Scattering matrix of the interface
|
|
|
- Maximilian Booth
- 5 years ago
- Views:
Transcription
1 Scattering matrix of the interface Let us consider a generalied version of the roblem: when waves are incident on the interface from both media scattering: 0 E A ex j B ex j y 0, 0, 1, 1, 0 E C ex j D ex j y D ex j 1, 0, B ex j0, Aex j C ex j 1, 1, 0, Scattering from layered media 3
2 Scattering matrix of the interface Matching the solutions results in the scattering matrix of the interface: matrix relating the amlitudes of the reflected waves to those of the incident waves at the interface B T A C T D S 0 D ex j 1, 0, B ex j0, Aex j C ex j 1, 1, 0, 0 0 T 1 T 1 1 1, 1, 0, Scattering from layered media 4
3 Scattering matrix of the interface For the TM case: 0 H Aex j B ex j y 1, 1,,, 0 H C ex j D ex j y B TM T TM A C TTM TM D T TM TM TM 1 S TM TM 0 0, B ex j0, Aex j T TM 1 TM 1 TM D ex j 1, C ex j 0 1, 1, 1 0, 0 1, 1, 0, 0 0 Scattering from layered media 5
4 Scattering matrix of the interface If the interface is not located at = 0, but at = 0 we can still use the same result, but should use the correct amlitudes at the interface ex j0, 0 B T ex j0, 0 A ex j C T ex j D 1, 0 1, 0 0 D ex j 1, 0, B ex j0, Aex j C ex j 1, 1, 0, 0 0 Scattering from layered media 6
5 Scattering by a dielectric slab Let us go one ste further and consider the scattering by a dielectric slab of finite thicness We again distinguish the and TM cases The tangential wave vector is again the same in all layers Solution can be obtained by matching the fields at the two interface lanes, 0 1, 0 0, 0 i i i t i d r Scattering from layered media 7
6 Scattering by a dielectric slab Solution for the electric field inside each layer for reduced fields, 0 1, 0 0, 0 D ex j 1, 0, B ex j0, Aex j E ex j, C ex j 1, d 0 Scattering from layered media 8
7 Scattering by a dielectric slab Instead of matching fields use the interface scattering matrices B 1 A C 1 D ex j 1 1 1, d D 1 ex j 1, d C d 1 1 ex j 1, d E , 1, 0, 1, 1 1,, 1,, Scattering from layered media 9
8 Scattering by a dielectric slab esulting overall reflection and transmission coefficients 10 1 B ex j1, d A j d ex 1, T ex j1, d ex 1, E A j d Similar results for TM scattering, just relace TM 1 0, 0 1, 1 0, 0 1, 1 1 TM 1, 1, 1, 1, Scattering from layered media 30
9 Scattering by a dielectric slab in vacuum A more ractical case: a dielectric slab in vacuum 10 cos sin cos sin 0, 1, i d i 0, 1, i d i i 1 1, 0, 10 1, 0, 10 TM cos sin d i d i cos sin d i d i 0 1 d0 d 0 i i 1 10 TM TM i r Scattering from layered media 31
10 Scattering by a dielectric slab in vacuum Overall reflection coefficient for scattering: 10 1 ex 1, 10 j1, d j d 1 ex 0, 1, 0, 1, j0, 1, cot 1, d cos, sin, ( ) sin 0, 0 i 1, 0 d i i d i 1 d j d cos ( ) cos cot ( ) d i i i i 0 Scattering from layered media 3
11 Scattering by a dielectric slab in vacuum Overall reflection coefficient for TM scattering: TM 1 ex 1, 10 TM j1, d j d 10 TM 1 ex 1 0, 0 1, 1 0, 0 1, 0 1 0, 1, cot 1, j d cos, sin, ( ) sin 0, 0 i 1, 0 d i i d i TM cos sin d i i d d i d i j d i i i cos sin ( ) cos cot ( ) d 0 Scattering from layered media 33
12 Scattering by a dielectric slab in vacuum eflection coefficient of the and TM mode becomes ero if 1 ex j d =0 1, n 1, d n, n 1,, sin i d 0d Phenomenon caused by (almost) standing waves in slab due to multile reflections, similar to Fabry-Perrot, resonant tunneling Can occur when the slab is thicer than half roagation wave length inside the slab d d d 0 d Scattering from layered media 34
13 Scattering by a dielectric slab in vacuum In addition, we have the usual Brewster angle for TM scattering where reflection becomes ero d cos sin 0 sin 1 d i i d i Normal incidence 0 same and TM values aart from a minus sign (why?) i 1 d 0d TM 1 j cot d d d d Almost horiontal incidence / 1 1 Scattering from layered media 35 i TM
14 eflection from a dielectric slab in vacuum Plots for a slab with a relative dielectric constant of 4 dd dd 6.5 TM TM i (deg) i (deg) Scattering from layered media 36
15 eflection from a dielectric slab in vacuum Note also that if we ee the angle constant and change the frequency then an oscillatory behavior is observed due to the standing wave henomenon i 0 i 45 deg TM 0d 0d Scattering from layered media 37
16 Scattering from a general layered medium So far we considered a number of secific cases, now we turn to the general case, N 1 0 N, 0 N, BN ex jn, A ex j N A ex j N 1 N 1, 1, 0 0, 0 B1 ex j1, A ex j 1 1, B0 ex j0, A ex j 0 0, x Scattering from layered media 38
17 Scattering from a general layered medium Our aim is to find the overall reflection and, erhas, transmission coefficients B A 0 0 T A N 1 A 0 Lie for a single slab, we would lie to use the exressions for interface scattering But, the scattering matrix is not the right quantity for analying a stac of multile layers Combining scattering matrices of different layers is not easy Scattering from layered media 39
18 Scattering from a general layered medium Let us again return to a single interface between media B ex j, T A ex j, C ex j T D ex j 1, 1, Instead of relating amlitudes of scattered waves to those of incident waves, we relate waves in layer i+1 to those in layer i S D j ex 1,, B ex j, Aex j C j ex 1, 1, 0, 0 Scattering from layered media 40
19 Scattering from a general layered medium Let us again return to a single interface between media C ex j 1, 1 S ex 1S1 S A j 11S S, D ex j S S 1 B ex j 1, 1 11, In terms of the reflection coefficient M M D j ex 1, Transfer matrix, B ex j, Aex j C j ex 1, 1, 0, 0 Scattering from layered media 41
20 Scattering from a general layered medium Note again, that the matrix relates the wave amlitudes Now consider the full roblem N N N 1 N 1 0 B1 ex j1, A ex j 1 1, B0 ex j0, A ex j 0 0, N, BN ex jn, A ex j N BN 1 ex jn 1, A ex j N 1 N 1, Scattering from layered media 4
21 Scattering from a general layered medium We have ex j 1, A 1 ex j 1,, A M ex j B ex j B 1, 1, A A 1 1, 1,, B Q M Q 1 B Q ex j 0 0 ex j M 1, 1, 1 1 1, 1, 1 1 Scattering from layered media 43
22 Scattering from a general layered medium ex j A 1, 1 ex N N N j A 0, 0 0 M ex j B ex j B N 1, N N 1 0, 0 0 M M Q M Q M Q M N 1, N 3,,1 1,0 N 1 Q e j, 0 d d 1 e j 0, d N N 1 1 N 1 N 1 N, BN ex j N, A ex j N BN 1 ex j N 1, A ex j N 1 N 1, B1 ex j1, A ex j 1 1, 0 0 B0 ex j0, A ex j 0 0, Scattering from layered media 44
23 Scattering from a general layered medium We have found the overall transfer matrix of the structure The overall reflection and transmission coefficient: ex j A 1, 1 ex N N N j A M 11 M 1 0, 0 0 ex j B M M ex j B N 1, N N 1 1 0, 0 0 B N 1 ex 0, T ex ex j j j 0, 0 B A 0 M M N 1, N N M 11 ex j A 0, 0 0 M A M M Scattering from layered media 45
24 Scattering from a general layered medium Examle: single dielectric slab in vacuum M M Q M M M 1,0,1,1 1, d 0 d 0 ex( j d) , 1 ex j 1, d Q1 0 ex( j1, d) 10 1 ex 1, j d Scattering from layered media 46
25 Scattering from a general layered medium This method involves the multilication of a lot of matrices if there are many layers There exist another technique which yields a simler, recurrent equation for the reflection coefficient Consider two adjacent layers, and B 1 ex j 1, A ex j 1 1, A ex j, B ex j, Scattering from layered media 47
26 Scattering from a general layered medium Imagine that somehow we now the ratio of the forward and bacward moving waves in the (+1)-th layer at r 1 B ex j 1 1, 1 A ex j 1 1, 1 1 eflection coefficient at 1 What can be said of this ratio in the -th at? 1 1 B 1 ex j 1, A ex j 1 1, A ex j, B ex j, Scattering from layered media 48
27 Scattering from a general layered medium Use the transfer matrix (or scattering matrix) ex j A 1, 1, 1, 1 ex j A M 11 M 1, 1, 1, ex j B M 1, 1 1 M ex j B, r B ex j, A ex j, One finds the recurrent relationshi r M r M ex j d 1, 1, , 1 1, 1, M ex j 1, d 1 M1 r 1 Scattering from layered media 49
28 Scattering from a general layered medium In terms of interface reflection arameters: r r ex j d 1, 1 1, 1 1, ex j 1, d 1 r 1 emember that for and TM scattering: 1,, 1,, 1, 1, TM 1, 1, 1, 1, But, what about the initial condition of this recurrent relation? Scattering from layered media 50
29 Scattering from a general layered medium There is no reflection in the tomost layer! Our initial condition is rn 1 0 The recurrent relation can then N 1 N r N be calculated all the way down to the overall reflection coefficient 1 r 1 r 0 0 r 0 Scattering from layered media 51
30
REFLECTION AND TRANSMISSION BAND STRUCTURES OF A ONE-DIMENSIONAL PERIODIC SYSTEM IN THE PRESENCE OF ABSORPTION
Armenian Journal of Physics, 0, vol. 4, issue,. 90-0 REFLECTIO AD TRASMISSIO BAD STRUCTURES OF A OE-DIMESIOAL PERIODIC SYSTEM I THE PRESECE OF ABSORPTIO A. Zh. Khachatrian State Engineering University
Focal Waveform of a Prolate-Spheroidal IRA
Sensor and Simulation Notes Note 59 February 6 Focal Waveform of a Prolate-Sheroidal IRA Carl E. Baum University of New Mexico Deartment of Electrical and Comuter Engineering Albuquerque New Mexico 873
Dispersion relation of surface plasmon wave propagating along a curved metal-dielectric interface
Disersion relation of surface lasmon wave roagating along a curved metal-dielectric interface Jiunn-Woei Liaw * and Po-Tsang Wu Deartment of Mechanical Engineering, Chang Gung University 59 Wen-Hwa 1 st
Lecture 2: Dispersion in Materials. 5 nm
Lecture : Disersion in Materials 5 nm What Haened in the Previous Lecture? Maxwell s Equations Bold face letters are vectors! B D = ρ f B = E = t Curl Equations lead to E P E = με + μ t t Linear, Homogeneous,
Uniformly best wavenumber approximations by spatial central difference operators: An initial investigation
Uniformly best wavenumber aroximations by satial central difference oerators: An initial investigation Vitor Linders and Jan Nordström Abstract A characterisation theorem for best uniform wavenumber aroximations
E p,rms = 240 V E rms = 120 V N p N s C. f = 60 Hz R = 3.8 L
Discussion Question 1A P1, Week 1 Power in AC Circuits An electronic device, consisting of a simle C circuit, is designed to be connected to an American-standard ower outlet delivering an EMF of 1 V at
School of Electrical and Computer Engineering, Cornell University. ECE 5330: Semiconductor Optoelectronics. Fall Due on Nov 20, 2014 by 5:00 PM
School of Electrical and Computer Engineering, Cornell University ECE 533: Semiconductor Optoelectronics Fall 14 Homewor 8 Due on Nov, 14 by 5: PM This is a long -wee homewor (start early). It will count
Solutions: Homework 7
Solutions: Homework 7 Ex. 7.1: Frustrated Total Internal Reflection a) Consider light propagating from a prism, with refraction index n, into air, with refraction index 1. We fix the angle of incidence
Lecture 9. Transmission and Reflection. Reflection at a Boundary. Specific Boundary. Reflection at a Boundary
Lecture 9 Reflection at a Boundary Transmission and Reflection A boundary is defined as a place where something is discontinuous Half the work is sorting out what is continuous and what is discontinuous
Round-off Errors and Computer Arithmetic - (1.2)
Round-off Errors and Comuter Arithmetic - (.). Round-off Errors: Round-off errors is roduced when a calculator or comuter is used to erform real number calculations. That is because the arithmetic erformed
Electromagnetic Waves
Electromagnetic Waves Maxwell s equations predict the propagation of electromagnetic energy away from time-varying sources (current and charge) in the form of waves. Consider a linear, homogeneous, isotropic
Today in Physics 218: stratified linear media I
Today in Physics 28: stratified linear media I Interference in layers of linear media Transmission and reflection in stratified linear media, viewed as a boundary-value problem Matrix formulation of the
Complex Analysis Homework 1
Comlex Analysis Homework 1 Steve Clanton Sarah Crimi January 27, 2009 Problem Claim. If two integers can be exressed as the sum of two squares, then so can their roduct. Proof. Call the two squares that
E( x ) [b(n) - a(n, m)x(m) ]
![E( x ) [b(n) - a(n, m)x(m) ]](/thumbs/86/93794049.jpg "E( x ) [b(n) - a(n, m)x(m) ]")
Homework #, EE5353. An XOR network has two inuts, one hidden unit, and one outut. It is fully connected. Gie the network's weights if the outut unit has a ste actiation and the hidden unit actiation is
The Arm Prime Factors Decomposition
The Arm Prime Factors Decomosition Arm Boris Nima arm.boris@gmail.com Abstract We introduce the Arm rime factors decomosition which is the equivalent of the Taylor formula for decomosition of integers
Higher order theory for analytic saddle point approximations to the Ρ Ρ and Ρ Ś reflected arrivals at a solid/solid interface
Higher order theory for analytic saddle oint aroximations to the Ρ Ρ and Ρ Ś reflected arrivals at a solid/solid interface P.F Daley ABSTACT The high frequency solution to the roblem of a Ρ P and Ρ S reflected
Pretest (Optional) Use as an additional pacing tool to guide instruction. August 21
Trimester 1 Pretest (Otional) Use as an additional acing tool to guide instruction. August 21 Beyond the Basic Facts In Trimester 1, Grade 8 focus on multilication. Daily Unit 1: Rational vs. Irrational
Supplementary Information for Negative refraction in semiconductor metamaterials
Supplementary Information for Negative refraction in semiconductor metamaterials A.J. Hoffman *, L. Alekseyev, S.S. Howard, K.J. Franz, D. Wasserman, V.A. Poldolskiy, E.E. Narimanov, D.L. Sivco, and C.
Lecture Outline. Scattering at an Interface Sunrises & Sunsets Rainbows Polarized Sunglasses 8/9/2018. EE 4347 Applied Electromagnetics.
Course Instructor Dr. Raymond C. Rumpf Office: A 337 Phone: (915) 747 6958 E Mail: rcrumpf@utep.edu EE 4347 Applied Electromagnetics Topic 3i Scattering at an Interface: Examples Examples These notes may
Today in Physics 218: stratified linear media II
Today in Physics 28: stratified linear media II Characteristic matrix formulation of reflected and transmitted fields and intensity Examples: Single interface Plane-parallel dielectric in vacuum Multiple
7.3 Problem 7.3. ~B(~x) = ~ k ~ E(~x)=! but we also have a reected wave. ~E(~x) = ~ E 2 e i~ k 2 ~x i!t. ~B R (~x) = ~ k R ~ E R (~x)=!
7. Problem 7. We hve two semi-innite slbs of dielectric mteril with nd equl indices of refrction n >, with n ir g (n ) of thickness d between them. Let the surfces be in the x; y lne, with the g being
I Poles & zeros. I First-order systems. I Second-order systems. I E ect of additional poles. I E ect of zeros. I E ect of nonlinearities
EE C28 / ME C34 Lecture Chater 4 Time Resonse Alexandre Bayen Deartment of Electrical Engineering & Comuter Science University of California Berkeley Lecture abstract Toics covered in this resentation
Lecture 2: Thin Films. Thin Films. Calculating Thin Film Stack Properties. Jones Matrices for Thin Film Stacks. Mueller Matrices for Thin Film Stacks
Lecture 2: Thin Films Outline Thin Films 2 Calculating Thin Film Stack Properties 3 Jones Matrices for Thin Film Stacks 4 Mueller Matrices for Thin Film Stacks 5 Mueller Matrix for Dielectrica 6 Mueller
MATH 2710: NOTES FOR ANALYSIS
MATH 270: NOTES FOR ANALYSIS The main ideas we will learn from analysis center around the idea of a limit. Limits occurs in several settings. We will start with finite limits of sequences, then cover infinite
βi β r medium 1 θ i θ r y θ t β t
W.C.Chew ECE 350 Lecture Notes Date:November 7, 997 0. Reections and Refractions of Plane Waves. Hr Ei Hi βi β r Er medium θ i θ r μ, ε y θ t μ, ε medium x z Ht β t Et Perpendicular Case (Transverse Electric
Fourier Series Tutorial
Fourier Series Tutorial INTRODUCTION This document is designed to overview the theory behind the Fourier series and its alications. It introduces the Fourier series and then demonstrates its use with a
NONRELATIVISTIC STRONG-FIELD APPROXIMATION (SFA)
NONRELATIVISTIC STRONG-FIELD APPROXIMATION (SFA) Note: SFA will automatically be taken to mean Coulomb gauge (relativistic or non-diole) or VG (nonrelativistic, diole-aroximation). If LG is intended (rarely),
3 December Lesson 5.5
Preparation Assignments for Homework #8 Due at the start of class. Reading Assignments Please see the handouts for each lesson for the reading assignments. 3 December Lesson 5.5 A uniform plane wave is
NUMERICAL AND THEORETICAL INVESTIGATIONS ON DETONATION- INERT CONFINEMENT INTERACTIONS
NUMERICAL AND THEORETICAL INVESTIGATIONS ON DETONATION- INERT CONFINEMENT INTERACTIONS Tariq D. Aslam and John B. Bdzil Los Alamos National Laboratory Los Alamos, NM 87545 hone: 1-55-667-1367, fax: 1-55-667-6372
Thickness and refractive index measurements using multiple beam interference fringes (FECO)
Journal of Colloid and Interface Science 264 2003 548 553 Note www.elsevier.com/locate/jcis Thickness and refractive index measurements using multile beam interference fringes FECO Rafael Tadmor, 1 Nianhuan
ME scope Application Note 16
ME scoe Alication Note 16 Integration & Differentiation of FFs and Mode Shaes NOTE: The stes used in this Alication Note can be dulicated using any Package that includes the VES-36 Advanced Signal Processing
Module 5 : Plane Waves at Media Interface. Lecture 36 : Reflection & Refraction from Dielectric Interface (Contd.) Objectives
Objectives In this course you will learn the following Reflection and Refraction with Parallel Polarization. Reflection and Refraction for Normal Incidence. Lossy Media Interface. Reflection and Refraction
Waveguide Principles
CHAPTER 8 Waveguide Principles In Chapter 6, we introduced transmission lines, and in Chapter 7, we studied their analysis. We learned that transmission lines are made up of two (or more) parallel conductors.
Module 5 : Plane Waves at Media Interface. Lecture 39 : Electro Magnetic Waves at Conducting Boundaries. Objectives
Objectives In this course you will learn the following Reflection from a Conducting Boundary. Normal Incidence at Conducting Boundary. Reflection from a Conducting Boundary Let us consider a dielectric
The Finite-Difference Time-Domain Method for Electromagnetics with MATLAB Simulations
The Finite-Difference Time-Domain Method for Electromagnetics with MATLAB Simulations Atef Z. Elsherbeni and Veysel Demir SciTech Publishing, Inc Raleigh, NC scitechpublishing.com Contents Preface Author
Solutions to Problems in Goldstein, Classical Mechanics, Second Edition. Chapter 9
Solutions to Problems in Goldstein, Classical Mechanics, Second Edition Homer Reid October 29, 2002 Chater 9 Problem 9. One of the attemts at combining the two sets of Hamilton s equations into one tries
CSE 599d - Quantum Computing When Quantum Computers Fall Apart
CSE 599d - Quantum Comuting When Quantum Comuters Fall Aart Dave Bacon Deartment of Comuter Science & Engineering, University of Washington In this lecture we are going to begin discussing what haens to
Multilayer Reflectivity
Multilayer Reflectivity John E. Davis jed@jedsoft.org January 5, 2014 1 Introduction The purpose of this document is to present an ab initio derivation of the reflectivity for a plane electromagnetic wave
Orthogonal Polynomial Ensembles
Chater 11 Orthogonal Polynomial Ensembles 11.1 Orthogonal Polynomials of Scalar rgument Let wx) be a weight function on a real interval, or the unit circle, or generally on some curve in the comlex lane.
Chapter 4 Reflection and Transmission of Waves
4-1 Chapter 4 Reflection and Transmission of Waves ECE 3317 Dr. Stuart Long www.bridgat.com www.ranamok.com Boundary Conditions 4- -The convention is that is the outward pointing normal at the boundary
Problem 8.0 Make Your Own Exam Problem for Midterm II by April 13
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science 6.007 Electromagnetic Energy: From Motors to Lasers Spring 2011 Problem Set 8: Electromagnetic Waves at Boundaries
All-fiber Optical Parametric Oscillator
All-fiber Otical Parametric Oscillator Chengao Wang Otical Science and Engineering, Deartment of Physics & Astronomy, University of New Mexico Albuquerque, NM 87131-0001, USA Abstract All-fiber otical
gap trans inc n=1 z Jackson 7.3 Homework Problem Solution Dr. Christopher S. Baird University of Massachusetts Lowell
Jackson 7.3 Homework Problem Solution Dr. Christopher S. Baird University of Massachusetts Lowell PROBLEM: Two plane semi-infinite slabs of the same uniform, isotropic, nonpermeable, lossless dielectric
ECE 604, Lecture 17. October 30, In this lecture, we will cover the following topics: Reflection and Transmission Single Interface Case
ECE 604, Lecture 17 October 30, 2018 In this lecture, we will cover the following topics: Duality Principle Reflection and Transmission Single Interface Case Interesting Physical Phenomena: Total Internal
Solutions to Problem Set 5
Solutions to Problem Set Problem 4.6. f () ( )( 4) For this simle rational function, we see immediately that the function has simle oles at the two indicated oints, and so we use equation (6.) to nd the
EXERCISES Practice and Problem Solving
EXERCISES Practice and Problem Solving For more ractice, see Extra Practice. A Practice by Examle Examles 1 and (ages 71 and 71) Write each measure in. Exress the answer in terms of π and as a decimal
E o e associated with a light field (both the real part and the. ikr t. under the assumptions that J free
Reiew Problems Chaters 1-5 True and False Questions E1. T or F: The otical index of any material aries with frequency. E2. T or F: The frequency of light can change as it enters a crystal. E3. T or F:
Lecture Outline. Scattering From a Dielectric Slab Anti Reflection Layer Bragg Gratings 8/9/2018. EE 4347 Applied Electromagnetics.
Course Instructor Dr. Raymond C. Rumpf Office: A 337 Phone: (95) 747 6958 E Mail: rcrumpf@utep.edu EE 4347 Applied Electromagnetics Topic 3k Multiple Scattering Multiple These Scattering notes may contain
3x3 transfer matrix modelling Matteo Cherchi, VTT Technical Research Centre of Finland
3x3 transfer matrix modelling Matteo Cherchi, VTT Technical esearch Centre of Finland Unlike common devices based on ring resonators, the structure in Fig..a involves not only 2x2 couplers but also a 3x3
Chap. 1 Fundamental Concepts
NE 2 Chap. 1 Fundamental Concepts Important Laws in Electromagnetics Coulomb s Law (1785) Gauss s Law (1839) Ampere s Law (1827) Ohm s Law (1827) Kirchhoff s Law (1845) Biot-Savart Law (1820) Faradays
Meshless Methods for Scientific Computing Final Project
Meshless Methods for Scientific Comuting Final Project D0051008 洪啟耀 Introduction Floating island becomes an imortant study in recent years, because the lands we can use are limit, so eole start thinking
Machine Learning: Homework 4
10-601 Machine Learning: Homework 4 Due 5.m. Monday, February 16, 2015 Instructions Late homework olicy: Homework is worth full credit if submitted before the due date, half credit during the next 48 hours,
Summary of Beam Optics
Summary of Beam Optics Gaussian beams, waves with limited spatial extension perpendicular to propagation direction, Gaussian beam is solution of paraxial Helmholtz equation, Gaussian beam has parabolic
Electromagnetic fields and waves
Electromagnetic fields and waves Maxwell s rainbow Outline Maxwell s equations Plane waves Pulses and group velocity Polarization of light Transmission and reflection at an interface Macroscopic Maxwell
mA Volt
etaile solution of IS 4 (C) Conventional Paer I Sol. (a) (i) Conuctivity is a egree to which a secifie material conucts electricity an gives iea how much smooth flow is of electricity by a carrier. Mobility
Klein Tunneling. PHYS 503 Physics Colloquium Fall /11
Klein Tunneling PHYS 503 Physics Colloquium Fall 2008 9/11 Deeak Rajut Graduate Research Assistant Center for Laser Alications University of Tennessee Sace Institute Email: drajut@utsi.edu Web: htt://drajut.com
Preliminary Topics in EM
ECE 53 1 st Century Electromagnetics Instructor: Office: Phone: E Mail: Dr. Raymond C. Rumpf A 337 (915) 747 6958 rcrumpf@utep.edu Lecture #1 Preliminary Topics in EM Lecture 1 1 Lecture Outline Maxwell
Waveguide Coupler I. Class: Integrated Photonic Devices Time: Fri. 8:00am ~ 11:00am. Classroom: 資電 206 Lecturer: Prof. 李明昌 (Ming-Chang Lee)
Waveguide Couler I Class: Integrated Photonic Devices Time: Fri. 8:am ~ 11:am. Classroom: 資電 6 Lecturer: Prof. 李明昌 (Ming-Chang Lee) Waveguide Couler n 1 > n n Waveguide 1 n 1 n Waveguide n 1 n How to switch
Montgomery self-imaging effect using computer-generated diffractive optical elements
Otics Communications 225 (2003) 13 17 www.elsevier.com/locate/otcom Montgomery self-imaging effect using comuter-generated diffractive otical elements J urgen Jahns a, *, Hans Knuertz a, Adolf W. Lohmann
Polarization of light
Laboratory#8 Phys4480/5480 Dr. Cristian Bahrim Polarization of light Light is a transverse electromagnetic wave (EM) which travels due to an electric field and a magnetic field oscillating in phase and
Lecture 15: Resonant Tunneling Diode. Operation Bi-stable switch Oscillator Fundamental Physics Application Example
Lecture 5: Resonant Tunneling Diode Oeration Bi-stable switch Oscillator Fundamental Physics Alication Examle --8 Lecture 5, High Seed Deices Resonant Tunneling Diode An RTD consists of two large bandga
Controllable Spatial Array of Bessel-like Beams with Independent Axial Intensity Distributions for Laser Microprocessing
JLMN-Journal of Laser Micro/Nanoengineering Vol. 3, No. 3, 08 Controllable Satial Array of Bessel-like Beams with Indeendent Axial Intensity Distributions for Laser Microrocessing Sergej Orlov, Alfonsas
Notes on Instrumental Variables Methods
Notes on Instrumental Variables Methods Michele Pellizzari IGIER-Bocconi, IZA and frdb 1 The Instrumental Variable Estimator Instrumental variable estimation is the classical solution to the roblem of
Electromagnetic Waves Across Interfaces
Lecture 1: Foundations of Optics Outline 1 Electromagnetic Waves 2 Material Properties 3 Electromagnetic Waves Across Interfaces 4 Fresnel Equations 5 Brewster Angle 6 Total Internal Reflection Christoph
Supplementary Figure 1. Schematics of light transmission and reflection from a slab confined between
Supplementary Figures: Supplementary Figure. Schematics of light transmission and reflection from a slab confined between two infinite media. Supplementary Figure. Reflectivity of a magneto-electric slab
Notes on pressure coordinates Robert Lindsay Korty October 1, 2002
Notes on ressure coordinates Robert Lindsay Korty October 1, 2002 Obviously, it makes no difference whether the quasi-geostrohic equations are hrased in height coordinates (where x, y,, t are the indeendent
1 The formation and analysis of optical waveguides
1 The formation and analysis of optical waveguides 1.1 Introduction to optical waveguides Optical waveguides are made from material structures that have a core region which has a higher index of refraction
UNIT I ELECTROSTATIC FIELDS
UNIT I ELECTROSTATIC FIELDS 1) Define electric potential and potential difference. 2) Name few applications of gauss law in electrostatics. 3) State point form of Ohm s Law. 4) State Divergence Theorem.
Today in Physics 218: Fresnel s equations
Today in Physics 8: Fresnel s equations Transmission and reflection with E parallel to the incidence plane The Fresnel equations Total internal reflection Polarization on reflection nterference R 08 06
Trigonometric Identities
Trigonometric Identities An identity is an equation that is satis ed by all the values of the variable(s) in the equation. We have already introduced the following: (a) tan x (b) sec x (c) csc x (d) cot
Pulse Propagation in Optical Fibers using the Moment Method
Pulse Proagation in Otical Fibers using the Moment Method Bruno Miguel Viçoso Gonçalves das Mercês, Instituto Suerior Técnico Abstract The scoe of this aer is to use the semianalytic technique of the Moment
Phase velocity and group velocity (c) Zhengqing Yun,
Phase velocity and grou velocity (c) Zhengqing Yun, 2011-2012 Objective: Observe the difference between hase and grou velocity; understand that the grou velocity can be less than, equal to, and greater
N M O 0 1 Q P. (26.2)
Astronomy 03/403, all 999 6 Lecture, December 999 6 A single vacuum-dielectric interface Practical optical systems always involve lots of vacuum-dielectric interfaces, so we should use the formalism above
Predicting the constitutive behaviour of microsphere-filled elastomers: the influence of shell buckling and interaction
Predicting the constitutive behaviour of microshere-filled elastomers: the influence of shell buckling and interaction William J. Parnell Professor of Alied Mathematics and EPSRC Research Fellow School
8.7 Associated and Non-associated Flow Rules
8.7 Associated and Non-associated Flow Rules Recall the Levy-Mises flow rule, Eqn. 8.4., d ds (8.7.) The lastic multilier can be determined from the hardening rule. Given the hardening rule one can more
22.615, MHD Theory of Fusion Systems Prof. Freidberg Lecture 13: PF Design II The Coil Solver
.615, MHD Theory of Fusion Systems Prof. Freidberg Lecture 13: PF Design II The Coil Solver Introduction 1. Let us assume that we have successfully solved the Grad Shafranov equation for a fixed boundary
NEGATIVE REFRACTION BY A TWO-SIDED MUSHROOM STRUCTURE WITH LOADED VIAS
NEGATIVE REFRACTION BY A TWO-SIDED MUSHROOM STRUCTURE WITH LOADED VIAS Candra S. R. Kaipa, Alexander B. Yaovlev Mário G. Silveirina, and Stanislav I. Maslovsi Metamaterials : Te Fift International Congress
PROFIT MAXIMIZATION. π = p y Σ n i=1 w i x i (2)
PROFIT MAXIMIZATION DEFINITION OF A NEOCLASSICAL FIRM A neoclassical firm is an organization that controls the transformation of inuts (resources it owns or urchases into oututs or roducts (valued roducts
Highly improved convergence of the coupled-wave method for TM polarization
. Lalanne and G. M. Morris Vol. 13, No. 4/Aril 1996/J. Ot. Soc. Am. A 779 Highly imroved convergence of the couled-wave method for TM olarization hilie Lalanne Institut d Otique Théorique et Aliquée, Centre
Polarization of light: Malus law, the Fresnel equations, and optical activity.
Polarization of light: Malus law, the Fresnel equations, and otical activity. PHYS 3330: Exeriments in Otics Deartment of Physics and Astronomy, University of Georgia, Athens, Georgia 30602 (Dated: Revised
Visualizing Free and Forced Harmonic Oscillations using Maple V R5*
Int. J. Engng Ed. Vol. 15, No. 6,. 437±455, 1999 0949-149X/91 $3.00+0.00 Printed in Great Britain. # 1999 TEMPUS Publications. Visualizing Free and Forced Harmonic Oscillations using Male V R5* HARALD
LECTURE 3 BASIC QUANTUM THEORY
LECTURE 3 BASIC QUANTUM THEORY Matter waves and the wave function In 194 De Broglie roosed that all matter has a wavelength and exhibits wave like behavior. He roosed that the wavelength of a article of
Wave Propagation in Uniaxial Media. Reflection and Transmission at Interfaces
Lecture 5: Crystal Optics Outline 1 Homogeneous, Anisotropic Media 2 Crystals 3 Plane Waves in Anisotropic Media 4 Wave Propagation in Uniaxial Media 5 Reflection and Transmission at Interfaces Christoph
Onset of Jet decoherence in dense QCD media
Onset of Jet decoherence in dense QCD media Yacine Mehtar-Tani In collaboration with Carlos A. Salgado and Konrad Tywoniuk PRL 106 (2011) arxiv:1009.2965 [he-h] arxiv:1102.4317 [he-h] Y. M.-T. and K. Tywoniuk,
Calculating Thin Film Stack Properties. Polarization Properties of Thin Films
Lecture 6: Thin Films Outline 1 Thin Films 2 Calculating Thin Film Stack Properties 3 Polarization Properties of Thin Films 4 Anti-Reflection Coatings 5 Interference Filters Christoph U. Keller, Utrecht
EE 205 Dr. A. Zidouri. Electric Circuits II. Two-Port Circuits Two-Port Parameters. Lecture #42
EE 05 Dr. A. Zidouri Electric Circuits Two-Port Circuits Two-Port Parameters Lecture #4-1 - EE 05 Dr. A. Zidouri The material to be covered in this lecture is as follows: o ntroduction to two-port circuits
THE IMPACT OF ELEVATED MASTS ON LIGHTNING INCIDENCE AT THE RADIO-BASE-STATION VICINITIES
X International Symosium on Lihtnin Protection 9 th -13 th November, 9 Curitiba, Brazil THE IMPACT OF ELEVATED MASTS ON LIGHTNING INCIDENCE AT THE RADIO-BASE-STATION VICINITIES Rosilene Nietzsch Dias 1,
PHYS 301 HOMEWORK #9-- SOLUTIONS
PHYS 0 HOMEWORK #9-- SOLUTIONS. We are asked to use Dirichlet' s theorem to determine the value of f (x) as defined below at x = 0, ± /, ± f(x) = 0, - < x
The asymmetric lossy near-perfect lens
journal of modern otics, 2002, vol. 49, no. 10, 1747 1762 The asymmetric lossy near-erfect lens S. ANANTHA RAMAKRISHNA, J. B. PENDRY The Blackett Laboratory, Imerial College, London SW7 2BZ, UK; e-mails:
Diode laser emission
Lecture 9/1 Diode laser emission x Diode laser emission has oblong cross-section. Y-axis with large divergence angle is called fast axis X-axis with smaller divergence angle is called slow axis Lecture
SCATTERING OF ELECTROMAGNETIC WAVES ON METAL NANOPARTICLES. Tomáš Váry, Juraj Chlpík, Peter Markoš
SCATTERING OF ELECTROMAGNETIC WAVES ON METAL NANOPARTICLES Tomáš Váry, Juraj Chlpík, Peter Markoš ÚJFI, FEI STU, Bratislava E-mail: tomas.vary@stuba.sk Received xx April 2012; accepted xx May 2012. 1.
Chapter 2 Arithmetic Functions and Dirichlet Series.
Chater 2 Arithmetic Functions and Dirichlet Series. [4 lectures] Definition 2.1 An arithmetic function is any function f : N C. Examles 1) The divisor function d (n) (often denoted τ (n)) is the number
26 Standing waves, radiation pressure
26 Standing waves, radiation pressure We continue in this lecture with our studies of wave reflection and transmission at a plane boundary between two homogeneous media. In case of total reflection from
Edward S. Rogers Sr. Department of Electrical and Computer Engineering. ECE318S Fundamentals of Optics. Final Exam. April 16, 2007.
Edward S. Rogers Sr. Department of Electrical and Computer Engineering ECE318S Fundamentals of Optics Final Exam April 16, 2007 Exam Type: D (Close-book + two double-sided aid sheets + a non-programmable
Analytic Solutions for Periodically Loaded Transmission Line Modeling
Analytic Solutions for Periodically Loaded Transmission Line Modeling Paul G. Huray, huray@sc.edu Priya Pathmanathan, Intel priyap@qti.qualcomm.com Steve Pytel, Intel steve.pytel@ansys.com April 4, 2014
3.1 The Plane Mirror Resonator 3.2 The Spherical Mirror Resonator 3.3 Gaussian modes and resonance frequencies 3.4 The Unstable Resonator
Quantum Electronics Laser Physics Chapter 3 The Optical Resonator 3.1 The Plane Mirror Resonator 3. The Spherical Mirror Resonator 3.3 Gaussian modes and resonance frequencies 3.4 The Unstable Resonator
Metamaterials. Peter Hertel. University of Osnabrück, Germany. Lecture presented at APS, Nankai University, China
University of Osnabrück, Germany Lecture presented at APS, Nankai University, China http://www.home.uni-osnabrueck.de/phertel Spring 2012 are produced artificially with strange optical properties for instance
Optimal Recognition Algorithm for Cameras of Lasers Evanescent
Otimal Recognition Algorithm for Cameras of Lasers Evanescent T. Gaudo * Abstract An algorithm based on the Bayesian aroach to detect and recognise off-axis ulse laser beams roagating in the atmoshere
Principles of Computed Tomography (CT)
Page 298 Princiles of Comuted Tomograhy (CT) The theoretical foundation of CT dates back to Johann Radon, a mathematician from Vienna who derived a method in 1907 for rojecting a 2-D object along arallel
REFLECTION AND REFRACTION AT A SINGLE INTERFACE
REFLECTION AND REFRACTION AT A SINGLE INTERFACE 5.1 THE BEHAVIOUR OF LIGHT AT A DIELECTRIC INTERFACE The previous Chapters have been concerned with the propagation of waves in empty space or in uniform,