Fields and Waves I

Fields and Waves I Lecture 23 Reflection and Transmission at Normal Incidence K. A. Connor Electrical, Computer, and Systems Engineering Department Rensselaer Polytechnic Institute, Troy, NY

These Slides Were Prepared by Prof. Kenneth A. Connor Using Original Materials Written Mostly by the Following: • Kenneth A. Connor – ECSE Department, Rensselaer Polytechnic Institute, Troy, NY • J. Darryl Michael – GE Global Research Center, Niskayuna, NY • Thomas P. Crowley – National Institute of Standards and Technology, Boulder, CO • Sheppard J. Salon – ECSE Department, Rensselaer Polytechnic Institute, Troy, NY • Lale Ergene – ITU Informatics Institute, Istanbul, Turkey • Jeffrey Braunstein – Chung-Ang University, Seoul, Korea Materials from other sources are referenced where they are used. Those listed as Ulaby are figures from Ulaby’s textbook. Fields and Waves I

Fields and Waves I

Figure References for Previous Slide http://z.about.com/d/goamsterdam/1/0/V/2/-/-/canal_reflection-1.jpg http://www.alanbauer.com/ http://contrapunctus.net/league/photo/pcd0077/003.php?fmt=base_jpeg&set=1 http://www.indelibleinc.com/kubrick/films/2001/images.html http://www.widerange.org/images/large/palaReflection.jpg Fields and Waves I

From H.G. Wells The Invisible ManSignet Classic, 2002 Fields and Waves I

Overview • EM Waves in Lossless Media • Wave Equation & General Solution • Energy and Power • EM Waves in Lossy Media • Skin Depth • Approximate wave parameters • Low Loss Dielectrics • Good Conductors • Power and Power Deposition • Wave Polarization • Linear, circular & elliptical • Reflection and Transmission at Normal Incidence • Plane Waves at Oblique Incidence Fields and Waves I

Normal incidence MEDIUM 2 η2 MEDIUM 1 η1 incident plane wave transmitted plane wave reflected plane wave • wave is normally incident on an infinite interface separating two different media • impedance discontinuity • similar to the transmission lines • EM waves represented with rays or wavefronts Fields and Waves I

Step 1 As with transmission lines, the very first step is to write down the general solution for the electric and magnetic field waves in each of the media in the problem. Part of writing down the fields is to draw the little diagram with the three mutually perpendicular vectors for each component of the plane wave. Maybe the first step should be to review the properties of transmission line waves since we will be doing identical analysis for uniform plane waves. Fields and Waves I

Lossless media • two lossless, homogenous, dielectric media MEDIUM 2 ε2,μ2 MEDIUM 1 ε1,μ1 . . . . . z=0 Incident wave Fields and Waves I

Lossless media transmitted wave reflected wave Fields and Waves I

Step 2 Next we write down the boundary conditions that obtain for the waves we are to analyze. Note from the diagram that both the electric and magnetic fields have only tangential components. For a conducting boundary the electric field must be zero if it is only tangential. This is possible by having the sign of the reflected wave be the negative of the incident wave while their magnitudes are the same. For a dielectric boundary, both the electric and magnetic fields must be continuous. That is, the field on one side of the boundary (incident + reflected) must equal the field on the other side of the boundary (transmitted). Fields and Waves I

Boundary conditions Tangential component of the electric field should be continuous across the boundary Tangential component of magnetic field should be continuous (no current source) Note that inc + ref = trans not inc = ref + trans At the boundary (z=0): or or Fields and Waves I

Example 1 A 10 GHz plane wave has an electric field magnitude of 100 V/m and propagates in the az direction through a perfect dielectric with = 9. E is in the ax direction. a. What are the incident E and H phasors? b. At z = 0, the wave strikes a perfect conductor. What are the reflected E and H phasors? c. Use the boundary conditions to find the surface current density in the conductor. d. Draw the standing wave pattern for E and H (include numbers for amplitude and position). e. Simulate this case with sing_bnd.m by using a large imaginary dielectric for region 2. f. Calculate the total E and H. (phasor & time domain form). Fields and Waves I

Example 1 Fields and Waves I

Standardize notation We now use the standardized notation of reflection and transmission coefficients, just as we did with transmission lines. Ratio of the reflected wave magnitude to the incident wave magnitude. (We use the electric field by convention.) Ratio of the transmitted wave magnitude to the incident wave magnitude. (We use the electric field by convention.) Fields and Waves I

reflection and transmission coefficients Normally incident Normally incident Γandτare real for lossless dielectric media Normally incident For nonmagnetic media Fields and Waves I

transmission line analogy • One to one correspondence between the transmission line parameters and plane wave parameters • incident and reflected waves create a standing wave pattern Standing wave ratio • if η1= η2Γ=0 S=1 • η2= 0 (perfect conductor) Γ=-1 S= ∞ • Smith chart can be used • the max and min locations of the electric field intensity from the boundary are defined by the same expressions for the voltage max and min locations Fields and Waves I

Example 2 The same wave as in example 1 strikes a dielectric-air boundary at z=0 as shown below. a. Find the reflection and transmission coefficients. b. What are the reflected and transmitted electric field phasors? c. What are the reflected and transmitted H phasors? What is Ht/Hi? d. What is the standing wave ratio in the dielectric? Sketch the standing wave pattern for E and H. Run sing_bnd.m for this problem. e. What is the average power density of the incident, reflected, and transmitted waves? Fields and Waves I

Power flow in lossless media The average power density flowing in medium 1 The average power density flowing in medium 2 For lossless media Fields and Waves I

General Solution Ei & Er Et Hi & Hr Ht Boundary What quantities can be specified or calculated? Magnitude of incident E, dielectric properties of each region, intrinsic impedance of each region, frequency, wavelength, incident power, reflected power, transmitted power, transmission coefficient, reflection coefficient, standing wave ratio … Fields and Waves I

Lossless Transmission Lines Uniform Plane Waves in Lossless Media Total voltage and current: Total fields: Phase velocity: Propagation constant: Characteristic/Intrinsic impedance: Fields and Waves I

Lossless Transmission Lines Uniform Plane Waves in Lossless Media Generalized Reflection Coefficient: Total again: Fields and Waves I

Lossless Transmission Lines Uniform Plane Waves in Lossless Media Line or Wave Impedance: Also: Fields and Waves I

Lossless Transmission Lines Uniform Plane Waves in Lossless Media At another location z’: Continuity of Z(z) at a boundary between two regions: Fields and Waves I

Lossless Transmission Lines Uniform Plane Waves in Lossless Media Input impedance: Fields and Waves I

A C B G F D E K J H I Region 1 Region 2 Region 3 z z = 0 z = d Multiple Boundaries If A is incident, each reflection produces the additional waves shown. Fields and Waves I

Multiple Boundaries The waves take the usual general form in each region. Fields and Waves I

Radomes http://igscb.jpl.nasa.gov/network/site/areq.html http://www.cmmacs.ernet.in/nal/picts/ Fields and Waves I

Radomes http://www.air-and-space.com/2003%20Miramar%20Airshow%20statics%20page%202.htm Fields and Waves I

http://www.hiaper.ucar.edu/photo_gallery/031802.html Radomes Fields and Waves I

http://en.wikipedia.org/wiki/File:Navy-Radome.jpg Radomes Fields and Waves I

Radomes http://www.collegeem.qc.ca/ena/avionique/photos/antennes/radar.htm http://www.radome.net/nws.html Fields and Waves I

Example 3 A 10 GHz radar transmitter is used in the configuration shown below. Note that the radome-outside air boundary is identical to the boundary examined in example 2. Fields and Waves I

Example 3 a. What is |E|/|H| at the z=0 boundary of example 2? (equivalent to the region 2-3 boundary in this problem). Compare it with the value in air. b. Now refer to the full radome problem. Where can you put the left boundary so that |E|/|H| in the radome matches that in the air on the left? For mechanical reasons, the radome must be more than 2 cm thick. c. What is for this value of d? d. What is if d is 0.2 mm thinner than designed? Fields and Waves I

Summary of the radome problem Thus, since regions 1 and 3 are the same, the input impedance gives a perfect match and no reflection occurs. Fields and Waves I

Another common multiple boundary application The radome is a half wavelength thick. We can also use a layer one quarter wavelength thick to eliminate reflections from a lens (at least at a particular frequency). Thus, since the input impedance is the same as the intrinsic impedance of region 1, we again have a perfect match and no reflection occurs. Fields and Waves I

Anti-Reflection Coating http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/antiref.html#c3 Fields and Waves I

Anti-Reflection Coating AR coatings are similar to the coatings found on microscopes and camera lenses. They consist of several layers of metal oxides applied to the front and back lens surfaces. Because of the layering effect, AR coatings sometimes have a hint of green or purple color, depending on the individual manufacturer's formula. For an experiment at Oberlin, the coated lens was optimized for the middle of the visible spectrum so red and blue are reflected to form violet http://www.oberlin.edu/physics/catalog/demonstrations/optics/coatedlens.html http://news.thomasnet.com/fullstory/23211/1782 Fields and Waves I

Multiple vs Single Layer Coating From left to right a lens without coating, single coated and multicoated. From the first to the third image the light transmission improved from 96 to 99.5% http://www.astrosurf.org/lombry/reports-coating.htm Fields and Waves I

Multiple vs Single Layer Coating The principle of coatings is to reduce the light reflecting on the glass surface. If the coating has a quarter wavelength thickness and the glass yields an index of refraction higher than the one of the coating the two reflections are in phase opposition and cancel. For one multicoated surface the transmission can increase up to 3.5%. Single Multiple http://www.kenrockwell.com/tech/lenstech.htm Fields and Waves I

Anti-Reflection Coating One of the characteristics of an AR coating is the colour of the residual 1% reflection on the lens - sometimes called the bloom. On modern broadband Reflection Free lenses it can be tuned to be either a soft green or blue without compromising the quality of the anti-reflection properties. The AR bloom should not be confused with a permanent lens tint. An AR bloom is almost imperceptible and can only be seen when holding the lens up to sunlight or artificial light. http://www.siltint.com/Ophthalmic_products/technical.htm Fields and Waves I

Question From the point of view of an EE, CSE or EPE, what are we doing when we eliminate reflections? Impedance Matching A great deal of what we do as engineers is really impedance matching. When impedances match, we usually have the optimum operating conditions we seek. Fields and Waves I

Boundary between lossy media • two lossy media MEDIUM 2 ε2,μ2, σ2 MEDIUM 1 ε1,μ1, σ1 . . . . . z=0 Medium 1 Fields and Waves I

Boundary between lossy media Medium 2 . Γandτare real for lossless dielectric media Fields and Waves I

Fields and Waves I