Introduction to Photonics PDF 2020/2021

Introduction to Photonics by Carsten Fallnich, prof. dr. Winter term 2020/2021 © Thinkstock Wave & Fourier optics Introduction to Photonics by Carsten Fallnich November 16, 2020 - Pa...

Introduction to Photonics by Carsten Fallnich, prof. dr. Winter term 2020/2021 © Thinkstock Wave & Fourier optics Introduction to Photonics by Carsten Fallnich November 16, 2020 - Page: 2 Waves eellaa.be Introduction to Photonics by Carsten Fallnich November 16, 2020 - Page: 3  The 3D wave equation for the electric field A light wave can propagate in any direction in space. So we must allow the space derivative to be 3D:  2 E  2E  2E  2E  2E  2 E −  2 = 0 or + + −  2 = 0 t x 2 y 2 z 2 t which has the solution: E ( x, y, z, t ) = E0 exp[i(k  r −  t )] where k  ( kx , k y , kz ) k 2  k x2 + k y2 + k z2 r  ( x, y , z ) and k  r  kx x + k y y + kz z Introduction to Photonics by Carsten Fallnich November 16, 2020 - Page: 4 Longitudinal vs. transveral waves Longitudinal: A light wave is a transverse wave and motion is along has both electric and magnetic the direction of Propagation 3D vector fields: Transverse: … however, for most of the problems motion is transverse the magnetic contribution can be neglected, to the direction of such that only the electrical field is relevant. Propagation Introduction to Photonics by Carsten Fallnich November 16, 2020 - Page: 5 Could there be longitudinal contributions? E_longitud. E_transversal Consider that the electrical field is represented by a vector! Introduction to Photonics by Carsten Fallnich November 16, 2020 - Page: 6 Plane (optical) waves Introduction to Photonics by Carsten Fallnich November 16, 2020 - Page: 7 Waves in phasor diagram Introduction to Photonics by Carsten Fallnich Saleh/Teich, Fundamentals of Photonics November 16, 2020 - Page: 8 Types of waves Spherical wave Plane wave Introduction to Photonics by Carsten Fallnich Saleh/Teich, Fundamentals of Photonics November 16, 2020 - Page: 10 Types of waves   Spherical wave k k Plane wave Introduction to Photonics by Carsten Fallnich Saleh/Teich, Fundamentals of Photonics November 16, 2020 - Page: 11 Spherical wave becomes planar at infinity Introduction to Photonics by Carsten Fallnich Saleh/Teich, Fundamentals of Photonics November 16, 2020 - Page: 12 Transformation from plane to spherical or vice versa Introduction to Photonics by Carsten Fallnich November 16, 2020 - Page: 13 Superposition of electrical fields Electric fields: Intensity: e.g. two fields: Interference Terms ! Introduction to Photonics by Carsten Fallnich November 16, 2020 - Page: 14 Interference dependencies Measurable intensity: Electric field solution: Maximum interference for identical polarizations Maximum interference for identical frequencies Interference depends on relative phase Introduction to Photonics by Carsten Fallnich November 16, 2020 - Page: 15 Waves produce "beats" Individual waves Sum Envelope Irradiance Introduction to Photonics by Carsten Fallnich November 16, 2020 - Page: 16 Optical Path Difference is important Introduction to Photonics by Carsten Fallnich November 16, 2020 - Page: 17 Interference Fringe Contrast Introduction to Photonics by Carsten Fallnich November 16, 2020 - Page: 18 Constructive/destructive interference Introduction to Photonics by Carsten Fallnich November 16, 2020 - Page: 19 Michelson interferometer Interferometer … accomplish phase-to-amplitude transfer, i.e., phase is becoming measurable by (phase) comparison with reference beam! Introduction to Photonics by Carsten Fallnich November 16, 2020 - Page: 20 Michelson interferometer with divergent beam The Photonics Handbook Introduction to Photonics by Carsten Fallnich November 16, 2020 - Page: 21 Interferograms showing aberra- tions Introduction to Photonics by Carsten Fallnich The Photonics Handbook November 16, 2020 - Page: 22 Summation of amplitudes of finite wave packets Doubling the amplitudes No impact Introduction to Photonics by Carsten Fallnich November 16, 2020 - Page: 23 Interference of crossed beams e.g. for manufacturing of Fiber-Bragg- Gratings (FBG‘s), Laser-Doppler- Velocimetry (LDV or LDA) etc. Standing transverse waves Introduction to Photonics by Carsten Fallnich Saleh/Teich, Fundamentals of Photonics November 16, 2020 - Page: 24 Analogy b/w waveguide and potential well drhart.ucoz.com Introduction to Photonics by Carsten Fallnich November 16, 2020 - Page: 25 Huygens principle of elementary waves Diffraction: Plane The far-field is the Fourier-transform wave Spherical of the near-field! wave(s) Introduction to Photonics by Carsten Fallnich November 16, 2020 - Page: 26 Application of Huygens principle 1 2 Snellius‘ law: 1 = c1  c 2 = 2  n( 1) n( 2 ) Different phase velocities result in spatial spreading, e.g. by a prism Matter #1 Vacuum Interface Matter Matter #2 Introduction to Photonics by Carsten Fallnich November 16, 2020 - Page: 28  Interfering spherical waves also yield a standing wave Antinodes Note the different node patterns ! Introduction to Photonics by Carsten Fallnich November 16, 2020 - Page: 29 Interference of circular water waves.liquidgravity.nz Introduction to Photonics by Carsten Fallnich November 16, 2020 - Page: 30 Interference by wavefront division (e.g. Young‘s double slit experiment) Optical path difference determines bright or dark area at the screen! The idea is central e.g. for holography, ultrafast photography, and acousto-optic modulators etc. Introduction to Photonics by Carsten Fallnich November 16, 2020 - Page: 31 Multiple Beam Interference (e.g. at a grating) (Phase) grooves can be used instead of slits for OPD. Introduction to Photonics by Carsten Fallnich November 16, 2020 - Page: 32 MBI results in sharper maxima … … by re-distributing the light! Analogy between spatial and temporal domain, e.g. more modes allow shorter pulses ! Introduction to Photonics by Carsten Fallnich November 16, 2020 - Page: 33 Diffraction patterns … analogous to (temporal) light pulses! Introduction to Photonics by Carsten Fallnich web.utk.edu November 16, 2020 - Page: 34 Superpos. of waves at diff. frequencies Destructive superposition superposition Constructive Introduction to Photonics by Carsten Fallnich November 16, 2020 - Page: 35 Diffractive optics Bristle surface at the sea mouse de.wikipedia.org Data storage on a CD/DVD/BluRay Disc Introduction to Photonics by Carsten Fallnich November 16, 2020 - Page: 36 The sea mouse Length:15-20 cm Diameter: 5 cm Habitat: 1 bis 2000 m OSA Optics & Photonics News, Februar Introduction to Photonics by Carsten Fallnich November 16, 2020 - Page: 37 2003, Vol. 14, No. 2 Further photonic crystals in nature Morpho rhetenor Opt. Express 9, 567 (2001) Bio. Sci. 266, 1403 (1999) http://www.bugguy012002.co m/MORPHIDAE.html Proc. Nat. Acad.. USA, 100, 3µm 12576 (2003) Physics Today 57, 18 (2004) Introduction to Photonics by Carsten Fallnich November 16, 2020 - Page: 38 Two-dimensional 300 nm SiO2 - Cladding photonic crystal 500 nm Nb2O5 – Waveguide layer 2000 nm SiO2 - Substrate 300nm SiO2 n=1.43 500nm Nb2O5 n=2.1 2000nm SiO2 Missing holes form an optical waveguide as holes on the side act as highly reflective mirrors. Introduction to Photonics by Carsten Fallnich November 16, 2020 - Page: 39 Periodical structures for diffraction healingtoday.com USB4000 (Ocean Optics, Inc.) Introduction to Photonics by Carsten Fallnich November 16, 2020 - Page: 40 Diffractive optics for channel separation B A λ1 P1 Fiber 1 λ1 , λ 2 P2 Fiber 2 Input λ2 fiber Q d θ2 θ1 d λ1 = d sin( θ1 ) λ2 = d sin( θ2 ) d  sin(  ) = m   (m = 0,1, 2, 3,...) Introduction to Photonics by Carsten Fallnich November 16, 2020 - Page: 41 Anti-reflection coating With kind support by Physical Optics lectures by Rick Trebino “Notice that the center of the round glass plate looks like it’s missing. It’s not! There’s an “anti-reflection coating” there (on both the front and back of the glass).” Introduction to Photonics by Carsten Fallnich November 16, 2020 - Page: 42 Dielectric mirrors 100 T 90 r 80 a n 70 s 60 Tm [%] H i 50 s 40 L s i 30 o 20 n [%] 10 0 400 600 800 1000 1200 1400 1600 1800 2000 Wellenlänge [nm] Transmission Spectra of QWHL layer stacks (nL= 1,45 und nH= 2,30; center wavelength 1000nm for 1, 3, 5, 7, 9, 11 or 23 layers on fused silica (n=1.46). unpolarized light, normal incidence Introduction to Photonics by Carsten Fallnich November 16, 2020 - Page: 43  Double chirped mirrors v16110 1,0 Design 0,8 Measurement Transmittance 0,6 Ion Beam 0,4 Sputtering 56 Layers 0,2 TiO2/SiO2 0,0 500 550 600 650 1000 1500 Wavelength [nm] Introduction to Photonics by Carsten Fallnich November 16, 2020 - Page: 44 Interference phenomena …are dependent on the superposition of the involved fields and their relative optical path differences to each other. Introduction to Photonics by Carsten Fallnich November 16, 2020 - Page: 45 Multi-beam interference Introduction to Photonics by Carsten Fallnich November 16, 2020 - Page: 46 Fabry-Perot-Interferometer (FPI) … e.g. for the measurement of mirror Airy function Reflectivities or the loss between the mirrors. Introduction to Photonics by Carsten Fallnich Demtröder, Experimentalphysik November 16, 2020 - Page: 47 Fabry-Perot cavity as light analyzer … … of light frequency spectrum … of mirror or internal losses (i.e. “Ring-Down Spectroscopy“) Introduction to Photonics by Carsten Fallnich November 16, 2020 - Page: 48 A resonance (filter) structure results: Transmission Reflection Optical analogy to quantum mechanical double potential wall = finesse Characteristics can be used to stabilize laser frequency Introduction to Photonics by Carsten Fallnich November 16, 2020 - Page: 49 Fourier optics Introduction to Photonics by Carsten Fallnich November 16, 2020 - Page: 50 Fourier Transformation Animation by Lucas V. Barbosa (Own work) [Public domain], via Wikimedia Commons Introduction to Photonics by Carsten Fallnich Demtröder, Experimentalphysik I, Kap. 11 November 16, 2020 - Page: 51 Spatial Fourier transformation Saeh/Teich Introduction to Photonics by Carsten Fallnich Saleh/Teich, Fundamentals of Photonics November 16, 2020 - Page: 52 Transfer function of optical systems How to apply the spatial Fourier transformation? Introduction to Photonics by Carsten Fallnich Saleh/Teich, Fundamentals of Photonics November 16, 2020 - Page: 53 Spatial Fourier transformation fourier.eng.hmc.edu/e101/lectures/ Introduction to Photonics by Carsten Fallnich Image_Processing/node6.html November 16, 2020 - Page: 54 2D Fourier Transform: a square function Consider a square function in the xy plane: f(x,y) FT{f(x,y)} f(x,y) = rect(x) rect(y) y The 2D Fourier Transform splits into x the product of two 1D Fourier Transforms: FT{f(x,y)} = sinc(kx) sinc(ky) This picture is an optical determination of the Fourier Transform of the square function! Introduction to Photonics by Carsten Fallnich Optics lecture by Rick Trebino November 16, 2020 - Page: 55 Image- und Fourier-Space Image Fourier transform Introduction to Photonics by Carsten Fallnich topmotosfotos.blogspot.com November 16, 2020 - Page: 56 Spatial Fourier transformation, e.g., via lenses axial position angle Introduction to Photonics by Carsten Fallnich Saleh/Teich, Fundamentals of Photonics November 16, 2020 - Page: 57 Fourier filtering in a 4f-system Introduction to Photonics by Carsten Fallnich Saleh/Teich, Fundamentals of Photonics November 16, 2020 - Page: 58 Image filtering in Fourier plane Low-, high- or band-passing In the Fourier plane Introduction to Photonics by Carsten Fallnich Saleh/Teich, Fundamentals of Photonics November 16, 2020 - Page: 59 Spatial Fourier transformation Introduction to Photonics by Carsten Fallnich cns-alumni.bu.edu/~slehar/fourier/fourier.html#filtering November 16, 2020 - Page: 60 Which quantity does domiminate in spatial Fourier transformation? A) Amplitude B) Phase C) Both are equally of importance Make your choice … Introduction to Photonics by Carsten Fallnich November 16, 2020 - Page: 61 Evers vs. Fallnich Amplitude “Fallnich“ + Phase “Evers“ Introduction to Photonics by Carsten Fallnich November 16, 2020 - Page: 62 Evers vs. Fallnich (crosscheck) Amplitude “Evers“ + Phase “Fallnich“ Introduction to Photonics by Carsten Fallnich November 16, 2020 - Page: 63 Fourier transformation as a tool Remember transfer functions of ideal filters Free software download of ImageJ: rsb.info.nih.gov/ij/download.html Instructive examples of spatial Fourier transformation: cns-alumni.bu.edu/~slehar/fourier/ fourier.html#filtering Introduction to Photonics by Carsten Fallnich November 16, 2020 - Page: 64 Elimination of perturbations Introduction to Photonics by Carsten Fallnich November 16, 2020 - Page: 65 Pulse shaping with 4f-setup mbi.de Wavelength dependence of diffaction at a (transmission) grating: Introduction to Photonics by Carsten Fallnich web.physik.uni-rostock.de November 16, 2020 - Page: 66 Spectral phase of light pulses j(7) = 0 j(6) = 0 j(5) = 0 j(4) = 0 j(3) = 0 j(2) = 0 j(1) = 0 0 time 67 Introduction to Photonics by Carsten Fallnich November 16, 2020 - Page: 67 Spectral phase of light pulses j(7) = 1.2 0 p j(6) = 1.0 0 p j(5) = 0.8 0 p j(4) = 0.6 0 p j(3) = 0.4 0 p j(2) = 0.2 0 p j(1) = 0 0 time 68 Introduction to Photonics by Carsten Fallnich November 16, 2020 - Page: 68 Amplitudes/phases of spectral components Introduction to Photonics by Carsten Fallnich November 16, 2020 - Page: 69 Introduction to Photonics by Carsten Fallnich November 16, 2020 - Page: 70 Phase-dependent changes mbi.de Stretching and compression factor up to 10,000 ! Jean-Claude Diels & Wolfgang Rudolph Introduction to Photonics by Carsten Fallnich Ultrashort Laser Pulse Phenomena November 16, 2020 - Page: 71 Diffraction Light does not always travel in a straight line. It tends to bend around objects. This tendency is called “diffraction“. Light passing by edge Shadow of a hand illuminated by a Helium-Neon laser Electrons passing by an edge (Mg0 crystal) Introduction to Photonics by Carsten Fallnich Optics lecture by Rick Trebino November 16, 2020 - Page: 72 Take the length scales into account (Fresnel number) z Geometrical Diffraction: umbra: F d, F >> 1, λ