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Uniform Plane Waves: Propagation in Any Direction & Reflection from Dielectric Slabs

This resource explores the propagation of uniform plane waves in arbitrary directions, including observations in frequency and time domains. It also covers reflection and transmission from dielectric slabs under various conditions, providing solutions and examples. Learn about polarization of E and H fields, boundary conditions, reflection coefficients, and broadband strategies to enhance performance.

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Uniform Plane Waves: Propagation in Any Direction & Reflection from Dielectric Slabs

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  1. ELEG 648Plane waves II Mark Mirotznik, Ph.D. Associate Professor The University of Delaware Email: mirotzni@ece.udel.edu

  2. Uniform Plane Waves: Propagation in Any Arbitrary Direction z H f E q y x

  3. Uniform Plane Waves: Propagation in Any Arbitrary Direction z H f E q y x

  4. z H f E q y x Uniform Plane Waves: Propagation in Any Arbitrary Direction Since E and b are at right angles from each other. where and

  5. Uniform Plane Waves: Propagation in Any Arbitrary Direction Summary and Observations: Frequency Domain Time Domain Observation 1. E, H and b vectors are pointing in orthogonal directions. Observation 2. E and H are in phase with each other, however, H’s magnitude is smaller by the amount of the wave impedance

  6. Uniform Plane Waves: Propagation in 2D y H E Can we write this a bit more compact? q x

  7. Uniform Plane Waves: Propagation in 2D y H Can we write this a bit more compact? E q x

  8. Uniform Plane Waves: Propagation in 2D y H E What about the polarization of E? q x

  9. Uniform Plane Waves: Propagation in 2D y H E What about the polarization of E? q x

  10. Uniform Plane Waves: Propagation in 2D y H E What about the polarization of E? q x

  11. Uniform Plane Waves: Propagation in 2D What about the polarization of E? Two cases y y Parallel Polarization Perpendicular Polarization H H E E q q x x

  12. Uniform Plane Waves: Propagation in 2D y H What about H? E q x

  13. Uniform Plane Waves: Propagation in 2D What about the polarization of H? Two cases y y Parallel Polarization Perpendicular Polarization H H E E q q x x

  14. Reflection and Transmission Write down the electric fields in the two regions (2 unknowns, R and T)

  15. Reflection and Transmission Next find the magnetic fields in each region

  16. Reflection and Transmission Apply boundary conditions

  17. Reflection and Transmission

  18. Reflection and Transmission Write down the E field in both regions (4 unknowns, R, T, qr and qt)

  19. Reflection and Transmission Find the H field in both regions

  20. Reflection and Transmission Apply boundary conditions 2 equations and 4 unknowns We need two more equations. How do we get them?

  21. Reflection and Transmission

  22. Reflection and Transmission

  23. Reflection and Transmission

  24. Reflection and Transmission

  25. Reflection and Transmission

  26. Reflection and Transmission

  27. Example: Reflection from an Ocean Interface Reflection Coefficient Angle of Incidence, Degrees

  28. Region I Region III Region II z=d z=0 Reflection and Transmission from Dielectric Slabs 1. Normal Incidence

  29. Reflection and Transmission from Dielectric Slabs Region I: Region II: Region III: Boundary Conditions z=d z=0

  30. Reflection and Transmission from Dielectric Slabs Boundary Conditions z=0 z=d Four equations and four unknowns Solution for the Reflection Coefficient:

  31. Region I Region III Region II z=l2/2 z=0 Reflection and Transmission from Dielectric Slabs Special Cases I. Half Wavelength Thickness Slab

  32. Reflection and Transmission from Dielectric Slabs Special Cases II. Quarter Wavelength Thickness Slab Region I Region III Region II z=l2/4 z=0

  33. Reflection and Transmission from Dielectric Slabs: Example Region III Region I Region II z=0.25m z=0

  34. Reflection and Transmission from Dielectric Slabs: Example |R| Frequency, MHz

  35. How do we broaden the bandwidth around the zero reflection point? |R| Frequency, MHz

  36. One Solution is Multiple Dielectric Layers

  37. Reflection and Transmission from Dielectric Slabs 1. Oblique Incidence ( Parallel Polarization) fII ft fr fII fi Region I Region II Region III z=d z=0

  38. Reflection and Transmission from Dielectric Slabs Region I: Region II:

  39. Reflection and Transmission from Dielectric Slabs Region III: Boundary Conditions z=d z=0 Phase Matching Conditions

  40. Reflection and Transmission from Dielectric Slabs Six Equations and Six Unknowns

  41. Reflection and Transmission from Dielectric Slabs: Solution (parallel polarization) *note we have assumed all non-magnetic materials here

  42. Reflection and Transmission from Dielectric Slabs: Solution (perpendicular polarization) *note we have assumed all non-magnetic materials here

  43. fi Region III Region I Region II z=0.25m z=0 Reflection and Transmission from Dielectric Slabs: Example

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