光电子学第1章_光的波动性.ppt

Optoelectronics and Photonics Principles 2009.9 Course Outline nIntroduction (2 Periods) nWave Nature of light (4 Periods) nDielectric waveguides and optical fibers (8 Periods) nSemiconductor Science and Light Emitting Diodes (10 Periods) nStimulated Emission Devices Lasers (8 Periods ) nPhotodetectors (4 Periods) Chapter 1 Wave Nature of Light v1.1 Light Wave in a Homogeneous Medium v1.2 Refractive Index v1.3 Group Velocity and Group Index v1.4 Magnetic Field, Irradiance, and Poynting Vector v1.5 Snells Law and Total Internal Reflection (TIR) v1.6 Fresnels Equations v1.7 Multiple Interference and Optical Resonators v1.8 Goos-Hnchen Shift and Optical Tunneling v1.9 Temporal and Spatial Coherence Terms nelectromagnetic wave （电磁波） nmedium/ dielectric medium（媒质/ 电介质 ） nlight wave（光波）; nplane wave（平面波）; traveling wave（行波）; ntransverse wave（横波）; longitudinal wave（纵波）; nmonochromatic（单色/频）polychromatic （复色/频）; npropagation（传播）; noptical field（光场）; nwavefront（波前/阵面）. nwave vector/propagation constant（波矢量/传播常数）; nin phase (同相)；phase difference（相位差）; Terms nbeam diameter/beam divergence (光束直径、光束发散角); ninterfere/interference（干涉）; ndiffraction（衍射）;reflection（反射）; refraction（折射）; nphase velocity（相速度）; ndiverging/divergent wave（发散波）; n(an) isotropic（各向同/异性）; nspherical wave（球面波）; nlight source/beam/intensity/wavelength（光源/束/强/波长）; nwaist radius / spot size （束腰半径 / 腰斑）; nrefractive index（折射率）n; npermittivity（介电常数）; npermeability（磁导率）; Terms noptical frequency（光频）; nwave packet（波包）; nharmonic waves（简谐波); ngroup velocity/index（群速度/折射率）; ndispersion/ dispersive medium （色散 / 色散介质）; nPoynting vector（波印廷矢量） nIrradiance/instantaneous（辐射度/ 瞬时辐射度）; nenergy/power flow （能量/功率流）; nsilica/silicon（石英 / 硅）; ncrystal / noncrystal （晶体/非晶体）; npolarization/polarizability（偏振,极化/极化率）; ndipole/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 fiber 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, possibly 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 theory 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 secondary wavelet. These secondary wavelets combine to form a new wavefront 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. nThomas Youngs double slit experiment can only be explained in terms of waves. n Augustin Fresnel, in 1821, showed that light is a transverse wave. nJames Clerk Maxwell gave a final vindication of the wave theory by integrating electricity and magnetism into the four Maxwell equations. Thomas YoungAugustin FresnelJames Clerk Maxwell Newton Germination Period Geometrical Optics Wave Optics Quantum Optics Modern Optics Planck, Einstein Optic fiber History Huygens, Fresnel, MaxWell In 1900, Max Planck used the particle theory to explain the “blackbody spectrum”. In 1905, Albert Einstein postulated that electro- magnetic radiation is itself quantized in order to explain the photo- electric effect. Max Planck Albert Einstein Awarded the Nobel 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 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 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) describes a monochromatic plane wave of infinite extent traveling in the positive z direction as depicted in Figure 1.2. A. Plane Electromagnetic Wave nIn 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 this 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 nWe know form electromagnetism that time varying 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 nAccording to electromagnetic principles, a traveling electric field Ex as represented by Eq(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 Electromagnetic 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 polarization 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. nWe can also represent a traveling wave using the exponential notation since in which Re refers to the real part. We then need to 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) 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 Figure 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 distance 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 the 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 or 2z/. B. Maxwells Wave Equation In which 0 absolute permeability 0 absolute permittivity r 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 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 nEquation(5) assumes that the conductivity of the medium is zero. To find the time and space dependence 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 k Wave fronts r E k Wave fronts (constant phase surfaces) z ll l Wave fronts P O P A perfect spherical waveA perfect plane wave A divergent beam (a)(b)(c) Examples of possible EM waves nConsider the plane EM wave in Figure1.2. 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 nWe normally show wavefronts that are separated 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 diverging; 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 traveling 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) where 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 larger. 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 produced 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 nIn 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 practical 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. Rays 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” spherical wave. Gaussian Light Beam nMany 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 the 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 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 point 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 nSuppose that we reflect Gaussian beam back on itself so that the beam is traveling in the z direction 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 in +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 v1.1 Light Wave in a Homogeneous Medium v1.2 Refractive Index v1.3 Group Velocity and Group Index v1.4 Magnetic Field, Irradiance, and Poynting Vector v1.5 Snells Law and Total Internal Reflection (TIR) v1.6 Fresnels Equations v1.7 Multiple Interference and Optical Resonators v1.8 Goos-Hnchen Shift and Optical Tunneling v1.9 Temporal and Spatial Coherence 1.2 Refractive Index When an EM wave is traveling in a dielectric medium, the oscillating electric field polarizes 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 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 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 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 velocity 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 applied at the same frequency for both n and r . 1.2 Refractive Index If k is wave vector ( k=2/) and is the wavelength, both in free space, then in the medium kmedium=nk and medium= /n. Eq.(2) is in agreement with our intuition that light propagates more slowly in a denser medium that has a higher refractive index. We should note that the frequency v remains the same. 1.2 Refractive Index The refractive index of a medium is not necessarily the same in all directions. In non-crystal materials such as glasses and liquids, the material structure is the same in all directions and does not depend on direction. The refractive index is then isotropic. In crystals, however, the atomic arrangements and interatomic bonding are different along different directions. 1.2 Refractive Index Crystals, in general, have nonisotropic, or anisotropic, properties. Depending on the crystal structure, the relative permittivityr is different along different crystal directions. This means that, in general the refractive index n seen by a propagating electromagnetic wave in a crystal will depend on the value of r the direction of the oscillating electric field (that is long the direction of polarization ). 1.2 Refractive Index For example, suppose that the wave in Figure 1.1 is traveling along the z-direction in a particular crystal with is electric field oscillating along the x-direction. If the relative permittivity along this x-direction is r, then . The wave therefore propagates with a phase velocity that is c/nx. The variation of n with direction of propagating and the direction of the electric field depends on the particular crystal structure. 1.2 Refractive Index With the exception of cubic crystals ( such as diamond ), all crystals exhibit a degree of optical anisotropy that leads to a number of important applications as discussed in chapter 7. Typically, noncrystalline solids such as glasses and liquids, and cubic crystals are optically isotropic; they possess only one refractive index for all directions. Example 1.2.1 Relative permittivity and refractive index nThe relative permittivity for many materials can be vastly different at high and low frequencies because different polar