Wave Motion & EM Waves (IV) Chih-Chieh Kang Electrooptical Eng.Dept. STUT email:kangc@mail.stut.edu.tw

Electromagnetic wave Radiation field far from the antenna

Maxwell’s Equations Differential form Integral form

Maxwell’s Equations in Cartesian coordinates del operator ：electric field intensity [V/m] ：permittivity [s2C2/ m3kg] ：electric flux density [C/m2] ：permeability [mkg / C2] ：magnetic flux density [Wb/m2] ：charge density [C/m(2)] ：magnetic field intensity [A/m] J：current density [A/m2] in Cartesian coordinates del operator

3-D Wave equations for EM waves In free space, Maxwell’s equations  wave equations

Solutions of 3-D Wave Equations for EM Waves Every component of EM field obeys the 3-D scalar differential wave equation Solutions for time-harmonic plane waves propagating in the +k direction

Solutions of 3-D Wave Equations for EM Waves Take

TEM Waves

Relation between E and H in a Uniform Plane Wave In general, a uniform plane wave traveling in the +z direction may have both x- and y-components ：amplitude of E-field, ：amplitude of H-field phase constant intrinsic impedance

Energy Transport by EM Waves Poynting theorem electric energy density magnetic energy density Poynting vector determines the direction of energy flow

Energy Transport by EM Waves Poynting theorem : Electromagnetic power flow into a closed surface at any instant equals the sum of the time rates of increase of the stored electric and magnetic energies plus the ohmic power dissipated (or electric power generated, if the surface enclosed a source) within the enclosed volume.

Energy Transport by EM Waves

Energy Transport by EM Waves Time-averaged Poynting vector

Energy Transport by EM Waves Irradiance I : average energy per unit area per unit time The intensity of light wave is proportional to the square of the amplitude of the (electric) field.

Radiation Pressure & Momentum

References E. Hecht, Optics, Addison-Wesley. F. T. Ulaby, Fundamentals of Applied Electromagnetics, Prentice Hall. J. D. Cutnell, and K. W. Johnson, Physics, Wiley.