waveguide group velocity determination by spectral interference measurements in nsom bill brocklesby...
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Waveguide group velocity determination by spectral interference measurements in NSOM
Bill BrocklesbyOptoelectronics 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 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
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
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
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
Samples - Ta2O5 rib waveguides
• Ta2O5 waveguides designed for
supercontinuum generation (Mesophotonics, Ltd)
• Set of rib guides on SiO2, all on
Si wafer
Si wafer
SiO2
Ta2O5 guides
500nm
• Ta2O5 has high n2
• Can produce octave continuum with high-energy input pulses
• Typically multimode at 4m width
4m
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
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
input laser
guide output
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
• 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
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
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= 0.058
ng= 0.1
ng= 0.174
ng= 0.258
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
0.8nJ1.5nJ2.1nJ
0.8nJ1.5nJ2.1nJ
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
Mode calculation
• 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
TM00 TM01
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 ChaipiboonwongOptoelectronics 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