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1 × N hybrid radio frequency photonic splitter based on a dual-polarization dual-parallel Mach Zehnder modulator
Optics Communications 431 (2019) 10–13
Contents lists available at ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
1 × N hybrid radio frequency photonic splitter based on a dual-polarization dual-parallel Mach Zehnder modulator Sha Zhu a,b,c , Ming Li b,c , Xin Wang b , Ning Hua Zhu b,c , Wei Li a,b,c, * a b c
State Key Laboratory of Optical Fiber and Cable Manufacture Technology, Strategy Center, YOFC, Wuhan 430073, China State Key Laboratory on Integrated Optoelectronics, Institute of Semiconductors, Chinese Academy of Sciences, Beijing, 100083, China School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing, 100049, China
ARTICLE
INFO
Keywords: Radio frequency photonics Fiber optics Phase shift Frequency filtering Analog optical signal processing
ABSTRACT We report a 1 × N hybrid radio frequency (RF) photonic splitter with arbitrary phase shift and amplitude ratio using a dual-polarization dual-parallel Mach Zehnder modulator (DP-DPMZM). The DP-DPMZM is properly set to generate an orthogonally polarized single-sideband (SSB) modulated optical signal. By controlling a polarization controller (PC) and a polarizer (Pol.) that cascaded behind the modulator, an RF photonic splitter with arbitrary phase and amplitude ratio can be realized. Compared with previous reported works, the proposed RF splitter can be operated in a wide bandwidth since no optical or electrical filters are involved. The proposed scheme is theoretically analyzed and experimentally verified.
1. Introduction Microwave photonics (MWP) has attracted considerable interests recently through combining radio frequency (RF) engineering and photonic technology to overcome the electronic bottleneck problems. MWP systems cover the advantages of electronics and optics, such as high frequency, large bandwidth, easy tuning, low power consumption, low weight and immunity to electromagnetic interference. Therefore, numerous MWP links have been proposed to generate, transmit, process and detect RF signals [1–6]. In pure electronic domain, RF splitter is a fundamental element which always has fixed number of output ports, fixed amplitude ratio and fixed phase shift [7,8]. It is difficult to change the amplitude ratio and phase shift of an RF splitter. The number of the output ports is also hard to add or drop to accommodate different requirements. This drawback restricts its applications in signal processing and radar systems. Nevertheless, RF photonic splitter, which is constructed in MWP systems, has potential to achieve arbitrary phase shift and amplitude ratio between different outputs in a large bandwidth. The RF photonic splitter can be widely used in RF applications which need a lot of copies of a broadband signal with tunable phase and amplitude, such as multi-tap microwave photonic filters (MPFs) [9–11], complex microwave signal detection in radars [12,13], and analog encryption in RF signal dissemination systems [14]. Some MWP schemes have been reported to realize an RF photonic splitter [15–17]. For example,
a 1 × 2 arbitrary RF photonic splitter has been proposed using two different continuous lights [15,16]. However, 𝑁 laser diodes (LDs) are required to achieve a 1 × 𝑁 RF photonic splitter which makes the system costly and complicated. The phase shift between the two different RF outputs is adjusted by the bias of a dual-parallel Mach– Zehnder modulator (DPMZM). Thus, the phase shift for each branch of the RF photonic splitter cannot be tuned independently. We have reported a microwave photonic splitter using a polarization modulator (PolM) and an optical bandpass filter (OBPF) [17]. The use of an OBPF limits the operation bandwidth and tunability of the RF photonic splitter. In this paper, we propose a 1 × 𝑁 hybrid RF photonic splitter with arbitrary phase shift and amplitude ratio using a single dualpolarization dual-parallel Mach Zehnder modulator (DP-DPMZM). Compared with our previous work [17], no optical or electrical filters are involved in this scheme. Thus, the proposed RF splitter can be operated in a wide bandwidth. An orthogonally polarized singlesideband (SSB) modulated optical signal is generated by properly setting the DP-DPMZM. The RF splitter can be easily expanded to have 𝑁 branches using a 1 × 𝑁 optical splitter. By tuning the polarization controller (PC) and polarizer (Pol.) in each branch, the RF splitter can have independently tuned phase shift and amplitude ratio. The possibility of the proposed scheme is theoretically and experimentally verified.
* Corresponding author at: State Key Laboratory on Integrated Optoelectronics, Institute of Semiconductors, Chinese Academy of Sciences, Beijing, 100083, China. E-mail address: [email protected] (W. Li).
https://doi.org/10.1016/j.optcom.2018.09.008 Received 7 August 2018; Received in revised form 3 September 2018; Accepted 4 September 2018 Available online 8 September 2018 0030-4018/© 2018 Elsevier B.V. All rights reserved.
S. Zhu et al.
Optics Communications 431 (2019) 10–13
Fig. 1. The schematic of the proposed 1 × 𝑁 hybrid radio frequency (RF) photonic splitter with arbitrary phase shift and amplitude ratio. LD, laser diode; DP-DPMZM, dual-polarization dual-parallel Mach–Zehnder modulator; DPMZM, dual-parallel Mach–Zehnder modulator; PBS, polarization beam splitter; PBC, polarization beam combiner; 90◦ , 90◦ electrical coupler; PC, polarization controller; Pol., polarizer; PD, photodetector. Fig. 2. Measured (a) phase responses and (b) magnitude responses for one port of the RF photonic splitter by adjusting the phase difference 𝜃 between the two orthogonal polarization states generated by a PC.
2. Principle The structure of the proposed 1 × 𝑁 hybrid RF photonic splitter with arbitrary phase shift and amplitude ratio is shown in Fig. 1. The key component of the RF photonic splitter is a DP-DPMZM which consists of a polarization beam splitter (PBS), two DPMZMs (DPMZM1 and DPMZM2) at two orthogonal polarization states and a polarization beam combiner (PBC). The major structure of a DPMZM is a parent MZM with two sub-MZMs lying on each of its arms. A linearly polarized optical carrier is fiber-coupled into the DP-DPMZM with an angle of 45◦ to one principal axis of the PBS. The upper DPMZM1 driven by an RF signal is biased to generate a carrier suppressed single sideband (CS-SSB) modulated signal. Whereas, the lower DPMZM2 is set at maximum transmission point to let a pure optical carrier pass through with maximum optical power. By adjusting PCs in different branches, a 1 × 𝑁 RF photonic splitter is constructed successfully. Mathematically, when the DPMZM1 is driven by a RF signal, the optical field at the output of DPMZM1 is given by 𝐸𝑥 (𝑡) =
1 𝐸 𝑒𝑗𝜔0 𝑡 [𝑒𝑗𝛽 cos(𝜔𝑚 𝑡)+𝑗𝜑1 + 𝑒𝑗𝛽 cos(𝜔𝑚 𝑡+𝜋) ] 8 0 + [𝑒𝑗𝛽 sin(𝜔𝑚 𝑡)+𝑗𝜑2 + 𝑒𝑗𝛽 sin(𝜔𝑚 𝑡+𝜋) ]𝑒𝑗𝜙1 ,
Fig. 3. Measured (a) magnitude response and (b) phase response for one port of the RF photonic splitter by adjusting the rotation angle 𝛼 of the PC.
(1) PC [18,19]. A Pol. is cascaded with the PC to project the two orthogonal polarized optical signals onto a linear polarization state. Therefore, the optical field at the output of Pol. is
where 𝐸0 and 𝜔0 are the amplitude and angular frequency of the optical carrier, 𝑉 and 𝜔𝑚 are the peak-to-peak value and angular frequency of the driven RF signal, 𝛽 is the RF modulation index of DPMZM1 which is equal to 𝜋𝑉 ∕𝑉𝜋 , 𝑉𝜋 is the RF switching voltage, 𝜑1 = 𝜋𝑉𝐷𝐶1 ∕𝑉𝜋 , 𝜑2 = 𝜋𝑉𝐷𝐶2 ∕𝑉𝜋 and 𝜙1 = 𝜋𝑉𝐷𝐶𝑥 ∕𝑉𝜋 where 𝑉𝐷𝐶1 and 𝑉𝐷𝐶2 are the direct current (DC) biases of the two sub-MZMs, 𝑉𝐷𝐶𝑥 is the main DC bias of the DPMZM1. By setting 𝜑1 = 𝜋, 𝜑2 = 𝜋, and 𝜙1 = 𝜋/2, under small signal modulation condition, Eq. (1) can be rewritten as
𝐸𝑝𝑜𝑙. (𝑡) = cos 𝛼𝐸𝑥 𝑒𝑗𝜃 + sin 𝛼𝐸𝑦 𝑒−𝑗𝜃
(5)
When the optical signal is detected by a PD for square-law detection, the recovered RF signal is 𝑖(𝑡) = 𝐸𝑝𝑜𝑙. (𝑡) ⋅ 𝐸𝑝𝑜𝑙. (𝑡)∗ 𝜋 (6) ∝ sin(2𝛼)𝐽1 (𝛽) cos(𝜔𝑚 𝑡 − + 2𝜃). 2 As can be seen from Eq. (6), the amplitude and phase of the recovered RF signal can be tuned independently by adjusting the state of PC. Therefore, if there are 𝑁 branches in the RF photonic splitter, the amplitude ratio and phase shift for different branches can be tuned independently and arbitrarily. A 1 × 𝑁 hybrid RF photonic splitter with arbitrary phase shift and amplitude ratio is constructed.
𝜋 1 𝐸𝑥 (𝑡) = 𝐸0 𝐽1 (𝛽)𝑒𝑗[(𝜔0 +𝜔𝑚 )𝑡− 2 ] , (2) 2 where 𝐽1 (𝛽) is the first order Bessel function of the first kind. From Eq. (2) we could see that a CS-SSB modulated signal is generated successfully. In order to make the pure optical carrier pass through lower DPMZM2 with maximum optical power, the two sub-MZMs and parent MZM of the DPMZM2 are all biased at maximum transmission point. Hence, the optical signal at the output of DPMZM2 is
3. Experiments and results
1 𝐸 𝑒𝑗𝜔0 𝑡 . (3) 2 0 In transmission branch, a PC which consists of a quarter-wave, a half-wave, and a quarter-wave plates is used to adjust the polarization states of the optical signals according to the transfer function of [ ][ ] cos 𝛼 − sin 𝛼 𝑒𝑗𝜃 0 𝑃𝑃 𝐶 = (4) −𝑗𝜃 , sin 𝛼 cos 𝛼 0 𝑒 𝐸𝑦 (𝑡) =
A proof-of-concept experiment based on the scheme of Fig. 1 was carried out to verify the feasibility of the proposed RF photonic splitter. A linearly polarized optical carrier centered at 1550 nm was fibercoupled into a DP-DPMZM with an angle of 45◦ to one principal axis of the PBS. A vector network analyzer (VNA) generated an RF signal to drive the DPMZM1. By adjusting the DC biases of the DP-DPMZM as describe in Section 2, DPMZM1 worked at CS-SSB modulation state, while DPMZM2 was set to let the pure optical carrier pass through
where 𝛼 is the rotation angle, 𝜃 is the phase difference between the two orthogonal polarized components introduced by the birefringence in a 11
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Optics Communications 431 (2019) 10–13
two optical signals of the RF photonic splitter. Actually, the PBC is equivalent to a combination of two orthogonal polarizers which can ensure the optical signals at the output of PBC cannot interfere with each other. When the optical signals are detected by a PD, the recovered two RF signals will interfere with each other. The two-tap MPF is the summation of the two branches of the RF photonic splitter. Therefore, the transmission response of the two-tap MPF can be given by
Fig. 4. The configuration of a two-tap microwave photonic filter (MPF) using the proposed RF photonic splitter. LD, laser diode; DP-DPMZM, dualpolarization dual-parallel Mach–Zehnder modulator; OC, optical coupler; PC, polarization controller; ODL, optical delay line; PBC, polarization beam combiner; PD, photodetector.
𝐻(𝑓 ) = 𝑎1 𝑒𝑗𝜓1 + 𝑎2 𝑒𝑗(𝜓2 −2𝜋𝑓 𝜏0 ) = 𝑎1 𝑒𝑗𝜓1 [1 + 𝛾𝑒𝑗(𝛥𝜓−2𝜋𝑓 𝜏0 ) ],
(7)
where 𝑎1 and 𝑎2 are the amplitude of the recovered RF signals from the two branches, 𝜓1 and 𝜓2 are the phase of the recovered RF signals from the two branches, 𝜏0 is the time delay which is introduced by an optical delay line (ODL), 𝛾 = 𝑎2 ∕𝑎1 and ▵ 𝜓 = 𝜓2 − 𝜓1 is the amplitude ratio and phase shift between the two branches. Hence, as shown in Eq. (7), by adjusting the amplitude ratio 𝛾, the notch depth of the MPF can be changed. Besides, the position of the notch can be continuously tuned by adjusting the phase shift ▵ 𝜓 between the two branches. A two-tap MPF based on the setup shown in Fig. 4 was conducted to demonstrate the tunability of the proposed RF photonic splitter. The ODL introduces a time delay of 0.66 ns between the two branches of the two-tap MPF, which is corresponding to a free spectrum range (FSR) of 1.51 GHz as shown in Fig. 5(a) and 5(b). First, when the amplitude ratio 𝛾 of the RF photonic splitter remains fixed, i.e., 𝛾 = 0.85, we tune the position of the notch by changing the phase shift ▵ 𝜓 of the RF splitter. The corresponding magnitude response of the two-tap MPF is shown in Fig. 5(a). When the phase shift ▵ 𝜓 is equal to 160◦ , 90◦ and 45◦ , the position of the notch is tunable without changing the notch depth, FSR and shape of the transmission response of the two-tap MPF. Moreover, as can be seen from Fig. 5(b), when we adjust the amplitude ratio 𝛾 of the RF photonic splitter and keep the phase shift ▵𝜓 unchanged, the depth of the notch is tunable while the notch position, shape and FSR remain the same as before. Since the responsivity of the PD decreases with the frequency, the magnitude response of the two-tap MPF becomes gradually lower with the frequency.
Fig. 5. Measured transmission responses of the two-tap microwave photonic filter (MPF) by adjusting (a) the phase shift △𝜓 of the RF photonic splitter, and (b) the amplitude ratio 𝛾 of the RF photonic splitter.
with maximal optical power. The PC and Pol. in a branch can realize polarization-to-intensity modulation conversion. Finally, the optical signal was detected by a PD with bandwidth of 18 GHz. The recovered RF signal was fed into the VNA to measure the magnitude response and phase response of the RF photonic splitter. As described in Section 2, the phase shift and amplitude ratio of the RF photonic splitter is highly related to the PC. According to Eq. (4), the rotation angle 𝛼 and the phase difference 𝜃 of the PC can be tuned independently. A detailed instruction about the tuning of the PC can be found in [18,19]. Eq. (6) shows that the phase shift of the RF photonic splitter is controlled by 𝜃, while the amplitude ratio of the splitter is determined by 𝛼. Thus, we can arbitrarily and independently change the phase shift and the amplitude ratio of the RF photonic splitter. First, we changed the phase shift of the RF photonic splitter with a fixed amplitude ratio by tuning 𝜃 of the PC. Fig. 2(a) and (b) show the phase and magnitude responses of one port of the RF photonic splitter from 8 GHz to 18 GHz. The phase of the RF signal can be tuned continuously from −180◦ to 180◦ while the magnitude response only varies within 3 dB. The lower boundary of the RF photonic splitter is determined by the 90◦ hybrid coupler which has a flat 3-dB bandwidth from 8 to 18 GHz. It can be easily increased using a 90◦ hybrid coupler with larger bandwidth. In addition, as Section 2 shows, the magnitude of the recovered microwave signal is also tunable. Hence, when the rotation angle 𝛼 of the PC was tuned, we measured the magnitude and phase responses of the recovered microwave signal from 8 GHz to 18 GHz. The corresponding phase and magnitude responses are shown in Fig. 3(a) and (b). It can be seen that the magnitude of the microwave signal can be continuously tuned from 0 dB to −12 dB while the phase variation can be kept within 10◦ . For purpose of demonstrating the tunability of the proposed RF photonic splitter, we construct a two-tap microwave photonic filter (MPF) based on the scheme of Fig. 4. A PBC is used to couple the
4. Conclusion In conclusion, a 1 × 𝑁 hybrid RF photonic splitter with arbitrary phase shift and amplitude ratio has been experimentally demonstrated using a single DP-DPMZM. The DP-DPMZM is properly set to generate an orthogonally polarized single-sideband (SSB) modulated optical signal. By adjusting the PC in different branches, an RF photonic splitter is realized. Since no optical or electrical filters are involved, the RF photonic splitter has a broad operation bandwidth. If two branches of the splitter are coupled into a PBC for photoelectric conversion by a PD, a two-tap MPF can be constructed. Besides, the notch depth and position of the two-tap MPF transmission response could be tuned independently by changing the phase shift and amplitude ratio of the RF photonic splitter. Acknowledgments This work was supported in part by the National Natural Science Foundation of China under Grants 61335005, 61431003, 61335004, 61377069, and 61527820, in part by Instrument Developing Project of the Chinese Academy of Sciences under Grant YZ201602, and in part by Open Projects Foundation of Yangtze Optical Fiber and Cable Joint Stock Limited Company (YOFC), China (SKLD1701). References [1] J. Capmany, D. Novak, Microwave photonics combines two worlds, Nature Photon. 1 (2007) 319–330. [2] A.J. Seeds, K.J. Williams, Microwave photonics, J. Lightwave Technol. 24 (2006) 4628–4641. [3] D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales, J. Capmang, Integrated microwave photonics, Laser Photonics Rev. 7 (2013) 506–538.
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[4] J. Yao, Photonic generation of microwave arbitrary waveforms, Opt. Commun. 284 (2011) 3723–3736. [5] A.W. Rihaczek, Principles of High-Resolution Radar, Artech House, Norwood, MA, USA, 1996. [6] M.E. Manka, Microwave photonics electronic warfare technologies for Australian defence, in: IEEE International Topical Meeting on Microwave Photonics, MWP 2008, pp. 1–2. [7] A.R. Anderson, G.B. Backes, R.T. Demulling, D. Louwagie, T.C. Ortber, E.F. Sansone, RF splitter/combiner module, U.S. Patent 5, 909, 155 [P], 1999-6-1. [8] H.I. Swanson, RF splitter circuit, U.S. Patent 4, 680, 559 [P], 1987-7-14. [9] J. Capmany, B. Ortega, D. Pastor, A tutorial on microwave photonic filters, J. Lightwave Technol. 24 (2006) 201–229. [10] M. Sagues, R.G. Olcina, A. Loayssa, S. Sales, J. Capmany, Multi-tap complexcoefficient incoherent microwave photonic filters based on optical single-sideband modulation and narrow band optical filtering, Opt. Express 16 (2008) 295–303. [11] Y. Yan, J. Yao, A tunable photonic microwave filter with a complex coefficient using an optical RF phase shifter, IEEE Photon. Technol. Lett. 19 (2007) 1472–1474. [12] P. Ghelfi, F. Laghezza, F. Scotti, G. Serafino, A. Capria, S. Pinna, D. Onori, C. Porzi, M. Scaffardi, A. Malacarne, V. Vercesi, E. Lazzeri, F. Berizzi, A. Bogoni, A fully photonicbased coherent radar system, Nature 501 (2014) 341–345.
13
Contents lists available at ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
1 × N hybrid radio frequency photonic splitter based on a dual-polarization dual-parallel Mach Zehnder modulator Sha Zhu a,b,c , Ming Li b,c , Xin Wang b , Ning Hua Zhu b,c , Wei Li a,b,c, * a b c
State Key Laboratory of Optical Fiber and Cable Manufacture Technology, Strategy Center, YOFC, Wuhan 430073, China State Key Laboratory on Integrated Optoelectronics, Institute of Semiconductors, Chinese Academy of Sciences, Beijing, 100083, China School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing, 100049, China
ARTICLE
INFO
Keywords: Radio frequency photonics Fiber optics Phase shift Frequency filtering Analog optical signal processing
ABSTRACT We report a 1 × N hybrid radio frequency (RF) photonic splitter with arbitrary phase shift and amplitude ratio using a dual-polarization dual-parallel Mach Zehnder modulator (DP-DPMZM). The DP-DPMZM is properly set to generate an orthogonally polarized single-sideband (SSB) modulated optical signal. By controlling a polarization controller (PC) and a polarizer (Pol.) that cascaded behind the modulator, an RF photonic splitter with arbitrary phase and amplitude ratio can be realized. Compared with previous reported works, the proposed RF splitter can be operated in a wide bandwidth since no optical or electrical filters are involved. The proposed scheme is theoretically analyzed and experimentally verified.
1. Introduction Microwave photonics (MWP) has attracted considerable interests recently through combining radio frequency (RF) engineering and photonic technology to overcome the electronic bottleneck problems. MWP systems cover the advantages of electronics and optics, such as high frequency, large bandwidth, easy tuning, low power consumption, low weight and immunity to electromagnetic interference. Therefore, numerous MWP links have been proposed to generate, transmit, process and detect RF signals [1–6]. In pure electronic domain, RF splitter is a fundamental element which always has fixed number of output ports, fixed amplitude ratio and fixed phase shift [7,8]. It is difficult to change the amplitude ratio and phase shift of an RF splitter. The number of the output ports is also hard to add or drop to accommodate different requirements. This drawback restricts its applications in signal processing and radar systems. Nevertheless, RF photonic splitter, which is constructed in MWP systems, has potential to achieve arbitrary phase shift and amplitude ratio between different outputs in a large bandwidth. The RF photonic splitter can be widely used in RF applications which need a lot of copies of a broadband signal with tunable phase and amplitude, such as multi-tap microwave photonic filters (MPFs) [9–11], complex microwave signal detection in radars [12,13], and analog encryption in RF signal dissemination systems [14]. Some MWP schemes have been reported to realize an RF photonic splitter [15–17]. For example,
a 1 × 2 arbitrary RF photonic splitter has been proposed using two different continuous lights [15,16]. However, 𝑁 laser diodes (LDs) are required to achieve a 1 × 𝑁 RF photonic splitter which makes the system costly and complicated. The phase shift between the two different RF outputs is adjusted by the bias of a dual-parallel Mach– Zehnder modulator (DPMZM). Thus, the phase shift for each branch of the RF photonic splitter cannot be tuned independently. We have reported a microwave photonic splitter using a polarization modulator (PolM) and an optical bandpass filter (OBPF) [17]. The use of an OBPF limits the operation bandwidth and tunability of the RF photonic splitter. In this paper, we propose a 1 × 𝑁 hybrid RF photonic splitter with arbitrary phase shift and amplitude ratio using a single dualpolarization dual-parallel Mach Zehnder modulator (DP-DPMZM). Compared with our previous work [17], no optical or electrical filters are involved in this scheme. Thus, the proposed RF splitter can be operated in a wide bandwidth. An orthogonally polarized singlesideband (SSB) modulated optical signal is generated by properly setting the DP-DPMZM. The RF splitter can be easily expanded to have 𝑁 branches using a 1 × 𝑁 optical splitter. By tuning the polarization controller (PC) and polarizer (Pol.) in each branch, the RF splitter can have independently tuned phase shift and amplitude ratio. The possibility of the proposed scheme is theoretically and experimentally verified.
* Corresponding author at: State Key Laboratory on Integrated Optoelectronics, Institute of Semiconductors, Chinese Academy of Sciences, Beijing, 100083, China. E-mail address: [email protected] (W. Li).
https://doi.org/10.1016/j.optcom.2018.09.008 Received 7 August 2018; Received in revised form 3 September 2018; Accepted 4 September 2018 Available online 8 September 2018 0030-4018/© 2018 Elsevier B.V. All rights reserved.
S. Zhu et al.
Optics Communications 431 (2019) 10–13
Fig. 1. The schematic of the proposed 1 × 𝑁 hybrid radio frequency (RF) photonic splitter with arbitrary phase shift and amplitude ratio. LD, laser diode; DP-DPMZM, dual-polarization dual-parallel Mach–Zehnder modulator; DPMZM, dual-parallel Mach–Zehnder modulator; PBS, polarization beam splitter; PBC, polarization beam combiner; 90◦ , 90◦ electrical coupler; PC, polarization controller; Pol., polarizer; PD, photodetector. Fig. 2. Measured (a) phase responses and (b) magnitude responses for one port of the RF photonic splitter by adjusting the phase difference 𝜃 between the two orthogonal polarization states generated by a PC.
2. Principle The structure of the proposed 1 × 𝑁 hybrid RF photonic splitter with arbitrary phase shift and amplitude ratio is shown in Fig. 1. The key component of the RF photonic splitter is a DP-DPMZM which consists of a polarization beam splitter (PBS), two DPMZMs (DPMZM1 and DPMZM2) at two orthogonal polarization states and a polarization beam combiner (PBC). The major structure of a DPMZM is a parent MZM with two sub-MZMs lying on each of its arms. A linearly polarized optical carrier is fiber-coupled into the DP-DPMZM with an angle of 45◦ to one principal axis of the PBS. The upper DPMZM1 driven by an RF signal is biased to generate a carrier suppressed single sideband (CS-SSB) modulated signal. Whereas, the lower DPMZM2 is set at maximum transmission point to let a pure optical carrier pass through with maximum optical power. By adjusting PCs in different branches, a 1 × 𝑁 RF photonic splitter is constructed successfully. Mathematically, when the DPMZM1 is driven by a RF signal, the optical field at the output of DPMZM1 is given by 𝐸𝑥 (𝑡) =
1 𝐸 𝑒𝑗𝜔0 𝑡 [𝑒𝑗𝛽 cos(𝜔𝑚 𝑡)+𝑗𝜑1 + 𝑒𝑗𝛽 cos(𝜔𝑚 𝑡+𝜋) ] 8 0 + [𝑒𝑗𝛽 sin(𝜔𝑚 𝑡)+𝑗𝜑2 + 𝑒𝑗𝛽 sin(𝜔𝑚 𝑡+𝜋) ]𝑒𝑗𝜙1 ,
Fig. 3. Measured (a) magnitude response and (b) phase response for one port of the RF photonic splitter by adjusting the rotation angle 𝛼 of the PC.
(1) PC [18,19]. A Pol. is cascaded with the PC to project the two orthogonal polarized optical signals onto a linear polarization state. Therefore, the optical field at the output of Pol. is
where 𝐸0 and 𝜔0 are the amplitude and angular frequency of the optical carrier, 𝑉 and 𝜔𝑚 are the peak-to-peak value and angular frequency of the driven RF signal, 𝛽 is the RF modulation index of DPMZM1 which is equal to 𝜋𝑉 ∕𝑉𝜋 , 𝑉𝜋 is the RF switching voltage, 𝜑1 = 𝜋𝑉𝐷𝐶1 ∕𝑉𝜋 , 𝜑2 = 𝜋𝑉𝐷𝐶2 ∕𝑉𝜋 and 𝜙1 = 𝜋𝑉𝐷𝐶𝑥 ∕𝑉𝜋 where 𝑉𝐷𝐶1 and 𝑉𝐷𝐶2 are the direct current (DC) biases of the two sub-MZMs, 𝑉𝐷𝐶𝑥 is the main DC bias of the DPMZM1. By setting 𝜑1 = 𝜋, 𝜑2 = 𝜋, and 𝜙1 = 𝜋/2, under small signal modulation condition, Eq. (1) can be rewritten as
𝐸𝑝𝑜𝑙. (𝑡) = cos 𝛼𝐸𝑥 𝑒𝑗𝜃 + sin 𝛼𝐸𝑦 𝑒−𝑗𝜃
(5)
When the optical signal is detected by a PD for square-law detection, the recovered RF signal is 𝑖(𝑡) = 𝐸𝑝𝑜𝑙. (𝑡) ⋅ 𝐸𝑝𝑜𝑙. (𝑡)∗ 𝜋 (6) ∝ sin(2𝛼)𝐽1 (𝛽) cos(𝜔𝑚 𝑡 − + 2𝜃). 2 As can be seen from Eq. (6), the amplitude and phase of the recovered RF signal can be tuned independently by adjusting the state of PC. Therefore, if there are 𝑁 branches in the RF photonic splitter, the amplitude ratio and phase shift for different branches can be tuned independently and arbitrarily. A 1 × 𝑁 hybrid RF photonic splitter with arbitrary phase shift and amplitude ratio is constructed.
𝜋 1 𝐸𝑥 (𝑡) = 𝐸0 𝐽1 (𝛽)𝑒𝑗[(𝜔0 +𝜔𝑚 )𝑡− 2 ] , (2) 2 where 𝐽1 (𝛽) is the first order Bessel function of the first kind. From Eq. (2) we could see that a CS-SSB modulated signal is generated successfully. In order to make the pure optical carrier pass through lower DPMZM2 with maximum optical power, the two sub-MZMs and parent MZM of the DPMZM2 are all biased at maximum transmission point. Hence, the optical signal at the output of DPMZM2 is
3. Experiments and results
1 𝐸 𝑒𝑗𝜔0 𝑡 . (3) 2 0 In transmission branch, a PC which consists of a quarter-wave, a half-wave, and a quarter-wave plates is used to adjust the polarization states of the optical signals according to the transfer function of [ ][ ] cos 𝛼 − sin 𝛼 𝑒𝑗𝜃 0 𝑃𝑃 𝐶 = (4) −𝑗𝜃 , sin 𝛼 cos 𝛼 0 𝑒 𝐸𝑦 (𝑡) =
A proof-of-concept experiment based on the scheme of Fig. 1 was carried out to verify the feasibility of the proposed RF photonic splitter. A linearly polarized optical carrier centered at 1550 nm was fibercoupled into a DP-DPMZM with an angle of 45◦ to one principal axis of the PBS. A vector network analyzer (VNA) generated an RF signal to drive the DPMZM1. By adjusting the DC biases of the DP-DPMZM as describe in Section 2, DPMZM1 worked at CS-SSB modulation state, while DPMZM2 was set to let the pure optical carrier pass through
where 𝛼 is the rotation angle, 𝜃 is the phase difference between the two orthogonal polarized components introduced by the birefringence in a 11
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two optical signals of the RF photonic splitter. Actually, the PBC is equivalent to a combination of two orthogonal polarizers which can ensure the optical signals at the output of PBC cannot interfere with each other. When the optical signals are detected by a PD, the recovered two RF signals will interfere with each other. The two-tap MPF is the summation of the two branches of the RF photonic splitter. Therefore, the transmission response of the two-tap MPF can be given by
Fig. 4. The configuration of a two-tap microwave photonic filter (MPF) using the proposed RF photonic splitter. LD, laser diode; DP-DPMZM, dualpolarization dual-parallel Mach–Zehnder modulator; OC, optical coupler; PC, polarization controller; ODL, optical delay line; PBC, polarization beam combiner; PD, photodetector.
𝐻(𝑓 ) = 𝑎1 𝑒𝑗𝜓1 + 𝑎2 𝑒𝑗(𝜓2 −2𝜋𝑓 𝜏0 ) = 𝑎1 𝑒𝑗𝜓1 [1 + 𝛾𝑒𝑗(𝛥𝜓−2𝜋𝑓 𝜏0 ) ],
(7)
where 𝑎1 and 𝑎2 are the amplitude of the recovered RF signals from the two branches, 𝜓1 and 𝜓2 are the phase of the recovered RF signals from the two branches, 𝜏0 is the time delay which is introduced by an optical delay line (ODL), 𝛾 = 𝑎2 ∕𝑎1 and ▵ 𝜓 = 𝜓2 − 𝜓1 is the amplitude ratio and phase shift between the two branches. Hence, as shown in Eq. (7), by adjusting the amplitude ratio 𝛾, the notch depth of the MPF can be changed. Besides, the position of the notch can be continuously tuned by adjusting the phase shift ▵ 𝜓 between the two branches. A two-tap MPF based on the setup shown in Fig. 4 was conducted to demonstrate the tunability of the proposed RF photonic splitter. The ODL introduces a time delay of 0.66 ns between the two branches of the two-tap MPF, which is corresponding to a free spectrum range (FSR) of 1.51 GHz as shown in Fig. 5(a) and 5(b). First, when the amplitude ratio 𝛾 of the RF photonic splitter remains fixed, i.e., 𝛾 = 0.85, we tune the position of the notch by changing the phase shift ▵ 𝜓 of the RF splitter. The corresponding magnitude response of the two-tap MPF is shown in Fig. 5(a). When the phase shift ▵ 𝜓 is equal to 160◦ , 90◦ and 45◦ , the position of the notch is tunable without changing the notch depth, FSR and shape of the transmission response of the two-tap MPF. Moreover, as can be seen from Fig. 5(b), when we adjust the amplitude ratio 𝛾 of the RF photonic splitter and keep the phase shift ▵𝜓 unchanged, the depth of the notch is tunable while the notch position, shape and FSR remain the same as before. Since the responsivity of the PD decreases with the frequency, the magnitude response of the two-tap MPF becomes gradually lower with the frequency.
Fig. 5. Measured transmission responses of the two-tap microwave photonic filter (MPF) by adjusting (a) the phase shift △𝜓 of the RF photonic splitter, and (b) the amplitude ratio 𝛾 of the RF photonic splitter.
with maximal optical power. The PC and Pol. in a branch can realize polarization-to-intensity modulation conversion. Finally, the optical signal was detected by a PD with bandwidth of 18 GHz. The recovered RF signal was fed into the VNA to measure the magnitude response and phase response of the RF photonic splitter. As described in Section 2, the phase shift and amplitude ratio of the RF photonic splitter is highly related to the PC. According to Eq. (4), the rotation angle 𝛼 and the phase difference 𝜃 of the PC can be tuned independently. A detailed instruction about the tuning of the PC can be found in [18,19]. Eq. (6) shows that the phase shift of the RF photonic splitter is controlled by 𝜃, while the amplitude ratio of the splitter is determined by 𝛼. Thus, we can arbitrarily and independently change the phase shift and the amplitude ratio of the RF photonic splitter. First, we changed the phase shift of the RF photonic splitter with a fixed amplitude ratio by tuning 𝜃 of the PC. Fig. 2(a) and (b) show the phase and magnitude responses of one port of the RF photonic splitter from 8 GHz to 18 GHz. The phase of the RF signal can be tuned continuously from −180◦ to 180◦ while the magnitude response only varies within 3 dB. The lower boundary of the RF photonic splitter is determined by the 90◦ hybrid coupler which has a flat 3-dB bandwidth from 8 to 18 GHz. It can be easily increased using a 90◦ hybrid coupler with larger bandwidth. In addition, as Section 2 shows, the magnitude of the recovered microwave signal is also tunable. Hence, when the rotation angle 𝛼 of the PC was tuned, we measured the magnitude and phase responses of the recovered microwave signal from 8 GHz to 18 GHz. The corresponding phase and magnitude responses are shown in Fig. 3(a) and (b). It can be seen that the magnitude of the microwave signal can be continuously tuned from 0 dB to −12 dB while the phase variation can be kept within 10◦ . For purpose of demonstrating the tunability of the proposed RF photonic splitter, we construct a two-tap microwave photonic filter (MPF) based on the scheme of Fig. 4. A PBC is used to couple the
4. Conclusion In conclusion, a 1 × 𝑁 hybrid RF photonic splitter with arbitrary phase shift and amplitude ratio has been experimentally demonstrated using a single DP-DPMZM. The DP-DPMZM is properly set to generate an orthogonally polarized single-sideband (SSB) modulated optical signal. By adjusting the PC in different branches, an RF photonic splitter is realized. Since no optical or electrical filters are involved, the RF photonic splitter has a broad operation bandwidth. If two branches of the splitter are coupled into a PBC for photoelectric conversion by a PD, a two-tap MPF can be constructed. Besides, the notch depth and position of the two-tap MPF transmission response could be tuned independently by changing the phase shift and amplitude ratio of the RF photonic splitter. Acknowledgments This work was supported in part by the National Natural Science Foundation of China under Grants 61335005, 61431003, 61335004, 61377069, and 61527820, in part by Instrument Developing Project of the Chinese Academy of Sciences under Grant YZ201602, and in part by Open Projects Foundation of Yangtze Optical Fiber and Cable Joint Stock Limited Company (YOFC), China (SKLD1701). References [1] J. Capmany, D. Novak, Microwave photonics combines two worlds, Nature Photon. 1 (2007) 319–330. [2] A.J. Seeds, K.J. Williams, Microwave photonics, J. Lightwave Technol. 24 (2006) 4628–4641. [3] D. Marpaung, C. Roeloffzen, R. Heideman, A. Leinse, S. Sales, J. Capmang, Integrated microwave photonics, Laser Photonics Rev. 7 (2013) 506–538.
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