Configurable optical pulse synthesizer for multiple-waveform generation

Microelectronics Journal 88 (2019) 25–28

Contents lists available at ScienceDirect

Microelectronics Journal journal homepage: www.elsevier.com/locate/mejo

Configurable optical pulse synthesizer for multiple-waveform generation Xiaowei Dong a, b, *, Jianzhong Qi b a b

Institut National de la Recherche Scientifique-Energy, Materials and Telecommunications, Montreal, QC, H5A1K6, Canada College of Information Engineering, North China University of Technology, Beijing, 100144, China

A R T I C L E I N F O

A B S T R A C T

Keywords: Optical pulse synthesizer Multiple-waveform generation Configurable

In this paper, a much compact structure of configurable optical pulse synthesizer is proposed based on the signal processing theory. The desired optical pulse waveform is described by coherently overlapping the initial input pulse and its first-order, second-order differential signals, which are obtained by microring resonator (MR) working on the critical coupling condition. By optimizing the relative amplitudes and phases, output optical pulse can be tuned dynamically and several typical waveforms (e.g. flat-top, asymmetric triangular) are achieved. In addition, our results demonstrate that the proposed synthesizer can be applied for a variety of input sources (e.g. Gaussian or Sech-shape input pulses) with a certain range of temporal duration (FWHM ¼ 5ps–20ps).

1. Introduction Techniques for generation or synthesis of the user-defined temporal waveform have attracted considerable interest in a wide range of fields, such as high-speed optical signal processing [1], and all-optical retiming system [2]. According to the work principle, the commonly used schemes of optical pulse synthesis can be classified into Fourier-based frequency-domain method [3], frequency-to-time mapping approach [4] and direct time-domain technique [5]. One of the most popular implementations employing Fourier-based frequency-domain method is the 4f structure [6], which usually consists of two diffraction gratings and a spatial light modulator to separate and reshape the frequency components of input pulse. Drawbacks associated with this approach include the need for a high-quality bulk-optics setup and the sensitivity to environmental fluctuation [7]. These frequency-to-time mapping schemes usually consist of short optical pulse source, spectral shaper and dispersion medium. The spectral shaper is used to modify the spectral envelope of input pulse to a scaled version of the targeted temporal waveform and the dispersion medium is used to realize the mapping [8]. Although the spectral shaper can be achieved by mature waveguide-grating structures, it is still challenging to obtain large dispersion on the integrated chip. Customized optical pulse waveforms can also be synthesized by the direct time-domain approach [9]. By manipulating the amplitudes and phases of modulation sidebands, triangular and rectangular pulses have been obtained directly from a continuous lightwave [10]. However, the power ratio of these modulation harmonics should be carefully controlled to match the Fourier series

of the desired waveform, which reduces the flexibility and accuracy. In this paper, we present a novel configurable optical pulse synthesizer by exploring the first-order differential characteristic of microring resonator (MR). Compared with the schemes mentioned above, our structure is much compact, flexible and easy integration. 2. Structural model and theoretical background Based on the signal processing theory, any desired temporal pulse waveform can be described by the linear superposition of a Gaussian pulse and its successive time derivatives [11]: aout ðtÞ ¼

∞ X ∂r ain ðtÞ qr ∂t r r¼0

(1)

where ain ðtÞ, aout ðtÞ are the complex envelope of the input and output pulses, respectively; r 2 f0; 1; 2⋯g is the differential order; qr is the relative weight for each derivative. Although it is anticipated that optical pulse waveform with sharp temporal feature should be described by higher-order derivatives, a practical, realizable pulse waveform can be well approximated by a limited number of differentiations [5]. The use of higher-order differential signals requires more complex differentiators, which will degrade the energetic efficiency badly [12]. To give a reference, we calculate the power loss ratio (defined as: output pulse intensity relative to the input pulse intensity) from the first-order to the third-order derivatives, it is attenuated approximately 1012. Therefore, we present a much compact

* Corresponding author. College of Information Engineering, North China University of Technology, Beijing, 100144, China. E-mail address: [email protected] (X. Dong). https://doi.org/10.1016/j.mejo.2019.04.012 Received 28 May 2018; Received in revised form 1 March 2019; Accepted 17 April 2019 Available online 22 April 2019 0026-2692/© 2019 Published by Elsevier Ltd.

X. Dong, J. Qi

Microelectronics Journal 88 (2019) 25–28

Y1 Y2

MR1

×

q1

1

+

×

×

q2

2

×

MR2

Output pulse

pffiffiffiffiffiffiffiffiffiffiffi  pffiffiffi  ∂ain ðtÞ ⋅ expðjφ1 Þþ 1k⋅ j k ⋅ ∂t 2   pffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffi pffiffiffi ∂ ain ðtÞ ⋅ expðjφ2 Þ m2 ⋅ 1  k ⋅ 1  k ⋅ j k ⋅ ∂t 2 2 X ∂r ain ðtÞ qr ⋅ ⋅ expðjφr Þ ¼ ∂t r r¼0 m1 ⋅

(2)

By properly setting the relative weights of the normalized amplitudes and phases, optical pulse with different temporal waveforms can be achieved by coherently overlapping only the initial input pulse (zeroorder) and its first-order and second-order differentiations. 3. Results and discussions

(a)

Normalized Amplitude

Normalized Amplitude

In the followings, some examples of typical waveforms are provided to demonstrate performances of the proposed optical pulse synthesizer. The two microring-resonators (MR1, MR2) are designed to working on

0.8 0.6 0.4 0.2 0

Time /ps

0.2

25

50

1

-25

0

Time /ps

1

(b)

0.8 0.6 0.4

0.5

0.2 0 -50

-25

0

25

50

0 -0.5

-25

0.4 0.2 0 -50

50

-25

0

25

50

Time /ps

1

(c)

0.5 0 1

-0.5

-1 -50

25

0.6

the critical coupling condition and their central resonances are aligned to the input pulse's carrier wavelength. First, the waveform synthesizing capability for a transform-limited Gaussian input pulse ain ðtÞ ¼ expðt 2 = τ20 Þ is investigated. The full-width half-maximum (FWHM) of the input pulse's temporal duration is 10ps. The device performance for synthesizing different waveforms from non-Gaussian input pulses is also illustrated in the below. Since the temporal output is the result of overlapping initial input pulse and its first-order, second-order differential signals, the specific relative amplitudes and phases should be properly chosen to minimize the deviation of the synthesized output pulse and the desired target waveform. In this paper, we use the root-mean-square-error optimization algorithm to jointly search the relative amplitude and phase factors, so as to achieve a targeted output waveform with a pre-defined accuracy. Fig. 2 gives the normalized amplitudes of Gaussian input pulse and its first-order, second-order differentiations. The first-order differential signal is odd-symmetric with one central π-phase jump. The second-order differential signal is even-symmetric with two π-phase jumps. By setting the relative amplitudes and phases factors to q ¼ ð0; 1; 0Þ φ ¼ ð0; 0; 0Þ, a Hermite-Gaussian waveform constituted by two consecutive pulses is obtained, as shown in the insert of Fig. 2(b). When the relative amplitudes and phases factors are set as q ¼ ð0; 0; 1Þ φ ¼ ð0; 0; 0Þ, the waveform with one main peak and two sidelobes is obtained, as shown in the insert of Fig. 2(c). Next, we consider the probability to synthesize a flat-top waveform with FWHM of 27ps. Based on root-mean-square-error optimization algorithm, the relative amplitude and phase factors are obtained as q ¼ ð1; 0:4; 0:18Þ, φ ¼ ð0; 0:5π ; 0Þ. As can be seen from Fig. 3(a), the fluctuation in the synthesized pulse's top region is minimized to approximately match with the targeted flat-top waveform. But the rising and falling edges of synthesized pulse are not such sharp as the ideal rectangular waveform. This limitation can be improved if higher-order (e.g. thirdorder and forth-order) derivatives are employed. However, compared with the conventional waveform shaping method, our optical pulse synthesizer is much robust to the deviation of relative amplitude weights. When the relative phase factor remain unchanged (φ ¼ ð0; 0:5π ;0Þ), even

 pffiffiffi  aout ðtÞ ¼ m0 ⋅ j k ⋅ ain ðtÞ ⋅ expðjφ0 Þþ

-25

0.4

0.8

Fig.3. (a) Synthesized (black solid line) and targeted (blue dash line) flat-top waveform. (b) Impact of the relative amplitude deviations to the synthesized waveform. Red line: q ¼ ð1; 0:4; 0:18Þ (optimal value); Blue line: q ¼ ð0:8; 0:4; 0:18Þ Black line: q ¼ ð1; 0:32; 0:18Þ Green line: q ¼ ð1; 0:4; 0:144Þ.

optical pulse synthesizing structure, which includes only the input pulse (zero-order) and its first-order, second-order differentiations. Fig. 1 shows the schematic of the proposed optical pulse waveform synthesizer. The input optical pulse is divided into two taps by the first Ysplitter (Y1). In the first tap, there is no microring resonator (MR). Thus, output of the first branch is the initial input pulse. In the second tap, there is a microring resonator (MR1) working on the critical coupling condition, which can be approximated as the first-order differentiator [13]. After passing through MR1, the first-order differential optical pulse is divided further into two parts by the second Y-splitter (Y2). One part is delivered to the second branch and another part is differentiated once more by MR2 to obtain the second-order differential pulse. There are an amplitude adjuster (e.g. attenuator or amplifier) and a phase shifter (e.g. phase modulator or tunable delay-line) in each tap to set the relative amplitudes q ¼ ðq0 ; q1 ; q2 Þ and phases φ ¼ ðφ0 ; φ1 ; φ2 Þ of the initial input optical pulse (zero-order) and its first-order and second-order differentiations. Assuming that the splitting ratio of Y-splitters (Y1, Y2) is k and the central notch resonances of MR1, MR2 are aligned to the input optical frequency. Temporal output pulse of the synthesizer can be written as:

0 -50

0.6

×

(b)

1

0.8

0 -50

Fig. 1. Schematic structure of configurable optical pulse waveform synthesizer.

1

(a)

1

Normalized Intensity

Input pulse

Normalized Intensity

×

0

Normalized Amplitude

q0

0

Time /ps

25

50

0.8 0.6 0.4

-1 -50

0.2

-25

0

0 -50

Time /ps

-25

25

0

25

50 50

Fig. 2. Normalized amplitudes of (a) Gaussian input pulse; (b) First-order differential signal; (c)Second-order differential signal. Insert in (b): Hermite-Gaussian waveform (q ¼ ð0; 1; 0Þ; φ ¼ ð0; 0; 0Þ); Insert in (c): Pulse waveform with one main peak and two sidelobes (q ¼ ð0; 0; 1Þ; φ ¼ ð0; 0; 0Þ). 26

1

Microelectronics Journal 88 (2019) 25–28

(a)

Normalized Intensity

Normalized Intensity

X. Dong, J. Qi

0.8 0.6 0.4 0.2 0 -50

-25

0

25

1

Table 1 Optimized relative amplitude and phase factors of the synthesized waveforms.

(b)

0.8 0.6

0 -50

50

-25

0

25

Normalized Intensity

(a)

0.6 0.4 0.2

(b)

Normalized Intensity

Normalized Intensity

1

0

0.8 0.6 0.4 0.2 0 -80

-40

0

Time /ps

40

80

10

1

Sech-shape input pulse Amplitude

Phase

φ ¼ ð0; 0:5π ; 0Þ φ ¼ ð0; 0:37π ; 0Þ φ ¼ ð0; 0:63π ; 0Þ

q ¼ ð1; 0:4; 0:08Þ q ¼ ð1; 0:4; 0:08Þ q ¼ ð1; 0:4; 0:08Þ

φ ¼ ð0; 0:5π ; 0Þ φ ¼ ð0; 0:37π ; 0Þ φ ¼ ð0; 0:63π ; 0Þ

phase factors are: q ¼ ð1; 0:4; 0:08Þ, φ ¼ ð0; 0:5π ; 0Þ. Fig. 5(b)(c) are the synthesized asymmetric triangular waveforms from sech-shape input pulse with FWHM ¼ 20ps. The optimized relative amplitude and phase factors are: q ¼ ð1; 0:4;0:08Þ, φ ¼ ð0; 0:37π ; 0Þ and q ¼ ð1; 0:4; 0:08Þ φ ¼ ð0; 0:63π ; 0Þ, respectively. Table 1 list all the relative amplitude and phase factors of the synthesized waveforms above. Compared with the results of Gaussian input pulse, only the relative amplitude (q2 ) of second-order differential signals need to be tuned as the input pulse changing. When the input pulses with different temporal duration are used, it can be easily proven that the optimized relative amplitude and phase factors don't need tuning. The temporal duration of synthesized output pulse is approximately proportional to the input pulse. This is convenient for practical realization of output pulse with a certain range of duration.

0.8

Time /ps

Phase

q ¼ ð1; 0:4; 0:18Þ q ¼ ð1; 0:4; 0:18Þ q ¼ ð1; 0:4; 0:18Þ

Asymmetric triangular 1 Asymmetric triangular 2

50

Time /ps

-10

Amplitude

Flat-top 0.2

Fig. 4. Synthesized (black solid line) and targeted (blue dash line) asymmetric triangular waveforms with opposite sharp edges. The optimized amplitude and phase factors are: (a) q ¼ ð1; 0:4; 0:18Þ; φ ¼ ð0; 0:37π ; 0Þ; (b)q ¼ ð1; 0:4; 0:18Þ; φ ¼ ð0; 0:63π ; 0Þ, respectively.

0 -20

Gaussian input pulse

0.4

Time /ps

1

Synthesized waveforms

20

(c)

0.8

4. Conclusions

0.6

In this paper, we propose a much compact configurable optical pulse synthesizer by employing only two microring-resonators. Some interesting features of the proposed approach are demonstrated. First, by tuning only the relative phase (φ1 ) of the first-order derivative signal, this structure allows the synthesis of different output pulse waveforms (e.g. flat-top, asymmetric triangular) from a fixed input pulse source. Second, when the input pulse source is changed (e.g. Gaussian input pulse is changed into Sech-shape input pulse), the desired target pulse waveform can still be synthesized by tuning only the relative amplitude (q2 ) of the second-order differential signal. Third, the system is robust to a certain range of input pulse temporal duration and relative amplitude factors deviation, which are convenient for the dynamic configuration of practical application in the future.

0.4 0.2 0 -80

-40

0

Time /ps

40

80

Fig.5. (a)Synthesized flat-top waveform (black solid line) from sech-shape input pulse with FWHM ¼ 5ps (red dotted line). Amplitude and phase factors are: q ¼ ð1; 0:4; 0:08Þ, φ ¼ ð0:0:5π ; 0Þ; (b)(c) Synthesized asymmetric triangular waveform (black solid line) with opposite sharp edges from Sech-shape input pulse with FWHM ¼ 20ps (red dotted line). Amplitude and phase factors are: q ¼ ð1; 0:4; 0:08Þ, φ ¼ ð0; 0:37π ; 0Þ and q ¼ ð1; 0:4; 0:08Þ φ ¼ ð0; 0:63π ; 0Þ, respectively.

though the relative amplitude factor is deviated 20% from its optimal value, the fluctuations in the flat-top region are still less than 10% of the normalized intensity, as shown in Fig. 3(b)(According to the reviewer's suggestion, full intensity (from 0 to the top) has been provided in Fig. 3(b) for this revised manuscript.). Besides the aforementioned symmetric waveforms, our structure is also applied for synthesizing optical pulse with asymmetric temporal feature. By optimizing the relative amplitude and phase factors to q ¼ ð1; 0:4; 0:18Þ, φ ¼ ð0; 0:37π ; 0Þ and q ¼ ð1; 0:4; 0:18Þ, φ ¼ ð0; 0:63π ; 0Þ respectively, two asymmetric triangular waveforms with opposite sharp edges are achieved. Both of the obtained pulses show FWHM of 21ps and the corresponding results are given in Fig. 4(a) and Fig. 4(b). Due to only the relative phase (φ1 ) of first-order differential signal changes, this feature facilitates the practical dynamic configuration of various waveforms. Our proposed optical pulse synthesizer is by no means limited to Gaussian input pulse. Similar synthesizing capability can be applied for a variety of input pulses. For a sech-shape input optical pulse ain ðtÞ ¼ sec hðt=τ0 Þ, different output pulse waveforms can also be obtained by reoptimizing the relative amplitudes and phases. In addition, the proposed optical pulse synthesizer is tolerant to the variation of input pulse temporal duration. This is evaluated by injecting optical pulse with different FWHM. Fig. 5(a) is the synthesized flat-top waveform from sech-shape input pulse with FWHM ¼ 5ps. The optimized relative amplitude and

Acknowledgments Project supported by the Beijing Natural Science Foundation (Grant No. 4192022) and Foundation of China Scholarship Council (No. 201708110009). References [1] Frabcesca Parmigiani, Leif Katsuo Oxenlowe, Michael Galili, et al., All-optical 160Gbit/s retiming system using fiber grating based pulse shaping technology, J. Light. Technol. 27 (9) (2009) 1135–1141. [2] Francesca Parmigiani, Leif Katsuo Oxenlowe, Michael Galili, Morten Ibsen, Darko Zibar, Periklis Petropoulos, David J. Richardson, Anders Thomas Clausen, Palle Jeppesen, All-optical 160Gbit/s Retiming system using fiber grating based pulse shaping technology, J. Light. Technol. 27 (9) (2009) 1135–1141. [3] Jochen Schroder, A. Michael, F. Roelens, Liang B. Du, Arthur J. Lowery, Steve Frisken, Benjamin J. Eggleton, An optical FPGA: reconfigurable simultaneous multi-output spectral pulse-shaping for linear optical processing”, Optic Express 21 (1) (2013) 690–697. [4] Jeonghyun Huh, Azana Jose, Generation of high-quality parabolic pulses with optimized duration and energy by use of dispersive frequency-to-time mapping, Optic Express 23 (21) (2015) 27751–27762. [5] Shasha Liao, Yunhong Ding, Jianji Dong, Siqi Yan, Xu Wang, Xinliang Zhang, Photonic arbitrary waveform generator based on Taylor synthesis method, Optic Express 24 (21) (2016) 24390–24400. [6] M. Andrew, Weiner, “Ultrafast optical pulse shaping: a tutorial review”, Optic Commun. 284 (2011) 3669–3692.

27

X. Dong, J. Qi

Microelectronics Journal 88 (2019) 25–28 [11] H. Mohammad, Asghari, Josa Azana, Proposal and analysis of reconfigurable pulse shaping technique based on multi-arm optical differentiators, Optic Commun. 281 (2008) 4581–4588. [12] Reza Ashrafi, Mohammad H. Asghari, Azana Jose, Ultrafast optical arbitrary-order differentiators based on apodized long-period gratings, IEEE Photonics Journal 3 (3) (2011) 353–364. [13] Fangfei Liu, Tao Wang, Li Qiang, Ye Tong, Ziyang Zhang, Min Qiu, Yikai Su, Compact optical temporal differentiator based on silicon microring resonator, Optic Express 16 (20) (2008) 15880–15886.

[7] Shanhong You, Weidong Shao, Wenfeng Cai, Honglong Cao, M. Kavehrad, Analysis of ultrashort pulse shaping with programmable amplitude and phase masks, Chin. Optic Lett. 9 (3) (2011), 033201. [8] H.Y. Jiang, L.S. Yan, Y.F. Sun, et al., Photonic arbitrary waveform generation based on crossed frequency to time mapping, Optic Express 21 (5) (2013) 6488–6496. [9] Yang Jiang, Chuang Ma, Guangfu Bai, Xiaosi Qi, Yanlin Tang, Zhenrong Jia, Yuejiao Zi, Fengqin Huang, Tingwei Wu, Photonic microwave waveforms generation based on time-domain processing, Optic Express 23 (15) (2015), 1944219352. [10] Li Jing, Tigang Ning, Li Pei, Jian Wei, Haidong You, Hongyao Chen, Chan Zhang, Photonic-assisted periodic triangular-shaped pulses generation with tunable repetition rate, IEEE Photonics Technol. Lett. 25 (10) (2013) 952–954.

28