Lecture_20Jan10

Lecture_20Jan10 - Course ECE 299 Guided Wave Optics...

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ECE 299, Spring ‘10, Stiff-Roberts Page 1 January 20, 2010 Course: ECE 299 – Guided Wave Optics Location: Hudson Hall 115A Instructor: Dr. Stiff-Roberts Office: FCIEMAS 3511 Office Hours: Th 10:00am - 1:00pm Phone: 660-5560 E-mail: [email protected] Last Class This Class • Intro to Guided Wave Optics • EM Optics Review • Dielectric Media • Polarization • Propagation in Isotropic Media
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ECE 299, Spring ‘10, Stiff-Roberts Page 2 January 20, 2010 • In order to determine P (or M ), have to consider medium properties. Dielectric Media Properties of Dielectric Media (Definitions): • Linear – P is linearly related to E , principle of superposition applies. • Nondispersive – Response is instantaneous, i.e. P (t 0 ) is determined by E (t 0 ) and not by prior values of E. • Homogeneous – Relation between P and E is independent of the position r. • Isotropic – Relation between P and E is independent of direction of E , so medium looks the same from all directions. P and E are parallel. • Spatially nondispersive – Relation between P and E is local, i.e. P (r 0 ) is influenced only by E (r 0 ). P ( r ,t) E ( r ,t) Dielectric medium responds to applied electric field, E , and creates a polarization density, P . Electric Susceptibility, χ
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ECE 299, Spring ‘10, Stiff-Roberts Page 3 January 20, 2010 • For linear, nondispersive, homogeneous, isotropic medium (ideal case): Dielectric Media () E E E E P E D E P ε χ = + = + = + = = 1 0 0 0 0 0 μ 0 0 2 1 0 0 1 1 = = + = = n c c n Electric susceptibility, scalar constant in this case Electric permittivity of medium Relative permittivity or dielectric constant Refractive index Speed of light in a medium
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ECE 299, Spring ‘10, Stiff-Roberts Page 4 January 20, 2010 • For inhomogeneous medium (linear, nondispersive, isotropic): Dielectric Media E D E P ε χ = = 0 () r n n r r
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ECE 299, Spring ‘10, Stiff-Roberts Page 5 January 20, 2010 • For anisotropic medium (linear, nondispersive, homogeneous): Dielectric Media ij ij j j ij i j j ij i j i ε χ 3 , 2 , 1 , 0 = = = E D E P Relation between P and E depends on direction of E (or polarization) P and E are not necessarily parallel Each component of P is a linear combination of the three components of E Denote x, y, and z components 3x3 array of constants known as susceptibility tensor, describes dielectric properties of medium Electric permittivity tensor
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ECE 299, Spring ‘10, Stiff-Roberts Page 6 January 20, 2010 • For dispersive medium (linear, homogeneous, isotropic): Dielectric Media () ( ) = ' ' ' 0 dt t t t x t E P ε Relation between P and E is dynamic with memory rather than an instantaneous relation. Thus, there is a time delay between the input and output to the medium, which can be described by a linear system.
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This note was uploaded on 01/16/2011 for the course ECE 299 taught by Professor Staff during the Fall '08 term at Duke.

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Lecture_20Jan10 - Course ECE 299 Guided Wave Optics...

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