1. Wave Motion & EM Waves (IV)
Chih-Chieh Kang
Electrooptical Eng.Dept. STUT

2. Electromagnetic wave
Radiation field far from the antenna

3. Maxwell’s Equations
Differential form
Integral form

4. 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

5. 3-D Wave equations for EM waves
In free space, Maxwell’s equations  wave equations

6. 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

7. Solutions of 3-D Wave Equations for EM Waves
Take

8. TEM Waves

9. 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

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

11. 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.

12. Energy Transport by EM Waves

13. Energy Transport by EM Waves
Time-averaged Poynting vector

14. 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.

15. Radiation Pressure & Momentum

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