# HW3 - UNIVERSITY OF CALIFORNIA Santa Barbara Department of...

This preview shows pages 1–2. Sign up to view the full content.

UNIVERSITY OF CALIFORNIA Santa Barbara Department of Electrical and Computer Engineering Problem Set No. 3 Issued: October 17, 2007 Fall 2007 Due: October 24, 2007 ECE 201A 1. A general plane wave in an isotropic, homogenous, uniform and a source free medium can be described as 0 jk r EE e = G G i G G (a) Using Gauss' law show that 0 kE = G G i . (b) Substitute the given solution 0 jk r e = G G i G G into the homogenous wave equation 22 0 ωμε ∇+ = G G and show that general dispersion relationship for a plane wave can be written as 2 kk = G G i . (c) If the medium is lossy μ or ε or both can be complex hence k G is complex. Therefore '" kkj k =− G GG where ' k G and " k G are real vectors that describe the real and imaginary parts of the k G vector. Assuming that k G is in the xz plane write ' k G and " k G in terms of their components. Write an expression for the general plane wave having this complex k G vector. Comment on the directions of ' k G and " k G . (d) Show that the dispersion relationship found in part b can be written as two real equations given below. () 2 R e −= G G and 2 1 I m 2 G G i (e) Now assume that a plane wave is incident on a planar interface between two lossy media. Let's define the plane of incidence as the xz plane x being along the interface and z normal to the interface. Then the k G vector of the incident wave is known and can be expressed as '"' " ' " ˆˆ i i i ix ix x iz iz z k k j k a k j k a =− = − + − G Write similar equations for the k G vector of the reflected and transmitted waves.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 3

HW3 - UNIVERSITY OF CALIFORNIA Santa Barbara Department of...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online