N M O 0 1 Q P. (26.2)
|
|
- Doris Dawson
- 6 years ago
- Views:
Transcription
1 Astronomy 03/403, all Lecture, December A single vacuum-dielectric interface Practical optical systems always involve lots of vacuum-dielectric interfaces, so we should use the formalism above to obtain the relevant amplitude transmission reflection coefficients his can be done easily with Equations by taking medium zero to be vacuum medium to be a dielectric with index n, so that ε Y0, E Y, E µ ε Y0, M Y, M µ (6) (where are related by Snell s law), by taking medium to have zero thickness, so that the characteristic matrix is simply the unit matrix: L 0 M N M O 0 Q P (6) hen for E waves the amplitude transmission reflection coefficients are Y t 0 E Y0 + Y ε + µ (63) Y0 Y re Y0 + Y + ε µ ε µ, (64) while for M waves we get Y0 tm Y0 + Y ε + µ (65) Y Y rm 0 Y0 + Y + ε µ ε µ (66) or normal incidence on nonmagnetic bµ g materials these pairs of equations both reduce to 999 University of Rochester All rights reserved
2 Astronomy 03/403, all 999 t + n n r + n (67) (68) Among other things these expressions imply a limitation to the quantum efficiency of semiconductor detectors when their bare surfaces are illuminated normally, since in this case the quantum efficiency can be no larger than the (power) transmission of the front surface: some of the incident power is reflected n the argot of optics this is called a reflection loss Most detector semiconductors have rather high index for instance, n respectively for silicon germanium, for which the maximum quantum efficiency for bare surfaces is Y η Y t 0 4n + n a f (69) Reflection losses can be reduced or eliminated altogether by using thin dielectric layers as antireflection coatings, as you will find in this week s homework (problem ) 6 he abry-perot interferometer Let us return to the plane-parallel dielectric slab of igure 5, for we are now in a position to calculate the spectrum of its transmission easily or simplicity we assume that the medium is nonmagnetic surrounded by vacuum, that light is incident normally; then Y Y ε cos θ n (60) E M πnd πnd κ cos θ, (6) so the characteristic matrix of the slab is M L NM cosκ isin κ / Y iy sinκ cosκ O L QP N M πnd i πnd cos sin n πnd πnd insin cos O Q P (6) Of course Y for the media on either side of the slab, so the amplitude transmission coefficient, given by Equation 58, is t m + m + m + m πnd πnd cos i n+ nk J sin, (63) the (power) transmission is the square modulus of t times the ratio of Ys ( in this case), or 999 University of Rochester All rights reserved
3 Astronomy 03/403, all 999 τ tt* πnd πnd πnd π + K J nd cos i n sin cos + i n+ K J sin n n 4 πnd πnd π + + K J L + M + K J O nd 4cos n sin n 4 n n Psin 4 + L N M n + n KJ O Q P πnd sin + NM n πnd sin n KJ QP (64) his function has the expected series of transmission maxima: τ whenever the sine term vanishes, which takes place whenever the argument of the sine is an integer multiple of π: πdnt a f (65) πm m 0,,,, which is identical to Equation 54 he dielectric slab is more useful as a filter or a spectrometer if the surfaces are more reflective than the bare dielectric we just considered Note that the bare surface has a power reflectance given from Equation 68 by r n n + K J, (66) so that r a f a f a f a f n+ + n 4n n + n +, (67) r r n n + a f (68) n + n 4n n We can put this in Equation 68 to obtain τ + r r πnd sin K J (69) Note that the interference is determined by the phase lags from path lengths through the slab, which do not depend upon the values of reflectivity at the surfaces hus Equation 69 is more general than Equation 64, because the surface reflectivity can be independent of the refractive index: for example, by coating it with a reflective metal or dielectric film t is often written as 999 University of Rochester 3 All rights reserved
4 Astronomy 03/403, all 999 τ + sin φ, (60) where φ 4πnd / κnd, where r r K J (6) is called the coefficient of finesse he width of the transmission maxima varies with, larger values leading to narrower peaks he function in Equation 60 is called the Airy function, again in honor of the former Astronomer Royal of Engl ( not to be confused with the Airy disk, or the other Airy function, the latter describing the supernumerary arcs of a rainbow) t is plotted in igure 6 ransmission, τ r 005 r φ / r 095 igure 6: the Airy function, the transmission of the abry-perot interferometer t is of course possible to perform this derivation for obliquely-incident waves, but not as quickly as this, so we will just give the answer: it turns out that the only change necessary is in the argument of the sine in the denominator of Equation 60 (cf Equation 54) 4πnd φ κnd cos θ (6) 63 abry-perot spectrometers or large values of the coefficient of finesse, the transmission between peaks is very small, which suggests that isolating a single peak is a good way to make a narrow-b (high-resolution) filter urthermore, if the reflecting surfaces are placed on independently movable substrates, with a non-solid dielectric 999 University of Rochester 4 All rights reserved
5 Astronomy 03/403, all 999 medium in between, the wavelength at which the peak occurs is tunable his is the basis of the abry- Perot spectrometer, a class of astronomical instruments that is good for observation of images of astronomical objects in spectral-line light Let s compute the resolution of such a filter by calculating the wavelength interval corresponding to the half-peak-transmission points n terms of φ, these are found by setting φ/ + sin, (63) φ / or sin ± (64) f the peaks are very narrow (that is, if is large), φ is very close to πm, the small-angle approximation may be used: φ / ± (65) b g he relation between a small interval of φ a small interval of wavelength, δ φ δ, is thus governed by b g δ φ b g d d 4πnd π θ φδ δ H G 4 nd cos K J d d φ δ πm δ, δ (66) so from which we get δ φ π δ / d / i± m, (67) WHM δ/ + δ/ (68) πm mq Here we have defined the finesse of the abry-perot interferometer, Q π / n these terms the (reflectance-limited) spectral resolution of the interferometer is K J WHM, r 999 University of Rochester 5 All rights reserved mq (69) Note that the spectral resolution gets smaller (improves, in the spectroscopic sense) if the finesse Q or the order number m increases he isolation of a high-order peak of the Airy function is illustrated in igure 6 f one is interested in observations at a certain wavelength 0, say because there is a spectral line there, one can use one abry- Perot set in a low order there, in series with a higher-order one A wide-b filter of the type discussed in
6 Astronomy 03/403, all can be used to reject the higher orders of the low-order abry-perot; this interferometer, if narrow enough, rejects all but one order of the high-order abry-perot he abry-perot orders can be tuned by adjustment of d (or n) to scan the detector s response across the spectral line An example of this concept is explored in extra-credit Problem #7 in this week s homework High-order abry-perot interferometer ransmission Low-order abry-perot interferometer Long-wavelength-pass broadb filter Scan System (product of three above) 0 Wavelength igure 6: ransmission of a tem abry-perot spectrometer Because φ depends upon, reflectance isn t the only thing that can limit the resolution n Problem 4 of this week s homework, you will show that is a abry-perot is used in a diverging or converging beam of angular radius θ, the resolution can be no better than K J WHM, θ o keep beam divergence or convergence from spreading the beam unnecessarily, we want or b θ K J << θ H G K J WHM, WHM, r θ (630), (63) << mq (63) or high resolution / >000g, this usually means that the high-order abry-perot needs to be illuminated with a collimated beam, in order to keep θ as small as possible 999 University of Rochester 6 All rights reserved
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
More informationToday 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
More informationCalculating Thin Film Stack Properties
Lecture 5: Thin Films Outline 1 Thin Films 2 Calculating Thin Film Stack Properties 3 Fabry-Perot Tunable Filter 4 Anti-Reflection Coatings 5 Interference Filters Christoph U. Keller, Leiden University,
More informationCalculating 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
More informationAstronomy 203 practice final examination
Astronomy 203 practice final examination Fall 1999 If this were a real, in-class examination, you would be reminded here of the exam rules, which are as follows: You may consult only one page of formulas
More informationSpeed of Light in Glass
Experiment (1) Speed of Light in Glass Objective:- This experiment is used to determine the speed of propagation of light waves in glass. Apparatus:- Prism, spectrometer, Halogen lamp source. Theory:-
More informationLecture 7: Optical Spectroscopy. Astrophysical Spectroscopy. Broadband Filters. Fabry-Perot Filters. Interference Filters. Prism Spectrograph
Lecture 7: Optical Spectroscopy Outline 1 Astrophysical Spectroscopy 2 Broadband Filters 3 Fabry-Perot Filters 4 Interference Filters 5 Prism Spectrograph 6 Grating Spectrograph 7 Fourier Transform Spectrometer
More informationSome Topics in Optics
Some Topics in Optics The HeNe LASER The index of refraction and dispersion Interference The Michelson Interferometer Diffraction Wavemeter Fabry-Pérot Etalon and Interferometer The Helium Neon LASER A
More informationLecture 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
More informationToday 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
More informationLecture 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
More informationChapter 35. Interference
Chapter 35 Interference The concept of optical interference is critical to understanding many natural phenomena, ranging from color shifting in butterfly wings to intensity patterns formed by small apertures.
More informationSeptember 14, Monday 4. Tools for Solar Observations-II
September 14, Monday 4. Tools for Solar Observations-II Spectrographs. Measurements of the line shift. Spectrograph Most solar spectrographs use reflection gratings. a(sinα+sinβ) grating constant Blazed
More informationDiffraction gratings. B.Tech-I
Diffraction gratings B.Tech-I Introduction Diffraction grating can be understood as an optical unit that separates polychromatic light into constant monochromatic composition. Uses are tabulated below
More informationSCI. Scientific Computing International. Scientific Computing International. FilmTek. Raising Thin Film Metrology Performance to a New Level
FilmTek Raising Thin Film Metrology Performance to a New Level 1 Through Silicon Via (TSV) Metrology FilmTek TM TM TSV TSV Metrology Advantages Measure high aspect ratio TSV structures (up to 30:1) Measure
More informationPH 222-3A Spring 2010
PH -3A Spring 010 Interference Lecture 6-7 Chapter 35 (Halliday/Resnick/Walker, Fundamentals of Physics 8 th edition) 1 Chapter 35 Interference The concept of optical interference is critical to understanding
More informationOverview: Astronomical Spectroscopy
Overview: Astronomical Spectroscopy or How to Start Thinking Creatively about Measuring the Universe Basic Spectrograph Optics Objective Prism Spectrometers - AESoP Slit Spectrometers Spectrometers for
More informationSolutions: 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
More informationand the radiation from source 2 has the form. The vector r points from the origin to the point P. What will the net electric field be at point P?
Physics 3 Interference and Interferometry Page 1 of 6 Interference Imagine that we have two or more waves that interact at a single point. At that point, we are concerned with the interaction of those
More information34. Even more Interference Effects
34. Even more Interference Effects The Fabry-Perot interferometer Thin-film interference Anti-reflection coatings Single- and multi-layer Advanced topic: Photonic crystals Natural and artificial periodic
More informationOPTICAL Optical properties of multilayer systems by computer modeling
Workshop on "Physics for Renewable Energy" October 17-29, 2005 301/1679-15 "Optical Properties of Multilayer Systems by Computer Modeling" E. Centurioni CNR/IMM AREA Science Park - Bologna Italy OPTICAL
More informationWhere are the Fringes? (in a real system) Div. of Amplitude - Wedged Plates. Fringe Localisation Double Slit. Fringe Localisation Grating
Where are the Fringes? (in a real system) Fringe Localisation Double Slit spatial modulation transverse fringes? everywhere or well localised? affected by source properties: coherence, extension Plane
More informationPhys 531 Lecture 27 6 December 2005
Phys 531 Lecture 27 6 December 2005 Final Review Last time: introduction to quantum field theory Like QM, but field is quantum variable rather than x, p for particle Understand photons, noise, weird quantum
More informationUltra-narrow-band tunable laserline notch filter
Appl Phys B (2009) 95: 597 601 DOI 10.1007/s00340-009-3447-6 Ultra-narrow-band tunable laserline notch filter C. Moser F. Havermeyer Received: 5 December 2008 / Revised version: 2 February 2009 / Published
More informationδ(y 2an) t 1 (x y)dy, that is multiplied by the global aperture function of the size of the grating H(x) = 1 x < Na = 0 x > Na.
10 Spectroscopy Practical telescopes are usually based upon one or other of two quite separate optical principles interference and differential refraction. In reality, the author has never seen a prism
More informationCourse 2: Basic Technologies
Course 2: Basic Technologies Part II: X-ray optics What do you see here? Seite 2 wavefront distortion http://www.hyperiontelescopes.com/performance12.php http://astronomy.jawaid1.com/articles/spherical%20ab
More informationChapter 35 Diffraction and Polarization. Copyright 2009 Pearson Education, Inc.
Chapter 35 Diffraction and Polarization 35-1 Diffraction by a Single Slit or Disk If light is a wave, it will diffract around a single slit or obstacle. 35-1 Diffraction by a Single Slit or Disk The resulting
More informationPhys102 Lecture Diffraction of Light
Phys102 Lecture 31-33 Diffraction of Light Key Points Diffraction by a Single Slit Diffraction in the Double-Slit Experiment Limits of Resolution Diffraction Grating and Spectroscopy Polarization References
More informationLecture 6 Scattering theory Partial Wave Analysis. SS2011: Introduction to Nuclear and Particle Physics, Part 2 2
Lecture 6 Scattering theory Partial Wave Analysis SS2011: Introduction to Nuclear and Particle Physics, Part 2 2 1 The Born approximation for the differential cross section is valid if the interaction
More informationChapter 35 Diffraction and Polarization
Chapter 35 Diffraction and Polarization If light is a wave, it will diffract around a single slit or obstacle. The resulting pattern of light and dark stripes is called a diffraction pattern. This pattern
More information3 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
More informationEdward 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
More informationCHAPTER 6 INTRODUCTION TO SPECTROPHOTOMETRIC METHODS Interaction of Radiation With Matter
CHAPTER 6 INTRODUCTION TO SPECTROPHOTOMETRIC METHODS Interaction of Radiation With Matter 1 Announcements Add to your notes of Chapter 1 Analytical sensitivity γ=m/s s Homework Problems 1-9, 1-10 Challenge
More informationCHAPTER 6 INTRODUCTION TO SPECTROPHOTOMETRIC METHODS Interaction of Radiation With Matter
CHAPTER 6 INTRODUCTION TO SPECTROPHOTOMETRIC METHODS Interaction of Radiation With Matter Announcements Add to your notes of Chapter 1 Analytical sensitivity γ=m/s s Homework Problems 1-9, 1-10 Challenge
More informationChemistry Instrumental Analysis Lecture 2. Chem 4631
Chemistry 4631 Instrumental Analysis Lecture 2 Electromagnetic Radiation Can be described by means of a classical sinusoidal wave model. Oscillating electric and magnetic field. (Wave model) wavelength,
More informationElectromagnetic 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
More informationLecture 20 Optical Characterization 2
Lecture 20 Optical Characterization 2 Schroder: Chapters 2, 7, 10 1/68 Announcements Homework 5/6: Is online now. Due Wednesday May 30th at 10:00am. I will return it the following Wednesday (6 th June).
More informationProblem 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
More informationPhysical Optics 2018 Dr. Muwafaq Fadhil Al-Mishlab Third lecture [ Huygens Principle, Interference of light]
Physical Optics 2018 Dr. Muwafaq Fadhil Al-Mishlab Third lecture [ Huygens Principle, Interference of light] 1. Huygens principle Long before people understood the electromagnetic character of light, Christian
More informationProblem Set 5: Solutions
University of Alabama Department of Physics and Astronomy Department of Electrical and Computer Engineering PH 495/ECE 493 LeClair & Kung Spring 011 Problem Set 5: Solutions 1. Bekefi & Barrett 8.; Hecht
More informationLC circuit: Energy stored. This lecture reviews some but not all of the material that will be on the final exam that covers in Chapters
Disclaimer: Chapter 29 Alternating-Current Circuits (1) This lecture reviews some but not all of the material that will be on the final exam that covers in Chapters 29-33. LC circuit: Energy stored LC
More informationSupplementary 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
More informationLight as a Transverse Wave.
Waves and Superposition (Keating Chapter 21) The ray model for light (i.e. light travels in straight lines) can be used to explain a lot of phenomena (like basic object and image formation and even aberrations)
More informationFabry-Perot Interferometers
Fabry-Perot Interferometers Astronomy 6525 Literature: C.R. Kitchin, Astrophysical Techniques Born & Wolf, Principles of Optics Theory: 1 Fabry-Perots are best thought of as resonant cavities formed between
More informationChapter 3. Design for manufacture of Fabry-Perot cavity sensors
Chapter 3 Design for manufacture of Fabry-Perot cavity sensors When Fabry-Perot cavity sensors are manufactured, the thickness of each layer must be tightly controlled to achieve the target performance
More informationRefractive Index Measurement by Gain- or Loss-Induced Resonance
Refractive Index Measurement by Gain- or Loss-Induced Resonance 59 Refractive Index Measurement by Gain- or Loss-Induced Resonance Markus Miller Using a semiconductor optical resonator consisting of a
More informationThe science of light. P. Ewart
The science of light P. Ewart Oxford Physics: Second Year, Optics Parallel reflecting surfaces t images source Extended source path difference xcos 2t=x Fringes localized at infinity Circular fringe constant
More informationDesign of Attenuated Phase-shift shift Mask with ITO Absorber for Extreme Ultraviolet Lithography
MA-P18 7 EUVL Symposium Design of Attenuated Phase-shift shift Mask with Absorber for Extreme Ultraviolet Lithography Hee Young Kang and Chang Kwon Hwangbo Department of Physics, Inha University, Incheon
More informationEngineering Physics 1 Prof. G.D. Vermaa Department of Physics Indian Institute of Technology-Roorkee
Engineering Physics 1 Prof. G.D. Vermaa Department of Physics Indian Institute of Technology-Roorkee Module-04 Lecture-02 Diffraction Part - 02 In the previous lecture I discussed single slit and double
More informationLECTURE 23: LIGHT. Propagation of Light Huygen s Principle
LECTURE 23: LIGHT Propagation of Light Reflection & Refraction Internal Reflection Propagation of Light Huygen s Principle Each point on a primary wavefront serves as the source of spherical secondary
More informationSwing Curves. T h e L i t h o g r a p h y T u t o r (Summer 1994) Chris A. Mack, FINLE Technologies, Austin, Texas
T h e L i t h o g r a p h y T u t o r (Summer 1994) Swing Curves Chris A. Mack, FINLE Technologies, Austin, Texas In the last edition of this column, we saw that exposing a photoresist involves the propagation
More informationOPSE FINAL EXAM Fall 2016 YOU MUST SHOW YOUR WORK. ANSWERS THAT ARE NOT JUSTIFIED WILL BE GIVEN ZERO CREDIT.
CLOSED BOOK. Equation Sheet is provided. YOU MUST SHOW YOUR WORK. ANSWERS THAT ARE NOT JUSTIFIED WILL BE GIVEN ZERO CREDIT. ALL NUMERICAL ANSERS MUST HAVE UNITS INDICATED. (Except dimensionless units like
More informationThese notes may contain copyrighted material! They are for your own use only during this course.
Licensed for Personal Use Only DO NOT DISTRIBUTE These notes may contain copyrighted material! They are for your own use only during this course. Distributing them in anyway will be considered a breach
More informationTA/TI survey. Phy Phy
TA/TI survey https://webapps.pas.rochester.edu/secure/phpq/ Phy121 7 60 73 Phy123 1 6 11 Chapter 34 The Wave Nature of Light; Interference Units of Chapter 34 34-5 Interference in Thin Films 34-6 Michelson
More information1. Waves and Particles 2. Interference of Waves 3. Wave Nature of Light
1. Waves and Particles 2. Interference of Waves 3. Wave Nature of Light 1. Double-Slit Eperiment reading: Chapter 22 2. Single-Slit Diffraction reading: Chapter 22 3. Diffraction Grating reading: Chapter
More informationWeek 7: Interference
Week 7: Interference Superposition: Till now we have mostly discusssed single waves. While discussing group velocity we did talk briefly about superposing more than one wave. We will now focus on superposition
More informationElectricity & Optics
Physics 24100 Electricity & Optics Lecture 26 Chapter 33 sec. 1-4 Fall 2017 Semester Professor Koltick Interference of Light Interference phenomena are a consequence of the wave-like nature of light Electric
More informationChapter 10. Interference of Light
Chapter 10. Interference of Light Last Lecture Wave equations Maxwell equations and EM waves Superposition of waves This Lecture Two-Beam Interference Young s Double Slit Experiment Virtual Sources Newton
More informationFabry-Perot Measurement of Aeronomic Winds and Temperatures
FPI T 2014 Introduction section Page: 1 Fabry-Perot Measurement of Aeronomic Winds and Temperatures Mark Conde University of Alaska Fairbanks This talk is a tutorial on the technique of using Fabry-Perot
More informationMIDTERM 3 REVIEW SESSION. Dr. Flera Rizatdinova
MIDTERM 3 REVIEW SESSION Dr. Flera Rizatdinova Summary of Chapter 23 Index of refraction: Angle of reflection equals angle of incidence Plane mirror: image is virtual, upright, and the same size as the
More informationAstr 2310 Thurs. March 3, 2016 Today s Topics
Astr 2310 Thurs. March 3, 2016 Today s Topics Chapter 6: Telescopes and Detectors Optical Telescopes Simple Optics and Image Formation Resolution and Magnification Invisible Astronomy Ground-based Radio
More informationPOLARIZATION OF LIGHT
POLARIZATION OF LIGHT OVERALL GOALS The Polarization of Light lab strongly emphasizes connecting mathematical formalism with measurable results. It is not your job to understand every aspect of the theory,
More informationInterference. Part-2. Gambar: Museum Victoria Australia
Interference Part-2 Gambar: Museum Victoria Australia Amplitude Splitting Interferometer S 2. Michelson Interferometer The principle: amplitude splitting d HM D F B M1 Detector C M1 E Interference at F
More information1. Consider the biconvex thick lens shown in the figure below, made from transparent material with index n and thickness L.
Optical Science and Engineering 2013 Advanced Optics Exam Answer all questions. Begin each question on a new blank page. Put your banner ID at the top of each page. Please staple all pages for each individual
More informationMIDTERM 3 REVIEW SESSION. Dr. Flera Rizatdinova
MIDTERM 3 REVIEW SESSION Dr. Flera Rizatdinova Summary of Chapter 23 Index of refraction: Angle of reflection equals angle of incidence Plane mirror: image is virtual, upright, and the same size as the
More informationElectrodynamics Qualifier Examination
Electrodynamics Qualifier Examination August 15, 2007 General Instructions: In all cases, be sure to state your system of units. Show all your work, write only on one side of the designated paper, and
More informationSupporting information. Unidirectional Doubly Enhanced MoS 2 Emission via
Supporting information Unidirectional Doubly Enhanced MoS 2 Emission via Photonic Fano Resonances Xingwang Zhang, Shinhyuk Choi, Dake Wang, Carl H. Naylor, A. T. Charlie Johnson, and Ertugrul Cubukcu,,*
More informationFringe shifts in multiple-beam Fizeau interferometry
638 J. Opt. Soc. Am./Vol. 72, No. 5/May 1982 Fringe shifts in multiple-beam Fizeau interferometry Optical Sciences Center, University of Arizona, Tucson, Arizona 85721 Received August 7,1981; revised manuscript
More informationLecture 11: Introduction to diffraction of light
Lecture 11: Introduction to diffraction of light Diffraction of waves in everyday life and applications Diffraction in everyday life Diffraction in applications Spectroscopy: physics, chemistry, medicine,
More informationLecture PowerPoints. Chapter 24 Physics: Principles with Applications, 7 th edition Giancoli
Lecture PowerPoints Chapter 24 Physics: Principles with Applications, 7 th edition Giancoli This work is protected by United States copyright laws and is provided solely for the use of instructors in teaching
More informationMeasurements in Optics for Civil Engineers
Measurements in Optics for Civil Engineers I. FOCAL LENGTH OF LENSES The behavior of simplest optical devices can be described by the method of geometrical optics. For convex or converging and concave
More informationInterference. Gambar: Museum Victoria Australia
Interference Gambar: Museum Victoria Australia Formulation of Interference Intensity Superposition between two waves (point sources) Two separate point sources S 1 (x 1 ) and S 2 (x 2 ) generate EM waves
More informationScattering of light from quasi-homogeneous sources by quasi-homogeneous media
Visser et al. Vol. 23, No. 7/July 2006/J. Opt. Soc. Am. A 1631 Scattering of light from quasi-homogeneous sources by quasi-homogeneous media Taco D. Visser* Department of Physics and Astronomy, University
More informationExperiment 6: Interferometers
Experiment 6: Interferometers Nate Saffold nas2173@columbia.edu Office Hour: Mondays, 5:30PM-6:30PM @ Pupin 1216 INTRO TO EXPERIMENTAL PHYS-LAB 1493/1494/2699 NOTE: No labs and no lecture next week! Outline
More informationLecture notes 5: Diffraction
Lecture notes 5: Diffraction Let us now consider how light reacts to being confined to a given aperture. The resolution of an aperture is restricted due to the wave nature of light: as light passes through
More informationNumerical modeling of thin film optical filters
Numerical modeling of thin film optical filters Daniela Topasna and Gregory A Topasna Department of Physics and Astronomy Virginia ilitary Institute Lexington VA ASTRACT Thin films are an important and
More informationLECTURE 23: LIGHT. Propagation of Light Huygen s Principle
LECTURE 23: LIGHT Propagation of Light Reflection & Refraction Internal Reflection Propagation of Light Huygen s Principle Each point on a primary wavefront serves as the source of spherical secondary
More informationLet us consider a typical Michelson interferometer, where a broadband source is used for illumination (Fig. 1a).
7.1. Low-Coherence Interferometry (LCI) Let us consider a typical Michelson interferometer, where a broadband source is used for illumination (Fig. 1a). The light is split by the beam splitter (BS) and
More informationFrustrated Total Internal Reflection from Thin-Layer Structures with a Metal Film
ISSN 3-4X, Optics and Spectroscopy, 29, Vol. 16, No. 5, pp. 748 752. Pleiades Publishing, Ltd., 29. Original ussian Text N.D. Goldina, 29, published in Optika i Spektroskopiya, 29, Vol. 16, No. 5, pp.
More information10. Wavelength measurement using prism spectroscopy
Spk 0. Wavelength measurement using prism spectroscopy 0. Introduction The study of emitted spectra of electromagnetic waves by excited atoms makes for one of the most important methods to investigate
More informationThe EYE. Physics 1502: Lecture 32 Today s Agenda. Lecture 4. Announcements: Optics. Midterm 2: graded after Thanks Giving
Physics 1502: Lecture 32 Today s Agenda Announcements: Midterm 2: graded after Thanks Giving Homework 09: Friday December 4 Optics Eye interference The EYE ~f o objective I 2 L I 1 ~f e eyepiece 1 2 Compound
More informationLecture 9: Introduction to Diffraction of Light
Lecture 9: Introduction to Diffraction of Light Lecture aims to explain: 1. Diffraction of waves in everyday life and applications 2. Interference of two one dimensional electromagnetic waves 3. Typical
More informationChapter 2 Basic Optics
Chapter Basic Optics.1 Introduction In this chapter we will discuss the basic concepts associated with polarization, diffraction, and interference of a light wave. The concepts developed in this chapter
More informationChapter 8 Optical Interferometry
Chapter 8 Optical Interferometry Lecture Notes for Modern Optics based on Pedrotti & Pedrotti & Pedrotti Instructor: Nayer Eradat Spring 009 4/0/009 Optical Interferometry 1 Optical interferometry Interferometer
More informationOptical Systems Program of Studies Version 1.0 April 2012
Optical Systems Program of Studies Version 1.0 April 2012 Standard1 Essential Understand Optical experimental methodology, data analysis, interpretation, and presentation strategies Essential Understandings:
More informationLecture 4: Diffraction & Spectroscopy
Lecture 4: Diffraction & Spectroscopy d θ y L Spectra of atoms reveal the quantum nature of matter Take a plastic grating from the bin as you enter class. Lecture 4, p 1 Today s Topics Single-Slit Diffraction*
More informationDUV ( nm ) Characterization of Materials: A new instrument, the Purged UV Spectroscopic Ellipsometer,
WISE 2000, International Workshop on Spectroscopic Ellipsometry, 8 9 May 2000 DUV (150 350nm ) Characterization of Materials: A new instrument, the Purged UV Spectroscopic Ellipsometer, Pierre BOHER,,
More informationNature of Light Part 2
Nature of Light Part 2 Fresnel Coefficients From Helmholts equation see imaging conditions for Single lens 4F system Diffraction ranges Rayleigh Range Diffraction limited resolution Interference Newton
More informationHomework 3. 1 Coherent Control [22 pts.] 1.1 State vector vs Bloch vector [8 pts.]
Homework 3 Contact: jangi@ethz.ch Due date: December 5, 2014 Nano Optics, Fall Semester 2014 Photonics Laboratory, ETH Zürich www.photonics.ethz.ch 1 Coherent Control [22 pts.] In the first part of this
More informationPHYS 110B - HW #5 Fall 2005, Solutions by David Pace Equations referenced equations are from Griffiths Problem statements are paraphrased
PHYS 0B - HW #5 Fall 005, Solutions by David Pace Equations referenced equations are from Griffiths Problem statements are paraphrased [.] Imagine a prism made of lucite (n.5) whose cross-section is a
More informationOPTI510R: Photonics. Khanh Kieu College of Optical Sciences, University of Arizona Meinel building R.626
OPTI510R: Photonics Khanh Kieu College of Optical Sciences, University of Arizona kkieu@optics.arizona.edu Meinel building R.626 Important announcements Homework #1 is due. Homework #2 is assigned, due
More informationGRATING CLASSIFICATION
GRATING CLASSIFICATION SURFACE-RELIEF GRATING TYPES GRATING CLASSIFICATION Transmission or Reflection Classification based on Regime DIFFRACTION BY GRATINGS Acousto-Optics Diffractive Optics Integrated
More informationA) n 1 > n 2 > n 3 B) n 1 > n 3 > n 2 C) n 2 > n 1 > n 3 D) n 2 > n 3 > n 1 E) n 3 > n 1 > n 2
55) The diagram shows the path of a light ray in three different materials. The index of refraction for each material is shown in the upper right portion of the material. What is the correct order for
More informationSupplementary Information
1 Supplementary Information 3 Supplementary Figures 4 5 6 7 8 9 10 11 Supplementary Figure 1. Absorbing material placed between two dielectric media The incident electromagnetic wave propagates in stratified
More informationCHAPTER 9 ELECTROMAGNETIC WAVES
CHAPTER 9 ELECTROMAGNETIC WAVES Outlines 1. Waves in one dimension 2. Electromagnetic Waves in Vacuum 3. Electromagnetic waves in Matter 4. Absorption and Dispersion 5. Guided Waves 2 Skip 9.1.1 and 9.1.2
More informationPhysics 3312 Lecture 9 February 13, LAST TIME: Finished mirrors and aberrations, more on plane waves
Physics 331 Lecture 9 February 13, 019 LAST TIME: Finished mirrors and aberrations, more on plane waves Recall, Represents a plane wave having a propagation vector k that propagates in any direction with
More informationSupporting Information
Supporting Information Devlin et al. 10.1073/pnas.1611740113 Optical Characterization We deposit blanket TiO films via ALD onto silicon substrates to prepare samples for spectroscopic ellipsometry (SE)
More informationPhysics for Scientists & Engineers 2
Light as Waves Physics for Scientists & Engineers 2 Spring Semester 2005 Lecture 41! In the previous chapter we discussed light as rays! These rays traveled in a straight line except when they were reflected
More informationHigh-Resolution. Transmission. Electron Microscopy
Part 4 High-Resolution Transmission Electron Microscopy 186 Significance high-resolution transmission electron microscopy (HRTEM): resolve object details smaller than 1nm (10 9 m) image the interior of
More informationPHY410 Optics Exam #3
PHY410 Optics Exam #3 NAME: 1 2 Multiple Choice Section - 5 pts each 1. A continuous He-Ne laser beam (632.8 nm) is chopped, using a spinning aperture, into 500 nanosecond pulses. Compute the resultant
More information