光电子学第1章-光的波动性.ppt

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1、Optoelectronics and Photonics Principles,2009.9,Course Outline,Introduction(2 Periods)Wave Nature of light(4 Periods)Dielectric waveguides and optical fibers(8 Periods)Semiconductor Science and Light Emitting Diodes(10 Periods)Stimulated Emission Devices Lasers(8 Periods)Photodetectors(4 Periods),Ch

2、apter 1 Wave Nature of Light,1.1 Light Wave in a Homogeneous Medium1.2 Refractive Index 1.3 Group Velocity and Group Index1.4 Magnetic Field,Irradiance,and Poynting Vector1.5 Snells Law and Total Internal Reflection(TIR)1.6 Fresnels Equations1.7 Multiple Interference and Optical Resonators1.8 Goos-H

3、nchen Shift and Optical Tunneling1.9 Temporal and Spatial Coherence,Terms,electromagnetic wave（电磁波）medium/dielectric medium（媒质/电介质）light wave（光波）;plane wave（平面波）;traveling wave（行波）;transverse wave（横波）;longitudinal wave（纵波）;monochromatic（单色/频）polychromatic（复色/频）;propagation（传播）;optical field（光场）;wave

4、front（波前/阵面）.wave vector/propagation constant（波矢量/传播常数）;in phase(同相)；phase difference（相位差）;,Terms,beam diameter/beam divergence(光束直径、光束发散角);interfere/interference（干涉）;diffraction（衍射）;reflection（反射）;refraction（折射）;phase velocity（相速度）;diverging/divergent wave（发散波）;(an)isotropic（各向同/异性）;spherical wave（

5、球面波）;light source/beam/intensity/wavelength（光源/束/强/波长）;waist radius/spot size（束腰半径/腰斑）;refractive index（折射率）n;permittivity（介电常数）;permeability（磁导率）;,Terms,optical frequency（光频）;wave packet（波包）;harmonic waves（简谐波);group velocity/index（群速度/折射率）;dispersion/dispersive medium（色散/色散介质）;Poynting vector（波印廷矢

6、量）Irradiance/instantaneous（辐射度/瞬时辐射度）;energy/power flow（能量/功率流）;silica/silicon（石英/硅）;crystal/noncrystal（晶体/非晶体）;polarization/polarizability（偏振,极化/极化率）;dipole/dipolar polarization（双偶极子/偶极子极化）,Newton,Germination Period,Geometrical Optics,Wave Optics,Quantum Optics,Modern Optics,Planck,Einstein,Optic f

7、iber,History,Huygens,Fresnel,MaxWell,Isaac Newton,Published in 1704,Newton described light as a stream of particles,which was used to explain rectilinear propagation,develop theories of reflection and refraction.The particles in rays of different colors were supposed to have different qualities,poss

8、ibly of mass,size,or velocity.,Newton,Germination Period,Geometrical Optics,Wave Optics,Quantum Optics,Modern Optics,Planck,Einstein,Optic fiber,History,Huygens,Fresnel,MaxWell,He thought of light as a pressure wave in an elastic medium.,Huygens,a Dutch contemporary of Newton,developed the wave theo

9、ry of light.His explanation of rectilinear propagation is now known as“Huygens construction”.,A spherical wavefront W has an origin at P and a radius of r=ct after a time of t.Each point at the wavefront W generates a Huygens secondarywavelet.These secondary wavelets combine to form a new wavefront

10、W at time t,with the radii of the secondary wavelets being c(t-t).,Descartes,Christiaan Huygens,The wave theory of light was firmly established 100 years after Newtons Optics.Thomas Youngs double slit experimentcan only be explained in terms of waves.Augustin Fresnel,in 1821,showed thatlight is a tr

11、ansverse wave.James Clerk Maxwell gave a finalvindication of the wave theory by integratingelectricity and magnetism into the four Maxwellequations.,Thomas Young,Augustin Fresnel,James Clerk Maxwell,Newton,Germination Period,Geometrical Optics,Wave Optics,Quantum Optics,Modern Optics,Planck,Einstein

12、,Optic fiber,History,Huygens,Fresnel,MaxWell,In 1900,Max Planck used the particle theory to explain the“blackbody spectrum”.,In 1905,Albert Einsteinpostulated that electro-magnetic radiation is itself quantized in order to explain the photo-electric effect.,Max Planck,Albert Einstein,Awarded the Nob

13、el Prize in 1918.,Awarded the Nobel Prize in 1921.,If you cannot saw with a file or file with a saw,then you will be no good as an experimentalist.Jean Fresnel(17881827),Fresnel was a French physicist and a civil engineer for the French government who was one of the principal proponents of the wave

14、theory of light.,“Physicists use the wave theory on Mondays,Wednesdays and Fridays and the particle theory on Tuesdays,Thursdays and Saturdays”Sir William Henry Bragg,Ch.1 Wave Nature of Light,1.1 Light Wave in a Homogeneous Medium,A.Plane Electromagnetic Wave,Figure 1.1,A.Plane Electromagnetic Wave

15、,The mathematical form of a sinusoidal wave,for propagation along z,Ex electric field at position z at time t E0 amplitude of the wave k propagation constant,or wave number,given by 2/the angular frequency 0phase constant,(1),The argument(t-kz+0)is called the phase wave and denoted by.Equation(1)des

16、cribes a monochromatic plane wave of infinite extent traveling in the positive z direction as depicted in Figure 1.2.,A.Plane Electromagnetic Wave,In any plane perpendicular to the direction of propagation(along z),the phase of the wave,according to Eq(1)is constant,which means that the field in thi

17、s plane is also constant.A surface over which the phase of a wave is constant is referred to as a wavefront.A wavefront of plane wave is obviously a plane perpendicular to the direction of propagation as shown in Figure1.2.,A.Plane Electromagnetic Wave,We know form electromagnetism that time varying

18、 magnetic fields result in time varying electric fields(Faradays Law)and vice versa.A time varying electric field would set up a time varying magnetic field with the same frequency.,A.Plane Electromagnetic Wave,According to electromagnetic principles,a traveling electric field Ex as represented by E

19、q(1)would always be accompanied by a traveling magnetic field By with the same wave frequency and propagation constant(and k)but the directions of the two fields would be orthogonal as in Figure 1.1.Thus there is a similar traveling wave equation for the magnetic field component By.,A.Plane Electrom

20、agnetic Wave,We generally describe the interaction of a light wave with a nonconducting matter(conductivity,=0),through the electric field component Ex rather than By because it is the electric field that displaces the electrons in molecules or ions in the crystal and there by gives rise to the pola

21、rization of matter.However the two fields are linked as in Figure 1.1,and there is an intimate relationship between them.The optical field refers to the electric field Ex.,We can also represent a traveling wave using the exponential notation since in which Re refers to the real part.We then need to

22、take the real part of any complex result at and of calculations.Thus,we can write Eq.(1)as.,or,A.Plane Electromagnetic Wave,(2),In which is a complex number that represents the amplitude of the wave and includes the constant phase information.,A.Plane Electromagnetic Wave,When the electromagnetic(EM

23、)wave is propagating along some arbitrary direction k,as indicated in Figure 1.3,the electric field E(r,t)at a point r on a plane perpendicular to k is,in witch k is called wave vector,whose magnitude is the propagation constant k,kr is the product of k and the projection of r onto k,which is r in F

24、igure 1.3,so that kr=kr.If k has components kx,ky and kz along x,y and z,then kr=kxx+kyy+kzz.,(3),A.Plane Electromagnetic Wave,Figure 1.3,A.Plane Electromagnetic Wave,The relationship between time and space for a given phase is described by,During a time intervalt,this constant phase moves a distanc

25、e z.The phase velocity of this wave is therefore z/t.Thus the phase velocity v is,(4),in which v is the frequency(=2f),A.Plane Electromagnetic Wave,We are frequently interested in the phase difference at a given time between two point on a wave(Figure1.1)that are separated by a certain distance.If t

26、he wave is traveling along z with a wavevector k,as in Eq.(1),then the phase difference between two points separated by z is simply kz sincet is the same for each point.If this phase difference is 0 or multiples of 2 then the two points are in phase.Thus the phase difference can be expressed as kz o

27、r 2z/.,B.Maxwells Wave Equation,In which,0 absolute permeability0 absolute permittivityr relative permittivity,Condition:in a isotropic and linear dielectric medium,i.e.relative permittivity is the same in all directions and that is independent of electric field.,(5),In practice there are many types

28、 of possible EM waves.All these possible EM waves must obey a special wave equation that describes the time and space dependence of the electric field.Maxwells EM Wave Equation:,B.Maxwells Wave Equation,Equation(5)assumes that the conductivity of the medium is zero.To find the time and space depende

29、nce of the field,we must solve Eq.(5)in conjunction with the initial and boundary conditions.We can easily show that the plane wave in Eq.(1)satisfies Eq.(5).There are many possible waves that satisfy Eq.(5)that can therefore exist in nature.,B.Diverging Waves,Consider the plane EM wave in Figure1.2

30、.All constant phase surfaces are xy planes that are perpendicular to the z-direction.A cut of a plane wave parallel to the z-axis us shown in Figure1.4(a)in which the parallel dashed lines at right angles to the z-direction are wavefornts.,B.Diverging Waves,We normally show wavefronts that are separ

31、ated by a phase of 2 or a whole wavelength as in the figure.The vector that is normal to a wavefront surface at a point such as P represents the direction of wave propagation(k)at the point P.Clearly,the propagation vectors everywhere are all parallel and the plane wave propagates without the wave d

32、iverging;the plane wave has no divergence.The amplitude of the planar wave E0 does not depend on the distance from a reference point,and it is the same at all points on a given plane perpendicular to k,i.e.independent of x and y.,B.Diverging Waves,Spherical wave,A spherical wave is described by a tr

33、aveling field that emerges from a point EM source and whose amplitude decays with distance r from the source.At any point r from the source,the field is given by,(6),Substitute equation(6)into(5).Equation(6)is a solution of Maxwells equation.,A cut of a spherical wave is illustrated in Fig.1.4(b)whe

34、re it can be seen that wavefronts are spheres centered at the point source O.The direction of propagation k at any point such as P is determined by the normal to the wavefornt at that point.,Spherical wave,Clearly k vectors diverge out and,as the wave propagates,the constant phase surfaces become la

35、rger.Optical divergence refers to the angular separation of wavevectors on a given wavefront.The spherical wave has 360oof divergence.It is apparent that plane and spherical waves represent two extremes of wave propagation behavior from perfectly parallel to fully diverging wavevectors.They are prod

36、uced by two extreme sizes of EM wave source;an infinitely large source for the plane wave and a point source for the spherical wave.,Diverging Waves,In reality,an EM source is neither of infinite extent nor in point form,but would have a finite size and finite power.Figure 1.4(c)shows a more practic

37、al example in which a light beam exhibits some inevitable divergence while propagating;the wavefronts are slowly bent away thereby spreading the wave.Light rays of geometric optics are drawn to be normal to constant phase surfaces(wavefronts).Light rays therefore follow the wavevector directions.Ray

38、s in 1.4(c)slowly diverge away from each other.The reason for favoring plane waves in many optical explanations is that,at a distance far away from a source,over a small spatial region,the wavefronts will appear to be plane even if they are actually spherical.Figure 1.4(a)may be a small part of“huge

39、”spherical wave.,Gaussian Light Beam,Many light beams,such as the output from a laser,can be described by assuming that they are Gaussian beams.Figure 1.5 illustrates a Gaussian beam traveling along the z-axis.The beam still has an exp j(t-kz)dependence to describe propagation characteristics but th

40、e amplitude varies spatially away from the beam axis and also along the beam axis.Such as a beam has similarities to that in Figure 1.4(c);it slowly diverges and is the result of radiation from a source of finite extent.The light intensity distribution across the beam cross-section anywhere along z

41、is Gaussian.,Gaussian Light Beam,Figure 1.5,A Gaussian beam traveling along the z-axis,Gaussian Light Beam,Waist of the beam:the finite width 2w0 where the wave fronts are parallel,w0 is the waist radius and 2w0 is the spot size.,Beam diameter 2w(at any point z):the cross sectional area w2 at that p

42、oint contains 85%of the beam power.,Beam divergence:the angles 2 which is made by the increasing in beam 2w diameter with z at O.,The relation between waist and beam divergence is,(7),Gaussian Light Beam,Suppose that we reflect Gaussian beam back on itself so that the beam is traveling in the z dire

43、ction and converging towards O;simply reverse the direction of travel in Figure1.5(a).The wavefronts would be“straightening out,”and at O they would be parallel again.The beam would still have the same finite diameter 2w0(waist)at O.From then on,the beam again diverges out just as it did traveling i

44、n+z direction.The relationship in Eq.(7)therefore defines a minimum spot size to which a Gaussian beam can be focused.,Chapter 1 Wave Nature of Light,1.1 Light Wave in a Homogeneous Medium1.2 Refractive Index 1.3 Group Velocity and Group Index1.4 Magnetic Field,Irradiance,and Poynting Vector1.5 Snel

45、ls Law and Total Internal Reflection(TIR)1.6 Fresnels Equations1.7 Multiple Interference and Optical Resonators1.8 Goos-Hnchen Shift and Optical Tunneling1.9 Temporal and Spatial Coherence,1.2 Refractive Index,When an EM wave is traveling in a dielectric medium,the oscillating electric field polariz

46、es the molecules of the medium at the frequency of the wave.Indeed,the EM wave propagation can be considered to be the propagation of this polarization in the medium.The field and the induced molecular dipoles become coupled.The net effect is that the polarization mechanism delays the propagation of

47、 the EM wave.,1.2 Refractive Index,Put differently,it slows down the EM wave with respect to its speed in a vacuum where there are no dipoles with which the field can interact.The stronger the interaction between the field and the dipoles,the slower the propagation of wave.The relative permittivityr

48、 measures the ease with which the medium becomes polarized and hence it indicated the extent of interaction between the field and the induced dipoles.,1.2 Refractive Index,For a EM wave traveling in a nonmagnetic dielectric medium of reflectiver,the phase velocity v is given by,If the frequency v is

49、 in the optical frequency range,then r will be due to electronic polarization as ionic polarization will be too sluggish to respond to the field.However,at the infrared frequencies of below,the relative permittivity r also includes a significant contribution form ionic polarization and the phase vel

50、ocity is slower.,1.2 Refractive Index,For an EM wave traveling in free space,r=1 and,the velocity of light in vacuum.The ratio of the speed of light in free space to its speed in a medium is called refractive index n of the medium.,Note:The relationship between the refractive index n and r must be a