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Photonic generation of frequency-doubled microwave waveform based on a PDM-MZM modulator
Journal Pre-proof Photonic generation of frequency-doubled microwave waveform based on a PDM-MZM modulator Yuanyuan Li, Aijun Wen, Yong Zhang, Mingquan Liang
PII: DOI: Reference:
S0030-4018(19)30925-3 https://doi.org/10.1016/j.optcom.2019.124756 OPTICS 124756
To appear in:
Optics Communications
Received date : 11 September 2019 Revised date : 12 October 2019 Accepted date : 12 October 2019 Please cite this article as: Y. Li, A. Wen, Y. Zhang et al., Photonic generation of frequency-doubled microwave waveform based on a PDM-MZM modulator, Optics Communications (2019), doi: https://doi.org/10.1016/j.optcom.2019.124756. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.
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The Revised Paper Click here to view linked References
Photonic Generation of Frequency-doubled Microwave Waveform based on a PDM-MZM Modulator
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State Key Laboratory on Integrated Services Networks, Xidian University, No.2 South Taibai
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Road, Xi’an 710071, China 2
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Yuanyuan Li1,2, Aijun Wen1,2,*, Yong Zhang 1,2, Mingquan, Liang1,2
Collaborative Innovation Center of Information Sensing and Understanding at Xidian University, No.2 South Taibai Road, Xi’an 710071, China
Abstract
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A novel and simple photonic approach for frequency-doubled microwave waveforms generation based on a polarization division multiplexing Mach-Zehnder modulator (PDM-MZM) is proposed and experimentally demonstrated. The PDM-MZM is driven by a local oscillation (LO) signal through a 90 degree hybrid coupler. One sub-modulator of the PDM-MZM is biased at the peak
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transmission point and the other sub-modulator is biased at the null transmission point. The optical signals from the two arms are polarization multiplexed at the output of the PDM-MZM and then injected into a photodetector (PD) for photoelectrical conversion. By properly controlling the amplitudes of the LO signal, the triangular and square waveforms with a repetition rate twice the frequency of the LO signal can be generated. This scheme has features of compact, low-cost structure and simple operation. Simultaneously, the frequency of the generated waveform can be tuned over a wide bandwidth since there is no optical or electrical filter involved.
Keywords: Photonic microwave waveform generation; Triangular waveform; Square waveform; Doubling frequency.
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*Corresponding author. Tel./fax: +86 29 88204468 E-mail address: [email protected] (A. Wen)
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1. Introduction Microwave arbitrary waveform generation has attracted much attention during the past few years for its wide applications in various fields, such as radio frequency (RF) communication
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systems, modern radar, instrumentation measurements and so on [1-3]. Traditionally, arbitrary waveform signals are generated in the electrical domain, but the repetition rates of the generated
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arbitrary waveforms are usually small due to low frequency and small bandwidth of the electronic devices. Microwave photonic technology takes the advantages of wide and high frequency operation, light weight and immunity to electromagnetic interference. In recent years, microwave photonic technology has been widely used in various fields, such as photonic radar system and radio-over-fiber (RoF) system [4-6]. Photonic-assisted arbitrary waveform generation is a typical
arbitrary waveform generation.
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application, which provides new access to solving the electronic bottleneck problem of microwave
The triangular waveform that featured with linearly raising and falling edge in optical intensity has lots of advantages over any other waveforms. For instance, it is considered as a good choice
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for all-optical wavelength conversion, optical pulse compression and testing [7, 8]. Square waveform is also a classic waveform among a great variety of microwave arbitrary waveforms. Many schemes for generating triangular and square waveforms in the optical domain have been proposed so far. One typical approach is the optical spectra shaping method combined with frequency-to-time mapping [9, 10]. It uses optical spectral shapers, such as spatial light modulator and the fiber-optic spectral filter, to shape the spectral line first and then to do frequency-to-time mapping. This method, however, can only generate triangular waveforms with small duty cycle (<1). Compared with previous methods, external modulation of a continuous wave (CW) is a promising solution due to tunable frequencies of radio frequency signals and full duty cycle of the generated triangular pulses (=1).
Different methods based on external modulation have been verified in recent years [11-25]. Most of them focus on frequency-domain synthesis, where the waveforms are obtained by
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processing the amplitude and phase of different harmonic components. Based on the frequency-domain synthesis principle, so far, many photonics-assisted microwave waveform generators have been provided for triangular waveform and square waveform generation.
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However, the generated microwave waveform has a relatively low repetition rate, which is the same as the frequency of the driving signal [12-18]. To increase the repetition rate, a variety of frequency-doubled methods for microwave waveforms generation are proposed [19-26].
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Frequency double indicates that high-speed signals can be obtained with low-speed components, which will make the system cost effective and simple in architecture. In [19, 20], triangular
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waveform was generated by using a Mach-Zehnder modulator and a segment of fiber. These approaches have simple structures and cost less. However, the phase shift introduced by the dispersion fiber is frequency dependent, which limits the frequency tunable range. In [21], a MZM modulator and a spectrum shaper were used to produce triangular waveform with doubling frequency. But the use of optical-interleaver and fiber bragg grating limits the bandwidth of the
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system. Ref. [22, 23] proposed two different waveform generation methods based on cascaded modulator structures to generate triangular or square waveforms. These methods require no optical filters, but the cascaded modulator structures are relatively complex and have low stability. Another two photonic methods employing an integrated DP-QPSK modulator were proposed in
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[24, 25]. These methods have the advantage of relatively simple structure. But the DP-QPSK modulator requires six direct current (DC) biases, which may be seriously affected by bias drift and has poor stability. In addition, only triangular waveform was generated in Ref. [24], while only simulation was carried without experimental verification in [25]. In [26], a PDM-MZM modulator and a frequency tripler were used to produce double-frequency triangular waveforms. The use of frequency tripler will introduce other interference harmonics, which will deteriorate the performance of the generated waveforms.
In this paper, we propose a novel and simple photonic approach to generating frequency-doubled triangular and square-shaped waveforms by using a PDM-MZM modulator. One sub-modulator of the PDM-MZM modulator driven by a local oscillation (LO) signal is biased at the peak transmission point. The other sub-modulator of the PDM-MZM, driven by the same LO signal with a 90° phase shift, is biased at the null transmission point. The signal output
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from the PDM-MZM is orthogonal polarization multiplexed. Then the two signals in different polarization states enter the PD for photoelectric detection. By properly adjusting the power of the LO driving signal, triangular and square-shaped waveforms can be observed and the repetition
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rates of them are two times that of the LO signal. An experiment is performed to verify the feasibility. Triangular and square-shaped waveforms with repetition rates of 4 GHz and 6 GHz are
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successfully generated by using 2 GHz and 3 GHz LO driving signals, respectively.
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2. Operational principle and simulation analysis
Fig. 1. Schematic of the proposed photonics-assisted microwave waveform generator. LD, laser diode; PC, polarization controller; LO, local oscillator; PDM-MZM, polarization division multiplexing Mach–Zehnder modulator; 90° PR, 90° polarization rotator; PD, photodetector.
The schematic of the proposed photonics-assisted microwave waveform generator is shown in Figure.1. A light wave from a laser diode (LD) is injected into the PDM-MZM modulator. Mathematically, the optical carrier from the LD can be written as Ein t E0 exp jct , where E0 and c represent the amplitude and the angular frequency of the optical carrier, respectively.
The architecture of the PDM-MZM is showed in Fig.1 (a), consisting of a Y-shaped power divider, two sub-modulators (MZM1 and MZM2), a 90° polarization rotator and a polarization beam combiner (PBC). MZM1 is biased at the peak transmission point to generate even-order sidebands
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and MZM2 is biased at the null transmission point to generate odd-order sidebands. MZM1 and MZM2 are driven by the same LO signal generated from a microwave signal source, but the LO signal is input into MZM2 with a 90° phase shift. The LO signal is expressed as VLO V0 cos mt ,
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where V0 and m are the amplitude and the angular frequency of the LO signal. The signals output from MZM1 and MZM2 are given by 2 Ein exp( jm cos m t ) exp( jm cos m t ) 4 2 Ein = cos(m cos m t ) 2 n 2 Ein = J 0 (m)+ 2 (-1) J 2n (m)cos (2nm t ) 2 n=1
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EMZM 1 (t )
2 Ein exp( jm sin m t ) exp( jm sin m t ) 4 2 Ein = j sin(m sin m t ) 2 2 Ein = j 2 J 2n 1 (m) sin((2n 1)m t ) 2 n=1
EMZM 2 (t )
(1)
(2)
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V where is the insertion loss of the two sub-modulators, m 0 V is defined as the modulation
depth and V is the half-wave voltage of MZM1 and MZM2. The optical spectra of the signals at
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the output of MZM1 and MZM2 are shown in Fig.1 (b-c). Then the two signals are polarization multiplexed at the output of the PDM-MZM and the polarization multiplexed signal can be expressed as (t ) E EPDM MZM (t ) MZM 1 E MZM 2 (t )
2 Ein n J 0 (m)+ 2 (-1) J 2n (m)cos(2nm t ) 2 n=1 = 2 Ein j 2 J (m) sin((2n 1) t ) m 2n 1 2 n=1
(3)
The polarization multiplexed signal at the output of the PDM-MZM is then sent into the PD for photoelectric detection. The electrical current after PD is given by * I PD (t ) EMZM 1 E *MZM 1 EMZM 2 EMZM 2
E02 1 cos(2m cos m t ) 1 cos(2m sin m t) 4 2 n E0 = 1+ (-1) J 2n (2 m) cos( 2nm t ) J 2n (2m) cos( 2nm t ) 2 n=1 n=1 =
=I dc
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(4)
E02 J 4n 2 (2m) cos[(4n 2)m t ] 2 n=0
Where is the responsivity of the photodetector. Ignoring the higher-order items, equation (4)
can be rewritten as
I PD I dc
E02 J 2 (2m) cos(2mt ) J 6 (2m) cos(6mt ) 2
(5)
In principle, the approximate Fourier series expansion of a triangular waveform and a square
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waveform can be written as 1 1 Ttri (t ) n 2 cos(nt ) cos(t ) 9 cos(3t ) n 1,3 1 1 T (t ) sin(nt ) sin(t ) sin(3t ) squ 3 n 1,3 n
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(6)
By comparing equation (5) and (6) (letting 2m ), we can see that the triangular and square waveforms can be obtained under the following conditions, respectively.
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J 2 (2m) 9 J 6 (2m) J 2 (2m) 3 J 6 (2m)
(7)
According to equation (7), by properly adjusting the modulator index, namely the power of the LO signal, triangular and square waveforms can be generated. To generate triangular and square
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waveforms, the modulation indexes should be set to 1.95 and 2.22, respectively. It should be noted that an electrical 90° hybrid coupler is needed after the PD to satisfy the phase relationship when generating square waveforms.
Considering the finite extinction ratio (ER) of the modulator, we verified the effect of different
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ERs on waveform generation. Equation (3) and (4) can be rewritten as
(t ) E EPDM MZM (t ) MZM 1 EMZM 2 (t ) jm cos m t 1 2 e jm cos m t 2 Ein e 4 e jm sin m t 1 2 e jm sin m t
(8)
* I PD (t ) EMZM 1 E *MZM 1 EMZM 2 EMZM 2
E02 1 2 1 2 8 E02 =Idc 2 1 2 4 =
cos(2m cos m t ) 1 2 1 2 cos(2m sin m t )
J
n=0
4n 2
(9)
(2m) cos[(4n 2)m t ]
Where is the power splitter ratio of the two arms of the MZM1 and MZM2. The ER can be 2 defined as ER 1 . According to equation (9), we can find that the power ratio between 2
1
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the 2nd-order and the 6th-order components is not affected by the ER of the modulator. It is proved that the generated waveforms is almost unaffected by ER of the modulator. In order to demonstrate the function of the proposed approach, simulation analysis is carried out
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based on the computer software VPIphotonics Analyzer. A 3GHz LO signal is used to drive the PDM-MZM. The half-wave voltage of the two sub-modulators of PDM-MZM is set as 5 V and the extinction ratio is 35 dB. According to equation (7), the amplitude of the LO signal is set to
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3.105 and 3.535 to generate triangular waveform and square waveform respectively. The simulated electrical spectra and waveforms are shown in Fig.2. The power ratio of the 2nd-order
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and 6th-order harmonics of triangular waveform is 19.07 dB, as shown in Fig. 2(a). For the square waveform, the power ratio between the two frequencies is 9.5 dB, as shown in Fig. 2(c). We also calculate the root-mean square errors (RMSEs) of the waveforms to measure the error between simulated results and ideal value. The calculated RMSEs of the triangular waveform and square waveform are 0.0311 and 0.326 respectively, which are close to the ideal values of 0.0279 and
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0.3147. As can be seen in Fig.1 (b) and (d), the generated triangular waveform and square
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waveform both have a repetition rate of the 6 GHz, twice as that of the LO signal.
Fig. 2. Simulated electrical spectra and corresponding waveforms of the triangular waveform
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(a-b) and square waveform (c-d) with frequency of 6 GHz.
3. Experiment and discussion
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An experiment based on the configuration shown in Fig.1 is performed to verify the effectiveness of the proposed approach. A laser (LD, Emcore1782) operating at 1552.11 nm with
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an output optical power of 10dBm and a linewidth about 1 MHz is directly sent into the PDM-MZM modulator (Fujitsu, FTM7980EDA). The half-wave voltage and bandwidth of the
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PDM-MZM are 3.5V and 40 GHz, respectively. A microwave vector signal generated by a signal generator (LO, Rohde & Schwarz SMW200A) is split into two paths by an electrical 90° hybrid coupler, which can introduce a 90° phase difference between the two LO signals applied to MZM1
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and MZM2. The MZM1 is biased at the peak transmission point to generate the even-order optical sidebands. The MZM2 is biased at the null transmission point to generate the odd-order optical sidebands. In the experiment, we observe the polarization-multiplexed signal at the output of the
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PDM-MZM by using a PBS. As can be seen Fig. 3(a), the X-Polarized direction only contains the even-order sidebands, while the Y-Polarized direction shown in Fig. 3(b) only includes the odd-order sidebands.
Fig. 3. Optical spectra of the polarization multiplexed signal. (a) the X-Polarized signal; (b) the Y-Polarized signal.
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A.
Triangular waveform signals
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Fig. 4. Measured spectrum and waveforms. (a, b) electrical spectrum of the generated triangular waveforms with frequencies of 4-GHz and 6-GHz, (c, d) the corresponding waveforms.
The polarization-multiplexed optical signal is sent into the PD for photoelectric conversion. A
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PD (MPRV1331) with working bandwidth of 31GHz is applied. An electrical analyzer (R&S, FSV-30) which has a working bandwidth of 30 GHz and an oscilloscope (Keysight, DSOV334A) with sampling rate of 80GSa/s is used to analyze the electrical signals and waveforms. By appropriately adjusting the power of the LO driving signal, triangular and square waveforms are successfully generated. Fig. 4(a, b) show the electrical spectrum and Fig.4(c, d) are the generated triangular waveforms by applying 2-GHz and 3-GHz microwave signals, respectively. It can be observed that triangular waveforms with frequencies of 4 GHz and 6 GHz are produced and the power ratio between the 2nd-order and the 6th-order components are 19.19 dB and 19.23 dB, respectively, which is on the verge of ideal value (19.08 dB). Simultaneously, we have calculated the RMSEs of the experimentally generated triangular waveforms with frequencies of 4GHz and 6GHz, which are 0.0425 and 0.0492, respectively. The theoretical RMSE of the triangular waveforms approximated by the first two Fourier series components is 0.028. Compared with the
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simulated RMSE, the RMSEs of the practical waveforms exist deteriorations. This is because that the simulated analysis can suppress the spurious harmonics completely, while the experiment can’t. The appearance of the undesired harmonics leads to the deterioration of waveform performance.
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Square waveform
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B.
Fig. 5. Measured spectrum and waveforms. (a, b) electrical spectrum of square waveforms with frequencies of 4-GHz and 6-GHz, (c, d) the corresponding waveforms.
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The experimentally measured spectrum and waveforms of the generated square waveforms are shown in Fig. 5. Square waveforms with frequencies of 4 GHz and 6 GHz are generated by using 2 GHz and 3 GHz LO signals, respectively. The power ratio between the 2nd-order and the 6th-order frequencies are 9.64 dB and 9.61 dB, closing to the ideal value of 9.54 dB. The RMSEs of the experimentally generated square waveforms are also calculated, which are 0.344 and 0.3416, respectively.
From the above experiment results, we can see that there are some undesired harmonics existing in the electrical spectra and the RMSEs of the experimentally generated triangular and square waveforms have a little deterioration. The harmonics actually appear from the nonlinear transfer function of the MZM. But the extinction ratio and the direct current (DC) bias voltage of MZM can influence the amplitudes of the harmonic components. Under small signal modulation, when bias voltages are precise and extinction ratios is high, the magnitude of undesirable harmonics is
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very small and they are even not present. For example, if the DC bias voltage of MZM2 is deviated from the null transmission point, the optical carrier and other even-order sideband can’t be suppressed completely in the case of the finite extinction ratio. Thus, after photoelectric
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conversion, many undesirable harmonics occur in the electrical spectra, which influence the quality of waveforms. Similarly, if the DC bias voltage of MZM1 is deviated from the peak transmission point, there will be also many harmonic spurious harmonics. This problem can be
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mitigated by using DC source with higher adjustment precision. Meanwhile, the imprecise phase shift of the electrical 90° hybrid coupler is also responsible for the appearance of the undesirable
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harmonics. 4. CONCLUSION
In this work, we provided and verified a simple and tunable frequency-doubled triangular and square waveforms generator based on a PDM-MZM modulator. In this approach, triangular and square waveforms with repetition rates twice the frequency of the microwave reference signals are
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generated, which means that high-speed signals can be obtained by using low-speed components. The proposed structure uses no electrical or optical filter, so the systemic frequency tuning range and working bandwidth are not limited by filters. It’s worthy to point out that a much larger frequency tuning range than the demonstrated results can be achieved, which is restricted by the
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frequency dependent devices such as PD and electrical analyzer. Acknowledgments
This work was supported in part by the National Key Research and Development Program of China (2017YFB1104800), the National Natural Science Foundation of China (No. 61674119), the National Postdoctoral Program For innovative Talents in China (BX201600118), the Young Talent fund of University Association for Science and Technology in Shaanxi, China (20160109), the project funded by China Postdoctoral Science Foundation (No. 2017M613072), the Natural Science Basic Research Plan in Shaanxi Province of China(2017JM6002), the Key Research and Development Program from Government of Shaanxi Province(2017GY-093) Reference
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microwave waveforms via a dual-polarization modulator,” Optics Communications, vol. 384, pp. 1-6, Feb. 2017.
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PII: DOI: Reference:
S0030-4018(19)30925-3 https://doi.org/10.1016/j.optcom.2019.124756 OPTICS 124756
To appear in:
Optics Communications
Received date : 11 September 2019 Revised date : 12 October 2019 Accepted date : 12 October 2019 Please cite this article as: Y. Li, A. Wen, Y. Zhang et al., Photonic generation of frequency-doubled microwave waveform based on a PDM-MZM modulator, Optics Communications (2019), doi: https://doi.org/10.1016/j.optcom.2019.124756. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.
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The Revised Paper Click here to view linked References
Photonic Generation of Frequency-doubled Microwave Waveform based on a PDM-MZM Modulator
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State Key Laboratory on Integrated Services Networks, Xidian University, No.2 South Taibai
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Road, Xi’an 710071, China 2
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Yuanyuan Li1,2, Aijun Wen1,2,*, Yong Zhang 1,2, Mingquan, Liang1,2
Collaborative Innovation Center of Information Sensing and Understanding at Xidian University, No.2 South Taibai Road, Xi’an 710071, China
Abstract
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A novel and simple photonic approach for frequency-doubled microwave waveforms generation based on a polarization division multiplexing Mach-Zehnder modulator (PDM-MZM) is proposed and experimentally demonstrated. The PDM-MZM is driven by a local oscillation (LO) signal through a 90 degree hybrid coupler. One sub-modulator of the PDM-MZM is biased at the peak
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transmission point and the other sub-modulator is biased at the null transmission point. The optical signals from the two arms are polarization multiplexed at the output of the PDM-MZM and then injected into a photodetector (PD) for photoelectrical conversion. By properly controlling the amplitudes of the LO signal, the triangular and square waveforms with a repetition rate twice the frequency of the LO signal can be generated. This scheme has features of compact, low-cost structure and simple operation. Simultaneously, the frequency of the generated waveform can be tuned over a wide bandwidth since there is no optical or electrical filter involved.
Keywords: Photonic microwave waveform generation; Triangular waveform; Square waveform; Doubling frequency.
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*Corresponding author. Tel./fax: +86 29 88204468 E-mail address: [email protected] (A. Wen)
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1. Introduction Microwave arbitrary waveform generation has attracted much attention during the past few years for its wide applications in various fields, such as radio frequency (RF) communication
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systems, modern radar, instrumentation measurements and so on [1-3]. Traditionally, arbitrary waveform signals are generated in the electrical domain, but the repetition rates of the generated
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arbitrary waveforms are usually small due to low frequency and small bandwidth of the electronic devices. Microwave photonic technology takes the advantages of wide and high frequency operation, light weight and immunity to electromagnetic interference. In recent years, microwave photonic technology has been widely used in various fields, such as photonic radar system and radio-over-fiber (RoF) system [4-6]. Photonic-assisted arbitrary waveform generation is a typical
arbitrary waveform generation.
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application, which provides new access to solving the electronic bottleneck problem of microwave
The triangular waveform that featured with linearly raising and falling edge in optical intensity has lots of advantages over any other waveforms. For instance, it is considered as a good choice
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for all-optical wavelength conversion, optical pulse compression and testing [7, 8]. Square waveform is also a classic waveform among a great variety of microwave arbitrary waveforms. Many schemes for generating triangular and square waveforms in the optical domain have been proposed so far. One typical approach is the optical spectra shaping method combined with frequency-to-time mapping [9, 10]. It uses optical spectral shapers, such as spatial light modulator and the fiber-optic spectral filter, to shape the spectral line first and then to do frequency-to-time mapping. This method, however, can only generate triangular waveforms with small duty cycle (<1). Compared with previous methods, external modulation of a continuous wave (CW) is a promising solution due to tunable frequencies of radio frequency signals and full duty cycle of the generated triangular pulses (=1).
Different methods based on external modulation have been verified in recent years [11-25]. Most of them focus on frequency-domain synthesis, where the waveforms are obtained by
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processing the amplitude and phase of different harmonic components. Based on the frequency-domain synthesis principle, so far, many photonics-assisted microwave waveform generators have been provided for triangular waveform and square waveform generation.
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However, the generated microwave waveform has a relatively low repetition rate, which is the same as the frequency of the driving signal [12-18]. To increase the repetition rate, a variety of frequency-doubled methods for microwave waveforms generation are proposed [19-26].
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Frequency double indicates that high-speed signals can be obtained with low-speed components, which will make the system cost effective and simple in architecture. In [19, 20], triangular
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waveform was generated by using a Mach-Zehnder modulator and a segment of fiber. These approaches have simple structures and cost less. However, the phase shift introduced by the dispersion fiber is frequency dependent, which limits the frequency tunable range. In [21], a MZM modulator and a spectrum shaper were used to produce triangular waveform with doubling frequency. But the use of optical-interleaver and fiber bragg grating limits the bandwidth of the
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system. Ref. [22, 23] proposed two different waveform generation methods based on cascaded modulator structures to generate triangular or square waveforms. These methods require no optical filters, but the cascaded modulator structures are relatively complex and have low stability. Another two photonic methods employing an integrated DP-QPSK modulator were proposed in
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[24, 25]. These methods have the advantage of relatively simple structure. But the DP-QPSK modulator requires six direct current (DC) biases, which may be seriously affected by bias drift and has poor stability. In addition, only triangular waveform was generated in Ref. [24], while only simulation was carried without experimental verification in [25]. In [26], a PDM-MZM modulator and a frequency tripler were used to produce double-frequency triangular waveforms. The use of frequency tripler will introduce other interference harmonics, which will deteriorate the performance of the generated waveforms.
In this paper, we propose a novel and simple photonic approach to generating frequency-doubled triangular and square-shaped waveforms by using a PDM-MZM modulator. One sub-modulator of the PDM-MZM modulator driven by a local oscillation (LO) signal is biased at the peak transmission point. The other sub-modulator of the PDM-MZM, driven by the same LO signal with a 90° phase shift, is biased at the null transmission point. The signal output
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from the PDM-MZM is orthogonal polarization multiplexed. Then the two signals in different polarization states enter the PD for photoelectric detection. By properly adjusting the power of the LO driving signal, triangular and square-shaped waveforms can be observed and the repetition
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rates of them are two times that of the LO signal. An experiment is performed to verify the feasibility. Triangular and square-shaped waveforms with repetition rates of 4 GHz and 6 GHz are
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successfully generated by using 2 GHz and 3 GHz LO driving signals, respectively.
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2. Operational principle and simulation analysis
Fig. 1. Schematic of the proposed photonics-assisted microwave waveform generator. LD, laser diode; PC, polarization controller; LO, local oscillator; PDM-MZM, polarization division multiplexing Mach–Zehnder modulator; 90° PR, 90° polarization rotator; PD, photodetector.
The schematic of the proposed photonics-assisted microwave waveform generator is shown in Figure.1. A light wave from a laser diode (LD) is injected into the PDM-MZM modulator. Mathematically, the optical carrier from the LD can be written as Ein t E0 exp jct , where E0 and c represent the amplitude and the angular frequency of the optical carrier, respectively.
The architecture of the PDM-MZM is showed in Fig.1 (a), consisting of a Y-shaped power divider, two sub-modulators (MZM1 and MZM2), a 90° polarization rotator and a polarization beam combiner (PBC). MZM1 is biased at the peak transmission point to generate even-order sidebands
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and MZM2 is biased at the null transmission point to generate odd-order sidebands. MZM1 and MZM2 are driven by the same LO signal generated from a microwave signal source, but the LO signal is input into MZM2 with a 90° phase shift. The LO signal is expressed as VLO V0 cos mt ,
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where V0 and m are the amplitude and the angular frequency of the LO signal. The signals output from MZM1 and MZM2 are given by 2 Ein exp( jm cos m t ) exp( jm cos m t ) 4 2 Ein = cos(m cos m t ) 2 n 2 Ein = J 0 (m)+ 2 (-1) J 2n (m)cos (2nm t ) 2 n=1
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EMZM 1 (t )
2 Ein exp( jm sin m t ) exp( jm sin m t ) 4 2 Ein = j sin(m sin m t ) 2 2 Ein = j 2 J 2n 1 (m) sin((2n 1)m t ) 2 n=1
EMZM 2 (t )
(1)
(2)
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V where is the insertion loss of the two sub-modulators, m 0 V is defined as the modulation
depth and V is the half-wave voltage of MZM1 and MZM2. The optical spectra of the signals at
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the output of MZM1 and MZM2 are shown in Fig.1 (b-c). Then the two signals are polarization multiplexed at the output of the PDM-MZM and the polarization multiplexed signal can be expressed as (t ) E EPDM MZM (t ) MZM 1 E MZM 2 (t )
2 Ein n J 0 (m)+ 2 (-1) J 2n (m)cos(2nm t ) 2 n=1 = 2 Ein j 2 J (m) sin((2n 1) t ) m 2n 1 2 n=1
(3)
The polarization multiplexed signal at the output of the PDM-MZM is then sent into the PD for photoelectric detection. The electrical current after PD is given by * I PD (t ) EMZM 1 E *MZM 1 EMZM 2 EMZM 2
E02 1 cos(2m cos m t ) 1 cos(2m sin m t) 4 2 n E0 = 1+ (-1) J 2n (2 m) cos( 2nm t ) J 2n (2m) cos( 2nm t ) 2 n=1 n=1 =
=I dc
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(4)
E02 J 4n 2 (2m) cos[(4n 2)m t ] 2 n=0
Where is the responsivity of the photodetector. Ignoring the higher-order items, equation (4)
can be rewritten as
I PD I dc
E02 J 2 (2m) cos(2mt ) J 6 (2m) cos(6mt ) 2
(5)
In principle, the approximate Fourier series expansion of a triangular waveform and a square
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waveform can be written as 1 1 Ttri (t ) n 2 cos(nt ) cos(t ) 9 cos(3t ) n 1,3 1 1 T (t ) sin(nt ) sin(t ) sin(3t ) squ 3 n 1,3 n
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(6)
By comparing equation (5) and (6) (letting 2m ), we can see that the triangular and square waveforms can be obtained under the following conditions, respectively.
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J 2 (2m) 9 J 6 (2m) J 2 (2m) 3 J 6 (2m)
(7)
According to equation (7), by properly adjusting the modulator index, namely the power of the LO signal, triangular and square waveforms can be generated. To generate triangular and square
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waveforms, the modulation indexes should be set to 1.95 and 2.22, respectively. It should be noted that an electrical 90° hybrid coupler is needed after the PD to satisfy the phase relationship when generating square waveforms.
Considering the finite extinction ratio (ER) of the modulator, we verified the effect of different
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ERs on waveform generation. Equation (3) and (4) can be rewritten as
(t ) E EPDM MZM (t ) MZM 1 EMZM 2 (t ) jm cos m t 1 2 e jm cos m t 2 Ein e 4 e jm sin m t 1 2 e jm sin m t
(8)
* I PD (t ) EMZM 1 E *MZM 1 EMZM 2 EMZM 2
E02 1 2 1 2 8 E02 =Idc 2 1 2 4 =
cos(2m cos m t ) 1 2 1 2 cos(2m sin m t )
J
n=0
4n 2
(9)
(2m) cos[(4n 2)m t ]
Where is the power splitter ratio of the two arms of the MZM1 and MZM2. The ER can be 2 defined as ER 1 . According to equation (9), we can find that the power ratio between 2
1
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the 2nd-order and the 6th-order components is not affected by the ER of the modulator. It is proved that the generated waveforms is almost unaffected by ER of the modulator. In order to demonstrate the function of the proposed approach, simulation analysis is carried out
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based on the computer software VPIphotonics Analyzer. A 3GHz LO signal is used to drive the PDM-MZM. The half-wave voltage of the two sub-modulators of PDM-MZM is set as 5 V and the extinction ratio is 35 dB. According to equation (7), the amplitude of the LO signal is set to
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3.105 and 3.535 to generate triangular waveform and square waveform respectively. The simulated electrical spectra and waveforms are shown in Fig.2. The power ratio of the 2nd-order
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and 6th-order harmonics of triangular waveform is 19.07 dB, as shown in Fig. 2(a). For the square waveform, the power ratio between the two frequencies is 9.5 dB, as shown in Fig. 2(c). We also calculate the root-mean square errors (RMSEs) of the waveforms to measure the error between simulated results and ideal value. The calculated RMSEs of the triangular waveform and square waveform are 0.0311 and 0.326 respectively, which are close to the ideal values of 0.0279 and
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0.3147. As can be seen in Fig.1 (b) and (d), the generated triangular waveform and square
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waveform both have a repetition rate of the 6 GHz, twice as that of the LO signal.
Fig. 2. Simulated electrical spectra and corresponding waveforms of the triangular waveform
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(a-b) and square waveform (c-d) with frequency of 6 GHz.
3. Experiment and discussion
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An experiment based on the configuration shown in Fig.1 is performed to verify the effectiveness of the proposed approach. A laser (LD, Emcore1782) operating at 1552.11 nm with
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an output optical power of 10dBm and a linewidth about 1 MHz is directly sent into the PDM-MZM modulator (Fujitsu, FTM7980EDA). The half-wave voltage and bandwidth of the
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PDM-MZM are 3.5V and 40 GHz, respectively. A microwave vector signal generated by a signal generator (LO, Rohde & Schwarz SMW200A) is split into two paths by an electrical 90° hybrid coupler, which can introduce a 90° phase difference between the two LO signals applied to MZM1
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and MZM2. The MZM1 is biased at the peak transmission point to generate the even-order optical sidebands. The MZM2 is biased at the null transmission point to generate the odd-order optical sidebands. In the experiment, we observe the polarization-multiplexed signal at the output of the
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PDM-MZM by using a PBS. As can be seen Fig. 3(a), the X-Polarized direction only contains the even-order sidebands, while the Y-Polarized direction shown in Fig. 3(b) only includes the odd-order sidebands.
Fig. 3. Optical spectra of the polarization multiplexed signal. (a) the X-Polarized signal; (b) the Y-Polarized signal.
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A.
Triangular waveform signals
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Fig. 4. Measured spectrum and waveforms. (a, b) electrical spectrum of the generated triangular waveforms with frequencies of 4-GHz and 6-GHz, (c, d) the corresponding waveforms.
The polarization-multiplexed optical signal is sent into the PD for photoelectric conversion. A
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PD (MPRV1331) with working bandwidth of 31GHz is applied. An electrical analyzer (R&S, FSV-30) which has a working bandwidth of 30 GHz and an oscilloscope (Keysight, DSOV334A) with sampling rate of 80GSa/s is used to analyze the electrical signals and waveforms. By appropriately adjusting the power of the LO driving signal, triangular and square waveforms are successfully generated. Fig. 4(a, b) show the electrical spectrum and Fig.4(c, d) are the generated triangular waveforms by applying 2-GHz and 3-GHz microwave signals, respectively. It can be observed that triangular waveforms with frequencies of 4 GHz and 6 GHz are produced and the power ratio between the 2nd-order and the 6th-order components are 19.19 dB and 19.23 dB, respectively, which is on the verge of ideal value (19.08 dB). Simultaneously, we have calculated the RMSEs of the experimentally generated triangular waveforms with frequencies of 4GHz and 6GHz, which are 0.0425 and 0.0492, respectively. The theoretical RMSE of the triangular waveforms approximated by the first two Fourier series components is 0.028. Compared with the
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simulated RMSE, the RMSEs of the practical waveforms exist deteriorations. This is because that the simulated analysis can suppress the spurious harmonics completely, while the experiment can’t. The appearance of the undesired harmonics leads to the deterioration of waveform performance.
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Square waveform
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Fig. 5. Measured spectrum and waveforms. (a, b) electrical spectrum of square waveforms with frequencies of 4-GHz and 6-GHz, (c, d) the corresponding waveforms.
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The experimentally measured spectrum and waveforms of the generated square waveforms are shown in Fig. 5. Square waveforms with frequencies of 4 GHz and 6 GHz are generated by using 2 GHz and 3 GHz LO signals, respectively. The power ratio between the 2nd-order and the 6th-order frequencies are 9.64 dB and 9.61 dB, closing to the ideal value of 9.54 dB. The RMSEs of the experimentally generated square waveforms are also calculated, which are 0.344 and 0.3416, respectively.
From the above experiment results, we can see that there are some undesired harmonics existing in the electrical spectra and the RMSEs of the experimentally generated triangular and square waveforms have a little deterioration. The harmonics actually appear from the nonlinear transfer function of the MZM. But the extinction ratio and the direct current (DC) bias voltage of MZM can influence the amplitudes of the harmonic components. Under small signal modulation, when bias voltages are precise and extinction ratios is high, the magnitude of undesirable harmonics is
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very small and they are even not present. For example, if the DC bias voltage of MZM2 is deviated from the null transmission point, the optical carrier and other even-order sideband can’t be suppressed completely in the case of the finite extinction ratio. Thus, after photoelectric
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conversion, many undesirable harmonics occur in the electrical spectra, which influence the quality of waveforms. Similarly, if the DC bias voltage of MZM1 is deviated from the peak transmission point, there will be also many harmonic spurious harmonics. This problem can be
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mitigated by using DC source with higher adjustment precision. Meanwhile, the imprecise phase shift of the electrical 90° hybrid coupler is also responsible for the appearance of the undesirable
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harmonics. 4. CONCLUSION
In this work, we provided and verified a simple and tunable frequency-doubled triangular and square waveforms generator based on a PDM-MZM modulator. In this approach, triangular and square waveforms with repetition rates twice the frequency of the microwave reference signals are
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generated, which means that high-speed signals can be obtained by using low-speed components. The proposed structure uses no electrical or optical filter, so the systemic frequency tuning range and working bandwidth are not limited by filters. It’s worthy to point out that a much larger frequency tuning range than the demonstrated results can be achieved, which is restricted by the
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frequency dependent devices such as PD and electrical analyzer. Acknowledgments
This work was supported in part by the National Key Research and Development Program of China (2017YFB1104800), the National Natural Science Foundation of China (No. 61674119), the National Postdoctoral Program For innovative Talents in China (BX201600118), the Young Talent fund of University Association for Science and Technology in Shaanxi, China (20160109), the project funded by China Postdoctoral Science Foundation (No. 2017M613072), the Natural Science Basic Research Plan in Shaanxi Province of China(2017JM6002), the Key Research and Development Program from Government of Shaanxi Province(2017GY-093) Reference
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