-
Reconfigurable photonic temporal differentiator based on a
dual-drive Mach-Zehnder modulator
Yuan Yu,1,2 Fan Jiang,1 Haitao Tang,1 Lu Xu,1 Xiaolong Liu,1
Jianji Dong,1,2,3 and Xinliang Zhang 1,2,4
1Wuhan National Laboratory for Optoelectronics, Huazhong
University of Science and Technology, Wuhan 430074, China
2 School of Optical and Electronic Information, Huazhong
University of Science and Technology, Wuhan 430074, China
[email protected] [email protected]
Abstract: We propose and demonstrate a reconfigurable photonic
temporal differentiator based on a dual drive Mach-Zehnder
modulator (DDMZM). The differentiator can be reconfigured to
different differentiation types by simply adjusting the bias
voltage of DDMZM. Both simulations and experiments are carried out
to verify the proposed scheme. In the experiment, a pair of
polarity-reversed field differentiation and a pair of
polarity-reversed intensity differentiation are successfully
generated. The differentiation accuracy and conversion efficiency
versus the time delay are also investigated. ©2016 Optical Society
of America OCIS codes: (060.5625) Radio frequency photonics;
(070.1170) Analog optical signal processing; (200.4740) Optical
processing.
References and links 1. Y. Han, Z. Li, and J. Yao, “A microwave
bandpass differentiator implemented based on a
nonuniformly-spaced
photonic microwave delay-line filter,” J. Lightwave Technol.
29(22), 3470–3475 (2011). 2. N. Q. Ngo, S. F. Yu, S. C. Tjin, and
C. H. Kam, “A new theoretical basis of higher-derivative
optical
differentiators,” Opt. Commun. 230(1-3), 115–129 (2004). 3. J.
Capmany and D. Novak, “Microwave photonics combines two worlds,”
Nat. Photonics 1(6), 319–330 (2007). 4. R. Ashrafi and J. Azaña,
“Figure of merit for photonic differentiators,” Opt. Express 20(3),
2626–2639 (2012). 5. S. Pan and J. Yao, “Optical generation of
polarity- and shape-switchable ultrawideband pulses using a
chirped
intensity modulator and a first-order asymmetric Mach-Zehnder
interferometer,” Opt. Lett. 34(9), 1312–1314 (2009).
6. J. Niu, K. Xu, X. Sun, Q. Lv, J. Dai, J. Wu, and J. Lin,
“Instantaneous microwave frequency measurement using a photonic
differentiator and an opto-electric hybrid implementation,”
Asia-Pacific Microwave Photonics Conference 2010 (APMP2010), Hong
Kong, China, 26–28 April 2010.
7. X. Li, J. Dong, Y. Yu, and X. Zhang, “A tunable microwave
photonic filter based on an all-optical differentiator,” IEEE
Photonics Technol. Lett. 23(5), 308–310 (2011).
8. F. Zeng and J. Yao, “Ultrawideband impulse radio signal
generation using a high-speed electrooptic phase modulator and a
fiber-Bragg-grating-based frequency discriminator,” IEEE Photonics
Technol. Lett. 18(19), 2062–2064 (2006).
9. P. Li, H. Chen, X. Wang, H. Yu, M. Chen, and S. Xie,
“Photonic generation and transmission of 2-Gbit/s power-efficient
IR-UWB signals employing an electro-optic phase modulator,” IEEE
Photonics Technol. Lett. 25(2), 144–146 (2013).
10. J. Xu, X. Zhang, J. Dong, D. Liu, and D. Huang, “High-speed
all-optical differentiator based on a semiconductor optical
amplifier and an optical filter,” Opt. Lett. 32(13), 1872–1874
(2007).
11. F. Wang, J. Dong, E. Xu, and X. Zhang, “All-optical UWB
generation and modulation using SOA-XPM effect and DWDM-based
multi-channel frequency discrimination,” Opt. Express 18(24),
24588–24594 (2010).
12. V. Moreno, M. Rius, J. Mora, M. A. Muriel, and J. Capmany,
“Integrable high order UWB pulse photonic generator based on cross
phase modulation in a SOA-MZI,” Opt. Express 21(19), 22911–22917
(2013).
13. J. Xu, X. Zhang, J. Dong, D. Liu, and D. Huang, “All-optical
differentiator based on cross-gain modulation in semiconductor
optical amplifier,” Opt. Lett. 32(20), 3029–3031 (2007).
14. Q. Wang and J. Yao, “Switchable optical UWB monocycle and
doublet generation using a reconfigurable photonic microwave
delay-line filter,” Opt. Express 15(22), 14667–14672 (2007).
15. M. Bolea, J. Mora, B. Ortega, and J. Capmany, “Optical UWB
pulse generator using an N tap microwave photonic filter and phase
inversion adaptable to different pulse modulation formats,” Opt.
Express 17(7), 5023–5032 (2009).
#261143 Received 15 Mar 2016; revised 13 May 2016; accepted 15
May 2016; published 20 May 2016 © 2016 OSA 30 May 2016 | Vol. 24,
No. 11 | DOI:10.1364/OE.24.011739 | OPTICS EXPRESS 11739
-
16. F. Li, Y. Park, and J. Azaña, “Linear characterization of
optical pulses with durations ranging from the picosecond to the
nanosecond regime using ultrafast photonic differentiation,” J.
Lightwave Technol. 27(21), 4623–4633 (2009).
17. F. Liu, T. Wang, L. Qiang, T. Ye, Z. Zhang, M. Qiu, and Y.
Su, “Compact optical temporal differentiator based on silicon
microring resonator,” Opt. Express 16(20), 15880–15886 (2008).
18. L. M. Rivas, K. Singh, A. Carballar, and J. Azaña,
“Arbitrary-order ultrabroadband all-optical differentiators based
on fiber Bragg gratings,” IEEE Photonics Technol. Lett. 19(16),
1209–1211 (2007).
19. M. Li, D. Janner, J. Yao, and V. Pruneri, “Arbitrary-order
all-fiber temporal differentiator based on a fiber Bragg grating:
design and experimental demonstration,” Opt. Express 17(22),
19798–19807 (2009).
20. M. A. Preciado, X. Shu, P. Harper, and K. Sugden,
“Experimental demonstration of an optical differentiator based on a
fiber Bragg grating in transmission,” Opt. Lett. 38(6), 917–919
(2013).
21. M. Kulishov and J. Azaña, “Long-period fiber gratings as
ultrafast optical differentiators,” Opt. Lett. 30(20), 2700–2702
(2005).
22. Z. Chen, L. Yan, W. Pan, B. Luo, X. Zou, A. Yi, Y. Guo, and
H. Jiang, “Reconfigurable optical intensity differentiator
utilizing DGD element,” IEEE Photonics Technol. Lett. 25(14),
1369–1372 (2013).
23. J. Dong, A. Zheng, D. Gao, L. Lei, D. Huang, and X. Zhang,
“Compact, flexible and versatile photonic differentiator using
silicon Mach-Zehnder interferometers,” Opt. Express 21(6),
7014–7024 (2013).
24. A. Zheng, J. Dong, L. Lei, T. Yang, and X. Zhang, “Diversity
of photonic differentiators based on flexible demodulation of phase
signals,” Chin. Phys. B 23(3), 033201 (2014).
25. J. Dong, Y. Yu, Y. Zhang, B. Luo, T. Yang, and X. Zhang,
“Arbitrary-order bandwidth-tunable temporal differentiator using a
programmable optical pulse shaper,” IEEE Photonics J. 3(6),
996–1003 (2011).
1. Introduction
The temporal differentiation has attracted great interests due
to its wide applications in system controlling, electrocardiograph
(ECG) signal monitoring, radar signals analyzing and modern
communications [1, 2]. Conventional temporal differentiators
achieved in the electrical domain exhibits low processing speed and
narrow band [2]. Photonic processing of radio frequency (RF)
signals is a very promising technique for its intrinsic advantages,
such as large bandwidth, low loss, and immunity to electromagnetic
interference (EMI) [3]. As a branch, the temporal differentiation
realized by employing optical approaches exhibits advantages of
ultra fast processing and broad band, and has been extensively
investigated [1]. The temporal differentiators can be classified
into two categories: intensity differentiation and field
differentiation [4]. The optical intensity differentiator is used
to differentiate the intensity profile of the input waveform, which
is usually applied in the microwave photonics, such as
ultra-wideband (UWB) generation [5], microwave photonic frequency
measurement [6], and microwave photonic filter [7]. The optical
intensity differentiators can be realized by using phase modulation
[8, 9] or cross-phase modulation (XPM) [10–12] and frequency
discriminators, cross-gain modulation in a semiconductor optical
amplifier (SOA) [13], and superimposing delayed optical pulses [14,
15]. Meanwhile, the field differentiator is used to differentiate
the optical complex field (including the amplitude and phase) and
can be used for pulse reshaping, ultrashort pulse generation, and
achieving the odd-symmetric Hermite-Gaussian (OS-HG) pulses [16].
Many approaches have been proposed to realize the field
differentiation, such as using the microring resonator [17],
apodized fiber Bragg gratings (FBGs) [18–20], and long period fiber
gratings (LPGs) [21].
Besides the ultra-fast processing ability of the photonic
differentiator, the reconfigurability, which is the ability to
switch the differentiator from one differentiation type to another,
is also very attractive because it can increase the flexibility of
the differentiator to meet the requirements for dynamic
applications. Some approaches have been proposed to achieving
reconfigurable differentiators. Researchers in Yan’s group have
proposed to use a Mach-Zehnder modulator (MZM) and a
differential-group-delay (DGD) element to realize a reconfigurable
differentiator [22]. By changing the polarization state of the
input signal into the polarizer, three differentiation types, which
are a pair of polarity-reversed intensity differentiation and
positive field differentiation, are achieved. However, adjusting
and aligning the polarization state make the system complex and
only three differentiation types are achieved. The silicon based
Mach-Zehnder interferometer (MZI) has also been proposed to realize
a pair of polarity-reversed intensity modulation and a positive
field differentiation [23]. The reconfigurability is realized by
controlling the deviation of the optical wavelength from the MZI
transmission dip. Similarly, only three differentiation types are
achieved. It has
#261143 Received 15 Mar 2016; revised 13 May 2016; accepted 15
May 2016; published 20 May 2016 © 2016 OSA 30 May 2016 | Vol. 24,
No. 11 | DOI:10.1364/OE.24.011739 | OPTICS EXPRESS 11740
-
also been proposed to generate a pair of polarity-reversed
intensity and field differentiations by using an electro-optic
phase modulator (EOPM) and two cascaded delay interferometers (DIs)
[24]. Four differentiation types can be realized by adjusting the
resonant frequencies of the two DIs. However, precisely adjusting
the two MZIs increases the complexity of the system.
In this paper, a novel and reconfigurable optical differentiator
is proposed and experimentally demonstrated. The scheme is realized
based on a single dual-drive Mach-Zehnder modulator (DDMZM). The
input RF signal is equally divided into two parts at first and a
relative time delay between the two RF signals is introduced. Then
the two RF signals are applied to the two arms of DDMZM
respectively. The input continuous wave (CW) light is also equally
split into two parts by the Y branch coupler in the DDMZM and then
phase modulated by the two RF signals in each arm of the DDMZM,
respectively. After combining at the output of DDMZM, the two
phase-modulated signals are interfered and converted into optical
intensity signals. Our scheme shows good reconfigurability to any
first-order differentiator by electrically switching the
differentiation type. When the bias voltage of the DDMZM is
adjusted, all the four different differentiation types, which are a
pair of polarity-reversed intensity differentiators and a pair of
polarity-reversed field differentiators, are theoretically and
experimentally demonstrated. Compared with previously reported
schemes [22–24], no precise polarization adjustment or wavelength
alignment is needed in our scheme. Thus, our scheme is quite
simple. The scheme also shows good extinction ratio (ER) of all the
differentiated waveforms. The differentiation accuracy and the
conversion efficiency are also investigated.
2. Operation principle and simulations
Fig. 1. Operation principle of the proposed scheme. (a) is the
schematic diagram of the proposed scheme.(b1), (b2), (b3) and(b4)
represent the generation of the positive field differentiation,
negative field differentiation, positive intensity differentiation,
and negative intensity differentiation, respectively.
The operation principle of the proposed scheme is shown in Fig.
1. Figure 1(a) shows the schematic diagram of the proposed scheme.
A CW laser light is injected into a DDMZM and
#261143 Received 15 Mar 2016; revised 13 May 2016; accepted 15
May 2016; published 20 May 2016 © 2016 OSA 30 May 2016 | Vol. 24,
No. 11 | DOI:10.1364/OE.24.011739 | OPTICS EXPRESS 11741
-
equally split into two parts by the Y-branch coupler of the
DDMZM. Then the two optical beams are propagated along the upper
and the lower arms of the DDMZM, respectively. The electrical
signal is also equally divided into two parts and a certain time
delay is introduced in one signal. Then, the two electrical signals
are applied to the two RF ports of the DDMZM, respectively. Thus,
phase modulation occurs in both the upper and lower arms of the
DDMZM. The bias voltage of DDMZM is used to adjust the phase
difference of the two arms in DDMZM. At the output of DDMZM, the
two phase modulated signals are interfered and converted into
optical intensity signals.
The optical field injected into the DDMZM is assumed as
0 0 0cos( ),E E tω ϕ= + (1)
where 0E , 0ω and 0ϕ are the amplitude, angular frequency and
initial phase of the CW light respectively. When the CW light is
injected into the DDMZM, the optical power is also equally divided
into two parts and the two parts are launched to the upper and
lower arms of the DDMZM respectively. According to Eq. (1), when
the RF signals are applied to the DDMZM, the optical field in the
upper and lower arms of DDMZM can be expressed as
0 0 02 cos( ( ) / )
2upperE E t s t Vπω ϕ π= + + (2)
and
0 0 02 cos( ( ( )) / ),
2lower bE E t V s t Vπω ϕ π τ= + + + − (3)
respectively, where ( )s t is the electrical signal applied to
the RF port of the DDMZM, Vπ is the half wave voltage of the DDMZM,
bV is the bias voltage applied to the DDMZM, and τ is the time
delay of the RF signal applied to the lower arm. The derivation of
the four differentiation types is present as follows.
2.1 Positive field differentiation
When =bV Vπ , the optical power at the output of DDMZM can be
achieved by combining Eq. (2) and Eq. (3)
2 20( ) ( )2 [sin( )] ,out
s t s tP E τατ
− −= (4)
where / (2 )Vπα πτ= . It should be noted that if( ) ( )s t s t
τα
τ− − is sufficiently small, Eq. (4)
can be approximated as
2 20( ) ( )2( ) [ ] .out
s t s tP E τατ
− −≈ (5)
Ifτ is sufficiently small, Eq. (5) can be approximated as
2 20( )2( ) [ ] .out
s tP Et
α ∂≈∂
(6)
From Eq. (6), it can be concluded that the output optical power
is the first-order positive field differentiation of the input
signals. The generation of the positive field differentiation can
be illustrated as Fig. 1(b1). When the optical phase difference
caused by the bias voltage is π and the two data sequences has a
small time delay ofτ , constructive and destructive interferences
occur between the two phase-modulated signals and positive field
differentiation
#261143 Received 15 Mar 2016; revised 13 May 2016; accepted 15
May 2016; published 20 May 2016 © 2016 OSA 30 May 2016 | Vol. 24,
No. 11 | DOI:10.1364/OE.24.011739 | OPTICS EXPRESS 11742
-
is generated. If the max phase shift induced by the input data
is π, the differentiated signal can get its max amplitude.
2.2 Negative field differentiation
When the bias voltage is adjusted to make =0bV , the output
optical power can be expressed as
2 20( ) ( )2 {1 2sin [ ]}.
2outs t s tP E τα
τ− −= − (7)
The same to Eq. (4), when ( ) ( )2
s t s t τατ
− − can be considered as a small quantity, Eq. (7)
can be approximated as
2
2 20
( ) ( )2 {1 [ ] }.2out
s t s tP E α ττ
− −≈ − (8)
From Eq. (8), it can be observed that ifτ is sufficiently small,
the output optical power can be expressed as
2 2 2 20 0( )2 [ ] .out
s tP E Et
α ∂≈ −∂
(9)
From Eq. (9), it can be concluded that the output waveform is
the negative field differentiation of the input signal. The
generation of negative field differentiation can be illustrated as
Fig. 1(b2). When the phase shift caused by the bias voltage is 0,
negative field differentiation can be achieved after optical
interference. The phase shift of π can ensure the max amplitude of
the differentiated signal, which is the same as the positive field
differentiation.
2.3 Positive intensity differentiation
If the bias voltage is set at / 2Vπ , which means = / 2bV Vπ ,
the output optical power can be expressed as
2 20( )2 cos [ ].
4outs tP E
tπα ∂= −
∂ (10)
If ( )4
s tt
πα ∂ −∂
can be considered as a small quantity, Eq. (10) can be
approximated as
2
2 2 20
( ) ( )2 {(1 ) [ ] }.16 2out
s t s tP Et t
π παα α∂ ∂≈ − + −∂ ∂
(11)
The last term in the braces 2( )[ ]s tt
α ∂∂
is a second order small quantity and thus can be
neglected. Therefore, Eq. (11) can be simplified as
2
2 20
( )2 {(1 ) }.16 2out
s tP Et
π παα ∂≈ − +∂
(12)
In Eq. (12), 2
2 202 (1 )16
E πα − is a direct current (DC) component, and ( )2
s tt
πα ∂∂
is the first
order differentiation of the input signal. The combination of
the two terms is the positive intensity differentiation of the
input signal. The positive intensity differentiation can be
illustrated as Fig. 1(b3). However, there is a little difference
from the field differentiation. When the phase shift caused by the
input electrical data is π/2, the differentiated signal can achieve
its max amplitude.
#261143 Received 15 Mar 2016; revised 13 May 2016; accepted 15
May 2016; published 20 May 2016 © 2016 OSA 30 May 2016 | Vol. 24,
No. 11 | DOI:10.1364/OE.24.011739 | OPTICS EXPRESS 11743
-
2.4 Negative intensity differentiation
When the bias voltage is adjusted to make =- / 2bV Vπ , similar
to the positive differentiation, the output intensity signal can be
expressed as
2 20
( )2 cos [ ].4out
s tP Et
πα ∂= +∂
(13)
Equation (13) can be approximated as 2
2 20
( )2 {(1 ) }.16 2out
s tP Et
π παα ∂≈ − −∂
(14)
From Eq. (14), it can be observed that the output waveform is
the negative intensity differentiation of the input signal. The
generation of negative intensity differentiation can be illustrated
as Fig. 1(b4).
Therefore, by adjusting the bias voltage of DDMZM, a pair of
polarity-reversed intensity differentiation and a pair of
polarity-reversed field differentiation can be theoretically
achieved. In order to verify our analysis, simulations are carried
out and the simulated results are shown in Fig. 2.
In simulation, a Gaussian pulse with full width at half maximum
(FWHM) of 166 ps and a super-Gaussian pulse with FWHM of 65 ps are
used as input impulse respectively. Both the amplitudes of the
input Gaussian and super-Gaussian pulses are 1 V. The time delay
between the two signals is set at 10 ps. The half-wave voltage (Vπ
) in the both arms of the DDMZM is 3.5 V. Figure 2(a1) shows the
input Gaussian pulse. At first, the bias voltage of the DDMZM is
set at 3.5 V, which indicates that the phase difference between the
two arms of DDMZM is π. The optical waveform at the output of DDMZM
is shown as the black solid and rectangular curve in Fig. 2(a2). It
can be observed that the output waveform is the positive field
differentiation of the input signal. The ideal positive field
differentiation is also shown as the red dashed curve in Fig.
2(a2). It can be observed that the positive field differentiation
accords very well with the ideal result. Then, the bias voltage is
set at 0, which indicates that the phase difference between the two
arms is 0. The output waveform and the ideal negative
#261143 Received 15 Mar 2016; revised 13 May 2016; accepted 15
May 2016; published 20 May 2016 © 2016 OSA 30 May 2016 | Vol. 24,
No. 11 | DOI:10.1364/OE.24.011739 | OPTICS EXPRESS 11744
-
field differentiation are shown in Fig. 2(a3). It can be
observed that the achieved optical waveform accords very well with
the ideal negative field differentiation. Thus, when the bias
voltage of the DDMZM is 0, a negative field differentiation can be
obtained. Thirdly, the bias voltage is set at 1.75 V, which
indicates the phase difference between the two arms is π/2. The
output waveform is shown in Fig. 2(a4) and positive intensity
differentiation is achieved. The ideal positive intensity
differentiation is also shown in Fig. 2(a4). It can be observed
that the simulation result accords very well with the ideal
intensity differentiation. When the bias voltage is set at −1.75 V,
corresponding to a phase shift of π/2, the simulated output
waveform is shown in Fig. 2(a5) and a negative intensity
differentiation can be achieved. The ideal negative intensity
differentiation is also plotted in Fig. 2(a5). It can be observed
that the simulation result accords very well with the ideal
differentiations. Therefore, in simulation, it can be observed that
the four type differentiations are all accorded with the
corresponding ideal differentiations, respectively.
Meanwhile, the differentiations of a super-Gaussian pulse with
FWHM of 65 ps are also simulated and the simulation results are
shown in Fig. 2(b1)-(b5). It can be also observed that the
simulated four different types of differentiation all accord well
with the simulation results. Thus, in simulation, it can be
concluded that the proposed scheme can generate four different
types of differentiation by simply adjusting the bias voltage of
the DDMZM.
3. Experimental results and discussion
Fig. 3. Experimental setup of the proposed scheme (optical path:
red line; electrical path: black line). LD: laser diode; PC:
polarization controller; BPG: bit pattern generator; DBA: dual
broadband amplifier; DDMZM: dual-drive Mach-Zehnder modulator;
EDFA: erbium-doped fiber amplifier; VOA: variable optical
attenuator; DCA: digital communication analyzer.
To verify our analysis and theoretical simulation, an experiment
as illustrated in Fig. 3 is performed. A continuous wave (CW) light
emitted form a laser diode (LD, Alnair TLG-200) is injected into a
DDMZM (Fujitsu, FTM7937EZ611) via a polarization controller (PC).
The electrical pulse emitted from a bit pattern generator (BPG, SHF
44E) is equally divided into two parts by a radio frequency (RF)
splitter. Then the two signals are simultaneously amplified by a
dual broadband amplifier (DBA, Centellax OA4SMM4). One signal is
delayed with a certain time compared with the other signal by a RF
delay line. Then the two signals are applied to the two RF ports of
the DDMZM, respectively. After modulated by the DDMZM, the output
optical signals are power adjusted by an erbium-doped fiber
amplifier (EDFA) and variable optical attenuator (VOA). The digital
communication analyzer (DCA, Angilent Infiniium DCA-J86100C) is
used to measure the waveform of the generated optical pulses. In
the experiment, the relative time delay between the two arms is 12
ps. Figure 4 shows the experimental and simulated ideal results.
Figure 4(a) shows the input electrical pulse (black solid curve) in
the experiment and the fitted waveform (red dotted curve),
#261143 Received 15 Mar 2016; revised 13 May 2016; accepted 15
May 2016; published 20 May 2016 © 2016 OSA 30 May 2016 | Vol. 24,
No. 11 | DOI:10.1364/OE.24.011739 | OPTICS EXPRESS 11745
-
respectively. It can be noted that the data sequence is
“1011100110010001101110011001000 1101110”.
At first, when the bias voltage of DDMZM is set at −3.6 V and
the electrical voltage which controls the gain of DBA (vg) is set
at −0.6 V respectively, the output waveform is shown as the black
solid curve in Fig. 4(b). The ideal positive field differentiation
is shown as the red dotted curve in Fig. 4(b) for comparison. It
can be observed that the positive field differentiation is
successfully generated. Then, the bias voltage is adjusted at 1.6 V
and the generated waveform is shown as the black solid curve in
Fig. 4(c). The simulated waveform is shown as the red dotted curve
in Fig. 4(c). Therefore, the negative field differentiation is
successfully generated. The calculated average errors of the
positive field differentiation and the negative field
differentiation are 8.0% and 11.2%, respectively. The average error
is defined as the mean absolute deviation of measured
differentiation power from the ideal differentiation power during a
certain period of time [25]. The extinction ratio (ER) of the
positive field differentiation is 17.0 dB, and the ER of the
negative field differentiation is 19.1 dB, respectively. When the
bias voltage of DDMZM and vg are set at −2.3 V and −0.1 V
respectively, the output waveform is shown as the black solid curve
in Fig. 4(d). The ideal positive intensity differentiation is shown
as the red dotted curve in Fig. 4(d). It can be observed that
correct positive intensity differentiation is successfully
achieved. Compared with the simulated results, some small humps can
be observed in the experimental results. The humps are generated by
the nonideal electrical pulse. In Fig. 4(a), it can be observed
that the top of the measured electrical pulse is uneven. After
differentiation, the uneven top is converted to small humps. Thus,
some humps can be observed in the generated waveform. When the bias
voltage is adjusted at −5.8 V, the generated waveform is shown as
the black solid curve in Fig. 4(e). The ideal negative intensity
differentiation is shown as the red dotted curve in Fig. 4(e). It
can be observed that the negative intensity differentiation is
successfully generated. Similar to the positive intensity
differentiation generation, there are also some humps existing in
the generated waveform. The calculated average errors of the
positive intensity differentiation and the negative intensity
differentiation are 10.3% and 9.9%, respectively. The ER of the
positive intensity differentiation waveform is 23.4 dB, and the ER
of the negative intensity differentiation waveform is 23.3 dB,
respectively. Thus, it can be concluded that by adjusting the bias
voltage of the DDMZM, a pair of polarity-reversed field
differentiations and intensity differentiations are successfully
achieved. The reconfigurability from one differentiation type to
another is realized simply by adjusting bias voltage.
#261143 Received 15 Mar 2016; revised 13 May 2016; accepted 15
May 2016; published 20 May 2016 © 2016 OSA 30 May 2016 | Vol. 24,
No. 11 | DOI:10.1364/OE.24.011739 | OPTICS EXPRESS 11746
-
Fig. 4. Experimental and simulated results. (a) shows the
measured (black solid curve) and fitted (red dotted curve)
waveforms of the input signal; (b) shows the measured (black solid
curve) and simulated (red dotted curve) waveforms of positive field
differentiation; (c) shows the measured (black solid curve) and
simulated (red dotted curve) waveforms of negative field
differentiation; (d) shows the measured (black solid curve) and
simulated waveforms (red dotted curve) of positive intensity
differentiation; (e) shows the measured (black solid curve) and
simulated waveforms (red dotted curve) of negative intensity
differentiation.
By comparing the ideal and experimental results, it can be
observed that the pulse width achieved in the experiment is larger
than that in simulation. This is because there is a tradeoff
between the differentiation accuracy and conversion efficiency. In
the experiment, a smaller time delay can result in a more accurate
differentiation. However, the amplitude of generated waveform will
also be smaller. Therefore, the time delay should be neither too
large nor too small. In the experiment, the time delay is set at 12
ps to balance the pulse amplitude and the differential accuracy.
The influences of the time delay on the differentiation accuracy
and differentiation efficiency are also investigated. The measured
and simulated results are shown in Fig. 5.
Fig. 5. The influences of time delay on the differentiation
accuracy and differentiation efficiency. (a) shows the measured
input waveforms and differentiated waveforms with different time
delays. (b) shows the measured (rhombus) and simulated (dashed
curve) amplitudes of differentiated waveforms with different time
delay, and measured (rectangles) and simulated (solid curve) of the
average error with different time delay.
#261143 Received 15 Mar 2016; revised 13 May 2016; accepted 15
May 2016; published 20 May 2016 © 2016 OSA 30 May 2016 | Vol. 24,
No. 11 | DOI:10.1364/OE.24.011739 | OPTICS EXPRESS 11747
-
We take an 8-th order super-Gaussian pulse with FWHM of 372 ps
as the input pulse, shown as the black curve in Fig. 5(a). When the
time delay is 11.6 ps, the measured negative-intensity
differentiated waveform is shown as the green curve in Fig. 5(a).
It can be observed that the amplitude is quite small. When the
relative time delay is increased to 25.2 ps, 66.7 ps, and 125.9 ps,
the measured differentiated waveforms are shown as the yellow
curve, purple curve, and red curve, respectively. It can be
observed that the amplitude of the differentiated waveform is
increased when the relative time delay is increased. The measured
normalized amplitudes of the differentiated waveforms with
different time delays are shown as the rhombus in Fig. 5(b). The
normalized amplitude is defined as the ratio of the amplitude of
the differentiated waveform and the amplitude of the input pulse.
The predicted result is also present as the purple dashed curve for
comparison. It can be observed the measured and predicted results
accord well with each other. When the time delay is increased, the
normalized amplitude is also increased. If the time delay is
sufficiently large, the normalized amplitude of differentiated
waveform tends to reach its maximum value. The measured
(rectangles) and predicted (red solid trace) average errors are
also present in Fig. 5(b). It can be observed that when the time
delay is increased, the average error of differentiated waveform is
increased. However, it can be also observed that the measured
average error gets larger when the relative time delay is
sufficiently small. This is caused by the noise in the
differentiated waveform. When the time delay is too small, the
amplitude of differentiated waveform is also very small and the
signal to noise ratio (SNR) is deteriorated. The large noise level
will increase the average error. Thus, as the relative time delay
increased, the differentiation efficiency and error are both
increased. Therefore, there is a tradeoff between the
differentiation efficiency and accuracy.
In our scheme, it can be noted that a RF delay line is used to
introduce a relative time delay between the two phase modulated
optical signals of the two arms. Therefore, it is not an
all-optical approach and the operation bandwidth is limited by the
RF delay line. This disadvantage can be overcome by using the
optical delay. For example, by designing the DDMZM with one arm
longer than the other one, a relative time delay can be introduced
in the optical domain to overcome the bandwidth limitation set by
the RF delay line. Therefore, an all-optical differentiator can be
achieved.
4. Conclusion
A reconfigurable optical differentiator based on a DDMZM is
proposed and demonstrated. The reconfigurability is realized simply
by adjusting the bias voltage of the DDMZM. Both the simulation
results and experimental results demonstrate the generation of a
pair of polarity-reversed intensity differentiation and a pair of
polarity-reversed field differentiation. The differentiation
accuracy and conversion efficiency versus the time delay are also
simulated and analyzed. The results show that there is a tradeoff
between the differentiation accuracy and the conversion
efficiency.
Acknowledgments
This research was partially supported by the National Natural
Science Foundation of China (Grant No. 61501194, Grant No.
61475052), National Science Fund for Distinguished Young Scholars
(Grant No. 61125501), the NSFC Major International Joint Research
Project (Grant No. 61320106016), Foundation for Innovative Research
Groups of the Natural Science Foundation of Hubei Province (Grant
No. 2014CFA004), Hubei Provincial Natural Science Foundation of
China (Grant No. 2015CFB231), the Fundamental Research Funds for
the Central Universities (Grant No. HUST: 2016YXMS025), and
Director Fund of WNLO.
#261143 Received 15 Mar 2016; revised 13 May 2016; accepted 15
May 2016; published 20 May 2016 © 2016 OSA 30 May 2016 | Vol. 24,
No. 11 | DOI:10.1364/OE.24.011739 | OPTICS EXPRESS 11748