Guided Acoustic Wave Brillouin Scattering (GAWBS) in Photonic Crystal Fibers (PCFs) FRISNO-9 Dominique Elser 15/02/2007
GAWBS Theory Thermally excited acoustic fiber vibrations at certain resonance frequencies scatter light due to i) modulation of refractive index (photoelastic effect) ii) transversal acoustic phonons Conservation of energy: momentum: fiber incident photon scattered photon phonon transversal phonons if Page 1
Acoustic Modes in Standard Fibers R0,3 0,0 Radial modes R0,m induce phase noise by modulating the refractive index. TR4,0 2,5 2,0 Mixed torsional-radial modes TR2,m induce phase and polarization noise (by generating birefringence in the fiber). R. M. Shelby, M. D. Levenson, and P. W. Bayer, Phys. Rev. Lett. 54, 939 (1985). Page 2
Investigated Fibers Standard Fibers Photonic Crystal Fibers (PCFs) FS-PM-4611 3M HB800G Fibercore Lucent fiber NL-PM-700 Crystal Fibre PM-1550-01 Crystal Fibre PM NL 3.0 850 Crystal Fibre Highly birefringent #2 N. Joly, Ph. Russell Highly birefringent #9 N. Joly, Ph. Russell Phase noise discrete peaks over whole measured frequency spectrum discrete peaks over whole measured frequency spectrum reduced up to 250MHz highly reduced up to 200MHz enhanced between 500 and 800MHz partly reduced up to 500MHz, enhanced above not measured not measured Polarization noise discrete peaks over whole measured frequency spectrum discrete peaks over whole measured frequency spectrum not measured highly reduced up to 200MHz enhanced between 250 and 800MHz partly reduced up to 500MHz, enhanced above reduced below 190MHz, enhanced above reduced below 75MHz, enhanced above 300MHz Amplitude noise not visible not visible not measured not visible to be investigated high peak at 53MHz not measured several peaks between 90 and 380 MHz Quantum noise reduction 5.1dB polarization squeezing in FS-PM-7811 not measured 1.7dB amplitude squeezing by spectral filtering about to be measured not measured 1.7dB polarization squeezing in PM-NL-800 not measured not measured modify acoustic spectrum by spatial structuring (phononic crystal) Page 3
Phase Noise Measurement Setup Page 4
Polarization Noise Measurement Setup Page 5
Phase Noise Measurements solid line: R 0,m -modes dashed line: std. fiber Page 6
Polarization Noise Measurements solid line: TR 2,m -modes dashed line: std. fiber Page 7
Acoustic Simulations Specifications: geometry: infinitely long cylinder with cross section boundary conditions: free material: silica glass (E, ν, ρ) model: plane strain eigenfrequency analysis with small displacements Equations: Result: frequency and displacements for every mode Normalization: total vibrational energy for each mode (equipartition theorem) Page 8
Optical Simulations Specifications: wavelength, refractive index boundary conditions: continuity of tangential components at holes model: perpendicular hybrid mode analysis Equations: assume: Result: effective index and electric field for the fundamental mode Page 9
Light-Sound Coupling Strain-optical effect (photoelastic effect) Phase noise: phase shift: forward scattering efficiency: Polarization noise: phase shift difference: forward scattering efficiency: Page 10
Phase Noise Simulation of Std. Fiber Page 11
Cross Section Plots Page 12
Polarization Noise Sim. of Std. Fiber Page 13
Simulation of Phase Noise in PCF Page 14
Radial Cladding Modes Page 15
Cross Section Plots light field in PCF Δn for PCF Δn for standard fiber Page 16
Quasi-radial Hole Structure Modes Page 17
Simulation of Polarization Noise in PCF Page 18
Core Vibrations J. Beugnot, T. Sylvestre, H. Maillotte, G. Mélin, and V. Laude Guided acoustic wave Brillouin scattering in photonic crystal fibers Optics Letters 32, 17 (2007) Page 19
Conclusion and Outlook Acoustic spectrum of fibers can be modified by spatial structuring Reduction of noise in broad frequency range improve squeezing and quantum state transmission Investigate cladding-less fibers Tailor structure to also reduce high frequency noise Include longitudinal phonon components and damping in simulations Page 20