Optimization of
supercontinuum generation in
photonic crystal fibers for
pulse compression
Noah Chang
Herbert Winful,Ted Norris
Center for Ultrafast Optical Science
University of Michigan
What is Photonic Crystal?
A microstructured material is one that
is structured on the scale of the optical
wavelength. A diffraction grating is a
simple example. If the structure is
periodic - regularly repeating - then
the material is called a "photonic
crystal". This is analogous to a normal
crystal in which atoms or groups of
atoms are arranged in a repeating
pattern, except that the repeat period
is on a much larger scale.
z
(SEM image of a silicon inverse opal. This threedimensional Photonic Crystal consists of a fcc
close-packed lattice of air spheres (diameter 600
nm) that are coated with silicon (about 23% by
volume) and exhibits a complete photonic band
gap centered at 1.46 µm with a gap-to-midgap ratio
of 5%. The inset shows the theoretical modelling of
the structure. )
http://www-tkm.physik.uni-karlsruhe.de/~kurt/GroupPage/framtest.html
Photonic Crystal Fiber (PCF)
An SEM image of a photonic crystal fibre.
Note the periodic array of air holes, and the
central defect (a missing hole) that acts as
the fibre's core. The fibre is about 40
microns across.
A photograph of the far field pattern
emerging from a photonic crystal fibre. The
fibre was carrying red light from a heliumneon laser and green light from an argon
ion laser.
http://www.bath.ac.uk/physics/groups/opto/pcf.html
Commercially Available Crystal
Fiber A/S
Specifications
1. Small core highly nonlinear
PCF:
- Small core diameter (1.7µm, 2.0µm)
- High nonlinearity
- Zero dispersion in visible wavelength region
- Bending insensitive
2. Highly nonlinear polarization
maintaining PCF:
- High polarization retention
- Small core dimension
- Zero dispersion in visible wavelength region
- Bending insensitive
The top is a preform and the bottom are each
section of Highly nonlinear PCF, polarization
maintaining PCF and Large mode area PCF
from the left.
3. Large mode area PCF:
- Large core (15µm, 20µm)
- Low loss
- High power level without nonlinearity
http://www.rikei.co.jp/dbdata/products/producte249.html
Application of PCF
- Supercontinuum generation
- Four-wave mixing
- Raman amplification
- All optical switching based on XPM
- Ultrahigh power/Ultrashort pulse delivery
- Mode filtering
- Photonic crystal fiber coupler
- Tunable devices with micro-fluids in PCF
SC Generation from PCF
Measured GVD of PCF (squares) and a standard
single-mode fiber (circles).
Optical spectrum of continuum generated in a 75cm section of PCF. The dashed curve shows the
spectrum of the initial 0.8nJ 100-fs pulse
Advantages to generate SC with PCF:
(1) Zero-dispersion wavelength shifted to visible wavelength
broadened too much along propagation distance
(2) Very small effective core area
pulse not
nonlinearity increased by over 20 times
(3) All wavelength single mode
Jinendra K. Ranka etc., Optics Letters, vol. 25, 25(2000)
Application of Supercontinuum
- Single/sub cycle pulse by compression
- Optical coherence tomography
- Optical frequency metrology
- Optical source for WDM/DWDM
communication system
- Wideband tunable wavelength
conversion
Pulse Compressed to Sub-cycle
Propagation length = 1.5 mm (a)(b), 9 mm (c)(e), 4.5 mm (d). (e) subcycle
pulse compressed by a LC SLM (I=3.3 TW/cm^2,druation= 200 fs)
Husakou A. V. etc., Phys. Rev. Lett.,87,203901 (2001)
Fine structures of SC from simulation
(a) Output spectrum for an input peak power P=
16 kW and propagation distance = 250cm (b)
same as (a) but with 0.1% higher peak power
(c) High resolution window of the spectra in (a)
(solid curve) and (b) (dotted curve)
Alexander L. Gaeta, Opt. Lett. 27, 924
(2002)
Structures Revealed by FROG
(a) Entire SC averaged over 10,000 pulses. Spectral section of the SC exposed for (b)
10,000 shots, (c) 100 shots and (d) a single shot. (input pulse duration = 30 fs, energy = 1
nJ, propagation distance = 16 cm)
Xun Gu etc., Opt. Lett., 27, 1174, (2002)
Compressible or not
Necessary conditions for compression to
generate ultrashort pulse:
(1)Very broad spectrum
(2) Stable and smooth phase
Question:
Whether significant compression can
be practically achieved from SC?
200
9
100
8
0
7
-100
6
-200
5
-300
4
-400
500
600
700
800
900
wavelength [nm]
1000
1100
fiber dispersion and effective core area
versus wavelength for PCF
3
1200
∂S(Ω, z)
=
∂z
−i[β(ω0 + Ω, z) − β(ω0 , z) −Ωβ1(ω0 , z) −iα(ω0 + Ω, z)]S(Ω, z)
−iγP0 (1+
effective core area [um2]
fiber dispersion D [ps/nm/km]
Frequency Domain Propagation Equation
for Photonic Crystal Fiber (PCF)
Ω
ω0
)F{S(T, z)[S(T, z) + F−1{R(Ω)F{S(T, z) }}]}
2
2
R (Ω ) is the complex Raman susceptibility.
γ =
ω n
cA
2
eff
Advantages
(1) suitable for handling continuum over
a wide spectral range and that arbitrary
functions can be used to describe the
chromatic dispersion and loss.
(2) The Raman gain curve and hence the
Raman susceptibility are obtained
experimentally in frequency domain.
SC generated from PCF
6
10
Parameters for the input
pulse
4
supercontinuum [a.u.]
10
2
10
Central wavelength: 790nm
Pulse shape: sech2
Duration: 100 fs
Peak power: 8 kW (0.8 nJ/pulse)
0
10
-2
10
-4
10
Parameters for the algorithm
-6
10
550
600
650
700
750
800 850 900
wavelength [nm]
950
1000 1050 1100
SC generated after passage of different distances: 5
cm for the upper spectrum and 45 cm for the lower
Temporal resolution: 0.5 fs
Spectrum resolution: 30 GHz
Sample number: 2^14 (65536)
Evolution of SC along Propagation Distance
250
Three stages for SC generation:
30dB spectrum width [THz]
200
1st
150
2nd
100
2 kW
4 kW
6 kW
8 kW
50
0
2
4
6
8
distance [cm]
10
12
3rd
14
evolution of 30 dB spectrum width
along propagation distance
SPM + anomalous dispersion
pulse compressed and
spectrum broadened
Stronger nonlinearity + FWM in
normal dispersion region
SC generation
pulse breakup into spikes
peak power weakened
SC saturates
Example: given peak power=8 kW
Threshold distance: 2.2 cm
Saturation distance:4.5 cm
Parameters to Characterize SC
12
90
80
number of oscillations in 30dB bandwidth
10
threshold distance
saturation distance
distance [cm]
8
6
4
2
8kw
6kw
4kw
2kw
70
60
50
40
30
20
10
0
0
10
20
30
40
50
peak power [Kw]
60
70
80
(a) threshold distance and saturation distance
versus the peak power of the input pulse
0
0
5
10
propagation distance [cm]
(b) Number of oscillations in 30 dB
spectrum width versus distance
15
20
20
15
15
10
10
5
5
group delay [ps]
group delay [ps]
Group Delay Extremely Sensitive to
Input Power
0
-5
0
-5
-10
-10
-15
-15
-20
-100
-50
0
50
frequency [THz]
(a)
100
150
-20
-100
-50
0
50
frequency [THz]
100
(b)
group delay for 45 cm propagation distance with different input peak power:
(a) peak power=8 kW and (b) peak power=8.016 kW (0.2% different)
150
150
150
100
100
group delay dispersion [ps 2]
group delay dispersion [ps 2]
Group Delay Dispersion VS Input Power
50
0
-50
-100
-150
-100
50
0
-50
-100
-50
0
50
frequency [THz]
(a)
100
150
-150
-100
-50
0
50
frequency [THz]
100
150
(b)
group delay dispersion for 45 cm propagation distance with different input peak power:
(a) peak power=8 kW and (b) peak power=8.016 kW (0.2% different)
Pulse Compression by Ideal Compressor
Phase for SC:
16
14
intensity [a.u.]
12
10
8
6
4
ideal case
nonideal case
(ideal case)
φ SC1 (ω )
(nonideal case)
φ SC 2 (ω )
Ideal compressor:
φc (ω ) = −φ SC1 (ω )
Average compressor:
φ c (ω ) = −(φ SC1 (ω ) + φ SC 2 (ω )) / 2
Result:
slightly fluctuation of input
0
-40
-30
-20
-10
0
10
20
30
40
time [fs]
peak power
different
Pulse compression with ideal compressor to compensate substructure for Phase, GD,
SC phase generated under conditions:pulse duration =
GDD
amplified power
100 fs, propagation distance=45 cm,Peak power=8 kW
fluctuation and time shift for
(ideal case) and 8.016 kW (nonideal case)
compressed pulses
2
Normalized Time Shift and Fluctuation
for Compressed Pulses
0.6
0.1
0.09
0.5
0.08
0.4
time shift
0.06
0.3
0.05
0.04
0.2
0.03
fluctuation of peak power
0.07
0.02
0.1
0.01
0
0
0
5
10
15
20
25
30
35
40
45
50
distance [cm]
Time shift and fluctuation versus propagation distance. In the figure, the time
shift and fluctuation of peak power have been normalized to the duration and the
peak power of the compressed pulse with ideal compensation.
Optimum Distance to Compress Pulse
9.5
duration of compressed pulses [fs]
9
ideal compressor
LCSLM compressor
8.5
8
7.5
7
6.5
6
5.5
5
4.5
2
4
6
8
10
12
distance [cm]
14
16
18
duration of compressed pulses versus
distance for ideal compressor and LCSLM
20
LCSLM: liquid-crystal spatial light
modulator
Assume the 0.55-1.1 µm spectrum
is divided into 256 channels.
The phase of one channel is
assigned to cancel exactly the
mean phase within the spectral
range of this channel.
Optimum compressed distance =
5cm
given
duration of input pulse = 100fs
peak power = 8 kW
Compressed pulse
Duration : 5.15 fs
fluctuation: negligible
time shift: 0.12 fs.
Fluctuation and Time Shift under Different
Peak Power Fluctuations
0.35
0.7
0.6
ideal compressor
average compressor
ideal compressor
average compressor
0.25
0.5
normalized time shift
fluctuation of compressed pulse
0.3
0.2
0.15
0.4
0.3
0.1
0.2
0.05
0.1
0
0
0.005
0.01
0.015 0.02 0.025 0.03 0.035
fluctuation of peak power
0.04 0.045
0.05
0
0
0.005 0.01 0.015 0.02 0.025 0.03 0.035
fluctuation of peak power
0.04 0.045
Output peak power fluctuation and time shift vs input peak power fluctuation at the optimum
compression distance ( peak power = 8 kW, pulse duration = 100 fs, propagation distance = 5
cm)
0.05
Single-cycle Pulse Generation from SC
35
SC generated under conditions:
Duration of input pulse=100fs
Peak power = 80 kW
Propagation distance = 1.2
cm
ideal compressor
LCSLM
30
intensity [a.u.]
25
20
15
10
5
0
-20
-15
-10
-5
0
time [fs]
5
10
15
20
compressed single-cycle pulses obtained from
SC with 80 kW peak power for an input pulse
that propagates 1.2 cm in the PCF
Compressed pulse:
Duration=2.4 fs
(idealcompressor)
=2.54 fs (LCSLM)
Duration of single cycle =
2.64 fs
(at 790 nm)
Conclusion
- Three stages for SC evolution: initial broadening below a
certain threshold propagation distance, dramatic
broadening to a SC at a threshold distance, and finally,
saturation of the spectral width on propagation.
- Group delay and group delay dispersion of the SC are
sensitive to the input pulse peak power after further
propagation at the third stage.
- Fluctuations from the input pulse are amplified and
translated into fluctuations and time shift of the compressed
pulses.
- There exists an optimum compressed distance where
compressed pulses with negligible fluctuation and time shift
can be obtained.
For more information, please refer to
Chang GQ, Norris TB, Winful HG,OPTICS LETTERS 28 (7): 546-548 APR 1 2003