Wave Incidence Sandra CruzPol Electrical and Computer Engineering

Wave Incidence Sandra Cruz-Pol Electrical and Computer Engineering Dept. UPR-Mayaguez

Ex. Light traveling in air encounters the water; another medium.

Wave incidence u For many applications, like fiber optics, it’s necessary to know what happens to a wave when it meets a different medium. • How much is transmitted? • How much is reflected back?

We will look at… Normal incidence Wave arrives at 0 o from normal I. • II. Standing waves Oblique incidence Wave • • • arrives at another angle Snell’s Law and Critical angle Parallel or Perpendicular Brewster angle

Reflection at Normal Incidence x Et Ei ak Ht Incident wave Transmitted wave Er z y z=0 akr Hr Reflected wave Medium 1 Medium 2

Now in terms of equations … ¡ Incident wave Ei Hi ak Incident wave

Reflected wave ¡ Er It’s traveling along –z axis akr Hr Reflected wave

Transmitted wave Et Ht ak Transmitted wave

The total fields u u At medium 1 and medium 2 Tangential components must be continuous at the interface

Define u Reflection coefficient, G Note: • 1+ G= t u Transmission coefficient, t • Both are dimensionless and may be complex • 0≤|G|≤ 1

PE 10. 8 A 5 GHz uniform plane wave Eis =10 e-jbz ax in free space is incident normally on a large plane, lossless dielectric slab (z>0) having e = 4 eo and m=mo. Find: Answer: u the reflected wave Ers and -3. 33 ejb 1 z x V/m, u the transmitted wave Ets. 6. 67 e-jb 2 z x V/m where b 2 = 2 b 1 = 200 p/3

Case 1: u Medium 1 = perfect dielectric s 1=0 u Medium 2 = perfect conductor s 2=∞ Halla impedancias int. Refleccion, Transmisión Y campos http: //www. phy. ntnu. edu. tw/java/wave. Superposition/wave. Superpo sition. html

The EM field forms a Standing Wave on medium 1 |E 1 | 2 Eio z Conducting material

Standing Wave Applets u u u http: //www. phy. ntnu. edu. tw/java/wave. Superposi tion/wave. Superposition. html http: //www. ngsir. netfirms. com/englishhtm/Stat. W ave. htm http: //www. physics. smu. edu/~olness/www/03 fall 1320/applet/pipe-waves. html

Case 2: Medium 1 = perfect dielectric s 1=0 u Medium 2 = perfect dielectric s 2=0 u

Standing waves due to reflection Lossless Medium 1 |E 1| Eio (1+|G|) z Lossless Medium 2 At every half-wavelength, everything repeats…

Case 3: Medium 1 = perfect dielectric s 1=0 u Medium 2 = perfect dielectric s 2=0 u

Standing waves due to reflection Lossless Medium 1 |E 1 | Eio (1+|G|) z Eio (1 -|G|) Lossless Medium 2 At every half-wavelength, all em properties repeat

Standing Wave Ratio, s u u or Measures the amount of reflections, the more reflections, the larger the standing wave that is formed. Id s ea The ratio of |E 1|max to |E 1|min = N 1 l o ly ( re fle 0 d. B cti ) on s

PE 10. 9 u u u The plane wave E=50 sin (wt – 5 x) ay V/m in a lossless medium (m=4 mo, e=eo) encounters a lossy medium (m=mo, e=4 eo, s=0. 1 mhos/m) normal to the x-axis at x=0. Find ←Answers: G t =0. 8186 exp(j 171 o) o s =0. 23 exp(j 33. 56 ) Er =10. 03 = 40. 93 sin (wt +5 x + 171 o) y Et = 11. 5 e -6. 02 x sin (wt - 7. 83 x + 33. 6 o) y V/m

Ex. Antenna Radome A 10 GHz aircraft radar uses a narrowbeam scanning antenna mounted on a gimbal behind a dielectric radome. u Even though the radome shape is far from planar, it is approximately planar over the narrow extent of the radar beam. u If the radome material is a lossless dielectric with mr=1 and er=9, choose its thickness d such that the radome appears transparent to the radar beam. u Mechanical integrity requires d to be greater that 2. 3 cm. Antenna with radome Antenna with no radome

Power Flow in Medium 1 u The net average power density flowing in medium 1 Et Ei ak Hi Ht Incident wave Transmitted wave Er y z=0 ak ak H r r Reflected wave Medium 1 Medium 2

Power Flow in Transmitted wave u The net average power density flowing in medium 2 Et Ei ak Hi Ht Incident wave Transmitted wave Er y z=0 ak ak H r r Reflected wave Medium 1 Medium 2

Power in Lossy Media where

We will look at… Normal incidence Wave arrives at 90 o from the surface I. • II. Standing waves Oblique incidence (lossless) Wave • • • arrives at an angle Snell’s Law and Critical angle Parallel or Perpendicular Brewster angle