Lecture2 - 2.1.History Lecture 2 2. The nature of light...

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Unformatted text preview: 2.1.History Lecture 2 2. The nature of light 2.1. History 2.2. The dualism particle and wave: QED 2.3. Decisive experiments Hecht: Chapter 1 and additional reading referenced in the lecture notes A nice chronological overview of the history of optics and light is given in History of Optics Pioneers The main interest were The nature of light: particle or wave) Instrumentation (Astronomy) Vision Most recent Nobel Prize in Optics 2.1.1. QED The research leading to an understanding of the nature of light and the emission and absorption processes has been of paramount importance. It led to the development of quantum physics, reaching a high peak in the 1920s and a fruition towards the mid-century years with the completion of the very successful Quantum Electrodynamic (QED) theory. 2.2 Duality Particle -Wave In history that has been a long discussion about the character of light: See also Can you name experiments in which the particle and the wave character of light is displayed ? Here I will show some small experiments using the laser pointer Different treatment of light Feynman's Opinion (this should settle this question) I want to emphasize that light comes in this form: particles. It is very important to know that light behaves like particles, especially for those of you who have gone to school where you probably were told something about light behaving like waves. I'm telling you the way it does behave -like particles He is certainly right because particles also exhibit wave character in some instances. The light particles are called photons Wave picture Particle picture Geometric Optics QED In principle all optical phenomena which have been observed so far can be described in QED. In many instances, however, it is quite sufficient to describe light in a more intuitive way: Classical electromagnetic wave Photon picture OK, as long as we know the limit Geometric optics Feynman may disagree with that approach. In principle QED is not more difficult than electromagnetism. It would be interesting to base a modern optics course on QED. My predictions are that in not so far future will have to do this in order to explain state of the art application: I.E.: Quantum communication. 2.3 Decisive Experiments Speed of light Do you know of any obvious evidence that the speed of light is finite ? Today the speed of light can be measured more accurately than the meter can be defined. C is fixed to 2.99792458 x108 m/s Meter Speed of light Into the 16th century is was believed that the speed of light is infinite Galileo: finite but could not measure it Roemer: Jupiter moons Fizeau: Rotating mirror Michelson-Morley Frome: microwave interferometer and a Kerr cell shutter See also Photo Electric effect Blackbody radiation IR: The Photo electric effect In 1902, Lenard studied how the energy of photoelectrons emitted from a metal surface varied with the intensity of the light. To measure the energy of the ejected electrons, Lenard charged the collector plate negatively, to repel the electrons coming towards it. Lenard discovered that there was a well defined minimum voltage that stopped any electrons getting through, we'll call it Vstop. Vstop did not depend at all on the intensity of the light! Doubling the light intensity doubled the number of electrons emitted, but did not affect the energies of the emitted electrons. Photo electric effect (cont.) Additional observation: Use different colors the shorter wavelength, higher frequency light caused electrons to be ejected with more energy. Vstop depends on wavelength In 1902, Lenard studied how the energy of the emitted photoelectrons varied with the intensity of the light. He used a carbon arc light, and could increase the intensity a thousand-fold. The ejected electrons hit another metal plate, the collector, which was connected to the cathode by a wire with a sensitive ammeter, to measure the current produced by the illumination. To measure the energy of the ejected electrons, Lenard charged the collector plate negatively, to repel the electrons coming towards it. Thus, only electrons ejected with enough kinetic energy to get up this potential hill would contribute to the current. Lenard discovered that there was a well defined minimum voltage that stopped any electrons getting through, we'll call it Vstop. To his surprise, he found that Vstop did not depend at all on the intensity of the light! Doubling the light intensity doubled the number of electrons emitted, but did not affect the energies of the emitted electrons. The more powerful oscillating field ejected more electrons, but the maximum individual energy of the ejected electrons was the same as for the weaker field. Photo electric effect (explanations) 1. Experimental findings But Lenard did something else. With his very powerful arc lamp, there was sufficient intensity to separate out the colors and check the photoelectric effect using light of different colors. He found that the maximum energy of the ejected electrons did depend on the color --- the shorter wavelength, higher frequency light caused electrons to be ejected with more energy. This was, however, a fairly qualitative conclusion --- the energy measurements were not very reproducible, because they were extremely sensitive to the condition of the surface, in particular its state of partial oxidation. In the best vacua available at that time, significant oxidation of a fresh surface took place in tens of minutes. (The details of the surface are crucial because the fastest electrons emitted are those from right at the surface, and their binding to the solid depends strongly on the nature of the surface --- is it pure metal or a mixture of metal and oxygen atoms?) Blackbody Radiation Einstein 1905: Light are quanta with energy E=hv The rest of the explanation is simple: more intensity more quanta eVstop=hv-Work required to free electron The American experimental physicist Robert Millikan, who did not accept Einstein's theory, which he saw as an attack on the wave theory of light, worked for ten years, until 1916, on the photoelectric effect. He even devised techniques for scraping clean the metal surfaces inside the vacuum tube. For all his efforts he found disappointing results: he confirmed Einstein's theory, measuring Planck's constant to within 0.5% by this method. One consolation was that he did get a Nobel prize for this series of experiments. "(v ) dv = 8#hv 3 dv 1 3 hv / kT c e $1 IR: In 1905 Einstein gave a very simple interpretation of Lenard's results. He just assumed that the Explanation following classical electrodynamics and thermodynamics Considering the diskrete modes within a box and the average energy for each mode one finds 8#v dv kT c3 Rayleigh-Jeans distribution 2 Explanation using Planck hypotheses Energy of radiation modes is only possible in multiples of hv This assumption changes the statistics: The average energy in each mode is no longer kT, it is now: E = We get: Number of modes hv e hv / kT "(v ) dv = "1 8#v 2 dv hv 8#hv 3 dv 1 "(v ) dv = = c 3 e hv / kT $ 1 c 3 e hv / kT $ 1 The wave-particle duality in one and the same experiment Summary We reviewed today the different ways light can be (and has been in history) treated. Particle time Wave QED would be most appropriate We will use mostly simpler approaches to explain a subset of experiments Experimental arrangement of a two-slit experiment for electrons. Two paths are made available to the electron beam. (A. Tonomura et al. : American Journal of Physics 57 (1989) 117. There is plenty of experimental evidence which show that the classical theories are not sufficient. ! Similar experiment is also possible with light (see Hecht pg. 53 1 xperiments with beams of light or of electrons have been made such that both aspects waves and particles - are observed. For interference to occur it is among other things also necessary for the beam to have available more than one path from source to Modes in a cavity: standing waves Additional Slides # e cosk x " sink y " sink z& x x y z ( r r % % ey sink x x " cosk y y " sink zz( u(r ) = % % e sink x " sink y " cosk z( ( $ z x y z ' kx = l" m" n" , ky = , kz = a b d Number of possible k vectors is limited We have to consider, however, the additional condition r r " # u( r ) = 0 r r e "k =0 Only two degrees of freedom for each k-vector Number of modes our next task will be to calculate the number of modes in a frequency range from 0...!. This is identical to values of k between 0...2!!/c Energy Density Energy density per unit volume and unit frequency range # 8"v 2 & " v = pv E = % 3 ( kT % c ( $ ' kx = Volume of unit cell: Contains 1 mode #3 Vkunit" cell = With 2 degrees of freedom Vcavity Volume of k-space from 0...2!!/c l" m" n" , ky = , kz = a b d From classical thermodynamic we get, that the average energy of a vibration mode (1/2)kT per degree of freedom E = kT 4" (8" 3v 3 /c 3 ) 3 ! Number of modes 8 Vk = N = 2" Vk (v) 8$ 3 3 = Vv /c k Vunit#cell 3 Mode density ! pv = 1 dN = 8"v 2 /c 3 V dv k positive 8#v 2 dv wrong kT c3 Rayleigh-Jeans distribution Here we have assumed that the energy of the radiation is continuous. "(v ) dv = What' s wrong ? Average energy ? Intuitively: Number ? modes: OK of both ! Number of modes ? ! Planck Hypothesis Energy of radiation modes is only possible in multiples of hv With Planck Hypotheses we have entered Quantum-Electrodynamics the discrete nature of the energy can be understood if we associate quasi-particles with the E-M field: Photons Energy of photons: E=hv Energy of an electromagnetic field: nhv n= number of photons electromagnetic fields (like fields) are quantized: "Second quantization" energy still our treatment is semiclassical quantum 8#v 2 dv hv 8#v 2 dv 1 "(v ) dv = = % hv % hv / kT 3 hv / kT 3 c e $1 c e $1 Number of modes Number of quanta in cavity mode E n = nhv Average energy #AP A = i= 0 " " i i energy state Rel. thermal population E = 0 + 1" hv " e# hv / kT + 2" hv " e #2hv / kT + ....+ n " hv " e# nhv/ kT 1+ e# hv / kT + e#2hv / kT + ..+ e #nhv / kT hv e hv / kT " 1 Sum of all rel. probabilties #P i= 0 i = "(v ) dv = 8#v 2 dv hv 8#hv 3 dv 1 = 3 hv / kT 3 hv / kT c e $1 c e $1 This looks OK Einstein`s approach 1. 3 types of radiative processes 1. Spontaneous emission (A21) Absorption (B12) Stimulated emission (B21) This is almost Planck`s Formula "(v ) = A2 1e# hv / kT B1 2 # B2 1e# hv / kT 2 hv hv hv hv 1 Since absorption and stimulated emission are just inverse processes it is plausible that they have the same probabilitiy: "(v ) = A2 1 B1 2(e hv / kT # 1) Rate equations: dN1 0 = B2 1N 2 "(v) + A2 1N 2 # B1 2N1 "(v) dt dN 2 0 = # dN1 = #B2 1N 2 "(v) # A2 1N 2 + B1 2N1"(v) dt dt N2 B1 2 = N1 A2 1 + B2 1"(v) N2 = e"hv / kT N1 A2 1e# hv / kT B1 2 # B2 1e# hv / kT for the steady state: Boltzmann: ! "(v ) = 8#hv 3 1 Planck 3 hv / kT c e $1 A 8"hv 3 # of modes x energy of By comparison we find: 2 1 = B2 1 c3 mode "(v ) = In order to determine A21 or B21 we now just need to find one of them Probability of spontaneous emission In the semi-classical picture this type of transition cannot be explained. It is based on the (E-M) field quantization. In this view the E-M field can be seen as an essemble of harmonic oscillators (one for each mode) with an energy " 1$ E n = hv n + # 2% The zero point energy causes field fluctuations which induces the spontaneous emission. While the stimulated processes take place only in one mode (of the incident mode), spontanoeus emission takes place in all the modes which lie within the spectral width. From the viewpoint it is no longer surprising that the ratio of their probabilities is related to the number of modes. For electric dipole transition one finds: Ael = 16" 3v 3 el 2 3 2 1 3#o hc with el1 = 2 ^ % $ e r$ * 2 1 transition dipole moment ...
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This note was uploaded on 08/06/2008 for the course PHYS 352 taught by Professor Dierolf during the Fall '04 term at Lehigh University .

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