# 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)

Jump to: [1. Introduction] – [2.1. Set-up principle] – [2.2. Model] – [3.1 Experimental parameters] – [3.2. Dual-pulse regime] – [3.3. Rectangle and triangle waveform generation] – [4. Mode-locked pulse doublets generation from the un-seeded loop] and [5. Conclusion]

### 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.

Did you find this useful? Give us your feedback

HAL Id: hal-02163678

https://hal-univ-rennes1.archives-ouvertes.fr/hal-02163678

Submitted on 24 Jun 2019

HAL is a multi-disciplinary open access

archive for the deposit and dissemination of sci-

entic research documents, whether they are pub-

lished or not. The documents may come from

teaching and research institutions in France or

abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est

destinée au dépôt et à la diusion de documents

scientiques de niveau recherche, publiés ou non,

émanant des établissements d’enseignement et de

recherche français ou étrangers, des laboratoires

publics ou privés.

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

γ

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

(t–pτ)] = 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

##### References

More filters

••

H. Guillet de Chatellus

^{1}, Olivier Jacquin^{1}, Olivier Hugon^{1}, Wilfried Glastre^{1}+2 more•Institutions (2)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....

[...]

••

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....

[...]

••

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....

[...]