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by: Dr. Simeon Wiza


Dr. Simeon Wiza
GPA 3.96


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Class Notes
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This 26 page Class Notes was uploaded by Dr. Simeon Wiza on Wednesday September 9, 2015. The Class Notes belongs to PHYS 545 at University of Washington taught by Staff in Fall. Since its upload, it has received 25 views. For similar materials see /class/192448/phys-545-university-of-washington in Physics 2 at University of Washington.




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Date Created: 09/09/15
DAPPA Infl 39 a Negative Index of Refraction Materials and Applications in the Microwave Regime CG Parazzoli RB Greegor and BEC Koltenbah The Boeing Company Seattle WA 98124 Claudiogparazzoliboeingcom University of Washington June 3rd 2008 The purpose of computing is insight notnumbers R Hanning NPS mp9 OUTLINE Inil n39 What are Metamaterials 3 p space fabrication existence Normal amp Metamaterial RF Lenses PIM NIM GRIN eikonal Equation or Ray Tracing in a General Medium derivation numerical integration results example Experiments and Comparisons with Simulation near field focusing far field steering eikonal surfaces Conclusions What are the MetaMaterials and their location in the s u phase space glutAim u Plasmalike behavior k lt O evanescent wave Majority of isotropic dielectrics Validation of NlMs Using Snell39s Law Qantl ai Boeing Metamaterials team demonstrated negative index of refraction in the far field using a Snell39s law experiment in free space Effective Medium Simulation Free Space Experiment MWS FDTD NIM PIM uii quot E g r 2 n 39 I 17 gtx 1 2 901HWD1E1HNM TEFLON WEDGE A I DE 8quot oo39 WEDGE quot9 9quot Normalized E for the NIM and PIM Teflon wedge Phys Rev Lett 9010 107401 2003 Snell s Law Wedge Animations Bdfl 39 Normal Wedge NIM Wedge E r z cccc He 7 eeeee ozmmbm E2 7 z cccc ne 7 eeeeee 1b aaaaa 01 xxxx m2 NIM Lenses IDEINE39 n l The n 1 Lens Large refractive power Minimal reflectance Lenses Fabricated and Tested IDEINGquot PIM 2E2H NIM 1E1H NIM GRIN Nominal Design D 120 127 cm f D 148 GHz IEI39 Microw Ant Propag 2007 11 pp 108115 DARDA IDEIIB eikonal39 Equation or Ray Tracing in a General Medium Ii IMHWW39 v Derivation of the eikonal Equation for a General Medium 1 M3XW6quot Equation With The eikonal ansatz Maxwell Equation in the Harmonic time dependence eikonaI ansatz VXHih E0 Eemm h amp foh e0 VinikyH0 Vgxeiyh0 Hhexpika r VEE0 gt Igt V4e0 i ltlt 7 V39H0 Ieljkaa k I W 0 ByH 7 c has the physical D 7 5E meaning of an optical s and p are dyadlos path length IDEIAIB Derivation of the eikonal Equation for a General Medium 2 Define X as a column vector that contains the six components of the electromagnetic field X epezxphmpha V Xhse0 V xeiyh0 Substitute in WW0 gt A4rX 0 V4h0 Formally the eikonal equation for the optical path 4 is detAcr 0 IDEIAIB Explicit forms of eikonal Equation Isotropic Case For the isotropic case a and p are scalars A o 437 u o o it 0 t 0 u 0 ago 0 o u gt ia f fiwz0 where Standard textbook result DARDA IDEIIB Explicit forms of eikonal Equation Indefinite Medium For this example of anisotropy s and p are diagonal dyadics s 6ng p 61111x 7515253111213 7 51116117 7 5212 24 7 5313 34 811823832 f 8mzltw3 Wm 833812621 75112 7 52 1 12622 75113 7 53 1 1Z 3Z 7 5213 7 5312 M22632 0 Not a standard textbook result IDEIAIB Numerical Integration of eikonal Equation 1 Formally the first order non linear partial differential eikonal equation is Fgl x M x a x 0 139 123 dx 5 The characteristics method makes it formally equivalent to the system of ODE dgi 8F 8F 6F d 6F 6F 7 123 7 ds 8 1 d 418414284243843 d5 axrgla 17123 The explicit form ofthe system for the Indefinite medium case is 5 ds ag 3 3 74811141322 gjgk 2lxgj kgxi ZZdVaz f i123 7k1 11 E 517 2 BF 6 r 2 3 mw3i ahaLEA dr ax 6 ax ax ax 3 a 3 a a Z QWW QHZQW 1424f0 n123 nAnDA InfNE 6L Numerical Integration of eikonal Equation 2 To complete the integration of the ODE system the initial conditions for xi Q g and generalized Snell Law at material interfaces must be provided The solution of this system of equations rquot p Provides the initial values of g on the WW Launch Pad x 7i 10x1s06 i xaxsoe Launch Pad 06 F 06 By 1 a 2 Fta xs06 lrzxs06 l xs06 0 z FreeSpace Lens FreeSpace Region R1 Region R2 Region R3 Generalized Snell Law 12 D2 D1 0 gt kg ku R kugqm gt Continuity of Q optical path at the interface gt VHQV continuous in isotropic material and planar surface gt Snell Law 4 3 Tm iwig l 2 fn Sn 0 31m Cm 1 Optical Ray 5 at a R Rquot 0 With In the general Indefinite medium and curved surface gt M is quotr RquotR71 DAPPLI V Results of eikonal Calculations 1 Ray Tracing il Eikonal surfaces Indefinite medium 5 x y x 7117 00501x12 x 00001x12 m2 PIM Aper 3 ch b PIM Apcr 12 cm C NIM GRIN Aper 12 cm 0 3 x3 cm u Evolution ofthe eikonal surface through a the PIM and b GRIN Calculations Eikonal surfaces are shown at the following positions 1 launch pad violet 2 entrance to lens blue 3 exit of lens red and 4 furthertowards the focus green Comparing 2 and 3 in b we see that the optical paths diminish through the GRIN lens due to its negative phase velocity Plots of the eikonal value vs 6 for selected characteristic lines for the PIM solid and GRIN dashed Due to the shape of the PIM lens the lines refract at different positions This is not the case with the GRIN which also shows a sharper focus IDEIAIB GRIN Lens Design for 1E1H Inde nite medium Fabricated GRIN lens top location of various cell types bottom le and step wise approximation to smooth 2 p 1100501r2 00001 r4 gradient bottom rig t needed for 127 cm focal length Note that each unit cell A through 8 has a different index of refraction ranging from n 11 to 32 Index of Refraction z 00 20 40 60 Annular Unit Cell Locations Radius cm En EDEIIVEQ omparison of Measurements Simulations for the GRIN Lens Sim red Exp blue z 10cm 3 1Lquot 1 a E 39u a 5 i E a c 2 an Normalized ModEx 1o 15 20 5 0 Z cm Y cm Experimental top left amp FDTD simulated top right electric field amplitude of GRIN lens at 148 GHz The line plots bottom of the experimental blue and FDTD simulated red fields are in excellent agreement The focal spot is at 100 cm nAnDA Inll 39 9 A Comparisons of Experiment and Simulation For PIM NIM amp GRIN Lenses EXPERIMENTAL SETUP FOR LENS MEASUREMENTS nARDA fl 39 Small Dipole on XY PBand Horn Translation Stage 124 cm Aperture PW Source Network Analyzer and Translation Stage Controlled by Labview Running on a Laptop Sim amp Exp for Empty Aperture Illuminated by Planewave Source at 148 GHz afl 39 Experiment Simulation Microwave Studio MWS FDTD Maxwell Eq Solver ycm 5 5 2Wquot ycm 5 5 Zcm Sim red Exp blue y 0cm Sim Hid EXP blue Z 14cm A 1 A 1 a a g 03 8 08 E E 39U 06 a 06 g 3 E 04 E 04 2o 02 2 02 G G 5 15 20 5 1o 0 2 cm Y cm DARTIA Infl 39 DESIGN AND CHARACTERIZATION OF PIM LENS Rexolite s253 PIM Pathfinder Lens Used for Baseline Comparison QBDEIIVE gt 349mm R 750mm E 1270111111 x 1l9111111 gt 1quot 13711111 gt 50mm 4 L Sim amp Exp for PIM Lens Excited by Planewave amp Small Dipole at 148 GHz Wat7N0 Planewave to Determine Focal Spot and F omt Experiment Simulation Source for Steerlng Data MWS FDTD Using PIM Lens PLAN EWAVE MWS SIMULTATON Pimlen50501 Sim r901 EXP blue V 00m Sim red Exp blue z 10cm 5 1 a 1 E 08 g 03 39c 06 E 06 3 04 E E 04 2 02 g 02 9 1o 15 20 quot3 o DIPOLE SOURCE MWS SIMULATION Hum Hun PimlensO6O1a We mmw Far Field Experimental PIM Lens IF A EXP y20cm 2039 I I MWS IExl O O O no i 5 I C O E E E ThetaDeg x I 10 0 Lu 0008 7 PhiDeg l Far Field Experimental PIM Lens n 1014 A EXP yO cm In 1 I IMW IExl 0 o o no 0 ThetaDeg 20 20 phiDeg 0002 1 fut 39In r o 0000 quotquot l l l quotquot 20 10 0 10 Receiver Angle Deg 20


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