Supercontinuum generation - EECS @ UMich - University of Michigan
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
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
