The document outlines a research project focusing on using near-field scanning optical microscopy (NSOM) combined with spectral interferometry techniques to measure the electric field of light within photonic structures. It discusses the measurement of spectral amplitude, phase, and polarization, as well as the retrieval of group velocity and refractive index across various configurations. The findings highlight the advantages of NSOM for determining optical properties at a nanoscale level and for analyzing ultrafast laser pulses.

1. Slightly fishy? Combining NSOM with SEA TADPOLEJohanna Trägårdh, H. GersenUniversity of Bristol

2. Project aim
Measure the full electric field of light propagating in a photonic structure.
•Spectral amplitude, spectral phase and polarization Structure properties, n(w,x), dispersion
•Locally / on a sub-wavelength scale
•In a single point
•In the near-field

3. Description of a laser pulse
( ) ( ) ( )  w w w i E S e t I t e c c  i t t ( ) ( ) . ( ( ))
2
 1    w 
t w
Fourier
transform
(w)
S(w)
Absolute phase
( ) ( ) ( ) ... 2
2
2 0
1
0 0 1  w   w w   w w  
Equivalent to
a time delay
2nd order dispersion
Linear chirp in time

4. Crossed beam spectral interferometry
t=0
, cos 2 sin  (w)  (w)) ref sig ref sig sig ref S(ω y )  S (ω) S (ω) S (ω)S (ω) ( ky θ  
( ) ( ) ( ) ... 2
2
2 0
1
0 0 1  w   w w   w w  
Signal
Reference

5. NSOM on a waveguide
Optical amplitude
Amplitude
Si
SiO2
SiON
850nm
Sample
Near-field scanning optical microscope
Tuning fork
Fiberprobe
10 nm
Spatially Encoded Arrangement for Temporal Analysis by Dispersing a Pair of Light E-fields
Signal
(NSOM probe)
Reference
P. Bowlan, et al., Opt. Express 14, 11892(2006).

6. NSOM on a waveguide
Optical amplitude
Amplitude
40mm x 4.8mm
Topography
Si
SiO2
SiON
850nm
Optical Amplitude

7. NSOM and SEA TADPOLE
This measures:
•Spectral amplitude and phase
•In the near-field
•In a single point
•In 70 ms
Frequency w
y
))()(sin2cos,wwrefsigsigrefsigrefθky()ω()Sω(S)ω(S)ω(S)yω(S

8. Measuring the dispersion
The fringes in the interferogramwill shift as the phase of the detected light changes when the probe is moved

9. Measuring the dispersion
Spectral Phase
t=0
c
nwL
 
Refractive index
nmodel= 1.445
nMZ = 1.46
MZ

10. Measuring the group velocity
x=0
x=22 mm
The change in fringe tilt shows that the signal pulse has moved in time.
...)()()(22021100wwwww

11. Measuring the group velocity
A linear term in the spectral phase is equivalent to a time delay
t=0 ( ) ( ) ( ) ... 2
2
2 0
1
0 0 1  w   w w   w w  
w

 w
d
d
g Group delay: ( )  

12. Measuring the group velocity
Retrieved group velocity 1.98108
Group index ng=1.51
Group index from model ng=1.47
Fourier transform ( ) ( ) ( ) ( ) E S e E t i     w w w
Probe position

13. Conclusion
NSOM + SEA TADPOLE measures the full electric field of light
propagating in a photonic structure.
• Spectral amplitude, spectral phase (and polarization)
• In the near-field
• In a single point
• Retrieve group velocity and n(w,x)
SEA TADPOLE

15. Spectral interferometry on bulk optics
t=0
Angular frequency (THz)
Phase (rad)
(w)
S(w)
820 785 753
Wavelength (nm)
GDD=1163 fs2
GDDcalc=1142 fs2
( ) ( ) ( ) ... 2
2
2 0
1
0 0 1  w   w w   w w  
Frequency w
25mm BK7
No sample

16. Another way to track an ultrafast laser pulse in a photonic structure
AOM f=80.0 MHz
AOM f=80.07 MHz
Heterodyne detection in a Mach-Zehnderinterferometer
)cos()()(2detttItIISRw

17. Another way to track an ultrafast laser pulse in a photonic structure
We want to measure the phase and amplitude of the electric field of the light pulse, and also where it is in time.
AOM
AOM

18. Another way to track an ultrafast laser pulse in a photonic structure
We want to measure the phase and amplitude of the electric field of the light pulse, and also where it is in time.
AOM
AOM

19. Measuring the group velocity
t=0
Amplitude
t=67 fs
40mm x 4.8mm

20. Measuring the effective refractive index
t=0
Position (mm)
Fourier transform
n=1.46
ncalc=1.445
Frequency (1/nm)
t=0
A cos

21. Comparing the methods
Heterodyne detection in Mach-Zehnderinterferometer:
Measures effective refractive index (for centerfrequency).
Measures group index (with an accurate delay)
Requires scanning a large area –slow and requires periodic or invariant structures
t=0
Spectral interferometry:
Measures n(w)
Measures group index
Only requiresmeasurements in two or a few points.
In this configuration it requires a camera.