- Email: [email protected]
Photonic generation of microwave waveforms based on a dual-loop optoelectronic oscillator
Optics Communications 426 (2018) 158–163
Contents lists available at ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Photonic generation of microwave waveforms based on a dual-loop optoelectronic oscillator Chuang Ma a , Jinlong Yu a , Ju Wang a, *, Yang Yu a , Tianyuan Xie a , Enze Yang a , Yang Jiang b a b
School of Electrical and Information Engineering, Tianjin University, No. 92 Weijin Road, Tianjin 300072, China School of Physics, Guizhou University, Guiyang, 550025, China
ARTICLE
INFO
Keywords: Microwave waveform generation Optoelectronic oscillator Fiber optics Optical frequency comb
ABSTRACT A novel photonic scheme of microwave waveforms generator based on a dual-loop optoelectronic oscillator (OEO) is experimentally verified. A 10-GHz microwave signal generated by OEO is modulated onto the directly modulated laser (DML) and the phase modulator (PM) simultaneously. By adjusting the driven power of the DML and the PM and the phase difference between the pulse signal inputted into the PM and the PM’s driven signal, the desired optical spectrum is obtained. By passing appropriate dispersion, the optical spectrum can be converted into desired waveform. In this experiment, a series of waveforms with the shapes of sawtooth/reversed-sawtooth, triangle, and pulse are generated.
1. Introduction Generation of microwave waveform has been highly expected for applications in the fields of wireless communication, all-optical microwave signal processing, instrumentation systems and radars [1–4]. Traditionally, arbitrary microwave waveforms are generated by electronic methods but the frequencies of the generated signals are limited by the bandwidth of electronic devices. Compared with the electronic ones, photonic approaches exhibit more advantages, such as wide bandwidth, low loss and immunity to electromagnetic interference [5]. Nowadays, many photonic approaches for microwave waveform generation have been proposed. One popular way is to modulate a continuous wave (CW) externally, in which the third order approximation of microwave waveforms are generated by manipulating the phases and amplitudes of the modulation harmonics. Several demonstrations have carried out this process, such as dual-parallel Mach–Zehnder modulator (DP-MZM) [6–8] combined with dispersion elements or tunable optical band-pass filter (TOBF), polarization modulator (PolM) inserted in a Sagnac Loop [9], single-drive MZM based on optical interleaver (OI) [10], polarization-dependent modulation [11], microwave photonic filter (MPF) [12], two cascaded single-drive Mach–Zehnder modulators [13,14], or stimulated Brillouin scattering (SBS) [15]. Waveform generation by using time-domain synthesis [16,17] is another approach, in which the optical are modulated by a MZM with a sinusoidal driving signal and the desired triangular waveform can be obtained by the superposition of signal envelopes with frequency multiplexing and *
proper time delay [16], or directly overlapping two modulated signal envelopes [17]. Photonic generation of arbitrary waveforms can also be implemented through frequency-to-time mapping (FTTM) technique, such as triangle-shaped, rectangle-shaped and arbitrary-shaped pulses generator [18–21]. This approach shows good performance and ability in generating high order approximation of microwave waveforms. Summing up the schemes above, all of them are required an external microwave source to drive the modulator for generation of waveforms. Hence the quality of the generated waveforms is determined by the phase noise of the external microwave signals. Considering that an optoelectronic oscillator (OEO) can generate high-quality microwave signals [22], triangular waveform generators based on OEOs were reported [23,24]. In these works, the single-loop OEOs are used as the microwave divers, however, they are independent from the triangular waveform generation module, and only the triangular waveforms can be generated. Meanwhile, many other OEOs have been proposed in recent years, which might provide lots of possibilities for low-timingjitter waveforms generation. In this paper, a novel multiple microwave waveform signal generator based on a dual-loop OEO is proposed and experimentally demonstrated. When the oscillation is established, a 10-GHz microwave signal with the phase noise of −115.3 dBc/Hz @10 kHz is generated by OEO. Then the 10-GHz signal is modulated onto the directly modulated laser (DML) and the phase modulator (PM) simultaneously, to generate an optical frequency comb (OFC). A tunable optical delay line (ODL) inbetween is employed to shape the generated OFC. By utilizing the signal
Corresponding author. E-mail address: [email protected] (J. Wang).
https://doi.org/10.1016/j.optcom.2018.05.007 Received 8 April 2018; Received in revised form 25 April 2018; Accepted 2 May 2018 0030-4018/© 2018 Published by Elsevier B.V.
C. Ma et al.
Optics Communications 426 (2018) 158–163
expressed by Eq. (1), the wavelength and width of the OGPG and the amplitude of the driven signal of PM1 are set as 1551 nm, 0.2bit and 1.5 a.u. respectively. The waveform and the corresponding OFC of the generated pulse are shown in Fig. 2(a) and (b). It can be seen from Fig. 2(a) and (b) that the repetition rate of the pulse and the interval of the adjacent harmonic components are 10 GHz and 0.08 nm respectively. Then the shape of the OFC can be adjusted by changing the amplitude of the PM2’s driven signal and the phase difference between the pulse signal inputted into PM2 and the PM2’s driven signal. When they are set as 2.7 a.u. and 0.25𝜋, the OFC and corresponding waveform are shown in Fig. 2(c) and (d). Comparing Fig. 2(c) with Fig. 2(b) we can find that the OFC is shaped from Gauss shape to sawtooth shape. On the other hand, we can find that the waveform in Fig. 2(d) is still a 10-GHz Gaussian pulse by comparing it with Fig. 2(a). By passing about 57ps/nm dispersion (provided by about 3 km SMF which 𝐷 = 19 ps/(nm × km) in OptiSystem), a sawtooth waveform can be obtained, as seen in Fig. 3(a). Keeping the powers of driven signals of PM1 and PM2 unchanged and adjusting the phase difference between the pulse signal inputted into PM2 and the PM2’s driven signal to 0.75𝜋 and 1.5𝜋, the OFC can be shaped to reversed-sawtooth shape and triangular shape as shown in Fig. 3(b) and (d). The reversed-sawtooth waveform and triangular waveform can also be obtained after 57ps/nm and 87.4ps/nm dispersion in Fig. 3(c) and (e).
Fig. 1. Simulation diagrams of optical frequency combs generation. OGPG: optical Gaussian pulse generator, PM: phase modulator.
mode fiber (SMF) with appropriate length, the generated OFC can be converted into desired waveform. In this work, a sawtooth (or reversedsawtooth) waveform, a triangular waveform and a pulse with 10-GHz are experimentally generated. The external microwave source used in the conventional photonic waveform signals generation methods [6– 21] is replaced by the self-oscillating high-quality microwave signal generated by the OEO. In addition, the PM in this system not only plays a role in establishing the dual-loop OEO to suppress the side mode but also plays a role in shaping the OFC. 2. Principle The optical pulse of the DML driven by a sinusoidal signal can be expressed as [25] 𝐸(𝑡) = 𝐸0 exp[−
𝑡2 ] exp[−𝑗(𝜔0 𝑡 + 𝜃1 cos 2𝜋𝑓𝑚 𝑡)] 2𝑇02
3. Experiments
(1)
An experiment is performed based on the setup shown in Fig. 4 to verify the feasibility of the proposed scheme. A beam of CW light at 1550.08 nm is emitted by DML. After passing through SMF1, an ODL and a polarization controller (PC), the CW light is injected into a PM followed by an erbium-doped fiber amplifier (EDFA). The PC is used to align the polarization state of the input light with the axis of the PM. The EDFA is used for compensating the insertion loss in the system. Then the optical beam is divided into two parts by a 90% : 10% optical coupler (OC). One part (10%) acts as the optical signal output for generating microwave waveform, and the other part (90%) is converted into a microwave signal by a PD after passing through SMF2. Then the microwave signal is filtered by a band-pass filter (BPF) with the central frequency of 10 GHz and bandwidth of 10 MHz. After the BPF and an radio frequency (RF) amplifier (AM), the microwave signal is divided into two branches by an 3 dB electric coupler (EC). Then the two branches are fed back to the DML and the PM after passing through two tunable attenuators (TAs) respectively, completing the dual loops. In this scheme, the PM EDFA OC SMF2 (850 m) PD BPF AM AC and TA1 are formed a short cavity to ensure large mode spacing. The DML SMF1 (2000 m) ODL PC PM EDFA OC SMF2 (850 m) PD BPF AM AC and TA2 are formed a long cavity to ensure a narrow bandwidth, i.e., high Q factor [26]. This provides a guarantee for the production of high quality microwave waveforms. A 10-GHz microwave signal with low phase noise is achieved by the dual-loop OEO. It turns to be a completely single-loop OEO when the PM is taken off. The electrical spectrum measured by the spectrum analyzer (Agilent 8564EC) under this condition is shown in Fig. 5(a) by dotted line. It can be shown that the measured side mode suppression ratio (SMSR) is 32 dB and mode spacing is about 70.4 kHz, which corresponds to the 2850 m cavity. When the PM is inserted back, dual-loop OEO is established again. The measured electrical spectrum and phase noise are shown in Fig. 5(a) and (b) by solid line. It can be seen in Fig. 5(a) that the (SMSR) is improved from 32 dB to 60 dB. The phase noise of the generated microwave signal of the dual-loop OEO is −115.3 dBc/Hz at 10 kHz offset frequency as shown in Fig. 5(b). The corresponding root-mean-square (RMS) timing jitters of the signal is about 139.5 fs, calculated by integrating the noise power spectrum density measured above using the following equation [27]:
where 𝐸0 is the amplitude of optical field, 𝜔0 is the angular frequency, 𝑓𝑚 is modulation frequency, 𝜃1 is the equivalent phase modulation index of DML and 𝑇0 is the full width at half maximum (FWHM) of the pulse. When the pulse emitted from the DML is modulated by a PM driven by the sinusoidal signal with a frequency of 𝑓𝑚 , the modulated electrical field can be expressed as 𝐸(𝑡) = 𝐸0 exp(−
𝑡2 ) exp[−𝑗(𝜔0 𝑡 + 𝜃1 cos 2𝜋𝑓𝑚 𝑡 + 𝜃2 cos(2𝜋𝑓𝑚 𝑡 + 𝛥𝜑))] (2) 2𝑇02
where, 𝜃2 is the modulation index of the PM, and 𝛥𝜑 is the phase difference between the signal inputted into PM and the PM’s driven signal. The optical frequency of the pulse can be expressed by applying Jacobi Anger expansion to Eq. (2). 𝐸=
+∞ ∑
𝑇0 exp[−
𝑛=−∞ +∞ ∑
⊗
𝑇02 (𝑛𝑓𝑚 )2 2
(−𝑗)𝑛 𝐽𝑛 (𝜃1 ) ⊗
𝑛=−∞
]
+∞ ∑
(−𝑗)𝑛 𝐽𝑛 (𝜃2 ) exp(𝑗𝑛(𝛥𝜑))
(3)
𝑛=−∞
where 𝐽𝑛 is the Bessel function of the first kind of order 𝑛. The optical frequency chirp of the pulse can be described as 𝜕𝑉 1 𝜕2 𝛷 =− = −2𝜋𝑓𝑚2 [𝜃1 cos(2𝜋𝑓𝑚 𝑡) + 𝜃2 cos(2𝜋𝑓𝑚 𝑡 + 𝛥𝜙)] (4) 𝜕𝑡 2𝜋 𝜕𝑡2 where 𝜙 is the phase of the pulse. Obviously, this method is able to generate many comb lines with the frequency spacing of 𝑓𝑚 . The shape of the OFC can be adjusted by changing 𝜃1 , 𝜃2 and 𝛥𝜑. This process can be simulated by OptiSystem. The schematic of the simulation is illustrated in Fig. 1. A DML module is composed of an optical Gaussian pulse generator (OGPG) and a PM (PM1), which are driven by a 10-Gbit/s bit sequence and a 10-GHz sinusoidal signal respectively, in order to generate pulses. Then the generated pulses from the DML module are launched into the other PM (PM2) which is also driven by a 10-GHz sinusoidal signal. In the simulation the amplitudes of driven signals of PM1 and PM2 are proportional to 𝜃1 and 𝜃2 , respectively. The value of 𝛥𝜑 can be changed by changing the phase difference between the pulse signal inputted into PM2 and the PM2’s driven signal. For generating a Gaussian pulse
√
𝜎= 159
𝑓
2 ∫𝑓 max 𝐿(𝑓 )𝑑𝑓∕2𝜋𝑓𝑜𝑠𝑐 min
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Optics Communications 426 (2018) 158–163
Fig. 2. Simulation results: (a) waveform, (b) corresponding OFC of the Gaussian pulse generated by DML module; and (c) shaped OFC and (d) corresponding waveform when the amplitude of the PM2’s driven signal and the phase difference between the pulse signal inputted into PM2 and the PM2’s driven signal are set as 2.7 a.u. and 0.25𝜋.
Fig. 3. Simulation results of (a) sawtooth, (c) reversed-sawtooth, (e) triangular waveforms and the corresponding OFCs of (b) the reversed-sawtooth and (d) triangular waveforms.
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in Fig. 7(b) that the corresponding electrical spectrum is close to the Fourier series expansion of a sawtooth waveform [9]. Keeping TA1 and TA2 unchanged and adjusting the phase difference between the pulse signal inputted into the PM and the PM’s driven signal to 0.75𝜋, the OFC can be shaped to reversed-sawtooth shape as shown in Fig. 8(a). The reversed-sawtooth waveform can also be obtained after 66.005-ps/nm dispersion in Fig. 8(b). The electrical spectrum of the reversed-sawtooth waveform is not provided because there is almost no difference between the electrical spectrum of reversed and non-reversed sawtooth waveform. Since the phase relations between the harmonics are omitted in the ESA. Moreover, keeping TA1 and TA2 unchanged, the OFC can also be shaped to triangular shape as shown in Fig. 9(a) by adjusting the phase difference between the pulse signal inputted into the PM and the PM’s driven signal to 1.5𝜋. Comparing Fig. 9(a) with Fig. 6(a) or Fig. 8(a) we can find that the FHWM of the OFC is narrowed in this process. This means that the signs of chirps generated by the DML and the PM changed from same to opposite. After 89.840 ps/nm dispersion, the pulse is broadened to triangular waveform shown in Fig. 9(b). It can be seen that a 10-GHz triangular microwave waveform is successfully generated, the third-order harmonic of which is 18.9 dB lower than the first-order harmonic, as seen in Fig. 9(c).
Fig. 4. Schematic diagram of the proposed microwave waveform generator. LD: laser diode, DML: direct modulation laser, PC: polarization controller, ODL: optical delay line, OC: optical coupler, PM: phase modulator, EDFA: erbiumdoped fiber amplifier, SMF: single mode fiber, PD: photoelectric detector, BPF: band-pass filter, AM: amplifier, EC: electric coupler, TA: tunable attenuator.
where the 𝑓𝑜𝑠𝑐 is the oscillation frequency. This shows that microwave waveforms with low timing jitter can be generated in this structure. As the principle described, the generated OFC can be shaped by adjusting the amplitudes of the driven signals of the DML and the PM and the phase difference between the pulse signal inputted into the PM and the PM’s driven signal. In this system, they can be regulated by appropriately adjusting the TA1, TA2 and ODL respectively. Then the values of them are roughly set as 1.5a.u., 2.7a.u. and 0.25𝜋 by appropriately adjusting the TA1, TA2 and ODL. The generated OFC is shaped to sawtooth shape as shown in Fig. 6(a). The corresponding waveform keeps pulse shape unchanged during this process which is given by Fig. 6(b). It can be seen that a 10 GHz pulse train with about 20-ps width is generated. Then the pulse is broadened to sawtooth waveform after about 66.005-ps/nm dispersion. This has a small difference from the simulation result because the amplitudes of the driven signals of the DML and the PM and the phase difference between the pulse signal inputted into the PM and the PM’s driven signal are difficult to adjust precisely during the experiment. As shown in Fig. 7(a), a clean and stable sawtooth waveform at 10 GHz is experimentally generated. The measured rising time and falling time are 27-ps and 73-ps respectively. It can be seen
4. Conclusion The practicality and the significances of this approach are well exhibited by experimental verification above. A 10-GHz microwave signal with low phase noise and low timing jitter is generated. The PM in this system not only plays a role in establishing dual-loop OEO to suppress the side mode but also plays a role in shaping the OFC. By appropriately adjusting the driven power of the DML and the PM and the phase difference between the pulse signal inputted into the PM and the PM’s driven signal the desired OFC is generated. Then a sawtooth (or a reversed-sawtooth) waveform and a triangular waveform with 10-GHz are generated by appropriate dispersion. In theory, the system can also generate sawtooth, reversed-sawtooth and triangular waveforms with various duty cycles by changing the
Fig. 5. (a) electrical spectrums of single-loop OEO and dual-loop OEO are painted by dotted and solid lines respectively and (b) phase noise.
Fig. 6. (a) the OFC be shaped to sawtooth shape and (b) the corresponding waveform. 161
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Optics Communications 426 (2018) 158–163
Fig. 7. (a) Generated sawtooth waveform with repetition frequency of 10 GHz. (b) The corresponding electrical spectrum.
Fig. 8. (a) the OFC be shaped to reversed-sawtooth shape and (b) reversed-sawtooth waveform.
Fig. 9. (a) the OFC be shaped to triangular shape, (b) triangular waveform and (c) corresponding optical spectrum.
References
value of the dispersion. However, this method still has some inadequacies. It cannot generate arbitrary waveforms because the powers and the phases of the spectral harmonic components produced by the OEO cannot be individually adjusted.
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Acknowledgment This work was supported in part by the National Natural Science Foundation of China (Grant No. 61427817, 61775162 and 61465002). 162
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163
Contents lists available at ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Photonic generation of microwave waveforms based on a dual-loop optoelectronic oscillator Chuang Ma a , Jinlong Yu a , Ju Wang a, *, Yang Yu a , Tianyuan Xie a , Enze Yang a , Yang Jiang b a b
School of Electrical and Information Engineering, Tianjin University, No. 92 Weijin Road, Tianjin 300072, China School of Physics, Guizhou University, Guiyang, 550025, China
ARTICLE
INFO
Keywords: Microwave waveform generation Optoelectronic oscillator Fiber optics Optical frequency comb
ABSTRACT A novel photonic scheme of microwave waveforms generator based on a dual-loop optoelectronic oscillator (OEO) is experimentally verified. A 10-GHz microwave signal generated by OEO is modulated onto the directly modulated laser (DML) and the phase modulator (PM) simultaneously. By adjusting the driven power of the DML and the PM and the phase difference between the pulse signal inputted into the PM and the PM’s driven signal, the desired optical spectrum is obtained. By passing appropriate dispersion, the optical spectrum can be converted into desired waveform. In this experiment, a series of waveforms with the shapes of sawtooth/reversed-sawtooth, triangle, and pulse are generated.
1. Introduction Generation of microwave waveform has been highly expected for applications in the fields of wireless communication, all-optical microwave signal processing, instrumentation systems and radars [1–4]. Traditionally, arbitrary microwave waveforms are generated by electronic methods but the frequencies of the generated signals are limited by the bandwidth of electronic devices. Compared with the electronic ones, photonic approaches exhibit more advantages, such as wide bandwidth, low loss and immunity to electromagnetic interference [5]. Nowadays, many photonic approaches for microwave waveform generation have been proposed. One popular way is to modulate a continuous wave (CW) externally, in which the third order approximation of microwave waveforms are generated by manipulating the phases and amplitudes of the modulation harmonics. Several demonstrations have carried out this process, such as dual-parallel Mach–Zehnder modulator (DP-MZM) [6–8] combined with dispersion elements or tunable optical band-pass filter (TOBF), polarization modulator (PolM) inserted in a Sagnac Loop [9], single-drive MZM based on optical interleaver (OI) [10], polarization-dependent modulation [11], microwave photonic filter (MPF) [12], two cascaded single-drive Mach–Zehnder modulators [13,14], or stimulated Brillouin scattering (SBS) [15]. Waveform generation by using time-domain synthesis [16,17] is another approach, in which the optical are modulated by a MZM with a sinusoidal driving signal and the desired triangular waveform can be obtained by the superposition of signal envelopes with frequency multiplexing and *
proper time delay [16], or directly overlapping two modulated signal envelopes [17]. Photonic generation of arbitrary waveforms can also be implemented through frequency-to-time mapping (FTTM) technique, such as triangle-shaped, rectangle-shaped and arbitrary-shaped pulses generator [18–21]. This approach shows good performance and ability in generating high order approximation of microwave waveforms. Summing up the schemes above, all of them are required an external microwave source to drive the modulator for generation of waveforms. Hence the quality of the generated waveforms is determined by the phase noise of the external microwave signals. Considering that an optoelectronic oscillator (OEO) can generate high-quality microwave signals [22], triangular waveform generators based on OEOs were reported [23,24]. In these works, the single-loop OEOs are used as the microwave divers, however, they are independent from the triangular waveform generation module, and only the triangular waveforms can be generated. Meanwhile, many other OEOs have been proposed in recent years, which might provide lots of possibilities for low-timingjitter waveforms generation. In this paper, a novel multiple microwave waveform signal generator based on a dual-loop OEO is proposed and experimentally demonstrated. When the oscillation is established, a 10-GHz microwave signal with the phase noise of −115.3 dBc/Hz @10 kHz is generated by OEO. Then the 10-GHz signal is modulated onto the directly modulated laser (DML) and the phase modulator (PM) simultaneously, to generate an optical frequency comb (OFC). A tunable optical delay line (ODL) inbetween is employed to shape the generated OFC. By utilizing the signal
Corresponding author. E-mail address: [email protected] (J. Wang).
https://doi.org/10.1016/j.optcom.2018.05.007 Received 8 April 2018; Received in revised form 25 April 2018; Accepted 2 May 2018 0030-4018/© 2018 Published by Elsevier B.V.
C. Ma et al.
Optics Communications 426 (2018) 158–163
expressed by Eq. (1), the wavelength and width of the OGPG and the amplitude of the driven signal of PM1 are set as 1551 nm, 0.2bit and 1.5 a.u. respectively. The waveform and the corresponding OFC of the generated pulse are shown in Fig. 2(a) and (b). It can be seen from Fig. 2(a) and (b) that the repetition rate of the pulse and the interval of the adjacent harmonic components are 10 GHz and 0.08 nm respectively. Then the shape of the OFC can be adjusted by changing the amplitude of the PM2’s driven signal and the phase difference between the pulse signal inputted into PM2 and the PM2’s driven signal. When they are set as 2.7 a.u. and 0.25𝜋, the OFC and corresponding waveform are shown in Fig. 2(c) and (d). Comparing Fig. 2(c) with Fig. 2(b) we can find that the OFC is shaped from Gauss shape to sawtooth shape. On the other hand, we can find that the waveform in Fig. 2(d) is still a 10-GHz Gaussian pulse by comparing it with Fig. 2(a). By passing about 57ps/nm dispersion (provided by about 3 km SMF which 𝐷 = 19 ps/(nm × km) in OptiSystem), a sawtooth waveform can be obtained, as seen in Fig. 3(a). Keeping the powers of driven signals of PM1 and PM2 unchanged and adjusting the phase difference between the pulse signal inputted into PM2 and the PM2’s driven signal to 0.75𝜋 and 1.5𝜋, the OFC can be shaped to reversed-sawtooth shape and triangular shape as shown in Fig. 3(b) and (d). The reversed-sawtooth waveform and triangular waveform can also be obtained after 57ps/nm and 87.4ps/nm dispersion in Fig. 3(c) and (e).
Fig. 1. Simulation diagrams of optical frequency combs generation. OGPG: optical Gaussian pulse generator, PM: phase modulator.
mode fiber (SMF) with appropriate length, the generated OFC can be converted into desired waveform. In this work, a sawtooth (or reversedsawtooth) waveform, a triangular waveform and a pulse with 10-GHz are experimentally generated. The external microwave source used in the conventional photonic waveform signals generation methods [6– 21] is replaced by the self-oscillating high-quality microwave signal generated by the OEO. In addition, the PM in this system not only plays a role in establishing the dual-loop OEO to suppress the side mode but also plays a role in shaping the OFC. 2. Principle The optical pulse of the DML driven by a sinusoidal signal can be expressed as [25] 𝐸(𝑡) = 𝐸0 exp[−
𝑡2 ] exp[−𝑗(𝜔0 𝑡 + 𝜃1 cos 2𝜋𝑓𝑚 𝑡)] 2𝑇02
3. Experiments
(1)
An experiment is performed based on the setup shown in Fig. 4 to verify the feasibility of the proposed scheme. A beam of CW light at 1550.08 nm is emitted by DML. After passing through SMF1, an ODL and a polarization controller (PC), the CW light is injected into a PM followed by an erbium-doped fiber amplifier (EDFA). The PC is used to align the polarization state of the input light with the axis of the PM. The EDFA is used for compensating the insertion loss in the system. Then the optical beam is divided into two parts by a 90% : 10% optical coupler (OC). One part (10%) acts as the optical signal output for generating microwave waveform, and the other part (90%) is converted into a microwave signal by a PD after passing through SMF2. Then the microwave signal is filtered by a band-pass filter (BPF) with the central frequency of 10 GHz and bandwidth of 10 MHz. After the BPF and an radio frequency (RF) amplifier (AM), the microwave signal is divided into two branches by an 3 dB electric coupler (EC). Then the two branches are fed back to the DML and the PM after passing through two tunable attenuators (TAs) respectively, completing the dual loops. In this scheme, the PM EDFA OC SMF2 (850 m) PD BPF AM AC and TA1 are formed a short cavity to ensure large mode spacing. The DML SMF1 (2000 m) ODL PC PM EDFA OC SMF2 (850 m) PD BPF AM AC and TA2 are formed a long cavity to ensure a narrow bandwidth, i.e., high Q factor [26]. This provides a guarantee for the production of high quality microwave waveforms. A 10-GHz microwave signal with low phase noise is achieved by the dual-loop OEO. It turns to be a completely single-loop OEO when the PM is taken off. The electrical spectrum measured by the spectrum analyzer (Agilent 8564EC) under this condition is shown in Fig. 5(a) by dotted line. It can be shown that the measured side mode suppression ratio (SMSR) is 32 dB and mode spacing is about 70.4 kHz, which corresponds to the 2850 m cavity. When the PM is inserted back, dual-loop OEO is established again. The measured electrical spectrum and phase noise are shown in Fig. 5(a) and (b) by solid line. It can be seen in Fig. 5(a) that the (SMSR) is improved from 32 dB to 60 dB. The phase noise of the generated microwave signal of the dual-loop OEO is −115.3 dBc/Hz at 10 kHz offset frequency as shown in Fig. 5(b). The corresponding root-mean-square (RMS) timing jitters of the signal is about 139.5 fs, calculated by integrating the noise power spectrum density measured above using the following equation [27]:
where 𝐸0 is the amplitude of optical field, 𝜔0 is the angular frequency, 𝑓𝑚 is modulation frequency, 𝜃1 is the equivalent phase modulation index of DML and 𝑇0 is the full width at half maximum (FWHM) of the pulse. When the pulse emitted from the DML is modulated by a PM driven by the sinusoidal signal with a frequency of 𝑓𝑚 , the modulated electrical field can be expressed as 𝐸(𝑡) = 𝐸0 exp(−
𝑡2 ) exp[−𝑗(𝜔0 𝑡 + 𝜃1 cos 2𝜋𝑓𝑚 𝑡 + 𝜃2 cos(2𝜋𝑓𝑚 𝑡 + 𝛥𝜑))] (2) 2𝑇02
where, 𝜃2 is the modulation index of the PM, and 𝛥𝜑 is the phase difference between the signal inputted into PM and the PM’s driven signal. The optical frequency of the pulse can be expressed by applying Jacobi Anger expansion to Eq. (2). 𝐸=
+∞ ∑
𝑇0 exp[−
𝑛=−∞ +∞ ∑
⊗
𝑇02 (𝑛𝑓𝑚 )2 2
(−𝑗)𝑛 𝐽𝑛 (𝜃1 ) ⊗
𝑛=−∞
]
+∞ ∑
(−𝑗)𝑛 𝐽𝑛 (𝜃2 ) exp(𝑗𝑛(𝛥𝜑))
(3)
𝑛=−∞
where 𝐽𝑛 is the Bessel function of the first kind of order 𝑛. The optical frequency chirp of the pulse can be described as 𝜕𝑉 1 𝜕2 𝛷 =− = −2𝜋𝑓𝑚2 [𝜃1 cos(2𝜋𝑓𝑚 𝑡) + 𝜃2 cos(2𝜋𝑓𝑚 𝑡 + 𝛥𝜙)] (4) 𝜕𝑡 2𝜋 𝜕𝑡2 where 𝜙 is the phase of the pulse. Obviously, this method is able to generate many comb lines with the frequency spacing of 𝑓𝑚 . The shape of the OFC can be adjusted by changing 𝜃1 , 𝜃2 and 𝛥𝜑. This process can be simulated by OptiSystem. The schematic of the simulation is illustrated in Fig. 1. A DML module is composed of an optical Gaussian pulse generator (OGPG) and a PM (PM1), which are driven by a 10-Gbit/s bit sequence and a 10-GHz sinusoidal signal respectively, in order to generate pulses. Then the generated pulses from the DML module are launched into the other PM (PM2) which is also driven by a 10-GHz sinusoidal signal. In the simulation the amplitudes of driven signals of PM1 and PM2 are proportional to 𝜃1 and 𝜃2 , respectively. The value of 𝛥𝜑 can be changed by changing the phase difference between the pulse signal inputted into PM2 and the PM2’s driven signal. For generating a Gaussian pulse
√
𝜎= 159
𝑓
2 ∫𝑓 max 𝐿(𝑓 )𝑑𝑓∕2𝜋𝑓𝑜𝑠𝑐 min
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Fig. 2. Simulation results: (a) waveform, (b) corresponding OFC of the Gaussian pulse generated by DML module; and (c) shaped OFC and (d) corresponding waveform when the amplitude of the PM2’s driven signal and the phase difference between the pulse signal inputted into PM2 and the PM2’s driven signal are set as 2.7 a.u. and 0.25𝜋.
Fig. 3. Simulation results of (a) sawtooth, (c) reversed-sawtooth, (e) triangular waveforms and the corresponding OFCs of (b) the reversed-sawtooth and (d) triangular waveforms.
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in Fig. 7(b) that the corresponding electrical spectrum is close to the Fourier series expansion of a sawtooth waveform [9]. Keeping TA1 and TA2 unchanged and adjusting the phase difference between the pulse signal inputted into the PM and the PM’s driven signal to 0.75𝜋, the OFC can be shaped to reversed-sawtooth shape as shown in Fig. 8(a). The reversed-sawtooth waveform can also be obtained after 66.005-ps/nm dispersion in Fig. 8(b). The electrical spectrum of the reversed-sawtooth waveform is not provided because there is almost no difference between the electrical spectrum of reversed and non-reversed sawtooth waveform. Since the phase relations between the harmonics are omitted in the ESA. Moreover, keeping TA1 and TA2 unchanged, the OFC can also be shaped to triangular shape as shown in Fig. 9(a) by adjusting the phase difference between the pulse signal inputted into the PM and the PM’s driven signal to 1.5𝜋. Comparing Fig. 9(a) with Fig. 6(a) or Fig. 8(a) we can find that the FHWM of the OFC is narrowed in this process. This means that the signs of chirps generated by the DML and the PM changed from same to opposite. After 89.840 ps/nm dispersion, the pulse is broadened to triangular waveform shown in Fig. 9(b). It can be seen that a 10-GHz triangular microwave waveform is successfully generated, the third-order harmonic of which is 18.9 dB lower than the first-order harmonic, as seen in Fig. 9(c).
Fig. 4. Schematic diagram of the proposed microwave waveform generator. LD: laser diode, DML: direct modulation laser, PC: polarization controller, ODL: optical delay line, OC: optical coupler, PM: phase modulator, EDFA: erbiumdoped fiber amplifier, SMF: single mode fiber, PD: photoelectric detector, BPF: band-pass filter, AM: amplifier, EC: electric coupler, TA: tunable attenuator.
where the 𝑓𝑜𝑠𝑐 is the oscillation frequency. This shows that microwave waveforms with low timing jitter can be generated in this structure. As the principle described, the generated OFC can be shaped by adjusting the amplitudes of the driven signals of the DML and the PM and the phase difference between the pulse signal inputted into the PM and the PM’s driven signal. In this system, they can be regulated by appropriately adjusting the TA1, TA2 and ODL respectively. Then the values of them are roughly set as 1.5a.u., 2.7a.u. and 0.25𝜋 by appropriately adjusting the TA1, TA2 and ODL. The generated OFC is shaped to sawtooth shape as shown in Fig. 6(a). The corresponding waveform keeps pulse shape unchanged during this process which is given by Fig. 6(b). It can be seen that a 10 GHz pulse train with about 20-ps width is generated. Then the pulse is broadened to sawtooth waveform after about 66.005-ps/nm dispersion. This has a small difference from the simulation result because the amplitudes of the driven signals of the DML and the PM and the phase difference between the pulse signal inputted into the PM and the PM’s driven signal are difficult to adjust precisely during the experiment. As shown in Fig. 7(a), a clean and stable sawtooth waveform at 10 GHz is experimentally generated. The measured rising time and falling time are 27-ps and 73-ps respectively. It can be seen
4. Conclusion The practicality and the significances of this approach are well exhibited by experimental verification above. A 10-GHz microwave signal with low phase noise and low timing jitter is generated. The PM in this system not only plays a role in establishing dual-loop OEO to suppress the side mode but also plays a role in shaping the OFC. By appropriately adjusting the driven power of the DML and the PM and the phase difference between the pulse signal inputted into the PM and the PM’s driven signal the desired OFC is generated. Then a sawtooth (or a reversed-sawtooth) waveform and a triangular waveform with 10-GHz are generated by appropriate dispersion. In theory, the system can also generate sawtooth, reversed-sawtooth and triangular waveforms with various duty cycles by changing the
Fig. 5. (a) electrical spectrums of single-loop OEO and dual-loop OEO are painted by dotted and solid lines respectively and (b) phase noise.
Fig. 6. (a) the OFC be shaped to sawtooth shape and (b) the corresponding waveform. 161
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Fig. 7. (a) Generated sawtooth waveform with repetition frequency of 10 GHz. (b) The corresponding electrical spectrum.
Fig. 8. (a) the OFC be shaped to reversed-sawtooth shape and (b) reversed-sawtooth waveform.
Fig. 9. (a) the OFC be shaped to triangular shape, (b) triangular waveform and (c) corresponding optical spectrum.
References
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Acknowledgment This work was supported in part by the National Natural Science Foundation of China (Grant No. 61427817, 61775162 and 61465002). 162
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