DOCSLIB.ORG

Wavefront Distortion of the Reflected and Diffracted Beams Produced By

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Wavefront Distortion of the Reflected and Diffracted Beams Produced By Lu et al. Vol. 24, No. 3/March 2007/J. Opt. Soc. Am. A 659 Wavefront distortion of the reflected and diffracted beams produced by the thermoelastic deformation of a diffraction grating heated by a Gaussian laser beam Patrick P. Lu, Amber L. Bullington, Peter Beyersdorf,* Stefan Traeger,† and Justin Mansell‡ Ginzton Laboratory, Stanford University, Stanford, California 94305-4085, USA Ray Beausoleil HP Laboratories, 13837 175th Place NE, Redmond, Washington 98052-2180, USA Eric K. Gustafson,** Robert L. Byer, and Martin M. Fejer Ginzton Laboratory, Stanford University, Stanford, California 94305-4085, USA Received April 20, 2006; revised September 13, 2006; accepted September 18, 2006; posted September 26, 2006 (Doc. ID 70078); published February 14, 2007 It may be advantageous in advanced gravitational-wave detectors to replace conventional beam splitters and Fabry–Perot input mirrors with diffractive elements. In each of these applications, the wavefront distortions produced by the absorption and subsequent heating of the grating can limit the maximum useful optical power. We present data on the wavefront distortions induced in a laser probe beam for both the reflected and dif- fracted beams from a grating that is heated by a Gaussian laser beam and compare these results to a simple theory of the wavefront distortions induced by thermoelastic deformations. © 2007 Optical Society of America OCIS codes: 000.2780, 050.1950, 120.3180, 120.6810. 1. INTRODUCTION that are not optically transparent, thus increasing the list of possible materials available for this application. Many optical systems contain transmissive components In this paper, we present a model for the thermoelastic such as lenses and beam splitters. Laser power incident wavefront distortions caused by surface heating of reflec- on these is partially absorbed by their substrates. At high tive optics and compare it with experimental results for powers, substrate absorption produces wavefront distor- both the reflected and diffracted beams from a thermally tions through thermal-lensing and thermoelastic distor- loaded grating. We also make calculations comparing tions. This is especially relevant for advanced thermoelastic deformations of a surface-heated grating gravitational-wave interferometers,1–4 which will require with thermal lensing due to substrate absorption in a several kilowatts of circulating power at the beam splitter transmissive beam splitter. to obtain the required phase sensitivity. Both the genera- tion and the handling of such high optical power will be challenging. Kilowatt-class laser designs for gravitational-wave interferometry based on Nd:YAG 2. HELLO AND VINET’S ANALYSIS OF have been proposed,5 and it is likely that lasers for this THERMOELASTIC DISTORTIONS application will be a reality within the current decade. Thermoelastic distortions arise from nonuniform heating However, high laser power will produce wavefront distor- caused by light absorbed in the reflective and antireflec- tions in both the beam splitters and Fabry–Perot input tive coatings on the surface of a mirror and in the mirror mirrors; these distortions are more likely to limit the cir- substrate. These problems were examined by Winkler et culating power in advanced gravitational-wave detectors al. in 199113,14 using a simple thermal model of this effect than the available laser power. While advanced based on dimensional analysis in gravitational-wave in- gravitational-wave interferometers will probably use terferometers and produced estimates of the size of the ef- some form of active thermal compensation to reduce the fect agreeing to a factor of ϳ2 with the exact results pre- effects of laser beam heating-induced distortion,6 it could viously obtained by Hello and Vinet15,16 and discussed be advantageous to eliminate the degradation caused by below. substrate absorption by using reflective rather than Hello and Vinet15,16 developed an exact result for the transmissive components.7–12 The use of reflective optics distortions induced in the surface of a right circular cyl- not only eliminates substrate absorption and thermal inder of radius a and thickness h, under thermal loading lensing, it also allows for the use of substrate materials by surface absorption of a Gaussian light beam of 1/e2 ra- 1084-7529/07/030659-10/$15.00 © 2007 Optical Society of America 660 J. Opt. Soc. Am. A/Vol. 24, No. 3/March 2007 Lu et al. dius w, including both conductive and radiative cooling. In the steady state, the difference of the temperature field inside the mirror and the surrounding temperature field, T=Tint−Text, obeys the Laplace equation, 2T͑r,z͒ =0, ͑1ٌ͒ subject to the boundary conditions on the barrel ͑r=a͒,at the front surface (the plane z=−h/2), and at the back sur- face (the plane z=h/2): T͑r,− h/2͒ץ T͑a,z͒ץ − ␬ =4␴ЈT3 T͑a,z͒,−␬ zץ z extץ 2P = ⑀ exp͑−2r2/w2͒ −4␴ЈT3 T͑r,− h/2͒, ␲w2 ext T͑r,h/2͒ץ − ␬ =4␴ЈT3 T͑r,h/2͒. ͑2͒ z ext Fig. 2. Fractional deviation between the simplified theory andץ the exact model of Hello and Vinet versus optic size. The x axis indicates the scaling of the optic relative to a fixed beam size of These dictate the balance between the power absorbed w=3.5 cm. The aspect ratio of the optic was held fixed, with h from a Gaussian beam of power P and spot size w with an =a. Fractional deviations were calculated at r=2w by taking the intensity profile, difference between the simplified and exact theories and dividing by the exact theory. An emissivity of 0.5 was used. 2P I͑r͒ = exp͑−2r2/w2͒, ͑3͒ ␲w2 3. SIMPLIFIED ANALYSIS Here, we develop a simplified analysis, which reproduces and the power radiated according to the Stefan– the results of Hello and Vinet for most cases of interest Boltzmann relation linearized in T, where ⑀ is the fraction and is convenient for design calculations. The approxi- of the incident power absorbed, ␴Ј is the Stefan– mate computation is based on the observation that cylin- Boltzmann constant corrected for the emissivity of the drical mirrors of radius aϾ2w and thickness hϾ2w are material, and ␬ is the thermal conductivity of the mirror expected in all currently discussed advanced substrate. The coordinate system, geometry of the mirror, gravitational-wave interferometers due to considerations and the orientation of the Gaussian heating beam are of optical losses and mirror thermal noise. Under these shown in Fig. 1. In the analysis of Hello and Vinet, an ex- conditions, we assume that the temperature and elastic act solution for the temperature field is expressed as a distortions in a finite mirror can be approximated by the Dini series, and then this temperature field is used to solutions for a half-infinite mirror out to radii where the compute the thermoelastic surface distortions. intensity of the light beam becomes negligible, ϳrՆ2w. We have compared Hello and Vinet for gravitational-wave mirrors and reflective beam splitters of silicon, sapphire, and fused silica to our formalism. Over the range rϽ2w, the two theories differ by less than 11% in the worst case. Figure 2 compares the two theories for different materials and optic sizes. For the case described in our experiment, where a=12.7 mm, w=1.1 mm, and the substrate is BK-7, the two theories differ by ϳ0.3%. For this paper, we have used our simplified theory and believe that for studying gravitational-wave detector design, when somewhat more accuracy than is obtainable with the approach of Winkler et al.13,14 is required, the simpler expressions shown here may be more convenient than the exact expressions of Hello and Vinet. Our model uses the temperature profile in the half- infinite optic to estimate the distortions in a finite-sized mirror. Normalizing the temperatures to a characteristic value, 2⑀P T = , ͑4͒ Fig. 1. Coordinate system and geometry used to calculate the c ␲w␬ temperature field and the thermoelastic distortions. Note that we have selected the same coordinate system as Hello and Vinet ¯ (Ref. 16) in which the heated surface is in the plane z=−h/2. The according to T=T/Tc, and expressing the spatial dimen- heating beam is normally incident on the grating. sions in terms of the laser beam waist w as ¯r=r/w and Lu et al. Vol. 24, No. 3/March 2007/J. Opt. Soc. Am. A 661 ¯z=z/w, the boundary condition for the front face given in ings capable of handling high power have been demon- Eq. (2) can be written strated, for example, at Lawrence Livermore National Laboratory17 for stretching and compressing high-energy ¯ T 1 laser pulses. Several effects must be addressed before aץ − + T¯ = exp͑−2¯r2͒, ͑5͒ grating can be considered for use as a diffractive beam z ¯l¯ץ th splitter in a gravitational-wave interferometer.10 The ¯ ␬ ͑ ␴ 3 ͒ wavelength dependence of the diffraction angle couples where lth=wlth= / 4 ЈText characterizes the relative im- portance of radiation versus conduction for removing heat laser frequency noise to beam pointing fluctuations; the from the illuminated region and is the only parameter in spatial profile of the diffracted beam is in general ellipti- the solution for the thermal field. Appendix A shows that cal; and thermoelastic deformation of the substrate af- for a half-infinite mirror with a radiative boundary condi- fects the diffracted beam differently than the reflected tion on the reflective surface, which is also absorbing a beam. As discussed in Ref. 10, using the grating near the fraction of the laser light, the dimensionless temperature Littrow configuration reduces the ellipticity of the dif- can be written fracted beam, and the dispersion in the grating can be compensated for by using an additional grating or by ϱ ͓ 2 ͑ ¯ ͔͒ ͑ ͒ 1 exp − k /8 − k ¯z + h/2 J0 kr¯ double passing the grating to null the dispersion.
Load more

Recommended publications
  • Wavefront Decomposition and Propagation Through Complex Models with Analytical Ray Theory and Signal Processing Paul Cristini, Eric De Bazelaire
    Wavefront decomposition and propagation through complex models with analytical ray theory and signal processing Paul Cristini, Eric de Bazelaire To cite this version: Paul Cristini, Eric de Bazelaire. Wavefront decomposition and propagation through complex models with analytical ray theory and signal processing. 2006. hal-00110279 HAL Id: hal-00110279 https://hal.archives-ouvertes.fr/hal-00110279 Preprint submitted on 27 Oct 2006 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. March 31, 2006 14:7 WSPC/130-JCA jca_sbrt Journal of Computational Acoustics c IMACS Wavefront decomposition and propagation through complex models with analytical ray theory and signal processing P. CRISTINI CNRS-UMR5212 Laboratoire de Mod´elisation et d'Imagerie en G´eosciences de Pau Universit´e de Pau et des Pays de l'Adour BP 1155, 64013 Pau Cedex, France [email protected] E. De BAZELAIRE 11, Route du bourg 64230 Beyrie-en-B´earn, France [email protected] Received (Day Month Year) Revised (Day Month Year) We present a novel method which can perform the fast computation of the times of arrival of seismic waves which propagate between a source and an array of receivers in a stratified medium.
    [Show full text]
  • Model-Based Wavefront Reconstruction Approaches For
    Submitted by Dipl.-Ing. Victoria Hutterer, BSc. Submitted at Industrial Mathematics Institute Supervisor and First Examiner Univ.-Prof. Dr. Model-based wavefront Ronny Ramlau reconstruction approaches Second Examiner Eric Todd Quinto, Ph.D., Robinson Profes- for pyramid wavefront sensors sor of Mathematics in Adaptive Optics October 2018 Doctoral Thesis to obtain the academic degree of Doktorin der Technischen Wissenschaften in the Doctoral Program Technische Wissenschaften JOHANNES KEPLER UNIVERSITY LINZ Altenbergerstraße 69 4040 Linz, Osterreich¨ www.jku.at DVR 0093696 Abstract Atmospheric turbulence and diffraction of light result in the blurring of images of celestial objects when they are observed by ground based telescopes. To correct for the distortions caused by wind flow or small varying temperature regions in the at- mosphere, the new generation of Extremely Large Telescopes (ELTs) uses Adaptive Optics (AO) techniques. An AO system consists of wavefront sensors, control algo- rithms and deformable mirrors. A wavefront sensor measures incoming distorted wave- fronts, the control algorithm links the wavefront sensor measurements to the mirror actuator commands, and deformable mirrors mechanically correct for the atmospheric aberrations in real-time. Reconstruction of the unknown wavefront from given sensor measurements is an Inverse Problem. Many instruments currently under development for ELT-sized telescopes have pyramid wavefront sensors included as the primary option. For this sensor type, the relation between the intensity of the incoming light and sensor data is non-linear. The high number of correcting elements to be controlled in real-time or the segmented primary mirrors of the ELTs lead to unprecedented challenges when designing the control al- gorithms.
    [Show full text]
  • Megakernels Considered Harmful: Wavefront Path Tracing on Gpus
    Megakernels Considered Harmful: Wavefront Path Tracing on GPUs Samuli Laine Tero Karras Timo Aila NVIDIA∗ Abstract order to handle irregular control flow, some threads are masked out when executing a branch they should not participate in. This in- When programming for GPUs, simply porting a large CPU program curs a performance loss, as masked-out threads are not performing into an equally large GPU kernel is generally not a good approach. useful work. Due to SIMT execution model on GPUs, divergence in control flow carries substantial performance penalties, as does high register us- The second factor is the high-bandwidth, high-latency memory sys- age that lessens the latency-hiding capability that is essential for the tem. The impressive memory bandwidth in modern GPUs comes at high-latency, high-bandwidth memory system of a GPU. In this pa- the expense of a relatively long delay between making a memory per, we implement a path tracer on a GPU using a wavefront formu- request and getting the result. To hide this latency, GPUs are de- lation, avoiding these pitfalls that can be especially prominent when signed to accommodate many more threads than can be executed in using materials that are expensive to evaluate. We compare our per- any given clock cycle, so that whenever a group of threads is wait- formance against the traditional megakernel approach, and demon- ing for a memory request to be served, other threads may be exe- strate that the wavefront formulation is much better suited for real- cuted. The effectiveness of this mechanism, i.e., the latency-hiding world use cases where multiple complex materials are present in capability, is determined by the threads’ resource usage, the most the scene.
    [Show full text]
  • Wavefront Coding Fluorescence Microscopy Using High Aperture Lenses
    Wavefront Coding Fluorescence Microscopy Using High Aperture Lenses Matthew R. Arnison*, Carol J. Cogswelly, Colin J. R. Sheppard*, Peter Törökz * University of Sydney, Australia University of Colorado, U. S. A. y Imperial College, U. K. z 1 Extended Depth of Field Microscopy In recent years live cell fluorescence microscopy has become increasingly important in biological and medical studies. This is largely due to new genetic engineering techniques which allow cell features to grow their own fluorescent markers. A pop- ular example is green fluorescent protein. This avoids the need to stain, and thereby kill, a cell specimen before taking fluorescence images, and thus provides a major new method for observing live cell dynamics. With this new opportunity come new challenges. Because in earlier days the process of staining killed the cells, microscopists could do little additional harm by squashing the preparation to make it flat, thereby making it easier to image with a high resolution, shallow depth of field lens. In modern live cell fluorescence imag- ing, the specimen may be quite thick (in optical terms). Yet a single 2D image per time–step may still be sufficient for many studies, as long as there is a large depth of field as well as high resolution. Light is a scarce resource for live cell fluorescence microscopy. To image rapidly changing specimens the microscopist needs to capture images quickly. One of the chief constraints on imaging speed is the light intensity. Increasing the illumination will result in faster acquisition, but can affect specimen behaviour through heating, or reduce fluorescent intensity through photobleaching.
    [Show full text]
  • Topic 3: Operation of Simple Lens
    V N I E R U S E I T H Y Modern Optics T O H F G E R D I N B U Topic 3: Operation of Simple Lens Aim: Covers imaging of simple lens using Fresnel Diffraction, resolu- tion limits and basics of aberrations theory. Contents: 1. Phase and Pupil Functions of a lens 2. Image of Axial Point 3. Example of Round Lens 4. Diffraction limit of lens 5. Defocus 6. The Strehl Limit 7. Other Aberrations PTIC D O S G IE R L O P U P P A D E S C P I A S Properties of a Lens -1- Autumn Term R Y TM H ENT of P V N I E R U S E I T H Y Modern Optics T O H F G E R D I N B U Ray Model Simple Ray Optics gives f Image Object u v Imaging properties of 1 1 1 + = u v f The focal length is given by 1 1 1 = (n − 1) + f R1 R2 For Infinite object Phase Shift Ray Optics gives Delta Fn f Lens introduces a path length difference, or PHASE SHIFT. PTIC D O S G IE R L O P U P P A D E S C P I A S Properties of a Lens -2- Autumn Term R Y TM H ENT of P V N I E R U S E I T H Y Modern Optics T O H F G E R D I N B U Phase Function of a Lens δ1 δ2 h R2 R1 n P0 P ∆ 1 With NO lens, Phase Shift between , P0 ! P1 is 2p F = kD where k = l with lens in place, at distance h from optical, F = k0d1 + d2 +n(D − d1 − d2)1 Air Glass @ A which can be arranged to|giv{ze } | {z } F = knD − k(n − 1)(d1 + d2) where d1 and d2 depend on h, the ray height.
    [Show full text]
  • Adaptive Optics: an Introduction Claire E
    1 Adaptive Optics: An Introduction Claire E. Max I. BRIEF OVERVIEW OF ADAPTIVE OPTICS Adaptive optics is a technology that removes aberrations from optical systems, through use of one or more deformable mirrors which change their shape to compensate for the aberrations. In the case of adaptive optics (hereafter AO) for ground-based telescopes, the main application is to remove image blurring due to turbulence in the Earth's atmosphere, so that telescopes on the ground can "see" as clearly as if they were in space. Of course space telescopes have the great advantage that they can obtain images and spectra at wavelengths that are not transmitted by the atmosphere. This has been exploited to great effect in ultra-violet bands, at near-infrared wavelengths that are not in the atmospheric "windows" at J, H, and K bands, and for the mid- and far-infrared. However since it is much more difficult and expensive to launch the largest telescopes into space instead of building them on the ground, a very fruitful synergy has emerged in which images and low-resolution spectra obtained with space telescopes such as HST are followed up by adaptive- optics-equipped ground-based telescopes with larger collecting area. Astronomy is by no means the only application for adaptive optics. Beginning in the late 1990's, AO has been applied with great success to imaging the living human retina (Porter 2006). Many of the most powerful lasers are using AO to correct for thermal distortions in their optics. Recently AO has been applied to biological microscopy and deep-tissue imaging (Kubby 2012).
    [Show full text]
  • Huygens Principle; Young Interferometer; Fresnel Diffraction
    Today • Interference – inadequacy of a single intensity measurement to determine the optical field – Michelson interferometer • measuring – distance – index of refraction – Mach-Zehnder interferometer • measuring – wavefront MIT 2.71/2.710 03/30/09 wk8-a- 1 A reminder: phase delay in wave propagation z t t z = 2.875λ phasor due In general, to propagation (path delay) real representation phasor representation MIT 2.71/2.710 03/30/09 wk8-a- 2 Phase delay from a plane wave propagating at angle θ towards a vertical screen path delay increases linearly with x x λ vertical screen (plane of observation) θ z z=fixed (not to scale) Phasor representation: may also be written as: MIT 2.71/2.710 03/30/09 wk8-a- 3 Phase delay from a spherical wave propagating from distance z0 towards a vertical screen x z=z0 path delay increases quadratically with x λ vertical screen (plane of observation) z z=fixed (not to scale) Phasor representation: may also be written as: MIT 2.71/2.710 03/30/09 wk8-a- 4 The significance of phase delays • The intensity of plane and spherical waves, observed on a screen, is very similar so they cannot be reliably discriminated – note that the 1/(x2+y2+z2) intensity variation in the case of the spherical wave is too weak in the paraxial case z>>|x|, |y| so in practice it cannot be measured reliably • In many other cases, the phase of the field carries important information, for example – the “history” of where the field has been through • distance traveled • materials in the path • generally, the “optical path length” is inscribed
    [Show full text]
  • Shack–Hartmann Wavefront Sensor with Array of Phase Coded Masks
    Shack–Hartmann wavefront sensor with array of phase coded masks NITIN DUBEY,* RAVI KUMAR, JOSEPH ROSEN School of Electrical and Computer Engineering, Ben-Gurion University of the Negev, P.O. Box 653, Beer-Sheva 8410501, Israel *Corresponding author: [email protected] Shack-Hartmann wavefront sensors (SHWS) are generally used to measure the wavefront curvature of light beams. Measurement accuracy and the sensitivity of these sensors are important factors for better wavefront sensing. In this study, we demonstrate a new type of SHWS with better measurement accuracy than the regular SHWS. The lenslet array in the regular SHWS is replaced with an array of coded phase masks and the principle of coded aperture correlation holography (COACH) is used for wavefront reconstruction. Sharper correlation peaks achieved by COACH improve the accuracy of the estimated local slopes of the measured wavefront and consequently improve the reconstruction accuracy of the overall wavefront. Experimental results confirm that the proposed method provides a lower mean square wavefront error by one order of magnitude in comparison to the regular SHWS. Shack-Hartmann wavefront sensor (SHWS) was developed for pattern created by illuminating a single CPM with a plane wave. The optical metrology purposes [1] and later has been used in various intensity response in each cell of the array is shifted according to the other fields, such as adaptive optics [2], microscopy [3], retinal average slope of the wavefront in each corresponding cell. Composing imaging [4], and high-power laser systems [5]. Usually, in SHWS a the entire slopes yields a three-dimensional curvature used as an microlens array is used to measure the wavefront local gradients.
    [Show full text]
  • From Scattering to Wavefronts: What’S in Between? Michael Mrochen, Phd
    From Scattering to Wavefronts: What’s in between? Michael Mrochen, PhD Swiss Federal Institute of Technology Institute of Biomedical Engineering IROC Institute for Refractive and Oculoplastic Surgery Zürich Switzerland Foreword • This is a report on a work in progress ! • Geometric-optical methods are used to develop an analytical theory for surface scattering on rough surface sturctures (irregular structures). • Parts of this work are published in: – SPIE Proceedings Ophthalmic Technologies (1998,1999) – Laser Physics 12: 1239-1256 (2002) – Laser Physics 12: 1333-1348 (2002) Clinical observation: Hartmann -Shack and Tscherning wavefront measurements demonstrate an increased background noise when the tearfilm breaks up. Clinical observation: Hartmann -Shack and Tscherning wavefront measurements demonstrate an increased background noise before and after LASIK After LASIK Before LASIK Clinical observation: Some eyes have irregular surface structures that are not reasonably described in terms of modes (Zernike, Taylor, ...) Striae Cornea after complicated LASIK BSCVA: 20/50 decentered measurement Centered measurement Problem ! Clinical observations indicate that there are other sources of optical errors that are not detected or described or measured by the currently used wavefront sensors. -> Visual symptoms do not correlate well with wavefront data in such complicated cases Question ?! What are the optical effects of such irregular structures ? Irregular structures = surface roughness Optical effects of that might detoriate the image quality
    [Show full text]
  • Predictive Dynamic Digital Holography
    Mechanical and Aerospace Engineering Beam Control Laboratory Predictive Dynamic Digital Holography Sennan Sulaiman Steve Gibson Mechanical and Aerospace Engineering UCLA [email protected] 1 1 Mechanical and Aerospace Engineering Beam Control Laboratory Predictive Dynamic Digital Holography Sennan Sulaiman Steve Gibson Mechanical and Aerospace Engineering UCLA [email protected] Thanks to Mark Spencer and Dan Marker AFRL, Kirtland AFB 2 2 Mechanical and Aerospace Engineering Beam Control Laboratory Motivation • Digital holography has received heightened attention in recent applications: – Optical Tweezing – Adaptive Optics – Wavefront Sensing • Major advantages of digital holography over classical AO: – Fewer optical components required – No wavefront sensing device required (Shack-Hartmann or SRI) – Versatility of processing techniques on both amplitude and phase information • Digital holography drawback: – Iterative numerical wavefront propagation and sharpness metric optimization • Computationally intensive 3 Mechanical and Aerospace Engineering Beam Control Laboratory Classical Adaptive Optics Optical Beam with Corrected Wavefront Adaptive Image of Wavefront (Phase) Optics Distant Point Source Sensor Algorithm Sharpened (Beacon) Image Adaptive Optics with Wavefront Prediction Optical Beam with Wavefront Corrected Wavefront Adaptive Image of Prediction Wavefront (Phase) Optics Distant Point Source Sensor Adaptive Algorithm Sharpened (Beacon) & Optimal Image Wavefront prediction compensates for loop delays due to sensor readout, processing,
    [Show full text]
  • Huygens-Fresnel's Wavefront Tracing in Non-Uniform Media
    12th International Conf. on Mathem.& Num. Aspects of Wave Propag., Karlsruhe (Germany), July 20-24, 2015 Huygens-Fresnel’s wavefront tracing in non-uniform media F.A. Volpe, P.-D. Létourneau, A. Zhao Dept Applied Physics and Applied Mathematics Columbia University, New York, USA 1 Motivation 1: validate unexpected EC full-wave results, and find more, but at ray tracing costs • Faster than full-wave, more informative than ray-tracing (diffraction, scattering, splitting, …) • Not replacing full-wave, but can guide it – (e.g. scan large spaces, select interesting cases) • Might replace ray tracing in real-time? • Full-waves in EC range are rare – >106 cubic wavelength • But found unexpected effects, t.b.c.: – O couples with X at fundamental harmonic – High production of EBWs at UHR – Collisionless damping of EBWs at UHR • Concern for ITER: deposition in wrong place • Fictitious, due to reduced wpe and wce? 2 Motivation 2: test old/new ideas too complicated for analytical treatment and too time-consuming for full-wave • EBWs – Electromagnetic nature – Interband tunneling • oblique propagation, large Larmor radii, non-circular orbits, non-sine-waves – Autoresonance (N||=1 but N100…) – Cherenkov radiation – Nonlinear • Affecting ne and B in which they propagate • Mode Conversions – Must evanescent barrier be thinner than wavelength or skin depth? – Parametric decay – Chaotic trajectories – Auto-interference of coexisting O, X and B – Self-scattering (e.g. of O off ne modulation by X or B) • Generic Wave Physics – Ponderomotive (density pump-out by ECH?) – Beam Broadening due to finite frequency bandwidth – Broadening by Scattering off “blobs” 3 Simple idea: numerically implement Huygens-Fresnel’s principle of diffraction • Huygens construction: “each element of a wavefront may be regarded as the center of a secondary disturbance which gives rise to spherical wavelets".
    [Show full text]
  • Seismic Ray Tracing and Wavefront Tracking in Laterally Heterogeneous Media
    Seismic ray tracing and wavefront tracking in laterally heterogeneous media N. Rawlinson ∗, J. Hauser, M. Sambridge Research School of Earth Sciences, Australian National University, Canberra ACT 0200, Australia 1 Introduction 1.1 Motivation One of the most common and challenging problems in seismology is the prediction of source-receiver paths taken by seismic energy in the presence of lateral variations in wavespeed. The solution to this problem is required in many applications that exploit the high frequency component of seismic records, such as body wave tomography, migra- tion of reflection data and earthquake relocation. The process of tracking the kinematic evolution of seismic energy also brings with it the possibility of computing various other wave-related quantities such as traveltime, amplitude, attenuation, or even the high fre- quency waveform, which can then be compared to observations. The difficulties associated with locating a two point path arise from the non-linear re- lationship between velocity and path geometry. Fig. 1, which shows a fan of ray paths ∗ Corresponding author. Email addresses: [email protected] (N. Rawlinson), [email protected] (J. Hauser), [email protected] (M. Sambridge). From: Advances in Geophysics, 49, 203-267. Published in 2007. v(km/s) 2 3 4 5 6 7 0 10 20 30 40 50 60 70 80 90 100 0 0 −10 −10 −20 −20 Depth (km) −30 −30 −40 −40 0 10 20 30 40 50 60 70 80 90 100 Distance (km) Fig. 1. Trajectories followed by a uniform fan of 100 rays emitted by a source point (grey dot) in a smoothly varying heterogeneous medium.
    [Show full text]