1、Engineering Optics and Optical Techniques, LN No. 1Prof. K. D. Kihm, Spring 20071Engineering Optics and Optical TechniquesLN#1. Electromagnetic Basics and Maxwells Equations (Sections 3-1, 3-2, Appendix 1)Propagation of Waves (Chapter 2, Sections 3-3, 3-4)Experimental evidence shows that light propa
2、gates as a form of waves consisting transverse, time-varying electric and magnetic fields. The two amplitude-varying transverse vectors, electric field strength E and magnetic field strength H, oscillate at the right angles to each other in phase and to the direction of propagation. They can be expr
3、essed in the form of four fundamental equations known as Maxwells Equations.“It is true that nature begins by reasoning and ends by experience. Nevertheless, we must begin with experiments and try through it to discover the reason.”- Leonardo da Vinci Homework #1-1 Read of Chapter 1 for “Brief Histo
4、ry” of Optical Science(Clerk) Maxwells Equations (1865) Light is most certainly electromagnetic nature(Classical electrodynamics)For vacuum, air, water or glass (no space charge or ion density, zero electric conductivity):Key: Interdependence of E and BtEBtBEo0Or their combined and reduced forms, 22
5、22tBtEooWhere E: Electric field Force/Charge, N/CB : Magnetic induction Force/Charge/Velocity, Ns/Cm)(HEngineering Optics and Optical Techniques, LN No. 1Prof. K. D. Kihm, Spring 20072Fluid Dynamics vs. ElectromagneticsContinuity Analogy: vs. VjV: flow velocity j: electric current fluxExtended Analo
6、gy Fluid Dynamics ElectromagneticsFieldg-Field: Fg = mg E-Field: FE = qEM-Field: FM = qVBContinuityFlow current flux V= volume flow/area/time= TLsmQ2Electric current flux j= electric charge flow/area/time= smC2Volume flow rate q:dAVq Electric charge flow rate i: Ampere = C/sdAjiVolume continuity:, :
7、 fluid density0Vt Electric charge continuity:, E: charge density0jtESteady state0V 0jIncompressible flow Zero or constant space charge conditionjEngineering Optics and Optical Techniques, LN No. 1Prof. K. D. Kihm, Spring 20073Arc Angle vs. Solid AngleArc angle: defined as RdsTotal arc length: toal2t
8、oalSolid angle: defined as (normally outward vector definition)RdaTotal surface area: toalR2224toal R dsddaRdEngineering Optics and Optical Techniques, LN No. 1Prof. K. D. Kihm, Spring 20074Coulombic or Gauss LawExperimental finding by Gauss, kgmsCvacumrqFroo 3212121 /0854.4*Electric permittivity :
9、measure of the degree to which the material is permeated by the E-field, i.e., the permittivity is higher for more electrically conducting material. For example, for water at 20 C is approximately 80, and goes to infinity for a o/perfect conductor if exists. When goes to infinity, charges spread out
10、 uniformly in o/no time to result in “0” Coulombic force.*”o” indicates free surface, vacuum or air.Note: Gauss Law is an inverse square law for the force between charges, which is the central nature of the force and allows the linear superposition of the effects of different charges.Electric Field
11、241rqEoFF-q1+q2rEE q1 rEngineering Optics and Optical Techniques, LN No. 1Prof. K. D. Kihm, Spring 20075Maxwells 1st Equation: Electric Field Conservation in Free Space0EThe total force acting on da by q is given as: drdarndaEoo 2241cs41 4dtoalFor the entire surrounding surface, Gauss Theorem Vdqnda
12、EEo1Divergence theorem: VEdnaTherefore, oEFor a vacuum or free space* , 0E0E*Most optically thin materials like glass or water can be treated electric charge free. Engineering Optics and Optical Techniques, LN No. 1Prof. K. D. Kihm, Spring 20076Maxwells 2nd Equation: Steady Magnetic Field Conservati
13、on0B*Experimental evidence by Biot & Savart (1820) shows that wires carrying electric currents produce deflections of permanent magnetic dipoles placed around it. This inspires that an electric current creates the magnetic induction (or equivalently magnetic field B or dB).Maxwells 3rd Equation: Mut
14、ually perpendicular E & BtBEFaradys Induction Law (1831) states that a time-varying magnetic flux passing through a closed conducting loop results in the generation of a current around the loop, i.e.,The notion is that a time-varying magnetic field will have an electric field associate with it. This
15、 also shows that E and B must be perpendicular each other.Maxwells 4th Equation: to(Strictly speaking, the above equation is valid for nearly non-conducting or di-electric medium.)Amperes Circutal Law states that a time-varying E-field and j induces a B-field.The notion is that a time-varying E-fiel
16、d will be accompanied by a B-field.* : magnetic permeability in vacuumdegree of measure of 27/104Ckgmomagnetic induction (B) for a given magnetic field strength (H), i.e., .*Ferro-magnetic materials have high values of permeability. If interested in detailed analysis for the derivations of the above
17、 Maxwells equations, refer to Section 3.1 of the textbook, and for more great details refer to “Classical Electrodynamics (3rd ed.)” by J. D. Jackson, Wiley, 1999. Engineering Optics and Optical Techniques, LN No. 1Prof. K. D. Kihm, Spring 20077Maxwells Equation for Free Space, Vacuum and Air:0EBtE
18、= E (x,t) and B = B (x,t)tEoUsing a vector identity, , the 3rd and 4th equations are expressed as:B22222 tBzyxo2222 tEzyExo= 3 108 m/s: speed of light in vacuumco1(This ensures the wave nature of light.)(Maximum in vacuum and slower in a denser medium)*Analogy to potential field in acoustics:Acousti
19、c pressure wave equations: with a being the speed of sound.221taEngineering Optics and Optical Techniques, LN No. 1Prof. K. D. Kihm, Spring 20078SOUND WAVES - Pressure Waves (Longitudinal) Needs medium where it travels.*The speed of sound a: A primary means of information traveling in a media by pro
20、pagation of locally pressurized compression, i.e., pressure waves. Thus, a denser material can transfer the information on the local pressurization more efficiently and faster. The speed of sound is faster in a denser medium. paLIGHT WAVES Electromagnetic Waves (Transverse) Medium is not necessary.I
21、n vacuum:In a medium:*The speed of light c is the fastest for vacuum and slower for a denser medium. (e.g. mirage or mirror-like road surface on a hot and sunny day)Engineering Optics and Optical Techniques, LN No. 1Prof. K. D. Kihm, Spring 200791-D Wave Equation and Plane WavesMaxwells Equation for
22、 E- field: 2222 tEzyExo Linear* 2nd order PDE22,1,txVxtGeneral solutions are: Vtxgctxfct 21,Since the waves are harmonic (sine or cosine), we chooseVtxkAtxsin,and also, VtxkAtt sini,Thus, or : wave propagation number2kwave frequencyangular frequency2wave number1wave periodNow more generally, * tkxie
23、AtkxAkVtxAtx Imsinsin,*Linearity conditions: 1) If and are solutions, is also a solution.12212) If is a solution, C is also a solution.1* sincoeiEngineering Optics and Optical Techniques, LN No. 1Prof. K. D. Kihm, Spring 2007101-D Wave Equation and Plane Waves Defn of plane: collection of all r vect
24、ors.0orkor cnst(k is the wave propagation direction.)A set of planes over which varies in space sinusoidally, i.e., a way to express wave rpropagation kAsinEngineering Optics and Optical Techniques, LN No. 1Prof. K. D. Kihm, Spring 200711*Example: general expressions for 2-D wavescossin2cossin csi0z
25、ykzy zyxkxryx Thus, the wave is expressed as: tzyAt cosin2i,The second wave is expressed as,0 tzBtzy2sin,And the resulting superposed wave is given as.superodEngineering Optics and Optical Techniques, LN No. 1Prof. K. D. Kihm, Spring 200712Poynting Vector and IrradianceThe radiant energy per unit vo
26、lume, or energy density, u:ooEBEBuu22energy/volume = force*length/length*3 = force/length*2 = pressure Homework: EOC problem 3-82uoEand Homework #2-1Bcoc/1Engineering Optics and Optical Techniques, LN No. 1Prof. K. D. Kihm, Spring 200713The radiant energy flux, or radiation power per unit area, i.e.
27、, Poynting vector S:IntesiyRadioArePowS EBcuctAtelvumTirEnegy ootoal 21Note: The energy density has a pressure dimension.The Poynting vector has a pressure velocity dimension.or in a vector form, Poynting vectortBEctSoo21tu)(Energy beam AEngineering Optics and Optical Techniques, LN No. 1Prof. K. D.
28、 Kihm, Spring 200714The irradiance, the time-average energy per unit area per unit time, I: 2/2/11TtoTt dtBtEcdStSI where and .trkEtocstrktocsUsing, 21s12/Tt dtr: Irradiance: Time-Averaged Radiation Power per Unit Area2oEcI(Intensity)* and .ConstrI2ConstrEo*The irradiance is proportional to 1/r2 (In
29、verse Square Law)and the amplitude of E-field, ,drops off inversely with r. oEngineering Optics and Optical Techniques, LN No. 1Prof. K. D. Kihm, Spring 200715Radiation PressureBasis for the corpuscular theory: the light is a stream of (weightless, m = 0) particles?Radiation pressure , thus cf. cSuV
30、EAFpAcF mVdtaFTime-average radiation pressure is perfectly absorbing surfaceIp perfectly reflecting surfacecS2E-o-C. 3-29 Time-average radiation pressure for an oblique incidence at an angle with thenormal?*Possible applications: Optical levitation of a small particleMicro-capsule accelerator (parti
31、cle gun)Poynting vector SEngineering Optics and Optical Techniques, LN No. 1Prof. K. D. Kihm, Spring 200716Homework Assignment #1Due by 6:45 p.m. on January 23 (Tuesday), 2007 at the classroom.Homework #2-1For a plane wave propagating in vacuum, show that . Hint: section 3.2.1BcEHomework # 2-2For an
32、 Nd:YAG laser generate 400 mJ/pulse light wave with its pulse duration of 7 ns. Calculate the maximum radiation pressure that the laser can exert on a totally reflecting surface. Also calculate the maximum diameter of a totally reflecting silver particle that the laser can levitate against the gravity for the pulse duration. Assume the laser illumination diameter of 10-microns hitting the particle. Solve End-of-Chapter problems: 3-5, 3-14, 3-15, 3-19, and 3-33.
