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Wave Incidence at Oblique angles

Wave Incidence at Oblique angles. Sandra Cruz-Pol ECE Dept. UPRM. Quiz VIERNES . Uno de los problemas asignados en el prontuario Enviar contestaciones a preguntas en Word por email. Wave Incidence. Normal incidence Wave arrives at 90 o from the surface Standing waves

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Wave Incidence at Oblique angles

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  1. Wave Incidenceat Oblique angles Sandra Cruz-Pol ECE Dept. UPRM

  2. Quiz VIERNES • Uno de los problemas asignados en el prontuario • Enviar contestaciones a preguntas en Word por email

  3. Wave Incidence • Normal incidence Wave arrives at 90o from the surface • Standing waves • Oblique incidence (lossless) Wave arrives at an angle • Snell’s Law and Critical angle • Two types: Parallelor Perpendicular • Brewster angle

  4. Oblique incidence First, we need to define: • Expression for uniform plane wave traveling in any direction • The Normal , an • Plane of incidence • Angle of incidence x Medium 2 : e2,m2 Medium 1 : e1, m1 qr qt y qi z z=0

  5. Oblique incidence • Uniform plane wave in general form the radius or position vector the wave number or propagation vector • For losslessunbounded media, k = b

  6. Oblique Incidence x Medium 2 : e2,m2 Medium 1 : e1, m1 kr kt qr qt z y qi z=0 ki

  7. Look at the direction of travel x Medium 2 : e2,m2 Medium 1 : e1, m1 kr kt qr qt z y qi kix ki z=0 kiz

  8. kiz qi kix ki Expression for Waves

  9. Tangential E must be Continuous From this we know that frequency is a property of the wave. So is color. So 700nm is not always red!! Give example of bathing suit.

  10. Snell Law • Equating, we get or where, the index of refraction of a medium, ni , is defined as the ratio of the phase velocity in free space (c) to the phase velocity in the medium.

  11. Critical angle, qc …All is reflected • When qt =90o, the refracted wave flows along the surface and no energy is transmitted into medium 2. • The value of the angle of incidence corresponding to this is called critical angle, qc. • If qi > qc, the incident wave is totally reflected.

  12. Fiber optics • Light can be guided with total reflections through thin dielectric rods made of glass or transparent plastic, known as optical fibers. • The only power lost is due to reflections at the input and output ends and absorption by the fiber material (not perfect dielectric).

  13. Optical fibers have cylindrical fiber core with index of refraction nf, surrounded by another cylinder of lower, nc < nf , called a cladding. • For total reflection: [Figure from Ulaby, 1999] Acceptance angle

  14. Exercise: optical fiber • An optical fiber (in air) is made of fiber core with index of refraction of 1.52 and a cladding with an index of refraction of 1.49. • Find the acceptance angle: Answer: 17.5 degrees

  15. Parallel polarization • It’s defined as E is || to incidence plane x Medium 1: e1, m1 Er Et kt kr qr qt z y z qi Ei z=0 ki Medium 2 : e2,m2

  16. Equating for continuity, the tangent fields Which components are tangent to the interface between two surfaces? • y and x At z = 0 (interface):

  17. Reflection and Transmission Coefficients: Parallel Incidence • Reflection

  18. Reflection and Transmission Coefficients: Perpendicular Incidence

  19. Java Animation • http://www.amanogawa.com/archive/Oblique/Oblique-2.html

  20. Exercise A plane wave in air with Is incident upon planar surface of nonmagnetic dielectric material with er=4, on z>0, Find • The polarization of the incident wave • The angle of incidence • The time-domain expressions for the reflected electric and magnetic fields. • The average power density carried by the wave in the dielectric medium.

  21. Exercise A plane wave in free space with Is incident upon planar surface of nonmagnetic lossless dielectric material with er=4, on z>0, Find • The polarization of the incident wave • The angle of incidence and transmission • The reflection and transmission coefficients. • The E field in reflected and in dielectric • Brewster angle

  22. Brewster angle, qB • Is defined as the incidence angle at which the reflection coefficient is 0 (all transmission). • The Brewster angle does not exist for perpendicular polarization for nonmagnetic materials. * qB is known as the polarizing angle

  23. Reflection vs. Incidence angle. Reflection vs. incidence angle for different types of soil and parallel or perpendicular polarization.

  24. Exercise (Brewster angle) A wave in air is incident upon the flat boundary of a nonmagnetic soil medium with er=4, at qi=50o. • Find reflection and transmission coefficients for both incident polarizations, and the Brewster angle. • Answers: EMAG

  25. Summary

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