Mode - locked Lasers How are ultrashort pulses generated? Mode-locked lasers are most common Other (rarer) techniques include E-O modulation, modulation instability and compression An ultrashort pulse requires large bandwidth, this is obtained by having many longitudinal modes in the cavity lasing simultaneously However, multi-mode lasing just generates noise unless there is a fixed phase relationship among the modes, thus the term “mode-locking”.
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Mode-locked Lasers
How are ultrashort pulses generated?
Mode-locked lasers are most common
Other (rarer) techniques include E-O modulation, modulation instability and compression
An ultrashort pulse requires large bandwidth, this is obtained by having many longitudinal
modes in the cavity lasing simultaneously
However, multi-mode lasing just generates noise unless there is a fixed phase relationship
among the modes, thus the term “mode-locking”.
Generic Elements of Modelocked Lasers
1) Broadband gain medium
2) Cavity
mirrors, provide feedback
3) Output coupler
partially transmissive mirror, provides output
4) Anomalous dispersive element
Compensate normal dispersion in other elements
5) Modelocker
Active: phase modulator
Passive: saturable absorber
gD ML
For the basics of lasers see, for example, Verdeyen “Laser Fundamentals”
Gain Medium
g
Must be supplied with energy – the “pump”
Typical ultrafast lasers are pumped by another laser
Amplifies light by stimulated emission
Requires inversion – more atoms/molecules in the excited state – so that
stimulated emission overcomes absorption
Two categories:
3-level
Inferior – require strong pumping
Example: erbium, ruby
4-level
Preferred
Examples: ti:sapphire, organic dyes
The gain medium always operates in saturation
Gain: Ti:sapphire(the ultrafast work horse)
Titanium substitutes for an Al atom in the sapphire
(Al2O3) host crystal
There is a single optically active electron, levels are
split by crystal fields.
Effective 4 – level system due to Jahn-Teller effect:
Minimum in electronically excited state is shifted from
ground state with respect to a configuration coordinate
Relaxation occurs due to vibronic transitions
Yields very broad emission/gain spectrum
Excited state lifetime ~ 3.9 ms
Sapphire has excellent thermal & hardness properties
Other Gain Media
Material Gain Pump Comments
Dyes Various Excimer, Nd: YAG
SH, flashlamp
Messy, limited
lifetime,
toxic/carcinogenic
Diodes Various (~850
best)
Electrical Gain dyanmics
limit minimum
duration
Cr:LiSAF,
Cr:LiCAF
820-880 670 nm diode Poor thermal
properties
Cr:Forsterite 1300-1400 Nd:YAG
Cr:YAG 1500-1600 Nd:YAG Crystals rare
Erbium 1530-1560 980 or 1480 nm
diode
3 - level
General Saturation
General form for saturation of absorption
Propagation through an absorbing material with absorption coefficient a [cm-1]:
Idz
dIa
(gain is simply a < 0)
IIIdz
dI
S
1
0a
Where Is is the “saturation intensity”, i.e. the intensity for which the absorption is reduced to ½
its small signal value.
0.0 0.5 1.0 1.5 2.0 2.5 3.0
0.0
0.2
0.4
0.6
0.8
1.0
aa
0
I/Is
For absorption, Is depends on number of atoms, cross-section and relaxation rate
For gain, it also depends on pump rate
Output coupling
0.00 0.02 0.04 0.06 0.08 0.10
0.00
0.01
0.02
0.03
0.04
0.05
Ou
tpu
t p
ow
er
rela
tive
to
Is
Output coupler transmission
For a CW laser, the optimum output coupling is a trade off between
1) Extracting the power (increasing transmission); and
2) Decreasing the intracavity power because increased loss means gain less saturated
where To is the output coupler transmission, g0 is
small signal gain and L is other losses in the cavity
In the case of a passively mode-locked laser, one must also consider the issue of pulse stability, i.e.
maintaining high enough peak power, this depends on details of the mode-locking mechanism
1
0
0
TL
gTII osout
20
0
LgII
LgLT
smaxout
opto
g0 = 0.1
L = 0.01
The maximum is
In the situation of high cavity Q (low net loss), the output power is approximately
ABCD (Ray) Matrices(lightspeed review)
Represent propagation through optical elements
system matrix is simply product of matrices for individual elements
10
1n
d Propagation through a distance d in a medium with
index of refraction n. [Take care to not double count n.]
11
01
f
A thin lens with focal length f
12
01
R
Reflection from a spherical mirror with radius R. R > 0 for
center of curvature in positive propagation direction
Ray Optics: represent ray by vector:
Gaussian beams: describe transformation of beam parameter
r
r
Propagation of Gaussian beams through optical elements
Characterize a beam by
0izzq
Propagation through an element characterized by matrix is
DC
BA
DCq
BAqq
1
12
znwi
zRzz
zi
zz
z
izzq 2
0
22
0
22
0
111
00
1
12
Lqq
Check for free space1
0 1
L
Beam in resonator must be self-consistent, i.e., the same after one round trip.
Determine the ABCD matrix for one round trip in the resonator
matrix depends on starting point
Solve equation
DCq
BAqq
which gives 2 solutions (using fact that AD-BC =1 for ABCD matrices)
21 1
12 2
D A A D
q B B
Then construct the proper matrix to propagate to other points inside or outside the cavity
Cavity: Basics of Stability I
Cavity: Basics of Stability II
Use ABCD matrices, resonator stable if round-trip matrix satisfies