Chapter 4. The Intensity-Dependent Refractive Index
|
|
|
- Marian Harrington
- 6 years ago
- Views:
Transcription
1 Chapter. The Itesity-Depedet Refractive Idex - Third order oliear effect - Mathematical descriptio of the oliear refractive idex - Physical processes that give rise to this effect Referece : R.W. Boyd, Noliear Optics, Academic Press, INC. Noliear Optics Lab. Hayag Uiv.
2 . Descriptio of the Itesity-Depedet Refractive Idex Refractive idex of may materials ca be described by t... where, : weak-field refractive idex : d order idex of refractio it t ( ) e c. c. t ( ) ( ) * ( ) : optical Kerr effect ( rd order oliear effect) Noliear Optics Lab. Hayag Uiv.
3 Polarizatio : P( ) () () eff I Gaussia uits, eff () () () () () () Noliear Optics Lab. Hayag Uiv.
4 Appedix A. Systems of Uits i Noliear Optics (Gaussia uits ad MKS uits) ) Gaussia uits ; () P( t) () () t t t... statvolt P cm statcoulomb cm # # () () dimesioless cm statvolt () cm # statvolt The uits of oliear susceptibilities are ot usually stated explicitly ; rather oe simply states that the value is give i esu (electrostatic uits). Noliear Optics Lab. Hayag Uiv.
5 ) MKS uits ; C P m V m () P( t) () () t t t... () () t t t... : MKS () P( t) : MKS # 8.85 F/m, [F] [C/V] I MKS, I MKS, () dimesioless () () dimesiol ess m V m V () () C () V Cm V Noliear Optics Lab. Hayag Uiv.
6 ) Coversio amog the systems () statvolt V (MKS) ( ) DP D P () () (Gaussia) (MKS) (Gaussia) () (MKS) () (Gaussia) () () (MKS) () (Gaussia) () (MKS) ( ) () (Gaussia) () (MKS) () (Gaussia) () (MKS) ( ) () (Gaussia) Noliear Optics Lab. Hayag Uiv.
7 Alterative way of defiig the itesity-depedet refractive idex I c I ( ) ( ) (..) c c () c () ()? cm 7 ().95 ) W c ( esu esu xample) () CS ( :.9 esu),.58, I MW/ cm,?.95 cm () esu.58 / W I Noliear Optics Lab. Hayag Uiv.
8 Noliear Optics Lab. Hayag Uiv.
9 Physical processes producig the oliear chage i the refractive idex ) lectroic polarizatio : lectroic charge redistributio ) Molecular orietatio : Molecular aligmet due to the iduced dipole ) lectrostrictio : Desity chage by optical field ) Saturated absorptio : Itesity-depedet absorptio 5) Thermal effect : Temperature chage due to the optical field 6) Photorefractive effect : Iduced redistributio of electros ad holes Refractive idex chage due to the local field iside the medium Noliear Optics Lab. Hayag Uiv.
10 Noliear Optics Lab. Hayag Uiv.
11 . Tesor Nature of the rd Susceptibility Cetrosymmetric media F m r mb( r res r) r quatio of motio : r r r b ( r r) r e ( t) / m Solutio : it it i t ( t) e e e c. c Perturbatio expasio method ; () () ( ) ( ) ( ) ( r t r t r t r ) ( t)... ( ) e i t () () () r r r e ( t) / m () () () r r r () () () () () r r r b r r r () Noliear Optics Lab. Hayag Uiv.
12 lemet with eve umber of idex rd order polarizatio : ozero elemets : (Report) P P () () i () ( q) Ner ( q ) q jkl ( mp) () ijkl q m p j ( ) (,,, ) D jkl (,,, ) () ijkl q m th -rak tesor : 8 elemets p j m k m k where, D : Degeeracy factor (The umber of distict permutatios of the frequecy m,, p ) Let s cosider the rd order susceptibility for the case of a isotropic material. ad, l l p p (Report) Noliear Optics Lab. Hayag Uiv.
13 xpressio for the oliear susceptibility i the compact form : ijkl ijkl ik jl il jk xample) Third-harmoic geeratio : ( ) ijkl ( ) ( ) ( ij kl ik jl il jk ) xample) Itesity-depedet refractive idex : ( ) ijkl ijkl ( ) ( ) ( ij kl ik jl ) ( ijkl ) il jk Noliear Optics Lab. Hayag Uiv.
14 Noliear polarizatio for Itesity-depedet refractive idex P ( ) ( ) i jkl ijkl j k l ) 6 6 P ( i i i P i vector form Defiig the coefficiets, A ad B as A 6, B6 (Maker ad Terhue s otatio) P A B Noliear Optics Lab. Hayag Uiv.
15 I some purpose, it is useful to describe the oliear polarizatio by i terms of a effective liear susceptibility, as Pi ij j A ij j B where, ij A A B B Physical mechaisms ; ij i 6 j B 6 i j B/ A6, B/A, B/A, B'/ A B'/A' B'/A' : : : molecular orietatio oresoat electroic electrostrictio respose Noliear Optics Lab. Hayag Uiv.
16 . Noresoat lectroic Noliearities 6 # The most fast respose : a / v s [a (Bohr radius).5x -8 cm, v(electro velocity)c/7] Classical, Aharmoic Oscillator Model of lectroic Noliearities Approximated Potetial : () ijkl U r m r mbr Nbe ij kl ik jl il jk ( q, m,, p) m D( ) D( ) D( ) D( ) q Nbe ij kl ik jl il jk ( ) m D () ijkl m D p (..5) where, D i Accordig to the otatio of Maker ad Terhue, Nbe A B m D D Noliear Optics Lab. Hayag Uiv.
17 Far off-resoat case, D( ), b d () Ne m d 6 / Typical value of () N 7 () 5 cm rad/s,, d m9. esu 8 cm, 8 g e.8 esu Noliear Optics Lab. Hayag Uiv.
18 . Noliearities due to Molecular Orietatio The torque exerted o the molecule whe a electric field is applied : τ P iduced dipole momet Noliear Optics Lab. Hayag Uiv.
19 Secod order idex of refractio Chage of potetial eergy : du U pd p d d d p d cos cos si * Optical field (orietatioal relaxatio time ps order) : * U Mea polarizatio : ) With o local-field correctio : N cos si ( ) cos t Noliear Optics Lab. Hayag Uiv.
20 cos dcos dexp exp U U / / kt kt Defiig itesity parameter, J / kt cos i) J cos cos exp exp J cos J cos sid sid cos sid sid N : liear refractive idex Noliear Optics Lab. Hayag Uiv.
21 Noliear Optics Lab. Hayag Uiv. ii) J cos N cos N cos N cos N
22 Noliear Optics Lab. Hayag Uiv. si cos exp si cos exp cos cos d J d J J J kt N J N 5 5 Secod-order idex of refractio : kt N 5
23 Noliear Optics Lab. Hayag Uiv. ) With local-field correctio P loc p loc PNp ad P P N P N N () N N () () () N () () N or : Loretz-Lorez law kt N 5
24 8. lectrostrictio : Tedecy of materials to become compressed i the presece of a electric field Molecular potetial eergy : U pd d Force actig o the molecule : F U desity chage Noliear Optics Lab. Hayag Uiv.
25 Noliear Optics Lab. Hayag Uiv. Icrease i electric permittivity due to the desity chage of the material : Field eergy desity chage i the material = Work desity performed i compressig the material 8 8 u st st p V V p w So, electrostrictive pressure : 8 8 p e st where, e : electrostrictive costat
26 Noliear Optics Lab. Hayag Uiv. P st CP st P Desity chage : P C where, : compressibility 8 C e For optical field, 8 C e 8 C e C e e
27 it t e c. c. C e 6 <Classificatio accordig to the Maker ad Terhue s otatio> Noliear polarizatio : P P C e 6 () ( ) 8 () ( ) C e That is, CT e A, B 6 Noliear Optics Lab. Hayag Uiv.
28 e e : For dilute gas e / : For codesed matter (Loretz-Lorez law) xample) Cs, C - cm /dye, e () x - esu Ideal gas, C -6 cm /dye ( atm), e = - 6x - () x -5 esu Noliear Optics Lab. Hayag Uiv.
Hydrogen (atoms, molecules) in external fields. Static electric and magnetic fields Oscyllating electromagnetic fields
Hydroge (atoms, molecules) i exteral fields Static electric ad magetic fields Oscyllatig electromagetic fields Everythig said up to ow has to be modified more or less strogly if we cosider atoms (ad ios)
Chapter 2 Motion and Recombination of Electrons and Holes
Chapter 2 Motio ad Recombiatio of Electros ad Holes 2.1 Thermal Eergy ad Thermal Velocity Average electro or hole kietic eergy 3 2 kt 1 2 2 mv th v th 3kT m eff 3 23 1.38 10 JK 0.26 9.1 10 1 31 300 kg
Perturbation Theory I (See CTDL , ) Last time: derivation of all matrix elements for Harmonic-Oscillator: x, p, H. n ij n.
Perturbatio Theory I (See CTDL 1095-1107, 1110-1119) 14-1 Last time: derivatio of all matrix elemets for Harmoic-Oscillator: x, p, H selectio rules scalig ij x i j i steps of 2 e.g. x : = ± 3, ± 1 xii
5.76 Lecture #33 5/08/91 Page 1 of 10 pages. Lecture #33: Vibronic Coupling
5.76 Lecture #33 5/8/9 Page of pages Lecture #33: Vibroic Couplig Last time: H CO A A X A Electroically forbidde if A -state is plaar vibroically allowed to alterate v if A -state is plaar iertial defect
HE ATOM & APPROXIMATION METHODS MORE GENERAL VARIATIONAL TREATMENT. Examples:
5.6 4 Lecture #3-4 page HE ATOM & APPROXIMATION METHODS MORE GENERAL VARIATIONAL TREATMENT Do t restrict the wavefuctio to a sigle term! Could be a liear combiatio of several wavefuctios e.g. two terms:
EECS130 Integrated Circuit Devices
EECS130 Itegrated Circuit Devices Professor Ali Javey 9/04/2007 Semicoductor Fudametals Lecture 3 Readig: fiish chapter 2 ad begi chapter 3 Aoucemets HW 1 is due ext Tuesday, at the begiig of the class.
Physics 7440, Solutions to Problem Set # 8
Physics 7440, Solutios to Problem Set # 8. Ashcroft & Mermi. For both parts of this problem, the costat offset of the eergy, ad also the locatio of the miimum at k 0, have o effect. Therefore we work with
Lecture 25 (Dec. 6, 2017)
Lecture 5 8.31 Quatum Theory I, Fall 017 106 Lecture 5 (Dec. 6, 017) 5.1 Degeerate Perturbatio Theory Previously, whe discussig perturbatio theory, we restricted ourselves to the case where the uperturbed
Chapter 2 Motion and Recombination of Electrons and Holes
Chapter 2 Motio ad Recombiatio of Electros ad Holes 2.1 Thermal Motio 3 1 2 Average electro or hole kietic eergy kt mv th 2 2 v th 3kT m eff 23 3 1.38 10 JK 0.26 9.1 10 1 31 300 kg K 5 7 2.310 m/s 2.310
Andrei Tokmakoff, MIT Department of Chemistry, 5/19/
drei Tokmakoff, MT Departmet of Chemistry, 5/9/5 4-9 Rate of bsorptio ad Stimulated Emissio The rate of absorptio iduced by the field is E k " (" (" $% ˆ µ # (" &" k k (4. The rate is clearly depedet o
Lecture 6. Semiconductor physics IV. The Semiconductor in Equilibrium
Lecture 6 Semicoductor physics IV The Semicoductor i Equilibrium Equilibrium, or thermal equilibrium No exteral forces such as voltages, electric fields. Magetic fields, or temperature gradiets are actig
Chapter 5 Vibrational Motion
Fall 4 Chapter 5 Vibratioal Motio... 65 Potetial Eergy Surfaces, Rotatios ad Vibratios... 65 Harmoic Oscillator... 67 Geeral Solutio for H.O.: Operator Techique... 68 Vibratioal Selectio Rules... 7 Polyatomic
Lecture 3. Electron and Hole Transport in Semiconductors
Lecture 3 lectro ad Hole Trasort i Semicoductors I this lecture you will lear: How electros ad holes move i semicoductors Thermal motio of electros ad holes lectric curret via lectric curret via usio Semicoductor
Appendix K. The three-point correlation function (bispectrum) of density peaks
Appedix K The three-poit correlatio fuctio (bispectrum) of desity peaks Cosider the smoothed desity field, ρ (x) ρ [ δ (x)], with a geeral smoothig kerel W (x) δ (x) d yw (x y)δ(y). (K.) We defie the peaks
LECTURE 14. Non-linear transverse motion. Non-linear transverse motion
LETURE 4 No-liear trasverse motio Floquet trasformatio Harmoic aalysis-oe dimesioal resoaces Two-dimesioal resoaces No-liear trasverse motio No-liear field terms i the trajectory equatio: Trajectory equatio
Vibrational Spectroscopy 1
Applied Spectroscopy Vibratioal Spectroscopy Recommeded Readig: Bawell ad McCash Chapter 3 Atkis Physical Chemistry Chapter 6 Itroductio What is it? Vibratioal spectroscopy detects trasitios betwee the
TIME-CORRELATION FUNCTIONS
p. 8 TIME-CORRELATION FUNCTIONS Time-correlatio fuctios are a effective way of represetig the dyamics of a system. They provide a statistical descriptio of the time-evolutio of a variable for a esemble
Solid State Device Fundamentals
Solid State Device Fudametals ENS 345 Lecture Course by Alexader M. Zaitsev alexader.zaitsev@csi.cuy.edu Tel: 718 982 2812 4N101b 1 Thermal motio of electros Average kietic eergy of electro or hole (thermal
Introduction to Signals and Systems, Part V: Lecture Summary
EEL33: Discrete-Time Sigals ad Systems Itroductio to Sigals ad Systems, Part V: Lecture Summary Itroductio to Sigals ad Systems, Part V: Lecture Summary So far we have oly looked at examples of o-recursive
1. Hydrogen Atom: 3p State
7633A QUANTUM MECHANICS I - solutio set - autum. Hydroge Atom: 3p State Let us assume that a hydroge atom is i a 3p state. Show that the radial part of its wave fuctio is r u 3(r) = 4 8 6 e r 3 r(6 r).
Basic Physics of Semiconductors
Chater 2 Basic Physics of Semicoductors 2.1 Semicoductor materials ad their roerties 2.2 PN-juctio diodes 2.3 Reverse Breakdow 1 Semicoductor Physics Semicoductor devices serve as heart of microelectroics.
Bohr s Atomic Model Quantum Mechanical Model
September 7, 0 - Summary - Itroductio to Atomic Theory Bohr s Atomic Model Quatum Mechaical Model 3- Some Defiitio 3- Projects Temperature Pressure Website Subject Areas Plasma is a Mixture of electros,
SPEC/4/PHYSI/SPM/ENG/TZ0/XX PHYSICS PAPER 1 SPECIMEN PAPER. 45 minutes INSTRUCTIONS TO CANDIDATES
SPEC/4/PHYSI/SPM/ENG/TZ0/XX PHYSICS STANDARD LEVEL PAPER 1 SPECIMEN PAPER 45 miutes INSTRUCTIONS TO CANDIDATES Do ot ope this examiatio paper util istructed to do so. Aswer all the questios. For each questio,
Lecture 9: Diffusion, Electrostatics review, and Capacitors. Context
EECS 5 Sprig 4, Lecture 9 Lecture 9: Diffusio, Electrostatics review, ad Capacitors EECS 5 Sprig 4, Lecture 9 Cotext I the last lecture, we looked at the carriers i a eutral semicoductor, ad drift currets
1. Szabo & Ostlund: 2.1, 2.2, 2.4, 2.5, 2.7. These problems are fairly straightforward and I will not discuss them here.
Solutio set III.. Szabo & Ostlud:.,.,.,.5,.7. These problems are fairly straightforward ad I will ot discuss them here.. N! N! i= k= N! N! N! N! p p i j pi+ pj i j i j i= j= i= j= AA ˆˆ= ( ) Pˆ ( ) Pˆ
Orthogonal transformations
Orthogoal trasformatios October 12, 2014 1 Defiig property The squared legth of a vector is give by takig the dot product of a vector with itself, v 2 v v g ij v i v j A orthogoal trasformatio is a liear
Basic Physics of Semiconductors
Chater 2 Basic Physics of Semicoductors 2.1 Semicoductor materials ad their roerties 2.2 PN-juctio diodes 2.3 Reverse Breakdow 1 Semicoductor Physics Semicoductor devices serve as heart of microelectroics.
Exercises and Problems
HW Chapter 4: Oe-Dimesioal Quatum Mechaics Coceptual Questios 4.. Five. 4.4.. is idepedet of. a b c mu ( E). a b m( ev 5 ev) c m(6 ev ev) Exercises ad Problems 4.. Model: Model the electro as a particle
Nonequilibrium Excess Carriers in Semiconductors
Lecture 8 Semicoductor Physics VI Noequilibrium Excess Carriers i Semicoductors Noequilibrium coditios. Excess electros i the coductio bad ad excess holes i the valece bad Ambiolar trasort : Excess electros
PHY4905: Nearly-Free Electron Model (NFE)
PHY4905: Nearly-Free Electro Model (NFE) D. L. Maslov Departmet of Physics, Uiversity of Florida (Dated: Jauary 12, 2011) 1 I. REMINDER: QUANTUM MECHANICAL PERTURBATION THEORY A. No-degeerate eigestates
Answer: 1(A); 2(C); 3(A); 4(D); 5(B); 6(A); 7(C); 8(C); 9(A); 10(A); 11(A); 12(C); 13(C)
Aswer: (A); (C); 3(A); 4(D); 5(B); 6(A); 7(C); 8(C); 9(A); 0(A); (A); (C); 3(C). A two loop positio cotrol system is show below R(s) Y(s) + + s(s +) - - s The gai of the Tacho-geerator iflueces maily the
1 Adiabatic and diabatic representations
1 Adiabatic ad diabatic represetatios 1.1 Bor-Oppeheimer approximatio The time-idepedet Schrödiger equatio for both electroic ad uclear degrees of freedom is Ĥ Ψ(r, R) = E Ψ(r, R), (1) where the full molecular
PHYC - 505: Statistical Mechanics Homework Assignment 4 Solutions
PHYC - 55: Statistical Mechaics Homewor Assigmet 4 Solutios Due February 5, 14 1. Cosider a ifiite classical chai of idetical masses coupled by earest eighbor sprigs with idetical sprig costats. a Write
Exponential transient rotating waves and their bifurcations in a ring of unidirectionally coupled bistable Lorenz systems
Available olie at www.sciecedirect.com Procedia IUTAM 5 (2012 ) 283 287 IUTAM Symposium o 50 Years of Chaos: Applied ad Theoretical Expoetial trasiet rotatig waves ad their bifurcatios i a rig of uidirectioally
Sequences, Mathematical Induction, and Recursion. CSE 2353 Discrete Computational Structures Spring 2018
CSE 353 Discrete Computatioal Structures Sprig 08 Sequeces, Mathematical Iductio, ad Recursio (Chapter 5, Epp) Note: some course slides adopted from publisher-provided material Overview May mathematical
There are 7 crystal systems and 14 Bravais lattices in 3 dimensions.
EXAM IN OURSE TFY40 Solid State Physics Moday 0. May 0 Time: 9.00.00 DRAFT OF SOLUTION Problem (0%) Itroductory Questios a) () Primitive uit cell: The miimum volume cell which will fill all space (without
Review Problems 1. ICME and MS&E Refresher Course September 19, 2011 B = C = AB = A = A 2 = A 3... C 2 = C 3 = =
Review Problems ICME ad MS&E Refresher Course September 9, 0 Warm-up problems. For the followig matrices A = 0 B = C = AB = 0 fid all powers A,A 3,(which is A times A),... ad B,B 3,... ad C,C 3,... Solutio:
Optimally Sparse SVMs
A. Proof of Lemma 3. We here prove a lower boud o the umber of support vectors to achieve geeralizatio bouds of the form which we cosider. Importatly, this result holds ot oly for liear classifiers, but
Physics 232 Gauge invariance of the magnetic susceptibilty
Physics 232 Gauge ivariace of the magetic susceptibilty Peter Youg (Dated: Jauary 16, 2006) I. INTRODUCTION We have see i class that the followig additioal terms appear i the Hamiltoia o addig a magetic
PH 411/511 ECE B(k) Sin k (x) dk (1)
Fall-27 PH 4/5 ECE 598 A. La Rosa Homework-3 Due -7-27 The Homework is iteded to gai a uderstadig o the Heiseberg priciple, based o a compariso betwee the width of a pulse ad the width of its spectral
2C09 Design for seismic and climate changes
2C09 Desig for seismic ad climate chages Lecture 02: Dyamic respose of sigle-degree-of-freedom systems I Daiel Grecea, Politehica Uiversity of Timisoara 10/03/2014 Europea Erasmus Mudus Master Course Sustaiable
Phys 102 Lecture 25 The quantum mechanical model of light
Phys 102 Lecture 25 The quatum mechaical model of light 1 Recall last time Problems with classical physics Stability of atoms Atomic spectra Photoelectric effect Quatum model of the atom Bohr model oly
Microscopic Theory of Transport (Fall 2003) Lecture 6 (9/19/03) Static and Short Time Properties of Time Correlation Functions
.03 Microscopic Theory of Trasport (Fall 003) Lecture 6 (9/9/03) Static ad Short Time Properties of Time Correlatio Fuctios Refereces -- Boo ad Yip, Chap There are a umber of properties of time correlatio
Ray Optics Theory and Mode Theory. Dr. Mohammad Faisal Dept. of EEE, BUET
Ray Optics Theory ad Mode Theory Dr. Mohammad Faisal Dept. of, BUT Optical Fiber WG For light to be trasmitted through fiber core, i.e., for total iteral reflectio i medium, > Ray Theory Trasmissio Ray
Introduction to Astrophysics Tutorial 2: Polytropic Models
Itroductio to Astrophysics Tutorial : Polytropic Models Iair Arcavi 1 Summary of the Equatios of Stellar Structure We have arrived at a set of dieretial equatios which ca be used to describe the structure
Introduction To Discrete Mathematics
Itroductio To Discrete Mathematics Review If you put + pigeos i pigeoholes the at least oe hole would have more tha oe pigeo. If (r + objects are put ito boxes, the at least oe of the boxes cotais r or
The time evolution of the state of a quantum system is described by the time-dependent Schrödinger equation (TDSE): ( ) ( ) 2m "2 + V ( r,t) (1.
Adrei Tokmakoff, MIT Departmet of Chemistry, 2/13/2007 1-1 574 TIME-DEPENDENT QUANTUM MECHANICS 1 INTRODUCTION 11 Time-evolutio for time-idepedet Hamiltoias The time evolutio of the state of a quatum system
All Excuses must be taken to 233 Loomis before 4:15, Monday, April 30.
Miscellaeous Notes The ed is ear do t get behid. All Excuses must be take to 233 Loomis before 4:15, Moday, April 30. The PYS 213 fial exam times are * 8-10 AM, Moday, May 7 * 8-10 AM, Tuesday, May 8 ad
Apply change-of-basis formula to rewrite x as a linear combination of eigenvectors v j.
Eigevalue-Eigevector Istructor: Nam Su Wag eigemcd Ay vector i real Euclidea space of dimesio ca be uiquely epressed as a liear combiatio of liearly idepedet vectors (ie, basis) g j, j,,, α g α g α g α
FINAL EXAM PHYSICS 103 FALL 2004 A
FN EXM PHYSCS 3 F 4 ρ = V m ; p = F ; ph = ρgh; atm =.3 x 5 Pa, F B = rgv im, = -olume flow rate p + ½ρ + ρgh = p + ½ρ + ρgh flow i horizotal pipe: p + ½ρ = p + ½ρ T( C) = 9 5 [T( F) - 3]; T( F) = 5 9
AIT. Blackbody Radiation IAAT
3 1 Blackbody Radiatio Itroductio 3 2 First radiatio process to look at: radiatio i thermal equilibrium with itself: blackbody radiatio Assumptios: 1. Photos are Bosos, i.e., more tha oe photo per phase
Olli Simula T / Chapter 1 3. Olli Simula T / Chapter 1 5
Sigals ad Systems Sigals ad Systems Sigals are variables that carry iformatio Systemstake sigals as iputs ad produce sigals as outputs The course deals with the passage of sigals through systems T-6.4
A Brief Introduction to the Physical Basis for Electron Spin Resonance
A Brief Itroductio to the Physical Basis for Electro Spi Resoace I ESR measuremets, the sample uder study is exposed to a large slowly varyig magetic field ad a microwave frequecy magetic field orieted
EE 485 Introduction to Photonics Photon Optics and Photon Statistics
Itroductio to Photoics Photo Optics ad Photo Statistics Historical Origi Photo-electric Effect (Eistei, 905) Clea metal V stop Differet metals, same slope Light I Slope h/q ν c/λ Curret flows for λ < λ
1. pn junction under bias 2. I-Vcharacteristics
Lecture 10 The p Juctio (II) 1 Cotets 1. p juctio uder bias 2. I-Vcharacteristics 2 Key questios Why does the p juctio diode exhibit curret rectificatio? Why does the juctio curret i forward bias icrease
10. Second quantization: molecule-radiation interaction
10. Secod quatizatio: molecule-radiatio iteractio Now that the full molecular (sectios 7 through 9), eld (b), ad iteractio (b) Hamiltoia operators are i had, they ca be combied to yield the overall molecule-radiatio
ECE-S352 Introduction to Digital Signal Processing Lecture 3A Direct Solution of Difference Equations
ECE-S352 Itroductio to Digital Sigal Processig Lecture 3A Direct Solutio of Differece Equatios Discrete Time Systems Described by Differece Equatios Uit impulse (sample) respose h() of a DT system allows
Extended Electron in Constant Electric Field Part 1 : The net electric force Fe produced on the extended electron
1 Exteded Electro i Costat Electric Field Part 1 : The et electric force Fe produced o the exteded electro Hoa Va Nguye Email : hoaguye2312@yahoo.ca Abstract : Whe a exteded electro is subject to a exteral
point, requiring all 4 curves to be continuous Discontinuity in P
. Solutio Methods a Classical approach Basic equatios of stellar structure + boudary coditios i Classical (historical method of solutio: Outward itegratio from ceter, where l = m = ward itegratio from
Guiding-center transformation 1. δf = q ( c v f 0, (1) mc (v B 0) v f 0. (3)
Guidig-ceter trasformatio 1 This is my otes whe readig Liu Che s book[1]. 1 Vlasov equatio The liearized Vlasov equatio is [ t + v x + q m E + v B c ] δf = q v m δe + v δb c v f, 1 where f ad δf are the
MIT Department of Chemistry 5.74, Spring 2005: Introductory Quantum Mechanics II Instructor: Professor Andrei Tokmakoff
MIT Departmet of Chemistry 5.74, Sprig 5: Itroductory Quatum Mechaics II Istructor: Professor Adrei Tomaoff p. 97 ABSORPTION SPECTRA OF MOLECULAR AGGREGATES The absorptio spectra of periodic arrays of
Wave Motion
Wave Motio Wave ad Wave motio: Wave is a carrier of eergy Wave is a form of disturbace which travels through a material medium due to the repeated periodic motio of the particles of the medium about their
Ultrafast Optical Physics II (SoSe 2017) Lecture 2, April 21
Ultrafast Optical Physics II SoSe 7 Lecture pril Susceptibility a Sellmeier equatio Phase velocity group velocity a ispersio 3 Liear pulse propagatio Maxwell s Equatios of isotropic a homogeeous meia Maxwell
Math 778S Spectral Graph Theory Handout #3: Eigenvalues of Adjacency Matrix
Math 778S Spectral Graph Theory Hadout #3: Eigevalues of Adjacecy Matrix The Cartesia product (deoted by G H) of two simple graphs G ad H has the vertex-set V (G) V (H). For ay u, v V (G) ad x, y V (H),
Shadowgraph, Schlieren and Interferometry Part - 01
AerE 545 class otes #8 Shadowgraph, Schliere ad tererometry Part - Hui Hu Departmet o Aerospace Egieerig, owa State Uiversity Ames, owa 5, U.S.A dex o reractio: λ c / v > λ Deped o variatio o idex o reractio
Preliminary Examination - Day 1 Thursday, May 12, 2016
UNL - Departmet of Physics ad Astroomy Prelimiary Examiatio - Day Thursday, May, 6 This test covers the topics of Quatum Mechaics (Topic ) ad Electrodyamics (Topic ). Each topic has 4 A questios ad 4 B
5.74 TIME-DEPENDENT QUANTUM MECHANICS
p. 1 5.74 TIME-DEPENDENT QUANTUM MECHANICS The time evolutio of the state of a system is described by the time-depedet Schrödiger equatio (TDSE): i t ψ( r, t)= H ˆ ψ( r, t) Most of what you have previously
NARAYANA IIT ACADEMY INDIA XI -REG_Adv. Dt: Time: 09:00 AM to 12:00 Noon Max.Marks: 180
6..06 XI_Reg.ADV._Jee-Adv_03-Pkey & hits NARAYANA IIT ACADEMY INDIA XI -REG_Adv. Dt: 6--06 Time: 09:00 AM to :00 Noo Max.Marks: 80 KEY & SOLUTIONS PHYSICS CHEMISTRY MATHS C C 4 B A C 4 D 3 A 3 D 43 A 4
6.867 Machine learning, lecture 7 (Jaakkola) 1
6.867 Machie learig, lecture 7 (Jaakkola) 1 Lecture topics: Kerel form of liear regressio Kerels, examples, costructio, properties Liear regressio ad kerels Cosider a slightly simpler model where we omit
17 Phonons and conduction electrons in solids (Hiroshi Matsuoka)
7 Phoos ad coductio electros i solids Hiroshi Matsuoa I this chapter we will discuss a miimal microscopic model for phoos i a solid ad a miimal microscopic model for coductio electros i a simple metal.
ME 440 Intermediate Vibrations
ME 440 Itermediate Vibratios Th, Jauary 29, 2009 Sectio 1.11 Da Negrut, 2009 ME440, UW-Madiso Before we get started Last Time: Discussed about periodic fuctios Covered the Fourier Series Expasio Wet through
1. Linearization of a nonlinear system given in the form of a system of ordinary differential equations
. Liearizatio of a oliear system give i the form of a system of ordiary differetial equatios We ow show how to determie a liear model which approximates the behavior of a time-ivariat oliear system i a
PHYS-3301 Lecture 3. EM- Waves behaving like Particles. CHAPTER 3 The Experimental Basis of Quantum. CHAPTER 3 The Experimental Basis of Quantum
CHAPTER 3 The Experimetal Basis of Quatum PHYS-3301 Lecture 3 Sep. 4, 2018 3.1 Discovery of the X Ray ad the Electro 3.2 Determiatio of Electro Charge 3.3 Lie Spectra 3.4 Quatizatio 3.5 Blackbody Radiatio
3. Z Transform. Recall that the Fourier transform (FT) of a DT signal xn [ ] is ( ) [ ] = In order for the FT to exist in the finite magnitude sense,
![3. Z Transform. Recall that the Fourier transform (FT) of a DT signal xn [ ] is ( ) [ ] = In order for the FT to exist in the finite magnitude sense,](/thumbs/82/85448051.jpg "3. Z Transform. Recall that the Fourier transform (FT) of a DT signal xn [ ] is ( ) [ ] = In order for the FT to exist in the finite magnitude sense,")
3. Z Trasform Referece: Etire Chapter 3 of text. Recall that the Fourier trasform (FT) of a DT sigal x [ ] is ω ( ) [ ] X e = j jω k = xe I order for the FT to exist i the fiite magitude sese, S = x [
Castiel, Supernatural, Season 6, Episode 18
13 Differetial Equatios the aswer to your questio ca best be epressed as a series of partial differetial equatios... Castiel, Superatural, Seaso 6, Episode 18 A differetial equatio is a mathematical equatio
Free Space Optical Wireless Communications under Turbulence Channel Effect
IOSR Joural of Electroics ad Commuicatio Egieerig (IOSR-JECE) e-issn: 78-834,p- ISSN: 78-8735.Volume 9, Issue 3, Ver. III (May - Ju. 014), PP 01-08 Free Space Optical Wireless Commuicatios uder Turbulece
INEQUALITIES BJORN POONEN
INEQUALITIES BJORN POONEN 1 The AM-GM iequality The most basic arithmetic mea-geometric mea (AM-GM) iequality states simply that if x ad y are oegative real umbers, the (x + y)/2 xy, with equality if ad
5.80 Small-Molecule Spectroscopy and Dynamics
MIT OpeCourseWare http://ocw.mit.edu 5.80 Small-Molecule Spectroscopy ad Dyamics Fall 2008 For iformatio about citig these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. Lecture # 33 Supplemet
NONLINEAR OSCILLATIONS OF A FLOATING ELASTIC PLATE
Iteratioal Applied Mechaics Vol 46 o March (Russia Origial Vol 46 o October ) OLIEAR OSCILLATIOS OF A FLOATIG ELASTIC PLATE ÀÅ Buatov ad ÀÀ Buatov The multi-scales method is used to derive third-order
Lecture 4. We also define the set of possible values for the random walk as the set of all x R d such that P(S n = x) > 0 for some n.
Radom Walks ad Browia Motio Tel Aviv Uiversity Sprig 20 Lecture date: Mar 2, 20 Lecture 4 Istructor: Ro Peled Scribe: Lira Rotem This lecture deals primarily with recurrece for geeral radom walks. We preset
On the number of sums of three unit fractions
Notes o Number Theory ad Discrete Mathematics Vol. 9, 0, No., 8 O the umber of sums of three uit fractios Simo Brow School of Huma Life Scieces, Uiversity of Tasmaia, Locked Bag 0, Laucesto, Tasmaia 70,
EE / EEE SAMPLE STUDY MATERIAL. GATE, IES & PSUs Signal System. Electrical Engineering. Postal Correspondence Course
Sigal-EE Postal Correspodece Course 1 SAMPLE STUDY MATERIAL Electrical Egieerig EE / EEE Postal Correspodece Course GATE, IES & PSUs Sigal System Sigal-EE Postal Correspodece Course CONTENTS 1. SIGNAL
[ ] sin ( ) ( ) = 2 2 ( ) ( ) ( ) ˆ Mechanical Spectroscopy II
![[ ] sin ( ) ( ) = 2 2 ( ) ( ) ( ) ˆ Mechanical Spectroscopy II](/thumbs/72/66401300.jpg "[ ] sin ( ) ( ) = 2 2 ( ) ( ) ( ) ˆ Mechanical Spectroscopy II")
Solid State Pheomea Vol. 89 (003) pp 343-348 (003) Tras Tech Publicatios, Switzerlad doi:0.408/www.scietific.et/ssp.89.343 A New Impulse Mechaical Spectrometer to Study the Dyamic Mechaical Properties
Epsilons Near Zero limits in the Mie scattering theory
Epsilos Near Zero limits i the Mie scatterig theory M. Tagviashvili * Adroikashvili Istitute of Physics, 6 Tamarashvili st, 77, Tbilsi, Georgia * madoa.tagviashvili@grt.ge Abstract: The classical Mie theory
Maxwell's Equations in Media and Their Solution *
Maxwell's Equatios i Media ad heir Solutio * ao Zhag College of Nuclear Sciece ad echology, Beijig Normal Uiversity, Beijig 1875 taozhag@bu.edu.c Abstract Magetic field magetizatio, polarizatio ad iduced
Miscellaneous Notes. Lecture 19, p 1
Miscellaeous Notes The ed is ear do t get behid. All Excuses must be take to 233 Loomis before oo, Thur, Apr. 25. The PHYS 213 fial exam times are * 8-10 AM, Moday, May 6 * 1:30-3:30 PM, Wed, May 8 The
The Mathematical Model and the Simulation Modelling Algoritm of the Multitiered Mechanical System
The Mathematical Model ad the Simulatio Modellig Algoritm of the Multitiered Mechaical System Demi Aatoliy, Kovalev Iva Dept. of Optical Digital Systems ad Techologies, The St. Petersburg Natioal Research
photonics FDTD for Hydrodynamic Electron Fluid Maxwell Equations Photonics 2015, 2, ; doi: /photonics
Photoics 15,, 459-467; doi:1.339/photoics459 OPEN ACCESS photoics ISSN 34-673 www.mdpi.com/joural/photoics Article FDTD for Hydrodyamic Electro Fluid Maxwell Equatios Yigxue Zhao * ad Jijie Liu Departmet
Atoms in a Classical Light Field
Chapter 2 Atoms i a Classical Light Field Semicoductors like all crystals are periodic arrays of oe or more types of atoms. A prototype of a semicoductor is a lattice of group IV atoms, e.g. Si or Ge,
Chem Discussion #13 Chapter 10. Correlation diagrams for diatomic molecules. Key
Chem 101 017 Discussio #13 Chapter 10. Correlatio diagrams for diatomic molecules. Key 1. Below is a plot of the first 10 ioizatio eergies for a sigle atom i 3 rd row of the periodic table. The x- axis
Homework 3 Solutions
Math 4506 Sprig 04 Homework 3 Solutios. a The ACF of a MA process has a o-zero value oly at lags, 0, ad. Problem 4.3 from the textbook which you did t do, so I did t expect you to metio this shows that
CEE 522 Autumn Uncertainty Concepts for Geotechnical Engineering
CEE 5 Autum 005 Ucertaity Cocepts for Geotechical Egieerig Basic Termiology Set A set is a collectio of (mutually exclusive) objects or evets. The sample space is the (collectively exhaustive) collectio
Vibratory Motion. Prof. Zheng-yi Feng NCHU SWC. National CHung Hsing University, Department of Soil and Water Conservation
Vibratory Motio Prof. Zheg-yi Feg NCHU SWC 1 Types of vibratory motio Periodic motio Noperiodic motio See Fig. A1, p.58 Harmoic motio Periodic motio Trasiet motio impact Trasiet motio earthquake A powerful
PH 411/511 ECE B(k) Sin k (x) dk (1)
Fall-26 PH 4/5 ECE 598 A. La Rosa Homework-2 Due -3-26 The Homework is iteded to gai a uderstadig o the Heiseberg priciple, based o a compariso betwee the width of a pulse ad the width of its spectral
Semiconductors a brief introduction
Semicoductors a brief itroductio Bad structure from atom to crystal Fermi level carrier cocetratio Dopig Readig: (Sedra/Smith 7 th editio) 1.7-1.9 Trasport (drift-diffusio) Hyperphysics (lik o course homepage)
ADVANCED TOPICS ON VIDEO PROCESSING
ADVANCED TOPICS ON VIDEO PROCESSING Image Spatial Processig FILTERING EXAMPLES FOURIER INTERPRETATION FILTERING EXAMPLES FOURIER INTERPRETATION FILTERING EXAMPLES FILTERING EXAMPLES FOURIER INTERPRETATION
INF-GEO Solutions, Geometrical Optics, Part 1
INF-GEO430 20 Solutios, Geometrical Optics, Part Reflectio by a symmetric triagular prism Let be the agle betwee the two faces of a symmetric triagular prism. Let the edge A where the two faces meet be
Quantum Walks and Phase Transitions in Quadratic Nonlinear Waveguide Arrays
Quatum Walks ad Phase Trasitios i Quadratic Noliear Waveguide Arrays Adrey A. Sukhorukov joit work with Alexader S. Soltsev, Dragomir N. Neshev, Yuri S. Kivshar Noliear Physics Cetre, Australia Natioal
a b c d e f g h Supplementary Information
Supplemetary Iformatio a b c d e f g h Supplemetary Figure S STM images show that Dark patters are frequetly preset ad ted to accumulate. (a) mv, pa, m ; (b) mv, pa, m ; (c) mv, pa, m ; (d) mv, pa, m ;
Numerical Methods in Fourier Series Applications
Numerical Methods i Fourier Series Applicatios Recall that the basic relatios i usig the Trigoometric Fourier Series represetatio were give by f ( x) a o ( a x cos b x si ) () where the Fourier coefficiets