Transcript Document

Fibre nonlinearity as a monitor of ultrashort pulse
characteristics
Rama Chari
CAT, Indore 452013
R R Dasari Distinguished lecture series, Feb 28,2005
1
Complete measurement of an ultrashort pulse entails
measuring the amplitude ( or intensity ) and the phase in either
the spectral or temporal domain.
If we do not have a detector faster than the pulse then it is not
possible to measure the intensity and phase both by linear
measurements alone.
Fastest available detectors have a response time ~ few ps.
Expensive or cumbersome or both.
The way out :
Use the pulse to gate itself using optical nonlinearities.
2
Several methods already in use .
• Autocorrelation : intensity and interferometric
•Frequency resolved optical gating (FROG) and its
various versions
•Spectral phase interferometry for direct electric field
reconstruction (SPIDER)
3
Intensity Autocorrelation
• Autocorrelation width proportional to pulse
width
• Proportionality
shape
constant
depends
on
pulse
• Pulse shape only be reliably determined in
simple cases
• No direct signature of chirp (rely on TBP which
depends on shap)
4
Interferometric Autocorrelation
• Directly sensitive to chirp
• Width of fringes not pulse width but 1/spectral
width
• Contains Intensity Autocorrelation
• Harder to directly fit
•Algorithms like MOSAIC can be used to
generate
an
interferometric
autocorrelation trace whose shape is far more
sensitive to chirp than IAC.
5
FROG
•One of the most popular techniques for sub-ps pulses.
• A spectrogram of the autocorrelation is recorded and
iterative methods are used to retrieve the pulse phase and
amplitude.
•Fairly robust and well proven technique.
•Can be used in real time with fast algorithms.
6
SPIDER
•Interferometric technique for phase and amplitude
measurement.
•Iterative method not required.
• Experimentally more complicated to set up.
7
Pulse propagation in single mode optical fibres
Chromatic Dispersion : change in temporal width of the pulse
group velocity vg = c/[n+(dn/d)]
group velocity dispersion parameter 2 = d/ d(1/ vg)
For  < D, 2 > 0 , normal dispersion
For  > D, 2 < 0 , anomalous dispersion
In normal dispersion regime, pulse broadens as it moves along
the fibre .
8
blue
red
t
Tout = Tin [ 1+ (z/LD)2 ]1/2
9
•Self phase modulation : Spectral broadening and
modulation
Refractive index n eff = n () + n2I
Time dependent phase change NL(t) = n2k0L |E(t)|2
Instantaneous frequency (t)-0 = -d NL/dt
Consequences : chirp, broadening, modulations
•Other nonlinear effects : XPM, SRS etc
10
In normal dispersion regime
•Dispersion effects dominant at low powers, longer fibre
lengths.
L > LD=T02/|2|
•Nonlinearity dominant at higher powers, shorter fibre
lengths.
L >LNL = 1/P0
•Intermediate regime : both nonlinearity and GVD effects
have to be considered.
11
For a 10 ps, 1.06 m pulse, LD is ~ 8 Km.
For a 100 fs, 800 nm pulse, LD is ~ 28 cm.
For a 1.06 m, 10 ps pulse with energy 0.2 nJ
LNL is ~2.5 m
For a 800 nm, 100 fs pulse with energy 1 nJ
LNL is ~5 mm
12
If fibre length is comparable to both LD and LNL, then
both nonlinearity and GVD have to be considered.
The nonlinear Schrodinger describes the pulse
propagation

( z / z0 )  (t / t0 ) 2
i

 2V 2 V  / 4            [1]
V
  2V

V is the envelope function= Af(t/t0)
z0 is the normalized length = 0.322 (2c220/ |D())
A =  (P/P1)
P1=(nc Aeff/16  z0 n2).10-7 W
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This equation has to be solved numerically. Considering only
the lowest order nonlinearity, the nonlinear refractive index,
n2, causes a phase change of =n2E2 k0 L .
One outcome of this phase change is the generation of new
frequencies in the pulse spectrum and the appearance of the
modulation fringes in the spectrum due to interference of
frequency components generated from the different parts of
the pulse .
The input pulse parameters affect the features in the fiberbroadened spectra and this effect can be used to estimate the
input pulse parameters as we show below.
14
Features of the fibre-broadened spectra
Taking typical parameters of a picosecond Nd-YAG laser
Eq.1 is solved for different input pulse parameters. The
fiber length is kept at 100 m.
First we consider a transform limited Gaussian input pulse.
The Gaussian pulse shape function f(t/t0) had the following
form: f (t/ t0) = exp [1 + ic) (t/ t0 2)2 where : to =  /1.665 , 
- FWHM of the Gaussian pulse and t is in the time frame of
the pulse
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1.0
1.0
1.0
a. chirp : 0
0.5
b. chirp : 1
0.5
0.0
0.5
0.0
10630
10640
10650
1.0
0.0
10630
10640
10640
10650
0.0
10640
10650
10640
10650
f.
e. chirp : -2
0.5
10630
10630
1.0
d. chirp : -1
0.0
10650
1.0
0.5
c. chirp : 2
c hirp : 2
c hirp : -1
0.5
10630
10640
10650
0.0
10630
16
A time asymmetry in the input pulse makes the end peaks
asymmetric.
1.0
1.0
a.
input pulse shape
e.
chirp : 2
c.
chirp : 1
0.5
0.5
0.0
10630
10640
10650
0.0
10630
10640
10650
10640
10650
t
1.0
1.0
b.
chirp : 0
f.
chirp : -2
d.
chirp : -1
0.5
0.0
10630
1.0
0.5
10640
10650
0.0
10630
0.5
10640
10650
0.0
10630
17
Spectra for different symmetric pulse shapes. The shapes
are (a) Gaussian, (b) faster than Gaussian, (c) slower
than Gaussian
1
.0
a
.
a
b
c
0
.5
t
0
.0
1
0
6
3
0
1
0
6
4
0
1
0
6
5
0
1
0
6
6
0
1
0
6
3
0
1
0
6
4
0
1
0
6
5
0
1
0
6
6
0
1
0
6
4
0
1
0
6
5
0
1
0
6
6
0
1
.0
b
.
0
.5
0
.0
1
.0
c.
0
.5
0
.0
1
0
6
3
0
18
Experimental and calculated spectra for a 7 ps laser pulse.
1.0
1.0
a.
Pulse power : 4.75 W
0.5
0.5
0.0
-2
0.0
10620
1.0
10630
0
t
2
10640
10650
10660
10640
10650
10660
b.
Pulse power : 15.4 W
0.5
0.0
10620
10630
1.0
c.
Pulse power : 21 W
0.5
0.0
10620
10640
10660
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The starting point of these calculations was the measured
autocorrelation width and the pulse peak power as estimated
from the average power measurements. First a transform
limited gaussian pulse with these parameters was taken as the
guess input pulse and its spectrum after traversing the fiber
was calculated using Eq.1. This calculated spectrum (dashed
line in (a)) differs markedly from the experimental spectrum
(solid line curves). A comparison of the characteristics of this
calculated spectrum with the experimental spectrum gave a
guideline on how to modify the input pulse parameters like
shape, asymmetry and chirp to obtain a spectrum similar to
the experimental one. With this indication a suitable input
pulse was selected and the output spectrum recalculated. In
most cases, only a few trials were sufficient to generate a
spectrum reproducing the main features of the experimental
spectrum.
20
The 7 psec. Pulses of CW Nd:YVO4 are best described
by a pulse with a temporal shape which has a trailing
edge faster than Gaussian and has a chirp of +1.
21
Stability monitoring of laser pulses
Changes in pulse characteristics show up strongly in the
spectrum after the pulse traverses a length of fibre.
Therefore the difference between two pulses can be
identified simply by comparing their fibre-broadened
spectra.
A quantitative estimate can be done of just how sensitive
the spectra are to changes in pulse parameters.
22
A normalized difference spectrum can be defined as
Idiff() = (Iref()– Icurr() ) / Iref()
where Icurr () is the spectrum of the pulse being
compared with the reference pulse and Iref() is the
reference spectrum corresponding to the reference
pulse.
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Diff spectrum
0
-2
-4
-6
b.
-8
-10
10630
1.1 P
0.9 P
10640
10650
Diff spectrum
1.0
0.5
0.0
-0.5
1.01 P
0.99 P
a.
-1.0
10630
10640
10650
Wavelength (A)
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difference signal
0
-2
-4
chirp.2
chirp1
chirp.0
-6
-8
b.
-10
10630
10635
10640
10645
10650
wavelength A
difference signal
0
-2
-4
chirp0
chirp1
chirp.1
-6
-8
a.
-10
10630
10635
10640
10645
10650
wavelength A
25
diff spectrum
0
-2
-4
-6
-8
chirp.2
chirp..2
c.
-10
10630
10635
10640
10645
10650
wavelength A
diff spectrum
1
0
-1
-2
-3
-4
chirp.1
chirp..1
b.
-5
10630
10635
10640
10645
10650
10645
10650
wavelength A
diff spectrum
0
-2
-4
-6
-8
chirp.0
a.
-10
10630
10635
10640
wavelength A
26
CW mode-locked Ti:S laser
100 fs, 82 MHz
7.7 micron silica fibre
Triax 180 spectrograph
27
28
Power change of 2%
140
Direct spectrum compared
220
Broadened spectrum compared
120
165
Intensity
80
60
40
0
765
110
55
20
770
775
780
785
790
0
760
Wavelength(nm)
770
780
790
Wavelength(nm)
0.10
Difference spectrum
0.05
Normalized Difference
Intensity
100
0.00
-0.05
direct
broadened
-0.10
772
776
780
Wavelength(nm)
29
Spectrum change with addition of 6 mm of quartz in the beam path
120
120
Direct spectrumcompared
Broadened spectrum compared
100
100
80
Intensity
60
length of quartz
in beampath
0 mm
6 mm
40
0
800
60
40
20
20
805
810
815
820
825
830
0
800
835
Wavelength(nm)
805
810
815
820
825
830
Wavelength(nm)
0.25
Difference spectrum compared
0.20
0.15
Normalized Difference
Intensity
80
0.10
0.05
Pulse power : 923 W
0.00
-0.05
-0.10
814
direct
broadened
816
818
820
822
824
Wavelength(nm)
30
Conclusion
Fibre nonlinearity can serve as a sensitive sensor for
changes in ultrashort pulse parameters.
Advantages:
• Requires low power.
•Sensitive to change in any parameter.
•On-line, single measurement.
•Simple to implement.
Limitations
•Complete characterisation of the pulse not simple.
31
Acknowledgements
Experiments
Computation
Vijay Shukla
Fozia Aziz
S M Oak
Mahesh Chandran
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