1. Mode-Locked Erbium Doped Pulse Fiber Laser Using
the Kerr Effect
KYLE MCSWAIN1, GREG HOFFMAN1
1 Master’s Industrial Internship Program, University ofOregon, 1252 University ofOregon, Eugene, OR 97403-1252
Updated: 5 September 2016. The purpose of our project
was tobuild a pulsedfiber laser, containingerbiumdoped
fiber that utilizes the optical Kerr effect. We use an
artificial saturableabsorber inorder to generate pulsesin
the 1550 nm spectrum. The artificial saturable absorber
is composed of polarizing elements such as λ/2 and λ/4
wave plate as wellas a beamsplittingpolarizingcube. We
were able tocreate ≤400ps pulses withina 12 meter ring
cavity with peak spacing of about 60 ns. As a result of
these parameters, we believe we were able to obtain
pulses in the soliton pulse and stretched pulse regime.
© 2015 Optical Society of America
OCIS codes: (140.3490) Lasers, distributed-feedback; (060.2420) Fibers,
polarization-maintaining; (060.2370) Fiber optics sensors.
INTRODUCTION
Pulsed fiber lasers are commonly used inindustry foravariety of
applications. There are various chemical, medical and industrial
applications for pulsed lasers. As students of industry, we are
involved with industrial applications such as spectroscopy, optical
telecommunications and femtosecond laser machining. The use of
pulsed fiber laser was first experimentally demonstrated in1961;
therefore the applications still have plenty of development in the
future. Moreover, the first mode-locked fiber laser was only
recently applied in 1983 [1]. Mode locking is a phenomenon that
occurs when pulsed light is created and the maxima of different
modes oflight constructively interfere atthe samepoint, creating an
increase inintensity [2]. Weare interested increating pulses inthe
infrared spectrum, which is useful in the telecommunications
industry.
Mode lockingis animportant aspect to achieving pulses within a
laser system. There are two different types of mode locking, active
and passive. Activemode locking isthe lessinteresting of the two; it
involves mechanical means to “chop” the incident light inorder to
create pulsing, or adding in an external modulator signal to the
system. Furthermore, active mode locking has a disadvantage due
to the required use of anoptical modulator and as aresult typically
generates longer pulses [2]. Passive mode locking is more
interesting because it involves certain intracavity elements that
create the mode locking inanon-mechanical orpassive sense. The
advantage of passive mode locking is it can lead to much shorter
pulses, which can be very beneficial to a number of industrial
applications, such as laser machining. Through passive mode
locking, we attempt to achieve pulsing inboth the stretched pulse
and the soliton regime.
A. HAUS MASTER EQUATION
The pulse evolution in the resonator of a passive mode-locked
laser usingthe optical Kerr effect with artificial saturable absorption
isdescribed bythe Haus Master equation [3].
𝑎 𝑛+1
( 𝑡) = {1 + 𝑔 (1 +
1
𝛺 𝑔2
𝑑2
𝑑𝑡2
) − ( 𝑙 − γ| 𝑎( 𝑡)|2) − 𝑖δ| 𝑎( 𝑡)|2
+ 𝑖𝐷
𝑑2
𝑑𝑡2
} 𝑎 𝑛
( 𝑡) (1)
Where g represents the gain of the cavity, Ωg is the gain
bandwidth, tistime, listhe lossofthe cavity, a(t) isthe amplitude of
the intensity of the pulse, D isthe dispersion factor, and an(t) isthe
initial amplitude. The effects that change the characteristics of the
pulses throughout the ring cavity: the first term is the gain, second
term is the self-amplitude modulation (SAM) including the loss,the
third term isthe self-phase modulation (SPM) and the fourth term
is the group velocity dispersion (GVD). A soliton solution for the
equation considers the Kerr effects inaddition to the GVDandSPM.
𝑎( 𝑡) = 𝑎0 sech (
𝑡
𝑡 𝑝
) 𝑒
𝑖𝛽 ln[sech(
𝑡
𝑡 𝑝
)]
(2)
Where a0 represents the initial amplitude, tis time, and tp is the
time of the pulse, and β a factor of the GVD. In this solution, the
e^𝑖𝛽 ln[sech(𝑡 𝑡 𝑝)⁄ ] amounts to a chirp, which is a change in the
frequency within the carrier wave. The secant solution provides
insight that the shape of the pulse willup-chirp when β< 0within
the system, whereas when β> 0creates in a down-chirp. As the
wave travels through the fiber, the up-chirped pulse will compress
and the down-chirped pulse willbroaden [3].
Fig 1.Thesetup of our system consisting of Erbium doped gain
medium and silicapassivefiber.
SETUP

2. The Kerr mode-locked pulsed fiber laser consists of multiple
components, as seen infigure 1, beginning with the 980 nm pump
laser. After the 980nm pump, one side of the wavelength division
multiplexer (WDM) has two inputs, one receives 980 nm allowing
it inthe ring as well as allowing 1550nm light to transmit through
the other, which closes the ring cavity. The other end is acommon
fiber that allows both wavelengths to pass through. The common
fiber from the WDMisconnected tothe Liekki Er-30-4/125 Erbium
doped active fiber, which acts as a gain medium. As the 1550 nm
beam travels through the gain medium, an additional WDM is
encountered, this time inreverse, to dump any remaining 980 nm
light and send solely 1550 nm beam into the optical isolator. The
beam that travels through the optical isolator becomes
unidirectional meaning the beam can only travel in one direction
within the cavity. An optical bench consisting of ahalf-wave plate,
polarizer and quarter-wave plate is located after the isolator
resulting in transmission of high intensity light while attenuating
low-intensity light. After the components within the optical bench,
pulses travel through a95/5 output coupler where 95% ofthe light
is sent back into the cavity through the 1550 nm fiber of the initial
WDM and 5% of the beam is output from the ring cavity. The 5%
signal output will then be sent to the photodetector forobservation
onthe oscilloscope and spectral analyzer.
PROCEDURE
Tobegin the project wehad to findthe components necessary
for the ring cavity, as described inthe set-up section. Once wehad
found the necessary components, we needed to connectorize and
accurately measure the length of each, so we could determine the
round trip distance of the ring cavity. The accurate length of the
cavity was essential todetermine theperiod ofthe pulses within the
cavity. Thenext step was to test our predictions of the period using
well-polished connections andaccurate lengths. Withallthe passive
components connected, the only component we varied in the
system was the erbium-doped fiber.
Initially, we placed a 0.5 meter and then a 1meter long Moritex
Er-112 fiber within ourring cavity to attempt to achieve the soliton
regime. Incorporating the 0.5 and 1-meter long erbium cable ledto
anunstable signal withself-pulsing results. The self-pulsing wesaw
with the Er-112 fiber hadto do with ahighconcentration of erbium
ions[5].This caused stimulated emissionofneighboring ionswithin
acluster, creating self-pulsing. Moreover, wereplaced the Moritex
Er-112 fiber with a 7.5 meter LIEKKI Er-30 (Absorption 30 +/- 3
dB) fiber containing lower concentration [6]. With the Er-30 fiber
placed within the ring cavity, we found very distinct pulses with
minimal noise. To confirm that we were inthe soliton regime, we
input additional various lengths ofSMF-28 fiber ranging from 2to 4
meters. The SMF-28 has an opposite dispersion of the erbium and
allows additional non-doped fiber to beincluded into our system to
manipulate the GVD.
We collected and compared data from two different sources.
The first was noting the voltage of the signal on the Tektronix
DPO7354 3.5 GHz oscilloscope, using a Thorlabs 1.2 GHz
photodetector. Using this technique, we were able to determine
peak power, period and pulse width. The other process of
measurement included using the Advantest Q8381A optical
spectrum analyzer, which was able to observe the power profile as
afunction of wavelength.
OPTICAL KERREFFECT
The optical Kerr effect pertains to a change in the index of
refraction when high intensity light is incident onthe material. This
is a result of the small order of the nonlinear index of refraction
(~10-20). Unless the intensity ishigh enough, the nonlinear change
in index is negligible. We see that the new index of refraction is
represented by
𝑛 = 𝑛0 + 𝑛2 𝐼. (1.3)
Where n0 isthe linear index, n2 isthe non-linear index and Iisthe
intensity. We see that if the intensity is low, the factor of the non-
linear index isnot going to change the linear index. This change in
index is what gives rise to the self-phase modulation inthe system
[4].
A. SELF-PHASE MODULATION
Self-phase modulation isaresult of the Kerr effect inthe fiber. In
oursystem, light travels around the cavityinanelliptically polarized
state. The major and minor axis of the ellipse have different
magnitudes, thus have a different effect on the non-linear index of
refraction. These different effects onthe index of refraction lead to
each axis of the ellipsetravelling atdifferent speeds within the fiber.
Subsequently, this causes the ellipticity of the light to rotate as it
propagates through the loopof thesystem. Thiscomponent aswell
as the self-amplitude modulation of the polarizing elements led to
Kerr modelocking.
B. SELF-AMPLITUDE MODULATION
As the elliptically polarized light is incident upon the λ/2 wave
plate, the axis of the ellipse begins to rotate. If the λ/2 wave plate is
oriented as suchthat the major axis ofthe ellipseisaligned with the
polarizer, the polarizer allows the higher intensity light to pass
through as well as blocking out orthogonal, lower intensity light.
This attenuation of lower modes iswhat leads to mode locking the
light within the cavity. The combination of the optical Kerr effect
that leads to the self-phase modulation and the self-amplitude
modulation are what lead to mode locking short, high amplitude
pulses.
COMPARISON OFREGIMES
Once pulses were observed on the oscilloscope, we referred to
the spectrum analyzer to check which regime our pulses were in.
There are two regimes that pulses can be within, soliton or
stretched-pulse. These are represented by the power of each pulse
as a function of wavelength. Solitons occur when apulse resulting
from the ratio of passive fiber to active fiber within the ring cavity
has azero ornegative dispersion. Unique characteristics of solitons
consist of self-stabilizing and maintaining their spectral and
temporal shape inthe cavity due to the cancellation of the GVDand
SPM [3]. Solitons are quantized and expect a step-like feature as a
function of pump power.
In comparison, stretched-pulses occur when the overall
dispersion is positive. As a result there is a large difference of the
SPM and GVD. This causes the pulses being periodically stretched
and recompressed ineach resonator round-trip [2].Stretched pulse
regime has a linear trend as a function of pump power, as seen in
figure 2.

3. Fig 2. Linearcharacteristic of the stretched pulse regime.
RESULTS
Before webegan taking measurements, weobserved the power
out ofthe pumpand compared itto the power leaving the output
coupler. Wefound that there was about 450 mWleaving the pump
and measured about 2.3 mWof 1550 nm light leaving our5%
signal. Inorder to get the total power within the ring, wemultiply
by 20to get about 46mW. Wecansee that there isadecent
amount of losswithin the ring cavity.
Fig 3. Pulses with a period of about 60 ns displayed on the
oscilloscope.
Wewere able to produce modelocked pulsing within our cavity,
with aperiod closeto the round trip time of the cavity. These values
align with the theory wehad predicted. In our 12m loop, assuming
5ns/m for the light inthe cavity wewere able to get pulsing with a
period of about 60 ns, which can be seen in figure 3. Another
parameter wewere interested inwas the widthof the pulses within
the cavity. We measured an average pulse width of ≤400 ps. The
reason wereport that as less than orequal to is wewere limited by
the rate of collection of the different devices. The photodetector ran
at a frequency of 1.2 GHz and the o-scope was limited to 3.5 GHz,
corresponding to tenths of nanoseconds.
Fig4.Imagestaken from the spectrometer displaying the spectra
of the stretched pulse(left) and solitonregime (right).
Another aspect of the pulses we were observing was the
difference between the stretched pulse and the soliton regime. We
believe that wewere able toobserve bothregimes. Thetrouble with
calculating these different regimes was wewere unable to comeup
with an exact value forthe GVD of the erbium doped fiber. Wehad
found some values within the literature, which were inconclusive.
We also contacted the manufacturer and they were unsure of the
value. First, we estimated a negative overall dispersion, i.e. the
stretched pulse regime. Through the addition of enough passive
fiber, the system crossed over to the soliton regime. In figure 3, the
differences inspectra are what we believe to be the two different
regimes.
We can see in the left image of figure 4, the stretched pulse
regime, where we have one peak with no side modes. In the right
figure weseethat wehave some,however inconsistent, sidemodes.
These differences are what we believe are the two different
regimes.
Conclusion
The purpose of our project was to produce mode locked pulses,
in a fiber ring utilizing the optical Kerr effect. We were able to
produce pulses that were on the order of the round trip time with
the width on the order of what we expected. The other aspect we
were observing iswhat dispersion regime wewere in, the stretched
pulse orthe solitonregime. Ourresults are inconclusive, however it
appears we were able to obtain the soliton as well as the stretched
pulse regime. We believe we obtained both, however due to an
unknown value of GVD dispersion from the Er-30, we cannot be
certain.
In the future, multiple aspects of the experiment could be
improved. If various components were fusionspliced, as opposed to
connectorized that would improve the efficiency of the loop.
Additionally, by thermally and mechanically stabilizing the
components ofthe system, this couldimprove the stability. Further
improvements that couldbeexplored isincreasing thepump power
to the system, by coupling two pumps together and using an
improved oscilloscope to have more accurate results onthe order
offemtoseconds. Wecouldalso explore thedifferent concentrations
of the Erbium doped fiber to see if an increase in power with a
higher concentration couldproduce higher power pulses. Although
we achieved results that created very distinct pulses, we believe
better results could be produced using the techniques mentioned.
Overall, we established many skills such as fiber polishing
throughout this project and successfully mode-locked an Erbium
doped pulsefiber laser using the Kerr effect.
References
[1] N., Usechak G. "Mode Locking of Fiber Lasers at High Repetition Rates."
(n.d.): n. pag. University of Rochester, 2006. Web. 30 Aug. 2016.
[2] R. Paschotta. "Passive Mode Locking." Encyclopedia of Laser Physics and
Technology. RP Photonics Consulting GmbH, 2012. Web. 29 Aug. 2016.
[3] B. Boggs. "Mode-locked Erbium-Ytterbium Doped Fiber Laser." Mode-
locked Erbium-Ytterbium Doped Fiber Laser. University of Oregon,
Department of Physics, Advanced Projects Lab's Wiki, 6Sept. 2015. Web. 28
Aug. 2016.
[4] R. Paschotta. "Kerr Effect." Encyclopedia of Laser Physics and Technology.
RP Photonics Consulting GmbH, 2012. Web. 28 Aug. 2016.
[5] Moritex. "Standard PureCore™ Erbium Doped Optical Fibers." (2010): n.
pag. Moritex PureCore™ Erbium Doped Specialty Optical Fibers. Moritex, 1
Sept. 2016. Web.
[6] NLight. LIEKKI ®(n.d.): n. pag. LIEKKI. NLight. Web. 1 Sept. 2016.