All-Fiber Pulsed Lasers Based on Carbon Nanotubes€¦ · All-Fiber Pulsed Lasers Based on Carbon Nanotubes by M. C. Iván Hernández Romano Thesis submitted in partial fulfillment
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All-Fiber Pulsed Lasers
Based on Carbon Nanotubes
by
M. C. Iván Hernández Romano
Thesis submitted in partial fulfillment of the requirement for the degree of
DOCTOR EN CIENCIAS EN LA ESPECIALIDAD DE ÓPTICA
in
Instituto Nacional de Astrofísica, Óptica y Electrónica
This chapter mentions the fundamental principles of mode-locker laser and
describes the dynamics of various configurations paying more attention in fiber
configuration. A mathematical explanation of the behavior of saturable absorbers
(fast or slow according to their recovery time) is given and their optical properties
that are important for mode-locking are explained. Additionally, optical properties
of SWCNTs that are important for mode-locking operation are listed and briefly
explained and a review of the state of the art of saturable absorber based on
SWCNTs is also given. Finally, Q-switched laser dynamics is explained.
2.2 Mode-Locking
2.2.1 General Description
The simplest picture of a laser system consists of an optical cavity, or optical
resonator, with a gain medium inside it. However, to produce a pulse and to
produce shorther pulses has become a demonstration of ingenuity. Let’s analyze
our resonant cavity, it can be built by using two highly reflecting mirrors or by
using a ring resonator, as shown in Fig. 2.1 (a) and (b), respectively. When the
light is traveling inside the cavity, standing waves are generated by the
counterpropagating electromagnetic waves. Since the boundary conditions, few
frequencies can be supported by the cavity. This discrete set of frequencies is
known as longitudinal modes which all of them are multiple of the fundamental
cavity frequency which is given by [2.1]:
11
,2
c
nL (2.1)
where c is the velocity of light in vacuum, n is the refractive index of the medium
and L is the optical length of the resonator. Eq. (2.1) can also accurately model a
unidirectional ring fiber laser by considering 2l L .
Fig. 2.1 (a) Schematic of optical cavity with two mirrors, (b) Ring fiber cavity, WDM: Wave Division
Multiplexing.
Let’s now look at the amplifying medium. The longitudinal modes that oscillate
in the cavity are those where the gain exceeds the loss of the resonator and such
a gain is assumed to have a bandpass spectral response, see Fig. 2.2 (a). The way
that these modes add up to produce an output of our laser is essential to produce
the desired pulse output. In Fig. 2.2 (b), top to bottom, we show in phase the sum
of three modes, and the optical pulses generated by their sum. Moreover, there
are transversal modes inside the cavity but it is assumed that the laser is
oscillating in a single transversal mode (like in a single-mode optical fiber).
12
Fig. 2.2 (a) Laser gain and longitudinal modes; (b) Superposition of three equally spaced
frequency components which are all in phase.
The longitudinal modes that are oscillating inside the optical cavity have
different amplitudes and phases and summing all of them produces an average
intensity which varies in time. Therefore, by assuming that all modes have the
same amplitude and phase and then summing all of them, we get [2.1]
1 1
( ) 000 0
0 0
( )N N
ii t i tn n
n n
E t E e E e e , (2.2)
where 0E is the amplitude of the mode, n is the frequency of that mode and 0
is the phase of the mode. By defining n as 1n N n and rewriting Eq.
(2.2) we obtain a convenient expression,
1
( )100
0
( )N
i n ti N
n
E t E e e . (2.3)
Its intensity can be calculated using Eq. (2.3)
22
2 20 0 2
1 sin ( 2)( )
1 sin ( 2)
iN t
i t
e N tI t E E
e t. (2.4)
13
This equation tells us that the output of the laser will be a train of pulses whose
separation between them is given by [2.1]
2
,nd
Tc
(2.5)
and the pulse width is [2.1]
pulse
1 1,
gain bandwidtht
N (2.6)
where N is the number of mode in phase and is the separation between two
consecutives modes. When the output of laser has these features is referred as a
mode-locked laser. It was shown that by fixing the modes’ phase of an optical
cavity, we can produce a train of pulses whose width could be reduced by
increasing the number of modes that has the same phase, Eq. (2.6). The
techniques that have been used to implement mode-locked laser are active mode-
locking, synchronously mode-locking, and passively mode-locking. They will be
briefly described in the next section.
2.2.2 Active Mode-locking
An active mode-locked laser consists of a laser cavity that has an optical modulator
inside, Fig. 2.3 (a). This device will induce a modulation of the amplitude of each
longitudinal mode. It is said that this element modulates the losses in the cavity.
14
Fig. 2.3 (a) Active mode-locked laser, the modulator is driven at the cavity round-trip period; (b) illustration of gain and longitudinal modes when the modulator is driven at a frequency Ω; (c)
Periodic modulation loss and resulting mode-locked pulses.
When the modulator is driven by an electrical signal whose angular frequency
and modulation depth are m and m respectively; n is the phase of the mode
n and is the phase of the electrical signal, the time dependency of mode n of
frequency n can be written as [2.2]
( ) cos( ) 1 (1 cos( )) ,n n n n m me t E t t (2.7)
for convenience let’s rewrite it as
( ) (1 ) cos( )
cos ( )2
cos ( ) , 2
n n m n n
mn n m n
mn n m n
e t E t
E t
E t
(2.8)
where two side bands appear at either side of mode ( )ne t . In particular, if the
2m is equal to the fundamental frequency , then these sidebands
correspond to the two cavity modes adjacent to the original mode, see Fig. 2.3 (b).
In Fig. 2.3 (c) is illustrating a periodic modulation loss and the resulting optical
15
pulses, it should be notice that those pulses appear when the loss is minimum.
Since the sidebands are driven in-phase, the central mode and the adjacent modes
will be jointly phase-locked. Further operation of the modulator on the sidebands
produces phase-locking of the 2n and 2n modes, and so on, until all
modes in the gain bandwidth are locked. Locking the modes in this manner brings
about to generate an optical pulse traveling inside the cavity. When that happens it
is called active mode-locking. It is also possible modulate at m , where m is an
integer, and in this case the mode n can be couple to mode n m and n m .
When the frequency of the modulation is a multiple of the , this is called
harmonic mode-locking.
In practice, an acousto-optic or electro-optic modulator is place inside the
cavity to modulate the losses. For illustration propose, let’s show the FWHM pulse
width of an amplitude modulation mode-locked homogeneous laser [2.3]
1124 1
0.45 ,m m
m a
p
f (2.9)
where m mp is the round-trip gain coefficient and af is the atomic line width. It
should be notice that the pulse width is inverse to m , and af . Ones can easy
realize that the pulse width of the harmonic mode-locking is shorter than the active
mode-locking. Moreover, a mode-locked laser can be built up using a phase
modulator (FM) and in this case the pulse width should be given by the Eq. (2.9)
times the constant 1 42 . The performance of a homogeneous laser using a FM
modulator is essentially the same as with AM modulator; but the FM mode-locked
pulse gets a small frequency chirp equal in magnitude to the pulse width
modulation [2.3].
Harmonic mode-locking has to advantages: the train of pulses that generates
has a closer pulse spacing than the cavity round-trip time (higher repetition rate);
and the optical output can be synchronize to a radio frequency signal (RF). Hence,
harmonic mode-locking is really useful in optical fiber communication where the
16
repetition rate is low and a pulse train of gigahertz is desired. As it was shown,
high repletion rate can be obtained by using this technique but it cannot produce
shorter pulses (<1 ps) [2.4].
2.2.2.1 Synchronously pumped mode-locking
Synchronous pumping is obtained by pumping the gain medium of a laser with the
output beam of another mode-locked laser, Fig. 2.4. It is like switching on the gain
for only a very short period of time while the short pulse is passing through the
gain medium. Both lasers should have the same repetition rate in order to maintain
the necessary switch timing (this is one of the drawbacks of the technique because
the optical length of the two cavities needs to be equal with a typical accuracy of a
fraction of the laser wavelength).
Fig. 2.4 Illustration of the synchronous pumping method for mode-locking of a laser.
The formation of the pulse at the output of the laser is shown in Fig. 2.5,
where the resulting pulse is shorter than the pump pulse. This scheme is useful
when the upper-state lifetime of the gain medium is not much longer than the
17
cavity round-trip time [2.5]. Recently, it has been used Vertical-External-Cavity
Surface Emitting lasers to obtain synchronously mode-locked laser [2.6].
Fig. 2.5 Schematic illustration of the pulse formation in a synchronously pumped mode-locked
laser.
2.2.3 Passive mode-locking
Passive mode-locking is similar to active mode-locking, but the optical modulator is
replace by a saturable absorber (SA), Fig. 2.6, which is a nonlinear optical element
that has a constant optical absorption to low intensities, but it decreases as the
laser intensity rise.
Fig. 2.6 Schematic setup of a passive mode-locked laser.
18
Passive mode-locking stars from noise fluctuation in the laser. One strong noise
spike experiences less loss per round-trip that other weaker noise spikes; and
hence this particular noise spike will be more strongly during the following cavity
round trip. This process goes on until the noise spike reaches a steady state and a
stable pulse train has been formed. Besides, if the response time (recovery time)
of the nonlinearity is sufficiently fast, the optically driven modulation function gets
faster as the pulse becomes shorter. Thus, the pulse shortening action can remain
effective even for very short pulses. Since the recovery time of the SA is really fast,
shorter pulses can be obtained. In general, the fast loss modulation introduced by
the recovery time is faster than any electronically driven loss modulation used to
drive any optical modulator.
Several kinds of SAs exist, but they can be classified into two: slow SA and fast
SA. In the next two sections both of them will be described.
2.2.3.1 Saturable absorber
A saturable absorber is a material that has decreasing light absorption with
increasing light intensity. This phenomenon can occur in a medium with absorbing
dopant ions, when a strong optical intensity leads to depletion of the ground state
of these ions. Similar effects can occur in direct gap semiconductors, as the
intensity increases photo-excitation causes the states near the edge of the
conduction and valence bands to fill, blocking any further absorption. At high
enough intensity, the semiconductor becomes transparent to light at photon
energies just above the bandedge [2.7]. This phenomenon is related with the third
optical nonlinearity [2.8]. Different materials have been used as saturable absorber
such as organic dyes, colored filter glasses, dye-doped crystals, semiconductor,
and recently Single Wall Carbon Nanotubes (SWCNTs).
19
2.2.3.2 Saturation model
The most common saturable absorber (organic dye solution and semiconductor)
can be model by a four-level system, see Fig. 2.7. The transition is a resonant
absorption for the laser radiation (1→2), and the absorption strength is
proportional to the population densities 1 2N N (where jN is the density in units
of m-3 of absorbers in level j ). The total density of absorbers is AN . The 2→3 and
4→1 relaxations are taken to be very fast. The 3→4 recovery time is finite and is
denoted A . It is assumed that the laser radiation does not interact with 3→4
transition and the absorption spectrum is homogenously broadened which can be
considered constant within the mode-locked bandwidth.
Fig. 2.7 Model of a four-level saturable absorber.
The saturation of the absorber can be described with the following differential
equation [2.4]:
2
311 2
0
( )( ),A
A A
a tNNN N
t A (2.10)
with
1 3 2 4 and N 0. AN N N N (2.11)
20
In Eq. (2.10), the first term on right is the relaxation out of level 3 and the second
term represents stimulated absorption. The pulse is normalized so that 2
( )a t
gives the time-dependent power carried by the pulse. A is the 1→2 absorption
cross section, 0 is the photon energy, and AA is the beam cross-section area in
the absorber. The Eq. (2.10) can be rewrite as
2
11 1( )
,A
A A A
a t NN N N
t P (2.12)
where
,A
AA A
AP (2.13)
is the absorber saturation power. Assuming a small loss per pass, the time-
dependent loss term ( )l t is proportional to the ground-state absorber density 1N
[2.4]:
1( ) ( ) ,2A
al t N t l (2.14)
where al is the length of the absorber medium.
Solving 1( )N t form Eq. (2.12) produces two important limiting cases. These
cases are determined from the comparison between the magnitude of the recovery
time A and that of the mode-locked pulse width pt . The first occurs when
A pt , and it is known as a fast saturable absorber. The second one is when
A pt , and it is identified as a slow saturable absorber. In the following two
sections these cases will be discussed.
21
2.2.3.3 Fast saturable absorber
In the case of a fast saturable absorber, the absorber recovery time is much faster
than the pulse duration (A pt ). In this manner, it is assumed that the
absorption instantaneously follows the absorption of a certain power 2
( )a t . Then
Eq. (2.12) convers into
2
11( )
0 ,A
A A A
a t NN N
P (2.15)
and solving for 1N
1 2( ) .
( )1
A
A
NN t
a t
P
(2.16)
1( )N t and ( )l t vary instantaneously with the laser power 2
( )a t . An increment in
the laser power produces a reduction in the absorption; therefore the peak of the
mode-locked pulse will experience lower loss than will the wings of the pulse [2.4].
Haus’s master equation can describe this passive mode-locking technique very
well [2.4]
0
2
2 2
1 ( ) ( )( ) ( ) ( ) 0,
c
d a t da tg t l t l a t T
dtdt (2.17)
where ( )g t is the gain, 0l is the linear time-independent cavity loss, and T is a
time shift arising due to the nonlinear pulse shaping action of ( )l t and ( )g t ; and
it is usually small compared to the steady-state pulse width.
It is possible to solve Eq. (2.17) by assuming that 2
( )a t remains sufficiently
below the saturation power AP and using Eq. (2.14) and Eq. (2.16), A complete
explanation of the solution of this equation is in [2.4], [2.9], [2.10]. With this
solution and the Eq. (2.17), we can figure out the dynamic of the pulse formation.
22
Fig. 2.8 shows the time dependence saturable absorption as a function of the
normalized time together with the position of the saturated gain level and the
pulse power. It is observed that the net gain before and after the pulse must be
zero. This is, in fact, a stability condition since if the net gain were positive before
or after the pulse, perturbations before or after the pulse would grow in amplitude.
Fig. 2.8 Pulse-shaping gain and loss dynamics for fast-saturable absorber mode-locking.
2.2.3.4 Slow saturable absorber
In the case of a slow saturable absorber, the excitation pulse duration is much
shorter than the recovery time of the absorber (A pt ). Thus, in Eq. (2.12) the
first term on the right is neglected and Eq. (2.12) reduces to:
2
11
( ).
A A
a tNN
t P (2.18)
The solution of the equation is
2
( ) ( )1 1 1
( ) ( )( ) exp exp ,
A A A
ti ia t U t
N t N dt NP U
(2.19)
23
where
2
( ) ( ) and .A A A
t
U t a t dt U P (2.20)
Here ( )1
iN is the initial absorber population in level 1 just before the laser pulse,
( )U t is the pulse energy up to time t , and AU is the absorber saturation energy.
One can obtain an insight on the pulse formation process itself, a complete
treatment of the problem can be seen in [2.4], [2.9], [2.10], by solving Eq. (2.17)
together with Eq. (2.14) and Eq. (2.19). In this case, dynamic gain saturation
supports the pulse formation process, Fig. 2.9, and pulses much shorter than the
recovery time of the saturable absorber are obtained [2.11].
Fig. 2.9 Pulse-shaping gain and loss dynamics for fast-saturable absorber mode-locking.
Dynamic gain saturation means that the gain experiences a fast pulse-induced
saturation that will recover back between consecutive pulses. Therefore, an
effective ultrashort net-gain window can be formed by the combined saturation of
24
the absorber and the gain, if the absorber can saturate and recover faster than the
gain, while the saturable absorber recovery time is much longer than the pulse
duration. Therefore, the absorber would preferentially absorb the leading edge of
the pulse, whereas gain depletion would cause loss on the trailing edge.
2.2.3.5 Characterization of saturable absorber
The nonlinear optical properties of a saturable absorber can be determined by
knowing four macroscopic parameters. The macroscopic properties of a SA are the
recovery time A , the modulation depth 0 , the nonsaturable absorption ns ,
and the saturation intensity/fluence ( / )sat satI F . The pulse generation process is
based on them, as well as the determination of the saturable absorber
performance. The recovery time is the decay time of photon-generated carriers
after the absorber is excited by a high optical intensity. It is usually measured by a
standard pump-probe technique [2.12]. The modulation depth is defined as the
maximum possible change in optical absorption , and the nonsaturable
absorption is part of the absorber loss which cannot be saturated even at high
intensity. A low value of ns is wanted to increase the modulation depth. The
saturation intensity satI is defined as the optical intensity that it takes in a steady
state to reduce the modulation depth to half its initial value. The fluence is the
incident pulse energy per unit surface area ( Asat satF I ). The last three
properties can be determined by using a Z-scan technique or a power-dependent
transmission experiment (this setup will be shown in the next chapter); these two
techniques measure the transmission of a SA at different input pump powers
levels. Pulse lasers, whose pulse width is shorter than the recovery time of the
sample, are used to implement these setups.
25
One can model the SA as a two photon absorption process by assuming that
the SA responds instantaneously to the optical intensity (fast absorber model of a
SA). The intensity-dependence absorption ( )I can be written as:
( ) .1
ns
sat
II
I
(2.21)
Fig. 2.10 shows the absorption as a function of peak intensity. We can figure out
that nslin . By normalizing , we get :
0( ),
1 1
ns lin
linsat sat
I
I II I
(2.22)
where the modulation depth is 0 lin . In the following chapter this model
will be used to fit the SA’s data.
5 10 15 20 25 30 35 40
0.32
0.34
0.36
0.38
0.40
ns
Ab
so
rpti
on
Input intensity (MW/cm2)
lin
Fig. 2.10 Using the fast absorber model the nonlinear absorption data was fitting.
Different materials have been used for SAs and each of one has its advantages
and drawbacks. In order to get an insight of these SAs a brief review will be
presented in the following sections.
26
2.2.3.6 Organic dye as a saturable absorber
Mode locking was first demonstrated in the mid-1960s by using a ruby laser [2.13],
and an Nd:glass laser [2.14]; both of them are solid-state laser. Nevertheless, at
that time solid-state lasers could not generate continuous-wave mode-locked
output, but they produced mode-locked picosecond pulses that are modulated with
a much longer Q-switched pulse envelope, which has a much lower repetition rate.
This regimen is called Q-switched mode-locking. At that time, 1970s and 1980s,
the dye lasers became so popular because they did not show Q-switching
instabilities and they could generate really short pulses. The first sub-picosecond
passively mode-locked dye lasers were shown in 1974, [2.15], [2.16], and the first
sub-100 fs colliding pulse mode-locked (CPM) dye laser was demonstrated in 1981
[2.17]. Using CPM, it was possible to generate pulses as short as 27 fs with
average output power of about 20 mW [2.18]. Furthermore, pulses as short as 6 fs
were reached by additional amplification and external pulse compression but only
at much lower repetition rates [2.19]. Nonetheless, dye lasers suffer from
significant disadvantages such as rapid degradation during operation, limited
output power, and the need for pumping e.g. with green or blue light, making the
pump sources expensive. Since dyes are poisonous and often even carcinogenic,
dealing with them should be done with a lot of care. For these reasons, others
techniques were suitable and less health dangerous that took over the generation
of short pulse generation.
2.2.3.7 Kerr-lens mode locking
The nonlinear effect based on χ(3) is known as Kerr effect and in a Kerr medium
the refractive index is nonlinear and depends on light intensity [2.20]. Due to the
high intracavity intensities, the Kerr effect is relevant in most ultrafast lasers.
These nonlinear refractive index changes bring about a lens focusing effect which
can describe in the following way: if a beam with a Gaussian profile is passing
through a Kerr media, the beam is more intensity at the center than at the edges
27
and for that reason the refractive index of the medium will become higher at the
center than at the edges of the beam; this effect behaves like a lens. The focusing
of the light depends on the intensity of the beam and on the path length that the
beam travels inside the material [2.1]. This leads to a so-called Kerr lens with an
intensity-dependent focusing effect which can be exploited for a passive mode-
locking mechanism.
Kerr lens mode-locking (KLM) is the most important method for pulse
generation from broadband solid-state laser. The first KLM of Ti:sapphire laser was
implemented in 1991 and it produced a pulse width of 6 fs [2.21]. An improved
mode-locking was demonstrated by Spinelli when a hard aperture was
appropriately placed in the cavity [2.22]. Fig. 2.11 shows a schematic illustration of
the pulse shortening of the KLM; this scheme has a hard aperture, with small
diameter, placed at a suitable location inside the cavity in order to introduce high
loss to the CW mode. Moreover, if a pulse of light with higher intensity than the
CW mode is traveling inside the cavity, it can generate self-focusing at the hard
aperture. Hence this reduction of the laser mode area for high intensities at the
aperture gives rise an effective fast saturable absorber (artificial SA). The same
aperture effect was achieved by reducing the beam radius (by Kerr lens effect) in
the gain medium, thus the short pulses undergo higher effective gain because the
pulses have a better spatial overlap with the pumped region [2.23]. Regardless of
all these features, there are some drawbacks like KLM lasers are not self-starting,
their laser cavities requires stringent mirror alignment, a clean environmental to
minimize losses and they operated close to the stability limit.
Fig. 2.11 Pulse shortening by dynamic self-focusing, or KLM, L1 and L2 are lenses.
28
2.2.3.8 Additive pulse mode-locking
The first exploited method for producing a self-amplitude modulation, via the
optical Kerr effect, used the nonlinear phase shift to modify the interference
between two coupled laser cavities. It was Additive Pulse Mode-Locking (APM) and
The main cavity has the gain medium and it is coupled to an auxiliary cavity
trough a partially reflector mirror. The lengths of the cavities are almost the same.
When one pulse hits the partially reflector mirror in the main cavity, part of the
pulse is reflected to the main cavity and another is transmitted into the auxiliary
cavity. The transmitted and reflected pulses will meet at the partially reflecting
mirror at the same time and they will interfere because the lengths of the two
cavities are nearly equal. The overall reflectivity seen by the main cavity depends
on the phase between these two sets of pulses. The highest reflectivity occurs
when the round-trip phases of the two cavities are identical (modulo 2 ) [2.4]. A
nonlinear medium is placed in the auxiliary cavity to produce self-amplitude
modulation. If the pulses of each cavity are out of phase and the nonlinear phase
shift bring them closer to being in phase, the overall reflectivity of the main cavity
increases. Thus, the peak of the pulses has the highest reflectivity due to self-
amplitude modulation. On the other hand, if the nonlinear phase shift increases
the mismatch between the pulses of each cavity, the reflectivity of the main cavity
will decrease and mode-locking will be suppressed. For this reason the relative
29
cavity length in APM lasers should be interferometrically stabilized (this is a
disadvantage). Two techniques are the most used to implement APM lasers using
optical fiber; they are nonlinear amplifying loop mirror (NALM) and nonlinear
polarization rotation.
A typical NALM layout is shown in Fig. 2.13, it consists of a 3 dB coupler which
splits the incident light into two equal intensities that counter propagates. The
important issue for a NALM is to place the gain very close to the end of the loop,
this asymmetry causes that one wave is first amplified to high power and then
undergo SPM (self-phase modulation); the other wave undergoes SPM at low
power and at the output is amplified. Furthermore, if the phase shift is close to
for the central intense part, this part of the pulse is transmitted, whereas pulse
wings are reflected because of their lower power levels and smaller phase shift.
This brings about output pulses that are narrower compared with themselves at
the entrance. Due to this behavior, the NALM is considered like a fast SA (artificial
SA). The first time that the NALMs were used was in 1991 [2.24] - [2.27]. They
are also used in figure-eight laser configuration [2.25].
Fig. 2.13 Pulse shortening by a NALM with an asymmetrically placed gain element.
Intensity dependent nonlinear polarization rotation also provides a mechanism
for artificial SA as shown in Fig. 2.14. To enforce unidirectional operation in the
30
laser cavity there are a gain medium, an output coupler, and an isolator. Other
elements are incorporated to promote nonlinear polarization evolution; these
include the two polarization controllers, a birefringent fiber piece, and a polarizer.
Nonlinear polarization evolution can occur either in birefringent or nonbirefringent
fibers. In nonbirefringent fibers, the nonlinear polarization evolution takes the form
of ellipse rotation, which is a superposition of two different circular polarization
states with different intensities. If they undergo different nonlinear shift phase,
because of different self-phase modulation and cross-phase modulation, their
combination can result in an intensity dependent polarization rotation. If the
system is well adjusted, the maximum transmission at the output polarizer occurs
at the highest intensity. The technique of nonlinear polarization rotation was first
used for passive mode-locked laser in 1992, [2.28], [2.29], [2.30]. The shortest
pulse obtained by this technique was 42 fs with energy < 1 nJ, using an Nd-doped
fiber laser in a Fabry-Perot configuration [2.31]. In a Erbium ring cavity
configuration pulses < 100 fs with energies > 0.5 nJ were obtained [2.32]. One of
the main drawbacks of these lasers is that they are very sensitive to environmental
instability due to their interferometric nature [2.33].
Fig. 2.14 Layout for mode-locked fiber ring laser exploiting nonlinear polarization rotation. In this implementation the required polarizer function is included in the isolator, PC: polarization controller.
31
2.2.3.9 Semiconductor saturable absorber
Semiconductor Saturable Absorber (SESAM) consists of an antiresonant
semiconductor Fabry-Pérot etalon formed by a semiconductor layer grown on top
of a highly reflecting semiconductor Bragg mirror and covered by a dielectric
reflector. Usually, the semiconductor layer contains absorptive quantum-well
layers. This device can work at a wide variety of wavelengths by engineering the
bandgap of the quantum wells. The recovery time of SESAMs vary between a few
nanosecond for Q-switching applications and few picosecond for ultrafast lasers
[2.34].
SESAMs based on IIIV group binary and ternary semiconductor in the form of
multi quantum well are the most popular SAs [2.35]. Up to now, SESAMs have
been widely deployed to mode locked solid state lasers in a broad spectral range,
between 800 and 1550 nm, and they are grown by molecular beam epitaxy (MBE)
or metal organic vapor phase epitaxy (MOVBE) on distributed Bragg reflectors
[2.36]. These stringent fabrication methods (which are the shortcomings of
SESAMs) also require an ion implantation to create defects in order to reduce the
recovery time [2.37], [2.38].
2.2.4 Hybrid mode-locking
The improvement of the mode-locked laser performance can be achieved by
combining more than one mode-locking technique and this is called hybrid mode
locking. One way to implement a hybrid mode locked laser is by placing an
amplitude or phase modulator inside a passively mode-locked fiber laser. Typically
in hybrid mode-locking, the active modulation assists in pulse formation and helps
to stabilize the mode-locking process, while the SA is responsible for significant
reduction of the final pulse duration [2.4]. Since the modulator can operate at
multiples of the fundamental frequency of the cavity, the laser’s repetition rate can
reach gigahertz.
32
The first hybrid mode-locked laser was reported in 1991 [2.39], since then,
other configuration were implemented to improve laser performance.
Subpicosecond pulses at a repetition rate of 0.5 GHz were generated in 1994 by
using sigma configuration. This laser was made by coupling a linear section (that
contained a fiber amplifier and a passive mode-locking element composed of
quarter wave plates and a Faraday rotator) with a loop of polarization-maintaining
fiber that has a LiNbO3 inside it [2.40]. Based on the same configuration, a diode-
pumped stretched pulse erbium doped fiber laser was implemented and it
produced pulses whose energy and duration were 1.3 nJ and 1.5 ps, respectively
[2.41].
It is feasible to build a hybrid mode locked laser by combining these two
passive mode-locking techniques. In 1996, a SA was added to a mode-locked laser
based on nonlinear polarization rotation and it produced pulses whose energy and
duration were 100 pJ and 200 fs, respectively [2.42].
2.3 Optical properties of SWCNTs
Since SWCNTs were discovered in 1993 [2.43], they have been extensively studied
due to their astonishing optical properties; such as ultrafast recovery time [2.44],
high third-order optical nonlinearities [2.45], and in particular by the tunability of
their band-gap energy when the diameter of the SWCNTs is modified [2.46]. Due
to these optical properties, SWCNTs are good to fabricated saturable absorbers. By
choosing the correct nanotube diameter it is feasible to work at a specific
wavelength. They also show absorption from the UV to the near IR.
SWCNTs have a wide variety of potential applications including optical limiters
The fundamental dynamics of an active Q-switched laser are shown
schematically in Fig. 2.17. The cavity losses are set at high value (low Q), when
the modulator does not allow the laser oscillates, while the pumping laser store
energy (by the inversion of the population) which increases the gain, Fig. 2.17.
When the modulator allows laser oscillations, the cavity losses are low (high Q); an
energy short pulse grows from spontaneous emission and gathers the energy
stored in the cavity (the inversion of population is depleted by this). Then, the
cavity losses are high when the modulator does not allow laser oscillations again.
40
Fig. 2.17 Schematic illustration of the Q-switching process.
2.5.3 Passive Q-switching
Passive Q-switching can be generated by placing a SA inside the laser cavity.
Several kinds of SAs have been used as crystalline materials Co2+:ZnS [2.93],
Co2+:ZnSe [2.94], semiconductor compounds [2.95], and semiconductor saturable
absorber mirrors (SESAM) [2.96]. Lately, doped fiber has been used as SA to
generate Q-switching pulses in all fiber lasers [2.97], [2.98].
We are going to show a simple derivation of relevant parameters of passively
Q-switching lasers. Let’s consider a gain medium (inside a laser cavity) whose
length is gL to provide a time-dependent round trip intensity gain coefficient g t ,
a SA with a saturable loss coefficient q t (unbleached value 0q and bleached
value 0); and output coupler with transmission outT and output coupling
coefficient outl , defined by 1 exp( )out outT l ; and a nonsaturable loss pl . The
total nonsaturable loss coefficient per round trip is out pl l l . The saturation
41
energy of the absorber AE is assumed to be small compared with the saturation
energy of the gain medium LE [2.99].
The stored energy in the pumped gain material is proportional to the excitation
density 2N , the photon energy Lh at the lasing wavelength, and the pumped
volume gAL [2.99]:
2stored g LE AL N h . (2.23)
The intensity gain coefficient per round trip is 22 L gg N L , in a standing wave
cavity, where L is the emission cross section of the laser material. This can be
rewrite as [2.99]
2L
stored LL
hE Ag E g , (2.24)
with the saturation energy LE of the laser medium given by [2.99]
2L
LL
hE A . (2.25)
If a Q-switched pulse reduces the gain by [2.99]
i fg g g , (2.26)
where ,i fg are the intensity gain coefficient just before and after the pulse. It
releases the energy released LE E g . The output pulse energy can be obtained by
multiplying the released energy with the output coupling efficiency [2.99]:
outp L L i
out p
lE E g E g
l l. (2.27)
Since ig g , the quantity L iE g is an upper limit for the attainable pulse
energy. To determine g is necessary to solve the rate equation, but an easy
42
solution can be obtained by considering four different phases of a Q-switched
pulse cycle.
a) In the first phase the absorber is in its unbleached state. The pulse stars
to develop when the gain is equal to the unsaturated value of the losses
[2.99]:
0ig l q . (2.28)
The power in the cavity begins from spontaneous emission noise and it
keeps growing until it is big enough to bleach the absorber.
b) In the second phase, the SA is fully bleached and the power grows
quickly until the gain starts to be depleted (net gain 0ig l q q with
0q ). The pulse maximum is reached when the net gain is zero, i.e.,
g l [2.99].
c) In the third phase, the power inside the cavity decays due to depletion
of the gain but the pulse extracts energy in this phase.
d) In the fourth phase, the absorber recovers its unbleached state and the
gain increases its value by the pumping.
The first phase starts all over again when the gain is equal to the threshold level. A
schematically illustration of the gain, loss and power in a passively Q-switched
laser cavity is shown in Fig. 2.18. For large output coupling ratios 0l q the gain
difference can be expressed by [2.99]:
02g q . (2.29)
Inserting Eq. (2.29) into Eq. (2.27) we obtain an expression for the pulse energy:
0 02 , .
2outl
pl out p
lhE A q l q
l l (2.30)
Both the gain ( g ) and the pulse energy can be increased by increasing 0q and
l . Nonetheless, the available gain limits the value of 0ig l q [2.99]. Moreover,
43
the parasitic losses increase with the increase in the modulation depth. Optimized
pulse energy can be achieved for values of l close to 0l q , for a SA with
nonsaturable loss.
Fig. 2.18 Evolution of power, gain and loss in a passively Q-switched laser [2.99].
The repetition rate of the Q-switched laser can be derived by dividing the
average output power by the output pulse energy [2.99]. The average power can
be written as ,av s P P thP P P , where PP is the pump power, ,P thP is the
threshold pump power, and s is the slope efficiency. The repetition rate is given
by [2.99]:
,
1s P P th
repP
P Pf r
E, (2.31)
where r is defined as the ratio of the pump power to the threshold pump power.
The pump power and the threshold power can be written as [2.99]:
0 0, .
2 2
p pP th
l L p l L p
h A h AP g P l q (2.32)
44
Here ph is the pump photon energy, p is the pumping efficiency, and L is the
upper state life-time of the gain medium. Inserting Eq. (2.27) and Eq. (2.32) into
Eq. (2.31) and using Eq. (2.29), the repetition rate can be expressed as [2.99]:
0 0 0 0
02rep
L L
g l q g l qf
g q. (2.33)
The repetition rate can also be estimated (at pump power well above the
threshold) by relating it to the ratio of absorbance pump power and absorbed
threshold pump power [2.100]
,
,
p abs
abs thresh L
Pf
P, (2.34)
where ,p absP is the total amount of the pump power absorbed with the lasing
mode volume, and ,abs threshP is the pump power required for reaching the
threshold inversion density. The last expression shows that the repetition rate
depends linearly on pump power assuming traditional theory.
So far, all the analysis that has been presented here is based on the theory of
microchip laser [2.99], where it is assumed low duty cycle and constant inversion
in a short cavity. In contrast, fiber lasers have higher duty cycle and longer cavity
lengths with large gain; the description of these cavities should be done by taking
into account more consideration. In 2008, a paper that describes passively Q-
switched fiber laser was published [2.101].
The saturation of the gain g in a Q-switched laser can be described by the
rate equation [2.101]:
0
,
,g sat g
dg t g t g gP t
dt E (2.35)
and the saturable absorption q can be found from a similar equation [2.101]:
0
,
,a sat a
dq t q t q qP t
dt E (2.36)
45
where ,sat gE and ,sat aE are the saturation energies and g and a the recovery
times for the saturable gain and loss, respectively. The temporal evolution of the
intracavity power P is given by [2.101]:
,r
dP Pg l q
dt T (2.37)
where rT is the cavity round-trip time. If the gain recovery is shorter than the time
between pulses and is long enough to let the SA saturated by the Q-switched
pulse, the recovery time of the absorber does not play an important role [2.101].
In this analysis two cases are going to be considered, when the system operates
near the threshold ( 0 0g q l ) and when the system operates far above the
threshold ( 0 0g q l ). The former correspond to a similar case that has been
analyzed; see Fig. 2.18 and Fig. 2.19 (a). The latter occurs by a strong pumping
which causes that the gain reaches a gain value above 0q l and then it
decreases to a value lower than 0q l , compare Fig. 2.18 with Fig. 2.19 (b).
Fig. 2.19 Schematic illustration of the temporal evolution of the cavity gain/loss and the output power during Q-switched laser pulse formation (a) close to lasing threshold, (b) far above the
lasing threshold [2.101].
46
During the gain recovery stage, between consecutive pulses, the intracavity
power is too small to cause any gain saturation. From Eq. (2.35) the gain can be
evaluated with 0P t [2.101]:
0 0 0exp ,gg t l q g t g (2.38)
assuming an unbleached saturation absorber. Here the gain reaches 0l q at the
time 0t (dashed line in Fig. 2.19 (b)). At the time 0t the pulse power starts
to develop from noise level 00P t P . When the pumping is above threshold,
the gain increases to reaches the value 0 ,sat g gg E . When the gain 0g is close to
the threshold gain, the gain recovers to 0g l q [2.101]. On the other hand,
when the gain is much higher than the threshold gain, the gain recovers to a much
higher value [2.101]. The intracavity power during gain recovery is [2.101]:
2 0 00exp 0.5
g r
g l qP t P t
T. (2.39)
Using this equation it is possible to express the time needed for the gain to be
recovered from the threshold value to the onset of the gain saturation when
0 ,sat g gP t g E [2.101]:
0 ,
0 0 0
2log
g r sat g
g
T g Et
g l q P. (2.40)
At this time the gain has recovered to the value [2.101]
0 ,0 0 0
0
2 logsat gr
ig g
g ETg l q g l q
P. (2.41)
47
Using the expression log 1 0ig l g g [2.99], that gives the gain
reduction during the Q-switching process; it is possible to evaluate the total gain
variation [2.101]:
,0 0 0 0
0
2 2 2 log 2 1sat gr
thresholdg g
ET Pg q g l q q APP
, (2.42)
with [2.101]
, 00
0 0
2 log , .sat gr
g g threshold
E gT PA l q
P P l q (2.43)
Using Eq. (2.42) the pulse energy and the repetition rate expression can be rewrite
for a passively Q-switched fiber laser. Let’s remind ourselves that the pulse energy
is given by ,released sat gE E g and the repetition rate is given by Eq. (2.33). It is
easily to realize that the pulse energy (as well as the output power) depends on
the pump power in contrast to the nearly constant pulse energy obtained using the
near-threshold (low duty cycle) analysis [2.101]. Moreover, the repetition rate also
depends on the pump power. It is also possible to derive an equation that evaluate
the pulse duration and it is [2.101]:
7.04 rT
g. (2.44)
From Eq. (2.44) we can realize that the pulse duration is directly proportional
to the cavity-round trip, which means longer pulse duration for longer cavities and
shorter pulse duration for shorter cavities [2.101].
48
2.6 References
[2.1] W. T. Silfvast, Laser fundamentals (Cambridge, third edition, UK 2004).
[2.2] C. Rulliere, “Methods for the generation of ultrashort laser pulses:
mode-locking” in Femtosecond laser pulses: principles and experimets,
A. Ducasse, C. Rulliere, and B. Couillaud, eds. (Second edition, Springer,
2003).
[2.3] A. E. Siegman, Lasers (University Science Books, Sausalito, California,
1986).
[2.4] M. Weiner, Ultrafast Optics (Wiley, USA, 2009).
[2.5] C. K. Chan and S. O. Sari, “Tunable dye laser pulse converter for
production of picosecond pulses.” Appl. Phys. Lett. 25, 403-406 (1974).
[2.6] W. Zhang, et al., “Femtosecond synchronously mode-locked vertical-
[2.92] M. Delgado-Pinar, D. Zalvidea, A. Diez, P. Perez-Millan, and M. V.
Andres, “Q-switching of an all-fiber laser by acousto-optic modulation of
a fiber Bragg grating,” Opt. Express 14, 1106-1112 (2006).
[2.93] M. Laroche, A. M. Chardon, J. Nilsson, D. P. Shepherd, W. A. Clarckson,
S. Girard and R. Moncorgé, “Compact diode-pumped passively Q-
switched tunable Er-Yb double-clad fiber laser,” Opt. Lett. 27, 1980-
1982 (2002).
[2.94] V. N. Philippov, A. V. Kiryanov and S. Unger, “Advanced configuration of
erbium fiber passively Q- switched laser with Co2+:ZnSe crystal as
saturable absorber,” IEEE Photonics Technol. Lett. 16, 57-59 (2004).
[2.95] A. Agnesi, S. Morello, C. Piccino, G. Reali, and G. Sun, “Diode-pumped
Neodymium lasers repetitively Q-switched by Cr 4+:YAG solid-state
saturable absorber,” IEEE J. Sel. Top. Quantum Electron. 3, 45-52
(1997).
[2.96] R. Paschotta, R. Häring, E. Gini, H. Melchior, U. Keller, H. L. Offerhaus
and D. J. Richardson, “Passively Q-switched 0.1-mJ fiber laser system at
1.53 μm,” Opt. Lett. 24, 388-390 (1999).
[2.97] S. D. Jackson, “Passively Q-switched Tm3+-doped silica fiber lasers,”
Appl. Opt. 46, 3311-3317 (2007).
[2.98] A. S. Kurkov, E. M. Sholokhov, and O. I. Medvedkov, “All fiber Yb-Ho
pulsed laser,” Laser Phys. Lett. 6, 135-138 (2008).
[2.99] G. J. Spühler, R. Paschotta, R. Fluck, B Braun, M. Moser, G. Zhang, E.
Gini, and U. Keller, “Experimentally confirmed design guidelines for
passively Q-switched microchip lasers using semiconductor saturable
absorber,” J. opt. Soc. Am. B 16, 376-388 (1999).
59
[2.100] J. J. Zayhowski and C. Dill III, “Diode-pumped passively Q-switched
picosecond microchip lasers,” Opt. Lett. 19, 1427-1429 (1994).
[2.101] R. Herda, S. Kivistö, and O. G. Okhotnikov, “Dynamic gain induced pulse
shortening in Q-switched laser,” Opt. Lett. 33, 1011-1013 (2008).
60
Chapter 3 Fabrication process and nonlinear
absorption measurements of PDMS/SWCNT and SU8-2075/SWCNT
films as SA
3.1 Introduction
This chapter has two main objectives; the first is to describe the fabrication
process of SA films based on polymers doped with SWCNTs. The second is to
characterize the nonlinear optical properties of these films by implementing an all-
fiber power dependent transmission setup.
One way to assembly a SA is by placing a thin film doped with SWCNTs
between two fiber connectors. The first polymer used to implement this kind of
SAs was polyvinyl alcohol (PVA) [3.1], but this film suffers from OH absorption loss
because water must be used as a solvent to disperse them. This becomes
disadvantageous for a thick film or a waveguide with a large optical path length.
Other polymer that have shown good results are carboximethyl cellulose (CMC)
[3.2], dimethylformamide (DMF) [3.3], polymide [3.4], and poly-3-hexylthiophene
(P3HT) [3.4], [3.6]. On the other hand, by using two fiber collimators and by
putting a film doped with SWCNTs between them it is possible to obtain a SA. This
technique has been implemented by using polymers such as
polymethylmethacrylate (PMMA), polystyrene (PS) [3.7], and polycarbonate (PC)
[3.8]. Moreover, in order to have a smooth surface these three films need to be
polished. Since the thickness of the PMMA and PS films were 1 mm, it was not
possible to set the film between two fiber connectors. The use of fiber collimator
requires alignment and the system is no robust again mechanical vibration.
61
In this work, we purpose to fabricate thin films of PDMS and SU8-2075 doped
with SWCNTs and then these films are set between two fiber angle connectors in
order to assembly a SA. The fabrication process of the two films is simple and does
not require expensive material or special equipment. In the case of the PDMS
films, either the PDMS polymer or materials used to fabricate the film (such acrylic
layers) are cheap, and good results can be obtained. In the case of SU8-2075 film,
given the functionality of this polymer for integrated devices, we believe that this
material could be very useful for the development of integrated non-linear devices
for different photonic applications.
3.2 SWCNTs as a Saturable Absorber
Among the different properties that make SWCNTs highly attractive is that their
energy bang gap varies inversely with the nanotubes diameter [3.9]. Therefore, if
the diameter of the nanotubes is properly selected they will operate at a specific
wavelength. Using this property, SAs operating from 1035 nm to 1600 nm have
been developed [3.10]. Since we are interested in working at a wavelength around
1550 nm, we chose the diameter of the SWCNTs from 0.8 to 1.2 nm. The SWCNTs
were purchased from the company Unidym and they were synthesized by high-
pressure CO (HiPCO) method.
Since we are interested in fabricating a SA as a thin film using PDMS and SU8-
2075 doped with SWCNTs, the most important issue is the absorption of the films.
The absorption of the films is directly related with the concentration of the
SWCNTs and the thickness of the films. If the concentration of SWCNTs is too
high, the nanotubes tend to bundle and such effect degrades their nonlinear
response (losses by scattering). This also increases the absorption of the film and
the composite can be damaged very easily. If we let a fix concentration and we
modify the thickness of film we can control the absorption value, but there is a
limit on the maximum film thickness that can used without compromising higher
losses due to diffraction. Therefore, finding an optimum concentration of SWCNTs
62
and the adequate thickness is the first step in the process of the fabrication of our
thin films. Based in our experiments we found that a good concentration for the
SWCNTs is 0.125 wt% and the thickness can be from 100 μm to 200 μm. This
optimum concentration value is very similar to the reported in a recent publication
which provides optimum mode-locked operation [3.11].
3.3 Fabrication process of thin films using
SWCNTs
3.3.1 Fabrication of PDMS/SWCNT thin films
Polydimethylsiloxane (PDMS) belongs to a group of polymeric organosilicon
compounds that are commonly referred to as silicones. PDMS has been used in
several optical applications such as lens fabrication, micro-fluidic devices,
waveguides, as a polymer to fill specialty fibers, etc. This material has also been
used to implement a SA but in a tapper configuration [3.11]. The main drawback
of such configuration is the need to fabricate a taper and thus the need for special
equipment as well as the problem of reproducibility.
In order to fabricate a thin film of PDMS doped with SWCNTs, a new and
simple process was developed. A critical issue when mixing carbon nanotubes with
a polymer is to achieve a well dispersed solution. The formation of bundles of
SWCNTs in the polymer matrix is detrimental for the nonlinear optical absorption,
which is the fundamental phenomenon to create a SA device [3.13]. In order to
fully disperse the SWCNTs, rather than mixing the nanotubes directly in the
polymer, we first disperse them in the polymer solvent. Since the solvent for PDMS
is chloroform, the SWCNTs were dispersed in chloroform and the suspension was
sonicated during 30 minutes. The concentration of SWCNTs was selected at 0.125
wt% for optimum operation of the film. After the nanotubes are fully dispersed
PDMS was slowly added to the solvent, and the new mixture was placed in the
63
ultrasonic bath and on the stirring machine for 2 hours and 3 hours, respectively.
Twenty percent of the solution weight is chloroform and eighty percent of the
solution weight is PDMS. After that, we add ten percent of the total solution weight
of the curing agent for the PDMS. Curing of the PDMS is obtained by an
organometallic cross-linking reaction to give an optically transparent polymer.
The fabrication process of PDMS/SWCNT film is described in Fig. 3.1. Two
acrylic layers were used to fabricate a cell whose thickness depends on the spacers
between them.
Fig. 3.1 Schematic representation: (a) two acrylic layers and the spacer between them. (b) Lateral view of the cell fill up with PDMS/SWCNT.
Acrylic material is used instead of any other material because PDMS doped with
SWCNTs does not stick to it. The PDMS/SWCNT solution was poured into the cell
and it was cured by heating up the sample at 95 ºC for one hour and then we let it
rest for 24 hours. After this process the cell can be separated and the resulting film
is equal to the thickness of the spacer, with very smooth surfaces. Using this
method, the thickness of PDMS/SWCNT films can be controlled accurately by
simply changing the thickness of the spacers. The thickness of the film was 200
μm.
64
3.3.2 Fabrication of SU8-2075/SWCNT thin films
The SU8 material has the advantage that is a well-known and inexpensive material
employed for micro-fabrication. Additionally, since SU8 is a photosensitive material,
its potential application on integrated waveguide devices provides a nice ground
for their study. The fabrication process of the SU8/SWCNT films requires few and
very simple steps to achieve well dispersed SWCNTs, and also the film thickness
can be accurately controlled.
In order to avoid bundle formation, the SWCNTs were first dispersed in the
solvent of SU8-2075 (Cyclopentanone) and this suspension was sonicated for 30
minutes. After the nanotubes are fully dispersed, SU8-2075 was added slowly to
the solution and the new mixture was placed in the ultrasonication bath and in the
stirring machine for 2 hours and 3 hours, respectively. The mixture of SU8-2075
and cyclopentanone was made by using 4 ml and 1 ml, respectively. SWCNTs were
incorporated in order to maintain a concentration of 0.125 wt%. The simplest way
to implement a SA with this composite is by making a thin film that can be placed
between two angled fiber connectors. To accomplish this task a technique was
developed to fabricate thin films using the SU8-2075/SWCNT mixture. The
technique requires inexpensive materials that help us to make cells whose
thickness can be controlled by changing the spacer thickness. First we made a
solution of PDMS polymer (Polydimethylsiloxane) which is mixed with ten percent
of the curing agent from the total PDMS weight. At the same time we cut two
glasses (microscope slide) and on top of them we deposited a layer of PDMS by
spin coating, see Fig. 3.2(a). The spin coater was operated at 2000 rpm for 30
seconds. After that, the glasses were heated on a hot-plate at 95 ºC for one hour.
Two spacers were placed between the two PDMS layers as shown in Fig. 3.2(b).
The PDMS material on the glass helps to peel-off the cured composite material
very easily without any complex procedure, while maintaining polished surfaces.
65
Fig. 3.2 Schematic of the cell fabrication process: (a) Deposition of a PDMS layer on a glass
substrate. (b) Thickness and position of the spacers on the cell.
The SU8-2075/SWCNT solution was poured into the cell and the solution was
cured according to the specification of the SU8-2075 polymer taking into account
that the film thickness was 100 µm, see Fig. 3.3. In order to cure the SU8-
2075/SWCNT, first the cell requires a prebake step on a hot-plate at a temperature
of 65 ºC for 2 min. After the pre-bake we let the cell cool down for 5 min, and we
put the cell at 95 ºC for 5 min. The cell was exposed to UV light using a KarlSuss
mask aligner during 50 sec (exposure energy 240 mJ/cm2). After the UV exposure,
the cell was heated at 65 ºC for 2 min and immediately heated at 95 ºC for 6.5
min. After this process we let the cell rest for one day. The cell was separated to
obtain a film whose thickness was equal to the thickness of the spacer (100 μm in
this case). It should be worth mentioning that the cell thickness can be easily
controlled by changing the spacer thickness.
66
Fig. 3.3 Lateral view of the cell with SU8-2075/SWCNT.
3.3.3 Implementation of a saturable absorbers by
using a PDMS film and a SU8 film
Both PDMS and SU8-2075 films were cut and placed between two FC/APC
connectors in order to have an all-fiber SA device. For accomplishing this task, first
an angle connector was screwed in a sleeve; meanwhile, a small section of the film
(PDMS or SU8-2075) was cut and placed in the tip of another angle connector
which was screwed latter in the other end of the sleeve, see Fig. 3.4. Index
matching liquid was not used because the FC/APC connectors suppress reflections.
This configuration shows to be easily assembled and does not need a special
alignment which makes it a sturdy device. Moreover, this technique used to
assembly a SA is free of any complex procedure and any expensive special
equipment. However, one drawback is always present in this configuration and is
related to the coupling losses due to non-physical contact between the connectors.
When the light travels through the film, it diffracts causing a coupling loss between
connectors. As the sample became thicker the coupling loss is bigger. For the
PDMS film whose thickness is 200 μm, the coupling loss was estimated to be -1.5
dB and for the SU8-2075 films whose thickness is 100 μm, the coupling loss was
estimated to be -1.2 dB.
67
Fig. 3.4 Implementation of a SA using either a PDMS/SWCNT or a SU8-2075/SWCNT film.
3.4 Characterization of Saturable Absorber
3.4.1 Methods to characterizer a Saturable Absorber
Z-scan technique is a wide used method in nonlinear optics to measure the
nonlinear refractive index and non-linear absorption coefficient. The technique
consists in moving a sample along the waist of a Gaussian beam with the main
goal of varying the laser-power density on the sample, which reaches its maximum
at the focal point. An analysis of the transmitted beam through the sample as a
function of the sample position, Z, is carried out either in the open or in the close-
aperture scheme. Open-aperture Z-scan is used for the investigation of processes
associated with nonlinear absorption, while close-aperture Z-scan is used to
investigate nonlinear refraction [3.14].
3.4.2 Measurement of the nonlinear absorption of the
saturable absorber
The implementation of an all-fiber power dependent transmission setup is feasible
by means of a pulsed laser, an optical attenuator, a polarization controller, an
optical coupler and a power meter, see Fig. 3.5. A commercial mode-locked fiber
68
laser (MenloSystems, Optical Frequency Synthesizer FC1500-250) with a pulse-
width of 150 fs and a repetition rate of 250 MHz was used. The optical attenuator
plays an important function in this setup because it gives us the capability of
changing the average optical power that is hitting the sample (in this case we are
unable to change the spot size of the beam that hits the sample as in a Z-scan
technique). Furthermore, by playing with the polarization controller we can obtain
the maximum absorption from the film (the film exhibited a slight polarization
dependence). The light is split by an optical coupler and 10% of light is directly
detected with a photo-detector to obtain the input average power, while 90% is
sent through the film. Using these two power measurements; power dependent
transmission of the film can be calculated.
The nonlinear absorption can be determined accurately by using a laser pulse
whose pulse duration is narrower that the recovery time of the material. Since the
recovery time of the SWCNTs has been measured to be less than 1 ps [3.15],
pulses on the order of 150 fs are more than enough to charactize the composite
films. By using the setup shown in Fig. 3.5, we sent pulses of 150 fs at a repletion
rate of 250 MHz without any additional dispersion compensation. The maximum
output power of the laser is 10 dBm, but to characterize the PDMS and SU8-2075
films it was not necessary to apply so much power because the peak power
achieved by the laser at low power was enough to saturate the samples.
Fig. 3.5 All fiber power dependence transmission setup. PC: Polarization Controller; VOA: Variable Optical Attenuator.
69
In the nonlinear optics literature there are several different ways to report the
data from the power dependent transmission setup. The way of the data are
plotted gives specific information regarding the performance of the device that can
be useful for some experimental configuration [3.16]. Fig. 3.6 and Fig. 3.7 show
four different ways of plotting the data for illustration propose. Extracting the most
important parameters that characterize a SA is easily done by plotting the
normalized absorption as a function of the peak intensity; see Fig. 3.6 (c) and Fig.
3.7 (c).
-18 -16 -14 -12 -10 -8 -6 -4 -2 01.6
1.7
1.8
1.9
2.0
2.1
2.2
0.45dB
De
vic
e l
oss (
dB
)
Input average power (dBm)
0 5 10 15 20 25 30 35 4059
60
61
62
63
64
65
66
67
68
69
0 = 7%
Tra
nsm
issio
n (
%)
Input peak intensity (MW/cm2)
(a) (b)
0 5 10 15 20 25 30 35 40
0.81
0.84
0.87
0.90
0.93
0.96
0.99
1.02
Isat = 2.4 MW/cm2
No
rma
lize
d A
bso
rpti
on
Input peak intensity (MW/cm2)
0 = 16.5%
ns
= 83.5%
0 1 2 3 4 5 60.80
0.82
0.84
0.86
0.88
0.90
0.92
0.94
0.96
0.98
1.00
1.02
No
rma
lize
d A
bso
rpti
on
Fsat
= 0.27 m J/cm2
0
= 16.5%
Input Fluence (m J/cm2)
(c) (d)
Fig. 3.6 PDMS/SWCNT film (200 μm). (a) Device loss as function of input power (dB); (b) Transmission vs. input peak intensity; (c) Normalized absorption vs. input peak intensity; (d)
Normalized absorption vs. input intensity.
70
-28 -26 -24 -22 -20 -18 -16 -14 -12 -10 -81.40
1.45
1.50
1.55
1.60
1.65
1.70
1.75
De
vic
e l
oss (
dB
)
Input average power (dBm)
0.22 dB
0 5 10 15 2067.0
67.5
68.0
68.5
69.0
69.5
70.0
70.5
71.0
71.5
72.0
Tra
nsm
issio
n (
%)
Input peak intensity (MW/cm2)
3.4%
(a) (b)
0 5 10 15 200.88
0.90
0.92
0.94
0.96
0.98
1.00
1.02
ns
= 90%
Isat = 0.7 MW/cm2
0 = 10 %
No
rma
lize
d A
bso
rpti
on
Input peak intensity (MW/cm2)
0.0 0.5 1.0 1.5 2.0 2.5 3.00.88
0.90
0.92
0.94
0.96
0.98
1.00
1.02
0 = 10 %
Fsat = 91.26 pJ/cm2
No
rma
lize
d A
bso
rpti
on
Input Fluence (m J/cm2)
(c) (d)
Fig. 3.7 SU8-2075/SWCNT film (100 μm). (a) Device loss as function of input power (dB); (b)
Transmission vs. input peak intensity; (c) Normalized absorption vs. input peak intensity; (d)
Normalized absorption vs. input intensity.
Combining equations (2.21) and (2.22) we obtain
0( ) ,1
ns
sat
II
I
(3.1)
71
where ( )I is the intensity-dependent absorption, 0
is the modulation depth, and
satI is the saturation intensity. It is easy to realize that the nonsaturable absorption
is a percentage of the linear absorption and the saturable absorption is equivalent
to the modulation depth.
The PDMS film was the first to be tested in the setup of Fig. 3.5. In Fig. 3.6 (a)
we plotted the device loss as a function of input average power. The linear loss for
the PDMS film is 2.15 dB. As shown in Fig. 3.6 (a), when the input power start
increasing the device loss starts to decrease. The device loss is reduced by an
approximate value of 0.45 dB. On the other hand, the transmission is incremented
by 7% and it is easily noticed in Fig. 3.6 (b). Additional information can be taken
out from Fig. 3.6 (c), where the saturation intensity is 2.4 MW/cm2, the modulation
depth is 16.5% and the nonsaturable absorption is 83.5%. Fig. 3.6 (d) shows how
the normalized absorption changes as the input fluence (pulse energy per unit
surface area) is increased. We obtain a saturation fluence of 0.27 μJ/cm2.
The SU8-2075 film was also tested in the setup of Fig. 3.5. In Fig. 3.7 (a) we
plotted the device loss as a function of input average power. The linear loss for the
SU8-2975 film is 1.67 dB. As shown in Fig. 3.7 (a) the device loss is reduced by
approximately 0.22 dB when the input average power is increased. Also shown in
Fig. 3.7 (b) is the transmission which is incremented by 3.4% as the peak intensity
is incremented. The saturation intensity is 0.7 MW/cm2, the modulation depth is
10% and the nonsaturable absorption is 90% can be extracted from Fig. 3.7 (c).
Finally, the normalized absorption changes as a function of the input fluence is
shown in Fig. 3.7 (d), which provides a saturation fluence of 91.26 pJ/cm2.
F. Wang et al. developed a film doped with SWCNTs using a (P3HT) and they
determined its optical properties by using an all-fiber power dependent
transmission setup [3.6]. They reported that the saturation intensity, the
modulation depth and nonsaturable absorption are 5.1 MW/cm2, 12.3% and
87.5%, respectively. Making a comparison between these optical properties and
the properties reported here, we can say that saturation intensity of the PDMS’s is
72
lower by 2.7 MW/cm2, the modulation depth of the PDMS is higher by 4.2% and
the nonsaturable absorption of the PDMS is lower by 4% than their film. In the
case of the SU8-2075 film, it has lower saturation intensity and modulation depth
and higher nonsaturable absorption. However, the optical properties of these two
films are as good as the ones reported by F. Wang. Moreover, as we mentioned at
the beginning, the fabrication process of these two films are inexpensive and does
not require especial equipment.
3.5 Summary
The main goal of this chapter was to show special features of the SWCNTs that
should be taken into account when choosing the nanotubes for a SA. A description
of the fabrication process and how to assembly a SA are shown. Furthermore, it is
shown how to measure the nonlinear absorption by using an all-fiber power
dependent transmission setup. The PDMS/SWCNT film has a big modulation depth
16.5%, which is good for stabilizing the cavity pulses [3.11]. On the other hand,
although the SU8-2075/SWCNT film has a lower modulation depth (10%), this
should be good enough for implementing a SA. Since we used the same
concentration of SWCNTs in both samples, this low modulation depth is due to the
film thickness.
3.6 References
[3.1] A. G. Rozhin, Y. Sakakibara, S. Namiki, M. Tokumoto, H. Kataura, and Y.
Achiba, “Sub-200-fs pulsed erbium-doped fiber laser using a carbon
nanotube-polyvinylalcohol mode locker,” Appl. Phys. Lett. 88, 051118
(2006).
[3.2] A. V. Tausenev, E. D. Obraztsova, A. S. Lobach, A. I. Chernov, V. I.
Konov, P. G. Kryukov, A. V. Konyashchenko, and E. M. Dianov, “177 fs
erbium-doped fiber laser mode locked with a cellulose polymer film
73
containing single-wall carbon nanotubes,” Appl. Phys. Lett. 92, 171113
(2008).
[3.3] K. Kashiwagi, S. Yamashita, and S. Y. Set, “Optically manipulated
deposition of carbon nanotubes onto optical fiber end,” Jpn. J. Appl.
Phys. 46, L988-L990 (2007).
[3.4] N. Nishizawa, Y. Seno, K. Sumimura, Y. Sakakibara, E. Itoga, H.
Kataura, and K. Itoh, “All-polarization-maintaining Er-doped ultrashort-
pulse fiber laser using carbon nanotube saturable absorber,” Opt.
Express 16, 9429-9435 (2008).
[3.5] F. Shohda, T. Shirato, M. Nakazawa, J. Mata, and J. Tsukamoto, “147
fs, 51 MHz soliton fiber laser at 1.56 μm with a fiber-connector-type
[3.9] H. Kataura, Y. Kumazawa, Y. Maniwa, I. Umezu, S. Suzuki, Y. Ohtsuka,
and Y. Achiba, “Optical properties of single-wall carbon nanotubes,”
Synth. Met. 103, 2555-2558 (1999).
74
[3.10] T. Hasan, Z. Sun, F. Wang, F. Bonaccorso, P. H. Tan, A. G. Rozhin, and
A. C. Ferrari, “Nanotube-polymer composites for ultrafast photonics,”
Adv. Mater. 21, 3874-3899 (2009).
[3.11] J. C. Chiu, Y. F. Lan, C. M. Chang, X. Z. Chen, C. Y. Yeh, C. K. Lee, G. R.
Lin, J. J. Lin, and W. H. Cheng, “Concentration effect of carbon
nanotube based saturable absorber on stabilizing and shortening mode-
locked pulse,” Opt. Express 18, 3592-3600 (2010).
[3.12] K. Kieu and M. Mansuripur, “Femtosecond laser pulse generation with a
fiber taper embedded in carbon nanotube/polymer composite,” Opt.
Lett. 32, 2242-2244 (2007).
[3.13] H.W. Lee, J. H. Yim, A. J. Kiran, I. H. Baek, S. Lee, D.-I. Yeom, Y. H.
Ahn, K. Kim, J. Lee, H. Lim and F. Rotermund, “Bundling influence on
ultrafast optical nonlinearities of single-walled carbon nanotubes in
suspension and composite film,” Appl. Phys. B 97, 157-162 (2009).
[3.14] E. W. Van Stryland, M. Sheik-Bahae, in Characteristics techniques and
tabulations for organic nonlinear optical materials (Eds: M. G. Kuzy, C.
W. Dirk, Marcel Dekker, New York, 1998).
[3.15] J-S. Lauret, C. Voisin, G. Cassabois, C. Delalande, P. Roussignol, O. Jost,
and L. Capes, “Ultrafast carrier dynamics in single-wall carbon
nanotubes,” Phys. Rev. Lett. 90, 057404 (2003).
[3.16] F. Wang, Single-wall carbon nanotubes – polymer composites as
saturable absorber for ultrafast mode-locked fibre lasers, Ph. D Thesis,
University of Cambridge, 2008.
75
Chapter 4
Passively mode-locked Erbium fiber laser using PDMS/SWCNT and
SU8/SWCNT films as SA
4.1 Introduction
Compact sources of short pulses with high-repetition-rates are highly desirable for
a wide range of applications such as optical communication, metrology systems,
and optical clocks. Passively mode-locked fiber lasers are preferred to generate
short pulses rather than active mode-locked lasers, since they do not need
expensive modulators as mode-locker devices and the pulse quality is better. A SA
is an essential optical device that a passive mode-locked laser should have in order
to produce short pulses. It is well known that a SA works like an optical
discriminator introducing large loss to low intensities but low loss to high
intensities. Different kinds of these devices exist, but the most common is the
semiconductor SA whose fabrication process requires sophisticate equipment and a
clean room environment. During the last ten years, SAs based on SWCNTs have
been implemented and they generate picosecond and femtosecond pulses. The
key issue has been how to incorporate the SWCNTs in the laser cavity. This has
been solved by mixing the nanotubes with a polymer, and the solution can then be
cured to achieve a solid material with SWCNTs incorporated into the polymer. The
SA can now be placed in a laser cavity using several fiber laser configurations. The
process of fabricating thin film doped with SWCNTs is the simplest way to
implement a SA that interacts directly with the electric field [4.1] - [4.3]. We can
also have the interaction of the evanescent electric field with the nanotubes by
making tapers (covering with polymer or by spraying the nanotubes) [4.4], [4.5],
76
deposition of carbon around microfiber [4.6], D-shaped fibers [4.7], hollow optical
fibers [4.8], and special deposition [4.9]. Even when evanescent field devices show
good results, a stringent fabrication process has to be developed to accomplish an
adequate nonlinear interaction length. Moreover, all the techniques mentioned
above require special equipment and materials to obtain stable optical pulses.
In this chapter two passively mode-locked fiber lasers are implemented by
using both PDMS/SWCNT and SU8-2075/SWCNT films as a SA. The advantages of
building these lasers are the simple steps to fabricate the films, the process of
fabrication does not need special equipment or material (low price of the material),
their robustness (no systems of lenses and no special alignment is required), and
the quality of the optical pulses. We should be mention that PDMS doped with
SWCNT has been used before in a tapered fiber configuration [4.4], but having to
produce a taper presents reproducibility issues, or the need of expensive
equipment to obtain consistent tapers. Additionally we have to pay a great deal of
attention in order to optimize the nonlinear interaction length, and to avoid high
nonlinearities and large group velocity dispersion values at the waist of the taper
[4.10]. Speaking about SU8-2075, this is the first time that this polymer has been
used to implement a SA doped with SWCNTs. This polymer is a well-known and
inexpensive material employed for micro-fabrication. Furthermore, since SU8 is a
photosensitive material it has a great potential for the development of nonlinear
integrated waveguide devices.
This chapter is devoted to study how these lasers work at different pump
powers and the output of the laser is also characterized by taking its optical
spectrum, radio frequency spectrum, pulse width, and the average power.
77
4.2 Mode-locked fiber laser configuration
A passively mode-locked fiber ring cavity laser was built using a PDMS/SWCNT film
as a SA. A 3 m long erbium doped fiber (EDF) was used as the laser gain medium
(the peak absorption of the EDF was 94.59 dB at 1530 nm) and a laser diode
operating at 980 nm was used as the pump source via a 980/1550 WDM fiber
coupler. This WDM has an integrated isolator to guarantee unidirectional operation
in the laser cavity. The PDMS/SWCNT SA device was introduced in the fiber ring
laser, as shown in Fig. 4.1. Since the PDMS/SWCNT film exhibits slight polarization
dependence due to the random arrangement of the SWCNTs within the PDMS
polymer matrix, a polarization controller (PC) was inserted in the laser cavity.
Using a 3-dB coupler we extract 50% of the intracavity light while the remaining
50% is launched back into the laser cavity as feedback. For studying laser
dynamics, a 3-dB coupler was used to split the output of the laser into two paths.
One of the 50% ports was connected to an Optical Spectrum Analyzer (OSA ANDO
AQ6317B), while the other 50% port was split by another 3-dB coupler, whose
output ports were connected to a second harmonic generation (SHG
Femtochrome) autocorrelator and a photo-detector with a bandwidth of 16 GHz
(Discovery DSC 40S). Before the light reaches the autocorrelator it was passed
through an Erbium doped fiber amplifier. The electrical signal generated by the
photo-detector was sent to an oscilloscope and to an electrical spectrum analyzer
(RF HP-8566A).
As part of the characterization of the system, Fig. 4.2 shows output power as
function of the current, L-I curve of the pump diode laser.
78
Fig. 4.1 Schematic of the passively mode-locked fiber laser developed by using a PDMS/SWCNT
film between two connectors. WDM: wavelength division multiplexer; PC: Polarization Controller; OSA: Optical Spectrum Analizer; EDFA: Erbium Doped Fiber Amplifier.
0 30 60 90 120 150 180 2100
30
60
90
120
150
180
210
Ou
tpu
t P
ow
er
(mW
)
Pump Current (mA)
Fig. 4.2 Output power vs. pump current.
Before attempting to observe pulsed operation due to the PDMS/SWCNT SA,
the ring laser was first operated using a PDMS film without SWCNTs. As expected
continuous wave (CW) operation was achieved for any pumping power. We also
modified the PC at different pumping levels, and there was no indication of
79
nonlinear polarization rotation mode-locking since there is no polarizing element in
the laser cavity.
4.3 Mode-locked fiber laser results using
PDMS/SWCNT as SA
After placing the PDMS/SWCNT SA in the laser, a pulse train is attained above a
threshold power of 36 mW, this can be observed by a regular train of pulses
detected by the oscilloscope, see Fig. 4.3 (a). This pulse-train has a repetition rate
of 22.73 MHz which corresponds to a cavity length of 8.8 m. The frequency tones
are shown in Fig. 4.3 (b) and the first tone corresponds to the fundamental cavity
frequency as it was expected. The data plotted in Fig. 4.3 was obtained when the
pump power was at 85 mW because at that pump power the shortest pulse was
obtained. This will be explained latter.
0 100 200 300 400
0.00
0.02
0.04
Inte
sit
y (
a.
u.)
Time (ns)
50 100 150 200-80
-70
-60
-50
-40
dB
Frequency (MHz)
(a) (b)
Fig. 4.3 Mode-locked laser output characteristics at a pump power of 85 mW
(a) Pulse train of mode-locked laser; (b) RF tones.
80
From 36 to 90mW of pump power, the laser generated stable pulses which can
be optimized by playing with the PC. This means that shorter pulse width and
more stable train of pulses can be obtained by doing this. Furthermore, it was
noticed that the central wavelength of the laser could be detuned when the PC
was set in different positions; this detuning is approximately 0.5 nm. We believed
that this detuning behavior could be related with the fact that the SWCNTs change
the erbium fluorescent shape.
In order to analyze the dynamics of the laser when different pump powers
were applied, an experiment was done. First, the output of the laser was optimized
by playing with the PC at the pump power of 36 mW, and then the pump power
was increased in steps of 6 mW until it reached 90 mW. This experiment
demonstrates that the central wavelength of the laser is moving to shorter
wavelengths as shown in Fig. 4.4 (a). It is easy to observe that the central
wavelength at a pump power of 36 mW is 1566.71 nm and the central wavelength
at 90 mW is 1565.01 nm. Hence the total shift of the central wavelength is 1.7 nm.
81
Pump Power
36mA 42mA
48mA 54mA
60mA 66mA
72mA 78mA
84ma 90mA
1560 1562 1564 1566 1568 1570 1572-70
-65
-60
-55
-50
-45
-40
-35
-30
dB
m
Wavelength (nm)
(a)
-6 -4 -2 0 2 4 60.0
0.5
1.0
36mA
42mA
48mA
54mA
60mA
66mA
72mA
78mA
84mA
90mA
No
rma
lize
d I
nte
nsit
y (
a.u
.)
Delay Time (ps)
(b)
Fig. 4.4 Mode-Locked laser at different pump powers: (a) Optical spectrum and (b) Autocorrelation
trace.
This shift of the central wavelength must be linked with the changes in the
gain profile due to the combination of power and tubes (SWCNTs have a
broadband absorption spectrum). Moreover, at these different pump powers the
82
pulse-width of the pulses were measured by using the autocorrelator. The pulse-
width of the pulses is obtained after autocorrelation deconvolution of the measured
pulses, as shown in Fig. 4.4 (b), and assuming a sech2 profile. By plotting the
pulse-width and the time-bandwidth product (TBP) as a function of the pump
power we can find the shortest pulse and the minimum TBP, as shown in Fig. 4.5
(a). Additionally, the output power as a function of the pump power was also
plotted in Fig. 5 (b); the saturation behavior observed in this plot is related with
the saturation of the gain medium.
30 45 60 75 900.0
0.5
1.0
1.5
2.0
Pump Power (mW)
Pu
lse
Wid
th (
ps)
0.2
0.3
0.4
0.5
0.6
TB
P
30 40 50 60 70 80 90 1000
2
4
6
Ou
tpu
t P
ow
er(
mW
)
Pump Power (mW)
(a) (b)
1560 1565 1570-70
-60
-50
-40
-30
Wavelength (nm)
dB
m
-6 -4 -2 0 2 4 60.0
0.5
1.0
No
rma
lize
d I
nte
nsit
y (
a.u
.)
Delay Time (ps)
(c) (d)
Fig. 4.5 (a) Output pulse duration and time-bandwidth product at different pump powers, (b) Output power vs. pump power; Laser output characteristics at pump power of 85mW: (d)
Optical spectrum, (c) Autocorrelation trace.
83
We can notice from Fig. 4.4 (b) and Fig. 4.5 (a) that the pulse-width and TBP
are reduced as the pump power increases, until they reach their minimum value at
a maximum power of 85 mW. The optical spectrum of the laser at this pump
power reveals a peak wavelength of 1565.3 nm, with a spectral width at FWHM of
2 nm, as shown in Fig. 4.5 (c). The temporal width of the autocorrelation trace
was 2.23 ps, as shown in Fig. 4.5 (d), which corresponds to a pulse width of 1.26
ps assuming a sech2 pulse profile. This corresponds to a TBP of 0.318, which is
close enough to transform-limited sech2 pulses [4.11].
Using the data that were obtained at a pump power of 85 mW, it is feasible to
calculate the corresponding peak power. The peak power that is inside and outside
the cavity is 161.31 W and the output power is 4.89 mW. Furthermore, the energy
per pulse is 203.26 pJ, the fluence is 404.36 μJ/cm2, and the peak intensity is
320.92 MW/cm2. This peak intensity corresponds to a 134 times the saturation
intensity (2.4 MW/cm2) showed in the last chapter. Although the SA is fully
saturated, it worked for five continuous hours. This PDMS/SWCNT film can deal
with high power which is an important feature in a SA.
4.4 Mode-locked fiber laser results using SU8-2075/SWCNT as SA
Another passively mode-locked fiber ring cavity laser was built using a SU8-
2075/SWCNT film as a SA. The cavity has almost the same elements that the
previous laser, but the cavity length is much longer (the length of the fiber
connectors is longer); see Fig. 4.6 and Fig. 4.1. This variation in length modified
the repetition rate of this laser providing a lower value than the one assembled
with the PDMS/SWCNT SA. The SU8-2075 polymer doped with SWCNTs should
support more power than the PDMS; thus a (90/10) output coupler is used to have
more power inside the cavity laser. Besides, the length of the EDF is 3 m.
84
Fig. 4.6 Schematic of the passively mode-locked fiber laser developed using a PDMS/SWCNT film
between two connectors. WDM: wavelength division multiplexer; PC: Polarization Controller.
Before attempting to observe pulsed operation due to the SU8-2075/SWCNT
SA, the ring laser was first operated using a SU8-2075 film without SWCNTs. As
expected continuous wave (CW) operation was achieved for any pumping power.
We also modified the PC at different pumping levels, and there was no indication
of nonlinear polarization rotation mode-locking since there is no polarizing element
in the laser cavity.
This laser configuration was tested as the previous one and similar results were
found. A stable pulse train was observed within a pump power ranging from 36 to
88 mW, and the minimum pulse with duration was achieved with a pump power of
88 mW; remembering that the pulses can be optimized by playing with PC. We
also did the same experiment to observe the behavior when different pump
powers were applied. First the PC was set to optimize the pulse-width at a pump
power of 36 mW. Afterwards, different powers were applied that gave rise to a
shift of the central wavelength of the spectrum to shorter wavelengths as shown
before. At the optimum pumping power (88 mW), a pulse-train with a repetition
rate of 21.27 MHz was observed with a maximum output power of 1 mW. The
repetition rate corresponds to the laser cavity length of 9.4 m. The measured
85
pulse-train is shown in Fig. 4.7 (a). The frequency tones are shown in Fig. 4.7 (b),
and the first tone corresponds to the fundamental cavity frequency as expected.
The optical spectrum of the laser reveals a peak wavelength of 1565.3 nm, with a
spectral width at FWHM of 3.26 nm, as shown in Fig. 4.7 (c). The FWHM temporal
duration of the autocorrelation trace was 1.536 ps, as shown in Fig. 4.7 (d),
corresponding to a deconvolved pulse duration of 871 fs, assuming sech2 pulse
profile. This corresponds to a time-bandwidth product (TBP) of 0.344, which is
close enough to transform-limited sech square pulses [4.11].
0 100 200 300 400 500
0.00
0.02
0.04
Inte
nsit
y (
a.
u.)
Time (ns)
50 100 150 200-80
-70
-60
-50
-40
dB
Frequency (MHz)
(a) (b)
1565 1570 1575-50
-45
-40
-35
-30
-25
d
Bm
Wavelength (nm)
-4 -3 -2 -1 0 1 2 3 40.0
0.5
1.0
No
rma
lize
d I
nte
nsit
y (
a.u
.)
Delay Time (ps)
(c) (d) Fig. 4.7 Mode-locked laser output characteristics at a pump power of 88 mW (a) Pulse train of