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# Intro To Graduate Research ECE 69500

Purdue

GPA 3.59

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This 59 page Class Notes was uploaded by Cassidy Casper on Saturday September 19, 2015. The Class Notes belongs to ECE 69500 at Purdue University taught by Staff in Fall. Since its upload, it has received 25 views. For similar materials see /class/207905/ece-69500-purdue-university in Electrical Engineering & Computer Science at Purdue University.

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Date Created: 09/19/15

Extraordinary Transmission Through Small Apertures Rand Jean Elizabeth Strehlow Jeffrey Ziebarth Background II Apertures are a key component in photographic devices III Limits amount of light entering device III Prevent overexposure of filmdetector III Smaller apertures provide greater depth of field Our Classical Understanding El Single slit experiment El Plane wave incident on a narrow slit llllllllllllllll El Diffraction pattern results El Pattern is determined by wavelength aperture size and angle of incidence Our Classical Understanding III Reason for pattern multiple quotpoint sources along the length of slit interfere with each other I Known As Huygens Fresnel principle III A gt slit width then slit acts as a single point source and radiates evenly in all directions Demonstration httpwwwfaIstadcomrippe Cl New Discoveries El EIEIEIEI In 1997 T W Ebbesen et al discover unexpectedly high transmission through sub wavelength apertures Light incident on a hole arrays in Ag and Cr H A Bethe 1944 predicts Teff quot r M4 Teff found to be 2 when it should be 10393 Hypothesize that Surface Plasmons SP are responsible Surface Plasmons a brief Review courtesy of Prof Shalaev s Lecture Notes El Bloch Periodic dielectric constant couples waves for which the k kLSI O ksp i 777G vectors differ by a reciprocal lattice vector G I Strong coupling occurs when a 1lgd 51116 c 12 k 2 gurgd 5p 6 gm 8d where litAm k g 0C lGl27rP mxp k II Graphic representation 1 2P khan 2 k Nature Article Overview Arrays of submicron cylindrical holes display unexpected zero order transmission spectra when the period of the array is smaller than the wavelength Transmission efficiency can be above unity Experimental results suggest that phenomenon is due to the coupling of light with surface plasmons T W Ebbesen H J Lezec H F Ghaemi T Thio and P A Wolff quotExtraordinary optical transmission through subwavelength hole arraysquot Nature vol 391 pp 667669 February 1998 Experiment Overview Silver film with thickness t 02 pm Cylindrical holes created by sputtering surface with Ga ions using FIB system 5 nm resolution Hole diameter d varied from 150 nm to 1 pm Periodicity 00 between 06 and 18 pm FIG 1 Focused iou beam image of a twodimensional hole army in a polycrystallme silver lm with lm thickness r 200 um hole diameter d 150 um and period ao900 11111 H F Ghaemi T Thio DE Grupp T W Ebbesen and H J Lezec quotSurface plasmons enhance optical transmission through subwavelength holesquot Phys Rev B vol 58 pp 67796782 September 1998 T W Ebbesen H J Lezec H F Ghaemi T Thio and P A Wolff quotExtraordinary optical transmission through subwavelength hole arraysquot Nature vol 391 pp 667669 February 1998 ZeroOrder Transmission Spectrum El Transmission spectra recorded on UVnear IR 6 spectrophotometer with 39 incoherent light source El Narrow bulk silver plasmon peak atA 326 nm El Minima at periodicity 00 and 00512 Transmission intensin 00 El Above 00 no diffraction n 550 1500 1550 m from the array or from Wavelengthmm individual holes 0009 umd150nmt200 nm T W Ebbesen H J Lezec H F Ghaemi T Thio and P A Wolff Extraordinary optical transmission through sub wavelength hole arrays Nature vol 391 pp 667 669 February 1998 ZeroOrder Transmission Spectrum Confd II Peaks increasingly stronger after 00 at longer wavelengths 5 II Maximum transmitted intensity at A 1370 nm II Absolute transmission efficiency 2 2 at the maximum Transm39ssion intensin 00 II Transmittivity of the array 2 7 l 7 scales linearly with the surface area of the holes II Bethe s prediction for assingle 10 0 560 10 00 1500 2COO Wavelength nm 010 09 pm 0 150 nm t 200 nm T W Ebbesen H J Lezec H F Ghaemi T Thio and P A Wolff quotExtraordinary optical transmission through sub wavelength hole arraysquot Nature vol 391 pp 667 669 February 1998 PeriodicityHole Diameter El Periodicity determines the position of the peaks El Peak width appears to be 7 Ifquot dependant on td El Spectra for various square arrays as a function of Aao I Solid line Ag 00 06 pm of 150 nm t 200 nm I Dashed line Au do 10 pm of 350 nm t 300 nm I Dashed dotted line Cr 00 10 pm of 500 nm t 100 nm Transmission intensity au 1 15 2 25 Wavelength period T W Ebbesen H J Lezec H F Ghaemi T Thio and P A Wolff quotExtraordinary optical transmission through subwavelength hole arraysquot Nature vol 391 pp 667669 February 1998 9 Metal Thickness II Bulk plasmon peak I 8 decreases rapIdly II Intensity of longer wavelength peaks A 6 decrease approximately linearly with thickness I For two identical Ag arrays with different thicknesses For both arrays 010 06 mm d 150 nm I Solid line 1 200 nm I Dashed line 1 500 nm this spectrum has been quot multiplied by 175 for comparison Transmission intensity 0 0 200 400 600 800 1000 1200 Wavelength nm T W Ebbesen H J Lezec H F Ghaemi T Thio and P A Wolff quotExtraordinary optical transmission through subwavelength hole arraysquot Nature vol 391 pp 667669 February 1998 Hole Geometry in Array El Changing hole shape can change intensity El Position of peaks shifts to longer wavelengths as aspect ratio of holes is Increased Mum m 15 10 as Am 500 car 700 uoa 900 1a warmquot mm no F G Focused ion beam images of two periodic sllbwave lenglh hole arrays fabricaled in a 200 um thick gold lm Both arrays have a period of 425 nm a An array consisting of with a diameter of 1 0 nm b An array con sisting of i39eciangular holes of 75 X 225 nmz K J Klein Koerkamp s Enoch F B Segerink NF van Hulst and L Kuipers quotStrong Influence of Hole shape on Extraordinary Transmission through Periodic Array of Subwavelength Holesquot Phys Rev Lett vol 92 May 2004 Single Hole Geometry El Optimum depth of surface corrugations is a few times the skin depth of the metal Optimal geometry for enhanced transmission is a series of concentric grooves around a central aperture WIth mean Fig 2 Elemon inicmgmplisofsingla aperture surrounded by rachus Rk kP and groove circulnrsurfncecorrugationP750nm width W P2 El T Thio el al quotGiant optical transmission of subrwavelenglh apertures physics and applications Nanotechnology vol 13 pp 429432 May 2002 Evidence of Surface Plasmons 1 Hole arrays fabricated on Ge do not exhibit enhanced transmission l Transmission intensin We I Must have a metallic film 2 Angular dependence of spectrum 0 I I I 4L I Peaks change In 1000 1200 1600 1300 Wavelength nm lntenSIty and Spllt Into Spectra for a square Ag array 610 09 m d 150 nm new peaks t 200 nm The individual spectra are offset vertically by 01 from one another for clarity T W Ebbesen H J Lezec H F Ghaemi T Thio and P A Wolff quotExtraordinary optical transmission through subwavelength hole arraysquot Nature vol 391 pp 667669 February 1998 Findings of Nature Article III Coupling of light with SP5 observed in transmission not reflection III Metal air interface has distinctly different SP modes than metal quartz interface but identical spectra result regardless of which side is illuminated II quotresults indicate a number of unique features that cannot be explained with existing theories T W Ebbesen H J Lezec H F Ghaemi T Thio and P A Wolff quotExtraordinary optical transmission through subwavelength hole arraysquot Nature vol 391 pp 667669 February 1998 Alternative theory to Light enhancement Cl III Experimental evidence points to light enhancement as well as suppression II Careful measurement has shown enhancements of 7X max and not lOOOX as previously proposed III New theory of composite diffracted evanescent waves CDEW fits experimental data for light spectrum through corrugated arrays in metal and dielectrics Diffracted Eva nescent Waves 5 N E g ikoi radiative modes Top Vrew O O 39 gt 6 O O x Kgt Mai evanescent modes slde View CDEW gt I Light emerging from aperture have both radiative and evanescent modes I Latter CDEW produces interference patterns which gives rise to ig t enhancement as well as light suppression Henri J Lezec and Tineke This August znmvm 12 No16 OPTiCS EXPRESS 3647 Parallel Array Experiment Experimenul data 650 750 I Light enhancement varying with array Wavelength nm number at various wavelengths indicating some phase difference with incident and diffracted wave 39 Henri J Lezec and Tineke Thio August 2004 Vol 12 No 16 0 SP theory does not Include phase OPTICS EXPRESS 3647 differences Model Comparison cDEw Model Similar except at larger wavelengths where CDEW model predicts enhancement while SP model predicts suppression P 550 nm AM MMGo nri J Lezec and Tineke Thio August 2004 Vol12 N016 0PTlCS EXPRESS 3647 CDEW fit to Experiment Emmi Good t of CDEW model to experiment Fit is slightly out of phase for blue end of spectrum but perfect t at red to infra red end NM7 Henm LelaandTmekeThmAugustZDDdVa 12mm 15 ovncssxrnssszw Investigating SP contribution D 680 700 620 640 es Weveiength nm 580 600 Effect on gain spectrum GM of increas39n hole grating radial distance by increments of P10 increasing ring num er producessharp peaks an artifact Consistent with interference effects and not HenriJLezeca OPTICS EXPRESS 35 7 nd rineke This August 2004 Vc 12 No 15 Applications of SP s III Enhanced digital interconnect communications III Improved electronic displays and lighting III Improved microscopy and lithography III Possibility for optical computation III Improved data storage SP interconnects II SP s take advantage ofthe best of optics in terms of speed of signal and miniaturization of modern electronic circuits III SP are also have long range propagation 1mm making it suitable for integration with conventional electronics LED enhancement El InGaNGaN QW coupled with SP from Ag coating greatly enhances spontaneous emission OLED coupled with SP have shown orders of magnitude increase in light emission SP s have a lot increased stimulated emission in GaAs lasers and thus improved efficiencies Lithography amp Microscopy III The concentrating of E fields by SP lead to enhanced local exposure and thus increased photoresist resolution III SP excitation enhancing evanescent modes of super lenses allowing for below diffraction limit resolution Super lens resolution A 40 W i vim sweriens quot wuhoul5ngterlnns so B zu C 10 39 o Nano patterns from A Focused Ion beam B Lithography using super lens C Conventional lithography Ekmel Ozbay er al Science 31118912005 Other applications El With the ability to couple light and electron density the possibility of forming hybrid logic devices that operate on charge movement and speed of EM radiation is present El In addition improvements of lensing including that below the diffraction limit increases optical storage density Other Applications Cont d III Chemical applications Mass spectrometry molecule sensing reaction monitoring III Biologicalapplications bio sensing drug delivery aid Namephptphiee amp Metamateria eig Professor Vladimir M Shalaev ECE695S Si Substrate This course was prepared with M Brongersma and 8 Fan from Stanford Their help is highly appreciated Nanophotonics and Metamaterials Instructor Professor Vladimir M Shalaev MSEE270 and BRK2295 4949855 Email Office hour Tue 23pm Grader TA Mark Thoreson BNCBRK 1226 tel 4963308 office hour Thu 23pm email mthoresopurdueedu Course Web page to download lecture notes Recommended Textbook 1 Photonic Crystals Molding the ow of light By Joannopoulos Meade and Winn Princeton University Press Princeton 1995 2 Sun ace Plasmons Plasmonics Fundamentals and Applications by S Maier Springer 2007 3 Near eld optics Principles of NanaOptics by L Novotny and B Hecht Cambridge 2007 Grading 30 homework 30 midterm exam 40 final presentation and report Overview of the Course Part I Introduction to light interaction with matter Derivation Wave Equation in matter from Maxwell s equations Dielectric properties of insulators semiconductors and metals bulk Light interaction with nanostructures and microstructures compared with A Part II Photonic Crystals Electromagnetic effects in periodic media Media with periodicity in 1 2 and 3dimensions Applications Omnidirectional reflection sharp waveguide bends Light localization Superprism effects Photonic crystal fibers Part III Metal optics plasmonics and nanophotonics Light interaction with O 1 and 2 dimensional metallic nanostructures Guiding and focusing light to nanoscale below the diffraction limit Nearfield optical microscopy Transmission through subwavelength apertures Part IV Metamaterials Metamaterials optical magnetism and negative refractive index Superlens and Hyperlens Cloaking Transformation optics Overview in Images K V Vahala etal Phys Rev Lett 85 p74 2000 Wm I J D Joannopoulos et al Nature vol386 p1439 1997 Si substrate l 1 8 Lin et al Nature vol 394 p 2513 1998 T Thio et al Optics Letters 26 19721974 2001 JR Krenn et al EurophysLett 60 663669 2002 Motivation Major breakthroughs are often materials related 0 Stone Age Iron Age Si Age metamaterials 0 People realized the utility of naturally occurring materials 0 Scientists are now able to engineer new functional nanostructured materials Is it possible to engineer new materials with useful optical properties oYes o Wonderful things happen when structural dimensions are z klightand much less This course talks about what these things areand why they happen What are the smallest possible devices with optical functionality 0 Scientists have gone from big lenses to optical fibers to photonic crystals to 0 Does the diffraction set a fundamental limit 0 Possible solution metal opticsplasmonics Designing New Functional Devices We need to be able to solve the following problem 8 6 Light Interaction with Matter Maxwell s Equations Divergence equations Curl equations 63 V D pf V x E at 6D V B O V X H J at D Electric flux density B Magnetic flux density E Electric field vector H Magnetic field vector p charge density J current density Constitutive Relations Constitutive relations relate flux density to polarization of a medium Electric E When P is proportional to E A DgOEPEgE l v Electric polarization vector Material dependentll 80 Dielectric constant of vacuum 885 103912 CZN39lm392 Fm 8 Material dependent dielectric constant Total electric flux density Flux from external Efield flux due to material polarization Magnetic B u0H u0MH Magnetic flux density Magnetic field vector Magnetic polarization vector u0 permeability of free space 41Tx10397 Hm Note For now we will focus on materials for which M20 Bu0H Divergence Equations How did people come up with V 1 p Coulomb 0 Charges of same sign repel each other and or and 0 Charges of opposite sign attract each other and 0 He explained this using the concept of an electric field 75 qlgt Every charge has some field lines associated with it c He found Larger charges give rise to stronger forces between charges 0 Coulomb explained this with a stronger field more field lines Divergence Equations Gauss s Law Gauss 17771855 jDdszngdsszdv A A V Efield related to enclosed charge Gauss s Theorem very general jFdszjVde Jrr A V Combining the 2 Gauss s DdszjVdeszdv q Vsz A V V The other divergence eq V B O is derived in a similar way from IBdS 0 A Curl Equations How did people come up with V X H 2 1J 7 H D increasing when charging the capacitor Ampere 17751836 Changes in el flux giH dl IZ DJds Q Magnetic field induced by 1 t c A Electrical currents Curl Equations 6D Ampere gfjHdlJa DJjds c A 6 SfjHdljVxHd3jEJjds C A A Stokes theorem ftF39dlJVgtltF39dS C A Other curl eq VxE aB 6t Derived in a similar way from ij dl Ja BdS C A a ijdlJVgtltEdS Ja BdS C A A Stokes Summary Maxwell s Equations Divergence equations Curl equations 63 at v B 0 V X H a D J 6t Flux lines start and end Changes in fluxes give rise to fields on Charges or peles Currents give rise to Hfields Note No constants such as uo 80 u g c appear when Eqs are written this way The Wave Equation Plausibility argument for existence of EM waves H H E E E Curl eguations Changing E field results in changing H field results in changing E field The real thing 2 Goal Derive a wave equation V2Ur 1 forE and H 7 v2 6t2 Solution Waves propagating with Ur t ReU0 reXpiat a phase velocity v lt Position Time Starting point The curl eguations The Wave Equation for the Efield 1 82Er t I VZE Goa m V2 atz GB 6H Cuqusm Vle 7 lt uygymammmwmuw0omw b VXHQJ at Step 1 Try and obtain partial differential equation thatjust depends on E Apply curl on both side of a 6H 6VXH VgtltVgtltEVgtlt 0 at 0 61 Step 2 Substitute b into a 62D aJ aZP aJ VgtltVgtltE g 0 612 0 at I 0 0 0 612 0 at DEP Coollooks like a wave equation already The Wave Equation for the Efield Compare V th I Use vector identity VXVX E VV E 39 Q Verify that VE 0 when 1 pf 0 2 8r does not vary significantly within a A distance 62E WP 61 2 Resu39t39 V E 8 a7 05 In orderto solve this we need 1 Find PE 2 Find JEsomething like Ohm s law JE O39E we will look at this aterfor now assume JE O Dielectric Media Linear Homogeneous and Isotropic Media P linearly proportional to E P 801E x is a scalar constant called the electric susceptibility Q 62E aZP V2E g 0 0 612 0 612 32E 62E 2 VZE050050Z0801Z 62 2 l l l m V E 0505 All the materials properties 62E 612 Define relative dielectric constant as 3r 2 1 5 Results from P Note 1 ln anisotropic media Pand E are not necessarily parallel 25301ij 1 Note2 ln nonlinear media P 801E 80252E2 80253E3 Properties of EM Waves in Bulk Materials We have derived a wave equation for EM waves 2 V2E 88 IuOOralz Speed of an EM Wave in Matter Speed of the EM wave 62E 1 62E Compare VZE u 5 3r and VZE 0 0 al2 v2 6t2 Q v2 1 ii 080 8r 8r Where c02 180 p0 1885x1o12 c2m3kg 47 x 107 m kgc2 30 x 108 ms2 Optical refractive index Refractive index is defined by n E 15 1 1 v Note Including polarization results in same wave equation with a different gr Q C becomes V Refractive Index Various Materials Refractive index n SrTO3 Amorphous sekemum A5253 glass AgCl Sapphwre w NaCl Calcne Quartz crysta AlAIH l ll l l l 10 Dispersion Relation Dispersion relation 03 03k 2 2E t Derived from wave equation VZE ht 2 a c t Substitute E zt ReE z 0 eXp ikr 100 quot2 Result k2 2a2 0 C 39 i Check this 1 2 v 02 C zk2 g n k Group velocity V 5 da g dk 60 C Phase velocity Vph k n gr 1 Z Electromagnetic Waves 2 2 Solution to V2Ergtl 12 C Monochromatic waves Ert Re Ekaexpiikr iwt Check these H r I Re H wexp iik r iwl are SOIU onS TEM wave Symmetry Maxwell s Equations result in E L Ht propagation direction Optical intensity Time average of Poynting vector 30 Ertgtlt H at Light Propagation Dispersive Media Relation between P and E is dynamic The relation Pr l 801E030 assumes an instantaneous response In real life Prz 50 I dl39xl l39Erl39 CD P results from response to E over some characteristic time T Function xt is a scalar function lasting a characteristic time T Et xtt xtt O for t gt t causality t EM waves in Dispersive Media Relation between P and E is dynamic Prl80 I dl39xl l39Erl39 EM wave Ert ReEka eXp ik r iat Pr t RePk co eXp ik r 100 Relation between complex amplitudes Pka 50 5010 E k 60 Slow response of matter mdependent behavior This follows by equation of the coefficients of expioat check this It also follows that 5a 80 1 Absorption and Dispersion of EM Waves Transparent materials can be described by a purely real refractive index n EM wave E zt ReE k 0 eXp ikz 100 2 2 c 2 a DisperSIon relation 0 k Q ki gm Absorbing materials can be described by a complex n It follows that k Jr 9n39mquot 911419119 2 i i C C C Investigate sign E zt ReEk co exp i z z not Traveling wave Decay Note gn39 kon39 Q n act as a regular refractive index a 22nquot 2k0nquot Q on is the absorption coefficient 0 Absorption and Dispersion of EM Waves n is derived quantity from X next lecture we determine x for different materials Complex n results from a complex X z 139 1391quot n 1 nn39z nquot 1 241 39z39 quot Z Z Z nn39 itllg39igquot or 2k0nquot 0 Weakly absorbing media 1 Whenxltlt1andx ltlt1I 1Zlilllz1 llilquot 1 Refractive index n39 1 39 2 Absorption coefficient a 2k0nquot OZquot Summary Maxwell s Equations Curl Equations lead to 2 2 6E 2 VE 8 Linear Homogeneous and Isotropic Media under certain conditions PzgozE Wave Equation with v cn 2 82Er t VZE r r7 CZ atZ In real life Relation between P and E is dynamic Prl80fdl39xl l39Erl39 Pka 80aEka This will have major consequences ll Next 2 Lectures Real and imaginary part of X are linked o KramersKronig 0 Origin frequency dependence of x in real materials Derivation of X for a range of materials 0 Insulators Lattice absorption Urbach tail color centers 0 Semiconductors Energy bands excitons o Metals Plasmons plasmonpolaritons Useful Equations and Valuable Relations 6D Maxwell s Equations Divergence Equations v1p Curl Equations VXH EJ VI 0 v X E aB 6t Constitutive relations D 80EP so sozE so 11E aggrE B0H0MDHDIMH1IMHDH Gauss s Law JD dS IsEdS Ipdv A A V 6D Maxwell also gE H39dlzm Jrjj39dg C A Dynamic relation between P and E Prt 5 0 I dt xt t Ert and Pka SozwEkw Dispersive and absorbing materials Ezt ReEzweXp i z ziwt a a H H where z n k0n absorption coefficient 0 2 n 2k0n C C Handy Math Rules Vector identities VXVXE VVE V2E VgEngEEVg Gauss theorem F 39ds 21Vde Stokes C FdlJ VgtltFds C A

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