Lect19NonNormalInc - ECE 3030 Electromagnetic Fields and...

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1 ECE 3030 Electromagnetic Fields and Waves Fall 2009 Lecture 19 2098/10/9 Non-Normal Incidence of Waves at Interfaces Reflection and Transmission Boundary Conditions 1 Rana and Swartz 06/5/25 Electromagnetic Fields and Waves – Fall 2009 Lecture 19: Instructor: Dr. Wesley E. Swartz Snell’s Law Total Internal Reflection Brewster’s Angle z =0 z o t μ ε tk Et Ht t θ o i x Transverse Electric (TE) wave rk Er Hr ik Ei Hi i r i n t n i i E t Uniaxial Media Applications – Demo of Problem 11.1 z k k ˆ = E z k k ˆ = E y x () = r E r E r E 0 0 0 0 0 0 r D r D r D z y x e o o z y x c n k e e o e ω = = n k o o o o = = 3 Rana and Swartz 06/5/25 Electromagnetic Fields and Waves – Fall 2009 Lecture 19: The field inside the plate at z=L is: So factor out the smaller one so that the difference is positive. Pick the difference that gives the needed difference in phase Linear: z =0 z = L L k k j L k j o L z o e o e y ˆ x ˆ e 2 E r E = + = ( ) 0 L k k o e > c A uniaxial plate with the principal axis indicated. + = = 2 ˆ ˆ 0 y x E r E o z + = z k j z k j o o e e y e x E r E ˆ ˆ 2 Get new polarization: Waves at Interfaces – TE and TM Waves i k E i H i o i o t x Transverse Electric (TE) wave i k E i H i Transverse Magnetic (TM) wave 4 Rana and Swartz 06/5/25 Electromagnetic Fields and Waves – Fall 2009 Lecture 19: Definitions: Plane of incidence: The plane containing the incident wavevector and a vector that is normal to the interface is called the plane of incidence. In the figure above the x-z plane is the plane of incidence. TE wave: If the E-field of the wave is perpendicular to the plane of incidence then the wave is called a TE-wave . TM wave: If the H-field of the wave is perpendicular to the plane of incidence then the wave is called a TM-wave . z =0 z i k TE Wave - Wavevectors x Transverse Electric (TE) wave r k E r H r t k E t H t i k i r t 5 Rana and Swartz 06/5/25 Electromagnetic Fields and Waves – Fall 2009 Lecture 19: z =0 z o i o t E i H i [] z x k z k x k k i i i iz ix i ˆ cos ˆ sin ˆ ˆ + = + = c n k i i o i = = z x k z k x k k r r r rz rx r ˆ cos ˆ sin ˆ ˆ = + = c n k k i i o i r = = = z x k z k x k k t t t tz tx t ˆ cos ˆ sin ˆ ˆ + = + = c n k t t o t = = TE Wave – First Boundary Condition z =0 z o t x t k E t H t t o i Transverse Electric (TE) wave r k E r H r i k E i H i i r 6 Rana and Swartz 06/5/25 Electromagnetic Fields and Waves – Fall 2009 Lecture 19: Use boundary conditions (1) At z = 0 the E-field parallel to the interface must be continuous across the interface for all x This gives: r k j r r k j i z r i e E y e E y r E . . 0
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Lect19NonNormalInc - ECE 3030 Electromagnetic Fields and...

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