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