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Electromagnetic Waves

by: Mrs. Lisette Will

Electromagnetic Waves OPTI 6104

Mrs. Lisette Will
GPA 3.78


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This 3 page Class Notes was uploaded by Mrs. Lisette Will on Sunday October 25, 2015. The Class Notes belongs to OPTI 6104 at University of North Carolina - Charlotte taught by Staff in Fall. Since its upload, it has received 11 views. For similar materials see /class/228886/opti-6104-university-of-north-carolina-charlotte in Optical Studies at University of North Carolina - Charlotte.


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Date Created: 10/25/15
Spiing2008 Opti6104 Midterm Midterm Due 362009 in my of ce Please note that N E k U Students can only use textbook class notes and math handbooks No other materials including online material are allowed NO software is allowed for computational purpose All problems are designed to be handled analytically Students are not allowed to talk to or work with others on this exam If the student is convicted of any of these above heshe will get zero point out of this exam NO late submission Zero point if late Spiing2008 Opti6104 Midterm 1 15 points 510 Let E E7 r expiat and H H7 r expiat be solutions to Maxwell s equations a Show that E and H also satisfy Maxwell s equations When both fields and their complex conjugate are solution to Maxwell s equations what does this imply to these fields Hint very simple answer don t make it too complicated b Show that IF the conjugate waves defined as E Erexpiat and H Hrexpiat Also satisfy the wave equations what does this imply to the optical properties of this material 2 30 points 101010 In the far zone and long wavelength approximation Le 1 ltlt 1 ltlt r where d and it are the dimension of the current distribution and wavelength respectively the vector potential can be approximated by jky 37 08 4 1R 2W dl39 r Considering a linear antenna orients along 2 direction and has a length d The antenna is excited in such a way that the sinusoidal current makes a full wavelength of oscillation 18 21 sinlltz where kd 271 a Under the far zone and long wavelength approximation calculate the vector potential excited by such currents b Calculate the magnetic field 37 and electric field EH under the far zone approximation kr gtgt 1 c Calculate the Poynting vector at the far eld 3 10 points A oscillating electiical monopole is composed of a single electrical charge whose magnitude oscillates in time with an angular frequency 03 Does such oscillating monopole radiate in the far eld Give clearly your reasoning Note that this is a concept test so a simple reasoning but need to be convincing will be weighted as much as complicated mathematical proof 4 15 points 510 a If the index of refraction is expressed as a function of wavelength 2 show that the group velocity can be written as C V g n itdndt Spring2008 Opti6104 Midterm b Derive an expression for the group velocity vg given the refractive index below Neza0 a2 N827 n ikl 2 2 i 2 2 480WW0KW0 W 72 Sggma gKWU W 72 5 30 points 1515 The envelop of a laser pulse will remain undisturbed in shape provided the second and highorder terms in the expansion of ak around lg7 can be neglected Now consider the case when the secondorder terms is not too small and cannot be neglected that is dza dk2 da 1 2 wkWgglk kg 106 160 a Find the envelop function of a pulse with a spectral distribution Altkgt Altkgexp k k0 2 4qz b Find the width of the envelope function as a function of time t The following integral may be useful l E J00 exp 0tx2 xdx Fexm a where the real part of amust be positive


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