Stable Laser Resonator Modeling: Mesh Parameter Determination and Empty Cavity Modeling


 Robert Holt
 11 months ago
 Views:
Transcription
1 Stable Laser Resonator Modeling: Mesh Parameter Determination and Empty Cavity Modeling Justin Mansell, Steve Coy, Kavita Chand, Steve Rose, Morris Maynard, and Liyang Xu MZA Associates Corporation
2 Outline Introduction & Motivation Choosing a WaveOptics Mesh MultiIteration Imaging Stable Resonator Modeling Conclusions 2
3 Introduction and Motivation When evaluating a new laser gain medium, it is common to build a multimode stable resonator around the gain medium to demonstrate maximum extraction. Modeling multimode lasers is difficult because The modes tend to interact with the saturable gain medium and create modeling instabilities and The mesh requirements for a multimode stable resonator are very resource intensive. 3
4 Laser Resonator Architectures: Stable vs. Unstable Stable Unstable Rays captured by a stable resonator will never escape geometrically. All rays launched in an unstable resonator (except the onaxis ray) will eventually escape from the resonator. 4
5 HermiteGaussian Modes HG=HermiteGaussian HG modes are orthogonal modes of a stable resonator with infinite internal apertures. HG modes tend to appear clearly in rectangularaperture resonators. 5
6 LaguerreGaussian Modes LG=LaguerreGaussian LG modes are orthogonal modes of a stable resonator with infinite internal apertures. LG modes tend to appear clearly in circularaperture resonators. 6
7 The Iterative Fourier Transform (aka Fox & Li) Technique A field is propagated through repeated roundtrips until the field has converged to a stable field distribution. This is a commonly used technique for simplifying the 3D solution of Maxwell s Equations into a 2D problem (i.e. GerchbergSaxon technique) A. G. Fox and T. Li. Resonant modes in a maser interferometer, Bell Sys. Tech. J. 40, (March 96). A. G. Fox and T. Li, Computation of optical resonator modes by the method of resonance excitation, IEEE J. Quantum Electronics. QE4, (July 968). 7
8 Comments on Fox & Li Solutions Solution is for an instantaneous state, which is typically the steadystate of the laser. Stable resonators are much more computationally intensive to model than unstable resonators. We attribute this to the geometric output coupling of an unstable resonator. Larger eigenvalue difference between fundamental mode and the next higherorder mode. Not generally appropriate for pulsed or timevarying solutions unless the timevarying nature is much slower than a resonator roundtrip time. This is analogous to a splittime modeling techniques. 8
9 Example Resonator: RADICL Laser Output R c = 0m λ =.353e6m Saturable Gain Medium L = 0.254m Flat Mirror Other Parameters L resonator = 0.8 m D ap = 0.06 m (mirrors and gain) g ss = %/cm I sat = kw/cm 2 Curved Mirror Data source: Eppard, M., McGrory, W., and Applebaum, M. "The Effects of WaterVapor Condensation and Surface Catalysis on COIL Performance", AIAA Paper No , May
10 Predicted Gaussian Radius TEM00 Mode Radius for Plano Concave Resonator L = 0.8m L( R 2 L) ω ω 0 ω R 2 R 2 L L.35 m R = R 2 =0m 0 2.mm.0656mm 0
11 WaveOptics Mesh Determination
12 Calculation : HalfRoundTrip Estimate based on two limiting apertures analysis [Coy/Mansell]: N 4DD z 2 4 6cm.35 m 6cm 80cm 3,688, N 2.87E8 8.8x06 m NOTE: This is for a half of a round trip. 3,688 points per dimension Very Difficult 2
13 Calculation 2: Full RoundTrip Mesh points = 6 * Fresnel number (Mansell, SPIE 2007) a = half limiting aperture size = 3 cm λ =.35 μm 2 a N f L L =.7524 m = (L + (L*R/2)/(R/2L)) = ( ) m N f = 39 for the 6 cm aperture, 6*N f = 6256 mesh points in each dimension Still Difficult 3
14 Calculation 3: Maximum Angular Content Ray Optics Analysis of a Stable Laser Resonator (D) A ray launched parallel to the optical axis will oscillate back and forth across the resonator cavity The rays slope increases until it crosses the center of the cavity, then decreases. This gives us an estimate of max. Using ray optics we estimate max~= 0.0 for this resonator. Obtained with ray tracing with a ray at the edge of the aperture. 4
15 radius (m) / angle (radians) Rays and Angles Unwrapped radius theta roundtrips Graphical Method of Determining the Number of RoundTrips to Image 5
16 Number of RoundTrips to Image/Repeat PlanoConcave Stable Resonator Linearized PlanoConcave Stable Resonator Image Planes 6
17 Calculation 3: Maximum Angular Content (2) Now that we have, we can immediately obtain the constraint on the mesh spacing by applying the Nyquist criterion: 2 max.35 m m Finally, we can obtain the constraint on N by imposing the requirement that no rays leaving the cavity from one side should be able to wraparound and reenter the cavity from the other side: N D max z 6cm m 80cm 58 This method makes the greatest use of resonator information, so we believe it to wellrepresent the minimum mesh size required. NOTE: 3,688 / 58 ~ = number of roundtrips to image 7
18 Examining the Ray Tracing As is typical of a stable resonator, a ray launched at the edge of the resonator walks to the other side of the resonator and then back to the starting side. For this resonator, this process takes ~ roundtrips Therefore, the angle required is approximately reduced by a factor of. How can we find the number of round trips to image? 8
19 Analytical Method to Determine the Number of RoundTrips to Image This problem can be addressed using ray matrices. Consider a resonator with a roundtrip raymatrix given by M. In N roundtrips, the raymatrix will be given by M N. To reproduce any input ray, we need to determine the number of round trips to make the identity matrix, or M N =I. A C B D N M N This can be determined numerically, but can also be addressed using eigenvalue analysis. The approach on the right derives an equation for N assuming a planoconcave resonator with length L and the end mirror radius of curvature equal to 2f. 9 I 0 0 M M N 0 2k M L X M L / / X tan N N v f i N f / tan e L / e f v 2L j jn N N f i X X X 2k 0 L L / 2 2 j 2 0 / f X X 2 f L
20 Example of Analytical Method Resonator Setup M L / / f f 2L L 2 L / / f f L = 0.8 m R = 0 m f eff = 5 m X N tan 2 L / f M 0 0 I 20
21 Numerical Method of Determining the Number of RTs to Image A ray launched parallel to the optical axis will oscillate back and forth across the resonator cavity Round  Trip ABCD Matrix M rt M rt 0 0 Rays selfreplicate every ~ round trips through the cavity 2
22 maximum resonator angle / maximum ray angle(radians) Angular Bandwidth Requirement Dependence on RTs to Image Data y=0.66 * x Varying the end mirror radius of curvature (ROC) allows us to study the relationship between the iterations to image and the reduction in the maximum angular content N  iterations to image 22
23 WaveOptics Mesh Initial Conclusions When modeling a stable resonator, the reduction in required angular bandwidth can be reduced by approximately the number of roundtrips (iterations) required to image times 2/3. The number of roundtrips required to reimage can be determined numerically, graphically, or analytically (through eigen analysis). 23
24 Stable Resonator Without Gain 24
25 Example Laser Resonator Setup Secondary Mirror Flat / R nominal =95% Primary Mirror ROC = 0m R nominal =00% 0.8 m 25
26 26 Wave Train Model
27 Gaussian that reproduced itself in a roundtrip matched theory. Experiment: Launch a Gaussian beam through a single round trip and evaluate the size after one roundtrip..067 mm Theory : mm Note: mesh spacing was 0.02 mm 27
28 Parameters R c (Radius of curvature of secondary mirror) = 0 m Cavity Length = 0.8 m Propagation grid = 256 by 56 µm (4.3 mm diameter) Wavelength = µm Reflectivity of output mirror = 95 % Initial Field = BwomikTopHat field of 6 cm initial Radius and 5000 amplitude Normalization = Iterations = 0000 Varying Aperture diameter 28
29 Seeded all laser modes initially with a Bwomik field. Bwomik Field is a plane wave with random phase that tends to seed all the modes of a resonator. This is implemented in LaserGridInitializers.h. 29
30 Converged Resonator Field Dependence on Internal Aperture Diameter 30
31 Larger aperture results approximate the theory more accurately. Iterations = 0000 Aperture diameter = 2.0 mm Aperture diameter = 4.0 mm NOTE: Theory is TEM 00 shape. 3
32 Bigger apertures require more iterations to converge. Iterations = 0000 Aperture diameter = 5.0 mm Aperture diameter = 7.0 mm NOTE: Theory is TEM 00 shape. 32
33 The 5mm case begins to approach convergence after 50,000 iterations. Iterations = Aperture diameter = 5.0 mm Iterations = Aperture diameter = 5.0 mm NOTE: Theory is TEM 00 shape. 33
34 The 5mm diameter aperture was reasonably well converged after 75,000 iterations. Iterations = Aperture diameter = 5.0 mm 75,000 iterations takes about 3 hours NOTE: Theory is TEM 00 shape. 34
35 Intensity CrossSection Comparison for 5mm Aperture Cases with Different Iteration Numbers 35
36 Variation of Output Intensity with Last 99 Frames of 0,000 with 5mm Diameter Aperture Note the repeating pattern every frames. 36
37 Variation of Output Intensity with Last 99 Frames of 50,000 with 5mm Diameter Aperture Note the repeating pattern every frames.
38 Variation of Output Intensity with Last 99 Frames of 75,000 with 5mm Diameter Aperture All these frames look good
39 Stable Resonator Model Conclusions The WaveTrain stable resonator model showed that the models with larger aperture (~5 times w 0 ) converged very close to the theoretical shape in many (75,000) iterations. Even fairly early in the iterations, the beam intensity shape repeats itself every iterations, as is predicted by theory. 39
40 Conclusions In stable resonator modeling, the number of roundtrip iterations to image directly impacts the waveoptics mesh requirements. We showed three different techniques for determining the number of roundtrips to image: analytical, graphical, and numerical. Using this theory, we have shown that our stable resonator model without gain matches well with the theoretical predictions. 40
41 Future Work and Acknowledgements We need to perform more anchoring to experimental data to complete the verification of this new technique. Experiment: Aperture in a small stable resonator. We need to consider how the different frequencies impact model performance. Acknowledgements A. Paxton and A. E. Siegman for technical discussions Funded via the LADERA contract 4
42 Questions? (505) x22 42
Thick Lenses and the ABCD Formalism
Thick Lenses and the ABCD Formalism Thursday, 10/12/2006 Physics 158 Peter Beyersdorf Document info 12. 1 Class Outline Properties of Thick Lenses Paraxial Ray Matrices General Imaging Systems 12. 2 Thick
More informationGaussian Beam Calculator for Creating Coherent Sources
Gaussian Beam Calculator for Creating Coherent Sources INTRODUCTION Coherent sources are represented in FRED using a superposition of Gaussian beamlets. The ray grid spacing of the source is used to determine
More informationReflection and Refraction
Reflection and Refraction Theory: Whenever a wave traveling in some medium encounters an interface or boundary with another medium either (or both) of the processes of (1) reflection and (2) refraction
More informationExperiment 6. Snell s Law. Use Snell s Law to determine the index of refraction of Lucite.
Experiment 6 Snell s Law 6.1 Objectives Use Snell s Law to determine the index of refraction of Lucite. Observe total internal reflection and calculate the critical angle. Explain the basis of how optical
More informationLASCAD Tutorial No. 1: Modeling a laser cavity with end pumped rod
LASCAD Tutorial No. 1: Modeling a laser cavity with end pumped rod Revised: January 15, 2009 Copyright 20062009 LASCAD GmbH Table of Contents 1 Starting LASCAD and Defining a Simple Laser Cavity...1
More informationLecture Notes (Reflection & Mirrors)
Lecture Notes (Reflection & Mirrors) Intro:  plane mirrors are flat, smooth surfaces from which light is reflected by regular reflection  light rays are reflected with equal angles of incidence and reflection
More informationMEFT / Quantum Optics and Lasers. Suggested problems from Fundamentals of Photonics Set 1 Gonçalo Figueira
MEFT / Quantum Optics and Lasers Suggested problems from Fundamentals of Photonics Set Gonçalo Figueira. Ray Optics.3) AberrationFree Imaging Surface Determine the equation of a convex aspherical nonspherical)
More informationnormal angle of incidence increases special angle no light is reflected
Reflection from transparent materials (Chapt. 33 last part) When unpolarized light strikes a transparent surface like glass there is both transmission and reflection, obeying Snell s law and the law of
More informationAP* Optics Free Response Questions
AP* Optics Free Response Questions 1978 Q5 MIRRORS An object 6 centimeters high is placed 30 centimeters from a concave mirror of focal length 10 centimeters as shown above. (a) On the diagram above, locate
More informationUsing Skew Rays to Model Gaussian Beams
Using Skew Rays to Model Gaussian Beams Host: Paul Colbourne, Lumentum Zemax, LLC 2016 1 Topics we ll cover today: Using skew rays to represent a Gaussian beam. Use of UserDefined Surfaces to generate
More informationPlace a straw in the glass of water and record your observations in each case.
Refraction Investigations You will find the Refraction slideshow notes helpful as you complete these investigations. How Refraction Affects What We See: Part 1 You probably won t find anyone who is not
More informationDiscover how to solve this problem in this chapter.
A 2 cm tall object is 12 cm in front of a spherical mirror. A 1.2 cm tall erect image is then obtained. What kind of mirror is used (concave, plane or convex) and what is its focal length? www.totalsafes.co.uk/interiorconvexmirror900mm.html
More informationChapter 32 Light: Reflection and Refraction. Copyright 2009 Pearson Education, Inc.
Chapter 32 Light: Reflection and Refraction Units of Chapter 32 The Ray Model of Light Reflection; Image Formation by a Plane Mirror Formation of Images by Spherical Mirrors Index of Refraction Refraction:
More informationLecture 6. Dielectric Waveguides and Optical Fibers. Slab Waveguide, Modes, VNumber Modal, Material, and Waveguide Dispersions
Lecture 6 Dielectric Waveguides and Optical Fibers Slab Waveguide, Modes, VNumber Modal, Material, and Waveguide Dispersions StepIndex Fiber, Multimode and Single Mode Fibers Numerical Aperture, Coupling
More informationDome and Mirror Seeing Estimates for the Thirty Meter Telescope
Dome and Mirror Seeing Estimates for the Thirty Meter Telescope John S. Pazder a, Konstantinos Vogiatzis b, and George Z. Angeli b, a National Research Council Canada, Herzberg Institute of Astrophysics
More informationCollege Physics 150. Chapter 25 Interference and Diffraction
College Physics 50 Chapter 5 Interference and Diffraction Constructive and Destructive Interference The Michelson Interferometer Thin Films Young s Double Slit Experiment Gratings Diffraction Resolution
More informationEssential Physics I. Lecture 13:
Essential Physics I E I Lecture 13: 110716 Reminders No lecture: Monday 18th July (holiday) Essay due: Monday 25th July, 4:30 pm 2 weeks!! Exam: Monday 1st August, 4:30 pm Announcements 250 word essay
More informationWhat is it? How does it work? How do we use it?
What is it? How does it work? How do we use it? Dual Nature http://www.youtube.com/watch?v=dfpeprq7ogc o Electromagnetic Waves display wave behavior o Created by oscillating electric and magnetic fields
More informationWhere n = 0, 1, 2, 3, 4
Syllabus: Interference and diffraction introduction interference in thin film by reflection Newton s rings Fraunhofer diffraction due to single slit, double slit and diffraction grating Interference 1.
More informationConfiguration of Light Sources
UseCase.0012 (1.0) Configuration of Light Sources Keywords: LED, laser, harmonic fields, harmonic fields set, spectra, pulses, polarization Description This use case explains how light sources are configured
More informationLASer Cavity Analysis and Design
The unique combination of simulation tools for LASer Cavity Analysis and Design LASCAD is an industryleading software package providing multiphysics analysis of the complicated interaction between thermal
More informationPolarization of Light
Polarization of Light Introduction Light, viewed classically, is a transverse electromagnetic wave. Namely, the underlying oscillation (in this case oscillating electric and magnetic fields) is along directions
More informationPHYSICS. Chapter 34 Lecture FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E RANDALL D. KNIGHT
PHYSICS FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E Chapter 34 Lecture RANDALL D. KNIGHT Chapter 34 Ray Optics IN THIS CHAPTER, you will learn about and apply the ray model of light Slide 342
More informationCollege Physics B  PHY2054C
Young College  PHY2054C Wave Optics: 10/29/2014 My Office Hours: Tuesday 10:00 AM  Noon 206 Keen Building Outline Young 1 2 3 Young 4 5 Assume a thin soap film rests on a flat glass surface. Young Young
More informationSimulating Reflector Antenna Performance with GRASP9
Simulating Reflector Antenna Performance with GRASP9 Bruce Veidt National Research Council of Canada bruce.veidt@nrc.ca and Walter Brisken NRAO Socorro wbrisken@aoc.nrao.edu September 2011 Opening Remarks
More informationDiffraction at a single slit and double slit Measurement of the diameter of a hair
Diffraction at a single slit and double slit Measurement of the diameter of a hair AREEJ AL JARB Background... 3 Objects of the experiments 4 Principles Single slit... 4 Double slit.. 6 Setup. 7 Procedure
More informationThe Law of Reflection
If the surface off which the light is reflected is smooth, then the light undergoes specular reflection (parallel rays will all be reflected in the same directions). If, on the other hand, the surface
More informationLIGHT SCATTERING THEORY
LIGHT SCATTERING THEORY Laser Diffraction (Static Light Scattering) When a Light beam Strikes a Particle Some of the light is: Diffracted Reflected Refracted Absorbed and Reradiated Reflected Refracted
More informationGeometric Field Tracing through an Off Axis Parabolic Mirror
UseCase.0077 (1.0) Geometric Field Tracing through an Off Axis Parabolic Mirror Keywords: focus, geometric field tracing, diffractive field tracing Description This use case explains the usage of the
More informationDiffraction Gratings
Diffraction Gratings 1. How a Diffraction Grating works? Diffraction gratings are optical components with a period modulation on its surface. Either the transmission (or the phase) changes in a periodic
More information9. Polarizers. Index of. Coefficient of Material Wavelength ( ) Brewster angle refraction (n)
9. Polarizers All polarized light is to some degree elliptical in nature. Basic states of polarization like linear and circular are actually special cases of elliptically polarized light which is defined
More informationChapter 33 Continued Properties of Light. Law of Reflection Law of Refraction or Snell s Law Chromatic Dispersion Brewsters Angle
Chapter 33 Continued Properties of Light Law of Reflection Law of Refraction or Snell s Law Chromatic Dispersion Brewsters Angle Dispersion: Different wavelengths have different velocities and therefore
More informationθ =θ i r n sinθ = n sinθ
θ i = θ r n = 1 sinθ1 n2 sin θ 2 Index of Refraction Speed of light, c, in vacuum is 3x10 8 m/s Speed of light, v, in different medium can be v < c. index of refraction, n = c/v. frequency, f, does not
More informationOptics: Laser Light Show Student Advanced Version
Optics: Laser Light Show Student Advanced Version In this lab, you will explore the behavior of light. You will observe reflection and refraction of a laser beam in jello, and use a diffraction pattern
More informationFast scanning method for onedimensional surface profile measurement by detecting angular deflection of a laser beam
Fast scanning method for onedimensional surface profile measurement by detecting angular deflection of a laser beam Ryo Shinozaki, Osami Sasaki, and Takamasa Suzuki A fast scanning method for onedimensional
More informationarxiv: v1 [physics.classph] 11 Feb 2012
arxiv:202.2404v [physics.classph] Feb 202 Refractive index of a transparent liquid measured with a concave mirror Introduction Amitabh Joshi and Juan D Serna 2 Department of Physics, Eastern Illinois
More informationName Section Date. Experiment Reflection and Refraction
Name Section Date Introduction: Experiment Reflection and Refraction The travel of light is often represented in geometric optics by a light ray, a line that is drawn to represent the straightline movement
More informationReflection and Image Formation by Mirrors
Purpose Theory a. To study the reflection of light Reflection and Image Formation by Mirrors b. To study the formation and characteristics of images formed by different types of mirrors. When light (wave)
More informationPassive intracavity phase locking of laser channels
Optics Communications 63 (006) 60 64 www.elsevier.com/locate/optcom Passive intracavity phase locking of laser channels iran Shimshi *, Amiel A. Ishaaya, Vardit Ekhouse, Nir Davidson, Asher A. Friesem
More informationPH 2223A Fall Diffraction Lectures Chapter 36 (Halliday/Resnick/Walker, Fundamentals of Physics 8 th edition)
PH 2223A Fall 2012 Diffraction Lectures 2829 Chapter 36 (Halliday/Resnick/Walker, Fundamentals of Physics 8 th edition) 1 Chapter 36 Diffraction In Chapter 35, we saw how light beams passing through
More informationExperiment 3: Reflection
Model No. OS8515C Experiment 3: Reflection Experiment 3: Reflection Required Equipment from Basic Optics System Light Source Mirror from Ray Optics Kit Other Required Equipment Drawing compass Protractor
More informationPHYSICS 213 PRACTICE EXAM 3*
PHYSICS 213 PRACTICE EXAM 3* *The actual exam will contain EIGHT multiple choice quiztype questions covering concepts from lecture (16 points), ONE essaytype question covering an important fundamental
More informationGenerally astigmatic Gaussian beam representation and optimization using skew rays
Generally astigmatic Gaussian beam representation and optimization using skew rays Paul D. Colbourne Lumentum, 61 Bill Leathem Dr., Ottawa, ON, Canada, KJ 0P7 ABSTRACT Methods are presented of using skew
More informationDiffraction. Singleslit diffraction. Diffraction by a circular aperture. Chapter 38. In the forward direction, the intensity is maximal.
Diffraction Chapter 38 Huygens construction may be used to find the wave observed on the downstream side of an aperture of any shape. Diffraction The interference pattern encodes the shape as a Fourier
More informationI. Meshing and Accuracy Settings
Guidelines to Set CST Solver Accuracy and Mesh Parameter Settings to Improve Simulation Results with the Time Domain Solver and Hexahedral Meshing System illustrated with a finite length horizontal dipole
More informationThe goal of this lab is to give you a chance to align and use a Pockel s Cell.
880 Quantum Electronics Lab Pockel s Cell Alignment And Use The goal of this lab is to give you a chance to align and use a Pockel s Cell. You may not take this lab unless you have read the laser safety
More informationFresnel's biprism and mirrors
Fresnel's biprism and mirrors 1 Table of Contents Section Page Back ground... 3 Basic Experiments Experiment 1: Fresnel's mirrors... 4 Experiment 2: Fresnel's biprism... 7 2 Back ground Interference of
More informationx 2 + y 2 + z 2 = 1 = ˆr ŷ = ±y cosθ z (a) The half angle of the cones (inside the material) is just given by the critical angle sinθ c n = 3.
Exercise.6 The results of this problem are somewhat general and apply to any rectangular parallelepiped with source located at any position inside. One can see this as follows. The direction of an arbitrary
More informationHolographic Elements in Solar Concentrator and Collection Systems
Holographic Elements in Solar Concentrator and Collection Systems Raymond K. Kostuk,2, Jose Castro, Brian Myer 2, Deming Zhang and Glenn Rosenberg 3 Electrical and Computer Engineering, Department University
More informationAP Physics Problems  Waves and Light
AP Physics Problems  Waves and Light 1. 19754 (Physical Optics) a. Light of a single wavelength is incident on a single slit of width w. (w is a few wavelengths.) Sketch a graph of the intensity as
More informationRCS Measurement and Analysis of Rectangular and Circular Crosssection Cavities
RCS Measurement and Analysis of Rectangular and Circular Crosssection Cavities Abhinav Bharat, M L Meena, S. Sunil Kumar, Neha Sangwa, Shyam Rankawat Defence Laboratory, DRDO Jodhpur, India342011 Abstract
More informationRefraction at a single curved spherical surface
Refraction at a single curved spherical surface This is the beginning of a sequence of classes which will introduce simple and complex lens systems We will start with some terminology which will become
More informationCh. 25 The Reflection of Light
Ch. 25 The Reflection of Light 25. Wave fronts and rays We are all familiar with mirrors. We see images because some light is reflected off the surface of the mirror and into our eyes. In order to describe
More informationLED Optics Designer 1.6. User's Guide
Limited Liability Company «LED Optics Design» 151217, Molodogvardeyskaya str., Samara, 443001, Russian Federation Tel.: +78463322764, Fax: +78463325620 http://ledopticsdesign.com, info@ledopticsdesign.com
More informationPlanoConvex Lenses. Read further. Catalog Items BK7 PlanoConvex Lenses. Description. Standard specifications. Features.
PlanoConvex Lenses (PCX) PCX positive focal length lenses have flat surface on one side and spherical surface on the other. They are used for focusing beams in telescopes, collimators or condenser systems,
More informationHighPower Femtosecond Lasers
HighPower Femtosecond Lasers FEATURES 190 fs ps tunable pulse duration Up to 2 mj pulse energy Up to 20 W average power Single pulse 1 MHz tunable repetition rate Includes pulse picker for pulseondemand
More informationDevelopment of a Finite Element Method Mode Solver Application for Optical Waveguides
Development of a Finite Element Method Mode Solver Application for Optical Waveguides An. Kichidis Dept. of Informatics Aristotle University of Thessaloniki Thessaloniki GR54124 Tel: 302310998407 akihidis@gmail.com
More informationOptics INTRODUCTION DISCUSSION OF PRINCIPLES. Reflection by a Plane Mirror
Optics INTRODUCTION Geometric optics is one of the oldest branches of physics, dealing with the laws of reflection and refraction. Reflection takes place on the surface of an object, and refraction occurs
More informationUnit I Light and Optics
Unit I Light and Optics Outline By the time you finish this, you should understand the following aspects of our experiment: 1) Why you produce a grating pattern when you cross two laser beams. 2) What
More informationLaser sensors. Transmitter. Receiver. Basilio Bona ROBOTICA 03CFIOR
Mobile & Service Robotics Sensors for Robotics 3 Laser sensors Rays are transmitted and received coaxially The target is illuminated by collimated rays The receiver measures the time of flight (back and
More informationReflection, Refraction and Polarization of Light
Reflection, Refraction and Polarization of Light Physics 246/Spring2012 In today's laboratory several properties of light, including the laws of reflection, refraction, total internal reflection and polarization,
More informationFLAP P6.2 Rays and geometrical optics COPYRIGHT 1998 THE OPEN UNIVERSITY S570 V1.1
F1 The ray approximation in optics assumes that light travels from one point to another along a narrow path called a ray that may be represented by a directed line (i.e. a line with an arrow on it). In
More informationMultiple optical traps from a single laser beam using a mechanical element
Multiple optical traps from a single laser beam using a mechanical element J.A. Dharmadhikari, A.K. Dharmadhikari, and D. Mathur * Tata Institute of Fundamental Research, 1 Homi Bhabha Road, Mumbai 400
More informationNew Opportunities for 3D SPI
New Opportunities for 3D SPI JeanMarc PEALLAT Vi Technology St Egrève, France jmpeallat@vitechnology.com Abstract For some years many process engineers and quality managers have been questioning the benefits
More informationRefraction and Polarization of Light
Chapter 9 Refraction and Polarization of Light Name: Lab Partner: Section: 9.1 Purpose The purpose of this experiment is to demonstrate several consequences of the fact that materials have di erent indexes
More informationChapter 38 Wave Optics (II)
Chapter 38 Wave Optics (II) Initiation: Young s ideas on light were daring and imaginative, but he did not provide rigorous mathematical theory and, more importantly, he is arrogant. Progress: Fresnel,
More information13. Brewster angle measurement
13. Brewster angle measurement Brewster angle measurement Objective: 1. Verification of Malus law 2. Measurement of reflection coefficient of a glass plate for p and s polarizations 3. Determination
More informationPHY 112: Light, Color and Vision. Lecture 11. Prof. Clark McGrew Physics D 134. Review for Exam. Lecture 11 PHY 112 Lecture 1
PHY 112: Light, Color and Vision Lecture 11 Prof. Clark McGrew Physics D 134 Review for Exam Lecture 11 PHY 112 Lecture 1 From Last Time Lenses Ray tracing a Convex Lens Announcements The midterm is Thursday
More informationSecondary grating formation by readout at Braggnull incidence
Secondary grating formation by readout at Braggnull incidence Ali Adibi, Jose Mumbru, Kelvin Wagner, and Demetri Psaltis We show that when a dynamic hologram is read out by illumination at the Bragg nulls
More informationRay Optics. Lecture 23. Chapter 34. Physics II. Course website:
Lecture 23 Chapter 34 Physics II Ray Optics Course website: http://faculty.uml.edu/andriy_danylov/teaching/physicsii Today we are going to discuss: Chapter 34: Section 34.13 Ray Optics Ray Optics Wave
More informationPhysics 11 Chapter 18: Ray Optics
Physics 11 Chapter 18: Ray Optics "... Everything can be taken from a man but one thing; the last of the human freedoms to choose one s attitude in any given set of circumstances, to choose one s own way.
More informationRay Optics. Ray model Reflection Refraction, total internal reflection Color dispersion Lenses Image formation Magnification Spherical mirrors
Ray Optics Ray model Reflection Refraction, total internal reflection Color dispersion Lenses Image formation Magnification Spherical mirrors 1 Ray optics Optical imaging and color in medicine Integral
More informationBe careful not to leave your fingerprints on the optical surfaces of lenses or Polaroid sheets.
POLARIZATION OF LIGHT REFERENCES Halliday, D. and Resnick, A., Physics, 4 th edition, New York: John Wiley & Sons, Inc, 1992, Volume II, Chapter 481, 482, 483. (2weights) (1weightexercises 1 and 3
More informationRefraction and Polarization of Light
Chapter 9 Refraction and Polarization of Light Name: Lab Partner: Section: 9.1 Purpose The purpose of this experiment is to demonstrate several consequences of the fact that materials have di erent indexes
More informationLesson Plan Outline for Rainbow Science
Lesson Plan Outline for Rainbow Science Lesson Title: Rainbow Science Target Grades: Middle and High School Time Required: 120 minutes Background Information for Teachers and Students Rainbows are fascinating
More information22.4. (a) (b) (c) (d)
mλl 22.2. Because ym = increasing λ and L increases the fringe spacing. Increasing d decreases the fringe d spacing. Submerging the experiment in water decreases λ and decreases the fringe spacing. So
More informationLight. Form of Electromagnetic Energy Only part of Electromagnetic Spectrum that we can really see
Light Form of Electromagnetic Energy Only part of Electromagnetic Spectrum that we can really see Facts About Light The speed of light, c, is constant in a vacuum. Light can be: REFLECTED ABSORBED REFRACTED
More informationLENSES DDC TECHNOLOGIES
LENSES Optical Glass Planoconvex Lenses... 2 Optical Glass Planoconcave Lenses... 3 Optical Glass Biconvex Lenses... 4 Optical Glass Biconcave Lenses... 5 Fused Silica Planoconvex Lenses... 6 Fused
More informationIntroduction. Part I: Measuring the Wavelength of Light. Experiment 8: Wave Optics. Physics 11B
Physics 11B Experiment 8: Wave Optics Introduction Equipment: In Part I you use a machinist rule, a laser, and a lab clamp on a stand to hold the laser at a grazing angle to the bench top. In Part II you
More informationDisplacement Measuring I nterferometry
Field Guide to Displacement Measuring I nterferometry Jonathan D. Ellis SPIE Field Guides Volume FG30 John E. Greivenkamp, Series Editor SPIE PRESS Bellingham, Washington USA Vll Glossary of Terms and
More informationThe image is virtual and erect. When a mirror is rotated through a certain angle, the reflected ray is rotated through twice this angle.
1 Class XII: Physics Chapter 9: Ray optics and Optical Instruments Top Concepts 1. Laws of Reflection. The reflection at a plane surface always takes place in accordance with the following two laws: (i)
More informationOn Fig. 7.1, draw a ray diagram to show the formation of this image.
1 A small object is placed 30 cm from the centre of a convex lens of focal length 60 cm An enlarged image is observed from the other side of the lens (a) On Fig 71, draw a ray diagram to show the formation
More informationAnalysis of the Gaussian Beam on a Corrugated Dielectric Interface
(An ISO 3297: 27 Certified Organization) Vol. 3, Issue 9, September 214 Analysis of the Gaussian Beam on a Corrugated Dielectric Interface Mohamed B. El_Mashade 1, Adel Shaaban 2 Department of Electrical
More informationOrbital angular momentum (OAM) is a special property of certain beams of light, called optical
1 Introduction Orbital angular momentum (OAM) is a special property of certain beams of light, called optical vortex beams, which appear as ringshaped intensity distributions around a dark core. The existence
More informationOptics Part 1. Vern Lindberg. March 5, 2013
Optics Part 1 Vern Lindberg March 5, 2013 This section of the course deals with geometrical optics refraction, reflection, mirrors, lenses, and aberrations. Physical optics, interference, diffraction,
More informationCALCULATION OF 3D ROUGHNESS MEASUREMENT UNCERTAINTY WITH VIRTUAL SURFACES. Michel Morel and Han Haitjema
CALCULATION OF 3D ROUGHNESS MEASUREMENT UNCERTAINTY WITH VIRTUAL SURFACES Michel Morel and Han Haitjema Eindhoven University of Technology Precision Engineering section P.O. Box 513 Whoog 2.107 5600
More informationPlane Wave Imaging Using Phased Array Arno Volker 1
11th European Conference on NonDestructive Testing (ECNDT 2014), October 610, 2014, Prague, Czech Republic More Info at Open Access Database www.ndt.net/?id=16409 Plane Wave Imaging Using Phased Array
More informationOptimizing the TracePro Optimization Process
Optimizing the TracePro Optimization Process A TracePro Webinar December 17, 2014 Presenter Presenter Dave Jacobsen Sr. Application Engineer Lambda Research Corporation Moderator Mike Gauvin Vice President
More informationPY106 Class31. Index of refraction. Refraction. Index of refraction. Sample values of n. Rays and wavefronts. index of refraction: n v.
Refraction Index of refraction When an EM wave travels in a vacuum, its speed is: c = 3.00 x 10 8 m/s. In any other medium, light generally travels at a slower speed. The speed of light v in a material
More informationIAP: Laborkurs moderne Physik. Versuchsanleitung Fourier Optik. September 11, Sara Peeters.
IAP: Laborkurs moderne Physik Versuchsanleitung Fourier Optik September 11, 2012 Sara Peeters Büro A75 sara.peeters@iap.unibe.ch Stefan Preisser Büro A26 stefan.preisser@iap.unibe.ch Contents 1 Introduction
More informationGeometrical Optics. Name ID TA. Partners. Date Section. Please do not scratch, polish or touch the surface of the mirror.
Geometrical Optics Name ID TA Partners Date Section Please do not scratch, polish or touch the surface of the mirror. 1. Application of geometrical optics: 2. Real and virtual images: One easy method to
More informationEdge and local feature detection  2. Importance of edge detection in computer vision
Edge and local feature detection Gradient based edge detection Edge detection by function fitting Second derivative edge detectors Edge linking and the construction of the chain graph Edge and local feature
More informationOptics: Reflection and Refraction (approx. completion time: 2.5 h) (3/28/11)
Optics: Reflection and Refraction (approx. completion time: 2.5 h) (3/28/11) Introduction In this lab you will investigate the reflection and refraction of light. Reflection of light from a surface is
More informationPhysical properties of prism foil and its pedagogical applications. Faculty of mathematics and physics, University of Ljubljana, Slovenia
Physical properties of prism foil and its pedagogical applications Mihael Gojkošek, gojkosek@fmf.unilj.si Gorazd Planinšič, gorazd.planinsic@fmf.unilj.si Faculty of mathematics and physics, University
More informationExperiment 9. Law of reflection and refraction of light
Experiment 9. Law of reflection and refraction of light 1. Purpose Invest light passing through two mediums boundary surface in order to understand reflection and refraction of light 2. Principle As shown
More informationGPR DATA ANALYSIS OF AIRFIELD RUNWAY USING MIGRATION VELOCITY SIMULATION ALGORITHM
GPR DATA ANALYSIS OF AIRFIELD RUNWAY USING MIGRATION VELOCITY SIMULATION ALGORITHM Ramya M and Krishnan Balasubramaniam Centre for Nondestructive Evaluation, Department of Mechanical Engineering, Indian
More informationFlow Field of Truncated Spherical Turrets
Flow Field of Truncated Spherical Turrets Kevin M. Albarado 1 and Amelia Williams 2 Aerospace Engineering, Auburn University, Auburn, AL, 36849 Truncated spherical turrets are used to house cameras and
More informationFinal Exam and End Material Test Friday, May 12, 10:0012:00
Final Exam and End Material Test Friday, May 12, 10:0012:00 Test rooms: Instructor Sections Room Dr. Hale F, H 104 Physics Dr. Kurter B, N 125 BCH Dr. Madison K, M B10 Bertelsmeyer Dr. Parris J St. Pats
More informationSimulation of Transition Radiation from a flat target using CST particle studio.
Simulation of Transition Radiation from a flat target using CST particle studio. K. Lekomtsev 1, A. Aryshev 1, P. Karataev 2, M. Shevelev 1, A. Tishchenko 3 and J. Urakawa 1 1. High Energy Accelerator
More informationPHYSICS EXPERIMENTS (LIGHT)
PHYSICS EXPERIMENTS (LIGHT) In the matter of physics, the first lessons should contain nothing but what is experimental and interesting to see. A pretty experiment is in itself often more valuable than
More information