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Instant and efficient second-harmonic generation
and downconversion in unprepared graded-index
multimode fibers
M. A. EFTEKHAR,1,*Z.SANJABI-EZNAVEH,1J. E. ANTONIO-LOPEZ,1F. W. W ISE,2D. N. CHRISTODOULIDES,1
AND R. AMEZCUA-CORREA1
1CREOL, College of Optics and Photonics, University of Central Florida, Orlando, Florida 32816-2700, USA
2School of Applied and Engineering Physics, Cornell University, Ithaca, New York 14853, USA
*Corresponding author: m.a.eftekhar@knights.ucf.edu
Received 25 May 2017; revised 19 July 2017; accepted 19 July 2017; posted 31 July 2017 (Doc. ID 295880); published 30 August 2017
We show that germanium-doped graded-index multimode
silica fibers can exhibit relatively high conversion efficien-
cies (∼6.5%) for second-harmonic generation when excited
at 1064 nm. This frequency-doubling behavior is also found
to be accompanied by an effective downconversion. As op-
posed to previous experiments carried out in single- and
few-mode fibers where hours of preparation were required,
in our system, these χ2related processes occur almost in-
stantaneously. The efficiencies observed in our experiments
are, to the best of our knowledge, among the highest ever
reported in unprepared fibers. © 2017 Optical Society of
America
OCIS codes: (060.4370) Nonlinear optics, fibers; (190.2620)
Harmonic generation and mixing; (190.4223) Nonlinear wave mixing;
(190.4380) Nonlinear optics, four-wave mixing.
https://doi.org/10.1364/OL.42.003478
Second-harmonic generation (SHG) in silica single-mode op-
tical fibers was first reported by Österberg and Margulis [1,2].
This was quite surprising given that amorphous systems like
silica glass are not expected to exhibit a χ2nonlinearity. This,
in turn, incited considerable interest in the physics and appli-
cations of these effects, especially in single-mode fibers [3–8].
In early experiments, SHG was observed only after preparing
the fiber by exposing it to the pump wavelength for several
hours. While this process still remains poorly understood, a
number of schemes have proved effective in increasing its con-
version efficiency and reducing the required preparation time.
Such techniques include, for example, seeding a fiber with a
second-harmonic (SH) signal along with the pump light [3],
using polling techniques like thermal [9,10] and corona poling
[11], and applying a transverse dc electric field in order to break
the inversion symmetry of the material system [5]. Electron
implantation was also utilized along similar lines [12]. It is im-
portant to note that most of these experiments were conducted
primarily in single-mode or few-mode fibers where only the
fundamental mode was excited [13].
Quite recently, multimode fibers (MMFs) have made a
strong comeback in multichannel communication systems
when used in conjunction with spatial division multiplexing
[14]. In parallel to these activities, there has been also a resur-
gence of interest in their nonlinear properties [15–23]. In prin-
ciple, their larger cross section can be exploited to generate
power spectral densities that are orders of magnitudes higher
than those expected from single-mode fibers [20]. In addition,
the many degrees of freedom provided by these highly multi-
moded structures can be exploited to tailor, at will, their output
frequency content [24,25]. In this respect, geometric paramet-
ric instabilities (GPIs) and beam cleaning were observed for the
first time in parabolic-index MMFs [20,26]. Second-harmonic
generation was also recently observed along with their GPI side-
bands in optically polled graded-index multimode fibers [27].
In this study, the fiber was first prepared by exposing it for a few
minutes to a second-harmonic signal generated from a KTP
crystal. Subsequently, SHG conversion up to 1% was reported
a few hours after the fiber was prepared.
Here, we experimentally demonstrate high SHG conversion
efficiencies (∼6.5%) in heavily multimode parabolic-index ger-
manium-doped optical fibers. Unlike previous studies, this con-
version occurred without first preparing the fiber via any of the
schemes outlined before. Even more importantly, the SHG was
found to reach a maximum in an almost instantaneous manner.
In our experiments, this frequency-doubling was also accom-
panied by an efficient downconversion process in the near-
IR regime (2128 nm). The effect of input pump power on the
efficiency of these processes was also investigated. Cutback
measurements performed on our fiber revealed that SHG effec-
tively unfolded along the first 4–5 m. In all cases, the recorded
output beam profiles (pump and SH) were found to exhibit a
Gaussian-like shape and a speckle-free pattern.
A schematic representation of the experimental setup used
is depicted in Fig. 1. The optical source is an amplified
Q-switched microchip laser, producing 400 ps pulses at a rep-
etition rate of 500 Hz and with peak powers up to 200 kW.
3478 Vol. 42, No. 17 / September 1 2017 / Optics Letters Letter
0146-9592/17/173478-04 Journal © 2017 Optical Society of America
Each pulse carries 95 μJ of energy at 1064 nm. The laser beam
is coupled to the multimode fiber samples using a 50 mm focal
length lens with efficiencies exceeding 80%. To control the in-
put power, a half-wave plate and a polarizing beam splitter cube
were employed. The fiber was fixed on a three-axis translation
stage. The visible and NIR portions of the output spectra were
collected by a multimode patch cord and were analyzed using
two different optical spectrum analyzers covering the wave-
length range from 350 to 1750 nm (ANDO AQ 6315E) and
1200 to 2400 nm (Yokogawa AQ6375). To record the beam
profile of the second-harmonic signal, a CCD camera was used
along with a 532 nm filter having 10 nm FWHM. In our ex-
periments, two different MMFs were utilized. The first one was
a low differential modal group delay multimode graded-index
fiber with a core diameter of 50 μm and a refractive index con-
trast of ∼1.6 ×10−2. The second MMF was of the step-index
type having a numerical aperture of 0.22 and a core diameter of
105 μm. Both these fibers were germanium-doped and fabri-
cated by Prysmian Group. At 1064 nm, the parabolic MMF
used is expected to support ∼250 modes while at 532 it is
expected to support ∼1000 modes.
The output spectra, collected at the end of a 5 m long
parabolic-index MMF, are depicted in Fig. 2for three different
input power levels. Figure 2(a) shows the spectrum when the
average input power is ∼16 mW (Pp−p80 kW). In addition
to pump and Raman sidebands, a distinct peak at 532 nm is
clearly visible—signifying the onset of SHG. This peak is ac-
companied by another rather strong line located at 560 nm,
resulting from the frequency-doubling of the first Stokes
Raman peak (R1) at 1.118 μm. As can be seen in Fig. 2(b),
by increasing the input power, a few other peaks start to appear
in the vicinity of the pump’s second harmonic. In particular, the
line at 587 nm corresponds to the frequency-doubling of the
second Stokes Raman wave at 1.176 μm. In addition, two other
peaks can be prominently seen at 546 nm and 577 nm. The
first one can be attributed to a sum-frequency generation of
the pump and the first Stokes peak, while the second one can
be attributed to a sum-frequency generation resulting from the
first and second Stokes Raman peaks. This clearly indicates that
the χ2response of the fiber is indeed at play. Other significant
frequency peaks appearing around 720 nm correspond to side-
bands generated from GPI that takes place in parabolic multi-
mode fibers, as also demonstrated in previous studies [19,20].
It should be noted that the distinct feature seen at 806 nm is the
residual pump from our laser. By further raising the input
power, a series of peaks starts to emerge between 420 and
490 nm, which can be ascribed to sum-frequency generation
between the pump or the Raman peaks and the first visible
GPI sideband located at 720 nm [Fig. 2(c)].
We would like to note that these lines do not result from any
GPI sideband generation at 532 nm, as evidenced from the fact
that they only appear on the higher frequency side of the sec-
ond harmonic (i.e., the generation is not symmetric). In all
cases, we found that the power in the SH signal depends on
the initial launching conditions, thus allowing one to optimize
the SHG conversion by tuning the input (i.e., by selecting ap-
propriate mode groups). In that case, the multiplicity of modes
involved can always allow for phase matching to occur between
different mode groups in a very large number of ways. In gen-
eral, SHG in multimode systems can result either from the
Fig. 1. Schematic of the setup used for SHG and downconversion
in MMFs. Pulses from a Q-switched microchip laser at 1064 nm are
coupled into a MMF. PBSC, polarizing beam splitter cube; M1 and
M2, Mirrors; OSA, optical spectrum analyzer.
Fig. 2. (a) Output spectrum measured at the end of a 5 m long
parabolic MMF when excited with 400 ps 80 kW peak power pulses.
SHG from the pump is evident at 532 nm. The line at 560 nm is due
to the frequency-doubling of first Stokes Raman wave. (b) Increasing
the input pump power to 110 kW results in the appearance of extra
peaks in the vicinity of 532 nm (green cluster). (c) A further increase in
the input pump power to 140 kW leads to other χ2induced peaks
in the 420–490 nm (blue cluster) wavelength range. SB1represents the
first GPI sideband.
Letter Vol. 42, No. 17 / September 1 2017 / Optics Letters 3479
same pump mode (2βω
m;nβ2ω
k;l) or from two different
modes carrying the pump (βω
m;nβω
i;jβ2ω
k;l)[28].
Figure 3shows the NIR portion of the spectrum, which also
displays a series of peaks. The strongest line in this region is
located at 2.128 μm, corresponding to the downconverted
wavelength of the pump, generated along with the second har-
monic because of the χ2nonlinearity. Our experiments re-
vealed that any change in the power level of the produced
SH was always accompanied by a similar change in the down-
converted signal. Another significant feature in this figure is the
spectral band around 2 μm. This line corresponds to the first
NIR-GPI sideband. Some of the spectral components between
2.13 and 2.35 μm also match the downconversion of the first
Stokes Raman waves.
As a next step, we repeated these experiments in the previ-
ously mentioned step-index MMF. Even in this case, the pres-
ence of the second harmonic was evident in the spectrum.
However, our measurements showed that the generated green
light (SH) was always very weak, by almost 2 orders of magni-
tude below that observed in the parabolic fiber. Further increas-
ing the input pump power or prolonging the exposure time of
this step-index MMF to the pump did very little in enhancing
the generated SH signal. The same is also true for the downcon-
verted wavelength. One possible explanation behind this differ-
ence in performance can be attributed to the GPI process that is
only possible in parabolic fibers. One of the direct byproducts
of GPI is the generation of strong lines both in the visible as well
as the UV part of the spectrum. As has been shown before,
exposing the fiber to green, blue, or the UV wavelengths can
enhance SHG up to 10 times [29]. As a result, in our experi-
ments, the GPI-induced wavelengths in the red/blue may act as
enabling sources in “preparing”the fiber toward generating more
efficiently the SH and downconverted signals.
A surprising result in our experiments was the fact that SHG
occurred almost instantaneously in the parabolic MMF—even
in the absence of any preparation. Figure 4demonstrates the
evolution of the generated SH in a 5 m long parabolic fiber as a
function of time. A 532 nm bandpass filter was used to select
the second-harmonic signal. The ensued SHG was monitored
for 4 h. The pump signal was initially blocked for a few minutes
before initiating these measurements. As soon as the pump
was unblocked, green light at 532 nm always emerged and was
measured using a power meter. To make sure that this instant
SHG does not result from any previous exposure of the fiber to
the pump, we repeated this same experiment with totally un-
exposed fiber segments. In all cases, SHG took place almost
immediately after the laser beam was coupled into the fiber.
As can be seen in Fig. 4, the SH output power experiences
fluctuations during the first few minutes. Our observations
indicate that these oscillations become progressively less pro-
nounced and as a result, the output SH slowly stabilizes around
its initial value. It is worth mentioning that these fluctuations
(10%) are always present. This behavior can be explained by
considering the continuous formation and erasure of internal
gratings induced by the co-propagating GPI-sideband colors.
The reason behind this instant buildup of the χ2process is
still unclear to us.
In another set of experiments, we investigated the depend-
ence of the conversion efficiency on the input pump power.
These studies were conducted again in a 5 m long parabolic
MMF. These results are shown in Fig. 5. For each power level,
the initial conditions were tuned to yield the highest attainable
SHG efficiency. As demonstrated in this figure, the efficiency
of this process tends to monotonically increase with pump
power. However, once the average input powers exceeds
20 mW (∼Pp−p100 kW) the SHG saturates and hence
Fig. 3. NIR portion of the spectrum collected at the end of a 5 m
long parabolic MMF when pumped at 110 kW peak power. The
prominent peak at 2128 corresponds to the pump downconversion.
The peak at 2 μm results from the first NIR GPI sideband.
Fig. 4. Temporal evolution of the generated second harmonic, mea-
sured at the output of a 5 m long GI-MMF. The peak power used was
110 kW. The measurements were carried out for over 4 h. Once the
oscillations settle down, the SH power level is restored to its initial value.
Fig. 5. Output power conversion SH efficiency measured at the end
of a 5 m long GI-MMF. The SHG monotonically increases with the
pump power. The process saturates at 100 kW.
3480 Vol. 42, No. 17 / September 1 2017 / Optics Letters Letter
the efficiency no longer changes. In this regime, the maximum
achievable peak power conversion was found to be 6.5%,
which, to the best of our knowledge, is among the highest
observed in unprepared fibers.
The effect of fiber length on the SHG process was previously
investigated in single-mode fibers. In these studies, it was found
that only the first few tens of centimeters are responsible for
SHG [1]. Here, we probed the same behavior in parabolic
MMFs having different lengths. These results are depicted in
Fig. 6. As opposed to single-mode fibers, in our case, we found
that the SHG kept increasing with distance, way beyond the
first 50 cm (Fig. 6), and it only seems to saturate after 4.5 m.
The output beam profile distributions at the pump wave-
length and SH (532 nm) are plotted in Fig. 7for different
pump power levels. In accord with previous observations
[20,26], the beam at the pump wavelength was found to be
clean and speckle-free. Similarly, the beam profile for the
SH 532 nm line had a Gaussian-like shape and was again
speckle-free, a surprising result given the low power levels at
SH (532 nm). This may be due to the fact the pump clean-
up, in turn, induces a similar effect in the SH, i.e., by populat-
ing lower-order modes.
In conclusion, we have shown that germanium-doped para-
bolic multimode silica fibers can exhibit relatively high SHG
conversion efficiencies and downconversion. Unlike previous
experiments, these χ2related processes occurred immediately
without any preparation. Of interest would be to consider
the potential of the χ2downconversion process as a source
for biphoton generation in quantum optics. Our results may
pave the way toward alternative platforms for SHG and
downconversion.
Funding. Office of Naval Research (ONR) (MURI
N00014-13-1-0649); HEL-JTO (W911NF-12-1-0450);
Army Research Office (ARO) (W911NF-12-1-0450); Air
Force Office of Scientific Research (AFOSR) (FA9550-
15-10041); Qatar National Research Fund (QNRF) (NPRP
9-020-1-006).
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Fig. 6. Power conversion efficiency for different fiber lengths. The
efficiency tends to increase with distance in the parabolic MMF.
Fig. 7. Output beam profile at (a)–(c) 1064 nm and (d)–(f) 532 nm
after a 5 m long parabolic MMF, as a function of input power.
Letter Vol. 42, No. 17 / September 1 2017 / Optics Letters 3481
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