光学光学光学光学 (8).pdf
《光学光学光学光学 (8).pdf》由会员分享,可在线阅读,更多相关《光学光学光学光学 (8).pdf(81页珍藏版)》请在得力文库 - 分享文档赚钱的网站上搜索。
1、-338-Chapter 8 Polarization and Propagation of Light in Crystal (Chap 8,Hecht;Chap 7,Zhao)The light field in the classical E-M theory is a vector field.The component has direction,this direction of is called polarization of light.We neglect this vector feature before by treating it as scalar(using s
2、ymbol)in cases such vector nature can be neglected.In this chapter we shall give it a detailed look.The polarization is not only in itself an important property of light which has many applications,it is also related in quantum the spin of photon,and the Jones vector treatment on polarization uses s
3、ame mathematical tools as in quantum.The polarization indeed is a two-level system in quantum mechanics,and our treatment here will pay dividents later in study of quantum mechanics.8-1 Polarization Type of Light(1)Natural light(Unpolarized light)The direction of is randomly distributed,say at some
4、fixed space,measuring the polarization at different times,the result is something like the figure shown:E?E?UE?-339-Question:The field as shown appears to be averaged to zero for the natural light,then why the average intensity of natural light?The answer is that each component is incoherent!It is f
5、rom independent emission of atoms/molecules,belongs to independent wave trains.So there is no fixed phase relation and it is intensity that sums up,a scalar summation instead of vector summation.(2)Partial polarized light.The direction is random and the amplitude depends on direction.The description
6、 of the partial polarized light is actually most difficult in math(compare to the polarized light introduced below).The accurate description in classical physics is Stokes vector which will not be treated in our course,but briefly discussed in Hechts;the formal treatment would be density matrix meth
7、od in statistical mechanics and will not be introduced here.A very useful picture from the density matrix method is that we can treat the partial polarized light as a combination of natural light plus a polarized light.That is why it is called partial polarized.Above are two types of unpolarized lig
8、ht.For polarized light,the E?0-340-direction of has fixed relation over space and time.i.e.it is predictable.These polarized light can be:(3)Linear polarized light.does not change direction over space and time,always along same line Apparently all linear polarized light can be superposition of two o
9、rthogonal linear polarized light(with same frequency)are unit vectors along (or )direction.Previously in the discussion of superposition of waves,we stated that for the sum of waves to show interference,they have to have parallel components of polarization,and the phase difference between the waves
10、determine the intensity.Here we shall see that adding waves with perpendicular(“orthogonal”more precisely)polarization generally changes the polarization of light;the phase difference between the E?E?110 x1y1EE cos(kzt)E icos(kzt)E jcos(kzt)=+?220 x2y2EE cos(kzt)E icos(kzt)E jcos(kzt)=+?xii0iyii0iE|
11、E|cos,E|E|sin=j,iV,H?y,x?-341-orthogonal components will determine the polarization state(type).For a linear polarized light,the phase difference between the two orthogonal components is either 0 in the figure)or.(4)Circular Polarized light.What happens if the two orthogonal polarized light,with pha
12、se difference.i.e.Then what is?We will have circular polarized light if,a quite special case in this sense.For(V leads H)at a fixed space point,say,looking into the direction of lights propagation.for x=0 clearly is not changing over time.But its direction is rotating clockwise with 1(E?2()E?iEHjEV,
13、0)tkz(cosiEExH=?)tkz(cosjEEyV+=?VHEEE?+=xy and EE2=2=0z=)t(cosiEx)tcos(-jEy+2=2y2x2|E|E|E+=-342-angular frequency This is called right circular polarized If fixed in time,say t=0,the polarization over place:We define right-circular polarized in the sense of how it changes over time.Similarly for At
14、fixed space over time,left circular polarized light is shown in the figure.Note means lag in phase(lags)kz(cosiEx)2kz(cosjEy2=0VEHE-343-means lead in phase(leads)This is in accordance of the convention we choose by adopting as wave.So it is conventional to say that if the V component leads in phase
15、by,it is right circular(of course the amplitudes for the H,V components are equal);if V lags by,then it is left circular.(5)Elliptical polarized light For the superposition of or,the polarization state will be what is called elliptical.Linear polarized and circular polarized light are special cases
16、for such superposition.(Fig.8.7,Hecht.Fig.910,Zhaos P244,Vol.1,or Fig.35,Pg.191,Vol.2)Looking into the direction of propagation,at fixed space and the polarization changes over time:(6)Superposition of orthogonal oscillation with different frequencies h,v are integers The superposition at fix space
17、point(say z=0)would be what is known as Lessajou Figure.For example h=2,v=1,would change with 0oenn ooeevcnvcn=-360-Positive crystal or?Huygenss method(drawing)to get lights propagation(dtails in Zhaos book Vol.2 Chap.7;1.3)e light is parallel or perpendicular with OA:Above are the three special and
18、 simplest forms of light propagation in uniaxial crystal.They are also simplest to understand using Huygens principle.These 3 special cases will be all we need for the manipulation of polarization.For the general case(not required for this course),if the angle between e light and OA are not or,the d
19、irection of propagation of energy(ray direction)and the direction of equal-phase wave front no longer overlaps.(Direction of wave vector).oevv 090k?-361-Ray direction:direction of energy flow,given by the Poynting vector,perpendicular to E,H.Wave vector:Normal direction to the equal phase wave front
20、.It is perpendicular to the D,H in a media,and in anisotropic media,the D,E are not along same direction as we shall see below.?Phase velocity,ray velocity,phase velocity surface,ray velocity surface.(optional for this course)Fig.8-1 ,S=EH?k?=ekOA=eSOA=eekS2eiNS=-362-The direction of energy propagat
21、ing(Poynting vector)is different from wave vector.This is caused by that in crystal,generallyare not parallel.:electric displacement.(8-9)where (8-10)polarizability Susceptibility tensor Thus (8-11)Dielectric tensor In isotropic media,is a scalar,and(8-11)shows that in isotropic media.In the anisotr
22、opic media,is generally a tensor.(3 3 matrix)By properly choosing x,y,z direction in crystal,we can have in diagonal form,i.e.For isotropic crystal For uniaxial crystal +=22eiiNkeS?ek?D,E?D?PED0?+=EP0?=EE)1(D00?=+=1=+E|D?x111213xy0212223yz313233zDEDDEEDE=?=zyx000000 xyz=xyz=-363-For biaxial crystal
23、Clearly in anisotropic media,are not parallel.From the Maxwell equation of E-M wave in crystal,for plane wave in forms of (the derivation is quite messy and thus omitted here)We have,So the propagation of energy()and propagation of equal-phase wavefront()is different in direction and velocity in ani
24、sotropic media.For e light in uniaxial crystal,we need to define and distinguish two velocities:Ray velocity,and phase velocity (8-12)Note that in Zhaos book,Fig 1-5,1-7,1-8,1-9,1-10,the velocities used to draw the ellipse are ray velocities.For the e light,in definition of,the (or),(or)are phase ve
25、locities according to definition of n.However in cases of propagation along or perpendicular to OA,the ray velocity and phase velocity are equal.(See Fig 1-12,Zhaos).As derived in the Zhaos book,Pg.174,the angle between and xyzD,E?)trk(ieA?kHD?SHE?HD,E?S?k?rvNv cosvvrN=oovcn=eevcn=ov|vevvS?k?-364-wi
- 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 8 光学
限制150内