1. 02/20/2015PHY 712 Spring 2015 -- Lecture 161 PHY 712 Electrodynamics 9-9:50 AM Olin 103 Plan for Lecture 16: Read Chapter 7 1.Plane polarized electromagnetic waves 2.Reflectance and transmittance of electromagnetic waves – extension to anisotropy and complexity

2. 02/20/2015PHY 712 Spring 2015 -- Lecture 162

3. 02/20/2015PHY 712 Spring 2015 -- Lecture 163

4. 02/20/2015PHY 712 Spring 2015 -- Lecture 164 Analysis of Maxwell’s equations without sources -- continued:

5. 02/20/2015PHY 712 Spring 2015 -- Lecture 165 Analysis of Maxwell’s equations without sources -- continued: Both E and B fields are solutions to a wave equation:

6. 02/20/2015PHY 712 Spring 2015 -- Lecture 166 Analysis of Maxwell’s equations without sources -- continued: Note: , n, k can all be complex; for the moment we will assume that they are all real (no dissipation).

7. 02/20/2015PHY 712 Spring 2015 -- Lecture 167 Analysis of Maxwell’s equations without sources -- continued: E0E0 B0B0 k

8. 02/20/2015PHY 712 Spring 2015 -- Lecture 168 Reflection and refraction of plane electromagnetic waves at a plane interface between dielectrics (assumed to be lossless)  ’  ’  k’ kiki kRkR iR 

9. 02/20/2015PHY 712 Spring 2015 -- Lecture 169 Reflection and refraction -- continued  ’  ’  k’ kiki kRkR iR 

10. 02/20/2015PHY 712 Spring 2015 -- Lecture 1610 Reflection and refraction -- continued  ’  ’  k’ kiki kRkR iR 

11. 02/20/2015PHY 712 Spring 2015 -- Lecture 1611 Reflection and refraction -- continued  ’  ’  k’ kiki kRkR iR 

12. 02/20/2015PHY 712 Spring 2015 -- Lecture 1612 Reflection and refraction -- continued  ’  ’  k’ kiki kRkR iR 

13. 02/20/2015PHY 712 Spring 2015 -- Lecture 1613 Reflection and refraction -- continued  ’  ’  k’ kiki kRkR iR  s-polarization – E field “polarized” perpendicular to plane of incidence

14. 02/20/2015PHY 712 Spring 2015 -- Lecture 1614 Reflection and refraction -- continued  ’  ’  k’ kiki kRkR iR  p-polarization – E field “polarized” parallel to plane of incidence

15. 02/20/2015PHY 712 Spring 2015 -- Lecture 1615 Reflection and refraction -- continued  ’  ’  k’ kiki kRkR iR 

16. 02/20/2015PHY 712 Spring 2015 -- Lecture 1616 For s-polarization For p-polarization

17. 02/20/2015PHY 712 Spring 2015 -- Lecture 1617 Special case: normal incidence (i=0,  =0)

18. 02/20/2015PHY 712 Spring 2015 -- Lecture 1618 Multilayer dielectrics (Problem #7.2) n1n1 n2n2 n3n3 kiki kRkR ktkt kbkb kaka d

19. 02/20/2015PHY 712 Spring 2015 -- Lecture 1619 Extension of analysis to anisotropic media --

20. 02/20/2015PHY 712 Spring 2015 -- Lecture 1620 Consider the problem of determining the reflectance from an anisotropic medium with isotropic permeability   and anisotropic permittivity    where: By assumption, the wave vector in the medium is confined to the x-y plane and will be denoted by The electric field inside the medium is given by:

21. 02/20/2015PHY 712 Spring 2015 -- Lecture 1621 Inside the anisotropic medium, Maxwell’s equations are: After some algebra, the equation for E is: From E, H can be determined from

22. 02/20/2015PHY 712 Spring 2015 -- Lecture 1622 The fields for the incident and reflected waves are the same as for the isotropic case. Note that, consistent with Snell’s law: Continuity conditions at the y=0 plane must be applied for the following fields: There will be two different solutions, depending of the polarization of the incident field.

23. 02/20/2015PHY 712 Spring 2015 -- Lecture 1623 Solution for s-polarization

24. 02/20/2015PHY 712 Spring 2015 -- Lecture 1624 Solution for p-polarization

25. 02/20/2015PHY 712 Spring 2015 -- Lecture 1625 Extension of analysis to complex dielectric functions