Arbitrary waveform generator and differentiator employing an integrated optical pulse shaper

Abstract

We propose and demonstrate an optical arbitrary waveform generator and high-order photonic differentiator based on a four-tap finite impulse response (FIR) silicon-on-insulator (SOI) on-chip circuit. Based on amplitude and phase modulation of each tap controlled by thermal heaters, we obtain several typical waveforms such as triangular waveform, sawtooth waveform, square waveform and Gaussian waveform, etc., assisted by an optical frequency comb injection. Unlike other proposed schemes, our scheme does not require a spectral disperser which is difficult to fabricate on chip with high resolution. In addition, we demonstrate first-, second- and third-order differentiators based on the optical pulse shaper. Our scheme can switch the differentiator patterns from first- to third-order freely. In addition, our scheme has distinct advantages of compactness, capability for integration with electronics.

Full text

Arbitrary waveform generator and
differentiator employing an integrated optical
pulse shaper
Shasha Liao,1 Yunhong Ding,2 Jianji Dong,1,* Ting Yang,1 Xiaolin Chen,1
Dingshan Gao,1,3 and Xinliang Zhang1
1Wuhan National Laboratory for Optoelectronics, School of Optoelectronic Science and Engineering, Huazhong
University of Science and Technology, Wuhan, 43007, China
2Department of Photonics Engineering, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark
3State Key Laboratory on Integrated Optoelectronics, College of Electronic Science and Engineering, Jilin
University, Changchun 130012, China
*jjdong@mail.hust.edu.cn
Abstract: We propose and demonstrate an optical arbitrary waveform
generator and high-order photonic differentiator based on a four-tap finite
impulse response (FIR) silicon-on-insulator (SOI) on-chip circuit. Based on
amplitude and phase modulation of each tap controlled by thermal heaters,
we obtain several typical waveforms such as triangular waveform, sawtooth
waveform, square waveform and Gaussian waveform, etc., assisted by an
optical frequency comb injection. Unlike other proposed schemes, our
scheme does not require a spectral disperser which is difficult to fabricate
on chip with high resolution. In addition, we demonstrate first-, second- and
third-order differentiators based on the optical pulse shaper. Our scheme
can switch the differentiator patterns from first- to third-order freely. In
addition, our scheme has distinct advantages of compactness, capability for
integration with electronics.
©2015 Optical Society of America
OCIS codes: (070.1170) Analog optical signal processing; (200.0200) Optics in computing;
(130.3120) Integrated optics devices; (320.5540) Pulse shaping.
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1. Introduction
Optical arbitrary waveform generation (OAWG) plays a critical role in many applications,
such as generating optical ultra-wide band (UWB) signal [1, 2], optical pulse radar [3], all-
optical temporal differentiator [4, 5], and test of optical communication system. Although lots
of OAWG schemes were reported using mature fiber grating techniques [2, 6–12], one of the
#236566 - $15.00 USD
Received 19 Mar 2015; revised 24 Apr 2015; accepted 27 Apr 2015; published 29 Apr 2015
© 2015 OSA
4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.012161 | OPTICS EXPRESS 12162

most promising solutions is prone to be the miniaturization and integration with photonic
integrated circuits, such as using indium phosphide (InP) platform [13, 14], silica on silicon
[15], silicon nitride [16–18] or silicon platform [19, 20]. To generate arbitrary waveform in
optical domain, one needs a source of optical frequency comb [21] and an optical pulse
shaper [22]. The pulse shaper consists of a spectral disperser to separate the frequency comb
line by line, complex modulator array, and an opposite spectral disperser to combine these
frequency lines. S. J. B. Yoo et al presented an integrated array waveguide grating scheme in
InP and silicon platforms, respectively [23, 24]. These schemes showed very excellent
performances, with compact size and very low power consumption. However, it is still
difficult to manipulate the comb lines one by one in integrated spectral disperser when the
comb spacing is very small. It is a big challenge for the chip fabrication with high resolution.
Another feasible solution is to design a reconfigurable whole spectral function and then use
fiber dispersion to form a temporal function with frequency-to-time mapping [25–27]. But in
fact, the on-chip mapping device with adequate large dispersion is very difficult to achieve. In
our previous work, we have demonstrated a programmable optical filter with integrated
silicon platform, which is based on four-tap FIR structure [28]. This structure is widely used
in many aspects, such as dispersion compensation [29] and time delay [30]. And this structure
can be regarded as an optical pulse shaper and the principle is similar to the scheme presented
by Yongwoo Park et al. in 2007 [31]. Comparing to previous pulse shaper, the chip
fabrication is very simple and no spectral disperser is required.
In this paper, we further demonstrate an OAWG and high-order photonic differentiator
based on a four-tap FIR silicon integrated circuit. By thermally controlling the amplitude and
phase of each tap, we obtain several typical waveforms such as triangular waveform,
sawtooth waveform, square waveform and Gaussian waveform, etc. Furthermore, we
demonstrate first-, second- and third-order differentiation based on the optical pulse shaper,
whose spectra were tailored to the transfer functions of temporal differentiators. Especially,
our scheme can switch the differentiator patterns from first- to third-order freely on a fixed
photonic chip, and this is unable in our previous works such as cascaded microrings or
cascaded Mach-Zehnder interferometers (MZIs) [32, 33]. Moreover, our scheme has distinct
advantages of compactness, small power consumption and capability for integration with
electronics [34, 35].
2. Optical arbitrary waveform generation
1
X
2 MMI
Time de lays Amplitude modulator
Phase modulator
Heat er
Fig. 1. Schematic diagram of the proposed on-chip pulse shaper.
The pulse shaper is based on a four-tap FIR structure. The pattern structure is monolithically
integrated on an SOI wafer, with the advantages of easy fabrication and compact footprint.
The pulse shaper architecture is shown in Fig. 1. The input signal is divided into four taps by
cascaded multimode interferometer (MMI) couplers, and then propagates through the four
taps with a series of time delays. An amplitude modulation unit (realized by a MZI with one
arm phase-modulated) and a phase modulation unit are present on each tap. All phase
modulation units are controlled by thermal electrodes. Assuming that the amplitudes and
phases of the four taps are α1, α2, α3, α4 and
φ
1,
φ
2,
φ
3,
φ
4, respectively, and the time delay
#236566 - $15.00 USD
Received 19 Mar 2015; revised 24 Apr 2015; accepted 27 Apr 2015; published 29 Apr 2015
© 2015 OSA
4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.012161 | OPTICS EXPRESS 12163

between two adjacent taps is τ, the transfer function of the optical pulse shaper can be
expressed as
()
()
4
0
1
=n
jn
n
n
He
ωτ φ
ωα
+
=
 (1)
where ω is angular frequency of light. Equation (1) indicates that the output spectrum can be
reshaped by modifying the relative amplitude weights and phase shifts of the four taps.
Assuming that the relative time delay between two consecutive taps is 10 ps, a pulse shaper
can be obtained with a free spectral range (FSR) of 100 GHz.
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Time (ps)
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0.8
1
Intensity (a.u.)
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1
Intens ity (a.u.)
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1
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0.8
1
Intensity (a.u.)
(a) (b)
(c) (d)
Simu lated Id eal
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0
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1
Intens ity (a.u .)
(e)
0
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0.8
1
Intens ity (a.u.)
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Time (ps)
(f)
31.54 ps 22.8 ps
16 ps 16 ps
12 ps 18.3 ps
Fig. 2. Simulated waveforms (red solid line) of the pulse shaper and the ideal ones (blue dash
line) of (a) square waveform (the amplitude array and phase array are [0.93, 1, 1, 0.94] and
[0.305π, 0.013π, −0.015π, 0.23π], respectively), (b) isosceles triangular waveform (the
amplitude array and phase array are [0.69, 1, 0.75, 0.114] and [-0.05π, −0.4π, −0.1π, −0.1π],
respectively), (c) and (d) sawtooth waveforms (the amplitude array and phase array are [0.15,
0.46, 0.77, 1], [0.5π, −0.1π, −0.3π, 0.09π] and [1, 0.77, 0.46, 0.15], [0.09π, −0.3π, −0.1π, 0.5π],
respectively), (e) and (f) Gaussian waveforms (the amplitude array and phase array are [0.2, 1,
0.5, 0], [0, 0, 0, 0] and [0.65, 1, 0.65, 0], [0.1π, 0, 0, 0], respectively).
Several typical waveforms can be achieved by jointly tuning both amplitude and phase
arrays for all taps. The target waveform can be designed by calculating the amplitude and
phase array according to Fourier transformation. Figure 2(a) shows an example of square
waveform generation with the pulse shaper. The amplitude array and phase array of this case
are α = [0.93, 1, 1, 0.94] and
φ
= [0.305π, 0.013π, −0.015π, 0.23π], respectively. And the
simulated output waveform is shown as the red solid line. The full width at half maximum
(FWHM) of the simulated square waveform is 31.54 ps. In Fig. 2(b) we set the amplitude
array and phase array to α = [0.69, 1, 0.75, 0.114] and
φ
= [-0.05π, −0.4π, −0.1π, −0.1π],
respectively, and we can achieve isosceles triangular waveform by this pulse shaper. The
FWHM of the simulated isosceles triangular waveform is 22.8 ps. Then we simulate a
sawtooth waveform by setting the amplitude and phase array to α = [0.15, 0.46, 0.77, 1] and
φ
= [0.5π, −0.1π, −0.3π, 0.09π], respectively. In order to achieve the opposite sawtooth
waveform, we can just reverse the amplitude and phase array, i.e. α = [1, 0.77, 0.46, 0.15] and
φ
= [0.09π, −0.3π, −0.1π, 0.5π], respectively. The corresponding simulated waveforms are
shown in Figs. 2(c) and 2(d). The FWHM of the simulated sawtooth waveform is 16 ps. By
setting the amplitude and phase array to α = [0.2, 1, 0.5, 0] and
φ
= [0, 0, 0, 0], respectively, a
Gaussian waveform with a FWHM of 12 ps can be achieved. The corresponding simulated
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Received 19 Mar 2015; revised 24 Apr 2015; accepted 27 Apr 2015; published 29 Apr 2015
© 2015 OSA
4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.012161 | OPTICS EXPRESS 12164

waveform is shown in Fig. 2(e). And a Gaussian waveform with a FWHM of 18.3 ps can be
obtain when the amplitude and phase array are α = [0.65, 1, 0.65, 0] and
φ
= [0.1π, 0, 0, 0],
respectively. The corresponding simulated waveform is shown in Fig. 2(f). Note that the
amplitude and phase arrays in these cases are particularly calculated with Fourier
transformation of target waveforms. The ideal waveforms of square waveform, isosceles
triangular waveform, sawtooth waveforms and Gaussian waveforms are also shown in the
Figs. 2(a)-2(f) (blue dash line) for comparison. The FWHMs are 30.7 ps, 23 ps, 14.5 ps, 12 ps
and 18.3 ps, respectively. As shown in Fig. 2, the simulated waveforms are in good
agreements with the ideal ones. Very little distortion can be found due to the loss of high
frequency components. The simulated waveforms in Fig. 2 are all impulse response of the
pulse shaper.
The microscopic image of the fabricated pulse shaper is shown in Fig. 3. The pulse shaper
is fabricated on an SOI wafer with 250 nm thick top silicon layer and 3 μm thick buried oxide
(BOX). The height of the waveguide is 250 nm and the relative time delay of the four taps is
10 ps. The bending radius of the waveguide is 20μm. The size of our pulse shaper is only 2
mm2. Fully etched apodized grating couplers [36] are used as input and output ports. A single
step of E-beam lithography and inductively coupled plasma reactive ion etching (ICP-RIE) is
used to fabricate the grating couplers and silicon waveguides, simultaneously. Then a 700 nm
thick silica is deposited on the sample. Another layer of 700 nm boro-phospho-silicate-glass
(BPSG) is deposited annealed in nitrogen condition in order to planarize the surface. After
that, the top glass layer is thinned to 1μm by buffered hydrofluoric acid (BHF) etching.
Finally, heater patterns (100 nm Ti) are formed by E-beam lithography followed by metal
deposition and lift-off. The on-chip insertion loss of our pulse shaper is 9 dB when there is no
voltages applied to the electrodes. The loss of the coupling from the grating to fiber is about
11dB for both sides. All four taps are fabricated with metal thermal conductors to tune the
amplitude and phase respectively. The insertion loss can be effectively reduced by
introducing an aluminum mirror by flip-bonding process [37].
Grating couple
1X 2 MMI
Amplitude electrodes Phase electrodes
500.00μm
Fig. 3. Metallurgical microscopy image of the on-chip pulse shaper.
SMF
PM
EA
RF
PC1
TLD
OTDL
MZM
PC2
Bias
EDFA1
Optical frequency comb generator
Grat ing
coupler
EDFA3
OSC
Filter
EDFA2
PC3
HP-EDFAHNLF
ATT
Fig. 4. Experimental setup of the arbitrary waveform generation with employing the on-chip
pulse shaper.
In order to characterize our on-chip pulse shaper, we use the experimental setup as shown
in Fig. 4 to generate several typical waveforms. A continuous wave (CW) light is emitted
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4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.012161 | OPTICS EXPRESS 12165

from the tunable laser diode (TLD) with a precisely tuning resolution of 100 kHz. The light is
modulated by the Mach–Zehnder modulator (MZM) and phase modulator (PM), which are
driven by a tunable radio frequency (RF) signal (10 GHz initially). Because of the
polarization sensitivity, there are two polarization controllers (PCs) placed before the MZM
and PM. A 5-km single mode fiber (SMF) is used to compensate the incident chirps to
generate more and flatter optical frequency comb lines. A 1020-m high nonlinear fiber
(HNLF) is used afterwards to increase the optical frequency comb lines by self-phase
modulation. By using this optical frequency comb generator, we can achieve about 80
spectral lines at 10 GHz. Since the transmission spectrum of the pulse shaper is periodical, a
tunable optical band-pass filter is used to pick out one period of the spectrum of the silicon
chip. In this experiment we use two vertical grating couplers to couple the light from fiber to
silicon waveguide and the output signal from waveguide to fiber. Because of the polarization
sensitivity of the grating couplers, a polarization controller (PC) is placed before the input
grating coupler. The electrodes of the amplitude and phase arrays are contacted by a probe pin
array spaced with 250 μm. Variable voltages generated from independent power supplies are
applied to different pins in the array. Finally the output temporal waveform is measured by a
high speed oscilloscope (OSC) with a bandwidth of 500 GHz (Eye-Checker 1000C) and the
measured waveforms are all averaged by 11.
Figure 5 shows the measured waveforms and spectra of the generated optical frequency
comb (OFC) and the input signal launched into the pulse shaper. The spectrum of the OFC is
shown in Fig. 5(a) as the blue solid line. A flat OFC of about 80 lines with power deviation
less than 5-dB can be obtained. And the spectrum of the signal after the band-pass filter is
also shown in Fig. 5(a) as the red solid line. The bandwidth of the band-pass filter is 0.8 nm.
The waveforms of the OFC and input signal are shown in Fig. 5(b), and the FWHMs are 3.5
ps and 11.2 ps. The repetition rates of OFC and input signal are both 10 GHz.
1540 1544 1548 1552 1556
-35
-30
-25
-20
-15
-10
-5
0
Normalized Power (dB)
Wavelength (nm)
-60 -30 030 60
0
0.2
0.4
0.6
0.8
1Input
OFC
(a) (b)
Intens ity (a.u.)
Time (ps)
Fig. 5. (a) Measured spectra of OFC (blue solid line) and input signal (red solid line), (b)
measured waveforms of OFC (blue solid line) and input signal (red solid line).
Figure 6(a) shows the measured square waveform. The FWHM of the measured
waveform is 29.2 ps, and the output waveform is shown as the blue solid line. The signal to
noise ratio (SNR) is 39.34 dB. To achieve this waveform, we adjust all the voltages applied
on the amplitude electrodes and phase electrodes so that the output of pulse shaper matches
well with the simulated condition. With similar method, we can achieve isosceles triangular
waveform, which is shown in Fig. 6(b) as the blue solid line. The FWHM is 19.4 ps and the
SNR is 42.51 dB. Two opposite sawtooth waveforms are shown in Figs. 6(c) and 6(d) with
the FWHMs of 15.5 ps and 14.5 ps, respectively. The SNRs of the two sawtooth waveforms
are 41.56 dB and 42.16 dB, respectively. The slight difference of the FWHMs may result
from the unbalance power of each tap. Gaussian waveforms with the FWHMs of 12 ps and
18.3 ps are shown in Figs. 6(e) and 6(f). The SNRs are 40.25 dB and 38.17 dB, respectively.
The ideal ones are also shown as the red dash line for comparison.
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4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.012161 | OPTICS EXPRESS 12166

0
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1
Intens ity (a.u.)
-40 -20 0 20 4 0
Time (ps)
(j)(i)
-40 -20 0 20 4 0
Time (ps)
0
0.2
0.4
0.6
0.8
1
Intens ity (a.u.)
0
0.2
0.4
0.6
0.8
1
Intens ity (a.u.)
-40 -20 0 20 40
Time (ps)
-40 -20 0 20 40
Time (ps)
0
0.2
0.4
0.6
0.8
1
Intens ity (a.u.)
0
0.2
0.4
0.6
0.8
1
-40 -20 0 20 4 0
Time (ps)
Intens ity (a.u.)
-40 -20 0 20 40
Time (ps)
0
0.2
0.4
0.6
0.8
1
Intens ity (a.u.)
Measured Ideal
(b)
(c) (d)
(g) (h)
-40 -20 0 20 40
0
0.2
0.4
0.6
0.8
1
Intens ity (a.u.)
Time (ps)
(a)
-40 -20 0 20 40
Time (ps)
0
0.2
0.4
0.6
0.8
1
Intens ity (a.u.)
-40 -20 0 20 4 0
Time (ps)
0
0.2
0.4
0.6
0.8
1
Intens ity (a.u.)
(e) (f)
Square
waveform
Isoscel es
tria ngular
waveform
Saw tooth
waveform
Saw tooth
waveform
Gaussian
waveform
Gaus sian
waveform
Obliq ue
tria ngular
waveform
Obliq ue
tria ngular
waveform
Obliq ue
tria ngular
waveform
Flat-top
waveform
Fig. 6. Measured waveforms (blue solid line) of the pulse shaper and ideal ones (red dash line)
of (a) square waveform, (b) isosceles triangular waveform, (c) and (d) sawtooth waveform, (e)
and (f) Gaussian waveform, (g), (h) and (i) oblique triangular waveform, (j) flat-top waveform.
In order to demonstrate that our scheme can generate more general waveforms, we adjust
the voltages controlling both amplitude and phase arrays to achieve some oblique triangular
waveforms and flat-top waveform. Figures 6(g) and 6(h) are two opposite oblique triangular
waveforms with the FWHMs of 19.55 ps and 20.1 ps, respectively. The SNRs of the two
oblique triangular waveforms are 38.77 dB and 39.59 dB, respectively. The ideal ones are
also shown as the red dash line, and the FWHMs are 19.6 ps. Figure 6(i) is another kind of
oblique triangular waveform, the FWHMs of the measured waveform and the ideal one are
15.88 ps and 15 ps, respectively. The SNR of the oblique waveform is 39.19 dB. The
measured flat-top waveform is shown in Fig. 6(j), the FWHMs of the measured one and ideal
one are both 23 ps. And the SNR of the measured flat-top waveform is 39.83 dB. The
temporal resolution of all the generated waveforms is 10 ps and the temporal window of our
pulse shaper is about 40 ps. As shown in Fig. 6, the measured waveforms are in good
agreements with the ideal ones, that is to say, our scheme has a good performance on
waveform generation. Figure 7(a) shows the spectra of input optical frequency comb (blue
solid line) and the output square waveform (black dotted line). And the spectrum of the pulse
shaper is also shown as the red dash line. Figures 7(b) to 7(j) are the spectra of optical
frequency comb and the output isosceles triangular waveform (7(b)), sawtooth waveform
(7(c) and 7(d)), Gaussian waveform (7(e) and 7(f)), oblique triangular waveform (7(g), 7(h)
and 7(i)) and flat-top waveform (7(j)).
#236566 - $15.00 USD
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© 2015 OSA
4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.012161 | OPTICS EXPRESS 12167

1549.2 1549.6 1550 1550.4 1550.8
1549 1549.5 1550 1550.5
-60
-40
-20
0
-60
-40
-20
0
1549 1549.4 1549.8 1550.2
Wavelength (nm)
1549 1549.4 1549.8 1550.2
Wavelength (nm)
1549 1549.4 1549.8 1550.2
Wavelength (nm)
1549 1549.4 1549.8 1550.2
Wavelength (nm)
-60
-40
-20
0
-60
-40
-20
0
-60
-40
-20
0
-60
-40
-20
0
1549 1549.4 1549.8 1550.2
Wavelength (nm)
Wavelength (nm)
1549.2 1549.6 1550 1550.4
Wavelength (nm)
-60
-40
-20
0
1549 1549.4 1549.8 1550.2
Wavelength (nm)
-60
-40
-20
0
Normalized Power (dB)
Normalized Power (dB)
Wavelength (nm) Wavelength (nm)
1549.2 1549.6 1550 1550.4
-60
-40
-20
0
-60
-40
-20
0
(a) (b)
(c) (d)
(e) (f)
(g) (h)
(i) (j)
Input Pulse shaper Output
Fig. 7. Measured spectra of input optical frequency comb and output waveforms of (a) square
waveform, (b) isosceles triangular waveform, (c) and (d) sawtooth waveform, (e) and (f)
Gaussian waveform, (g), (h) and (i) oblique triangular waveform, (j) flat-top waveform.
3. First- to third-order differentiators
Optical differentiator attracts lots of interests due to its potential wide applications in optical
analog processing [38–40], pulse characterization and ultra-high-speed coding. And it is one
of the most important applications of OAWG. Here we demonstrate the first- to third-order
differentiators by our pulse shaper.
Equation (1) indicates that the output spectrum can be reshaped by modifying the relative
amplitude weights and phase shifts of the four taps. We can obtain a first- to third-order
differentiators by controlling both amplitude and phase arrays to make sure that the transfer
functions of the pulse shaper match the spectra of the first-, second- and third-order
differentiators.
Figures 8(a1) and 8(a2) show the simulated amplitude response and phase response of
first-order differentiator of the pulse shaper (blue solid line). Based on Fourier transformation,
the amplitude and phase array are set by α = [0.0675, 1, 0.028, 1],
φ
= [-π, -π, π, −0.15π],
respectively. Figures 8(b1) and 8(b2) show the simulated amplitude response and phase
response of second-order differentiator of the pulse shaper (blue solid line). The amplitude
and phase array are α = [0.38, 0.746, 1, 0.38],
φ
= [-0.075π, 0.13π, 0.06π, −0.025π],
respectively. Figures 8(c1) and 8(c2) show the simulated amplitude response and phase
response of third-order differentiator of the pulse shaper (blue solid line). The amplitude and
#236566 - $15.00 USD
Received 19 Mar 2015; revised 24 Apr 2015; accepted 27 Apr 2015; published 29 Apr 2015
© 2015 OSA
4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.012161 | OPTICS EXPRESS 12168

phase array are α = [0.18, 0.624, 1, 0.48],
φ
= [0.04π, 0.08π, 0.01π, −0.03π], respectively. The
ideal ones are also shown in the Figs. 6(a1)-(c2) as the red dash line for comparison. As
shown in Fig. 8, the simulated spectra are in good agreements with the ideal ones, indicating
the potential of our pulse shaper to be an order-tunable differentiator.
Amplitude (a.u.)
Frequency (GHz)
Phase (π)
Frequency (GHz)
0
0.5
1
-50 050
-50 050
0
0.5
1
-50 050
0
0.5
1
(a1)
-50 050
-1
0
1
(a2)
(b1)
(c1)
-50 050
-1
0
1
(b2)
-50 050
(c2)
-1
1
0
Simu lated Id eal
Fig. 8. Simulated amplitude-frequency responses/ phase-frequency responses (blue solid line)
of the pulse shaper and the ideal ones (red dash line) of different order differentiators, (a1) and
(a2) amplitude-frequency and phase-frequency responses of first-order differentiator (the
amplitude array and phase array are [0.0675, 1, 0.028, 1] and [-π, -π, π, −0.15π], respectively),
(b1) and (b2) amplitude-frequency and phase-frequency responses of second-order
differentiator (the amplitude array and phase array are [0.38, 0.746, 1, 0.38] and [-0.075π,
0.13π, 0.06π, −0.025π], respectively), (c1) and (c2) amplitude-frequency and phase-frequency
responses of third-order differentiator (the amplitude array and phase array are [0.18, 0.624, 1,
0.48] and [0.04π, 0.08π, 0.01π, −0.03π], respectively).
Figures 9(a)-9(c) show the measured spectra (blue solid line) of the pulse shaper under
different amplitude and phase array conditions for the first-, second- and third-order
differentiators, respectively. The ideal frequency responses (red dash line) for these
differentiators are also shown for comparison. Good agreements between the ideal and the
measured transfer functions are achieved in a finite bandwidth.
1549.6 1549.9 1550.2
0
0.2
0.4
0.6
0.8
1
Amplitude (a.u.)
Wavelength (nm) 1549.5 1549.8 1550.1
0
0.2
0.4
0.6
0.8
1
Amplitude (a.u.)
Wavelength (nm)
1549.4 1549.7 1550
Wavelength (nm)
0
0.2
0.4
0.6
0.8
1
Amplitude (a.u.)
Measured
Ideal
Measured
Ideal
Measured
Ideal
(a) (b) (c)
Fig. 9. Measured and ideal spectra of (a) first-, (b) second-, and (c) third-order differentiators.
The experimental setup for the first- to third-order differentiator is the same as that of
OAWG, which is shown in Fig. 4. Figure 10(a) shows the spectra of input pulse (blue solid
line) and the output first-order differentiation pulse (black dotted line). And the spectrum of
the pulse shaper is also shown as the red dash line. We tune the central wavelength of TLD to
be aligned with the resonant notch of pulse shaper. Figures 10(b) and 10(c) are the spectra of
input pulses and the output second- and third-order differentiation pulses. The input signal
carriers are also well aligned with the pulse shaper resonant notches. Figure 11(a) shows the
input pulse generated by the optical frequency comb generator. The FWHM of the pulse is
11.2 ps. We adjust the all the voltages applied on the amplitude electrodes and phase
electrodes to achieve a first-order differentiator spectrum, and fine tune the TLD central
#236566 - $15.00 USD
Received 19 Mar 2015; revised 24 Apr 2015; accepted 27 Apr 2015; published 29 Apr 2015
© 2015 OSA
4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.012161 | OPTICS EXPRESS 12169

wavelength to align with the resonant notch. The central wavelength of the TLD is 1549.9 nm
under this condition. We measure the temporal waveforms of first-order differentiation signal,
which is shown in Fig. 11(b) as the blue solid line. The SNR of the signal is 35.45 dB. Then
we adjust the all the voltages applied on the amplitude electrodes and phase electrodes to
achieve the second- and third-order differentiator spectra, still fine tune the TLD central
wavelength to align with the resonant notch. The central wavelengths of the TLD are 1549.7
nm and 1549.7 nm, respectively. And we measure the temporal waveforms of second- and
third-order differentiation, which are shown in Figs. 11(c)-11(d), respectively. The SNRs of
the second-order and third-order differentiation signals are 34.75 dB and 34.67 dB,
respectively. It can be seen that the shape of the measured differentiated pulses fit well with
the simulated ones, but the pulsewidths of the measured pulses are much larger than the
simulated ones. The FWHM of the measured first-order differentiation pulse is 22.54 ps, and
that of the simulated one is only 17.6 ps. The pulse broadening is 28.1%. The FWHM of the
measured second-order differentiation pulse is 7.2 ps, and that of the simulated one is 5.6 ps.
The pulse broadening is 28.3%. The FWHM of the measured output third-order
differentiation pulse is 21.22 ps, and that of the simulated one is 14.8 ps. The pulse
broadening is 43.4%. The reason of this phenomenon is that the bandwidth of the input pulse
is larger than the operation bandwidth of pulse shaper.
Normalized Power (dB)
1549.1 1549.7 1550.3
-60
-40
-20
0
Wavelength (nm)
1549 1549.6 1550.2
-60
-40
-20
0
Wavelength (nm)
Wavelength (nm)
1549.2 1549.8 1550.4
-60
-40
-20
0
Input Pulse shaper Output
(a) (b) (c)
Fig. 10. Measured spectra of input pulse and output differentiation signals of (a) first-order, (b)
second order, and (c) third-order.
Intensity (a.u.)
0
0.2
0.4
0.6
0.8
1
Measured
Simu lated
Time (ps)
-60 -30 03060
Time (ps)
-60 -30 03060
Intens ity (a.u.)
0
0.2
0.4
0.6
0.8
1
Measured
Simu late d
Measured
Simu lated
Time (ps)
-60 -30 03060
Intens ity (a.u.)
0
0.2
0.4
0.6
0.8
1
Measured
Fitted
Time (ps)
-60 -30 03060
Intensity (a.u.)
0
0.2
0.4
0.6
0.8
1
(a) (b)
(c) (d)
Fig. 11. Experimental results for different order differentiations, (a) input pulse, (b)-(d)
temporal waveforms for first-, second- and third-order differentiations, respectively.
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4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.012161 | OPTICS EXPRESS 12170

In order to figure out pulse broadening issue, we simulate the output pulse broadenings of
input signals with different pulsewidths. Taking second-order differentiator for an example,
the output pulse broadening of different input pulsewidth signal is shown in Fig. 12. In our
scheme, the output differentiation pulse would not be distorted when the FWHM of the input
pulse is larger than 23.5 ps. The broadening increases with the decrease of pulsewidth of the
input signal, and would be almost 50% when the FWHM of the input pulse decreased to 10
ps.
In order to verify our prediction, we launch an input pulse with larger pulsewidth into the
chip and measured the new output differentiation pulse. The experiment setup is shown in
Fig. 13. Still a CW light is emitted from the TLD. The light is modulated by a MZM and a
PM, which are also driven by a 10 GHz RF signal to generate optical frequency comb lines.
But there are no SMF and HNLF in the experiment setup. So the lines are much fewer than
that in OAWG experiment, resulting in a much broader input pulse. Because the bandwidth of
the input spectrum (0.6 nm) is smaller than the FSR of the pulse shaper, no band-pass filter is
needed. Then two vertical grating couplers couple the light from fiber to silicon waveguide
and the output signal from waveguide to fiber. Because of the polarization sensitivity of the
couplers and waveguides, a PC is placed before the input grating coupler.
10 14 18 22
0
10
20
30
40
50
60
Input p ul se w idth ( ps)
Outp ut pu lse broad ening (% )
Fig. 12. Output pulse broadening with the pulsewidth of the input signal.
PM
EA
RF
PC1
TLD
OTDL
MZM
PC2
Bias
EDFA1
Grat ing
coupler
EDFA3
OSC
EDFA2
PC3
Fig. 13. Experimental setup of the different order differentiators with broader input pulse.
Figure 14(a) shows the input pulse generated by the new experiment setup. The FWHM of
the pulse is 25.4 ps. We control the all the voltages applied on the amplitude electrodes and
phase electrodes to achieve the first-order differentiator spectrum, and fine tune the TLD
central wavelength to align with the resonant notch. We measure the temporal waveform of
first-order differentiation signal, which is shown in Fig. 14(b) as the blue solid line. The SNR
of the signal is 35.01 dB. The ideal first-order differentiation signal is also shown as the red
dash line for comparison. Obviously, the output differentiation signal is not broadened. Then
we adjust the all the voltages applied on the amplitude electrodes and phase electrodes to
achieve the second- and third-order differentiator spectra, still fine tune the TLD central
wavelength to align with the resonant notch. And we measure the temporal waveforms of the
#236566 - $15.00 USD
Received 19 Mar 2015; revised 24 Apr 2015; accepted 27 Apr 2015; published 29 Apr 2015
© 2015 OSA
4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.012161 | OPTICS EXPRESS 12171

second- and third-order differentiations, which are shown in Figs. 14(c) and 14(d),
respectively. The SNRs of the second-order and third order differentiation signals are 24.04
dB and 23.99 dB, respectively. The output signals are not broadened, either, confirming our
prediction. We may also notice that the differentiation signals have larger distortions with the
ideal ones, which is caused by a low energy efficiency of photonic chip. The minimum
operation frequency bandwidth of our differentiator is about 31.25 GHz, and the maximum
operation frequency bandwidth is about 100 GHz (the pulse broadening is 30% for the first-
order differential). And the phase at the phase jump of first- and third-order differentiators
can vary with small changes of the tap’s phase. So we can also achieve fractional-order
differentiator by our scheme too.
The power consumption varies when the pulse shaper is in different functions, and the
maximum power consumption is about 100 mW. The spectrum of the pulse shaper is
periodical due to the four-tap FIR structure. The FSR of the filter is inversely proportional to
the time delay τ. Thus we can increase the FSR thereafter decrease the pulsewidth of OAWG
and increase the operation bandwidth of differentiator by decreasing the time delay. In
practical application, the time delay τ can be 0.5 ps to 20 ps for 4 taps because of the
fabrication error and large loss of the long waveguides. So the operation bandwidth of our
differentiator can varies between 0.12 nm to 16 nm. Comparing the measured arbitrary
waveforms and differentiation pulses with the simulations, moderate deviations appear, which
result from the non-uniform thermal conductivity of each electrode and device fabrication
imperfections. To mitigate the impact of thermal non-uniformities, we can increase the
distance between thermal heaters to prevent thermal crosstalk. Besides, the number of taps
influences the resolution of pulse shaper as well. We can obtain more elaborate waveforms by
fabricating FIR structures with eight or more taps.
Measured
Fitted
Time (ps)
-60 -30 03060
Intens ity (a.u.)
0
0.2
0.4
0.6
0.8
1
Time (ps)
-60 -30 03060
Intens ity (a.u.)
0
0.2
0.4
0.6
0.8
1
Measured
Simu lated
Time (ps)
-60 -30 03060
Measured
Simu lated
Intens ity (a.u.)
0
0.2
0.4
0.6
0.8
1
Time (ps)
-60 -30 03060
Intens ity (a.u.)
0
0.2
0.4
0.6
0.8
1
Measured
Simu lated
(a) (b)
(c) (d)
Fig. 14. Experimental results for different order differentiations of broader input pulse, (a)
input pulse, (b)-(d) temporal waveforms for first-, second- and third-order differentiations,
respectively.
4. Conclusions
We have proposed and demonstrated an optical arbitrary waveform generator and high-order
photonic differentiator based on an FIR silicon integrated circuit. By adjusting the voltages to
control the amplitude and phase of each tap, we have implement several typical waveforms
such as isosceles triangular waveform, sawtooth waveform, square waveform, oblique
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Received 19 Mar 2015; revised 24 Apr 2015; accepted 27 Apr 2015; published 29 Apr 2015
© 2015 OSA
4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.012161 | OPTICS EXPRESS 12172

triangular waveform, flat-topped waveform and Gaussian waveform. And we also have
demonstrated first-, second- and third-order differentiators based on the optical pulse shaper.
Furthermore, we discussed the influence of the bandwidth of input pulse to a finite operation
bandwidth differentiator. Our scheme has distinct advantages of compactness, small power
consumption and capability for integration with electronics. And no high frequency resolution
disperser or coherent detection are required in our scheme. Our scheme can achieve first- to
third-order differentiator on a fixed photonic chip, which is unable in our previous schemes
such as cascaded microrings or cascaded Mach-Zehnder interferometers.
Acknowledgments
This work was supported in part by the National Basic Research Program of China (Grant No.
2011CB301704), the Program for New Century Excellent Talents in Ministry of Education of
China (Grant No. NCET-11-0168), a Foundation for Author of National Excellent Doctoral
Dissertation of China (Grant No. 201139), the National Natural Science Foundation of China
(Grant No. 11174096, 11374115, 61261130586 and 61475052), and the Opened Fund of the
State Key Laboratory on Integrated Optoelectronics (Grant No. 2011KFJ002) and the Danish
Council for Independent Research (DFF–1337-00152 and DFF–1335-00771).
#236566 - $15.00 USD
Received 19 Mar 2015; revised 24 Apr 2015; accepted 27 Apr 2015; published 29 Apr 2015
© 2015 OSA
4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.012161 | OPTICS EXPRESS 12173