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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 22 — Oct. 24, 2011
  • pp: 21945–21955
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Sharp tunable optical filters based on the polarization attributes of stimulated Brillouin scattering

Assaf Wise, Moshe Tur, and Avi Zadok  »View Author Affiliations


Optics Express, Vol. 19, Issue 22, pp. 21945-21955 (2011)
http://dx.doi.org/10.1364/OE.19.021945


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Abstract

Sharp and highly-selective tunable optical band-pass filters, based on stimulated Brillouin scattering (SBS) amplification in standard fibers, are described and demonstrated. Polarization pulling of the SBS-amplified signal wave is used to increase the selectivity of the filters to 30 dB. Pump broadening via synthesized direct modulation was used to provide a tunable, sharp and uniform amplification window: Pass-band widths of 700 MHz at half maximum and 1GHz at the −20dB points were obtained. The central frequency, bandwidth and shape of the filter can be arbitrarily set. Compared with scalar SBS-based filters, the polarization-enhanced design provides a higher selectivity and an elevated depletion threshold.

© 2011 OSA

1. Introduction

Optical tunable filters are widely used for channel selection within dense wavelength division multiplexing (DWDM) telecommunication networks ‎ [1

1. G. P. Agrawal, Fiber-Optic communication systems, third edition, (Wiley, 2002), Chapter 8, pp.330–403.

], for the reduction of amplified spontaneous emission noise following optical amplification [1

1. G. P. Agrawal, Fiber-Optic communication systems, third edition, (Wiley, 2002), Chapter 8, pp.330–403.

], as well as in microwave photonic processing setups [2

2. J. Capmany, B. Ortega, D. Pastor, and S. Sales, “Discrete-time optical processing of microwave signals,” J. Lightwave Technol. 23(2), 702–723 (2005). [CrossRef]

]. The primary figures of merit for tunable optical filters are low insertion loss, sharp transition between the pass-band and stop-bands, high side-lobe suppression, and a broad tuning range. Several mature technologies are available for the realization of passive tunable optical filters, such as fiber Bragg gratings (FBGs) ‎ [3

3. T. A. Strasser and T. Erdogan, “Fiber grating devices in high performance optical communication systems,” chapter 10 of Optical fiber telecommunications IVA – components. I. P. Kaminow, and T. Li (editors), San Diego, CA: Academic press, 2002.

], Fabry-Perot etalons (FPs) ‎ [4

4. A. Yariv, chapter 4 in Optoelectronics, pp. 110–116, Orlando FL: Saunders College Publishing, 4th Edition, 1991.

], Mach-Zehnder interferometers and ring resonators in planar light-guide circuits (PLCs) ‎ [5

5. C. R. Doerr, “Planar lightwave devices for WDM,” chapter 9 of Optical fiber telecommunications IVA – components. I. P. Kaminow, and T. Li (editors), San Diego, CA: Academic press, 2002.

]. In such passive filters the bandwidth and spectral transmission shape are typically fixed. In contrast, active tunable optical filters allow for adjusting not only the transmission wavelength, but also the width and shape of the pass-band as well. In addition, active filters may amplify the signal within the frequency range of choice.

Active tunable optical filters have been previously proposed and demonstrated based on stimulated Brillouin scattering (SBS) in standard optical fibers [6

6. T. Tanemura, Y. Takushima, and K. Kikuchi, “Narrowband optical filter, with a variable transmission spectrum, using stimulated Brillouin scattering in optical fiber,” Opt. Lett. 27(17), 1552–1554 (2002). [CrossRef] [PubMed]

,7

7. A. Zadok, A. Eyal, and M. Tur, “GHz-wide optically reconfigurable filters using stimulated Brillouin scattering,” J. Lightwave Technol. 25(8), 2168–2174 (2007).[REMOVED IF= FIELD] [CrossRef]

]. SBS requires the lowest activation power of all non-linear effects in silica optical fibers. In SBS, a strong pump wave and a typically weak, counter-propagating signal wave optically interfere to generate, through electrostriction, a traveling longitudinal acoustic wave. The acoustic wave, in turn, couples these optical waves to each other [8

8. R. W. Boyd, Nonlinear Optics, third edition, (Academic Press, 2008).

]. The SBS interaction is efficient only when the difference between the optical frequencies of the pump and signal waves is very close (within a few tens of MHz) to a fiber-dependent parameter, the Brillouin shift ΩB, which is on the order of 2π⋅11·109 [rad/sec] in silica fibers at room temperature and at telecommunication wavelengths [8

8. R. W. Boyd, Nonlinear Optics, third edition, (Academic Press, 2008).

]. An input signal whose frequency is ΩB lower than that of the pump (‘Stokes wave’), experiences SBS amplification. SBS has found numerous applications, including distributed sensing of temperature and strain [9

9. M. Nikles, L. Thévenaz, and P. Robert, “Brillouin gain spectrum characterization in single-mode optical fibers,” J. Lightwave Technol. 15(10), 1842–1851 (1997). [CrossRef]

], fiber lasers [10

10. J. C. Yong, L. Thévenaz, and B. Y. Kim, “Brillouin fiber laser pumped by a DFB laser diode,” J. Lightwave Technol. 21(2), 546–554 (2003). [CrossRef]

], optical processing of high frequency microwave signals [11

11. A. Loayssa and F. J. Lahoz, “Broadband RF photonic phase shifter based on stimulated Brillouin scattering and single side-band modulation,” IEEE Photon. Technol. Lett. 18(1), 208–210 (2006). [CrossRef]

,12

12. A. Loayssa, J. Capmany, M. Sagues, and J. Mora, “Demonstration of incoherent microwave photonic filters with all-optical complex coefficients,” IEEE Photon. Technol. Lett. 18(16), 1744–1746 (2006). [CrossRef]

] and even optical memories [13

13. Z. Zhu, D. J. Gauthier, and R. W. Boyd, “Stored light in an optical fiber via stimulated Brillouin scattering,” Science 318(5857), 1748–1750 (2007). [CrossRef] [PubMed]

]. Over the last six years SBS has been highlighted as the preferred mechanism in many demonstrations of variable group delay setups [14

14. L. Thevenaz, “Slow and Fast Light Using Stimulated Brillouin Scattering: A Highly Flexible Approach,” in Slow Light – Science and Applications, J. B. Khurgin and R. S. Tucker Eds. (CRC press, 2009), pp. 173–193.

,15

15. A. Zadok, A. Eyal, and M. Tur, “Stimulated Brillouin scattering slow light in optical fibers,” Appl. Opt. 50(25), E38–E49 (2011). [CrossRef]

], often referred to as slow and fast light.

2. Principle of operation

e^sigoutmax=T(L)e^siginmax;e^sigoutmin=T(L)e^siginmin      (6)

For low pump power values, the integrated impact of the Brillouin amplification almost solely depends on the relative orientations of the pump and signal SOP’s along the fiber, as determined by the fiber birefringence. Hence, it is not surprising that the relationships of Eq. (6) do not depend on the Brillouin interaction. Yet, it is interesting to note that both numerically and experimentally, Eqs. (4-6) also hold, at least approximately, even for strong pumps and considerable Brillouin gains [16

16. A. Zadok, E. Zilka, A. Eyal, L. Thévenaz, and M. Tur, “Vector analysis of stimulated Brillouin scattering amplification in standard single-mode fibers,” Opt. Express 16(26), 21692–21707 (2008). [CrossRef] [PubMed]

].

An input signal of arbitrary SOP can be decomposed along the basis of e^siginmax and e^siginmin:
Esig(0)=ae^siginmax+be^siginmin.      (7)
Following SBS amplification, the output signal vector becomes:
EsigSBS(L)=aGmaxe^sigoutmax+bGmine^sigoutmin.      (8)
On the other hand, if the signal wave is subject to birefringence alone, the output vector is instead given by:
Esigbiref(L)=ae^sigoutmax+be^sigoutmin.      (9)
For long enough [16

16. A. Zadok, E. Zilka, A. Eyal, L. Thévenaz, and M. Tur, “Vector analysis of stimulated Brillouin scattering amplification in standard single-mode fibers,” Opt. Express 16(26), 21692–21707 (2008). [CrossRef] [PubMed]

], randomly and weakly birefringent fibers, the expected magnitudes of the maximum and minimum amplification are |Gmax|2=exp[23g(ωsig)L] and |Gmin|2=exp[13g(ωsig)L]=|Gmax|2 [16

16. A. Zadok, E. Zilka, A. Eyal, L. Thévenaz, and M. Tur, “Vector analysis of stimulated Brillouin scattering amplification in standard single-mode fibers,” Opt. Express 16(26), 21692–21707 (2008). [CrossRef] [PubMed]

]. For a sufficiently strong pump |Gmax|>>|Gmin|, and unless a is vanishingly small, Eq. (8) describes polarization pulling of the output probe wave towards a particular state, e^sigoutmax, which is determined by the pump polarization. The effectiveness of the pulling is governed by the ratio |Gmax|/|Gmin|. Equations (8) and (9) also show that SBS introduces a difference between the output SOP of amplified signal components, for which g(ωsig) is significant, and that of unamplified components, for which g(ωsig) is negligible. It is therefore possible to further discriminate between amplified and unamplified spectral components of a broadband signal wave, using a properly aligned polarizer.

Let e^pol denote the state of a polarizer placed at the signal output, z = L:
e^pol(L)=pmaxe^sigoutmax+pmine^sigoutmin,      (10)
where pmax,min are the projections of e^pol onto e^sigoutmax and e^sigoutmin, respectively. At the polarizer output, the amplitude of an out-of-band, unamplified signal component is given by:
Asigbiref=a(e^pole^sigoutmax)+b(e^pole^sigoutmin)=apmax+bpmin.      (11)
With proper alignment of the output polarizer, Asigbiref can be set to zero, signifying the (theoretical) complete rejection of out-of-band components. On the other hand, the amplitude of an SBS-amplified signal component at the polarizer output is:
AsigSBS=aGmax(e^pole^sigoutmax)+bGmin(e^pole^sigoutmin)=aGmaxpmax+bGminpmin=apmax(GmaxGmin)      (12)
The final equality in Eq. (12) is met when Eq. (11) is set to zero. Due to the differential gain of SBS, in-band components are retained and even amplified.

To calculate the SBS gain of the signal components we assume the signal input to be of unity power (|a|2+|b|2=1) so that:
InbandGain=|AsigSBS||a|2+|b|2=12=|apmax*|2|GmaxGmin|2Gmax>>Gmin|apmax*|2|Gmax|2      (13)
Subject to the constraint of complete out-of-band rejection (Asigbiref=0 in Eq. (11)) together with |pmax|2+|pmin|2=1, it is easy to show that this in-band SBS gain can become as high as 0.25|Gmax|2, provided: |a|2=|pmax|2=0.5. Thus, the amplification of the polarization-assisted SBS process, at the high pump power limit, is only 6dB lower than that of a corresponding scalar process, when the latter is aligned for maximum gain. However, while polarization discrimination can achieve very high rejection (theoretically infinite) for the unamplified out-of-band components, the power transfer for these components in the scalar process is unity. We conclude that the polarization discrimination filtering proposed in this work can achieve much higher selectivity than its scalar counterpart.

Figure 1
Fig. 1 Simulation results for the signal power gain at the output of an SBS amplification process, using a 3.6 km-long highly nonlinear fiber (HNLF) and a 0.7 GHz-wide, 13.5 dBm pump. The pump is assumed to be undepleted. In the lower curve (a), the input signal's SOP was chosen with equal projections on the states of maximum and minimum SBS amplification (a=b=1/2, see text), and an output polarizer was aligned for maximal rejection of unamplified signal components (pmax,min=±1/2, see text). The upper curve (b) shows the corresponding power gain with no output polarizer, and with the input signal SOP aligned for maximum amplification (a = 1).
presents simulation results of the relative optical power transmission of the signal wave, as a function of the frequency offset from the pass-band center. In the simulations, Eq. (1) and (3) were directly integrated. A 3.5 km-long highly non-linear fiber (HNLF) with an SBS gain coefficient γ0 = 2.9 [W⋅m]−1 was used. The fiber was simulated as 1000 cascaded birefringent media that are randomly oriented, with a polarization beat length of 40 m and a polarization coupling length of 10 m [16

16. A. Zadok, E. Zilka, A. Eyal, L. Thévenaz, and M. Tur, “Vector analysis of stimulated Brillouin scattering amplification in standard single-mode fibers,” Opt. Express 16(26), 21692–21707 (2008). [CrossRef] [PubMed]

,18

18. M. Wuilpart, “Distributed measurement of polarization properties in single-mode optical fibres using a reflectometry technique”, Ph.D. Thesis, Faculte Polytechnique de Mons (2003).

]. The pump power was set to 13.5 dBm, and its PSD was uniform within a 0.7 GHz-wide region. The pump was assumed to be undepleted. Curve 1(b) shows the signal power gain for an SBS process with no output polarizer, and with the signal input SOP aligned for maximum amplification (a = 1). A filtering selectivity of |Gmax|2 = 16.5 dB is obtained. In curve (a), the signal input SOP was chosen so that a=b=1/2, and an output polarizer was aligned to pmax,min=±1/2. The in-band amplification of the polarization-assisted filter was lowered by 10 dB, in agreement with the prediction of Eq. (13), where for the specific, rather modest pump power, Gmin cannot be ignored and |GmaxGmin|2 must be used instead of |Gmax|2. However, the polarizer helps to significantly attenuate the out-of-band components so that the filtering selectivity is much improved. Two observations to be noted in Fig. 1(a): (i) The slightly larger amplification towards the pass-band edges originates from the complex nature Gmax and Gmin: while both are real numbers in the band center, they have different phases at the edges, resulting in somewhat higher values for |GmaxGmin|2; (ii) The gradual transition between the pass-band and stop-bands is due to the convolution form of g(ωsig), (Eq. (2). Lastly, the lower in-band amplification is expected to defer the onset of depletion to higher signal power levels.

3. Experiment results

Light from a tunable laser diode was used to generate the SBS signal wave. The laser output was double-sideband modulated using a LiNbO3 Mach-Zehnder interferometer (Electro-Optical Modulator – EOM), driven by a swept sine wave of frequency ΩRF, in the range of 2π⋅13.5-2π⋅16.5 GHz. The tunable laser carrier wavelength and the radio-frequency (RF) modulation were chosen so that one of the sidebands scanned the SBS amplification spectral window that was induced by the pump wave, as in Fig. 5
Fig. 5 The generation of the SBS signal wave. (a-b): Schematic spectrum of double-sideband modulated tunable laser. The radio-frequency (RF) modulation waveform is a swept sine-wave ΩRF in the 2π⋅13.5 to 2π⋅16.5 GHz range. Depending on ΩRF, the upper modulation sideband could fall within the SBS amplification spectral region induced by the pump (a), or outside that region (b). (c): Spectrum of signal wave following propagation in the FUT and after filtering by a 5 GHz-wide FBG, which retains the upper modulation sideband only. The additional 1MHz amplitude modulation of the carrier is not shown.
. The modulated signal wave was launched into the FUT from the end opposite to that of the pump input. Following propagation through the FUT, the signal was filtered by a 5 GHz-wide fiber Bragg grating (FBG), which retained only the side-band of interest and blocked off the carrier wavelength, Rayleigh back-scatter of the pump wave and the other sideband. Lastly, the signal passed through a Polarization controller (PC) and a linear polarizer. The filtered signal power at the polarizer output was observed directly by a 125 MHz-wide photo-detector. In order to distinguish between the signal the induced SBS-ASE, the RF sine wave at ΩRF was further amplitude modulated by a 1-MHz tone, and the detector output power was measured by an RF spectrum analyzer (RFSA), using zero-span at 1MHz with a resolution bandwidth of 100Hz.

First, the optical power transmission of a scalar SBS-based filter without polarization discrimination was characterized (as in [7

7. A. Zadok, A. Eyal, and M. Tur, “GHz-wide optically reconfigurable filters using stimulated Brillouin scattering,” J. Lightwave Technol. 25(8), 2168–2174 (2007).[REMOVED IF= FIELD] [CrossRef]

]). In this set of measurements, the output polarizer was removed, and the input SOP of the signal was adjusted using PC4 for maximum amplification. The carrier frequency of the tunable laser was set to 15 GHz below the center of the SBS amplification band, as induced by the pump wave. Figure 6
Fig. 6 Relative sideband power gain of a scalar SBS-based filter, without polarization enhancement. Input signal power levels: (a) −3.1 dBm, (b) −8.2 dBm and (c) −13.1 dBm. A 13.5 dBm, 0.7 GHz-wide pump signal was used (Fig. 3).
shows the measured optical power gain of the sideband of interest as a function of ΩRF, which was scanned around 2π⋅15GHz. Measurements were taken for several signal power levels in the range of −18.1 to 2.7 dBm. A maximum selectivity of 22 dB was achieved in the undepleted pump regime. Pump depletion reduces the filter selectivity to 12.7 dB when the input signal power is raised to 2.7 dBm.

4. Discussion

In this work we have demonstrated a significant enhancement in the performance of SBS-based tunable band-pass filters. The improvement relies on the vector properties of the SBS amplification: the output SOP of amplified signal components is pulled towards a specific state, whereas the SOP of unamplified signal components is unaffected by SBS. Polarization-based discrimination, with judicious alignment of the input SOPs, provides an improvement in the filter selectivity in the undepleted pump regime. In addition, the depletion threshold of the filter is elevated as well. Care must be taken, though, in the application of the filter above the depletion threshold, as the transfer of broadband Stokes waves could be different from that of monochromatic signals. The filter bandwidth can be arbitrarily increased (up to ~10GHz [14

14. L. Thevenaz, “Slow and Fast Light Using Stimulated Brillouin Scattering: A Highly Flexible Approach,” in Slow Light – Science and Applications, J. B. Khurgin and R. S. Tucker Eds. (CRC press, 2009), pp. 173–193.

]) by further pump broadening, at the expense of lower gains and increased vulnerability to PMD. Finally, proper tracking and compensation of slow polarization drifts may be necessary for the stable, long-term operation of the filters [19

19. H. Sunnerud, C. Xie, M. Karlsson, R. Samuelsson, and P. Andrekson, “A comparison between different PMD compensation techniques,” J. Lightwave Technol. 20(3), 368–378 (2002). [CrossRef]

].

In conclusion, tunable and sharp optical band-pass filters were proposed and demonstrated, based on the insight that has been provided by the vector analysis of SBS in randomly birefringent fibers.

Acknowledgement

The work of M. Tur and A. Wise was supported in part by the Israeli Science Foundation (ISF).

References and links

1.

G. P. Agrawal, Fiber-Optic communication systems, third edition, (Wiley, 2002), Chapter 8, pp.330–403.

2.

J. Capmany, B. Ortega, D. Pastor, and S. Sales, “Discrete-time optical processing of microwave signals,” J. Lightwave Technol. 23(2), 702–723 (2005). [CrossRef]

3.

T. A. Strasser and T. Erdogan, “Fiber grating devices in high performance optical communication systems,” chapter 10 of Optical fiber telecommunications IVA – components. I. P. Kaminow, and T. Li (editors), San Diego, CA: Academic press, 2002.

4.

A. Yariv, chapter 4 in Optoelectronics, pp. 110–116, Orlando FL: Saunders College Publishing, 4th Edition, 1991.

5.

C. R. Doerr, “Planar lightwave devices for WDM,” chapter 9 of Optical fiber telecommunications IVA – components. I. P. Kaminow, and T. Li (editors), San Diego, CA: Academic press, 2002.

6.

T. Tanemura, Y. Takushima, and K. Kikuchi, “Narrowband optical filter, with a variable transmission spectrum, using stimulated Brillouin scattering in optical fiber,” Opt. Lett. 27(17), 1552–1554 (2002). [CrossRef] [PubMed]

7.

A. Zadok, A. Eyal, and M. Tur, “GHz-wide optically reconfigurable filters using stimulated Brillouin scattering,” J. Lightwave Technol. 25(8), 2168–2174 (2007).[REMOVED IF= FIELD] [CrossRef]

8.

R. W. Boyd, Nonlinear Optics, third edition, (Academic Press, 2008).

9.

M. Nikles, L. Thévenaz, and P. Robert, “Brillouin gain spectrum characterization in single-mode optical fibers,” J. Lightwave Technol. 15(10), 1842–1851 (1997). [CrossRef]

10.

J. C. Yong, L. Thévenaz, and B. Y. Kim, “Brillouin fiber laser pumped by a DFB laser diode,” J. Lightwave Technol. 21(2), 546–554 (2003). [CrossRef]

11.

A. Loayssa and F. J. Lahoz, “Broadband RF photonic phase shifter based on stimulated Brillouin scattering and single side-band modulation,” IEEE Photon. Technol. Lett. 18(1), 208–210 (2006). [CrossRef]

12.

A. Loayssa, J. Capmany, M. Sagues, and J. Mora, “Demonstration of incoherent microwave photonic filters with all-optical complex coefficients,” IEEE Photon. Technol. Lett. 18(16), 1744–1746 (2006). [CrossRef]

13.

Z. Zhu, D. J. Gauthier, and R. W. Boyd, “Stored light in an optical fiber via stimulated Brillouin scattering,” Science 318(5857), 1748–1750 (2007). [CrossRef] [PubMed]

14.

L. Thevenaz, “Slow and Fast Light Using Stimulated Brillouin Scattering: A Highly Flexible Approach,” in Slow Light – Science and Applications, J. B. Khurgin and R. S. Tucker Eds. (CRC press, 2009), pp. 173–193.

15.

A. Zadok, A. Eyal, and M. Tur, “Stimulated Brillouin scattering slow light in optical fibers,” Appl. Opt. 50(25), E38–E49 (2011). [CrossRef]

16.

A. Zadok, E. Zilka, A. Eyal, L. Thévenaz, and M. Tur, “Vector analysis of stimulated Brillouin scattering amplification in standard single-mode fibers,” Opt. Express 16(26), 21692–21707 (2008). [CrossRef] [PubMed]

17.

A. Zadok, S. Chin, L. Thévenaz, E. Zilka, A. Eyal, and M. Tur, “Polarization-induced distortion in stimulated Brillouin scattering slow-light systems,” Opt. Lett. 34(16), 2530–2532 (2009). [CrossRef] [PubMed]

18.

M. Wuilpart, “Distributed measurement of polarization properties in single-mode optical fibres using a reflectometry technique”, Ph.D. Thesis, Faculte Polytechnique de Mons (2003).

19.

H. Sunnerud, C. Xie, M. Karlsson, R. Samuelsson, and P. Andrekson, “A comparison between different PMD compensation techniques,” J. Lightwave Technol. 20(3), 368–378 (2002). [CrossRef]

20.

C. Y. Wong, R. S. Cheng, K. B. Letaief, and R. D. Murch, “Multiuser OFDM with adaptive subcarrier, bit, and power allocation,” IEEE J. Sel. Areas Comm. 17(10), 1747–1758 (1999). [CrossRef]

21.

M. Sagues and A. Loayssa, “Orthogonally polarized optical single sideband modulation for microwave photonics processing using stimulated Brillouin scattering,” Opt. Express 18(22), 22906–22914 (2010). [CrossRef] [PubMed]

OCIS Codes
(060.4370) Fiber optics and optical communications : Nonlinear optics, fibers
(190.0190) Nonlinear optics : Nonlinear optics
(290.5830) Scattering : Scattering, Brillouin

ToC Category:
Nonlinear Optics

History
Original Manuscript: August 1, 2011
Revised Manuscript: August 31, 2011
Manuscript Accepted: September 1, 2011
Published: October 21, 2011

Citation
Assaf Wise, Moshe Tur, and Avi Zadok, "Sharp tunable optical filters based on the polarization attributes of stimulated Brillouin scattering," Opt. Express 19, 21945-21955 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-22-21945


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References

  1. G. P. Agrawal, Fiber-Optic communication systems, third edition, (Wiley, 2002), Chapter 8, pp.330–403.
  2. J. Capmany, B. Ortega, D. Pastor, and S. Sales, “Discrete-time optical processing of microwave signals,” J. Lightwave Technol.23(2), 702–723 (2005). [CrossRef]
  3. T. A. Strasser and T. Erdogan, “Fiber grating devices in high performance optical communication systems,” chapter 10 of Optical fiber telecommunications IVA – components. I. P. Kaminow, and T. Li (editors), San Diego, CA: Academic press, 2002.
  4. A. Yariv, chapter 4 in Optoelectronics, pp. 110–116, Orlando FL: Saunders College Publishing, 4th Edition, 1991.
  5. C. R. Doerr, “Planar lightwave devices for WDM,” chapter 9 of Optical fiber telecommunications IVA – components. I. P. Kaminow, and T. Li (editors), San Diego, CA: Academic press, 2002.
  6. T. Tanemura, Y. Takushima, and K. Kikuchi, “Narrowband optical filter, with a variable transmission spectrum, using stimulated Brillouin scattering in optical fiber,” Opt. Lett.27(17), 1552–1554 (2002). [CrossRef] [PubMed]
  7. A. Zadok, A. Eyal, and M. Tur, “GHz-wide optically reconfigurable filters using stimulated Brillouin scattering,” J. Lightwave Technol.25(8), 2168–2174 (2007).[REMOVED IF= FIELD] [CrossRef]
  8. R. W. Boyd, Nonlinear Optics, third edition, (Academic Press, 2008).
  9. M. Nikles, L. Thévenaz, and P. Robert, “Brillouin gain spectrum characterization in single-mode optical fibers,” J. Lightwave Technol.15(10), 1842–1851 (1997). [CrossRef]
  10. J. C. Yong, L. Thévenaz, and B. Y. Kim, “Brillouin fiber laser pumped by a DFB laser diode,” J. Lightwave Technol.21(2), 546–554 (2003). [CrossRef]
  11. A. Loayssa and F. J. Lahoz, “Broadband RF photonic phase shifter based on stimulated Brillouin scattering and single side-band modulation,” IEEE Photon. Technol. Lett.18(1), 208–210 (2006). [CrossRef]
  12. A. Loayssa, J. Capmany, M. Sagues, and J. Mora, “Demonstration of incoherent microwave photonic filters with all-optical complex coefficients,” IEEE Photon. Technol. Lett.18(16), 1744–1746 (2006). [CrossRef]
  13. Z. Zhu, D. J. Gauthier, and R. W. Boyd, “Stored light in an optical fiber via stimulated Brillouin scattering,” Science318(5857), 1748–1750 (2007). [CrossRef] [PubMed]
  14. L. Thevenaz, “Slow and Fast Light Using Stimulated Brillouin Scattering: A Highly Flexible Approach,” in Slow Light – Science and Applications, J. B. Khurgin and R. S. Tucker Eds. (CRC press, 2009), pp. 173–193.
  15. A. Zadok, A. Eyal, and M. Tur, “Stimulated Brillouin scattering slow light in optical fibers,” Appl. Opt.50(25), E38–E49 (2011). [CrossRef]
  16. A. Zadok, E. Zilka, A. Eyal, L. Thévenaz, and M. Tur, “Vector analysis of stimulated Brillouin scattering amplification in standard single-mode fibers,” Opt. Express16(26), 21692–21707 (2008). [CrossRef] [PubMed]
  17. A. Zadok, S. Chin, L. Thévenaz, E. Zilka, A. Eyal, and M. Tur, “Polarization-induced distortion in stimulated Brillouin scattering slow-light systems,” Opt. Lett.34(16), 2530–2532 (2009). [CrossRef] [PubMed]
  18. M. Wuilpart, “Distributed measurement of polarization properties in single-mode optical fibres using a reflectometry technique”, Ph.D. Thesis, Faculte Polytechnique de Mons (2003).
  19. H. Sunnerud, C. Xie, M. Karlsson, R. Samuelsson, and P. Andrekson, “A comparison between different PMD compensation techniques,” J. Lightwave Technol.20(3), 368–378 (2002). [CrossRef]
  20. C. Y. Wong, R. S. Cheng, K. B. Letaief, and R. D. Murch, “Multiuser OFDM with adaptive subcarrier, bit, and power allocation,” IEEE J. Sel. Areas Comm.17(10), 1747–1758 (1999). [CrossRef]
  21. M. Sagues and A. Loayssa, “Orthogonally polarized optical single sideband modulation for microwave photonics processing using stimulated Brillouin scattering,” Opt. Express18(22), 22906–22914 (2010). [CrossRef] [PubMed]

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