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by: Favian Lemke


Favian Lemke
GPA 3.68

Unil Perera

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Unil Perera
Class Notes
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This 35 page Class Notes was uploaded by Favian Lemke on Monday September 21, 2015. The Class Notes belongs to PHYS 8510 at Georgia State University taught by Unil Perera in Fall. Since its upload, it has received 12 views. For similar materials see /class/209848/phys-8510-georgia-state-university in Physics 2 at Georgia State University.




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Date Created: 09/21/15
Physics of Nanostructures I Characteristic Parameters and time scale I I Surface Plasma Oscillations Plasmons I Main Problem I Interaction of Strong Fields with Atoms I I Thcoryand Equations I I Results and Discussions I Interaction of Strong Fields with Atoms 3930 Characteristic parameters and time scale average velocity of the valence electron v 2Ry 272eV quot me 0511MeVc2 1C a Fine structure constant c quoto 139 Characteristic parameters and time scale average distance Bohr radius 2 e V 2 2R Iquot 39t 47r uao 9 e39 m a z0529x10 m 8 39gUR 1quot an z 05x10 m I x I I l III 139 Characteristic parameters and time scale average orbit time 2700 0529x10m 272 8 x quot0 3x10 or II atomic unit oftime z orbi 137 Turbil z I x I 39 an 39 l I I valence electron in atoms 150 as valence electron molecules same as in atoms Vibrational motion of nuclei in molecules 100 meV 20 fs inner shell electrons lkeV 2 as Fairlie Surface Plasma Oscillations The electron charges on a metalvacuum or metaldielectric boundary can perform periodic oscillations of charge density which are called surface plasma oscillations Langmuri waves or plasma waves These oscillations can be excited by external optical elds at the interface Surface Plasmons EM waves are quantized in to units having energy I hm called photons Plasma waves are quantized in to units having energy E hmp called plasmons The plasmon is the quantization ofplasma oscillations 4mm 3 1 In cgs m Dispersion Relation of Surface Plasmons at 2 interface I39Ug x k xml El Exl909Ezle 1 9 lt0 E2 2 0 E22 eiCtd39kXll gt O a 6 6 where kx 39 3 0 39 a k 8 k gtcomplexorimagtnary C The elds have their maximwn in the surface and decay in both 2 directions exponentially and localized in the z direction within the ThomasFermi length of about IA 1515 ram matii Nmm mhlm Interaction of Strong Fields with Atoms Uhrashort singe orfew oscillation laser pulse Eu Eulcosal o 4 397 lt 331w Dipole approximation Spatial variations of the eld can be neglected This is because of the extension of the interacting system is in general much smaller than the wave length of the laser The typical wave length of 800 nm to the Bohr radius of 005 nm Ionization in a static electric eld Quasistatic ionization For high eld strength IOl2 Wcmz and long 800 nm wavelength ionization can be considered as quasi static Lee at any moment in time the atom gets ionized at a rate like in a static electric eld of strength Et Tunneling Ionization For any nonvanishing static eld at sufficiently large distances the total potential energy atomic binding r dipole eld is below the bound state energy and the electron can leave by tunneling through the potential barrier We consider strongfield electron emission that takes place when the energy barrier separating the metal electrons from the surrounding space whose height is de ned by work mction IP is slanted by a electric eld causing the electron tunneling Tunneling Innila on munanMm Tunneling Ionization Such a process occurs for relatively small values of the Keldysh parameter 7 2E2 where Up is the electron quiver cnergv IP 112 Kddysh 1mm TheoretPlty USSR 47 ms Keldysh parameter 7 1 a 21111 1 l eEUU coswr The quasistationaiy emission is of advantage for our purpose since its dependence on the parameters of the problem in particular absolute phase We can separate the electron emission process into two stages I Quantum tunneling stage p 2 Subsequent almost classical motion in the ee space In RB Cerium NJI Bum and 1 Brand PhysRcwlAu621259 1989 7 r 39I 5 L E 139 quot39 Exponential Dependence of Tunneling Ionization E tunneling probability exp21Jr I 2 6X pL3eh 11 I Strongly nonlinear exponentialdependence on parameters I Wave mechanic ofcryuam39ue solidi RA Smith 1969 Initial electron velocity after tunneling Outside the binding potential the electron more or less beltavex like afrec electron We can C1Sll S39lV the equation 12 motion classwaly or quantum mechanicaly tone can make a reasonable axxtttttption about initial pnsnion and INOML39HNUN at the end thtmnel total energy 7 potential energy 2 E e l rqu 4m r 2 2 h V2LH e l rEO E Llquot 2m 4750 r quot39 I expect velocity 0 at r I RB Calkiwi NH Burma and F Brunei PkyR vLar621259 1989 j Tunneling Probability per unit time 9 Et 6 AW Where unit step function 87 Fermi energy V electron stale density at Femii surface I 51 component of the timedependent local electric eld nomlal lo the surface Alc EJI u Landu mt EM my Quinlan Mechanics 1963 3 39 M W quot 39 Advantages of Metal Sih er Nanosystem Hie electron pIotoemission current exponentialb39 depends on the lime kinetics of the local optical electrical eld EH at ever point of the metal nanosystem I 390 nd this eld in an general caseOr a strong exeitation eld E would have been an extremely complicated unrealistic task However there are the following two properties of the metal nanosystems that make an approximate solution possible I The dielectric permittivity 8 of metals is large and negative 2 We consider nearit spectral region In this case the quality factor of the metal plasmon resonances is high enough ie lmgltlt Reg The Geometry ul39 lho Silver Vnnmtruclurts Surface plasma SP hf time as a function ofSl39 cxgcncncrgy hm Da l lap mild WA y In L II quot701 all E F0 rfs 1 4 M Hun WSAI 100 c 7 I fs 1139l 1t 56 100 97T t i u h 1 it In I 1 f3 50 100 lcmporu dqmndcncics 01 local clcclrlu optical l39x39cld Ihc cumponcnl in unih ul uwilullun l icld Iiquot at he upm ofquot Vxhupc 11 114 T I SSCV lhc rcd squares dcnnlc Ihc Icmpm al pnims cunmhuling lo the curran lllc hluc Inunglcs dcnolc Illc mulls lhal du nnl conlrihulc to he phnlncun39cnl z 30 T160155eV 1 20 05 N 39 10 WV x 10 20 30 4 Q 3 2 4 6 The red squares denote the temporal points cmmihullng m the current Z 30 20 J hw12SeV IOJ 0 x 054717 0 10 20 30 0 2 4 6 b Atmxmurmszm YSIW HKKMNHM 51250099


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