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

Yan-Nan Tan; Long Jin; Linghao Cheng; Zhan Quan; Mengping Li; Bai-Ou Guan

doi:10.1364/OE.20.006961

1. 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 [2–4] 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 [8–15]. The dual-wavelength-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 [10–12,16]. 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 dual-polarization fiber grating laser, large-range, continuous tuning of the RF-regime beat frequency can be realized [13–15]. The RF signal is generated from the beat note of the dual-polarization 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.

2. 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

2 k_{x_{0}, y_{0}} L = 2 M π

where L is the length of the laser cavity, M is an integer which denotes the order of resonant mode,

k_{x_{0}, y_{0}}

is the propagation constant for each polarization mode. Substituting

k_{x_{0}, y_{0}} = \frac{2 π}{c} ν_{x_{0}, y_{0}} n_{s,f}

into Eq. (1), the resonant condition is written as

\frac{2 π}{c} ν_{x_{0}, y_{0}} (n_{s,f} \cdot L) = 2 M π

where c is the speed of light in vacuum,

ν_{x_{0}, y_{0}}

is the lasing frequency of each polarization mode and n_s,f is the effective indexes along slow and fast axis of the optical fiber. The item n_s,fL is the optical length for each polarization mode. A RF-domain beat signal with the frequency

Δ ν_{0} = | ν_{x_{0}} - ν_{y_{0}} |

can be generated by the fiber laser. Deduced from Eq. (2), the beat frequency Δν₀ can be expressed by

Δ ν_{0} = \frac{B}{n_{0}} ν_{a v e}

where

B = n_{s} - n_{f}

represents the modal birefringence, n₀ is the average effective index, and

ν_{a v e} = (ν_{x_{0}} + ν_{y_{0}}) / 2

is the average lasing frequency . Equation (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 Δν₀ typically ranges from hundreds of megahertz to several GHz.

Fig. 1 Schematic diagram of the fiber laser for RF frequency tuning.

Download Full Size | PDF

To tune the beat frequency, the laser cavity is sliced into two sections. The lengths of which are l₁ and l₂, respectively. When rotating the l₂ section by an angle θ when aligning the two sections, the phase variation along + z axis within l₁ and l₂ can be described by use of Jones matrix, which is expressed by

T_{1} = (\begin{matrix} e^{i \frac{2 π n_{s} ν_{x}}{c} l_{1}} & 0 \\ 0 & e^{i \frac{2 π n_{f} ν_{y}}{c} l_{1}} \end{matrix})

T_{2} = R (θ) (\begin{matrix} e^{i \frac{2 π n_{s} ν_{x}}{c} l_{2}} & 0 \\ 0 & e^{i \frac{2 π n_{f} ν_{y}}{c} l_{2}} \end{matrix}) R (- θ)

where

R (θ) = (\begin{matrix} \cos θ & \sin θ \\ - \sin θ & \cos θ \end{matrix})

is the transfer matrix for coordinate transformation. The phase variation along –z axis within l₂ and l₁ sections can be expressed by

T_{3} = R (π - θ) (\begin{matrix} e^{i \frac{2 π n_{s} ν_{x}}{c} l_{2}} & 0 \\ 0 & e^{i \frac{2 π n_{f} ν_{y}}{c} l_{2}} \end{matrix}) R (- π + θ)

T_{4} = R (π) (\begin{matrix} e^{i \frac{2 π n_{s} ν_{x}}{c} l_{1}} & 0 \\ 0 & e^{i \frac{2 π n_{f} ν_{y}}{c} l_{1}} \end{matrix}) R (- π)

Assume the input matrix is $J_{i n} = (\begin{matrix} 1 \\ 1 \end{matrix})$ , the output matrix is

J_{o u t} = T_{4} T_{3} T_{2} T_{1} J_{i n}

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 y-polarization 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

\begin{array}{l} A \sin (\frac{2 π n_{s} L}{c} υ_{x}) + B \sin (\frac{2 π (n_{s} l_{1} + n_{f} l_{2})}{c} υ_{x}) = 0 \\ C \sin (\frac{2 π (n_{f} l_{1} + n_{s} l_{2})}{c} υ_{y}) + D \sin (\frac{2 π n_{f} L)}{c} υ_{y}) = 0 \end{array}

where A = cosθ(cosθ-sinθ), B = sinθ(cosθ + sinθ), C = sinθ(sinθ-cosθ), D = cosθ(cosθ + sinθ). 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 $J_{o u t} = (\begin{matrix} e^{i 2 k_{x_{0}} L} \\ e^{i 2 k_{y_{0}} L} \end{matrix})$

which indicates that the optical lengths for the two polarization modes do not change and the beat frequency maintains the original value Δν₀.

(2) θ = π/2 or 3π/2, which means the fast and slow axis exchange for l₂ section, the output matrix can be expressed by $J_{o u t} = (\begin{matrix} φ_{1} \\ φ_{2} \end{matrix}) = (\begin{matrix} e^{i 4 π (n_{s} l_{1} + n_{f} l_{2}) υ_{x} / c} \\ e^{i 4 π (n_{f} l_{1} + n_{s} l_{2}) υ_{y} / c} \end{matrix})$

The corresponding beat frequency can be expressed by

Δ ν_{m i n} = \frac{B}{n_{0}} ν_{a v e} \frac{| l_{1} - l_{2} |}{L} = Δ ν_{0} \frac{| l_{1} - l_{2} |}{L}

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 Δν₀, which is determined by the intrinsic birefringence of the fiber, to the minimal value Δν_min, by rotating the l₂ 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.

3. 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 high-speed 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 Δν₀ = 2.05 GHz.

Fig. 2 Experimental setup for the frequency tuning of RF signal with a dual-polarization fiber grating laser. ISO: Isolator; WDM: Wavelength-division multiplexer; PD: Photo-detector; PC: Polarization controller.

Download Full Size | PDF

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.

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.

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°.

Download Full Size | PDF

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 L₁/L_eff. Figure 4(a) shows the RF spectra measured for different amplitudes of L₁/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 L₁/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.

Fig. 4 (a) Measured RF spectra with different normalized effective length L₁/L_eff at θ = π/2. (b) Beat frequency change with normalized effective length L₁/L_eff at θ = π/2.

Download Full Size | PDF

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 variation. The beat frequency is measured at a frequency of 10 Hz. The fluctuation is about 0.2 MHz. Such small fluctuation is very likely due to the measurement error of the spectrum analyzer. Mode competition and surrounding perturbations may also contribute to this fluctuation. The stability can be potentially enhanced by proper packaging to further screen possible perturbations. Figure 5(b) shows the measured phase noise of the RF signal.

Fig. 5 (a) Measured frequency fluctuation over 30 min. (b) Measured phase noise of the proposed RF generator.

Download Full Size | PDF

The above theoretical analysis and experimental result suggest that the RF frequency can be tuned from the original beat frequency Δν₀ 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 Δν₀. 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.

4. Conclusion

In conclusion, multi-octave RF frequency tuning has been achieved by use of a dual-polarization 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.

Acknowledgments

This work was supported by the National Basic Research Program of China (973) Project (2012CB315603), the Key Project of the National Natural Science Foundation of China (60736039), and the Fundamental Research Funds for the Central Universities (21609102).

References and links

1. J. P. Yao, “Microwave photonics,” J. Lightwave Technol. 27(3), 314–335 (2009). [CrossRef]

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). [CrossRef]

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). [CrossRef]

4. X. S. Yao and L. Maleki, “Optoelectronic microwave oscillator,” J. Opt. Soc. Am. B 13(8), 1725–1735 (1996). [CrossRef]

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). [CrossRef]

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). [CrossRef] [PubMed]

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). [CrossRef]

8. X. Chen, Z. Deng, and J. P. Yao, “Photonic generation of microwave signal using a dual-wavelength single-longitudinal-mode ﬁber ring laser,” IEEE Trans. Microw. Theory Tech. 54(2), 804–809 (2006). [CrossRef]

9. G. Pillet, L. Morvan, M. Brunel, F. Bretenaker, D. Dolfi, M. Vallet, J.-P. Huignard, and A. Le Floch, “Dual-frequency laser at 1.5 μm for optical distribution and generation of high-purity microwave signals,” J. Lightwave Technol. 26(15), 2764–2773 (2008). [CrossRef]

10. J. Geng, S. Staines, and S. Jiang, “Dual-frequency Brillouin fiber laser for optical generation of tunable low-noise radio frequency/microwave frequency,” Opt. Lett. 33(1), 16–18 (2008). [CrossRef] [PubMed]

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 ﬁber ring laser,” Appl. Phys. B 91(1), 99–103 (2008). [CrossRef]

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). [CrossRef]

13. J. T. Kringlebotn, W. H. Loh, and R. I. Laming, “Polarimetric Er³⁺-doped fiber distributed-feedback laser sensor for differential pressure and force measurements,” Opt. Lett. 21(22), 1869–1871 (1996). [CrossRef] [PubMed]

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). [CrossRef]

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). [CrossRef]

16. M. C. Gross, P. T. Callahan, T. R. Clark, D. Novak, R. B. Waterhouse, and M. L. Dennis, “Tunable millimeter-wave frequency synthesis up to 100 GHz by dual-wavelength Brillouin fiber laser,” Opt. Express 18(13), 13321–13330 (2010). [CrossRef] [PubMed]

17. S. Rashleigh, “Origins and control of polarization effects in single-mode fibers,” J. Lightwave Technol. 1(2), 312–331 (1983). [CrossRef]

18. Y. O. Barmenkov, D. Zalvidea, S. Torres-Peiró, J. L. Cruz, and M. V. Andrés, “Effective length of short Fabry-Perot cavity formed by uniform fiber Bragg gratings,” Opt. Express 14(14), 6394–6399 (2006). [CrossRef] [PubMed]

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

Abstract

1. Introduction

2. Principle

3. Experiment

4. Conclusion

Acknowledgments

References and links

Cited By

Figures (5)

Equations (12)

Optics Express