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Advanced Photonics Congress (IPR, Networks, NOMA, PS, Sensors, SPPCom) © OSA 2017
Integrated Kerr Comb-based Reconfigurable Transversal Differentiator for Microwave Photonic Signal Processing Xingyuan Xu,1 Jiayang Wu,1 Mehrdad Shoeiby,2 Thach G. Nguyen,2 Sai T. Chu,3 Brent E. Little,4 Roberto Morandotti,5,6,7 Arnan Mitchell,2 and David J. Moss1,* 1
Centre for Micro-Photonics, Swinburne University of Technology, Hawthorn, VIC 3122, Australia 2 School of Engineering, RMIT University, Melbourne, VIC 3000, Australia Department of Physics and Material Science, City University of Hong Kong, Tat Chee Avenue, Hong Kong, China. 4 Xi’an Institute of Optics and Precision Mechanics Precision Mechanics of CAS, Xi’an, China. 5 INSR –Énergie, Matériaux et Télécommunications, 1650 Boulevard Lionel-Boulet, Varennes, Québec, J3X 1S2, Canada. 6 National Research University of Information Technologies, Mechanics and Optics, St. Petersburg, Russia. 7 Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 610054, China. Author e-mail address: *
[email protected] 3
Abstract: An integrated reconfigurable transversal differentiator is achieved based on an integrated nonlinear micro-ring resonator. The RF responses of different orders of differentiation are experimentally characterized. Systems demonstrations for Gaussian input signals are also performed. OCIS codes: (060.5625) Radio frequency photonics; (140.4780) Optical resonators; (190.7110) Ultrafast nonlinear optics.
1. Introduction In modern radar and communications systems, high-speed temporal differentiator has attracted great interests due to its wide applications in electrical signal generation, analyzing and processing. In light of photonic technologies’ rapid development, electronic bottleneck in terms of bandwidth and processing speed could be overcome by performing differentiation in optical domain [1], thus providing a competitive solution to meet the ever-increasing demand for processing speed and throughput. Many significant researches of optical temporal differentiator have been conducted in the last decade, although they offer many unique advantages, certain drawbacks of one form or another still exist and could greatly limit further applications. In [2], differentiator based on finite impulse response (FIR) delay-line structure was proposed where the taps were realized via discrete laser arrays. However, only first-order differentiation was demonstrated and the reconfigurability of the taps came at the expense of significantly increased cost and complexity. Another versatile differentiator based on a dual-drive Mach-Zehnder modulator was recently investigated [3], but the employed radio-frequency (RF) devices still imposed limitations on operating bandwidth. Other differentiators based on apodized fibre Bragg gratings [4] and critically-coupled silicon microring resonators (MRRs) [5] have also been reported, but these approaches either lack reconfigurability (in the former case), or involve stringent fabrication precision (in the latter case). In this paper, we report a reconfigurable transversal differentiator based on an integrated Kerr comb source and achieved first-order and second-order differentiation in one scheme. The Kerr frequency comb is generated by a MRR in Hydex glass [6], and forms a high-quality multi-wavelength source for the transversal filter [7], greatly reducing the cost, size, and complexity of the system. Moreover, by programming and shaping the comb accordingly, firstorder and second-order differentiation could be switched easily. It’s worth mentioning that, the large frequency spacing of the Kerr comb indicates an increased Nyquist zone, thus leading to a potential operation bandwidth of over 100 GHz. The RF magnitude and phase responses of the proposed differentiator are characterized, and systems demonstrations are performed for Gaussian input pulses. Good agreement between theory and experiment is obtained, verifying the effectiveness of our scheme. 2. Operation principle The spectral transfer function of an ideal temporal differentiator can be expressed as 𝐻(𝜔) = 𝑗(𝜔 − 𝜔0 )𝑁 ,
(1)
where ω and ω0 are the angular frequencies of the input signal and the carrier, respectively, and N is the order of the differentiator. The temporal first-order differentiation has a linear magnitude frequency response and a π phase jump at ω0, while second-order differentiation has a quadratic magnitude frequency response and linear phase at ω0. The ideal transfer function of Eq. (1) can be realized by a FIR transversal filter structure with a frequency response of −𝑗𝜔𝑛𝑇 𝐻(𝜔) = ∑𝑀−1 𝑛=0 𝑎𝑛 𝑒
(2)
where M is the number of taps, an is the tap coefficient of the nth tap, and T is the time delay between adjacent taps.
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Advanced Photonics Congress (IPR, Networks, NOMA, PS, Sensors, SPPCom) © OSA 2017
Fig. 1. (a) Schematic of the reconfigurable Kerr-comb-based microwave photonic differentiator. PUMP: Pump laser. EDFA: Erbium doped fibre amplifier. 1nm BPF: optical bandpass filter with 1nm bandwidth. OC: optical coupler. VNA: Vector network analyser. MZM: MachZehnder modulator. SMF: single mode fibre. PD: photodetector. (b) Picture of the fabricated Hydex MRR. (c) Optical spectrum of the generated Kerr comb in a 300-nm wavelength range. Inset shows zoom-in spectrum with a span of ~32 nm.
Fig. 1(a) illustrates our reconfigurable microwave photonic differentiator. It consists of two main modules: one is used for Kerr comb generation and shaping, the other performs a transversal filter. In the first module, a Kerr optical comb with almost equal line spacings was generated using an integrated Hydex MRR [6]. Fig. 1(b) shows the picture of fabricated Hydex MRR. Owing to the compact size and ultrahigh Q factor of the Hydex MRR, the generated Kerr comb provided a high quality multi-wavelength source for the subsequent transversal filter. Fig. 1(c) depicts the generated comb and gives details in the zoom-in view. As compared with more conventional laser diode array based differentiators [2], our cost, size and complexity were significantly reduced. The frequency comb then went through Waveshaper to shape the comb lines. The tap coefficients corresponding to differentiation operation were calculated based on the Remez algorithm [8]. Considering that negative tap coefficients were required, we employed a 2 2 balanced Mach-Zehnder modulator (MZM) in the second module [7]. It could simultaneously modulate the input RF signal on both the positive and negative slopes, thus yielding modulated signals with opposite phases and taps with negative coefficients. After being modulated, the tapped signals from one output of the MZM were delayed by a dispersive medium, then the tapped and delayed optical signals were combined, amplified, and converted to electrical signals before finally being sent to a vector network analyzer for characterization of RF amplitude and phase responses. Our scheme has a high degree of reconfigurability in free spectral range (FSR) and the order of differentiation. The time delay between adjacent taps was determined by the comb spacing and the accumulated dispersion. Therefore, the FSR of the differentiator can be easily adjusted by using different fibre lengths and different comb spacings. Moreover,
Fig. 2. Experimental results of proposed first-order and second-order differentiator. (a) Spectrum of the shaped optical comb, RF (b) amplitude and (c) phase responses of first-order differentiator; (d) Spectrum of the shaped optical comb, RF (e) amplitude and (f) phase responses of second-order differentiator.
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Advanced Photonics Congress (IPR, Networks, NOMA, PS, Sensors, SPPCom) © OSA 2017
Fig. 3. Measured temporal waveforms of (a) input Gaussian pulse, output pulse of (b) first-order and (c) second-order differentiator.
by adjusting tap coefficients via programming Waveshaper, different orders of differentiation could also be easily realized. 3. Experimental results In our experiment, the nonlinear MRR used to generate the Kerr comb was fabricated in the Hydex platform using CMOS compatible fabrication processes. The advantages of this platform include ultralow linear loss (~0.06 dB cm1 ), moderate nonlinearity parameter (~233 W-1 km-1), and particularly a negligible nonlinear loss up to extremely high intensities (~25 GW cm-2) [6]. The FSR of the MRR was ~1.6 nm, or ~200 GHz. Such a large FSR enables an increased potential Nyquist zone of over 100 GHz, which is difficult to achieve using mode-locked lasers and externallymodulated comb sources. By boosting the pump power to ~500 mW via an EDFA, a Type II Kerr optical comb was generated (Fig. 1(b)) over 200-nm wide, and flat over ~32 nm of the central spectrum. Several comb lines were selected and shaped by the waveshaper according to calculated tap coefficients. The calculated tap coefficients are [-0.0226, 0.0523, -0.1152, 1, -1, 0.1152, -0.052, 0.0226] for first-order differentiation, and [0.0241, -0.1107, 0.0881, 0.0881, 0.1107, 0.0241] for second-order differentiation. The optical spectrum after shaping is shown as Fig. 2 (a) and (d), which agree well with the ideal tap weights. The shaped comb lines were then divided into two parts according to the tap coefficients and fed into the 2×2 balanced MZM biased at quadrature, and propagated through 2.122-km of single mode fibre with a dispersion of 17.4 ps/(nm·km), corresponding to a time delay of ~59 ps between adjacent taps and yielding an effective FSR of ~16.9 GHz. The RF responses characterized by the vector network analyzer are shown in Fig. 2 (b), (c), (e), and (f). The amplitude frequency responses as well as the phase responses are consistent with theory. The phase error at the zero and null frequencies is attributed to filter tap coefficient errors, third-order dispersion in the fiber delay line and chirp of the MZM [7]. We also performed systems demonstrations of real-time signal differentiation for Gaussian input pulses. The Gaussian pulses generated by an arbitrary waveform generator are shown in Fig. 3(a), featuring a full width half maximum (FWHM) of ~0.12 ns. The output signal after differentiation was recorded by a fast sampling oscilloscope, as Fig. 3 (b) and (c) show, and the measured output waveforms agree well with theory, which further confirm the feasibility of our approach. 4. Acknowledgements This work was supported by the Australian Research Council Discovery Projects Program and NSERC Canada. 5. References [1] [2] [3] [4] [5] [6] [7] [8]
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