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OPTICS LETTERS / Vol. 39, No. 6 / March 15, 2014
Photonic-assisted microwave frequency multiplier based on nonlinear polarization rotation Jianyu Zheng,1 Hui Wang,1 Wei Li,1 Lixian Wang,1 Ting Su,2 Jianguo Liu,1,* and Ninghua Zhu1 1
The State Key Laboratory on Integrated Optoelectronics, Institution of Semiconductors, Chinese Academy of Sciences, Beijing 10083, China 2
The State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876, China *Corresponding author: [email protected]
Received December 17, 2013; revised January 20, 2014; accepted January 26, 2014; posted January 27, 2014 (Doc. ID 203240); published March 5, 2014 A photonic-assisted microwave frequency multiplier (MFM) based on the Kerr shutter is proposed and demonstrated. In this MFM, the nonlinear polarization rotation in the high nonlinear optical fiber is used for the first time to implement the light-controlled optical-carrier-suppressed modulation. The frequency-doubled microwave signal with the frequency up to 144 GHz is generated. The results of the experiment are in accordance with the theoretical prediction. © 2014 Optical Society of America OCIS codes: (060.4370) Nonlinear optics, fibers; (060.5625) Radio frequency photonics; (190.3270) Kerr effect; (230.4320) Nonlinear optical devices; (350.4010) Microwaves. http://dx.doi.org/10.1364/OL.39.001366
Recently, millimeter wave (MMW) and terahertz-wave (THz) have aroused great interest in the communication field because they could support the wireless communication system with ultra-high capacities (toward 100 Gb∕s) [1]. In order to implement the truly usercentered communication networking and extend the coverage of the wireless signals, the radio-over-fiber (ROF) system carried at the MMW or THz band was proposed where the wireless signal is converted to an optical analog signal in the center office and distributed to the base station (BS) via a long haul fiber. In the ROF system, the generation of high-quality photonic microwave signals is the crucially important part because it determines the reliability and complexity of the whole system [2]. Generating the photonic microwave based on frequencymultiplication by means of the electro-optical technology, in general, is the most feasible approach. In this approach, the quality of the frequency-multiplied microwave is reliable because it depends on the original microwave applied on the modulator. Actually, opticalcarrier-suppressed (OCS) modulation using a single electro-optic modulator (EOM) has been adopted widely in the 40 and 60 GHz ROF links to provide photonic frequency-doubled microwave [3,4]. However, due to the bandwidth limitation of the modulator, the photonic microwave, whose frequency goes beyond 75 GHz, is hardly generated, which implies that this method could not be used in an ROF system worked at W band (75–110 GHz) or even higher. In order to obtain the microwave with higher frequency, cascaded modulation using multiple EOMs and specially designed optical notch filters were proposed [5,6]. Meanwhile, the nonlinear conversion based on four-wave mixing was reported [7]. The combination of them was also demonstrated in [8–10]. Although the 132 GHz photonic microwave has been generated [9], these methods are hardly applied in practice owing to their high complexity, low conversion efficiency, and harsh operation requirement. Hence, in the reported ROFs worked at ultra-high frequency domain (>100 GHz), the photonic microwave was generated 0146-9592/14/061366-04$15.00/0
directly by optical heterodyning between two lights which were obtained from an optical comb source or two independent narrow-linewidth laser diodes [11–14]. Besides the problems from complexity and cost, the random phase fluctuation of the two lights results from the temperature shift, and external vibration could not be avoided because the two lights transmitted in the separated optical paths [14]. This phase fluctuation induces the very large noise of the generated microwave. Even if the complicated digital signal processing has already been carried out to remedy this defect in the BS [11–14], the transmission performance of the ROF system is still difficult to improve remarkably because of the low quality of the photonic microwave [14]. In this Letter, in order to obtain the high-quality microwave in ultra-high frequency domain, the frequencymultiplication based on the nonlinear polarization rotation (NPR) in the high nonlinear optical fiber (HNLF) is proposed and demonstrated experimentally. The lightcontrolled OCS modulation could be realized because the Kerr shutter is used as an all-optical Mach–Zehnder intensity modulator (MZ-IM) in the proposed microwave frequency multiplier (MFM). Hence, the frequency-doubled photonic microwave could be obtained in the optical domain directly. The frequency of the generated microwave is expected to reach the THz band due to the ultra-fast response time of the HNLF. Figure 1 shows the schematic diagram of the Kerr shutter. The principle of the proposed photonic-assisted MFM based on this device is stated as follow. When the
Fig. 1. Kerr shutter schematic diagram. HNLF, high nonlinear fiber. © 2014 Optical Society of America
March 15, 2014 / Vol. 39, No. 6 / OPTICS LETTERS
NPR occurs in an optical fiber, the fiber acts as a birefringent-phase plate [15]. The linearly polarized signal light (SL) E s decides the nonlinear parts of the refractive indexes in the x and y axis of the HNLF if the selfphase modulation is neglected [16]:
frequency of the PL. φ0 is the initial phase difference between the x axis and y axis components of the PL. After the polarizer, the PL could be expressed as 1 πP t exp jωp t j πs 2 P s;x bπP s t jφ0 exp jωp t j P πs;x π1 − bP s t φ0 π ; − expjψt sin 2 2P πs;x 2
E p;pol t
nx nx;1 2n2 jE s tj2 ; ny ny;1 2n2 bjE s tj2 ;
(1)
where nx and ny are the refractive indexes in the x and y axis of the HNLF, nx;1 and ny;1 are the linear part of the refractive indexes, n2 is the nonlinear-index coefficient, Es t is the amplitude of the SL. If the origin of the thirdorder susceptibility χ 3 is purely electronic, b 1∕3 [16]. The nonlinear part of the refractive index in the x axis of the HNLF could be expressed as Δnx 2n2 jE s tj2 2n2
P s t ; Aeff
(2)
where P s t is the optical power of the SL and Aeff is the effective area of the HNLF. Therefore, the corresponding phase shift of the probing light (PL) in the x axis induced by SL has the following expression, ΔΦp;x 2πΔnx Leff ∕λp πP s t∕P πs;x ;
P πs;x
Aeff λp ; 4n2 Leff
(4)
which is defined as half-wave optical power in x axis of the HNLF. Likewise, Δny 2n2 bjE s tj2 2n2 b
P s t ; Aeff
Aeff λp 1 1 · P πs;x · ; 4n2 Leff b b
3 2 p πP s t 2 jwpt 4 exp j P πs;x E p;x t 5; e E p;y t 2 exp j πPπs t jφ0
(10)
which is the chirp term of the modulated PL. Clearly, Eq. (9) is similar to the transfer formula of MZ-IM with chirp. As the SL is modulated by a sinusoidal microwave signal, P s t could be represented as P s t P m sinωm t, where P m and ωm are the optical power of the SL and angular frequency of the microwave signal, respectively. As the φ0 π, applying the Jacobi–Anger expansion to Eq. (9), we have Ep;pol t expjψt ·
∞ X n1
J 2n−1 β sin2n − 1wm t; (11)
where, β π1 bP m ∕2P πs;x and J 2n−1 is the (2n − 1)thorder Bessel function of the first kind. As can be seen, only odd-order sidebands are present at the output of the polarizer. Considering small-signal modulation condition, Eq. (10) can be simplified as (12)
When this optical signal is fed to a photodetector (PD), the photocurrent of the generated microwave signal is (6)
(7)
which is defined as half-wave optical power in the y axis of the HNLF. Hence, the field of the probing optical at the output of the HNLF is given by
π1 bP s t φ0 ; 2 2P πs;x
E p;pol t ≈ expjψt · J 1 β sin wm t:
where Δny is the nonlinear part of the refractive index in y axis of the HNLF induced by SL, ΔΦp;y is the phase shift of the PL y axis component induced by the SL. Correspondingly, P πs;y
ψt ωp t
(5)
and ΔΦp;y 2πΔny Leff ∕λp πP s t∕P πs;y ;
(9)
where
(3)
where Leff is the effective length of the HNLF, λp is the wavelength of the PL
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(8)
P s;y
Ep;x t and E p;y t are the amplitudes of the PL x axis and y axis components, respectively. ωp is the angular
It ∝ E p;pol · E p;pol −J 21 β cos2wm t:
(13)
We can see from Eq. (13) that a high-spectral-purity microwave signal with the frequency of 2ωm will be generated. Since the frequency multiplication factor is 2, theoretically, the phase noise of the frequency-multiplied microwave would be increased by 20 · log10 2 ≈ 6 dB from that of the original microwave [8]. To verify the principle of the proposed frequency multiplication based on NPR, an experimental setup was constructed, as shown in Fig. 2. The SL and PL were provided by laser diodes 1 and 2 (LD1 and LD2), whose wavelengths were 1550.12 and 1554.00 nm, respectively. The SL passed through the phase modulator (PM), the MZ-IM, the erbium-doped fiber amplifier (EDFA) in sequence and entered into the wave division multiplexing (WDM) add-drop thin film filter via the filter’s passed port. The WDM fiber is a polarization-maintaining component, which works at 1550.12 nm with 100-GHz channel separations. A 10 Gbit∕s nonreturn zero code with 215 − 1 pseudo-random bit sequence pattern was
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Fig. 2. Experimental setup of microwave frequency doubler using the Kerr shutter. LD, laser diode; PM, phase modulator; MZ-IM, Mach–Zehnder-intensity modulator; EDFA, erbiumdoped optical fiber amplifier; WDM filter, wave division multiplexing add-drop thin film filter; HNLF, high nonlinear fiber; OBPF, optical bandpass filter; PC, polarization controller; PD, photodetector.
applied on the PM to increase the stimulated Brillouin scattering (SBS) threshold value of the SL. The original microwave was carried on the SL through the MZ-IM. The EDFA was in charge of the power amplification of the SL. The PL was injected into the WDM filter via the reflected port. After the WDM filter, the SL polarization-modulated the PL by means of the NPR as they went through the 1 km HNLF together. The nonlinear coefficient, zero dispersion wavelength, and dispersion slope of the HNLF are 10 W−1 km−1 , 1552 nm, and 0.018 ps∕nm2 · km. Hence, we can work out that the half-wave optical power in the x axis of the HNLF is about 157 mW. The tunable optical bandpass filter was applied after the HNLF to filter out the modulated PL. The polarization direction of the PL was aligned with the principal axis of the polarizer by adjusting the PC. The PC was applied to compensate for the initial phase difference φ0 as well. The PL was received by the PD via the polarizer and converted to the frequency-doubled microwave as φ0 π. Note that in order to make the polarization of the lights steerable, all the components before the WDM filter were connected using the polarization-maintaining fiber (PMF). Moreover, unlike the customary rule, the key of the connector in the reflected port was modified to be aligned at an angle of 45° to the slow-axis of the PMF instead of at 0°. Hence, the PL’s polarization direction would be aligned at an angle of 45° to the slow-axis of the PMF at the reflected port as the light entered into the WDM filter. In this case, the SL and PL would be injected into the HNLF from the common port of the WDM filter with the relative angle of 45° accurately. The additional phase difference between the x axis and y axis components of the PL induced by the refractive index difference between the fast-axis and slow-axis of the PMF could be made up through the PC. Figures 3(a-1) and 3(b-1) display the optical and electrical spectra of the SL as an 18 GHz microwave applied on the MZ-IM in the form of double sideband (DSB) modulation (The optical spectrum was recorded as the PM was not operating.) As expected, the frequencydoubled photonic microwaves were generated as φ0 was set at π by the PC, whose optical and electrical spectra are illustrated in Figs. 3(a-2) and 3(b-2) [Fig. 3(b-3) is
Fig. 3. (a) Optical spectra and (b) electrical spectra of the SL and PL as the 18 GHz microwave applied on the MZ-IM in the form of the DSB modulation. Red circles s in (a-2) are applied to mark the chirp sidebands. (b-3) is the zoom-in view of (b-2).
the zoom-in view of microwave displayed in Fig. 3(b-2)]. As show in Fig. 3(a-2), the optical carrier suppression ratio (OCSR) was up to 20 dB. The optical sidebands marked by the red circles were the chirp sidebands which correspond to the chirp term [see Eqs. (9) and (10)]. Figure 3(b-2) displays that a 36 GHz microwave was generated whose power is approximately 20 dB greater than that of the harmonic component at 18 GHz. The phase noise of the generated 36 GHz microwaveq at an offset of 10 kHz was −96.2 dBc∕Hz, which presents a 6.2 dB phase-noise degradation compared with the 18 GHz original microwave (−102.4 dBc∕Hz at 10 kHz offset) shown in Fig. 3(b-1). The experimental comparison is in accord with the theoretical prediction. In order to investigate the performance of the proposed MFM as it worked at higher frequency, the 36 GHz microwave was applied on the MZ-IM in the form of the OCS modulation. The measured optical spectra of the SL and PL are shown in Figs. 4(a) and 4(b). It can be seen from Fig. 4(a) that the 72 GHz photonic microwave with OCSR of 20 dB was generated due to the OCS modulation of the MZ-IM. Finally, the frequency-quadruple (144 GHz) photonic microwave signal was generated on the PL as
Fig. 4. Optical spectra of the (a) SL and (b) PL as the 36 GHz microwave applied on the MZ-IM in the form of the OCS modulation. Red circles and green dots in (b) are applied to mark the chirp sidebands and harmonic-induced sidebands, respectively.
March 15, 2014 / Vol. 39, No. 6 / OPTICS LETTERS
φ0 π due to the NPR-induced-frequency-multiplication [see Fig. 4(b)]. The chirp sidebands were marked by the red circles. The green-dot-marked sidebands were induced by the 36 GHz harmonic component in the SL. It also can be seen that the OCSR of the generated photonic microwave was as low as 19 dB. In fact, the OCSR could be further increased through improving the polarization extinction ratio of the polarizer and the accuracy of the angle between the polarization directions of the PL and the SL. The electrical spectrum of the 144 GHz photonic microwave was not observed owing to the limited bandwidth of the test equipment. However, the photonic microwave with higher frequency can be obtained, because of the ultra-fast response time of the Kerr effect (fs level) in the HNLF. In our experiment, the output power and OCSR of the frequency-multiplied signal will be reduced dramatically as the phase difference φ0 drifts from π. Therefore, the PC should be replaced by a commercial polarization tracker to increase the stability of the device as the proposed method is applied in practice. As frequencyquadrupling the microwave signal, the proposed MFM will become sensitive to the SL’s spectrum, i.e., the bias point of the MZ-IM. Hence, a bias controlling device is necessary in order to enhance the stability of the MFM. Additionally, in order to improve the compactness, the NPR effect in the silicon waveguide rather than in the HNLF could be utilized [17]. In this case, the PM used in our experiment could be removed because the problem induced by the SBS is nonexistent. Obviously, due to inherent chirp and chromatic dispersion, the generated microwave will be distorted when it is transmitted to the BS via the long-haul fiber. However, when compared with the random phase fluctuation of the independent lights, the distortion could be calculated and compensated more easily by the mature technologies. In conclusion, a photonic-assisted MFM based on NPR was proposed and demonstrated for the first time. The Kerr shutter used in the MFM could be regarded as an all-optical MZ-IM with chirp. Because the process of the frequency multiplication is implemented in the optical domain, the problems from harsh operation requirement and bandwidth limitation of the cascaded modulation described in [5–10] could be avoided. Finally, the frequency-multiplied microwaves (up to 144 GHz) were generated as the Kerr shutter worked at the state of OSC modulation. Such findings are of great potential for applications in future ROF systems at W -band and even the
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THz band due to the low-complexity and ultra-fast response speed of the method. This work was partially supported by the Program of the National Natural Science Foundation of China (Grant Nos. 61090390, 61275078), by the National Basic Research Program of China (Grant Nos. 2012CB315702, 2012CB315703), by the Foundation for Innovative Research Groups of the National Natural Science Foundation of China (Grant No. 61021003), by the Funds for International Cooperation and Exchange of the National Natural Science Foundation of China (Grant No. 60820106004), and by the CAS Special Grant for Postgraduate Research, Innovation, and Practice. References 1. J. Federici and L. Moeller, J. Appl. Phys. 107, 111101 (2010). 2. A. J. Seeds and K. J. Williams, J. Lightwave Technol. 24, 4628 (2006). 3. Z. Jia, J. Yu, and G. Chang, IEEE Photon. Technol. Lett. 18, 1726 (2006). 4. J.-H. Seo, C.-S. Choi, Y.-S. Kang, and Y.-D. Chung, IEEE Trans. Microw. Theory Tech. 54, 959 (2006). 5. M. Mohmoud, X. Zhang, B. Hraimel, and K. Wu, Opt. Express 16, 10141 (2008). 6. S. Pan and J. Yao, IEEE Trans. Microw. Theory Tech. 58, 1967 (2010). 7. Q. Wang, H. Rideout, F. Zeng, and J. Yao, IEEE Photon. Technol. Lett. 18, 2460 (2006). 8. T. Wang, H. Chen, M. Chen, J. Zhang, and S. Xie, J. Lightwave Technol. 27, 2044 (2009). 9. W. Li and J. Yao, IEEE Photon. J. 2, 954 (2010). 10. B. Vidal, Opt. Lett. 37, 5055 (2012). 11. A. Kanno, K. Inagaki, I. Morohashi, T. Sakamoto, T. Kuri, I. Hosako, T. Kawanishi, Y. Yoshida, and K. Kitayama, Opt. Express 19, B56 (2011). 12. L. Deng, M. Beltran, X. Pang, X. Zhang, V. Arlunno, Y. Zhao, A. Caballero, A. Dogadaev, X. Yu, R. Llorente, D. Liu, and I. T. Monroy, IEEE Photon. Technol. Lett. 24, 383 (2012). 13. X. Li, Z. Dong, J. Yu, N. Chi, Y. Shao, and G. K. Chang, Opt. Lett. 37, 5106 (2012). 14. T. Nagatsuma, S. Horiguchi, Y. Minamikata, Y. Yoshimizu, S. Hisatake, S. Kuwano, Na. Yoshimoto, J. Terada, and H. Takahashi, Opt. Express 21, 23736 (2013). 15. Y. M. Chang, J. Lee, and J. H. Lee, Opt. Express 18, 20072 (2010). 16. G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, 2007). 17. L. Yin, J. Zhang, P. M. Fauchet, and G. P. Agrawal, Opt. Lett. 34, 476 (2009).
OPTICS LETTERS / Vol. 39, No. 6 / March 15, 2014
Photonic-assisted microwave frequency multiplier based on nonlinear polarization rotation Jianyu Zheng,1 Hui Wang,1 Wei Li,1 Lixian Wang,1 Ting Su,2 Jianguo Liu,1,* and Ninghua Zhu1 1
The State Key Laboratory on Integrated Optoelectronics, Institution of Semiconductors, Chinese Academy of Sciences, Beijing 10083, China 2
The State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876, China *Corresponding author: [email protected]
Received December 17, 2013; revised January 20, 2014; accepted January 26, 2014; posted January 27, 2014 (Doc. ID 203240); published March 5, 2014 A photonic-assisted microwave frequency multiplier (MFM) based on the Kerr shutter is proposed and demonstrated. In this MFM, the nonlinear polarization rotation in the high nonlinear optical fiber is used for the first time to implement the light-controlled optical-carrier-suppressed modulation. The frequency-doubled microwave signal with the frequency up to 144 GHz is generated. The results of the experiment are in accordance with the theoretical prediction. © 2014 Optical Society of America OCIS codes: (060.4370) Nonlinear optics, fibers; (060.5625) Radio frequency photonics; (190.3270) Kerr effect; (230.4320) Nonlinear optical devices; (350.4010) Microwaves. http://dx.doi.org/10.1364/OL.39.001366
Recently, millimeter wave (MMW) and terahertz-wave (THz) have aroused great interest in the communication field because they could support the wireless communication system with ultra-high capacities (toward 100 Gb∕s) [1]. In order to implement the truly usercentered communication networking and extend the coverage of the wireless signals, the radio-over-fiber (ROF) system carried at the MMW or THz band was proposed where the wireless signal is converted to an optical analog signal in the center office and distributed to the base station (BS) via a long haul fiber. In the ROF system, the generation of high-quality photonic microwave signals is the crucially important part because it determines the reliability and complexity of the whole system [2]. Generating the photonic microwave based on frequencymultiplication by means of the electro-optical technology, in general, is the most feasible approach. In this approach, the quality of the frequency-multiplied microwave is reliable because it depends on the original microwave applied on the modulator. Actually, opticalcarrier-suppressed (OCS) modulation using a single electro-optic modulator (EOM) has been adopted widely in the 40 and 60 GHz ROF links to provide photonic frequency-doubled microwave [3,4]. However, due to the bandwidth limitation of the modulator, the photonic microwave, whose frequency goes beyond 75 GHz, is hardly generated, which implies that this method could not be used in an ROF system worked at W band (75–110 GHz) or even higher. In order to obtain the microwave with higher frequency, cascaded modulation using multiple EOMs and specially designed optical notch filters were proposed [5,6]. Meanwhile, the nonlinear conversion based on four-wave mixing was reported [7]. The combination of them was also demonstrated in [8–10]. Although the 132 GHz photonic microwave has been generated [9], these methods are hardly applied in practice owing to their high complexity, low conversion efficiency, and harsh operation requirement. Hence, in the reported ROFs worked at ultra-high frequency domain (>100 GHz), the photonic microwave was generated 0146-9592/14/061366-04$15.00/0
directly by optical heterodyning between two lights which were obtained from an optical comb source or two independent narrow-linewidth laser diodes [11–14]. Besides the problems from complexity and cost, the random phase fluctuation of the two lights results from the temperature shift, and external vibration could not be avoided because the two lights transmitted in the separated optical paths [14]. This phase fluctuation induces the very large noise of the generated microwave. Even if the complicated digital signal processing has already been carried out to remedy this defect in the BS [11–14], the transmission performance of the ROF system is still difficult to improve remarkably because of the low quality of the photonic microwave [14]. In this Letter, in order to obtain the high-quality microwave in ultra-high frequency domain, the frequencymultiplication based on the nonlinear polarization rotation (NPR) in the high nonlinear optical fiber (HNLF) is proposed and demonstrated experimentally. The lightcontrolled OCS modulation could be realized because the Kerr shutter is used as an all-optical Mach–Zehnder intensity modulator (MZ-IM) in the proposed microwave frequency multiplier (MFM). Hence, the frequency-doubled photonic microwave could be obtained in the optical domain directly. The frequency of the generated microwave is expected to reach the THz band due to the ultra-fast response time of the HNLF. Figure 1 shows the schematic diagram of the Kerr shutter. The principle of the proposed photonic-assisted MFM based on this device is stated as follow. When the
Fig. 1. Kerr shutter schematic diagram. HNLF, high nonlinear fiber. © 2014 Optical Society of America
March 15, 2014 / Vol. 39, No. 6 / OPTICS LETTERS
NPR occurs in an optical fiber, the fiber acts as a birefringent-phase plate [15]. The linearly polarized signal light (SL) E s decides the nonlinear parts of the refractive indexes in the x and y axis of the HNLF if the selfphase modulation is neglected [16]:
frequency of the PL. φ0 is the initial phase difference between the x axis and y axis components of the PL. After the polarizer, the PL could be expressed as 1 πP t exp jωp t j πs 2 P s;x bπP s t jφ0 exp jωp t j P πs;x π1 − bP s t φ0 π ; − expjψt sin 2 2P πs;x 2
E p;pol t
nx nx;1 2n2 jE s tj2 ; ny ny;1 2n2 bjE s tj2 ;
(1)
where nx and ny are the refractive indexes in the x and y axis of the HNLF, nx;1 and ny;1 are the linear part of the refractive indexes, n2 is the nonlinear-index coefficient, Es t is the amplitude of the SL. If the origin of the thirdorder susceptibility χ 3 is purely electronic, b 1∕3 [16]. The nonlinear part of the refractive index in the x axis of the HNLF could be expressed as Δnx 2n2 jE s tj2 2n2
P s t ; Aeff
(2)
where P s t is the optical power of the SL and Aeff is the effective area of the HNLF. Therefore, the corresponding phase shift of the probing light (PL) in the x axis induced by SL has the following expression, ΔΦp;x 2πΔnx Leff ∕λp πP s t∕P πs;x ;
P πs;x
Aeff λp ; 4n2 Leff
(4)
which is defined as half-wave optical power in x axis of the HNLF. Likewise, Δny 2n2 bjE s tj2 2n2 b
P s t ; Aeff
Aeff λp 1 1 · P πs;x · ; 4n2 Leff b b
3 2 p πP s t 2 jwpt 4 exp j P πs;x E p;x t 5; e E p;y t 2 exp j πPπs t jφ0
(10)
which is the chirp term of the modulated PL. Clearly, Eq. (9) is similar to the transfer formula of MZ-IM with chirp. As the SL is modulated by a sinusoidal microwave signal, P s t could be represented as P s t P m sinωm t, where P m and ωm are the optical power of the SL and angular frequency of the microwave signal, respectively. As the φ0 π, applying the Jacobi–Anger expansion to Eq. (9), we have Ep;pol t expjψt ·
∞ X n1
J 2n−1 β sin2n − 1wm t; (11)
where, β π1 bP m ∕2P πs;x and J 2n−1 is the (2n − 1)thorder Bessel function of the first kind. As can be seen, only odd-order sidebands are present at the output of the polarizer. Considering small-signal modulation condition, Eq. (10) can be simplified as (12)
When this optical signal is fed to a photodetector (PD), the photocurrent of the generated microwave signal is (6)
(7)
which is defined as half-wave optical power in the y axis of the HNLF. Hence, the field of the probing optical at the output of the HNLF is given by
π1 bP s t φ0 ; 2 2P πs;x
E p;pol t ≈ expjψt · J 1 β sin wm t:
where Δny is the nonlinear part of the refractive index in y axis of the HNLF induced by SL, ΔΦp;y is the phase shift of the PL y axis component induced by the SL. Correspondingly, P πs;y
ψt ωp t
(5)
and ΔΦp;y 2πΔny Leff ∕λp πP s t∕P πs;y ;
(9)
where
(3)
where Leff is the effective length of the HNLF, λp is the wavelength of the PL
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(8)
P s;y
Ep;x t and E p;y t are the amplitudes of the PL x axis and y axis components, respectively. ωp is the angular
It ∝ E p;pol · E p;pol −J 21 β cos2wm t:
(13)
We can see from Eq. (13) that a high-spectral-purity microwave signal with the frequency of 2ωm will be generated. Since the frequency multiplication factor is 2, theoretically, the phase noise of the frequency-multiplied microwave would be increased by 20 · log10 2 ≈ 6 dB from that of the original microwave [8]. To verify the principle of the proposed frequency multiplication based on NPR, an experimental setup was constructed, as shown in Fig. 2. The SL and PL were provided by laser diodes 1 and 2 (LD1 and LD2), whose wavelengths were 1550.12 and 1554.00 nm, respectively. The SL passed through the phase modulator (PM), the MZ-IM, the erbium-doped fiber amplifier (EDFA) in sequence and entered into the wave division multiplexing (WDM) add-drop thin film filter via the filter’s passed port. The WDM fiber is a polarization-maintaining component, which works at 1550.12 nm with 100-GHz channel separations. A 10 Gbit∕s nonreturn zero code with 215 − 1 pseudo-random bit sequence pattern was
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OPTICS LETTERS / Vol. 39, No. 6 / March 15, 2014
Fig. 2. Experimental setup of microwave frequency doubler using the Kerr shutter. LD, laser diode; PM, phase modulator; MZ-IM, Mach–Zehnder-intensity modulator; EDFA, erbiumdoped optical fiber amplifier; WDM filter, wave division multiplexing add-drop thin film filter; HNLF, high nonlinear fiber; OBPF, optical bandpass filter; PC, polarization controller; PD, photodetector.
applied on the PM to increase the stimulated Brillouin scattering (SBS) threshold value of the SL. The original microwave was carried on the SL through the MZ-IM. The EDFA was in charge of the power amplification of the SL. The PL was injected into the WDM filter via the reflected port. After the WDM filter, the SL polarization-modulated the PL by means of the NPR as they went through the 1 km HNLF together. The nonlinear coefficient, zero dispersion wavelength, and dispersion slope of the HNLF are 10 W−1 km−1 , 1552 nm, and 0.018 ps∕nm2 · km. Hence, we can work out that the half-wave optical power in the x axis of the HNLF is about 157 mW. The tunable optical bandpass filter was applied after the HNLF to filter out the modulated PL. The polarization direction of the PL was aligned with the principal axis of the polarizer by adjusting the PC. The PC was applied to compensate for the initial phase difference φ0 as well. The PL was received by the PD via the polarizer and converted to the frequency-doubled microwave as φ0 π. Note that in order to make the polarization of the lights steerable, all the components before the WDM filter were connected using the polarization-maintaining fiber (PMF). Moreover, unlike the customary rule, the key of the connector in the reflected port was modified to be aligned at an angle of 45° to the slow-axis of the PMF instead of at 0°. Hence, the PL’s polarization direction would be aligned at an angle of 45° to the slow-axis of the PMF at the reflected port as the light entered into the WDM filter. In this case, the SL and PL would be injected into the HNLF from the common port of the WDM filter with the relative angle of 45° accurately. The additional phase difference between the x axis and y axis components of the PL induced by the refractive index difference between the fast-axis and slow-axis of the PMF could be made up through the PC. Figures 3(a-1) and 3(b-1) display the optical and electrical spectra of the SL as an 18 GHz microwave applied on the MZ-IM in the form of double sideband (DSB) modulation (The optical spectrum was recorded as the PM was not operating.) As expected, the frequencydoubled photonic microwaves were generated as φ0 was set at π by the PC, whose optical and electrical spectra are illustrated in Figs. 3(a-2) and 3(b-2) [Fig. 3(b-3) is
Fig. 3. (a) Optical spectra and (b) electrical spectra of the SL and PL as the 18 GHz microwave applied on the MZ-IM in the form of the DSB modulation. Red circles s in (a-2) are applied to mark the chirp sidebands. (b-3) is the zoom-in view of (b-2).
the zoom-in view of microwave displayed in Fig. 3(b-2)]. As show in Fig. 3(a-2), the optical carrier suppression ratio (OCSR) was up to 20 dB. The optical sidebands marked by the red circles were the chirp sidebands which correspond to the chirp term [see Eqs. (9) and (10)]. Figure 3(b-2) displays that a 36 GHz microwave was generated whose power is approximately 20 dB greater than that of the harmonic component at 18 GHz. The phase noise of the generated 36 GHz microwaveq at an offset of 10 kHz was −96.2 dBc∕Hz, which presents a 6.2 dB phase-noise degradation compared with the 18 GHz original microwave (−102.4 dBc∕Hz at 10 kHz offset) shown in Fig. 3(b-1). The experimental comparison is in accord with the theoretical prediction. In order to investigate the performance of the proposed MFM as it worked at higher frequency, the 36 GHz microwave was applied on the MZ-IM in the form of the OCS modulation. The measured optical spectra of the SL and PL are shown in Figs. 4(a) and 4(b). It can be seen from Fig. 4(a) that the 72 GHz photonic microwave with OCSR of 20 dB was generated due to the OCS modulation of the MZ-IM. Finally, the frequency-quadruple (144 GHz) photonic microwave signal was generated on the PL as
Fig. 4. Optical spectra of the (a) SL and (b) PL as the 36 GHz microwave applied on the MZ-IM in the form of the OCS modulation. Red circles and green dots in (b) are applied to mark the chirp sidebands and harmonic-induced sidebands, respectively.
March 15, 2014 / Vol. 39, No. 6 / OPTICS LETTERS
φ0 π due to the NPR-induced-frequency-multiplication [see Fig. 4(b)]. The chirp sidebands were marked by the red circles. The green-dot-marked sidebands were induced by the 36 GHz harmonic component in the SL. It also can be seen that the OCSR of the generated photonic microwave was as low as 19 dB. In fact, the OCSR could be further increased through improving the polarization extinction ratio of the polarizer and the accuracy of the angle between the polarization directions of the PL and the SL. The electrical spectrum of the 144 GHz photonic microwave was not observed owing to the limited bandwidth of the test equipment. However, the photonic microwave with higher frequency can be obtained, because of the ultra-fast response time of the Kerr effect (fs level) in the HNLF. In our experiment, the output power and OCSR of the frequency-multiplied signal will be reduced dramatically as the phase difference φ0 drifts from π. Therefore, the PC should be replaced by a commercial polarization tracker to increase the stability of the device as the proposed method is applied in practice. As frequencyquadrupling the microwave signal, the proposed MFM will become sensitive to the SL’s spectrum, i.e., the bias point of the MZ-IM. Hence, a bias controlling device is necessary in order to enhance the stability of the MFM. Additionally, in order to improve the compactness, the NPR effect in the silicon waveguide rather than in the HNLF could be utilized [17]. In this case, the PM used in our experiment could be removed because the problem induced by the SBS is nonexistent. Obviously, due to inherent chirp and chromatic dispersion, the generated microwave will be distorted when it is transmitted to the BS via the long-haul fiber. However, when compared with the random phase fluctuation of the independent lights, the distortion could be calculated and compensated more easily by the mature technologies. In conclusion, a photonic-assisted MFM based on NPR was proposed and demonstrated for the first time. The Kerr shutter used in the MFM could be regarded as an all-optical MZ-IM with chirp. Because the process of the frequency multiplication is implemented in the optical domain, the problems from harsh operation requirement and bandwidth limitation of the cascaded modulation described in [5–10] could be avoided. Finally, the frequency-multiplied microwaves (up to 144 GHz) were generated as the Kerr shutter worked at the state of OSC modulation. Such findings are of great potential for applications in future ROF systems at W -band and even the
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THz band due to the low-complexity and ultra-fast response speed of the method. This work was partially supported by the Program of the National Natural Science Foundation of China (Grant Nos. 61090390, 61275078), by the National Basic Research Program of China (Grant Nos. 2012CB315702, 2012CB315703), by the Foundation for Innovative Research Groups of the National Natural Science Foundation of China (Grant No. 61021003), by the Funds for International Cooperation and Exchange of the National Natural Science Foundation of China (Grant No. 60820106004), and by the CAS Special Grant for Postgraduate Research, Innovation, and Practice. References 1. J. Federici and L. Moeller, J. Appl. Phys. 107, 111101 (2010). 2. A. J. Seeds and K. J. Williams, J. Lightwave Technol. 24, 4628 (2006). 3. Z. Jia, J. Yu, and G. Chang, IEEE Photon. Technol. Lett. 18, 1726 (2006). 4. J.-H. Seo, C.-S. Choi, Y.-S. Kang, and Y.-D. Chung, IEEE Trans. Microw. Theory Tech. 54, 959 (2006). 5. M. Mohmoud, X. Zhang, B. Hraimel, and K. Wu, Opt. Express 16, 10141 (2008). 6. S. Pan and J. Yao, IEEE Trans. Microw. Theory Tech. 58, 1967 (2010). 7. Q. Wang, H. Rideout, F. Zeng, and J. Yao, IEEE Photon. Technol. Lett. 18, 2460 (2006). 8. T. Wang, H. Chen, M. Chen, J. Zhang, and S. Xie, J. Lightwave Technol. 27, 2044 (2009). 9. W. Li and J. Yao, IEEE Photon. J. 2, 954 (2010). 10. B. Vidal, Opt. Lett. 37, 5055 (2012). 11. A. Kanno, K. Inagaki, I. Morohashi, T. Sakamoto, T. Kuri, I. Hosako, T. Kawanishi, Y. Yoshida, and K. Kitayama, Opt. Express 19, B56 (2011). 12. L. Deng, M. Beltran, X. Pang, X. Zhang, V. Arlunno, Y. Zhao, A. Caballero, A. Dogadaev, X. Yu, R. Llorente, D. Liu, and I. T. Monroy, IEEE Photon. Technol. Lett. 24, 383 (2012). 13. X. Li, Z. Dong, J. Yu, N. Chi, Y. Shao, and G. K. Chang, Opt. Lett. 37, 5106 (2012). 14. T. Nagatsuma, S. Horiguchi, Y. Minamikata, Y. Yoshimizu, S. Hisatake, S. Kuwano, Na. Yoshimoto, J. Terada, and H. Takahashi, Opt. Express 21, 23736 (2013). 15. Y. M. Chang, J. Lee, and J. H. Lee, Opt. Express 18, 20072 (2010). 16. G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, 2007). 17. L. Yin, J. Zhang, P. M. Fauchet, and G. P. Agrawal, Opt. Lett. 34, 476 (2009).
