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**Wave Incidence at Oblique angles**

Dr. S. Cruz Wave Incidence at Oblique angles Sandra Cruz-Pol ECE Dept. UPRM Wave incidence at oblique angles

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**Quiz VIERNES Uno de los problemas asignados en el prontuario**

Enviar contestaciones a preguntas en Word por

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**Wave Incidence Normal incidence Wave arrives at 90o from the surface**

Dr. S. Cruz Wave Incidence Normal incidence Wave arrives at 90o from the surface Standing waves Oblique incidence (lossless) Wave arrives at an angle Snell’s Law and Critical angle Two types: Parallel or Perpendicular Brewster angle Wave incidence at oblique angles

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**Oblique incidence y First, we need to define:**

Dr. S. Cruz Oblique incidence First, we need to define: Expression for uniform plane wave traveling in any direction The Normal , an Plane of incidence Angle of incidence x Medium 1 : e1 , m1 Medium 2 : e2, m2 qr qt qi y z z=0 Wave incidence at oblique angles

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**Oblique incidence Uniform plane wave in general form**

Dr. S. Cruz Oblique incidence Uniform plane wave in general form the radius or position vector the wave number or propagation vector For lossless unbounded media, k = b Wave incidence at oblique angles

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**Oblique Incidence Medium 1 : e1 , m1 Medium 2 : e2, m2 kr kt qr qt y**

Dr. S. Cruz Oblique Incidence x Medium 1 : e1 , m1 Medium 2 : e2, m2 kr kt qr qt z y qi z=0 ki Wave incidence at oblique angles

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**Look at the direction of travel**

Dr. S. Cruz Look at the direction of travel x Medium 1 : e1 , m1 Medium 2 : e2, m2 kr kt qr qt z y qi kix ki z=0 kiz Wave incidence at oblique angles

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**Expression for Waves kiz kix ki qi Dr. S. Cruz**

Wave incidence at oblique angles

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**Tangential E must be Continuous**

Dr. S. Cruz Tangential E must be Continuous From this we know that frequency is a property of the wave. So is color. So 700nm is not always red!! Give example of bathing suit. Wave incidence at oblique angles

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**Snell Law Equating, we get or**

Dr. S. Cruz Snell Law Equating, we get or where, the index of refraction of a medium, ni , is defined as the ratio of the phase velocity in free space (c) to the phase velocity in the medium. Wave incidence at oblique angles

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**Critical angle, qc …All is reflected**

Dr. S. Cruz Critical angle, qc …All is reflected When qt =90o, the refracted wave flows along the surface and no energy is transmitted into medium 2. The value of the angle of incidence corresponding to this is called critical angle, qc. If qi > qc, the incident wave is totally reflected. Wave incidence at oblique angles

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Dr. S. Cruz Fiber optics Light can be guided with total reflections through thin dielectric rods made of glass or transparent plastic, known as optical fibers. The only power lost is due to reflections at the input and output ends and absorption by the fiber material (not perfect dielectric). Wave incidence at oblique angles

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Dr. S. Cruz Optical fibers have cylindrical fiber core with index of refraction nf, surrounded by another cylinder of lower, nc < nf , called a cladding. For total reflection: [Figure from Ulaby, 1999] Acceptance angle Wave incidence at oblique angles

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**Exercise: optical fiber**

Dr. S. Cruz Exercise: optical fiber An optical fiber (in air) is made of fiber core with index of refraction of 1.52 and a cladding with an index of refraction of 1.49. Find the acceptance angle: Answer: 17.5 degrees Wave incidence at oblique angles

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**Parallel polarization**

Dr. S. Cruz Parallel polarization It’s defined as E is || to incidence plane x Medium 1 : e1 , m1 Er Et kr kt qr qt z qi y z Ei z=0 ki Medium 2 : e2, m2 Wave incidence at oblique angles

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**Equating for continuity, the tangent fields**

Dr. S. Cruz Equating for continuity, the tangent fields Which components are tangent to the interface between two surfaces? y and x At z = 0 (interface): Wave incidence at oblique angles

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**Reflection and Transmission Coefficients: Parallel Incidence**

Dr. S. Cruz Reflection and Transmission Coefficients: Parallel Incidence Reflection Wave incidence at oblique angles

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**Reflection and Transmission Coefficients: Perpendicular Incidence**

Dr. S. Cruz Reflection and Transmission Coefficients: Perpendicular Incidence Wave incidence at oblique angles

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**Java Animation http://www.amanogawa.com/archive/Oblique/Oblique-2.html**

Dr. S. Cruz Java Animation Wave incidence at oblique angles

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**Exercise A plane wave in air with**

Dr. S. Cruz Exercise A plane wave in air with Is incident upon planar surface of nonmagnetic dielectric material with er=4, on z>0, Find The polarization of the incident wave The angle of incidence The time-domain expressions for the reflected electric and magnetic fields. The average power density carried by the wave in the dielectric medium. Wave incidence at oblique angles

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**Exercise A plane wave in free space with**

Dr. S. Cruz Exercise A plane wave in free space with Is incident upon planar surface of nonmagnetic lossless dielectric material with er=4, on z>0, Find The polarization of the incident wave The angle of incidence and transmission The reflection and transmission coefficients. The E field in reflected and in dielectric Brewster angle Wave incidence at oblique angles

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**Brewster angle, qB * qB is known as the polarizing angle**

Dr. S. Cruz Brewster angle, qB Is defined as the incidence angle at which the reflection coefficient is 0 (all transmission). The Brewster angle does not exist for perpendicular polarization for nonmagnetic materials. * qB is known as the polarizing angle Wave incidence at oblique angles

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**Reflection vs. Incidence angle.**

Dr. S. Cruz Reflection vs. Incidence angle. Reflection vs. incidence angle for different types of soil and parallel or perpendicular polarization. Wave incidence at oblique angles

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**Exercise (Brewster angle)**

Dr. S. Cruz Exercise (Brewster angle) A wave in air is incident upon the flat boundary of a nonmagnetic soil medium with er=4, at qi=50o. Find reflection and transmission coefficients for both incident polarizations, and the Brewster angle. Answers: EMAG Wave incidence at oblique angles

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**Summary Property Normal Incidence Perpendicular Parallel**

Dr. S. Cruz Summary Property Normal Incidence Perpendicular Parallel Reflection coefficient Transmission coefficient Relation Power Reflectivity Power Transmissivity Snell’s Law: Wave incidence at oblique angles

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