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

2. 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 QFE5, Fri 11:30am, 203 B) –Spectral interference between two pulses separated by small time interval NSOM can pick out this info with high spatial resolution

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

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

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

6. Samples - Ta 2 O 5 rib waveguides Ta 2 O 5 waveguides designed for supercontinuum generation (Mesophotonics, Ltd) Set of rib guides on SiO 2, all on Si wafer Si wafer SiO 2 Ta 2 O 5 guides 500nm Ta 2 O 5 has high n 2 Can produce octave continuum with high-energy input pulses Typically multimode at 4  m width 4m4m

7. NSOM geometry 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 CCD- based spectrometer 6mm Femtosecond laser pulses in (87fs, 70MHz, 0.8nJ/pulse) SNOM probe x y Continuum out 100nm uncoated pulled fiber tip, ~80nm tip diameter

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

9. 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

10. NSOM and mode beating Single frequency propagating along the guide in two modes will interfere, producing mode beating. Example - TM00, TM01 lateral intensity profile with distance –Beat length given by phase velocity difference NSOM tip on guide edge sees coupled intensity modulation Distance along guide Distance across guide

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

12. 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/v g ), we get  n g between 0.058 and 0.258  n g = 0.058  n g = 0.1  n g = 0.174  n g = 0.258

13. Effect of nonlinearity Pulse energy varied from 0.8nJ to 2.1nJ –No deviation of mode spacing in time Spectral broadening increases by x2 with pulse power 0.8nJ 1.5nJ 2.1nJ 0.8nJ 1.5nJ 2.1nJ

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

15. 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 TM00TM01 calculated index differences

16. 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

17. Acknowlegements John D. Mills, Tipsuda Chaipiboonwong Optoelectronics Research Centre, University of Southampton, SO17 1BJ, UK Jeremy J. Baumberg 3,4 [4] Dept of Physics and Astronomy, University Of Southampton, SO17 1BJ, UK Martin D.B. Charlton 2,3, Caterina Netti 3, Majd E. Zoorob 3, [2] School of Electronics and Computer Science, University of Southampton, SO17 1BJ, UK [3] Mesophotonics Ltd, Southampton Science Park, Southampton, SO16 7NP, UK