光学光学光学光学 (6).pdf
《光学光学光学光学 (6).pdf》由会员分享,可在线阅读,更多相关《光学光学光学光学 (6).pdf(56页珍藏版)》请在得力文库 - 分享文档赚钱的网站上搜索。
1、-230-Chapter 6 Diffraction The topics will be covered in this chapter are:1.Whats Diffraction(Zhaos,chap2 5.1 Hechts 10.1)2.Huygens Fresnel Principle(Kirchhoff equation)(Zhaos chap2 5.2,pg186;Hecht,10.4)3.Fresnel Diffraction(Zhaos chap2 6,pg194-206;Hecht,10.3.1-10.3.5)4.Fraunhoffer Diffraction(Zhaos
2、 chap2 7,pg209-230;Hecht,10.2.1)5.Grating(Zhaos chap4,Hechts,10.2.2-10.2.7)6-1 Whats Diffraction 6-1-1 Definition In Youngs Experiment,we used points to represent the two coherent sources.However in any reality,the sources themselves(aperture or slit in the experiments)have limited sizes,then an ins
3、tant question is:what is the field distribution after such opening:From geometric optics,if p is in the region spanned by angle d/R,then its -231-Ip|Ep|=|Es/(R+r)|.If p is outside the angle d/R,then Ip=0.Is this true?This is not always true as clearly demonstrated in the experiment shown in Figure b
4、elow:From the experimental observation,it is easy to conclude that (1)The distribution of energy on an observing plane I(p)is generally an interference pattern.The energy distribution has highs and lows.(2)Light does not propagate in a rectilinear form,its distribution“spread out”along the direction
5、 wherever it meets restriction.(3)The more restriction,the light seems spread out more.This gives the definition of diffraction.Diffraction(literally or phenomenally):Deviation of light from a rectilinear propagation Diffraction7(physical):interference of waves.(a continuous coherence sources)7 Ther
6、e is little difference from interference.In fact both interference and diffraction arise from superposition of waves.In interference we consider superpose discrete light sources,such as 2 light sources in Youngs:N in F-P case.Here in diffraction,we superpose continuous distribution of light sources
7、as stated in Huygens-Fresnel Principle.-232-The simplest model to treat diffraction is Huygens-Fresnel Principle(H-F-P):On the unobstructed wave front,every point serves as a source of spherical secondary wavelets(same).The complex amplitude of the optical field at any point beyond is a superpositio
8、n of all the wavelets.It is basically Huygens Principle+Superposition of waves.Simple picture of H-F-P in determining E(p)through a hole:a)For.Then of difference in OPL between any two paths,All secondary waves add at P constructively behaves as a point source.b)As increases,the interference at P fr
9、om all the secondary wavelets can either constructive or destructive-diffraction,meaning intensity there may be high or low.c)As such interference would cause light APPEAR to travel in linear form and we get geometric optics prediction.(We shall see that the diffraction arising from the boundary is
10、much smaller comparing to the light in the geometric allowed zone,which is the 0th order diffraction)Simple as its physical picture appear to be,solving the field at p/2ABL/2LAB -233-exactly for an arbitrary setup is actually an extreme complicate and difficult job,except for some simple cases which
11、 we are going to study in this course,namely the Fraunhoffer Diffraction and field of on-axis points in Fresnel diffraction.6-1-2 Fraunhoffer and Fresnel Diffraction To evaluate,the field at p we need to know:(1)field distribution of the secondary wavelets on(diffraction screen)(2)The field at p gen
12、erated by each secondary wavelets by principles of superposition The simple calculation is obtainable if the incoming and outgoing waves are planar wave,and such is Fraunhoffer Diffraction or Far-field diffraction.This requires that both the light source and the observation plane are infinitely dist
13、ant from the diffraction screen,or at least both paraxial and far field requirements are satisfied.This can be easily achieved in experiment by lenses:()E p-234-Then(1)The field Amplitude of the secondary wavelets on is constant.(2)The OPL used in the calculation(we shall explain this in detail late
14、r)only depends linearly on the two aperture variables,such linearity is the mathematical criterion for the Fraunhoffer diffraction.Applying the far-field criterion(in the optical region,far field includes the paraxial)d the size of the (6-1)R is the smaller distance between S and P to.As we shall se
15、e Fraunhoffer diffraction has many important applications and is also instrumental in the Fourier transform optics.Other arrangement does not satisfy(6-1)is called Fresnel diffraction.Fraunhoffer diffraction is only a special case for it.However,the treatment is more involving for the Fresnel type d
16、iffraction.We shall give a brief introduction for the Fresnel diffraction first,the goal is to illustrate:how to use H-F-P,and we only concerns the P on the central axis in this case.We are not going to treat the detailed distribution of the interference,d2dR-235-pattern for the off axis points in F
17、resnel-diffraction case.6-2 Huygens-Fresnel Principle(HFP)and Kirchhoff equation As we stated earlier that the HFP is basically the Huygens principle combined with superposition of the waves(The waves coming from the secondary wavelets).It is Kirchhoff who derived a correct mathematical representati
18、on for the HFP,which we only give out as a result8.For the more detailed derivation of the Kirchhoff theory,please refer to Hechts 10.4 (6-2)8 The theory is called Kirchoff scalar theory and is still an approximation from the rigorous treatment starting from Maxwell equations and correct boundary co
19、nditions.The exact solution to diffraction is far more complicated and Kirchoff theory is accurate enough in many cases.000()_()()(,)()ikropenareaopen areaeU pdU pKFU Q dr=?-236-(we shall give a proof on this later)Here I shall use U(p)as symbol for the field,instead of E(p)because we treat the fiel
20、d as a scalar field,this works when the vector feature of the field can be neglected(such as cases where the polarization all along same direction).Most part in(6-2)is quite intuitive:The field at P would depend on the area of the opening and the surface integral is over the open portion of the diff
21、raction screen;It also depends on the field at the opening and its propagation like a spherical source dictated by Huygens principle;the is called obliquity factor whose origin is not intuitive(like that of HFP)but can be derived with the Kirchhoff scalar theory.(6-2)is going to be the starting poin
22、t for us to deal with diffraction.6-3 Fresnel Diffraction through an open aperture A point source S A screen with aperture What is the field at P,U(P)?iK=001(,)(coscos)2F=+0(,)F -237-(Here P is a point on-axis defined by S and center of)6-3-1 Method of Half-Wavelength(/2)Plate Direct application of(
23、6-2)on this problem for the general setup would result in a nasty integral,the r has to be expressed as function of x,y of the surface area.We shall use an approximation method to evaluate such integral and this is the method of half-wavelength plate.Divide the opening aperture into orbital zone.The
24、 OPL from the edge of each neighboring zones to the field point P differs by/2.(Integral over area reduces to summation of zones)is the contribution to P by the jth/2 plate(zone).To evaluate,we need to first evaluate,the contribution to P by a very small zone on the jth/2 plate.According to the HFP
25、and Kirchhoff equation:(6-3)First the field at the diffraction screen is:(6-4)1()()njjU PUP=()jUp12jjrr=+()jUP()jd UP00()(,)ikrjjedUPKfUdr=00ikRjAUeR=-238-For the spherical surface,the obliquity factor is:(6-5)Next we evaluate the small area element(a belt shown by dashed lines in the figure):Put al
- 配套讲稿:
如PPT文件的首页显示word图标,表示该PPT已包含配套word讲稿。双击word图标可打开word文档。
- 特殊限制:
部分文档作品中含有的国旗、国徽等图片,仅作为作品整体效果示例展示,禁止商用。设计者仅对作品中独创性部分享有著作权。
- 关 键 词:
- 光学光学光学光学 6 光学
限制150内