Lect35EMscattering

Lect35EMscattering - ECE 3030 Electromagnetic Fields and...

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1 ECE 3030 Electromagnetic Fields and Waves Fall 2009 Lecture 35 2009/11/18 Electromagnetic Scattering From Objects Rayleigh Scattering 1 Swartz 06/5/25 Electromagnetic Fields and Waves – Fall 2009 Lecture 35: Instructor: Dr. Wesley E. Swartz Mei scattering Why the Sky is Blue Radar Range Equation in P out P Announcements Prelim 3 tomorrow night, starting at 7:30 in Phillips 101 Covers Dielectric interfaces Impedance matching with dielectrics and transmission line stubs Transmission line transients Antenna patterns from radiating elements Smith Chart usage Waveguides Bring a calculator, straight-edged ruler, 3 sheets of notes. 2 Swartz 06/5/25 Electromagnetic Fields and Waves – Fall 2009 Lecture 35: No Workshop Sections tomorrow. Scattering of Electromagnetic Waves from a Plane Interface z k k i ˆ E i H i ˆ E r H r z k k t ˆ E t H t o o o t x 3 Swartz 06/5/25 Electromagnetic Fields and Waves – Fall 2009 Lecture 35: Incident, transmitted, and reflected waves are all plane waves. The reflected and transmitted waves can also be called the scattered waves. z =0 z z k k i Scattering of Electromagnetic Waves from Objects Incident plane wave: Scattered wave:   r E i   r E s o 1 4 Swartz 06/5/25 Electromagnetic Fields and Waves – Fall 2009 Lecture 35: Questions: How does one find the scattered field? How much power from the incident field goes into the scattered field? In which direction(s) does the scattered power go? phase fronts Scattering of Electromagnetic Waves From Spherical Particles Assume that the particle radius is much smaller than the wavelength of the incident wave, i.e.: ka << 1 . When the above condition holds the scattering is called “ Rayleigh Scattering ”. When the above condition does not hold the scattering is called “ Mie Scattering ”. When ka << 1 , the particle sees a uniform E-field that is slowly 5 Swartz 06/5/25 Electromagnetic Fields and Waves – Fall 2009 Lecture 35: oscillating in time . Incident plane wave:   r E i o 1 a 2 Rayleigh Scattering: Basic Mechanism Incident plane wave:   r E i o 1 a 2 + + + + + - - - - - 6 Swartz 06/5/25 Electromagnetic Fields and Waves – Fall 2009 Lecture 35: One way to understand scattering is as follows: The incident E-field induces a time-varying dipole moment in the sphere (recall the electrostatics problem of a dielectric sphere in a uniform E-field from Demo 4 and Workshop 4. The time-varying dipole radiates like a Hertzian dipole, and this radiation is the scattered radiation.
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