Reconfigurable photonic temporal differentiator based on a dual-drive Mach-Zehnder modulator

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 polarityand 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 powerefficient 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).


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][11][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][19][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 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 polarityreversed intensity differentiators and a pair of polarity-reversed field differentiators, are theoretically and experimentally demonstrated.Compared with previously reported schemes [22][23][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.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.

Operation principle and simulations
The optical field injected into the DDMZM is assumed as where 0 E , 0 ω and 0 ϕ 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 and respectively, where ( ) s t is the electrical signal applied to the RF port of the DDMZM, V π is the half wave voltage of the DDMZM, b V 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.

Positive field differentiation
When = b V V π , the optical power at the output of DDMZM can be achieved by combining Eq. ( 2) and Eq. ( 3) where / (2 ) − − is sufficiently small, Eq. ( 4) can be approximated as Ifτ is sufficiently small, Eq. ( 5) can be approximated as 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 is generated.If the max phase shift induced by the input data is π, the differentiated signal can get its max amplitude.

Negative field differentiation
When the bias voltage is adjusted to make =0 b V , the output optical power can be expressed as The same to Eq. ( 4), when ( ) ( ) 2 s t s t τ α τ − − can be considered as a small quantity, Eq. ( 7) can be approximated as From Eq. ( 8), it can be observed that ifτ is sufficiently small, the output optical power can be expressed as 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.

Positive intensity differentiation
The last term in the braces is a second order small quantity and thus can be neglected.Therefore, Eq. ( 11) can be simplified as }. 16 2 In Eq. ( 12), When the phase shift caused by the input electrical data is π/2, the differentiated signal can achieve its max amplitude.

Negative intensity differentiation
When the bias voltage is adjusted to make =-/ 2 b V V π , similar to the positive differentiation, the output intensity signal can be expressed as Equation ( 13) can be approximated as }. 16 2 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 (V π ) 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 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.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), respectively.It can be noted that the data sequence is "1011100110010001101110011001000 1101110".

Experimental results and discussion
At first, when the bias voltage of DDMZM is set at −3.6 V and the electrical voltage which controls the gain of DBA (v g ) 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 v g 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.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.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 negativeintensity 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.

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.

Fig. 1 .
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 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.

Fig. 4 .
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.

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.