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Proceedings ArticleDOI

Pulse Doublets Generated by a Frequency-Shifting Loop Containing an Electro-Optic Amplitude Modulator

01 Jun 2019-pp 1-1

Abstract: Frequency-shifting loops (FSL) are ring resonators containing both an amplifier and a frequency-shifter, usually an acousto-optic modulator (AOFS) [1]. They are promising solutions to generate pulses with tunable and high repetition rates or for arbitrary RF waveform generation. Here we investigate an all-fibered frequency-shifting loop that includes an electro-optic amplitude modulator (EOM). At variance with preceding research, e.g. [1–3], the EOM creates at each round-trip two side-bands that recirculate inside the loop. We demonstrate an original double-pulse regime when the loop length is a multiple of the RF modulation wavelength applied to the modulator. By changing the bias voltage applied to the EOM, the interval between the pulses can be continuously adjusted. The system is modeled by a linear interference model that takes the amplitude modulation function and loop delay into account.
Topics: Amplitude modulation (55%), Amplifier (53%), Modulation (53%), Loop (topology) (51%), Amplitude (50%)

Summary (2 min read)

1. Introduction

  • Microwave photonics is an innovative multi- and interdisciplinary field that investigates the interaction between microwave and optical signals including microwave signal generation and processing [1–3], microwave-photonic systems [4,5], and broadband optical links for high-speed interconnects [6].
  • In particular, the generation of high repetition-rate optical pulses plays an important role in high-speed optical fiber and microwave photonics systems [7,8].
  • Few studies investigated single-sideband EOM #365251 https://doi.org/10.1364/OE.27.018766.
  • Instead of the single side-band AO frequency-shift or SSB-EOM, the loop will produce at each roundtrip two side-bands with opposite frequency-shifts.
  • The authors first present the method and the corresponding model in Section 2.

2.1. Set-up principle

  • It contains an electro-optic amplitude modulator (EOM) that induces a dual-sideband frequency shift per round-trip fm, and an erbium-doped fiber amplifier (EDFA) providing gain that partially compensates for the loop losses and enhances the number of relevant round-trips inside the loop, as in AOFS-based loops.
  • Besides, an optical filter permits to limit the output bandwidth and efficiently reduces parasitic loop oscillations, while a polarization controller also stabilizes the loop operation.
  • The EOM is driven by a radiofrequency synthesizer (SYN) and a bias voltage (DC).
  • The authors assume that the loop is below the laser threshold, i.e., the gain does not compensate for the losses.

2.2. Model

  • Γ is the static phase retardance of the EOM that can be controlled by the applied bias voltage Vb. Indeed, the authors may predict that the response of the amplitude-modulated loop in the time domain delivers a periodic series of pulse doublets.
  • With the increase of Γm, the delay gradually approaches one half period.
  • Note that Γm also has an influence on the pulse width.
  • These predictions are tested experimentally in the following.

3.1 Experimental parameters

  • The authors experimentally investigate the time response of the dual side-band frequency-shifting loop as depicted in Fig.
  • In order to avoid parasitic oscillations when the EDFA gain is raised, the authors use a 40 GHz-bandwidth (0.3 nm) optical filter inside the loop.
  • Here, at variance with the FS loop of Refs [10–12] where the wavelength of the seed laser is at one edge of the optical filter (single-sideband frequency comb), the authors set the wavelength of their laser at the center of the optical filter around 1552 nm (dual-sideband frequency comb).
  • The polarization controller (PC) is utilized to stabilize the polarization state of the laser signal to make the modulation depth higher and waveform more stable.
  • The detection setup consists in a 40 GHz-bandwidth photodiode and a high-resolution optical spectrum analyzer.

3.2. Dual-pulse regime

  • 3. Figures 3(a)-3(d) report the experimental results when n = 1 (fm = 6.737 MHz), 10 (67.37 MHz), 100 (673.7 MHz), and 500 (3.369 GHz), respectively.
  • As expected, the output optical spectrum contains a dual side-band RF comb, with the seed wavelength at the center and fm-harmonics on both sides.
  • Raising the gain to higher values leads to parasitic oscillations.
  • Moreover, the authors could observe that changes in the bias voltage influences the harmonics intensities.
  • Γm, the authors find that (i) the pulse width significantly increases and (ii) the delay decreases.

3.3. Rectangle and triangle waveform generation

  • Following the preceding conclusions, the authors find a simple means to generate a rectangle waveform with an adjustable duty cycle.
  • Corresponding simulations are depicted in Figs. 6(d)-6(f) showing a good agreement with the experimental results.
  • The waveform generation is not limited to the rectangle case.
  • It is well known that AOFS loops output waveform relies on the shifting frequency fm, and RF power, and the loop length.
  • Here, the authors find saw-tooth waveforms when they slightly detune the modulation frequency of the EOM off an integer value nfc.

4. Mode-locked pulse doublets generation from the un-seeded loop

  • For the sake of completeness, the authors investigate shortly the loop behavior without the seed laser when the gain exceeds the losses, i.e., when the loop is driven above laser threshold.
  • In particular picosecond pulse generation was demonstrated in erbium-doped fiber lasers using phase modulators [22–24].
  • Contrary to phase-modulated mode-locked lasers, here it appears that amplitude modulation leads to picosecond pulse doublet operation, a situation that, to the best of their knowledge, has never been reported.
  • Obviously, the double-pulse regime still exists in this un-seeded mode-locked operation.
  • Furthermore, it is interesting to note that the delay time is continuously tunable and also obeys Eq. (9), as shown for example in Fig. 8 with two different values of the bias voltage.

5. Conclusion

  • This experiment shows an alternative approach to AOFS loops, taking advantage of the inherent bandwidth and tunability of the EOM.
  • In addition, by properly setting the modulation frequency, adjustable rectangle and saw-tooth waveforms can be obtained.
  • Finally the double-pulse regime survives to above-threshold operation: without the seed, mode-locked picosecond pulse doublets are also generated with an adjustable delay.
  • Designing a loop with all polarization-maintaining fiber components, as well as acoustic and thermal isolation, would improve the stability.
  • The proof-of-concept demonstrated here could be extended to integrated photonics since optical rings, filters, and EOMs can be integrated on photonic platforms.

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Pulse doublets generated by a frequency-shifting loop
containing an electro-optic amplitude modulator
Hongzhi Yang, Marc Vallet, Haiyang Zhang, Changming Zhao, Marc Brunel
To cite this version:
Hongzhi Yang, Marc Vallet, Haiyang Zhang, Changming Zhao, Marc Brunel. Pulse doublets generated
by a frequency-shifting loop containing an electro-optic amplitude modulator. Optics Express, Optical
Society of America - OSA Publishing, 2019, 27 (13), pp.18766-18775. �10.1364/OE.27.018766�. �hal-
02163678�

Pulse doublets generated by a frequency-
shifting loop containing an electro-optic
amplitude modulator
HONGZHI YANG,
1,2
MARC VALLET,
2
HAIYANG ZHANG,
1
CHANGMING ZHAO,
1
AND MARC BRUNEL
2,*
1
School of Optics and Photonics, Beijing Institute of Technology, Beijing, China
2
Univ Rennes, CNRS, Institut FOTON – UMR 6082, 35000 Rennes, France
*marc.brunel@univ-rennes1.fr
Abstract: We investigate theoretically and experimentally an all-fibered frequency-shifting
loop which includes an electro-optic amplitude modulator (EOM) and an optical amplifier,
and is seeded by a continuous-wave laser. At variance with frequency-shifted feedback lasers,
or Talbot lasers, that contain an acousto-optic frequency shifter, the EOM creates at each
round-trip two side-bands that recirculate inside the loop. Benefiting from the high
modulation frequency of the EOM, a wide optical frequency comb up to 40 GHz is generated.
We demonstrate an original double-pulse regime when the loop length is a multiple of the RF
modulation wavelength applied to the modulator. The inter-pulse interval is governed by both
the bias voltage and modulation depth of the EOM. Besides, some typical waveforms such as
saw-tooth and rectangle are experimentally obtained by properly setting operating frequency,
bias voltage and the RF power. The system is modeled by a linear interference model that
takes the amplitude modulation function and loop delay into account. The model explains the
formation of pulse doublets and reproduces well all the experimental waveforms.
Furthermore, the un-seeded loop driven above threshold also generates mode-locked
picosecond pulse doublets with a continuously adjustable delay up to the modulation period.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Microwave photonics is an innovative multi- and interdisciplinary field that investigates the
interaction between microwave and optical signals including microwave signal generation
and processing [1–3], microwave-photonic systems [4,5], and broadband optical links for
high-speed interconnects [6]. In particular, the generation of high repetition-rate optical
pulses plays an important role in high-speed optical fiber and microwave photonics systems
[7,8]. In this respect, frequency-shifting loops (FSL), that are loop resonators containing both
an amplifier and an acousto-optic frequency-shifter (AOFS), have been demonstrated to be
promising solutions to generate Fourier-transform-limited pulses with tunable and ultrahigh
repetition rates [9–11]. When the frequency shift is tuned to a fraction of the cavity free-
spectral range, periodic pulse trains can be generated from a continuous-wave seed laser,
leading to a so-called “Talbot laser” due to the complete analogy with the spatial Talbot effect
[12]. Similar all-fiber set-ups have also been extended to applications such as high data-rates
in radio-over-fiber communications [13,14], real-time Fourier transformation of optical
signals [15] and have also recently been shown to produce arbitrary waveform generation
[16].
Frequency-shifted loops usually rely on the use of an acousto-optic frequency-shifter.
While it features high frequency conversion efficiency in the sub-100 MHz range, AOFS
have limited efficiency in the GHz range, and offer limited tunability. In this respect, EOM
offer much higher modulation frequency and bandwidth. Besides, EOM are compact and easy
to integrate with other fibered devices. Few studies investigated single-sideband EOM
Vol. 27, No. 13 | 24 Jun 2019 | OPTICS EXPRESS 18766
#365251
https://doi.org/10.1364/OE.27.018766
Journal © 2019
Received 25 Apr 2019; revised 31 May 2019; accepted 31 May 2019; published 19 Jun 2019

operation in FSLs: a multi-carrier source was built with high power flatness and stability [14],
and recently GHz repetition rates were demonstrated in the Talbot configuration [17]. In this
article, we investigate an all-fibered frequency-shifted feedback loop when a widely tunable
common, dual side-band, electro-optic amplitude modulator (EOM) is employed. Instead of
the single side-band AO frequency-shift or SSB-EOM, the loop will produce at each round-
trip two side-bands with opposite frequency-shifts. The carrier will also circulate together
with the multiple frequency-shifted sidebands. This raises questions about the ability to
generate a pulse train from a continuous-wave seed, the so-called continuous-to-pulse
conversion regime [11,12], or to generate arbitrary waveforms [16,18]. Furthermore, an
analytical model has to be derived in order to take into account the specific transfer function
of the EOM.
We first present the method and the corresponding model in Section 2. In particular, we
focus on the integer Talbot condition where predictions can be derived from simple algebra.
Section 3 presents the experimental results obtained with standard components at 1.55 µm
wavelength, looking at the influences of the EOM parameters on the FSL properties. Pulse
train generation and specific waveforms are investigated by precisely controlling the
modulating frequency, RF power and the bias voltage applied to the EOM. Then Section 4 is
devoted to the extension of the method to the un-seeded, mode-locked laser operation, and the
comparison with the results of Section 3. Finally, conclusions and perspectives are included
in Section 5.
2. Method
2.1. Set-up principle
We consider the fiber loop depicted in Fig. 1. It contains an electro-optic amplitude modulator
(EOM) that induces a dual-sideband frequency shift per round-trip f
m
, and an erbium-doped
fiber amplifier (EDFA) providing gain that partially compensates for the loop losses and
enhances the number of relevant round-trips inside the loop, as in AOFS-based loops.
Besides, an optical filter permits to limit the output bandwidth and efficiently reduces
parasitic loop oscillations, while a polarization controller also stabilizes the loop operation.
The round-trip time is τ = nL/c, where n is the group index of the loop fiber. This leads to a
fundamental loop frequency f
c
= 1/τ. A 2 × 2 optical coupler enables to seed the loop and to
extract a fraction of the circulating laser power. The EOM is driven by a radiofrequency
synthesizer (SYN) and a bias voltage (DC). We assume that the loop is below the laser
threshold, i.e., the gain does not compensate for the losses. The setup is similar to the one of
Refs [11–13] but the frequency-shift is provided by a common EOM instead of an AOFS.
Fig. 1. Sketch of the dual side-band FS loop. CW-SFL: continuous-wave single-frequency
laser; PD: photodiode; TBPF: tunable bandpass filter; PC: polarization controller; EOM:
Mach-Zehnder intensity modulator driven at frequency f
m
(SYN) and bias voltage V
b
(DC);
EDFA: erbium-doped Optical Fiber Amplifier.
Vol. 27, No. 13 | 24 Jun 2019 | OPTICS EXPRESS 18767

2.2. Model
In order to predict the output waveform, we derive a time-delayed interference model. Given
the transmission matrix of the coupler [t
ij
] and E
in
the input electric field of the coupler, the
output field E
out
can be written as follows:
1111 12
22
21 22
.
out in
out in
EE
tt
EE
tt

=




(1)
In the case of a lossless coupler, the t
ij
verify the condition t
11
t
22
t
12
t
21
= 1 [19]. At round-trip
p, the real transfer function of the EOM can be modeled as Υ
(p)
(t) = sin[Γ + Γ
m
sin(2πf
m
(t
pτ))], where Γ
m
is the modulating depth that depends on the RF power P
dc
. Γ is the static
phase retardance of the EOM that can be controlled by the applied bias voltage V
b
. If η and G
are the intensity loss of the loop and the intensity gain parameters, respectively, then we write
G
η
=
the overall amplitude transmission. To find out the field circulating inside the loop,
we calculate the electric field at output port 2. From Eq. (1), this field writes:
2211222
() ,
out in in
EttE tE=+ (2)
from which one gets:
(1)
2211222
() () ( ) ().
out in out
EttEttEt t
γτ
=+ ϒ
(3)
This formulation can be expanded using
(2)
2211222
() () (2)().
out in out
Et tEt tEt t
ττγτ
−= + ϒ
(4)
Inserting Eq. (4) into the right-hand side of Eq. (3), the equation can be expanded to N round-
trips in the loop:
()
2 21 1 21 22 1
1
1
() () () ( ).
p
N
pp l
out in in
p
l
EttEt tt tEtp
γ
τ
=
=
=+ ϒ
(5)
The experimentally accessible and useful signal is at the output port 1. If the input field at
port 1 is a single-frequency continuous-wave with power P
in
, then
1()
111 211222
1
1
() () ,
p
N
pp l
out in in
p
l
EttPtt t tP
γ
=
=
=+ ϒ
(6)
from which the power P
out
(t) can be derived:
2
1()
11 21 12 22
1
1
() () .
p
N
pp l
out in
p
l
P
tttt t tP
γ
=
=
=+ ϒ
(7)
In the following, we use Eq. (7) to calculate the output waveform. Note that contrary to the
theoretical model developed for AOFS loops [11,12], here no simple analytical formula can
be deduced. However, under the integer Talbot conditions f
m
= nf
c
, where n is an integer, we
find sin[2πf
m
(tpτ)] = sin(2πf
m
t). Then, in the limit N →+, the sum of the geometric series
in Eq. (7) can be simplified, leading to
2
21 12
11
22
sin ( )
() ,
1sin()
out in
tt t
P
tt P
tt
γθ
γθ
=+
(8)
Vol. 27, No. 13 | 24 Jun 2019 | OPTICS EXPRESS 18768

where we introduced θ(t) = Γ + Γ
m
sin(2πf
m
t). Since t
22
γsinθ(t) < 1 (assuming t
22
real positive),
obviously sinθ(t)/(1–t
22
γsinθ(t)) will be a sharp function peaked at θ(t) = π/2. As in the AOFS-
based loops, pulses are found when the Talbot condition is met, i.e., when the modulation
frequency is an integer number of times the loop frequency (or, equivalently, when the loop
length is an integer number of times the beat length). It is interesting to note that Eq. (8) is
independent of n, which means that the pulse shape is expected to be the same whatever the
modulation frequency, and that the pulses will become shorter as frequency increases.
According to Eq. (8), the important point, specific to our amplitude modulation case, is that
two temporally separated solutions satisfy Eq. (8) in one period 1/f
m
. Indeed, we may predict
that the response of the amplitude-modulated loop in the time domain delivers a periodic
series of pulse doublets. The delay Δt between the two pulses in one period 1/f
m
is found to be
1
12 /2
1sin .
2
mm
t
f
π
π

−Γ
Δ=

Γ

(9)
This shows that Γ and Γ
m
will have a strong influence on the delay. Sketches of the output
time responses with different Γ and Γ
m
are depicted in Figs. 2(a)-2(b). For example if Γ = π/2
then Δt = 1/(2f
m
), leading to a pulse repetition rate equal to twice the modulation frequency
(red curve in Fig. 2(a)).
Fig. 2. Sketches of output signal vs time, with (a) different Γ and (b) different Γ
m
. Simulation
output power with (c) Γ = π/3 (blue), 5π/12 (green), π/2 (red), 7π/12 (light blue), and 2π/3
(purple), and (d) Γ
m
= 0.5 (black), 0.55 (grey), 0.6 (yellow), 0.65 (brown), and 0.7 (green).
To further illustrate the influence of Γ and Γ
m
on the double-pulse operation, we perform
simulations based on Eq. (7) with N = 30 round-trips. Figure 2(c) depicts the simulation
results, with Γ
m
= 0.7 and γ = 0.9 for example, showing that the delay between the two pulses
increases with Γ. Then the influence of Γ
m
on the double-pulse is also simulated and depicted
in Fig. 2(d) when Γ = 2π/3. With the increase of Γ
m
, the delay gradually approaches one half
period. Note that Γ
m
also has an influence on the pulse width. Indeed, lower values of Γ
m
will
directly reduce the width of the optical-carried RF comb in the optical frequency domain,
hence leading to pulse widening. These predictions are tested experimentally in the following.
Vol. 27, No. 13 | 24 Jun 2019 | OPTICS EXPRESS 18769

Figures (9)
References
More filters

Journal ArticleDOI
01 Jul 2013-Optics Express
TL;DR: It is shown both theoretically and experimentally that frequency-shifted feedback (FSF) lasers seeded with a single frequency laser can generate Fourier transform-limited pulses with a repetition rate tunable and limited by the spectral bandwidth of the laser.
Abstract: We show both theoretically and experimentally that frequency-shifted feedback (FSF) lasers seeded with a single frequency laser can generate Fourier transform-limited pulses with a repetition rate tunable and limited by the spectral bandwidth of the laser. We demonstrate experimentally in a FSF laser with a 150 GHz spectral bandwidth, the generation of 6 ps-duration pulses at repetition rates tunable over more than two orders of magnitude between 0.24 and 37 GHz, by steps of 80 MHz. A simple linear analytical model i.e. ignoring both dynamic and non-linear effects, is sufficient to account for the experimental results. This possibility opens new perspectives for various applications where lasers with ultra-high repetition rates are required, from THz generation to ultrafast data processing systems.

42 citations


"Pulse Doublets Generated by a Frequ..." refers background in this paper

  • ...[1-3], the EOM creates at each round-trip two side-bands that recirculate inside the loop....

    [...]

  • ...Frequency-shifting loops (FSL) are ring resonators containing both an amplifier and a frequency-shifter, usually an acousto-optic modulator (AOFS) [1]....

    [...]

  • ...From the theoretical point of view, it would be interesting to elucidate connections with Talbot quadratic phases as observed in AOFS loops....

    [...]


Journal ArticleDOI
Hongzhi Yang1, Marc Brunel2, Haiyang Zhang1, Marc Vallet2  +2 moreInstitutions (2)
Abstract: We investigate the radio-frequency (RF) up-conversion and waveform generation properties of an optical fiber loop including a frequency shifter and an amplifier. By seeding the loop with a single-frequency continuous-wave laser, one can develop a wide optically carried RF comb, whose spectral extension is governed by the loop net gain. In addition, by choosing the fiber loop length and the RF shifting frequency, arbitrary waveforms can be generated. We present an analytical interference model that includes the time delay, the frequency shift, and the gain. Experiments are conducted with 1.06-μm fiber-optic components. Using a 200-MHz acousto-optic frequency shifter, we find a 19-fold up-conversion up to 3.8 GHz with a typical in-loop gain of 3. Various waveforms including bright and dark pulses, square- or triangle shaped are achieved by properly adjusting the loop length and the frequency shift. A good agreement between experimental and theoretical results is obtained. The fully fibered microwave-photonic source is applied to a laboratory Doppler velocimetry demonstration. The gain in sensitivity obtained with the up-converted signal is readily observed.

8 citations


"Pulse Doublets Generated by a Frequ..." refers background in this paper

  • ...[1-3], the EOM creates at each round-trip two side-bands that recirculate inside the loop....

    [...]


Proceedings ArticleDOI
L. Wang, Sophie LaRochelle1Institutions (1)
14 May 2017-
Abstract: We use an electro-optic frequency shifter in a Talbot laser to demonstrate pulse multiplication factors up to five using temporal fractional Talbot effect and achieve pulse repetition rates of tens of GHz.

7 citations


"Pulse Doublets Generated by a Frequ..." refers background in this paper

  • ...[1-3], the EOM creates at each round-trip two side-bands that recirculate inside the loop....

    [...]