Implementation of a widely tunable microwave signal generator based on dual-polarization fiber grating laser Qiang Yuan, Yizhi Liang, Long Jin,* Linghao Cheng, and Bai-Ou Guan Institute of Photonics Technology, Jinan University, Guangzhou 510632, China *Corresponding author: [email protected] Received 22 October 2014; revised 29 December 2014; accepted 2 January 2015; posted 6 January 2015 (Doc. ID 225522); published 29 January 2015
In this paper, we demonstrate the implementation of a widely tunable microwave signal generator based on a dual-polarization fiber grating laser. The laser contains two strong, wavelength-matched Bragg gratings photoinscribed in an Er-doped fiber and emits two polarization modes when pumped with a 980 nm laser diode. By beating the two modes, a microwave signal with a signal-to-noise ratio over 60 dB can be obtained. For a free running laser the fluctuations in intensity and frequency of the microwave signal are 1 dB and 5 kHz, respectively, and the noise level is about −40 dBc∕Hz at 1 kHz. The frequency can be continuously tuned from 1.8 to 15.1 GHz, by transversely loading the laser cavity and changing the intracavity birefringence by use of a piezoelectric transducer-based mechanical device. The measured response time rate of tuning is about 90 MHz/μs and the intensity fluctuation at different frequencies is less than 1.5 dB. The frequency fluctuation under loading is controlled within 1 MHz by introducing an electrical feedback. © 2015 Optical Society of America OCIS codes: (060.0060) Fiber optics and optical communications; (060.2380) Fiber optics sources and detectors. http://dx.doi.org/10.1364/AO.54.000895
1. Introduction
In the recent years, optical generation of microwave signals has received great interest since this method can offer signals with low phase noise and intrinsic frequency tunability. Photonic microwave signal generators can find applications in radar, wireless communications, and advanced instrumentation. Frequency tunable microwave signal generators have been proposed and demonstrated based on a number of techniques, including optical injection locking, optical phase-lock loop, and dual-wavelength lasers [1]. The dual-wavelength-laser approach relies on the implementation of a single-longitudinal-mode laser that emits an output at two wavelengths with identical or orthogonal polarizations [2–12]. The microwave signal can be generated as a result of the 1559-128X/15/040895-06$15.00/0 © 2015 Optical Society of America
beating between the two wavelengths. Compared with the former two approaches, the dual-wavelength-laser method does not need an extra wavelength reference because the two wavelengths are highly correlated in phase, which can greatly reduce the system cost and complexity. Dual-wavelength fiber laser has been proposed by use of a fiber Bragg grating (FBG) with two abrupt phase shifts incorporated in a long ring cavity [2–4]. The phase shifts produce two narrow peaks within the transmission dip of the FBG and determine the two lasing frequencies. The beat frequency can be mechanically tuned from 8.8 to 24.4 GHz by creating a strain gradient with a triangle cantilever or from 0.128 to 7 GHz by use of two piezoelectric transducers (PZTs) [3,4]. Alternatively, microchip lasers with two orthogonal polarization modes have been applied as a microwave signal generator. The beat frequency can be adjusted based on electro-optic effect or by rotating wave plates within the laser cavity [5–7]. 1 February 2015 / Vol. 54, No. 4 / APPLIED OPTICS
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Dual-polarization fiber grating lasers have been fabricated to implement a tunable microwave source [8–12]. The laser emits outputs along the two orthogonal polarizations and the beat frequency is tuned by transversely compressing the laser cavity to change the intracavity birefringence. Our preliminary work in [8] has just demonstrated the feasibility of frequency tunability but the quality and stability of the signal need further improvements. In this paper, we report on our latest progress on this work. First, the quality of the output microwave signal has been improved. The signal-to-noise ratio can be over 60 dB, and the phase noise is about −40 dBc∕Hz at 1 kHz. The fluctuations in intensity and frequency are 1 dB and 5 kHz, respectively, via the employment of polarization maintaining fibers and elimination of the unwanted optical feedback. Furthermore, by optimizing the PZT-based mechanic device, the frequency can be continuously tuned from 1.8 to 15.1 GHz. The response time rate of tuning is about 90 MHz/μs and the intensity fluctuation at different frequencies is less than 1.5 dB. The frequency fluctuation is within 1 MHz with electric feedback. Microwave sources in array can be further implemented for radar and instrumentation applications, taking advantage of the device compactness and intrinsic multiplexing capability of the lasers. 2. Experimental Setup and Working Principle
Figure 1 shows the experimental setup for the tunable microwave signal generator. The fiber grating laser has a distributed Bragg reflector (DBR) structure, containing two discrete, strong, wavelength-matched Bragg gratings in an Er-doped fiber (Fibercore, M-12). The gratings are inscribed by use of a 193 nm ArF excimer laser and a phase mask with a period of 1057.22 nm. The gratings are 6 mm in length and the grating separation is 5 mm. The coupling ratios of the two gratings are as high as above 25 dB, to provide strong optical feedback for the establishment of laser oscillation. We intend to fabricate gratings with equal lengths and reflectivities as possible, to obtain a
Fig. 1. Experimental setup of the tunable microwave signal generator. ISO, optical isolator; WDM, wavelength division multiplexer; PD, photodetector; PZT, piezoelectric transducer. Red lines: polarization-maintaining fibers. The WDM is also a polarization maintaining device. 896
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symmetrical mode profile. The DBR laser is annealed at 120°C for 2 h to release the internal stress induced by UV exposure. A 980-nm laser diode with an output power of 200 mW is used to pump the laser. The fiber grating laser, with an average output power of 100 μW, naturally emits single-longitudinal-mode outputs along x and y polarizations. The two polarization modes are different in lasing frequency due to the intrinsic birefringence, arising from the geometrical imperfection induced in the fiber drawing process. The optical spectrum of the laser output is measured with an optical spectrum analyzer with a resolution of 0.02 nm and the RF-domain beat signal can be observed and measured by use of a photodetector and an electronic spectrum analyzer (Anritsu, MS-2692A). An optical isolator is used to prevent unwanted optical feedback in terms of scatterings or end face reflections. The in-line polarizer is inserted before the photodetector to maximize the intensity of the beat signal. An electrical feedback can be applied to balance the slowly varying, random change in applied stress by applying a corresponding voltage change, if necessary. The resonant condition 2kx;y Lcav 2Mπ is satisfied for both polarization modes, where kx;y , Lcav , and M represent propagation constants, the effective cavity length, and the resonant order, respectively. Substituting kx;y 2π∕cνx;y nx;y into the resonant condition, the difference in lasing frequencies can be expressed by Δν jνx − νy j
B ν ; n0 0
(1)
where B is the intrinsic birefringence with a typical amplitude of 10−6 order, n0 and ν0 are the average mode index and average lasing frequency (of 1014 Hz order), respectively. As a result, a beat signal in the RF domain with a frequency Δν can be obtained. Equation (1) suggests that the beat frequency is dominantly determined by the intracavity birefringence. In the experiment, the birefringence is changed by applying transverse load to the laser cavity by use of a mechanical device, as shown in Fig. 1. The laser cavity, accompanied with another supporting fiber, is sandwiched between two glass plates with a thickness of 1 mm. The plates are used to prevent sharp stress distribution along the fiber as a result of the stress concentration effect. A PZT (PI-885.31) with dimensions of 13.5mm × 5mm × 5 mm and a maximum elongation of 13 μm is placed in contact with the top plate, to apply a transverse stress onto the middle region of the laser. The dimensions of the PZT and glass plates have been optimized to reach higher tuning efficiency while maintaining the output signal of the fiber laser. The PZT and the laser are clamped in a mechanical device and a prestress is applied to stabilize the fixing. When a driving voltage is applied, the PZT elongates to squeeze the fiber cavity and subject a transverse stress onto the laser cavity. Assume the optical fiber is homogeneous in elasticity, the birefringence change induced by the applied force can be expressed by [13]
δB 2n30 p12 − p11 1 vp F∕πrE;
(2)
where p11 and p12 represent the components of strainoptic tensor, E and νp denote Young’s modulus and Poisson’s ratio, respectively, F is linear density of force, r is the fiber radius. The corresponding beat frequency change can be expressed by δΔν 2n20 p12 − p11 1 vp Fν0 ∕πrE:
(3)
Equation (3) suggests that the beat frequency can be changed by the applied transverse load onto the laser cavity as a result of the elongation of the PZT. Substituting p11 0.121, p12 0.27, νp 0.16, E 69 GPa, r 62.5 μm, and n0 1.448 into Eq. (3), the calculated frequency change rate with applied force is 10.3 GHz/(N/mm). However, note that the Er-doped fiber has a weak intrinsic birefringence, the loading should be applied along the slow axis to reach maximum frequency tunability. 3. Experimental Result and Discussion A.
Characterization of the Microwave Signal
Figure 2(a) shows the measured spectrum of the beat signal and the optical spectrum of the laser output. The lasing wavelength is 1529.6 nm. The beat frequency is 323 MHz, corresponding to an intrinsic birefringence of 2.4 × 10−6. Note that the output frequency can be somewhat different because the UV illumination can induce a considerable birefringence change. The signal presents a signal to noise level above 60 dB. The phase noise spectrum presents a 1∕f profile over the range from 1 to 100 kHz, as a result of the nonequilibrium thermal fluctuations [14]. The noise level is −40 dBc∕Hz at 1 kHz. Figures 2(b) and 2(c) demonstrate the measured frequency and intensity fluctuations over 20 min. The frequency fluctuation is 5 kHz and the intensity fluctuation is 1 dB. We have found that the beat frequency can shift by 18 MHz by changing the polarization orientation of the input pump light, as a result of resonantly enhanced nonlinearity [15]. The polarization effect can be effectively removed via the employment of polarization maintaining fibers and WDM. In addition, the end face reflection and scattering can possibly introduce a perturbation to the lasing oscillation and the use of isolator is important for the stabilization of the output [16]. The geometrical parameters, including the lengths of the gratings and their separation, have been optimized. Due to the strong reflection of the gratings, the effective cavity length approximately equals the length of the grating separation. If the cavity is too short, lasing oscillation is difficult to establish. If the grating separation is too long, the laser output can contain multiple longitudinal modes and one cannot obtain stable RF signal.
Fig. 2. (a) Measured spectrum of the RF-domain beat signal. Inset: optical spectrum of the laser output. (b) Measured frequency fluctuation over 20 min. (c) Measured intensity fluctuation over 20 min.
B. Tunability of the Microwave Source
Figure 3(a) shows the measured beat frequencies as a function of applied driving voltages onto the PZT. The frequency changes from 1.8 to 15.1 GHz with the driving voltage from 0 to 80 V. As the PZT gradually elongates, a transverse stress is subjected onto the laser cavity, which can effectively change the intracavity birefringence and increase the beat frequency. In addition, the supporting beam deflects due to the elongation of the PZT and tightens the whole loading structure. As a result, the rate of the frequency 1 February 2015 / Vol. 54, No. 4 / APPLIED OPTICS
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change becomes higher with higher driving voltage. The frequency variations with increasing and decreasing voltages do not totally coincide due to the hysteresis loop of the PZT’s response. Figure 3(b) shows the measured spectra of the beat signal at different frequencies. The intensity fluctuation for different beat frequencies is no more than 1.5 dB. This fluctuation is a result of a slight change in cavity loss induced by the applied stress. The slow axis of the laser cavity is determined in advance, which is carried out by placing a small mass onto the cavity and measuring the corresponding frequency shift. We repeat this process for different loading orientations by rotating the fiber with two rotatable fiber holders and see along which direction the maximum frequency change can be obtained. That orientation is then marked before clamping it with the mechanical loading device. In order to test the response time of the device, a square wave signal with a period of 5 kHz is superimposed onto the driving voltage. Figure 4(a) shows the frequency variation at the rising edge of the signal. The response time rate is estimated as about 90 MHz/μs, limited by the elastic properties and geometry of the steel structure. The response time is also relevant with the deformation of the steel
Fig. 4. (a) Measured frequency variation when the driving voltage is at a rising edge of the applied square wave signal. (b) Measured phase noise spectrum before and after loading the laser cavity.
Fig. 3. (a) Measured beat-frequency variation with applied driving voltage. (b) Recorded beat note spectra at different frequencies (1–13 GHz). 898
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beam under loading. The driving voltage range of 80 V is programmed to be divided by 65,536 steps, and thereby the average minimum beat-frequency step is about 0.2 MHz. When applying a certain driving voltage, we found that the beat frequency is slowly varying with an unpredictable trend over hours. The maximum frequency shift can be several hundreds of megahertz. The long-term variation is measured under constant environmental temperature and is not likely a result of the temperature dependence of the piezoelectric response. This is a result of the creep of the supporting steel structures in tension. Figure 4(b) shows the measured phase noise spectrum of the beat signal with and without transverse loading, respectively. The noise level increases from −70 to about −65 dBc∕Hz at 10 kHz after the loading, and −40 to −20 dBc at 1 kHz, as a result of acoustic sensitivity. We have tested the output properties of the signal generator under static loading, by placing a mass onto the laser cavity. The beat frequency is changed to about 10 GHz and the frequency fluctuation is less than 0.5 MHz and the intensity fluctuation is less than 1 dB. This verifies the origin of the slowly varying frequency
variation from the mechanical structure. To stabilize the beat signal under loading, a close loop is established, as shown in Fig. 1. When the frequency change is out of tolerance (1 MHz in our experiment), a compensation voltage is applied to recover the original frequency. We have fabricated a number of fiber grating lasers and found that their maximum beat frequencies that can be achieved are around 15 GHz. If further increasing the transverse stress by controlling the driving voltage, the beat signal rapidly weakens and then disappears. The limitation in the tunable frequency range is described as follows. Figure 5 schematically shows the transmission spectrum of the Bragg grating pair without pump for both orthogonal polarizations. The transmission maxima within the grating transmission dip are a result of the multibeam interference. The resonant frequencies correspond to the lasing frequencies. When the laser cavity is loaded with a transverse stress along the y axis, the resonant frequencies change while the grating dips unchanged. According to the elasticoptic effect, νy decreases slightly and νx increases with a much higher rate, as presented by the dashed plots in Fig. 5(a). The grating dips have flat bottoms, indicating strong reflections and sufficient optical feedbacks. The spectral width of the flat region
Fig. 5. Schematic evolutions the transmission spectra of the grating pair when loading (a) over the blank region between the gratings and (b) over the whole laser cavity including the gratings.
is about 18 GHz, which determines the maximum frequency tuning range. When further increasing the stress, νx moves to the edge of the grating dip where the optical feedbacks are much weaker, and the lasing oscillation cannot be established at this polarization. As a result, the beat signal disappears. Possible strategies to increase the tuning range include decreasing the grating length or employing a chirped fiber grating to achieve wider transmission dip of the grating. However, it is difficult for the short uniform grating or the chirped grating to reach a reflectivity up to 25 dB to achieve laser threshold. An ideal method to overcome this limitation is to stress the whole cavity including the two gratings. As shown in Fig. 5(b), if the gratings are also stressed, the transmission maxima and the grating dips shift with identical rates. The two orthogonal polarization modes can be well maintained and much higher beat frequency can be obtained. However, in practice, we found it very difficult to obtain a uniform stress over the whole cavity. The stress gradient along the gratings can cause distortion of their transmission spectrum. The coupling strengths are therefore lowered and the lasing oscillation can be failed. 4. Conclusion
In conclusion, we have demonstrated the implementation of a widely tunable microwave signal generator based on a dual-polarization fiber grating laser. The laser emits single-longitudinal-mode output at the two orthogonal polarizations. By beating the two modes, a microwave signal with a signal-to-noise ratio over 60 dB can be obtained, whose frequency is determined by the intracavity birefringence. For a free running laser the fluctuations in intensity and frequency of the microwave signal are 1 dB and 5 kHz, respectively, and the noise level is about −40 dBc∕Hz at 1 kHz, by optimizing the inscription of the Bragg gratings and performing treatments to suppress the fluctuation of pump conditions and the external perturbations. The frequency can be continuously tuned from 1.8 to 15.1 GHz, by transversely loading the laser cavity and changing the intracavity birefringence by use of a PZT-based mechanical device. The measured response time rate of tuning is about 90 MHz/μs and the intensity fluctuation at different frequencies is less than 1.5 dB. The frequency fluctuation is controlled within 1 MHz via electric feedback. The proposed method presents an optically induced microwave signal generator with good signal quality, fast and wide tenability, and intrinsic multiplexing capability. This work was supported by National Natural Science Foundation of China under grants 61177074, 61235005, and 11474133, Guangdong Natural Science Foundation under grant S2013030013302, Department of Education, Guangdong Province under grant Yq2013021, and the Planned Science & Technology Project of Guangzhou under grant 2012J510028. 1 February 2015 / Vol. 54, No. 4 / APPLIED OPTICS
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References 1. J. Yao, “Microwave photonics,” IEEE J. Lightwave Technol. 27, 314–335 (2009). 2. X. Chen, Z. Deng, and J. P. Yao, “Photonic generation of microwave signal using a dual-wavelength single-longitudinalmode fiber ring laser,” IEEE Trans. Microw. Theory Tech. 54, 804–809 (2006). 3. M. Jiang, B. Lin, P. P. Shum, S. C. Tjin, X. Dong, and Q. Sun, “Tunable microwave generation based on a dual-wavelength single-longitudinal-mode fiber laser using a phase-shifted grating on a triangular cantilever,” Appl. Opt. 50, 1900–1904 (2011). 4. G. E. Villanueva, P. Pérez-Millán, J. Palací, J. L. Cruz, M. V. Andrés, and J. Martí, “Dual-wavelength DFB erbium-doped fiber laser with tunable wavelength spacing,” IEEE Photon. Technol. Lett. 22, 254–256 (2010). 5. J. Maxin, G. Pillet, B. Steinhausser, L. Morvan, O. Llopis, and D. Dolfi, “Widely tunable opto-electronic oscillator based on a dual-frequency laser,” IEEE J. Lightwave Technol. 31, 2919–2925 (2013). 6. Y. Qiao, S. Zheng, H. Chi, X. Jin, and X. Zhang, “Electrooptically tunable microwave source based on composite-cavity microchip laser,” Opt. Express 20, 29090–29095 (2012). 7. A. McKay and J. M. Dawes, “Tunable terahertz signals using a helicoidally polarized ceramic microchip laser,” IEEE Photonics Technol. Lett. 21, 480–482 (2009). 8. B. O. Guan, Y. Zhang, L. W. Zhang, and H. Y. Tam, “Electrically tunable microwave generation using compact dual-polarization fiber laser,” IEEE Photon. Technol. Lett. 21, 727–729 (2009).
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9. B. O. Guan, L. Jin, Y. Zhang, and H. Y. Tam, “Polarimetric heterodyning fiber grating laser sensors,” IEEE J. Lightwave Technol. 30, 1097–1112 (2012). 10. W. Liu, M. Jiang, D. Chen, and S. He, “Dual-wavelength single-longitudinal-mode polarization-maintaining fiber laser and its application in microwave generation,” J. Lightwave Technol. 27, 4455–4459 (2009). 11. S. Feng, C. Qi, Q. Li, W. Peng, S. Gao, and S. Jian, “Photonic generation of microwave signal by beating a dual-wavelength single longitudinal mode erbium-doped fiber ring laser based on the polarization maintaining fiber Bragg grating,” Microw. Opt. Technol. Lett. 55, 347–351 (2013). 12. A. Rosales-García, T. F. Morse, J. Hernández-Cordero, and M. Selim Unlu, “Single polarization-mode-beating frequency fiber laser,” IEEE Photon. Technol. Lett. 21, 537–539 (2009). 13. R. Gafsi and M. A. El-Sherif, “Analysis of induced-birefringence effects on fiber Bragg gratings,” Opt. Fiber Technol. 6, 299–323 (2000). 14. S. Foster, G. A. Cranch, and A. Tikhomirov, “Experimental evidence for the thermal origin of 1/f frequency noise in erbiumdoped fiber lasers,” Phys. Rev. A 79, 053802 (2009). 15. Y. Z. Liang, Q. Yuan, L. Jin, L. H. Cheng, and B. O. Guan, “Effect of pump light polarization and beat note stabilization for dual-polarization fiber grating laser sensors,” IEEE J. Sel. Top. Quantum Electron. 20, 5600208 (2014). 16. Y. Liang, L. Jin, Q. Yuan, L. Cheng, and B. O. Guan, “Detection of an extremely small mass with a dual-polarization fiber grating laser,” Proc. SPIE 9157, 91571C (2014).
In this paper, we demonstrate the implementation of a widely tunable microwave signal generator based on a dual-polarization fiber grating laser. The laser contains two strong, wavelength-matched Bragg gratings photoinscribed in an Er-doped fiber and emits two polarization modes when pumped with a 980 nm laser diode. By beating the two modes, a microwave signal with a signal-to-noise ratio over 60 dB can be obtained. For a free running laser the fluctuations in intensity and frequency of the microwave signal are 1 dB and 5 kHz, respectively, and the noise level is about −40 dBc∕Hz at 1 kHz. The frequency can be continuously tuned from 1.8 to 15.1 GHz, by transversely loading the laser cavity and changing the intracavity birefringence by use of a piezoelectric transducer-based mechanical device. The measured response time rate of tuning is about 90 MHz/μs and the intensity fluctuation at different frequencies is less than 1.5 dB. The frequency fluctuation under loading is controlled within 1 MHz by introducing an electrical feedback. © 2015 Optical Society of America OCIS codes: (060.0060) Fiber optics and optical communications; (060.2380) Fiber optics sources and detectors. http://dx.doi.org/10.1364/AO.54.000895
1. Introduction
In the recent years, optical generation of microwave signals has received great interest since this method can offer signals with low phase noise and intrinsic frequency tunability. Photonic microwave signal generators can find applications in radar, wireless communications, and advanced instrumentation. Frequency tunable microwave signal generators have been proposed and demonstrated based on a number of techniques, including optical injection locking, optical phase-lock loop, and dual-wavelength lasers [1]. The dual-wavelength-laser approach relies on the implementation of a single-longitudinal-mode laser that emits an output at two wavelengths with identical or orthogonal polarizations [2–12]. The microwave signal can be generated as a result of the 1559-128X/15/040895-06$15.00/0 © 2015 Optical Society of America
beating between the two wavelengths. Compared with the former two approaches, the dual-wavelength-laser method does not need an extra wavelength reference because the two wavelengths are highly correlated in phase, which can greatly reduce the system cost and complexity. Dual-wavelength fiber laser has been proposed by use of a fiber Bragg grating (FBG) with two abrupt phase shifts incorporated in a long ring cavity [2–4]. The phase shifts produce two narrow peaks within the transmission dip of the FBG and determine the two lasing frequencies. The beat frequency can be mechanically tuned from 8.8 to 24.4 GHz by creating a strain gradient with a triangle cantilever or from 0.128 to 7 GHz by use of two piezoelectric transducers (PZTs) [3,4]. Alternatively, microchip lasers with two orthogonal polarization modes have been applied as a microwave signal generator. The beat frequency can be adjusted based on electro-optic effect or by rotating wave plates within the laser cavity [5–7]. 1 February 2015 / Vol. 54, No. 4 / APPLIED OPTICS
895
Dual-polarization fiber grating lasers have been fabricated to implement a tunable microwave source [8–12]. The laser emits outputs along the two orthogonal polarizations and the beat frequency is tuned by transversely compressing the laser cavity to change the intracavity birefringence. Our preliminary work in [8] has just demonstrated the feasibility of frequency tunability but the quality and stability of the signal need further improvements. In this paper, we report on our latest progress on this work. First, the quality of the output microwave signal has been improved. The signal-to-noise ratio can be over 60 dB, and the phase noise is about −40 dBc∕Hz at 1 kHz. The fluctuations in intensity and frequency are 1 dB and 5 kHz, respectively, via the employment of polarization maintaining fibers and elimination of the unwanted optical feedback. Furthermore, by optimizing the PZT-based mechanic device, the frequency can be continuously tuned from 1.8 to 15.1 GHz. The response time rate of tuning is about 90 MHz/μs and the intensity fluctuation at different frequencies is less than 1.5 dB. The frequency fluctuation is within 1 MHz with electric feedback. Microwave sources in array can be further implemented for radar and instrumentation applications, taking advantage of the device compactness and intrinsic multiplexing capability of the lasers. 2. Experimental Setup and Working Principle
Figure 1 shows the experimental setup for the tunable microwave signal generator. The fiber grating laser has a distributed Bragg reflector (DBR) structure, containing two discrete, strong, wavelength-matched Bragg gratings in an Er-doped fiber (Fibercore, M-12). The gratings are inscribed by use of a 193 nm ArF excimer laser and a phase mask with a period of 1057.22 nm. The gratings are 6 mm in length and the grating separation is 5 mm. The coupling ratios of the two gratings are as high as above 25 dB, to provide strong optical feedback for the establishment of laser oscillation. We intend to fabricate gratings with equal lengths and reflectivities as possible, to obtain a
Fig. 1. Experimental setup of the tunable microwave signal generator. ISO, optical isolator; WDM, wavelength division multiplexer; PD, photodetector; PZT, piezoelectric transducer. Red lines: polarization-maintaining fibers. The WDM is also a polarization maintaining device. 896
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symmetrical mode profile. The DBR laser is annealed at 120°C for 2 h to release the internal stress induced by UV exposure. A 980-nm laser diode with an output power of 200 mW is used to pump the laser. The fiber grating laser, with an average output power of 100 μW, naturally emits single-longitudinal-mode outputs along x and y polarizations. The two polarization modes are different in lasing frequency due to the intrinsic birefringence, arising from the geometrical imperfection induced in the fiber drawing process. The optical spectrum of the laser output is measured with an optical spectrum analyzer with a resolution of 0.02 nm and the RF-domain beat signal can be observed and measured by use of a photodetector and an electronic spectrum analyzer (Anritsu, MS-2692A). An optical isolator is used to prevent unwanted optical feedback in terms of scatterings or end face reflections. The in-line polarizer is inserted before the photodetector to maximize the intensity of the beat signal. An electrical feedback can be applied to balance the slowly varying, random change in applied stress by applying a corresponding voltage change, if necessary. The resonant condition 2kx;y Lcav 2Mπ is satisfied for both polarization modes, where kx;y , Lcav , and M represent propagation constants, the effective cavity length, and the resonant order, respectively. Substituting kx;y 2π∕cνx;y nx;y into the resonant condition, the difference in lasing frequencies can be expressed by Δν jνx − νy j
B ν ; n0 0
(1)
where B is the intrinsic birefringence with a typical amplitude of 10−6 order, n0 and ν0 are the average mode index and average lasing frequency (of 1014 Hz order), respectively. As a result, a beat signal in the RF domain with a frequency Δν can be obtained. Equation (1) suggests that the beat frequency is dominantly determined by the intracavity birefringence. In the experiment, the birefringence is changed by applying transverse load to the laser cavity by use of a mechanical device, as shown in Fig. 1. The laser cavity, accompanied with another supporting fiber, is sandwiched between two glass plates with a thickness of 1 mm. The plates are used to prevent sharp stress distribution along the fiber as a result of the stress concentration effect. A PZT (PI-885.31) with dimensions of 13.5mm × 5mm × 5 mm and a maximum elongation of 13 μm is placed in contact with the top plate, to apply a transverse stress onto the middle region of the laser. The dimensions of the PZT and glass plates have been optimized to reach higher tuning efficiency while maintaining the output signal of the fiber laser. The PZT and the laser are clamped in a mechanical device and a prestress is applied to stabilize the fixing. When a driving voltage is applied, the PZT elongates to squeeze the fiber cavity and subject a transverse stress onto the laser cavity. Assume the optical fiber is homogeneous in elasticity, the birefringence change induced by the applied force can be expressed by [13]
δB 2n30 p12 − p11 1 vp F∕πrE;
(2)
where p11 and p12 represent the components of strainoptic tensor, E and νp denote Young’s modulus and Poisson’s ratio, respectively, F is linear density of force, r is the fiber radius. The corresponding beat frequency change can be expressed by δΔν 2n20 p12 − p11 1 vp Fν0 ∕πrE:
(3)
Equation (3) suggests that the beat frequency can be changed by the applied transverse load onto the laser cavity as a result of the elongation of the PZT. Substituting p11 0.121, p12 0.27, νp 0.16, E 69 GPa, r 62.5 μm, and n0 1.448 into Eq. (3), the calculated frequency change rate with applied force is 10.3 GHz/(N/mm). However, note that the Er-doped fiber has a weak intrinsic birefringence, the loading should be applied along the slow axis to reach maximum frequency tunability. 3. Experimental Result and Discussion A.
Characterization of the Microwave Signal
Figure 2(a) shows the measured spectrum of the beat signal and the optical spectrum of the laser output. The lasing wavelength is 1529.6 nm. The beat frequency is 323 MHz, corresponding to an intrinsic birefringence of 2.4 × 10−6. Note that the output frequency can be somewhat different because the UV illumination can induce a considerable birefringence change. The signal presents a signal to noise level above 60 dB. The phase noise spectrum presents a 1∕f profile over the range from 1 to 100 kHz, as a result of the nonequilibrium thermal fluctuations [14]. The noise level is −40 dBc∕Hz at 1 kHz. Figures 2(b) and 2(c) demonstrate the measured frequency and intensity fluctuations over 20 min. The frequency fluctuation is 5 kHz and the intensity fluctuation is 1 dB. We have found that the beat frequency can shift by 18 MHz by changing the polarization orientation of the input pump light, as a result of resonantly enhanced nonlinearity [15]. The polarization effect can be effectively removed via the employment of polarization maintaining fibers and WDM. In addition, the end face reflection and scattering can possibly introduce a perturbation to the lasing oscillation and the use of isolator is important for the stabilization of the output [16]. The geometrical parameters, including the lengths of the gratings and their separation, have been optimized. Due to the strong reflection of the gratings, the effective cavity length approximately equals the length of the grating separation. If the cavity is too short, lasing oscillation is difficult to establish. If the grating separation is too long, the laser output can contain multiple longitudinal modes and one cannot obtain stable RF signal.
Fig. 2. (a) Measured spectrum of the RF-domain beat signal. Inset: optical spectrum of the laser output. (b) Measured frequency fluctuation over 20 min. (c) Measured intensity fluctuation over 20 min.
B. Tunability of the Microwave Source
Figure 3(a) shows the measured beat frequencies as a function of applied driving voltages onto the PZT. The frequency changes from 1.8 to 15.1 GHz with the driving voltage from 0 to 80 V. As the PZT gradually elongates, a transverse stress is subjected onto the laser cavity, which can effectively change the intracavity birefringence and increase the beat frequency. In addition, the supporting beam deflects due to the elongation of the PZT and tightens the whole loading structure. As a result, the rate of the frequency 1 February 2015 / Vol. 54, No. 4 / APPLIED OPTICS
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change becomes higher with higher driving voltage. The frequency variations with increasing and decreasing voltages do not totally coincide due to the hysteresis loop of the PZT’s response. Figure 3(b) shows the measured spectra of the beat signal at different frequencies. The intensity fluctuation for different beat frequencies is no more than 1.5 dB. This fluctuation is a result of a slight change in cavity loss induced by the applied stress. The slow axis of the laser cavity is determined in advance, which is carried out by placing a small mass onto the cavity and measuring the corresponding frequency shift. We repeat this process for different loading orientations by rotating the fiber with two rotatable fiber holders and see along which direction the maximum frequency change can be obtained. That orientation is then marked before clamping it with the mechanical loading device. In order to test the response time of the device, a square wave signal with a period of 5 kHz is superimposed onto the driving voltage. Figure 4(a) shows the frequency variation at the rising edge of the signal. The response time rate is estimated as about 90 MHz/μs, limited by the elastic properties and geometry of the steel structure. The response time is also relevant with the deformation of the steel
Fig. 4. (a) Measured frequency variation when the driving voltage is at a rising edge of the applied square wave signal. (b) Measured phase noise spectrum before and after loading the laser cavity.
Fig. 3. (a) Measured beat-frequency variation with applied driving voltage. (b) Recorded beat note spectra at different frequencies (1–13 GHz). 898
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beam under loading. The driving voltage range of 80 V is programmed to be divided by 65,536 steps, and thereby the average minimum beat-frequency step is about 0.2 MHz. When applying a certain driving voltage, we found that the beat frequency is slowly varying with an unpredictable trend over hours. The maximum frequency shift can be several hundreds of megahertz. The long-term variation is measured under constant environmental temperature and is not likely a result of the temperature dependence of the piezoelectric response. This is a result of the creep of the supporting steel structures in tension. Figure 4(b) shows the measured phase noise spectrum of the beat signal with and without transverse loading, respectively. The noise level increases from −70 to about −65 dBc∕Hz at 10 kHz after the loading, and −40 to −20 dBc at 1 kHz, as a result of acoustic sensitivity. We have tested the output properties of the signal generator under static loading, by placing a mass onto the laser cavity. The beat frequency is changed to about 10 GHz and the frequency fluctuation is less than 0.5 MHz and the intensity fluctuation is less than 1 dB. This verifies the origin of the slowly varying frequency
variation from the mechanical structure. To stabilize the beat signal under loading, a close loop is established, as shown in Fig. 1. When the frequency change is out of tolerance (1 MHz in our experiment), a compensation voltage is applied to recover the original frequency. We have fabricated a number of fiber grating lasers and found that their maximum beat frequencies that can be achieved are around 15 GHz. If further increasing the transverse stress by controlling the driving voltage, the beat signal rapidly weakens and then disappears. The limitation in the tunable frequency range is described as follows. Figure 5 schematically shows the transmission spectrum of the Bragg grating pair without pump for both orthogonal polarizations. The transmission maxima within the grating transmission dip are a result of the multibeam interference. The resonant frequencies correspond to the lasing frequencies. When the laser cavity is loaded with a transverse stress along the y axis, the resonant frequencies change while the grating dips unchanged. According to the elasticoptic effect, νy decreases slightly and νx increases with a much higher rate, as presented by the dashed plots in Fig. 5(a). The grating dips have flat bottoms, indicating strong reflections and sufficient optical feedbacks. The spectral width of the flat region
Fig. 5. Schematic evolutions the transmission spectra of the grating pair when loading (a) over the blank region between the gratings and (b) over the whole laser cavity including the gratings.
is about 18 GHz, which determines the maximum frequency tuning range. When further increasing the stress, νx moves to the edge of the grating dip where the optical feedbacks are much weaker, and the lasing oscillation cannot be established at this polarization. As a result, the beat signal disappears. Possible strategies to increase the tuning range include decreasing the grating length or employing a chirped fiber grating to achieve wider transmission dip of the grating. However, it is difficult for the short uniform grating or the chirped grating to reach a reflectivity up to 25 dB to achieve laser threshold. An ideal method to overcome this limitation is to stress the whole cavity including the two gratings. As shown in Fig. 5(b), if the gratings are also stressed, the transmission maxima and the grating dips shift with identical rates. The two orthogonal polarization modes can be well maintained and much higher beat frequency can be obtained. However, in practice, we found it very difficult to obtain a uniform stress over the whole cavity. The stress gradient along the gratings can cause distortion of their transmission spectrum. The coupling strengths are therefore lowered and the lasing oscillation can be failed. 4. Conclusion
In conclusion, we have demonstrated the implementation of a widely tunable microwave signal generator based on a dual-polarization fiber grating laser. The laser emits single-longitudinal-mode output at the two orthogonal polarizations. By beating the two modes, a microwave signal with a signal-to-noise ratio over 60 dB can be obtained, whose frequency is determined by the intracavity birefringence. For a free running laser the fluctuations in intensity and frequency of the microwave signal are 1 dB and 5 kHz, respectively, and the noise level is about −40 dBc∕Hz at 1 kHz, by optimizing the inscription of the Bragg gratings and performing treatments to suppress the fluctuation of pump conditions and the external perturbations. The frequency can be continuously tuned from 1.8 to 15.1 GHz, by transversely loading the laser cavity and changing the intracavity birefringence by use of a PZT-based mechanical device. The measured response time rate of tuning is about 90 MHz/μs and the intensity fluctuation at different frequencies is less than 1.5 dB. The frequency fluctuation is controlled within 1 MHz via electric feedback. The proposed method presents an optically induced microwave signal generator with good signal quality, fast and wide tenability, and intrinsic multiplexing capability. This work was supported by National Natural Science Foundation of China under grants 61177074, 61235005, and 11474133, Guangdong Natural Science Foundation under grant S2013030013302, Department of Education, Guangdong Province under grant Yq2013021, and the Planned Science & Technology Project of Guangzhou under grant 2012J510028. 1 February 2015 / Vol. 54, No. 4 / APPLIED OPTICS
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