design of optical sensor, biosensors or particle surface scanners,lightscatteringbyparticlesonornearinfinitesurfacesisofinterest. Many techniques have been developed for analyzing scattering problems. Each of the available methods generally has a range of applicability that is determinedbythesizeoftheparticlerelativetothewavelengthoftheincident radiation.Classicalmethodsofsolutionlikethefinite-differencemethod,finite elementmethodorintegralequationmethod,owingtotheiruniversality,lead to computational algorithms that are expensive in computer resources. This significantlyrestrictstheiruseinstudyingelectromagneticscatteringbylarge particles. In the last years, the null-field method has become an efficient and powerful tool for rigorously computing electromagnetic scattering by single and compounded particles significantly larger than a wavelength. In many applications, it compares favorably to other techniques in terms of efficiency, accuracy,andsizeparameterrangeandistheonlymethodthathasbeenused in computations for thousand of particles in random orientation. VIII Preface The null-field method (otherwise known as the extended boundary condi- tionmethod,Schelkunoffequivalentcurrentmethod,Eswald–Oseenextinction theorem and T-matrix method) has been developed by Waterman [253,254] asatechniqueforcomputingelectromagneticscatteringbyperfectlyconduct- ing and dielectric particles. In time, the null-field method has been applied to a wide range of scattering problems. A compilation of T-matrix publica- tions and a classification of various references into a set of narrower subject categories has recently been given by Mishchenko et al. [172]. Peterson and Stro¨m [187,189], Varadan [233], and Stro¨m and Zheng [219] extended the null-field method to the case of an arbitrary number of particles and to mul- tilayered and composite particles. Lakhtakia et al. [135] applied the null-field methodtochiralparticles,whileVaradanetal.[236]treatedmultiplescatter- inginrandommedia.Anumberofmodificationstothenull-fieldmethodhave beensuggested,especiallytoimprovethenumericalstabilityincomputations for particles with extreme geometries. These techniques include formal mod- ifications of the single spherical coordinate-based null-field method [25,109], different choices of basis functions and the application of the spheroidal coor- dinateformalism[12,89]andtheuseofdiscretesources[49].Mishchenko[163] developed analytical procedures for averaging scattering characteristics over particle orientations and increased the efficiency of the method. At the same time,severalcomputerprogramsforcomputingelectromagneticscatteringby axisymmetric particles in fixed and random orientations have been designed. In this context, we mention the Fortran programs included with the book by Barber and Hill [8] and the Internet available computer programs developed by Mishchenko et al. [169]. For specific applications, other computer codes have been developed by various research groups, but these programs are cur- rently not yet publicly available. Thismonographisbasedonourownresearchactivityoverthelastdecade and is intended to provide an exhaustive analysis of the null-field method and to present appropriate computer programs for solving various scattering problems. The following outline should provide a fair idea of the main intent and content of the book. In the first chapter, we recapitulate the fundamentals of classical electro- magneticsandopticswhicharerequiredtopresentthetheoryofthenull-field method. This partcontains explicit derivations ofall important results andis mainly based on the textbooks of Kong [122] and Mishchenko et al. [169]. The next chapter provides a comprehensive analysis of the null-field method for various electromagnetic scattering problems. This includes scat- tering by –Homogeneous,dielectric(isotropic,uniaxialanisotropic,chiral),andper- fectly conducting particles with axisymmetric and nonaxisymmetric sur- faces – Inhomogeneous, layered and composite particles, – Clusters of arbitrarily shaped particles, and – Particles on or near a plane surface. Preface IX The null-field method is used to compute the T matrix of each individual particle and the T-matrix formalism is employed to analyze systems of par- ticles. For homogeneous, composite and layered, axisymmetric particles, the null-field method with discrete sources is applied to improve the numerical stabilityoftheconventionalmethod.Evanescentwavescatteringandscatter- ing by a half-space with randomly distributed particles are also discussed. To extend the domain of applicability of the method, plane waves and Gaussian laser beams are considered as external excitations. The last chapter covers the numerical analysis of the null-field method by presentingsomeexemplarycomputationalresults.Forallscatteringproblems discussed in the preceding chapters we developed a Fortran software package which is provided on a CD-ROM with the book. After a description of the Fortran programs we present a number of exemplary computational results with the intension to demonstrate the broad range of applicability of the method. These should enable the readers to adapt and extend the programs to other specific applications and to gain some practical experience with the methodsoutlinedinthebook.Becauseitishardlypossibletocomprehensively address all aspects and computational issues, we choose those topics that we think are currently the most interesting applications in the growing field of light scattering theory. As we are continuously working in this field, further extensions of the programs and more computational results will hopefully become available at our web page www.t-matrix.de. The computer programs have been extensively tested, but we cannot guarantee that the programs are freeoferrors.Inthisregard,weliketoencouragethereaderstocommunicate us any errors in the program or documentation. This software is published underGermanCopyrightLaw(Urheberrechtsgesetz,UrhG)andinthisregard thereadersaregrantedtherighttoapplythesoftwarebutnottocopy,tosell ordistributeitnortomakeitavailable tothepublicinanyform.Weprovide thesoftwarewithoutwarrantyofanykind.Noliabilityistakenforanylossor damages, direct or indirect, that may result through the use of the programs. This volume is intended for engineering and physics students as well as researchers in scattering theory, and therefore we decided to leave out rigor- ous mathematical details. The properties of scalar and vector spherical wave functions,additiontheoremsundertranslationandrotationofthecoordinate systems and some completeness results are presented in appendices. These can be regarded as a collection of necessary formulas. We would like to thank Elena Eremina, Jens Hellmers, Sorin Pulbere, Norbert Riefler, and Roman Schuh for many useful discussions and for per- formingextensivesimulationandvalidationtestswiththeprogramsprovided withthebook.WealsothankfullyacknowledgesupportfromDFG(Deutsche Forschungsgemeinschaft) and RFBR (Russian Foundation of Basic Research) which funded our research in light scattering theory. Bremen, Adrian Doicu April 2006 Thomas Wriedt Yuri Eremin X Preface Researching for and writing of this book were both very personal but shared experience. My new research activity in the field of inversion methods for atmospheric remote sensing has left me little free time for writing. Fortu- nately, I have had assistance of my wife Aniela. She read what I had written, spentcountlesshourseditingthemanuscriptandhelpedmeinthetestingand comparing of computer codes. Without the encouragement and the stimulus givenbyAniela,thisbookmightneverhavebeencompleted.Forherloveand support, which buoyed me through the darkest time of self-doubt and fear, I sincerely thank. Mu¨nchen, Adrian Doicu April 2006 Contents 1 Basic Theory of Electromagnetic Scattering ............... 1 1.1 Maxwell’s Equations and Constitutive Relations............. 1 1.2 Incident Field........................................... 9 1.2.1 Polarization ...................................... 9 1.2.2 Vector Spherical Wave Expansion ................... 15 1.3 Internal Field ........................................... 21 1.3.1 Anisotropic Media................................. 22 1.3.2 Chiral Media ..................................... 30 1.4 Scattered Field.......................................... 33 1.4.1 Stratton–Chu Formulas ............................ 34 1.4.2 Far-Field Pattern and Amplitude Matrix ............. 40 1.4.3 Phase and Extinction Matrices...................... 44 1.4.4 Extinction, Scattering and Absorption Cross-Sections .. 48 1.4.5 Optical Theorem .................................. 53 1.4.6 Reciprocity ....................................... 54 1.5 Transition Matrix ....................................... 57 1.5.1 Definition ........................................ 58 1.5.2 Unitarity and Symmetry ........................... 61 1.5.3 Randomly Oriented Particles ....................... 66 2 Null-Field Method......................................... 83 2.1 Homogeneous and Isotropic Particles....................... 84 2.1.1 General Formulation............................... 85 2.1.2 Instability ........................................ 89 2.1.3 Symmetries of the Transition Matrix................. 93 2.1.4 Practical Considerations............................ 95 2.1.5 Surface Integral Equation Method ................... 97 2.1.6 Spherical Particles................................. 99 2.2 Homogeneous and Chiral Particles.........................102 2.3 Homogeneous and Anisotropic Particles ....................104
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