Chapter X Interaction of L - Highlights

Lecture 17Chapter X Interaction of Light andSoundHighlightsPropagationof laserbeamsincrystalswith acousticwavesControlling thefrequency,intensity and direction of an optical beamPartiallyReflectingMirrorModelScattering of Light by SoundParticlePicture2.Raman-NathandBraggDiffraction3. BraggDiffractionofLightbyAcousticWaves-Analysis4. Deflection of Light by Sound

Lecture 17 Chapter X Interaction of Light and Sound Highlights 1. Scattering of Light by Sound 3. Bragg Diffraction of Light by Acoustic Waves - Analysis 2. Raman-Nath and Bragg Diffraction Controlling the frequency, intensity and direction of an optical beam Propagation of laser beams in crystals with acoustic waves 4. Deflection of Light by Sound Partially Reflecting Mirror Model Particle Picture

$ 10.1 Scattering of Light by SoundDiffraction of light by sound waves was predicted by Brillouin in 1922 anddemonstratedexperimentally sometenyearslaterDistanceAsoundwaveconsistsof sinusoidalZAverageIndexperturbation of the density ofthematerial, or strain, that travels at thesoundvelocityAn(z,t) = △nsin(の,t - k,z), / k,=vIndexofrefraction

§10.1 Scattering of Light by Sound A sound wave consists of sinusoidal perturbation of the density of the material, or strain, that travels at the sound velocity Index of refraction s s v Average Index Distance 0 z s v n(z,t) nsin( t k z)  =  s − s s s s  / k = v Diffraction of light by sound waves was predicted by Brillouin in 1922 and demonstrated experimentally some ten years later

S 1o.1 Scatteringof LightbySoundI.PartiallyReflectingMirrorsModelInterfere constructivelycondition(A) All the points on agivenmirrorcontribute inphase to the diffractiondirection...Forexample:IncidentopticalbeamOpticalpathdifference:AC-BDDiffractedbeammax(cos 0, -cos )Bn0, 0Hxx=0m=0,±1,±2m=0

§10.1 Scattering of Light by Sound I. Partially Reflecting Mirrors Model s s v x  i A  r  i  r B C D x = 0 n m x i r  (cos − cos ) = m = 0,1,2,. (A) All the points on a given mirror contribute in phase to the diffraction direction. Optical path difference: AC-BD i =r m = 0 For example: Interfere constructively condition -

S 1o.1 Scatteringof LightbySound(B)Diffractionfromany twoacousticphasefrontsadd up inphaseinthereflecteddirection..For example:Moving soundIncidentwavefunction(@s)opticalDiffractedbeam(o)beam(o+os)Opticalpathdifference:AO+OB22, sin 0= /nBBragg diffractionexamplea/n=0.5μmU, = 500MHzv,=300m/s0 ~ 4×10-2 rad ~ 3.5= V/v,=6×10-4cm

§10.1 Scattering of Light by Sound (B) Diffraction from any two acoustic phase fronts add up in phase in the reflected direction. s s v  A    B 0 Moving sound wavefunction (s ) For example: Optical path difference: AO+OB 2s sin  =  / n Bragg diffraction example  / n = 0.5m = 500MHz s = 300m/s s v / 6 10 cm −4 s = vs s =   4 10 rad 3.5 2    − 

S 10.1 Scattering of Light by SoundII.ParticlePicture of BraggDiffractionDual particle-wave nature of lightKConservation of momentumdiffracted22,sin0=a/nkd=k,+kkKincidentConservation of energyho;hod0=0, +0hoshohodho

§10.1 Scattering of Light by Sound II. Particle Picture of Bragg Diffraction Dual particle-wave nature of light kincident kdiffracted ks Conservation of momentum kd = ki +ks i s  d Conservation of energy d =i +s i  s d  d =i −s 2s sin  =  / n