February
1,
1994 / Vol.
19, No.
3 / OPTICS
LETTERS
201
Chirped
multilayer
coatings
for
broadband
dispersion
control
in
femtosecond
lasers
Robert Szipocs
and Kdrpdt Ferencz
Optical Coating
Laboratory, Research
Institute
for Solid State
Physics, P.O.
Box 49, H-1525
Budapest, Hungary
Christian Spielmann
and Ferenc
Krausz
Abteilung
Quantenelektronik
and Lasertechnik,
Technische
Universitit
Wien, Gusshausstrasse
27, A-1040 Wien,
Austria
Received August
23, 1993
Optical thin-film
structures exhibiting
high reflectivity
and
a nearly constant
negative group-delay
dispersion
over frequency
ranges as broad
as 80 THz are
presented. This
attractive combination
makes
these coatings
well
suited for intracavity
dispersion
control in broadband
femtosecond
solid-state
lasers. We address
design issues
and
the principle
of operation of
these novel devices.
The relevance
of intracavity
dispersion
control in
passively mode-locked
ultrashort-pulse
laser
was
recognized soon
after the
appearance of
the first
systems
operating
in the femtosecond
domain.'
Negative
dispersion
that is due
to wavelength-
dependent
refraction
in a pair of Brewster-angled
prisms
combined
with positive
material
dispersion
proved
to be an
efficient and
convenient
means of
controlling
the net group-delay
dispersion
(GDD)
inside the
laser cavity.
2
In solid-state
lasers femtosecond
pulse
generation
invariably relies
on a net negative
intracavity
GDD
because of an
ultrafast self-phase
modulation
caused
by the optical
Kerr effect
in the laser
medium.
Hence
prism pairs
have become
standard components
in
these systems.
The interplay
between negative
GDD
and Kerr-induced
self-phase
modulation, often
referred
to as solitonlike
shaping,
appears to be
the
dominant
pulse-forming
mechanism
that determines
the steady-state
pulse duration
in femtosecond
solid-
state lasers.
3
In
practical prism-pair-controlled
broadband laser
systems
a major limitation
to
ultrashort
pulse
generation
originates from
the
variation
of the intracavity
GDD
with wavelength.
The principal
source
of this high-order
dispersion
was found to
be the prism pair.
3
'
4
In this
Letter we
report the
novel development
of chirped
multilayer
mirror coatings
that can exhibit
essentially
constant
negative GDD
over a frequency
range
as broad
as
80 THz. Careful
design
permits higher-order
contributions
to
the mirror
phase dispersion
to
be kept
at low values
or to be
chosen such
that
high-order
phase errors
introduced
by other cavity
components
(e.g.,
the gain medium)
are canceled.
Replacing
the prism
pair with these
novel devices
offers the
potential of
generating pulses
that are
shorter
than previously
achievable directly
from the
laser. In
addition, this
simplifies the
cavity design
and may permit
the construction
of more
compact
and
reliable femtosecond
sources.
The
first thorough
investigations
of the frequency-
dependent
phase retardation
(phase dispersion)
of
multilayer
dielectric
coatings
date back
to the
early
1960's.5,
The emergence
of femtosecond
lasers
in
the
1980's
has led
to a
revival
of interest
in
this
field.
7
-'
3
Whereas
standard
quarter-wave
dielectric
mirrors
were
shown to
introduce
negligible
dispersion
at
the center
of their
reflectivity
bands,
7
'
8
various
specific
high-reflectivity
coatings
(Gires-Tournois
in-
terferometers,
double-stack
mirrors,
etc.)
with ad-
justable
GDD
(through
angle
tuning)
were devised
and used
for
the precise
control
of intracavity
dis-
persion
in
femtosecond
dye
lasers.'
4
"
5
However,
the
GDD
introduced
by
these mirr6r
coatings
is
accompa-
nied by
high cubic and
higher-order
dispersive
contri-
butions.
As a consequence,
a constant
GDD
could be
obtained
only
over a
limited
wavelength
range
(<10
THz). The difficulty
in realizing
broadband
GDD
control
relates
to the
physical
origin
of dispersion
in
these devices;
different frequency
components
are
trapped
for
different
periods
of time
in Fabry-Perot-
like
resonant structures.
A distinctly
different type
of GDD arises
from the
wavelength
dependence
of the
penetration
depth
of the incident
optical field
in multilayer
coatings.
This effect
does not rely
on the
presence of
resonant
structures
and offers
the possibility
of
realizing
a
GDD that
is a slowly
varying
function
of
wavelength
over
a broad
bandwidth.
A
constant
GDD
requires
a group
delay
that varies
approximately
linearly
with the
wavelength. A
wave packet
of a given
center wavelength
is most
efficiently
reflected by
a corresponding
quarter-wave
stack.
Therefore
a monotonic
variation
of the multilayer
period
throughout
the
deposition
process
(chirped
coat-
ing) should
result in a penetration
depth'
6
(and
thus
group delay)
that varies
monotonically
with
the wavelength.
However,
a previous
study of
chirped
multilayer
coatings
with layer
thicknesses
following
monotonic
variations
revealed
that
the
GDD is
strongly perturbed
by
some Fabry-Perot-
like resonances
in these simple
structures.'
7
Our
studies
have indicated
that the undesirable
resonant
features
can be almost
completely
eliminated by
0146-9592/94/030201-03$6.00/0
© 1994
Optical Society
of America
202
OPTICS LETTERS
/ Vol.
19, No. 3
/ February
1, 1994
slight
adjustment
of the layer
thicknesses.
This
finding has
been a most important
step toward
the
practical realization
of dispersive mirrors
having
a
group delay
that
is a linear
function
of optical
frequency.
In addition,
chirped multilayer
coatings
have the potential for extending the bandwidth
of
standard
low-dispersion
quarter-wave
mirrors.
A preliminary design
utilized a structure consisting
of 42
alternating layers of SiO
2
(n = 1.45) and TiO
2
(n = 2.3)
with optical thicknesses close
to a quarter of
0.8 ,um,
our selected center
wavelength.
The multi-
layer period was slightly increased
near the substrate
and decreased at
the air-coating interface
to produce
a group delay that increased with wavelength,
i.e.,
negative GDD. The mirrors
were required to be
highly reflecting and have a constant negative
GDD
over
the wavelength range
710-900 nm. Alterna-
tively the GDD
could be required to exhibit
a slight
linear variation
with a slope
suitable
for compensat-
ing the cubic phase
dispersion of the gain medium.
This is in
strong contrast to prism pairs,
in which the
ratio of cubic to
quadratic dispersion is determined
by
material
parameters
and the operation
wavelength.'
8
A
simple computer
refinement
algorithm's was
used
to minimize
the quadratic deviation
of the complex
reflectivity-versus-frequency function of
the actual
mirror design
from the required specification.
The
quadratic error was made up
of two parts, for the
amplitude and the phase
characteristics, whose rel-
ative
weights could be independently adjusted.
The
prescribed
value of negative GDD was increased step-
wise until the quadratic error started
to increase
rapidly. Accordingly the operating
negative GDD
was found to trade off against
a high reflectivity
and
a low variation of the prescribed
GDD-versus-
wavelength function.
This optimization
procedure enabled us to realize
the dispersive
mirror design shown in Fig. 1 (Ref.
20)
by use
of a standard electron-beam evaporation
technique.'
3
Our obtained
structure preserved
the feature of increasing layer
period toward the
substrate, even
though the variation is far from what
we consider as
linear. The calculated
reflectivity of
this design is larger than 99.9% around
the center
wavelength and drops
to :99.5% at 710 and 900 nm.
The nominal GDD of the mirror
is -- 45 fs
2
at
A = 800 nm, with a slight linear variation
yielding
a cubic dispersion
of =-33 fs
3
, which permits
a simultaneous
compensation of GDD and cubic
dispersion in a Ti:sapphire
laser.
The wavelength dependence of
the GDD exhibits a
weak oscillatory behavior,
with deviations less than
±5 fs
2
from the required
(linear) GDD function over
the wavelength range of 720-890 nm
(=80 THz).
The GDD of -45 fS
2
corresponds to a group-delay
difference of =22 fs between the extremes
of this spec-
tral range. As we show below,
for a 42-layer design
this is close to the maximum delay
difference that can
be
attained without making use
of resonances. Any
further
increase in GDD could be achieved only at
the
expense of resonant structures
(e.g., Gires-Tournois
interferometers)
appearing in the multilayer design,
which implies large variations in the GDD
over the
mirror reflectivity range.
Figure 2 plots the
computed electric-field distri-
bution inside the dielectric
mirror as a function of
wavelength.
As required, the penetration depth
(and thus the
group delay) increases approximately
linearly with the wavelength. The
figure also
gives clear evidence
of the high reflectivity
of the
mirror between
700 and 900 nm, as indicated
by the disappearance
of the optical field at the
substrate-coating
interface (optical distance 0).
The computed
group delay (first
derivative of
the
reflected phase with respect to frequency)
as
a function
of wavelength is depicted in Fig.
3
along with measured data. The experimental
data
were obtained by use of the white-light
interfer-
ometer technique of Knox et
al."1 To reduce the
experimental errors, we used 16 reflections
at
a -10° angle of incidence in the interferometer,
resulting in a measurement
accuracy of -1 fs.
These results demonstrate that dielectric
mirrors
with approximately constant
GDD over a broad
spectral range can be
designed and fabricated by use
of standard computation
and evaporation techniques,
respectively.
The maximum achievable
negative GDD is limited
by the
maximum group-delay difference that can
be
obtained
between the extremes of the reflectivity
range.
This in turn relates to the optical thickness
2.4
2.2
X
2.0
W 1.8
I-1.6
X 1.4
Ce
1.2
-1 0 1
2 3 4 5 6 7
8 9
OPTICAL THICKNESS (am)
Fig., 1. Theoretical refractive-index profile
of a
high-reflectivity
TiO
2
-SiO
2
multilayer coating designed
specifically for
broadband GDD control in femtosecond
lasers.
0.9
IEl
2
WAVELENGTH (pum)
OPTICAL DISTANCE (pim)
` 0.7
8
Fig. 2. Computed electric-field distribution
as a function
of wavelength in the chirped
dielectric structure shown
in Fig. 1.
February
1, 1994
/ Vol.
19,
No. 3
/ OPTICS
LETTERS
203
35 -
- 30
0
>. 25
i 20
0~
n 15
0
0
o
5' 10
700
750
800
850
900
WAVELENGTH
(nm)
Fig. 3.
Computed
group
delay
as a
function
of wave-
length
(solid
curve)
together
with
experimental
data
(squares)
for
the multilayer
design
of Fig.
1.
Note that
the absolute
delay
could
not be
measured;
therefore
a
wavelength-independent
constant
delay
was added
to
the
measured
relative
data.
of
the coating.
We
have
found
that
a simple
ap-
proximate
expression
for the
maximum
achievable
group-delay
difference
can be
written
as
A~max
-
2
(tchirped
- tqw)
(1)
C
where
tchirped
is the
optical
thickness
of the
chirped
multilayer
coating
and tqw
is
that of
a standard
quarter-wave
high
reflector
(R
> 99.9%)
consisting
of the
same
pair of
alternating
layer
materials.
In
physical
terms,
the
required
high
reflectivity
of
the
dispersive
mirror
calls
for
a minimum
optical
thick-
ness
of
t - tqw,
and
only
excess
layers
can
intro-
duce
an
appreciable
frequency-dependent
group
de-
lay
around
the
center
of the
high
reflectivity
band.
Assuming
that
the group
delay
varies
in a linear
manner
with
frequency,
we
see that
the
correspond-
ing upper
estimate
for
the GDD
is
given
simply
by
the
ratio of
Arm,,.
to
the mirror
bandwidth
Aw.
For
the
specific
case
of TiO
2
-SiO
2
mirrors
centered
around
A -
0.8 /.&m
we
have
tqw =
4 /.km,
yielding
ATm,,
-
27 fs
for our
8-Am-thick
structure,
in reasonable
agreement
with
the results
presented
in Fig.
3. With
the
number
of layers
fixed,
A
m,.
scales
linearly
with
the
chosen
center
wavelength
of the
dispersive
mirror.
For
a selected
operating
wavelength,
we
can increase
Armad
and
thus
the
magnitude
of broadband
negative
GDD
only
by
increasing
the
number
of layers,
which
is
limited
by scattering
and
absorption
losses
that are
due
to
structural
defects
and impurities
in
the
deposited
layers,
respectively.'
3
It is
expected
that
more
sophisticated
coating
techniques
will permit
the
production
of
higher-quality
layers
and
thereby
open
the
way
toward
the
realization
of more
complex
structures
with
higher
values
of
the negative
GDD
over
bandwidths
approaching
100
THz.
In
summary,
we
have
reported
a
novel
dielectric
mirror
providing
approximately
constant
negative
dispersion
over
a bandwidth
as
broad
as 80
THz.
The
presented
mirror
design
can
be
adopted
for
any
broadband
mode-locked
solid-state
laser
op-
erating
in the
wavelength
range
of
0.5-2
Itm
by
a
simple
resealing
of
the
layer
thicknesses.
With
suitable
layer
materials
this
spectral
range
can
be extended
well
into
the
ultraviolet
and infrared
spectra.
Furthermore,
engineering
the
wavelength
dependence
of the
penetration
depth
might
lead
to
interesting
applications
in
other
areas
of
physics
in
which
scattering
and
interference
in
quasi-periodic
structures
take
place.
We
thank
S.
M. J.
Kelly,
P.
Curley,
P.
Apai,
and
Zs.
Bor
for
helpful
discussions
and
A. J.
Schmidt,
E.
Wintner,
and
N. Kroo
for their
support.
This
research
was
sponsored
by
the
Au~strian
and Hun-
garian
Science
Foundations
under
grants
P-09710,
T-007376,
and
WTZ-O-U
Project
AL7.
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