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ECEN 5645 Class Meeting 5 Fresnel Relations

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Page 1: Fresnel Relations - Electrical, Computer & Energy Engineeringecee.colorado.edu/~ecen5645/pdfLectures/Class5.pdf · 2018. 9. 7. · Fresnel Relations Fresnel’s Problem 3 Plane Waves

ECEN5645ClassMeeting5

FresnelRelations

Page 2: Fresnel Relations - Electrical, Computer & Energy Engineeringecee.colorado.edu/~ecen5645/pdfLectures/Class5.pdf · 2018. 9. 7. · Fresnel Relations Fresnel’s Problem 3 Plane Waves
Page 3: Fresnel Relations - Electrical, Computer & Energy Engineeringecee.colorado.edu/~ecen5645/pdfLectures/Class5.pdf · 2018. 9. 7. · Fresnel Relations Fresnel’s Problem 3 Plane Waves

Fresnel’sProblem

Page 4: Fresnel Relations - Electrical, Computer & Energy Engineeringecee.colorado.edu/~ecen5645/pdfLectures/Class5.pdf · 2018. 9. 7. · Fresnel Relations Fresnel’s Problem 3 Plane Waves

3PlaneWaves

Ei(r) = exp(�jki · r)e?ki<latexit sha1_base64="liSIePEEgIB9ixEH3sQnPLNYqOk=">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</latexit><latexit sha1_base64="liSIePEEgIB9ixEH3sQnPLNYqOk=">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</latexit><latexit sha1_base64="liSIePEEgIB9ixEH3sQnPLNYqOk=">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</latexit><latexit sha1_base64="liSIePEEgIB9ixEH3sQnPLNYqOk=">AAACYnicdVFda9swFJW9du2yrU3bx+1BLAyywYIdNtI+DApl0McOmrYQByPL14kWWVal61Fj/Cf3tqe+9IdUSZOSjfaA4N5z7od0lGgpLAbBX89/sbH5cmv7Vev1m7c7u+29/QtblIbDkBeyMFcJsyCFgiEKlHClDbA8kXCZzE7m+uVvMFYU6hwrDeOcTZTIBGfoqLhdRQlMhKrhWjFjWPW5aUU5w2mS1T+aWHRXiWk+fY/gRne//FpRM6dHPC1wrSaaMqxXOTRNXEcajKYz4eaCStf2xO1O0Ds6PBp869OwFyxAHeMw+PrIdMgSZ3H7T5QWvMxBIZfM2lEYaBzXzKDgEtz80oJmfMYmMHKhYjnYcb2wqKEfHZPSrDDuKKQLdr2jZrm1VZ64yvnt7f/anHxKG5WYHY5roXSJoPjDoqyUFAs695umwgBHWbmAcSPcXSmfMsM4ul9pORMe3/58cNHvhUEv/NnvHJ8u7dgm78gH0iUhGZBjckrOyJBwcuttejvernfnt/w9/+Ch1PeWPQfkH/jv7wH1t7pV</latexit>

Er(r) = r exp(�jkr · r)e?kr<latexit sha1_base64="YyvXolfH3Eh2Hybkw/lXIZnQvlw=">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</latexit><latexit sha1_base64="YyvXolfH3Eh2Hybkw/lXIZnQvlw=">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</latexit><latexit sha1_base64="YyvXolfH3Eh2Hybkw/lXIZnQvlw=">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</latexit><latexit sha1_base64="YyvXolfH3Eh2Hybkw/lXIZnQvlw=">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</latexit>

Et(r) = t exp(�jkt · r)e?kt<latexit sha1_base64="vRAxK0VlNFX8gQGFR4Aihdc5ce8=">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</latexit><latexit sha1_base64="vRAxK0VlNFX8gQGFR4Aihdc5ce8=">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</latexit><latexit sha1_base64="vRAxK0VlNFX8gQGFR4Aihdc5ce8=">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</latexit><latexit sha1_base64="vRAxK0VlNFX8gQGFR4Aihdc5ce8=">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</latexit>

Page 5: Fresnel Relations - Electrical, Computer & Energy Engineeringecee.colorado.edu/~ecen5645/pdfLectures/Class5.pdf · 2018. 9. 7. · Fresnel Relations Fresnel’s Problem 3 Plane Waves

Senkrecht(TE)

Page 6: Fresnel Relations - Electrical, Computer & Energy Engineeringecee.colorado.edu/~ecen5645/pdfLectures/Class5.pdf · 2018. 9. 7. · Fresnel Relations Fresnel’s Problem 3 Plane Waves

TheWaves

Ei(r) = exp(�jki · r)e?<latexit sha1_base64="L2OiQw7fcctNPapBEnibLa9muPQ=">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</latexit><latexit sha1_base64="L2OiQw7fcctNPapBEnibLa9muPQ=">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</latexit><latexit sha1_base64="L2OiQw7fcctNPapBEnibLa9muPQ=">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</latexit><latexit sha1_base64="L2OiQw7fcctNPapBEnibLa9muPQ=">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</latexit>

Er(r) = r? exp(�jkr · r)e?<latexit sha1_base64="NF/37GU4Az/GNgtYWskJvYd9pzc=">AAACZnicdVFdaxNBFJ1dv9qoNbaID74MBiEKht2gpH0QCiL0sYJpC9mw3J29m4yZnR1n7oph2T/pm8+++DOcpEmJogcG7j3nfsycyYySjqLoRxDeun3n7r29/c79Bw8PHnUfH164qrYCx6JSlb3KwKGSGsckSeGVsQhlpvAyW7xf6Zdf0TpZ6U+0NDgtYaZlIQWQp9Jum2Q4k7rBLxqsheWrtpOUQPOsaD60qe1vE9u+fGfTxKA1CX4z/deft8rClyUir2inNJkDNdsc2zZt1p1+Nup8Z1fa7UWDk+OT0dshjwfRGtwzHqM3N0yPbXCedr8neSXqEjUJBc5N4sjQtAFLUij082uHBsQCZjjxoYYS3bRZ29TyF57JeVFZfzTxNbvb0UDp3LLMfOXq6u5vbUX+S5vUVBxPG6lNTajF9aKiVpwqvvKc59KiILX0AQgr/V25mIMFQf5nOt6Em7f/P7gYDuJoEH8c9k7PNnbssWfsOeuzmI3YKTtj52zMBPsZ7AeHwVHwKzwIn4RPr0vDYNNzxP5AyH8DanK8fw==</latexit><latexit sha1_base64="NF/37GU4Az/GNgtYWskJvYd9pzc=">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</latexit><latexit sha1_base64="NF/37GU4Az/GNgtYWskJvYd9pzc=">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</latexit><latexit sha1_base64="NF/37GU4Az/GNgtYWskJvYd9pzc=">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</latexit>

Et(r) = t? exp(�jkt · r)e?<latexit sha1_base64="G4qRLPdTWvYw49ihk+ccdl2K8AE=">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</latexit><latexit sha1_base64="G4qRLPdTWvYw49ihk+ccdl2K8AE=">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</latexit><latexit sha1_base64="G4qRLPdTWvYw49ihk+ccdl2K8AE=">AAACZnicdVFdaxNBFJ1dv9qoNbaID74MBiEKht2gpH0QCiL0sYJpC9mw3J29m4yZnR1n7oph2T/pm8+++DOcpEmJogcG7j3nfsycyYySjqLoRxDeun3n7r29/c79Bw8PHnUfH164qrYCx6JSlb3KwKGSGsckSeGVsQhlpvAyW7xf6Zdf0TpZ6U+0NDgtYaZlIQWQp9Jum2Q4k7rBLxqsheWrtpOUQPOsaD60KfW3iW1fvqM0MWhNgt9M//XnrbLwZYnIK9opTeZAzTbHtk2bdaefjTrf2ZV2e9Hg5Phk9HbI40G0BveMx+jNDdNjG5yn3e9JXom6RE1CgXOTODI0bcCSFAr9/NqhAbGAGU58qKFEN23WNrX8hWdyXlTWH018ze52NFA6tywzX7m6uvtbW5H/0iY1FcfTRmpTE2pxvaioFaeKrzznubQoSC19AMJKf1cu5mBBkP+Zjjfh5u3/Dy6GgzgaxB+HvdOzjR177Bl7zvosZiN2ys7YORszwX4G+8FhcBT8Cg/CJ+HT69Iw2PQcsT8Q8t91WryF</latexit><latexit sha1_base64="G4qRLPdTWvYw49ihk+ccdl2K8AE=">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</latexit>

Page 7: Fresnel Relations - Electrical, Computer & Energy Engineeringecee.colorado.edu/~ecen5645/pdfLectures/Class5.pdf · 2018. 9. 7. · Fresnel Relations Fresnel’s Problem 3 Plane Waves

BoundaryConditions

Needtwoequationsinrandtatz=0

Page 8: Fresnel Relations - Electrical, Computer & Energy Engineeringecee.colorado.edu/~ecen5645/pdfLectures/Class5.pdf · 2018. 9. 7. · Fresnel Relations Fresnel’s Problem 3 Plane Waves

Maxwell

r⇥H(r, t) = J(r, t) +@D(r, t)

@t<latexit sha1_base64="pBjdVZNdJhaoIjeN8tS3xx1MlmA=">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</latexit><latexit sha1_base64="pBjdVZNdJhaoIjeN8tS3xx1MlmA=">AAAChXicdVFbaxNBFJ5dL63xFvXRl8EgRNSwuxbTPkgL9qHoSwXTFrIhnJmcTYfOzq4zZ4Ww7D/xV/nWf+NsLqUGPTDwzfedw3cuotTKURRdB+Gdu/fu7+w+6Dx89PjJ0+6z52euqKzEkSx0YS8EONTK4IgUabwoLUIuNJ6Lq8+tfv4TrVOF+U6LEic5zI3KlATy1LT7KxU4V6bGHwashUXTSQ0IDSmpHF2aA12KrD5p+htom3f05tPm92VLeJtmFmSdlmBJgd5ox1tpzU0Gp9axMFUu0HZSNLNbrUy7vWhwsD8c7iV8BeIPa5Ac8HgQLaPH1nE67f5OZ4WscjQkNTg3jqOSJnVrJTV6p8phCfIK5jj20ICfcVIvt9jw156Z8ayw/hniS/Z2RQ25c4tc+Mx2FretteS/tHFF2f6kVqasCI1cGWWVH73g7Un4TFmUpBcegLTK98rlJfg9kj9cu4TNpPz/4CwZxNEg/pb0jr6u17HLXrJXrM9iNmRH7ISdshGTQRj0gzhIwp3wfbgXflylhsG65gX7K8LDPwKyxso=</latexit><latexit sha1_base64="pBjdVZNdJhaoIjeN8tS3xx1MlmA=">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</latexit><latexit sha1_base64="pBjdVZNdJhaoIjeN8tS3xx1MlmA=">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</latexit>

r⇥E(r, t) = �@B(r, t)

@t<latexit sha1_base64="MGknZNewjyw9baC9vovDa3o17ys=">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</latexit><latexit sha1_base64="MGknZNewjyw9baC9vovDa3o17ys=">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</latexit><latexit sha1_base64="MGknZNewjyw9baC9vovDa3o17ys=">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</latexit><latexit sha1_base64="MGknZNewjyw9baC9vovDa3o17ys=">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</latexit>

r ·D(r, t) = ⇢(r, t)<latexit sha1_base64="4ZlxC4R7o5ZRrDq7orWT+uFsQi8=">AAACSnicdVDPaxNBGJ2NVWv80WiPXgaDUEHCblpIexAKeih4qWDaQjaEb2a/TYbOzqwz3wphyd/nxZM3/wgvPVTEi7NJCm2pDwYe731v5psnSq08xfHPqHVv4/6Dh5uP2o+fPH221Xn+4sTbykkcSqutOxPgUSuDQ1Kk8ax0CIXQeCrO3zf+6Vd0XlnzmeYljguYGpUrCRSkSQdSgVNlavxiwDmYL9qpAaEhlZmltACaibz+sNi5om7xlt68S93M3pRCzJqqEOjaKZrs2n2TTjfuHewPBnt9viLJ7pr0D3jSi5fosjWOJ50faWZlVaAhqcH7URKXNK7BkZIaw4KVxxLkOUxxFKiBAv24Xlax4K+DkvHcunAM8aV6PVFD4f28EGGyWd/f9hrxLm9UUb4/rpUpK0IjVw/lleZkedMrz5RDSXoeCEinwq5czsCBpNB+U8LVT/n/yUm/l8S95FO/e/hxXccme8lesR2WsAE7ZEfsmA2ZZN/YL3bJfkffo4voT/R3NdqK1pltdgOtjX/G+LUh</latexit><latexit sha1_base64="4ZlxC4R7o5ZRrDq7orWT+uFsQi8=">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</latexit><latexit sha1_base64="4ZlxC4R7o5ZRrDq7orWT+uFsQi8=">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</latexit><latexit sha1_base64="4ZlxC4R7o5ZRrDq7orWT+uFsQi8=">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</latexit>

r ·B(r, t) = 0<latexit sha1_base64="i1h9KI6gK437kDmxmUoqpLJieP0=">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</latexit><latexit sha1_base64="i1h9KI6gK437kDmxmUoqpLJieP0=">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</latexit><latexit sha1_base64="i1h9KI6gK437kDmxmUoqpLJieP0=">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</latexit><latexit sha1_base64="i1h9KI6gK437kDmxmUoqpLJieP0=">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</latexit>

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Relations

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Airtoglass

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Parallel(TM)

Page 12: Fresnel Relations - Electrical, Computer & Energy Engineeringecee.colorado.edu/~ecen5645/pdfLectures/Class5.pdf · 2018. 9. 7. · Fresnel Relations Fresnel’s Problem 3 Plane Waves

3H-Fields

Hi(r) = exp(�jki · i)e?<latexit sha1_base64="pFtCRDyfyz2nEgT5CoRF48J7z3M=">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</latexit><latexit sha1_base64="pFtCRDyfyz2nEgT5CoRF48J7z3M=">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</latexit><latexit sha1_base64="pFtCRDyfyz2nEgT5CoRF48J7z3M=">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</latexit><latexit sha1_base64="pFtCRDyfyz2nEgT5CoRF48J7z3M=">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</latexit>

Hr(r) = rk exp(�jkr · r)e?<latexit sha1_base64="iVuNG3peogcDQSziU6OuVtUZ+gQ=">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</latexit><latexit sha1_base64="iVuNG3peogcDQSziU6OuVtUZ+gQ=">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</latexit><latexit sha1_base64="iVuNG3peogcDQSziU6OuVtUZ+gQ=">AAACanicdVFda9swFJW9buvSdcs66Bh9Ec0GWWHBDhtpHwqFvuSxhaUtxMHI8nWiRZY16XosGD/0L/atv6Av+xFV0qRkYzsguPec+yEdJVoKi0Fw6/lPNp4+e775orH1cvvV6+abnQtblIbDgBeyMFcJsyCFggEKlHClDbA8kXCZTE/n+uVPMFYU6hvONIxyNlYiE5yho+LmdZTAWKgKfihmDJsd1I0oZzhJsqpfx6a9Skz96djEkWaGSQkygl+6/fn7Sp260oinBa6VRxOG1SqHuo6rSIPRbj6odG1f3GwFnaPDo97XLg07wQLUMQ69L49MiyxxFjdvorTgZQ4KuWTWDsNA46hiBgWX4OaXFjTjUzaGoQsVy8GOqoVVNf3omJRmhXFHIV2w6x0Vy62d5YmrnF/d/q3NyX9pwxKzw1EllC4RFH9YlJWSYkHnvtNUGOAoZy5g3Ah3V8onzk2O7ncazoTHt/8/uOh2wqATnndbJ/2lHZtkj+yTNglJj5yQPjkjA8LJnbft7XrvvN/+jv/e33so9b1lz1vyB/wP9zazvkA=</latexit><latexit sha1_base64="iVuNG3peogcDQSziU6OuVtUZ+gQ=">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</latexit>

Ht(r) = tk exp(�jkt · r)e?<latexit sha1_base64="Sh1dgsgUy8euzCIodJv8hIgw3hc=">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</latexit><latexit sha1_base64="Sh1dgsgUy8euzCIodJv8hIgw3hc=">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</latexit><latexit sha1_base64="Sh1dgsgUy8euzCIodJv8hIgw3hc=">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</latexit><latexit sha1_base64="Sh1dgsgUy8euzCIodJv8hIgw3hc=">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</latexit>

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OtherRelation

Page 14: Fresnel Relations - Electrical, Computer & Energy Engineeringecee.colorado.edu/~ecen5645/pdfLectures/Class5.pdf · 2018. 9. 7. · Fresnel Relations Fresnel’s Problem 3 Plane Waves

BrewsterEffect

Page 15: Fresnel Relations - Electrical, Computer & Energy Engineeringecee.colorado.edu/~ecen5645/pdfLectures/Class5.pdf · 2018. 9. 7. · Fresnel Relations Fresnel’s Problem 3 Plane Waves

WhyBrewster?

Page 16: Fresnel Relations - Electrical, Computer & Energy Engineeringecee.colorado.edu/~ecen5645/pdfLectures/Class5.pdf · 2018. 9. 7. · Fresnel Relations Fresnel’s Problem 3 Plane Waves

SurfaceDipoles?

Page 17: Fresnel Relations - Electrical, Computer & Energy Engineeringecee.colorado.edu/~ecen5645/pdfLectures/Class5.pdf · 2018. 9. 7. · Fresnel Relations Fresnel’s Problem 3 Plane Waves
Page 18: Fresnel Relations - Electrical, Computer & Energy Engineeringecee.colorado.edu/~ecen5645/pdfLectures/Class5.pdf · 2018. 9. 7. · Fresnel Relations Fresnel’s Problem 3 Plane Waves

LaserPolarization