MIT OpenCourseWare http://ocw.mit.edu 3.23 Electrical, Optical, and Magnetic Properties of Materials 2007For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. Fall13.23 Fall 2007 – Lecture 16MAXWELL AND ELECTROMAGNETISMJames Clerk Maxwell3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007)CavendishLaboratoryImages removed due to copyright restrictions.3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007)2Cavendish Laboratory3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007)Last time1. p-n junctions, built-in voltage, rectification2 Bl h ill ti d ti it i i d t2. Bloch oscillations, conductivity in semiconductors3. Electron transport at the nanoscale4. Phonons, vibrational free energy, and the quasi-harmonic approximation5. Electron-phonon interactions, and phonon-phonon decaysImages removed due to copyright restrictions.3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007)3Study• Fox Optical Properties of Solids• Fox, Optical Properties of Solids, Appendix A and Chap 1.• Prof Fink lecture notes (to be posted)3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007)Image courtesy NASA.3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007)4Electric field, polarization, displacement3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007)+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ A complex crystal lattice can have a permanent intrinsic polarization P. Figure by MIT OpenCourseWare. 3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007)53.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007)Polarization in lead titanate3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007)+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ A complex crystal lattice can have a permanent intrinsic polarization P. + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ A complex crystal lattice can have a permanent intrinsic polarization P. Figures by MIT OpenCourseWare. 3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007) 673.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007)Dielectric constant, susceptibility3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007)8Magnetic response3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007)Maxwell equations ∇rrE1 ∂Br0∇×+E =0ct∂rrr14∂Dπr∇×H− =ct∂ crr∇⋅B =0rr∇⋅D =4πρ3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007)9Vector potential and gauges3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007)Vector potential and gauges3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007)10Summaryr rr∇×rrE +1 ∂B0=ε{dielectr{ic tensorr rB =µH{permeability tensor∇×E + =ct∂0rrr14∂Dπr∇×HJ− =ct∂ crrrr∇⋅B =0r rDE==επE+4 Pr rr rrrBH==µH+4πM∇⋅D =4πρE – electric field12 variables H – magnetic field8 scalar Maxwell D – electric displacementequationsB – magnetic displacement3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007)Electromagnetic waves3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007)11Electromagnetic waves3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007)Summaryrrrr11∂∂BH1⋅rr1rr⎛⎞1rr1rr∇×EE+ = 00⎯⎯µ→ ∇× + = ⎯⋅∇×⎯→∇×⎜⎟∇×E+ ∇× =ct∂∂µµct⎝⎠ctrr∇∇rr11∂∂∂0⋅∂2HHDE∂rrε∇×−11∂∂DE=⎯⎯tHH0∂→ ∇×=ε∂ct∂∂ct c22∂trrr⎛⎞1rε∂2E∇×⎜⎟∇×E + =0⎝⎠µct22∂rrr2µε∂2E∇−E22=0ct∂rrr2∇2Hµε∂ H03.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007)∇ H −=ct22∂0rrµε22∂ Er()∇=Ect22∂rExr,,yz,t= Eitkr0errω−⋅crk =ωµε0H∂∂12Refractive index3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007)Phase velocity3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall 2007)13Wave packets3.23 Electronic, Optical and Magnetic Properties of Materials - Nicola Marzari (MIT, Fall