ECE-616: Fall 2011
Lecture 27:
Ultrafast Pulse Shaping
Professor Andrew Weiner
Electrical and Computer Engineering
Purdue University, West Lafayette, IN USA
Lundstrom ECE-656 F11
1
PURDUE UNIVERSITY ULTRAFAST OPTICS & OPTICAL FIBER COMMUNICATIONS LABORATORY
Andrew M. Weiner
Purdue University
Ultrafast Pulse Shaping
A few references
Tutorial talk at CLEO 2010:
https://engineering.purdue.edu/~fsoptics/presentations/WeinerCLEOtutorial2010.pdf
"Femtosecond Pulse Shaping Using Spatial Light Modulators
,“
A. M. Weiner, Review
of Scientific Instruments
, 71,
1929-1960 (2000).
"Ultrafast Optical Pulse Shaping: A Tutorial Review," A. M. Weiner, Optics
Communications,
Femtosecond Pulse Shaping
Review article:
A.M. Weiner, Rev. Sci. Instr.
71
, 1929 (2000)
• Fourier synthesis via parallel spatial/spectral modulation
• Diverse applications: fiber communications, coherent quantum control,
few cycle optical pulse compression, nonlinear microscopy, RF photonics …
• Pulses widths from ps to few fs; time apertures up to ~1 ns
4f configuration inherently dispersion-free
Spectral
Dispersers:
Gratings
Prisms
VIPAs
AWGs
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Dispersion-free Pulse Transmission through 4f Shaper
Weiner, Heritage, and Kirschner, J. Opt. Soc. Am B
5
, 1563 (1988).
Output
Input
Reflective Pulse Shaper
•
Reduced size & component count
• Insertion loss as low as ~4 dB (including circulator!)
R.D. Nelson, D.E. Leaird, and A.M. Weiner, Optics Express (2003)
Grating
Mirror
LCM
Lens
PURDUE UNIVERSITY ULTRAFAST OPTICS & OPTICAL FIBER COMMUNICATIONS LABORATORY
Pulse Shaping Data
• Temporal analog to Young’s two slit interference experiment
• Highly structured femtosecond waveform obtained via simple
amplitude and phase filtering
ω
E(
ω
)
ω
(Intensity Cross-correlation)
Synthesis of Femtosecond Square Pulses
Shaping via microlithographic amplitude and phase masks
Cross-correlation
data
Theoretical
intensity
profile
Weiner, Heritage, and Kirschner,J. Opt. Soc. Am B 5, 1563 (1988).
Power
spectrum
Amplitude mask:
PURDUE UNIVERSITY ULTRAFAST OPTICS & OPTICAL FIBER COMMUNICATIONS LABORATORY
Pulse Shaping via Spectral Phase Control
( )
A
(
o
)
ψ ω =
Linear phase
ω− ω
Quadratic phase
Cubic phase
( )
(
)
2
o
B
ψ ω =
ω− ω
ψ ω =
( )
C
(
ω− ω
o
)
3
A>0
A=0
A<0
• Pulse position modulation
Weiner et al, IEEE J. Quant. Electron. 28, 908 (1992)
• Linear chirp
• Nonlinear chirp
Efimov et al, J. Opt. Soc. Am. B12,
1968 (1995)
( )
−∂ψ ω
( )
τ ω =
∂ω
chirp
compensated
chirped
Intentionally Generated Noise Bursts
Using Femtosecond Pulse Shaping
Pseudorandom phase pattern applied
to spectrum of 100 fs pulses
-
π
/2
π
/2
Pseudonoise
intensity profiles
(intensity
cross-correlation
technique)
Intensity
autocorrelations
PURDUE UNIVERSITY ULTRAFAST OPTICS & OPTICAL FIBER COMMUNICATIONS LABORATORY
“Shaping” of Incoherent and Nonclassical Light
Pe’er, Dayan, Friesem, and Silberberg,
Phys. Rev. Lett.
94
, 073601 (2005)
Wang and Weiner, Opt. Comm.
167
, 211 (1999)
Delay (ps)
-4 0 4
No shaping
Linear
spectral
phase
Incoherent Light:
Shaping the elec. field cross-correlation function
Nonclassical Light:
Shaping the two-photon wave function
Signal Idler
Signal Idler
Signal-idler delay (fs)
Signal-idler delay (fs)
-500 0 500
-500 0 500
Spectrum &
spectral phase
Sum
frequency
counts
1020 1060 1100
Wavelength (nm)
1020 1060 1100
Wavelength (nm)
Entangled
photon
source
Pulse
shaper
(parametric
down-conversion)
Ultrafast
coincidence
detector
(sum frequency
generation)
ASE
source
PD
(EDFA)
Pulse
shaper
Programmable Pulse Shapers:
Spatial Light Modulators
PURDUE UNIVERSITY ULTRAFAST OPTICS & OPTICAL FIBER COMMUNICATIONS LABORATORY
Fourier Transform Pulse Shaping
A variety of programmable modulator arrays
Programmable Pulse Shaping
One layer LCM:
phase-only shaping
Liquid Crystal Modulator (LCM) Arrays
Weiner et al, IEEE JQE 28, 908 (1992)
Wefers and Nelson, Opt. Lett. 20, 1047 (1995)
Two layer LCM:
independent amplitude and phase shaping
• ~400-1600 nm typical wavelength range
- recently extended to 260 nm in the UV
[(Tanigawa et al, Opt. Lett. 34, 1696 (2009)]
PURDUE UNIVERSITY ULTRAFAST OPTICS & OPTICAL FIBER COMMUNICATIONS LABORATORY
Liquid Crystal Modulator Array (LCM)
•
1-layer LCMs
: input polarization (
ŷ) aligned with LC molecules (ŷ)
for phase-only response
•
2-layer LCMs
: input polarization (
ŷ) vs.
45 for LC molecules
for phase-amplitude response
No applied voltage
With applied voltage
Longitudinal field tilts
molecules, changing
birefringence
1-layer LCM schematic
Typically 128-640 pixels on 100
µ
m centers
Phase vs. voltage response
0
Voltage (rms)
10
P
ha
s
e
c
h
an
ge
2
π
Pulse Shaping Results Using Phase
and Amplitude (2-Layer) LCM
Square pulse
Pulse sequence
Pulse sequence with
different chirp rates
Kawashima, Wefers, and Nelson, Annu. Rev. Phys. Chem. 46, 627 (1995)
• Independent phase and amplitude control allows generation of nearly
arbitrarily shaped waveforms.
-2 -1 0 1 2
Time (ps)
-2 -1 0 1 2
Time (ps)
-2 0 2
Time (ps)
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Dugan, Tull, and Warren, J. Opt. Soc. Am. B 14, 2348 (1997)
Programmable Pulse Shaping
Acousto-optic modulators (AOM)
RF arbitrary
waveform generator
Vibrates and changes refraction index
•
Spectral amplitude-phase shaping via diffraction from a traveling acoustic wave
• Traveling-wave mask; generally applicable only to amplifier systems;
reprogramming time ~ 10
µ
s (device dependent)
• Electronic arbitrary waveform generator provides amplitude-phase control, but
care needed to account for acoustic attenuation and nonlinearities
Dugan, Tull, and Warren, J. Opt. Soc. Am. B 14, 2348 (1997)
Programmable Pulse Shaping
Acousto-optic modulators (AOM)
~800-nm pulse sequence exhibiting constant,
linear, quadratic, cubic, and quartic
spectral phases
Shim, Strasfeld, Fulmer, and Zanni, Opt. Lett. 31, 838 (2006)
Mid-IR pulse shaping using Ge AOM
Spectrum
RF drive
• 260 nm – 5 µm demonstrated wavelength range
PURDUE UNIVERSITY ULTRAFAST OPTICS & OPTICAL FIBER COMMUNICATIONS LABORATORY
ULTRAFAST OPTICS AND OPTICAL FIBER COMMUNICATIONS LABORATORY
Acousto-optic Programmable Dispersive Filter (AOPDF)
An in-line pulse shaping technology – especially for amplified systems
• Phase matched polarization conversion mediated by acoustic wave
• Due to birefringence, output temporal profile related to acoustic spatial profile (controlled by
radio-frequency arbitrary waveform generator)
Representative numbers:
2.5 cm TeO
2
crystal, |n
2
-n
1
|=0.04
Acoustic velocity: 10
5
cm/s
Acoustic frequencies: 20 MHz around 52.5 MHz
Optical frequencies: 150 THz around 375 THz (800 nm)
Time aperture for pulse shaping: 3.3 ps
Acoustic transit time: 25 µs
Results from Pulse Shaping Theory
PURDUE UNIVERSITY ULTRAFAST OPTICS & OPTICAL FIBER COMMUNICATIONS LABORATORY
Pulse Shaping by Linear Filtering
(
) ( )
out
in
e
(t)
=
∫
dt h t t e
′
−
′
t
′
out
in
The Complexity of a Shaped Pulse
• Time-bandwidth product (BT = B/
δ
f = T/
δ
T) provides a measure of potential
complexity of a shaped pulse
• Equal to # of independent features in either frequency or time domain
• Favors large optical bandwidth / very short pulses
• Spectral resolution (and time aperture) limited by minimum SLM feature size,
finite optical spot size (related to the resolution of a grating spectrometer!)
pulse duration
~ 1/bandwidth (B)
spectral resolution
~ 1/time aperture (T)
bandwidth
time aperture
PURDUE UNIVERSITY ULTRAFAST OPTICS & OPTICAL FIBER COMMUNICATIONS LABORATORY
Pulse Shaping Masks: Intensity
Gray-level masks utilizing diffraction
(square pulse generation example)
Same Intensity Mask – Out of Focus Image
Emulates what happens in the actual pulse shaper:
importance of spectral resolution
PURDUE UNIVERSITY ULTRAFAST OPTICS & OPTICAL FIBER COMMUNICATIONS LABORATORY
Pulse Shaping Theory (I): Basics
( )
( ) ( )
out
in
E
ω =
M
αω
E
ω
α =
∂
x
=
spatial dispersion
∂ω
out
in
e
(t)
=
e (t) m(t / )
∗
α
1
( )
j t
m(t / )
M
e
d
2
ω
α =
αω
ω
π
∫
• For a transform-limited input pulse, pulse shaping generally does not decrease the
pulse duration (bandwidth is not increased).
Pulse Shaping Theory: Effect of Diffraction
Assume “spatial filter” selects fundamental Gaussian mode (e.g., single-mode
fiber, regenerative amplifier)
( )
(
)
2
2
out
o
in
E
ω
~
∫
dx M(x) exp -2 x-
αω
w
E ( )
ω
• Spectral smearing due to finite spot size
• Equivalent to a window function in the time domain
Filter function
e
out
(t) ~ e (t)
in
∗
m(t / ) exp
α
(
−
w t / 8
o
2 2
α
2
)
time window
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Phase-to-Amplitude Conversion due to Diffraction
Pseudorandom phase mask with abrupt 0-
π
phase transitions
• Each phase transition leads to a deep hole in the power spectrum.
• Such data validate theoretical treatment of diffraction effects in pulse shaping.
Sardesai, Chang, and Weiner,
J. Lightwave Tech. 16, 1953 (1998)
Selected Applications
PURDUE UNIVERSITY ULTRAFAST OPTICS & OPTICAL FIBER COMMUNICATIONS LABORATORY
-
Pulse shaping
-Dynamic spectral equalizers
-Dynamic wavelength processing
Applications in Optical Communications
Spatial light modulator
Control of phase, intensity, polarization …
Frequency-by-frequency, independently, in parallel
Spectral
disperser
Spectral
combiner
Broadband input
- Ultrashort pulse
- CW plus modulation
- Multiple wavelengths
Processed output
“Dynamic spectral processor”
“Pulse Shaping” in WDM: Intensity Control
Manipulation on a wavelength-by-wavelength basis
No concern for phase or for coherence between channels
Ford et al, J. Lightwave Tech.
17
, 904 (1999) [Lucent]
Ford et al, IEEE JSTQE
10
, 579 (2004) [Lucent]
Wavelength selective add-drop multiplexer (and wavelength selective switches)
Spectral gain equalizer
Liquid crystal version:
Patel and Silberberg, IEEE PTL
7
, 514 (1995)
MEMS
PURDUE UNIVERSITY ULTRAFAST OPTICS & OPTICAL FIBER COMMUNICATIONS LABORATORY
Programmable Fiber Dispersion Compensation
Using a Pulse Shaper: Subpicosecond Pulses
•
Coarse dispersion compensation using matched lengths of SMF and DCF
•
Fine-tuning and higher-order dispersion compensation using a pulse shaper as a
programmable spectral phase equalizer
•
Similar ideas apply to DWDM tunable dispersion compensation and
few femtosecond pulse compression.
Spectral phase equalizer
( )
−∂ψ ω
( )
τ ω =
∂ω
Higher-Order Phase Equalization Using LCM
Input and output pulses from 3-km dispersion-compensated link
Chang, Sardesai, and Weiner, Opt. Lett.
23
, 283 (1998)
Input pulse
Output pulse
(
with
quadratic &
cubic correction)
Output pulse
(
without
phase
correction)
already compressed
several hundred times
Applied phase
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460 fs transmission over 50 km SMF
-10
-5
0
5
10
15
20
Time (ps)
Int
ensi
ty
cr
oss
-co
rr
el
at
ion
(a.
u.
)
both second- and
third-order DC by pulse shaper
without DC
by pulse shaper
second-order DC
by pulse shaper
P
ha
s
e
(
ra
d)
0
20
40
60
80
100
0
32
64
96
128
Pixel #
2
π
π
(A)
(B)
Commercial
DCF module (
as is
) with spectral phase equalizer
•
~ 5 ns after SMF
• 13.9 ps after DCF
• 470 fs after quadratic/cubic phase
equalization
Z. Jiang, Leaird, and Weiner, Opt. Lett. 30, 1449 (2005)
Essentially
distortion-free!
•
Phase can be applied modulo 2
π
.
•
Quadratic, cubic, and higher order phase can
be applied independently.
•
Magnitude of phase sweep eventually limited
by need to adequately sample using fixed
number of pixels
Post-compensation of Pulse Distortion
in a 100-fs Chirped-Pulse Amplifier
SHG-FROG trace of original, phase
distorted amplified pulses
SHG-FROG trace after phase
equalization
Brixner, Strehle, and Gerber, Appl. Phys. B
68
, 281 (1999)
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Quantum Control of Two Photon Absorption in Cesium
1
2
E
1
Narrowband TPA
Anti-symmetric
around
ω
ο
/2
Dark Pulse
no TPA!
• Shaping spectral phase to manipulate interference between two photon absorption
pathways for creation of user selectable “dark “ or “light “ pulses
• Similar effects occur in second harmonic generation –
later applied for MIIPS pulse measurement technique
Meshulach and Silberberg, Nature 396, 239 (1998)
o
( )
sin
2
ω
ψ ω = α
ω −
Symmetric
around
ω
o
/2
o
( )
cos
2
ω
ψ ω = α
ω −
Sinusoidal
spectral
phase
High Power Pulse Compression in the 5-fs Regime
Wang, Wu, Li, Mashiko, Gilbertson , and Chang, Optics Express
16
, 14448 (2008)
Pulse shaper used both for measurement* and
compensation!
*Multiphoton intrapulse interference phase scan (MIIPS)
-e.g., Xu, Gunn, Dela cruz, Lozovoy and Dantus, JOSA B
23
, 750 (2006)
MIIPS traces
pre compensation
post compensation
Compression results
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• Exploitation of optical pulse shaping technology for cycle-by-cycle synthesis
of arbitrary RF waveforms beyond the speed of electronics solutions
• Approach scales from Gigahertz to Terahertz
RF Arbitrary Waveform Generation
-2
-1
0
1
2
3
Time (ns)
1.2/2.5/4.9 GHz FM Waveform
48/24 GHz FM Waveform
-2 0 2
Time (ps)
THz Phase Modulation
RF
Optical
Precompensation of antenna dispersion
Impulse
~195 ps
Chirped: ~2.17 ns
Predistorted
Input voltage
Output voltage
Compressed
~264 ps
Impulse Excitation of “Frequency-Independent” Antennas
