Abstract: A technique to implement an electrically tunable delay line with high bandwidth for trains of ultrashort optical pulses is presented. The system is based on the temporal self-imaging effect in fiber gratings and electrooptic modulation

Maria J Erro

Maria J Garde

Miguel A Muriel

Santiago Tainta

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Electrically Tunable Delay for Trains of Optical Pulses 
Santiago Tainta , Maria J. Erro , Maria J. Garde , Miguel A. Muriel 
Abstract: A technique to implement an electrically tunable delay line with high bandwidth for 
trains of ultrashort optical pulses is presented. The system is based on the temporal self-imaging 
effect in fiber gratings and electrooptic modulation. 
1. Introduction 
Optical delay lines are key elements in different applications, such as optical signal processing, buffers and 
synchronization devices in optical communication systems, or Optical Coherence Interferometry (OCT). Current 
techniques addressing delay lines and their tuning can be grouped in two categories. First, those based on the so-
called slow-light effect achieved by using waveguides based on photonic crystals or resonant elements [1], which 
tune the delay by varying the effective refractive index. A second approach uses dispersive elements whose delay 
depends on wavelength. Additional techniques for wavelength conversion and to avoid distortion are required in this 
case to tune the delay [2]. In this work, a new technique is presented for a fiber-integrated delay line which does not 
use resonant elements and operates on optical pulses trains. It results in a broad bandwidth scheme where elements 
for wavelength conversion are avoided. The delay is tuned by simply modifying an electric signal that is used to 
modulate the input pulse train. 
2. Proposed setup 
The proposed system operates on an ultrashort optical pulse train and is shown in Fig. 1. A Mode Locked Laser 
(MLL) is used to generate a 7Vrepetition rate pulse train. This input train of pulses can be considered as a train of 
Dirac delta functions evenly distributed in time, as the pulse duration is chosen to be much lower than the period of 
repetition. This pulse train is then phase-modulated using an Electrooptical Phase Modulator (EO-PM) with half-
wave voltage given by V%. The modulating signal is chosen to be a signal linear in time, whose constant slope we 
designate as C. The modulated train is then input to a dispersive medium, a Linearly Chirped Fiber Bragg Grating 
(LC-FBG) in our case. Its dispersion, </>, is to be selected so that it results in the temporal self-image effect with 
m=\ and 5=1 parameters, as defined in [3], which corresponds to if> = T0
2 /(2;r). 
EO-PM 
MLL 
II 1 1 
^ 
^ 
j . 
LC-FBG 
2vA\ 
At 
Fig. 1: Proposed setup. 
If this dispersion was applied to a non-modulated pulse train, the output would be a pulse train with the same rate 
but delayed by T0/2 [3]. Here, where a linear phase modulation is induced, the output, x(t), can be shown to be: 
C(/)Kexp f /^ jJ<j(/-Ai-*r0) (1) 
where 
A/ = Mi+-:r„ (2) 
However, a time linear electric signal can not be generated but for a finite time interval. Hence, this signal is 
replaced by a ramp with amplitude given by IV^ and a repetition rate given by T\. This ramp, given the inherent 
periodicity of phase modulation, is equivalent to a linear modulation with a slope C = +2;r/7,1, where the slope sign 
depends on the ramp direction. Moreover, in order to avoid the transitions between periods of the ramp so that a 
linear modulation can be assured, the optical pulses have to be placed only in the linear zones of the ramp. This can 
be achieved by limiting the ramp period to an integer multiple of the original pulse train period, Tx = kT0, where k is 
an integer number. With these conditions, the overall delay at the system output is deduced from eq. (2) to result in 
At-
T (3) 
Eq. (3) represents the sum of a constant term due to the self-image effect and a variable term inversely proportional 
to k, that is, proportional to the frequency of the electric ramp signal. Additionally, both positive and negative delays 
can be obtained as a function of the slope sign. Delay values, on the contrary side, are limited to a discrete set of 
values as a function of k. This drawback could be avoided with the use of an arbitrary shape wave generator, which 
could provide a phase bias to every pulse in an equivalent way as an ideal ramp would. 
3. Results 
A set of simulation runs were carried out using Optsim™ in order to validate the proposed system. As the pulsed 
source, a MLL with 10 GHz-repetition rate and 5 ps-width Gaussian pulses was used. Laser output was modulated 
with an electrooptical phase modulator featuring a 12.5 GHz bandwidth, 3 dB insertion losses, and 5 V half-wave 
voltage. In consequence, a 10 V amplitude ramp was applied as modulating signal, and its frequency was then varied 
from 0.5 to 10 GHz to see the effect on the delay. Both positive and negative ramps were used. The modulated 
signal is then dispersed using a 12.3 cm-long LC-FBG, chosen to give a 1590 ps2 dispersion -in good agreement 
with the required dispersion for T0 = 1/10 GHz- and about 0.8 nm bandwidth. Its frequency response was 
theoretically computed using mode coupling theory with an hyperbolic taper with a = 4 for smoothing. 
a. 
O 
5 0 
h 
CD 
•s 
a- 1-
(D 
O 
•*-' 
' \ 
1 
2 
3 
4 
5 
6 
7 
-^ 
<> 
E 
i _ 
CD 
o 
o 
a. 
n 
2-
1-
0-
,\ •'. i\ .-.-v. 
', \ :' • ¡ \j ••i\\ A 
; : y A/A \\ / \ 
¡ / A / A/ \ \\ / \ 
l, •' i : í : \ \ '• \ / \ 
W ! i n \ \W \ 
,-,jc.J-^XL)^jS: V 
1 
2 
3 
4 
5 
6 
7 
( -
I 
,' 
l' 
- - •* J. . 
100 
(a) 
50 
Time (ps) 
(b) 
100 
Fig. 2: Delayed pulse trains at the output for different values of the parameter k for the ramp signal (indicated in the onsets) with (a) positive or 
(b) negative slope. 
Fig. 2 (a) and (b) show the pulses at the system output for different ramp periods. A certain degree of deformation in 
the pulse shape can be appreciated and it is caused by the filtering introduced by the Bragg grating and the non-
idealities in the second order dispersion applied, basically the ripple in the group delay. It can be observed that the 
resulting delay is inversely proportional to k, i.e. directly proportional to the ramp frequency, as predicted by (3), 
and that positive or negative delays can be obtained depending on the ramp sign. But, being the achievable delay 
limited to a discrete set of values, the pulse can only be delayed up to half the bit period for each ramp sign. Both 
slopes are required then in order to tune the pulse over a whole bit period. This effect is shown in Fig. 3, where the 
delay is represented as a function of the modulating frequency, once the constant term T0/2 is removed. It is clear 
that both positive and negative ramps with frequencies lower than 5 GHz are required to get a tuning range of the 
whole bit, that is, 100 ps. 
4. References 
& 
> s 
JO 
Q 
IUU-
0-
100-
X x 
+ 
X 
+ 
> 
. i 
0 10 
Frequency (GHz) 
Fig. 3: Different delays introduced for the different values of k. 
[1] A. Melloni et al, "Tunable delay lines in silicon photonics: coupled resonators and photonic crystals, a comparison," IEEE Photon. J. 2, 181-
194 (2010). 
[2] C. Caucheteur et al, "All-fiber tunable optical delay line," Opt. Express 18, 3093-3100 (2010). 
[3] J. Azafla and M.A. Muriel, "Temporal Talbot effect in fiber gratings and its applications," App. Opt. 38, 6700-6704 (1999). 


Electrically Tunable Delay for Trains of Optical Pulses

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Electrically Tunable Delay for Trains of Optical Pulses

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