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
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

5. 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

6. Samples - Ta2O5 rib waveguides
Ta2O5 waveguides designed for supercontinuum generation (Mesophotonics, Ltd)
Set of rib guides on SiO2, all on Si wafer
Ta2O5 has high n2
Can produce octave continuum with high-energy input pulses
Typically multimode at 4m width
Ta2O5 guides
500nm
4m
SiO2
Si wafer

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

8. Spectrally-resolved NSOM data
One lateral position along guide
Spectral fringes are clear in NSOM data
Some spectral broadening via SPM
high n2 guides
Red traces are not NSOM sampled - no interference
90fs pulse, 800pJ
guide output
input laser

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
Distance along guide
Distance across guide
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

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/vg), we get ng between and 0.258
ng= 0.1
ng= 0.058
ng= 0.174
ng= 0.258

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

14. Sensitivity to waveguide coupling
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
Moving coupling lens lower

15. Mode calculation Mode calculation
TM00
TM01
Mode calculation
finite difference and effective index modeling
~20 modes supported
Ta2O5 index varied with wavelength appropriately to get group velocities
Uncertainties in Ta2O5 index - annealing issues
Measured index is qualitatively correct
Too many modes to assign confidently
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. Baumberg3,4
[4] Dept of Physics and Astronomy, University Of Southampton, SO17 1BJ, UK
Martin D.B. Charlton2,3, Caterina Netti3,
Majd E. Zoorob3,
[2] School of Electronics and Computer Science, University of Southampton, SO17 1BJ, UK
[3] Mesophotonics Ltd, Southampton Science Park, Southampton, SO16 7NP, UK