Waveguide group velocity determination by spectral interference measurements

Waveguide group velocity determination by spectral interference measurements in NSOM Bill Brocklesby Optoelectronics Research Centre University of Southampton, UK

Motivation/background • NSOM valuable for spatial measurements of propagation • Fs pulses give easily-resolvable spectral information about their propagation – Can measure evolution of continuum generation (Paper QFE 5, Fri 11: 30 am, 203 B) – Spectral interference between two pulses separated by small time interval • NSOM can pick out this info with high spatial resolution

Spectral interference • Overlap of frequencies from each pulse with different phases causes interference Pulse intensity vs time • Results in spectral ‘fringes’ which vary with pulse separation • Well-known from coherent control experiments Pulse spectrum

Samples - Ta 2 O 5 rib waveguides • • Ta 2 O 5 waveguides designed for supercontinuum generation (Mesophotonics, Ltd) • Ta 2 O 5 has high n 2 • Can produce octave continuum with high-energy input pulses Set of rib guides on Si. O 2, all on Si wafer • Typically multimode at 4 m width Ta 2 O 5 guides 500 nm 4 m Si. O 2 Si wafer

NSOM geometry SNOM probe y x Continuum out 6 mm • NSOM probe locked to surface via shear force • Uncoated probe samples evanescent field above guide – evanescent decay lengths different for each mode • Probe output to CCDbased spectrometer uncoated Femtosecond laser pulses in (87 fs, 70 MHz, 0. 8 n. J/pulse) pulled fiber tip, ~80 nm tip 100 nm diameter

Spectrally-resolved NSOM data • One lateral position along guide • Spectral fringes are clear in NSOM data 90 fs pulse, 800 p. J guide output • Some spectral broadening via SPM – high n 2 guides • Red traces are not NSOM sampled - no interference input laser

Transforming the spectral fringes • This is FT of spectral data NOT the time profile – Same for constant spectral phase • Spectral fringes produce peaks in time data • Separation of peaks increases with time – Group velocity differences • Many different mode differences

NSOM and mode beating nce a Dist • Single frequency propagating along the guide in two modes will interfere, producing mode beating. • Example - TM 00, TM 01 lateral intensity profile with distance alon ide g gu – Beat length given by phase velocity difference Distance across guide • NSOM tip on guide edge sees coupled intensity modulation

Local spectral fringe variation • For each frequency, mode beating produces regular intensity modulation in NSOM signal along guide Simulation of spectral intensity variation • Variation in phase velocity with wavelength causes spectral fringes at any particular length • Variation of spectral fringe separation with distance gives group velocity NSOM measurement of spectral intensity variation

Extracting group velocity information • Plotting peaks from previous graph • Different gradients give difference in group velocity between modes • Expressed in terms of group index (c/vg), we get ng between 0. 058 and 0. 258 ng= 0. 1 ng= 0. 058 ng= 0. 174 ng= 0. 258

Effect of nonlinearity • Pulse energy varied from 0. 8 n. J to 2. 1 n. J – No deviation of mode spacing in time • Spectral broadening increases by x 2 with pulse power 2. 1 n. J 1. 5 n. J 0. 8 n. J

Sensitivity to waveguide coupling • Change input coupling Mode disappears Mode appears – Change position of coupling lens – change mode distribution • Time pattern is sensitive to this – Particular differences appear and disappear from time profile Moving coupling lens lower

Mode calculation TM 00 TM 01 • Mode calculation – finite difference and effective index modeling – ~20 modes supported • Ta 2 O 5 index varied with wavelength appropriately to get group velocities – Uncertainties in Ta 2 O 5 index annealing issues • Measured index is qualitatively correct – Too many modes to assign confidently calculated index differences

Summary • Spectral interference changes spectrum sampled by NSOM probe from multimode waveguide • Much information available – Differences in mode group velocities directly measured – Phase velocity at each wavelength also available in principle - check on group velocity. – GVD via peak width? • Plans to repeat with smaller, better characterized guides – Fewer modes = more tractable – Well-defined index makes accurate mode calculation possible

Acknowlegements John D. Mills, Tipsuda Chaipiboonwong Optoelectronics Research Centre, University of Southampton, SO 17 1 BJ, UK Jeremy J. Baumberg 3, 4 [4] Dept of Physics and Astronomy, University Of Southampton, SO 17 1 BJ, UK Martin D. B. Charlton 2, 3, Caterina Netti 3, Majd E. Zoorob 3, [2] School of Electronics and Computer Science, University of Southampton, SO 17 1 BJ, UK [3] Mesophotonics Ltd, Southampton Science Park, Southampton, SO 16 7 NP, UK