Modern Classical Optics

Transcription

1 Modern Classical Optics GEOFFREY BROOKER Department of Physics University of Oxford OXPORD UNIVERSITY PRESS

2 Contents 1 Electromagnetism and basic optics Introduction The Maxwell equations Linear isotropic media Plane electromagnetic waves Energy flow Scalar wave amplitudes Dispersive media Electrical transmission lines Elementary (ray) optics The thin lens Sign Conventions Refraction at a spherical surface The thick lens Rays and waves 12 Problems 13 2 Fourier series and Fourier transforms Introduction Fourier series: spectrum of a periodic waveform Fourier series: a mathematical reshape The Fourier transform: spectrum of a non-periodic waveform The analytic signal The Dirac 5-function Frequency and angular frequency The power spectrum Examples of Fourier transforms A Single rectangular pulse The double pulse A 5-function pulse A regulär array of J-functions A random array of <J-functions An infinite sinewave Convolution and the convolution theorem Examples of convolution Sign choices with Fourier transforms 32 Problems* 33

3 x Contents 3 Diffraction Introduction Monochromatic spherical wave The Kirchhoff diffraction integral The Kirchhoff boundary conditions Simplifying the Kirchhoff integral Complementary screens: the Babinet principle The Fraunhofer condition I: provisional Fraunhofer diffraction in 'one dimension' Fraunhofer diffraction in 'two dimensions' Two ways of looking at diffraction Examples of Fraunhofer diffraction Fraunhofer diffraction and Fourier transforms The Fraunhofer condition II: Rayleigh distance and Fresnel number The Fraunhofer condition III: object and image The Fresnel case of diffraction Fraunhofer diffraction and optical resolution Surfaces whose fields are related by a Fourier transform Kirchhoff boundary conditions: a harder look 70 Problems 72 4 Diffraction gratings Introduction A basic transmission grating The multiple-element pattern Reflection grating Blazing Grating spectrometric instruments Spectroscopic resolution Making gratings Tricks of the trade Normal spectrum Correct illumination Shortening exposure times with a spectrograph Vacuum instruments Double monochromator An inventor's paradise Beyond the simple theory 99 Problems The Fabry-Perot Introduction Elementary theory Basic apparatus. ' The meaning of finesse Free spectral ränge and resolution Free spectral ränge 113

4 Contents xi Resolution Analysis of an etalon fringe pattern Flatness and parallelism of Fabry-Perot plates Designing a Fabry-Perot to do a job Practicalities of spectroscopy using a Fabry-Perot The Fabry-Perot as a source of ideas 122 Problems. 122 i 6 Thin films Introduction Basic calculation for one layer Matrix elimination of 'middle' amplitudes Reflected and transmitted waves Impedance concepts High-reflectivity mirrors Anti-reflection coatings Interference Alters Practicalities of thin-film deposition 141 Problems Ray matrices and Gaussian beams Introduction Matrix methods in ray optics Matrices for translation and refraction Reflections Spherical waves Gaussian beams Properties of a Gaussian beam Sign Conventions Propagation of a Gaussian beam Electric and magnetic fields 159 Problems Optical cavities Introduction Gauss-Hermite beams Cavity resonator Cavity modes The condition for a low-loss mode Finding the mode shape for a cavity Longitudinal modes High-loss cavities The symmetrical confocal cavity The confocal Fabry-Perot Choice of cavity geometry for a laser Selection of a desired transverse mode Mode matching 183 Problems 183

5 xii Contents» 9 Coherence: qualitative Introduction Terminology Young fringes: tolerance to frequency ränge Young fringes: tolerance to collimation Coherence area The Michelson stellar interferometer Aperture synthesis Longitudinal and transverse coherence Interference of two parallel plane waves Fast and slow detectors Coherence time and coherence length A Michelson interferometer investigating longitudinal coherence Fringe visibility Orders of magnitude Discussion What of lasers? The Young slits: another look Fast and slow detectors: another look Gräting monochromator: another look Polarized and unpolarized light 213 Problems Coherence: correlation functions Introduction Correlation function: definition Autocorrelation and the Michelson interferometer Normalized autocorrelation function Fringe visibility The Wiener-Khintchine theorem Fourier transform spectroscopy Partial coherence: transverse The van Cittert-Zernike theorem Intensity correlation Chaotic light and laser light The Hanbury Brown-Twiss experiment Stellar diameters measured by intensity correlation Classical and quantum optics 233 Problems Optical practicalities: etendue, interferometry, fringe localization Introduction Energy flow: etendue and radiance Conservation of etendue and radiance Longitudinal and transverse modes Etendue and coherence area 251

6 Contents xiii 11.6 Field modes and entropy Radiance of some optical sources Radiance of a black body Radiance of a gas-discharge lamp Radiance of a light-emitting diode (LED) Etendue and interferometers Etendue and spectrometers A design study: a Fourier-transform spectrometer Fringe localization 256 Problems Image formation: diffraction theory Introduction Image formation with transversely coherent illumination: informal Image formation: ideal optical system Image formation: imperfect optical system Microscope resolution: Abbe theory Abbe theory: introduction Abbe theory: explanation Improving the basic microscope Phase contrast Dark-ground illumination Schlieren Apodizing Holography The point spread function Optical transfer function; modulation transfer function. 284 Problems Holography Introduction Special case: plane-wave object beam and plane-wave reference beam The intensity of the reference beam The response of a Photographie emulsion The theory of holography Formation of an image What if we break a hologram in half? Replay with changed optical geometry The effect of a thick Photographie emulsion Phase holograms Gabor's holograms Practicalities Applications of holography 305 Problems 306 *

7 xiv Contents * 14 Optical fibres Introduction Fibre optics: basics Transverse modes Dispersion Material dispersion Intermodal and intramodal dispersion Multimode fibres Single-mode fibres 318 Problems Polarization Introduction Anisotropie media The mathematics of anisotropy The understanding of tensor EJJ The Faraday effect Optical activity 327 Problems Two modern optical devices Introduction Compact disc: description of the disc Compact disc: the encoding scheme Optics of reading a compact disc Feedback Systems Correction of tracking Correction of focus CD-ROM DVD The confocal microscope Confocal microscope: resolution The confocal microscope: depth of focus 344 Problems 345 Notes on selected problems 346 Bibliography 383 Index 387