Multi-octave tunable RF signal generation based on a dual-polarization fiber grating laser

A simple technique has been proposed and demonstrated to generate radio-frequency (RF) signal based on a fiber grating laser with multi-octave tunablity. The laser is fabricated by inscribing a wavelengthmatched Bragg grating pair in a short section of low-birefringence Er/Yb co-doped fiber. A RF signal can be obtained by beating the two-polarization mode output with its frequency determined by the birefringence within the cavity. By slicing the laser cavity into two sections and then aligning them with a rotated angle, the output beat frequency can be continuously tuned in a multi-octave frequency range as shown in the experiment from 2.05 GHz down to 289 MHz, as a result of the induced change in optical length for each polarization mode. The present technique has the advantages including simple scheme and large tuning range, and the ability of tuning could be further improved by use of active fibers with higher birefringence. ©2012 Optical Society of America OCIS codes: (060.2300) Fiber optics; (060.3510) Lasers, fiber; (060.2840) Heterodyne; (060.5625) Radio frequency photonics. References and links 1. J. P. Yao, “Microwave photonics,” J. Lightwave Technol. 27(3), 314–335 (2009). 2. J. Yu, Z. Jia, L. Yi, Y. Su, G.-K. Chang, and T. Wang, “Optical mililimeter-wave generation or up-conversion using external modulators,” IEEE Photon. Technol. Lett. 18(1), 265–267 (2006). 3. Y. Wu, X. B. Xie, J. H. Hodiak, S. M. Lord, and P. K. L. Yu, “Multioctave high dynamic range up-conversion optical heterodyned microwave photonic link,” IEEE Photon. Technol. Lett. 16(10), 2332–2334 (2004). 4. X. S. Yao and L. Maleki, “Optoelectronic microwave oscillator,” J. Opt. Soc. Am. B 13(8), 1725–1735 (1996). 5. L. A. Johansson and A. J. Seeds, “Generation and transmission of millimeter-wave data-modulated optical signals using an optical injection phase-locked loop,” J. Lightwave Technol. 21(2), 511–520 (2003). 6. N. H. Zhu, H. G. Zhang, J. W. Man, H. L. Zhu, J. H. Ke, Y. Liu, X. Wang, H. Q. Yuan, L. Xie, and W. Wang, “Microwave generation in an electro-absorption modulator integrated with a DFB laser subject to optical injection,” Opt. Express 17(24), 22114–22123 (2009). 7. Y.-S. Juan and F.-Y. Lin, “Photonics generation of broadly tunable microwave signals utilizing a dual-beam optically injected semiconductor laser,” IEEE Photon. J. 3(4), 644–650 (2011). 8. X. Chen, Z. Deng, and J. P. Yao, “Photonic generation of microwave signal using a dual-wavelength singlelongitudinal-mode ber ring laser,” IEEE Trans. Microw. Theory Tech. 54(2), 804–809 (2006). 9. G. Pillet, L. Morvan, M. Brunel, F. Bretenaker, D. Dolfi, M. Vallet, J.-P. Huignard, and A. Le Floch, “Dualfrequency laser at 1.5 μm for optical distribution and generation of high-purity microwave signals,” J. Lightwave Technol. 26(15), 2764–2773 (2008). 10. J. Geng, S. Staines, and S. Jiang, “Dual-frequency Brillouin fiber laser for optical generation of tunable lownoise radio frequency/microwave frequency,” Opt. Lett. 33(1), 16–18 (2008). 11. J. L. Zhou, L. Xia, X. P. Cheng, X. P. Dong, and P. Shum, “Photonic generation of tunable microwave signals by beating a dual-wavelength single longitudinal mode ber ring laser,” Appl. Phys. B 91(1), 99–103 (2008). 12. J. Sun, Y. Dai, X. Chen, Y. Zhang, and S. Xie, “Stable dual-wavelength DFB fiber laser with separate resonant cavities and its application in tunable microwave generation,” IEEE Photon. Technol. Lett. 18(24), 2587–2589 (2006). 13. J. T. Kringlebotn, W. H. Loh, and R. I. Laming, “Polarimetric Er-doped fiber distributed-feedback laser sensor for differential pressure and force measurements,” Opt. Lett. 21(22), 1869–1871 (1996). 14. 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(11), 727–729 (2009). #159393 $15.00 USD Received 5 Dec 2011; revised 20 Feb 2012; accepted 29 Feb 2012; published 12 Mar 2012 (C) 2012 OSA 26 March 2012 / Vol. 20, No. 7 / OPTICS EXPRESS 6961 15. S. Pajarola, G. Guekos, P. Nizzola, and H. Kawaguchi, “Dual-polarization external-cavity diode laser transmitter for fiber-optic antenna remote feeding,” IEEE Trans. Microw. Theory Tech. 47(7), 1234–1240 (1999). 16. M. C. Gross, P. T. Callahan, T. R. Clark, D. Novak, R. B. Waterhouse, and M. L. Dennis, “Tunable millimeterwave frequency synthesis up to 100 GHz by dual-wavelength Brillouin fiber laser,” Opt. Express 18(13), 13321– 13330 (2010). 17. S. Rashleigh, “Origins and control of polarization effects in single-mode fibers,” J. Lightwave Technol. 1(2), 312–331 (1983). 18. Y. O. Barmenkov, D. Zalvidea, S. Torres-Peiró, J. L. Cruz, and M. V. Andrés, “Effective length of short FabryPerot cavity formed by uniform fiber Bragg gratings,” Opt. Express 14(14), 6394–6399 (2006).


Introduction
Optical generation of RF signals has been widely investigated towards various applications including broadband wireless access and sensor networks, software-defined radio, and wireless communications [1].RF signals can be generated optically by employing harmonic generation through modulation of laser outputs [2][3][4] or by phase-locking of two laser outputs [5].All-optical methods have also been explored, by use of optical injection locking of two lasers [6,7], or the beat signal from a dual-wavelength fiber laser [8][9][10][11][12][13][14][15].The dualwavelength-laser approach presents the advantages of simple scheme and reduction of phase noise.
Frequency tunability is one major focus of optical generation of RF signals.Generally speaking, among the previously proposed schemes, beating of two laser outputs permits the largest tuning range of RF frequency due to the large tuning range of the lasing wavelength.However, tuning the wavelength of lasers with high reliability and stability cannot be easily achieved, limited by the requirement of complicated feedback control.Such feedback control normally contains electronic signal processing modules for electro-optical modulation, RF amplifications and mixing, and low-pass loop filtering.As a result, the frequency tunability of the optically generated RF signal is limited by the relatively narrow bandwidth of the electronic signal processing modules.
Alternatively, the frequency of the optically RF signal can be tuned through the adjustment of physical parameters of the optical fiber or fiber devices.Consequently, simpler configurations can be implemented for frequency tuning.A number of tunable RF sources have been demonstrated, e. g. by use of stimulated Brillion fiber laser and Fabry-Perot scheme [10][11][12]16].However, the tuning range is too small through temperature or strain adjustment.In addition, some of them cannot be continuously tuned.In contrast, by use of a dualpolarization fiber grating laser, large-range, continuous tuning of the RF-regime beat frequency can be realized [13][14][15].The RF signal is generated from the beat note of the dualpolarization mode output.The beat frequency is determined by the intra-cavity birefringence and can be tuned by subjecting electrically induced transverse force onto the laser cavity [13,14].Due to the absence of electronic signal processing, the confinement resulted from the employment of electronic devices can be avoided.Therefore, such schemes can potentially realize much wider frequency tuning range and thereby are more favorable.
In this paper, we present a simple technique for frequency control of RF signal generated by use of a dual-polarization fiber grating laser.By slicing the laser cavity into two sections and aligning them with a rotated angle, the beat frequency can be continuously adjusted from 2.05 GHz down to 289 MHz, as a result of the changed optical length for each polarization mode.The RF frequency can even reach zero in principle if the effective lengths of the two sections are identical.The present technique offers a cost effective method to realize a RF source with a large tuning range and simple scheme.

Principle
Figure 1 shows the schematic diagram for RF frequency tuning with a fiber laser.The laser is fabricated by composing two reflectors in an active fiber.The laser can operate in single longitudinal mode for each orthogonal polarization mode, when the cavity length is very short.Assume the x-and y-polarization modes correspond to the slow and fast axis, respectively.Both the polarization modes satisfy the resonant condition, which is expressed by 00 , 22 π where L is the length of the laser cavity, M is an integer which denotes the order of resonant mode,  3) suggests that the frequency of beat signal from the fiber grating laser is mainly determined by the intrinsic birefringence of the active fiber.This birefringence is a result of the inner thermal stress caused by the geometric imperfection during the fiber drawing process [17].The beat frequency Δν 0 typically ranges from hundreds of megahertz to several GHz.To tune the beat frequency, the laser cavity is sliced into two sections.The lengths of which are l 1 and l 2 , respectively.When rotating the l 2 section by an angle θ when aligning the two sections, the phase variation along + z axis within l 1 and l 2 can be described by use of Jones matrix, which is expressed by Assume the input matrix is 1 (5) Equations ( 4) and ( 5) describe that the longitudinal phase variations are changed as a result of the changes in optical length.Due to the rotation, the optical lengths for x-and ypolarization modes become closer.The beat frequencies ν x and ν y change correspondingly to fulfill the resonant condition.For simplicity, we can just take the phase variations along + z axis into consideration, because each polarization mode experiences a phase variation of Mπ along + z and -z direction, respectively.With Eqs.(4)(a) and 4(b), the resonant condition can be expressed by where The relation between beat frequency Δν and the angle θ can be obtained based on Eq. ( 6).Now we just consider the following two special cases: (1) θ = 0 or π, which means the fast and slow axis do not change.With Eq. ( 6), the output matrix J out can be simplified as      out (7) which indicates that the optical lengths for the two polarization modes do not change and the beat frequency maintains the original value Δν 0 .
(2) θ = π/2 or 3π/2, which means the fast and slow axis exchange for l 2 section, the output matrix can be expressed by The corresponding beat frequency can be expressed by This is the minimal beat frequency that can be achieved by this method, as a result of the offset in optical length between the dual polarization modes induced by the rotation.The above analysis suggests that the beat frequency can be tuned from Δν 0 , which is determined by the intrinsic birefringence of the fiber, to the minimal value Δν min , by rotating the l 2 section from 0 to π/2.When the laser cavity is sliced into two sections with identical effective lengths, the minimal beat frequency can even reach zero.

Experiment
Figure 2 shows the experimental setup for the beat frequency tuning based on the fiber grating laser.The laser is fabricated by inscribing a wavelength-matched Bragg grating pair into a Er/Yb co-doped active fiber, by use of a 193 nm excimer laser and a phase mask.The length of each grating is 3 mm and grating spacing is 12 mm.The reflectivities of the two grating are estimated to be 20 dB and 28 dB, respectively.Consequently, the effective length of the fiber grating laser is L eff = 12.87 mm.The contributions from the two gratings are estimated as 0.49 mm and 0.38 mm, respectively, according to [18].The corresponding longitudinal mode spacing is about 0.07 nm, which indicates that several resonant modes are established within the reflection peak.By controlling the exposure dosage, we can locate one of the resonant wavelength at right the center of the reflection peak and other resonant modes are suppressed.As a result, single-longitudinal-mode output of the fiber grating laser can be achieved.The 980 nm pump light was launched into the grating pair through a wavelength division multiplexer (WDM).The beat signal generated by the laser output is detected with a highspeed photo-detector and a RF spectrum analyzer.An in-line polarizer and a polarization controller are used to obtain maximum beat signal.The lasing wavelength is 1539.70 nm and the beat frequency is Δν 0 = 2.05 GHz.
The laser cavity is sliced into two sections with almost identical effective lengths, and then aligned with minimized insertion loss.The angle θ between the principle axes for the two sections is adjusted by use of a rotation stage.6).The RF frequency reaches the maximum value at 0° and 180° and minimum value at 90° and 270°, respectively, as shown in Fig. 3(b) inset, which is in accordance with the calculated result and the analysis in Sec. 2. However, the beat frequency did not reach zero as expected.This is partially attributed to the small difference in effective length of the two sections due to the facility limitation, and partially to the additional birefringence induced by the UV illumination.
The relation between the beat frequency and the lengths of the two sections has been investigated, by measuring the beat frequency at θ = π/2 with different normalized effective length L 1 /L eff .Figure 4(a) shows the RF spectra measured for different amplitudes of L 1 /L eff , when the minimal beat frequency is achieved through the adjustment of angle θ. Figure 4(b) shows the calculated and measured variation of the minimal beat frequency Δν min with L 1 /L eff .The calculated result is obtained based on Eq. ( 9).The deviation between the calculated and measured results mainly comes from the error of effective length when slicing the cavity.The above theoretical analysis and experimental result suggest that the RF frequency can be tuned from the original beat frequency Δν 0 down to Δν min , i. e., the frequency atθ = π/2.In order to enlarge the tuning range, an active fiber with higher birefringence can be used to obtain a higher Δν 0 .In addition, accurate length control for both of the sections is needed and the UV-induced additional birefringence should be reduced, to obtain a value of Δν min closer to zero.Note that the difference in lasing wavelength for the two orthogonal polarizations increases with fiber birefringence and the reflective peak might split.As a result, the laser might stop lasing due to the lack of optical feedback when a rotation is applied.The proposed technique only works when the bandwidths of the fiber gratings used as laser end reflectors are large enough to encompass the reflectivity of both fiber polarizations.In the experiment, the reflection bandwidth of the FBG is about 0.5 nm and the reflection is higher than 20 dB, which guarantees the lasing for different rotation angles.

Conclusion
In conclusion, multi-octave RF frequency tuning has been achieved by use of a dualpolarization fiber grating laser.By slicing the laser cavity and then aligning the two sections with a controllable rotation, the beat frequency was tuned from 2.05 GHz down to 289 MHz.Larger tuning range can be achieved by using an active fiber with higher birefringence.The minimal beat frequency can possibly be reduced to close zero through accurate length control and reduction of UV induced birefringence.The proposed technique offers a simple scheme of RF signal source with a large frequency tuning range.

Fig. 1 .
Fig. 1.Schematic diagram of the fiber laser for RF frequency tuning.
the transfer matrix for coordinate transformation.The phase variation along -z axis within l 2 and l 1 sections can be expressed by

Fig. 3 .
Fig. 3. (a) Measured RF spectra of the beat signal at different rotated angle θ.(b) Calculated and measured beat frequency as a function of rotation angle θ between 0° and 90°.Inset, result for full angle range from 0° and 360°.

Figure 3 (
Figure 3(a) shows the output RF spectrum of the beat signal when aligning the two sections with different angles.The beat frequency is tuned from 2.05 GHz when θ = 0 to 289 MHz when θ = π/2.Figure 3(b) shows the calculated and measured beat frequency as a function of the angle θ.The red curve represents the ideal frequency change with θ calculated with Eq. (6).The RF frequency reaches the maximum value at 0° and 180° and minimum value at 90° and 270°, respectively, as shown in Fig.3(b) inset, which is in accordance with the calculated result and the analysis in Sec. 2. However, the beat frequency did not reach zero as expected.This is partially attributed to the small difference in effective length of the two sections due to the facility limitation, and partially to the additional birefringence induced by the UV illumination.The relation between the beat frequency and the lengths of the two sections has been investigated, by measuring the beat frequency at θ = π/2 with different normalized effective length L 1 /L eff .Figure4(a) shows the RF spectra measured for different amplitudes of L 1 /L eff , when the minimal beat frequency is achieved through the adjustment of angle θ.Figure4(b)shows the calculated and measured variation of the minimal beat frequency Δν min with L 1 /L eff .The calculated result is obtained based on Eq. (9).The deviation between the calculated and measured results mainly comes from the error of effective length when slicing the cavity.

Figure 5 (
Figure 5(a) shows the measured frequency fluctuation over 30 min.The beat frequency is tuned to 328.5 MHz at the beginning but slowly drifts to 329 MHz due to the temperature