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1、 I LectureNote on Optics IIContents Chapter 1 General Properties of Wave.-3-1-1 Physical Feature:.-3-1-2 Mathematical Description of Wave-Differential Wave Equation.-3-1-3 Harmonic waves(a quick summary).-5-1-4 Phase and Phase velocity.-11-1-5 Superposition Principle.-12-1-6 Complex Representation a

2、nd Phasors.-14-1-7 Plane waves and Spherical waves.-21-1-8 Doppler Effect:.-23-Chapter2 Light as Electro-Magnetic Wave.-32-2-1 Maxwell Equation and Electro-Magnetic Wave.-32-2-2 Speed of light.-34-2-3 Transverse Wave.-36-2-4 Energy carried by E-M wave.-38-2-5 Momentum of E-M Field.-41-2-6 Photons.-4

3、5-2-7 Radiation(light)sourcesA classical treatment.-45-2-8 One Word on Polarization.-51-Chapter 3 The propagation of Light.-58-3-1 Treatise Based on Macroscopic Observations.-59-3-2 Huygenss Principle.-61-3-3 Fermats Principle.-63-3-4 Two examples using Snells equation.-67-3-5 Propagation of Light f

4、rom Scattering Point of View.-70-3-6 Fresnel Equations.-77-3-6-1 Amplitude,Brewster angle and Total Internal Reflection.-82-3-6-2 Phase shift.-84-3-6-3 Stokes Relation.-87-3-6-4 Evanescent Wave.-90-Chapter 4 Geometric Optics.-95-4-1 Jargons in geometric optic.-97-4-2 Fermats Principle.-100-4-3 Refra

5、ction at a Single Spherical Surface.-102-4-4 Paraxial Approximation.-103-4-5 Finite Imagery and Transverse Magnification.-110-4-6 Multiple Surfaces and Lagrange Helmholtz Relation.-113-4-7 Thin Lens.-115-4-8 Thin lens combination.-120-4-9 Thick Lenses and Lens System.-121-4-10 Graphical Method of Im

6、age Formation.-127-4-11 Analytical Ray Tracing and Matrix Method.-130-4-12 Apertures.-139-III4-13 Aberration.-149-Chapter 5 Interference,Interferometer and Coherence.-153-5-1 Superposition of Waves.-154-5-1-1 Superposition principle in linear optics.-155-5-1-2 Superposition of Waves with same,Parall

7、el 0E?.-157-5-1-3 Standing Waves.-158-5-1-4 The addition of waves of different frequency.-162-5-2 Interference and Coherence.-169-5-3 Wavefront Splitting Interference.-175-5-3-1 Interference of Two Point Sources.-175-5-3-2 Youngs Experiment.-177-5-3-3 A more Strict and Systematic Treatment.-180-5-4

8、Amplitude Splitting Interferometer-Interference by Thin film.-185-5-4-1 Fringes of Equal Thickness.-187-5-4-2 Fringes of equal inclination.-190-5-4-3 Michelson Interferometer.-193-5-5 Multiple Beam interference and Fabry-Perot interferometer.-198-5-5-1 Fabry-Perot Interferometer.-202-5-6 Coherent Th

9、eory.-207-5-6-1 Extended Monochromatic Source and Spatial Coherence.-209-5-6-2 Effect of Non-Monochromatic Light-Temporal Coherence.-212-5-6-3 Correlation Function Formal treatment of Coherence.-218-Chapter 6 Diffraction.-230-6-1 Whats Diffraction.-230-6-1-1 Definition.-230-6-1-2 Fraunhoffer and Fre

10、snel Diffraction.-233-6-2 Huygens-Fresnel Principle(HFP)and Kirchhoff equation.-235-6-3 Fresnel Diffraction through an open aperture.-236-6-3-1 Method of Half-Wavelength(/2)Plate.-237-6-3-2 Phasor Treatment and Vibrational Spirals(curves).-242-6-3-4 Babinet Principle.-246-6-3-5 Fresnel Zone Plate.-2

11、47-6-4 Fraunhoffer Diffraction by Single Slit.-250-6-4-1 Single Slit.-251-6-4-2 Rectangular Aperture.-254-6-4-3 The Characteristic of Diffraction Distribution.-256-6-4-4 Fraunhoffer Diffraction by Circular Aperture and Image Resolution.-259-6-5 Diffraction by Many Slits(Fraunhoffer Type).-263-6-5-1

12、Fraunhoffer-Diffraction by Many Slits.-263-6-5-2 Diffraction Grating and Grating Spectrometer.-273-Chapter 7 Fourier Optics.-286-7-1 Fourier Expansion(Fourier Series)and Fourier integrals.-286-7-1-1 Fourier Expansion of a Periodic Function.-288-IV7-1-2 Non-periodic functions Fourier Transform(Fourie

13、r Integral).-294-7-1-3.Dirac Delta Function .-305-7-1-4 Properties of Fourier Transform.-308-7-2 Fraunhoffer Diffraction from Fourier Optics point of view.-316-7-2-1 Fraunhoffer Diffraction.-317-7-2-2 Abbe imaging principle and image processing by spatial Filtering.-324-Chapter 8 Polarization and Pr

14、opagation of Light in Crystal.-338-8-1 Polarization Type of Light.-338-8-2 Polarizer.-345-8-3 Jones Vector for Polarized Light and Jones Matrix.-350-8-3-1 Jones Vector.-350-8-3-2 Jones matrix for operation on polarized light.-352-8-4 Propagation of light in Crystal-Birefringence.-353-8-4-1 Phenomena

15、 of Birefringence(Double refraction).-353-8-4-2 Microscopic explanation of Birefringence.-356-8-5 Crystal Optical Elements.-365-8-5-1 Birefrigent polarizers.-365-8-5-2 Wave platephase retarder.-365-8-5-4 Jones Matrix for polarizer and wave plate.-373-8-6 Optical activity(Circular Birefringence).-381

16、-8-6-1 Definition.-381-8-6-2 Optical Activity in Crystal.-382-8-6-3 Circular Birefringence.-383-8-6-4 Optical activity in solution.-386-8-6-5 Induced Circular BirefringenceFaraday effect.-387-()x-1-Optics -2-Question:Classical or Quantum?Why bother to treat the light field classically(classical opti

17、cs)since we have a more accurate description quantum mechanically.(Quantum optics)Answer:1.Quantum theory is though more accurate,but also more complicated.In many cases,the classical theory is much simple,as well as_ 2.Accurate:If we treat the statistical behavior(such as average)of large number of

18、 photons,the classical Electro-Magnetic theory is good enough.For Example:In spectroscopy,the light field(laser or conventional source)is treated classically,i.e.the effect of many photons can be represented very accurately by the classical electro-magnetic field;the atoms/molecules are treated quan

19、tum mechanically and this is called semi-classical theory.In most of this course,we are going to deal with the situations where Light can be treated as Electro-Magnetic wave(obeying Maxwell equation).It is instructive to first review some general properties of wave as Chapter 2 in Hechts book -3-Cha

20、pter 1 General Properties of Wave 1-1 Physical Feature:Classically:Particle:Localized quantity(or property),recall a mass point.Wave:non-localized,recall a sound wave etc.Such classical distinction between wave&particle will fail in quantum theory.1-2 Mathematical Description of Wave-Differential Wa

21、ve Equation (,)x t:1-dimension wave function,represents a spatial distribution and time evolution of wave:22222(,)1(,)x tx txt=(1-1)v in the(1-1)is the velocity of the wave.For 3-dimensional case,wave equation is:22221(,)(,)r tr tt=(1-2)-4-2222222xyz+Laplacian operator If a function(,)r t is a solut

22、ion of the wave equation,and its second partial derivative vs.space and time is non-trivial,then(,)r t represents a wave.A special example(as well as a common case in the course):Wave propagates with a constant shape and phase velocity.(,)()x tf xt=(Fig.2.3,2.4,pg13.Hecht)If you put this back to(1-1

23、),it certainly satisfy the wave equation.-5-The most general solution for wave equation(1-1)will be in the form of(,)()()x tF xvtG xvt=+where the functional form of F and G need to be determined by the initial conditions and boundary value,which will not be fully discussed in our course.It requires

24、Fourier Transform we shall discuss in the later part of the course1.We shall focus on some simple forms of the solution,as the next section concerns.1-3 Harmonic waves(a quick summary)(1)This is the simplest as well as a very important form of wave.(2)Any other wave function(,)x t can be represented

25、 as a superposition of such harmonic waves.(Fourier Expansion)For a harmonic wave(1-dimension):(,)cos()x tAk xt=(1-3)Or(,)cos()x tAkxt=Then:kk=Where 222;2T k=(1-4)The k is wave vector(in 1-D is just a number);|kis the angular 1 It can be found in any standard math textbooks dealing with partial diff

26、erential equations.-6-wave number;1=is the wave number;T is the period;1T=is the frequency;is the angular frequency;k=is the phase velocity.Given any two of,k,(or,),you can calculate the other.A wave has both spatial and temporal period.Fig2.7(pg17,Hecht)can be used as depicting generation of a harm

27、onic wave from a harmonic oscillation source.*Comment1:the harmonic waves represented by(1-3)are an idealized case,i.e.it is not realizable in real case.It is a wave with single frequency.To have this frequency defined,the wave train has to extend from to+in space and time domain(that is how mathema

28、tically defining a periodic function).Such wave is called Monochromatic Wave.(Since color is related to frequency,and single frequency is also called -7-monochromatic)The monochromatic wave is an idealization(as mass point with fixed energy in mechanics)because nothing last forever.Any real waves ar

29、e at best quasi-chromatic,and usually are a superposition of monochromatic waves:Example:limited wave train A wave train with limited length L(It only lasts from 0 to L at0t=),and thus strictly speaking is not a wave with single frequency(or wavelength).By looking at it,it is not hard to see that as

30、 the L gets large,the wave train will be pretty much a ideal harmonic wave with single frequency at certain k0;but if L is very small,it is far from it.The detailed math will be presented later in the due course(Fourier transform),here I shall just present the result.For such wave train,it can be ex

31、pressed as a superposition of many harmonic waves with different wave vectors k:0()()cos()txkkx dk+=Above is the Fourier Expansion of the wave function()x,and()k -8-is the weighting factor of the kth component,it is the expansion coefficient and also termed Fourier transform of()x.There is a famous

32、and important relation between the distribution width between original wave function()xand its Fourier Transform()k:2k x And in the above wave train xL=As Llarge,0k()cosxkx we see as L becomes large,the wave train approaches a harmonic wave,and this is called quasi-monochromatic.Comment 2:The phase

33、signs and relation with phase lead or lag In this course,very often we will compare the phase difference between two or more waves,from their phase difference we may say certain wave is leading or lagging in phase comparing with others.Here I shall discuss in detail about the relation of phase diffe

34、rence and lagging-leading in phase.(1)We use sinusoidal function(or complex function)to represent a wave,there is a choice of sign for the phase part:(,)cos()E z tAkzt=+is the conventional choice for a traveling wave along the+z direction(another choice is to put a minus sign inside the Cosine,since

35、 cos()cos()=this will give same physical results with physical reality attached to different signs).In this choice,the phase -9-difference between this wave and the 00cos()EAkzt=is.The figure above only shows the E(z,t),(for comparison,you can add the 0E yourself on the picture).It is clear from the

36、 picture that(,)cos()E z tAkzt=+Lags in phase comparing with00cos()EAkzt=.The delay(choose a same phase point,lets choose the maxim point of the sinusoidal wave in the figure)in the z coordinate is0(for same)kztkztt+=,/zzzk=.(The value will be set between 0)value means lags in phase and negative pha

37、se difference(0,-0).This reverses the relation between the signs in phase difference and lag-lead in phase for the wave propagates along-Z direction;this is of course because the-is the phase difference instead of as in the case for wave propagates along+z.To avoid the possible confusion due to the

38、sign change in for the two cases,I should express the wave propagates along the z direction as:(,)cos()cos()E z tAkztAkzt=+=+.This express the same wave propagates from right to left along the Z.Now the-k shows the direction of the wave and the+is the phase difference between it and the00cos()EAkzt=

39、.In this convention,the positive phase difference(+0)means lags in phase;and negative phase difference(+Lags in phase(,)0p t Leads in phase Thus,the complex representation is(1)Equivalent to the cosine representation,as long as we bear in mind the physical wave correspond to the real part of the com

40、plex.(2)The complex will simplify the calculation.Comments on the Equivalence of Euler expression and sinusoidal expression for waves:The complex expression of waves(Euler formula)is very useful;it simplifies many calculations comparing with the sinusoidal expressions of waves.I stated above that as

41、 long as you are aware that the real part of the complex expression corresponds to the physical wave,you can use the complex during the calculation,and if necessary(a lot of times it is not necessary)you take the real part of the complex result to express the physical wave.This statement needs a lit

42、tle bit polish in a sense that it depends on the calculation:If the required calculation would not mix the real and imaginary parts,such as adding,subtracting and differentiating waves,you can use the complex expression with confidence.It generates same results as the sinusoidal expression.(By takin

43、g the real part of the complex)However,if the calculation mixes the real and imaginary parts,such as multiply,generally two expressions will give different results,and you need to stick to the sinusoidal expressions(Not many calculations in this course belong to this class).Example:two waves at a fi

44、xed spatial point with same frequency,we calculate their product at that point over time:111cos()EAt=+;222cos()EAt=+.The corresponding complex expressions are:1()11itEAe+=and2()22itEA e+=.Then(*means complex conjugate):121212121212121cos()cos()cos()cos(2)2E EE EA AttA At=+=+12(2)121212realitE EA A e

45、E E+=-16-12()121212realiE EA A eE E=In the above calculation,using complex expression would give incorrect answers.Fortunately such calculation is not often in real physics,in most cases where we are interested in the multiplications,we are interested in its time average!I.e.we are interested in:121

46、201TTE EE E dtT=Then:121212121200111cos()cos(2)2TTTE EE E dtA AtdtTT=+If the average time T the time period of the oscillation,i.e.2T,the second term in the integral will become 0 after divided by T,then:1212121211cos()Re22TE EA AE E=Thus we can use complex expression 12E E to evaluate the time aver

47、age of the product,up to a constant factor 1/2.This is the basis that I will use complex expression to calculate the time average product of the fields in this course.One particular example is the average energy flux of the light is:2111111122TE EAE E=Here I use Eto represent real physical field and

48、 E to represent its complex expression.In this course,all the calculations involved satisfy the condition that the two representations would give same results(i.e.superposition,differentiation,time average of products etc.),so in my lecture notes,I just use E to represent the field in both cases to

49、save bookkeeping time.The reason I shall use Euler formula(the complex exponential form)to represent wave is not only due to math simplification as it may bring,but also the complex form of wave is a must later in the quantum mechanics,so wed better get used to it as early as possible.Phasor:vector

50、representation of the complex representation,just like the -17-vector representation of any complex number.()(,)()ipi tp tA p ee=This is very useful in summation of multiple waves with same frequency:()()()()jipipi ti tjjA p eeAp ee=The geometrical expression is provided in the figure below Example: