Waveguide group velocity determination by spectral interference measurements in NSOM

1
Waveguide group velocity determination by
spectral interference measurements in NSOM

• Bill Brocklesby
• Optoelectronics Research Centre
• University of Southampton, UK

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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 1130am, 203 B)
• Spectral interference between two pulses
  separated by small time interval
• NSOM can pick out this info with high spatial
  resolution

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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
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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
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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
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NSOM geometry
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
Femtosecond laser pulses in (87fs, 70MHz,
0.8nJ/pulse)
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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
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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

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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

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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
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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
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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
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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
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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

calculated index differences
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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

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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