第三讲 超短脉冲的产生

如监测化学反应过程，需飞秒尺度
The Generation of Ultrashort Laser Pulses
The importance of bandwidth
More than just a light bulb
Laser modes and mode-locking
Making shorter and shorter pulses
Small Milli (m) Micro (µ) Nano (n) Pico (p) Femto (f) Atto (a) 10-3 10-6 10-9 10-12 10-15 10-18
Big Kilo (k) Mega (M) Giga (G) Tera (T) Peta (P) 10+3 10+6 10+9 10+12 10+15

f (t mT )
The Fourier transform of an infinite train of pulses
An infinite train of identical pulses can be written:
E(t) = III(t/T) * f(t)
where f(t) represents a single pulse and T is the time between pulses. The Convolution Theorem states that the Fourier Transform of a convolution is the product of the Fourier Transforms. So:
E (t ) III(t / T ) f (t )
where f(t) is the shape of each pulse and T is the time between pulses.

m
(t / T m) f (t t) dt




m
time
Short pulse
frequency
time
frequency
For many years, dyes have been the broadband media that have generated ultrashort laser pulses.
Ultrafast solid-state laser media have recently replaced dyes in most labs.
What exactly is required to make an ultrashort pulse?
Answer:
A Mode-locked Laser
Okay, what’s a laser, what are modes, and what does it mean to lock them?
Mode-locker
Many pulse-shortening devices have been proposed and used.
Pulsed Pumping
Pumping a laser medium with a short-pulse flash lamp yields a short pulse. Flash lamp pulses as short as ~1 µs exist. Unfortunately, this yields a pulse as long as the excited-state lifetime of the laser medium, which can be considerably longer than the pump pulse. Since solid-state laser media have lifetimes in the microsecond range, it yields pulses microseconds to milliseconds long.
The Birth of Ultrafast Technology
Bet: Do all four hooves of a trotting horse ever simultaneously leave the ground?
Leland Stanford Eadweard Muybridge （马场老板） (英国摄影师)
E (w ) III(wT / 2p ) F (w
A train of pulses results from a single pulse bouncing back and forth inside a laser cavity of round-trip time T. The spacing between frequencies—called laser modes—is then w = p/T or n = 1/T.
Long and potentially complex pulse
Q-switching
Q-switching involves: Preventing the laser from lasing until the flash lamp is finished flashing, and Abruptly allowing the laser to lase.
If w = ቤተ መጻሕፍቲ ባይዱnp, So:
t
F {III(t )} III(wp
m
F {III(t)}
w 2p
The Shah function and a pulse train
Convolution
An infinite train of identical pulses (from a laser!) can be written:
Solid-state laser media have broad bandwidths and are convenient.
Laser power
Light bulbs, lasers, and ultrashort pulses
But a light bulb is also broadband.
Limiting factors Commercial lasers
But first: the progress has been amazing!
10ps Nd:glass Nd:YLF
Nd:YAG
Dye SHORTEST PULSE DURATION 1ps CW Dye Color Center 100fs CP M Dye S-P Dye Diode
Cr:LiS(C)AF Er:fiber
Nd:fiber Cr:YAG
The shortest pulse vs. year (for different media)
Cr:forsterite 10fs w/Compression Ti:sapphire
1965
1970
1975
1980
1985
1990
“Splash on a Glass” Curtis Hurley Junior High School student 1996
Time Resolution: a few microseconds
时间尺度
原子转动时间尺度： 皮秒 （1ps=10-12s） 原子振动时间尺度：飞秒 （1 fs=10-15s) 电子运动时间尺度： 阿秒 （1as=10-18s)，电子绕氢原子 核一周大约是150阿秒；
The "Trotting Horse” Controversy Palo Alto, CA 1872
Time Resolution: 1/60th of a second
Trotting Horse
'Doc' Edgerton - Strobe Photography
“How to Make Apple sauce at MIT” 1964 Harold Edgerton MIT, 1942
1995
2000
2005
YEAR
Continuous vs. ultrashort pulses of light
A constant and a delta-function are a Fourier-Transform pair. Irradiance vs. time Continuous beam: Spectrum
Ultrafast lasers often have thousands of modes.
A generic ultrashort-pulse laser
A generic ultrafast laser has a broadband gain medium, a pulseshortening device, and two or more mirrors:
Lecture 3 Generation of ultrashort pulses
The Metric System
We’ll need to really know the metric system because the pulses are incredibly short and the powers and intensities can be incredibly high. Prefixes:
Output intensity
Cavity Loss
0% Time
The pulse length is limited by how fast we can switch and the round-trip time of the laser and yields pulses 10 - 100 ns long.
What’s the real meaning of mode locking
Frequency domain: all longitudinal modes are in phase ( phase moded) Time domain: Form ultrashort pulses
Free running
t
III(t )
m
(t m)

The Fourier transform of the Shah function

m
t m) exp(iwt )dt


III(t)
m
t m) exp(iwt )dt exp(iwm)
Mode locking
Mode locked principle
Lasers modes: The Shah function
The Shah function, III(t), is an infinitely long train of equally spaced delta-functions.
Pulse-pumping Q-switching and distributed-feedback lasers Passive mode-locking and the saturable absorber Kerr-lensing and Ti:Sapphire Active mode-locking Other mode-locking techniques
time
frequency
Ultrashort pulse:
time
frequency
Long vs. short pulses of light
The uncertainty principle says that the product of the temporal and spectral pulse widths is greater than ~1. Irradiance vs. time Long pulse Spectrum
Generating short pulses = mode-locking
Locking the phases of the laser modes yields an ultrashort pulse.
Locked modes
Intensities
Numerical simulation of mode-locking