- Email: [email protected]
Slow-light generation through Brillouin scattering in As2S3 fibers
Optical Materials 32 (2009) 358–361
Contents lists available at ScienceDirect
Optical Materials journal homepage: www.elsevier.com/locate/optmat
Slow-light generation through Brillouin scattering in As2S3 fibers C. Florea a,*, M. Bashkansky b, J. Sanghera b, I. Aggarwal b, Z. Dutton c a
Global Strategies Group, Crofton, MD 21114, United States US Naval Research Lab, Washington, DC 20375, United States c BBN Technologies, Cambridge, MA 02138, United States b
a r t i c l e
i n f o
Article history: Received 19 February 2009 Received in revised form 13 July 2009 Accepted 4 September 2009 Available online 6 October 2009
a b s t r a c t We demonstrate efficient generation of slow-light in As2S3 single-mode fibers through stimulated Brillouin scattering using a 1548 nm DFB laser. Sinusoidal pulses with a 40-ns period have been delayed 19 ns with only 31 mW of launched power in 10 m of fiber. Ó 2009 Elsevier B.V. All rights reserved.
PACS: 42.65.Es 42.81.Cn Keywords: Chalcogenide fiber Stimulated Brillouin scattering Slow-light
1. Introduction The slow-light technique based on stimulated Brillouin scattering (SBS) in optical fibers has recently attracted interest as it allows a very simple and robust implementation of tunable optical pulse delays, using mostly standard telecom components. Especially important are non-silica-based fibers with higher nonlinearity since these require lower powers and shorter lengths for practical implementations. To date there have been reports of slow-light generation in Bioxide high-nonlinearity fiber [1], telluride fiber [2] and of very efficient slow and fast light generation in As2Se3 chalcogenide fiber [3]. Additionally, the SBS process has been studied in As2S3 glass fibers [4]. In this paper we demonstrate for the first time, to the best of our knowledge, slow-light generation in As2S3 fiber. This is important since the As2S3 fiber is a more robust and exhibits lower losses than the As2Se3 fiber which otherwise would be the ideal system for this type of applications. Due to better drawing parameters for example, the slope of gain versus launched pump power is higher than the best result previously obtained in As2Se3 fiber [2], as expected from the analysis of the SBS figure of merit in these fibers [4]. We, therefore, demonstrate 19 ns delay with only
* Corresponding author. Tel.: +1 202 404 2306. E-mail address: catalin.fl[email protected] (C. Florea). 0925-3467/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.optmat.2009.09.002
31 mW of launched pump power in 10 m of fiber. We also measure the critical power, the Brillouin shift and its linewidth. This paper continues with Section 2 in which we give details on the experimental setup, and Section 3 in which we present new data on Brillouin scattering parameters characterizing the As2S3 fiber. Section 4 contains the actual gain and delay data, while the last section, Section 5, contains brief analysis and conclusions. 2. Experimental setup The experimental setup is detailed in Fig. 1. The components contained within the dashed contour lines were only employed for the delay measurements. We used the typical approach of splitting the output of a DFB laser (at 1548 nm, in our case) in two components, one which will serve as a pump while the other will serve as a counter-propagating signal. The signal component is frequency shifted by a certain amount (fm) such as to match the Brillouin shift. Using a LiNbO3 modulator and a Wiltron 68147B Sweep Generator we generate two sidebands which are then separated by using a fiber Bragg grating (FBG) filter, custom made by Advanced Optics Solutions Gmbh. We used the FBG filter in reflection mode and hence a circulator was needed in front of the filter. The center frequency is suppressed through DC biasing. For the gain measurements, the signal is coupled into the chalcogenide fiber and the output is monitored with an OSA. For the delay measurements, the signal, prior to being
C. Florea et al. / Optical Materials 32 (2009) 358–361
359
Fig. 1. Experimental setup used for gain and delay (dashed contour line) measurements. Abbreviations: LD, laser diode; EOM, electrooptical modulator; FBG, fiber Bragg grating filter; EDFA, Er-doped fiber amplifier; VOA, variable optical attenuator; fPD, fast photodiode; Amp, electrical amplifier.
coupled into the fiber, is modulated (sine wave at 25 MHz) with a LiNbO3 modulator and a DS345 signal generator. The output is then passed through a variable optical attenuator (VOA) and detected with a fast photodiode and an amplifier on an oscilloscope. The VOA allowed us to control the signal on the detector such that we maintained the same signal (as low as possible) throughout the gain measurement to avoid any electronics-induced time response. The pump is amplified with a standard EDFA and passed through a circulator before being coupled into the chalcogenide fiber, counter-propagating with the signal. The circulator allows us to pick off the signal and send it to the detector. Coupling efficiency in excess of 60% was achieved for the pump. 3. Brillouin scattering parameters The in-house drawn fiber used in this work was similar to the one used in previous work [4] but this time the fiber was cabled and both ends were antireflection coated. The core and clad compositions are As39S61 and As38S62, respectively. The fiber had a core of 5.2 lm diameter1 and a clad of 150 lm diameter, while the loss at 1550 nm was measured to be 0.138 m1 (0.6 dB m1). We measured the effective area of the fundamental mode and have also determined the critical power, Pcr, for a 10-m length of fiber, directly from the variation, with pump power, of the counter-propagating signal generated through Brillouin scattering. We did so in order to check our previous estimate of the gB coefficient [4], which was obtained by rather qualitatively analyzing the spectral changes of signal. By using Aeff and Pcr to determine gB as detailed below, we are following the approach used in previous work [3,5] although a more exact analysis was proposed elsewhere [6]. The effective area (Aeff) was measured by imaging the fiber output on a vidicon camera using an appropriate microscope objective. We decided to actually measure the Aeff rather than to use a theoretical estimate [3] due to the fact that our fiber had a very high NA (greater than 0.30) making it possible for a second, higher order mode to contribute to the fundamental mode field. Our measuring system was calibrated by also imaging a patch of SMF28 fi1 The core diameter is found to vary slightly along the fiber within 5% of the quoted value.
ber with well-known mode-field diameter (MFD) of 10.4 ± 0.8 lm at 1550 nm. The two images are shown side by side in Fig. 2. The MFD for the chalcogenide fiber was thus determined to be 5.2 ± 0.4 lm. The critical power was measured by monitoring the intensity of the Brillouin scattered signal versus the launched, counter-propagating pump power.2 A more precise analysis is usually performed in silica fibers [7]. The pump source was a DFB laser amplified with an EDFA which was launched into the chalcogenide fiber using a free-space system (imaging lenses and alignment stage). The coupling efficiency was estimated from fiber throughput measurements. The reflected signal was collected using a circulator, and the values of the Brillouin peak were read directly from the optical spectrum analyzer (OSA). Several measurements were made which yielded an average Pcr of 29 ± 6 mW, which is close to the previously reported value [4] of 27 ± 3 mW. A typical data set is shown in Fig. 3. Using Eq. (1), in which a is the fiber loss and L is the fiber length, we estimate an effective fiber length (Leff) of 5.4 m. Finally, one can use these values for Aeff, Pcr, and Leff, to estimate the Brillouin scattering coefficient using Eq. (2), where k is a constant which reflects whether the polarization is maintained constant throughout the interaction (k = 1) or not (k = 0.5, our case). Using proper error analysis, we have determined the Brillouin scattering coefficient to be (5.7 ± 2.0) 109 m W1 for the As2S3 fiber used.
Leff ¼
1
a
P cr ffi 21
1 eaL
Aeff Leff g B k
ð1Þ
ð2Þ
Additionally, we have performed a linewidth measurement of the Brillouin signal using a small probe (8 lW) launched counter-propagating through the fiber. We manually tuned the microwave generator while monitoring the variation of the signal peak, as read from the OSA. The Brillouin shift was identified to be 7.96 GHz while the linewidth of the Brillouin shift was found to be 31 MHz, with typical data being represented in Fig. 4. The 2
There was no external signal launched into the fiber for this measurement.
360
C. Florea et al. / Optical Materials 32 (2009) 358–361
Fig. 2. Near-field imaging of the fiber output for the fibers: (a) SMF28 and (b) As2S3.
sine wave was read from the oscilloscope. Typical set of traces is shown in Fig. 5. We were limited in the observable gain and delay by the damage threshold of the AR coating, which unfortunately was lower than the threshold for the bare As2S3 glass. A slow variation of the amplified signal was observed which perhaps was due to the lack of polarization control in the setup. The overall results are represented in Fig. 6.
5. Analysis and conclusions
Fig. 3. Brillouin scattered signal in As2S3 fiber versus launched pump power.
We have characterized the Brillouin scattering process in As2S3 fiber and we have found that the Brillouin gain coefficient is (5.7 ± 2.0) 109 m W1, the frequency shift is 7.96 GHz, and the linewidth of the Brillouin shift if 31 MHz. The slope of gain-versus-power is twice as large as the best previously reported result [2]. This was expected based on the analysis of the figure of merit (FOM) for the SBS process in these fibers [3,4]. However, the gain slope we have obtained falls short of the theoretical estimate. Using the undepleted pump approximation, the small-signal gain is given theoretically by Eq. (3) (see [3,4]):
Gth ½dB ¼ 4:34
g B k Leff P Aeff
ð3Þ
Using the experimentally determined values for the involved parameters along with the associated uncertainties, Eq. (3) gives us a slope in the range [1.8, . . ., 5.0] dB mW1.
Fig. 4. Typical linewidth data at low pump power.
linewidth was measured at low pump powers.3 Linewidth narrowing was observed for higher powers with linewidths as small as 19 MHz being recorded. 4. Gain and delay data Gain and delay measurements using a small signal (8 lW) were performed in the chalcogenide fiber. For the gain measurement, the signal peak values were read from the OSA for different pump powers. For the delay measurement, the relative shift of the 3
A calibration of coupling efficiency for this measurement was not performed.
Fig. 5. Typical waveforms showing the delay for different pump powers.
C. Florea et al. / Optical Materials 32 (2009) 358–361
361
Fig. 6. Gain (a) and pulse delay (b) measurements in 10-m long As2S3 fiber at 1548 nm.
The inhomogeneity in the fiber core diameter which we have noticed, the potential presence of a second mode and the pump depletion approximation can be viewed as factors contributing to the discrepancy. The same factors can also influence the delay data. Once again we can predict theoretically how much the peak of the signal pulse would be delayed (Dt) by assuming an undepleted pump. The group velocity (given by vg = c/ng, c – speed of light, ng – total fiber group index) determines the time that a given pulse will take to travel the effective length of fiber. In the presence of the pump, the group velocity at the peak of the Brillouin gain will be modified according to Eq. (4) [8], where Dm is the linewidth (full-width halfmaximum) of the Brillouin shift:
G=Leff 1 nfg ¼ þ vg c 2 p Dm
References
ð4Þ
For a narrow linewidth pulse the delay, that is difference between the transit times required by the pulse with and without the pump, will then be given by Eq. (5) [8]:
Dt
g k Leff G ¼ B P 2p Dm Aeff 2p Dm
While in practical terms we obtained a 19 ns delay for only 31 mW of pump power, which is marginally better than the result in the As2Se3 fiber [2], these experimental values fall short of the theoretical expectations. The choice of the 25 MHz frequency for modulation of the signal was unfortunate since it turned out to be too close to the Brillouin linewidth, especially at low powers. Future work will try different modulation parameters and will also provide a study to gain an insight into the nature and origin of fiber imperfections and the role of polarization which can negatively influence the performance of this system. This understanding will pave the way forward for delays of the order of 20 ns with as little as 10 mW of launched power.
ð5Þ
Using the experimentally determined values for the involved parameters along with the associated uncertainties, Eq. (5) gives us a slope in the range [2.1, . . ., 5.9] ns mW1. For this type of fiber, Eq. (5) indicates theoretically that delays on the order of 100 ns or more can be obtained for reasonable powers.
[1] C. Jáuregui, H. Ono, P. Petropoulos, D.J. Richardson, OFC, Paper PDP2, 2006. [2] K.S. Abedin, G.-W. Lu, T. Miyazaki, Electron. Lett. 44 (2008) 16. [3] K.Y. Song, K.S. Abedin, K. Hotate, M.G. Herráez, L. Thévenaz, Opt. Exp. 14 (2006) 5860. [4] C.M. Florea, M. Bashkansky, Z. Dutton, J. Sanghera, I. Aggarwal, Opt. Exp. 14 (2006) 12063. [5] K.S. Abedin, Opt. Exp. 13 (2006) 10266. [6] K. Ogusu, IEEE Photon. Technol. Lett. 14 (2002) 947. [7] See, for example, A.B. Roffin, in: NIST Symposium on Optical Fiber Measurements, Technical Digest, 2004, pp. 23–28; A.B. Ruffin, M.-J. Li, X. Chen, A. Kobyakov, F. Annunziata, Opt. Lett. 30 (2005) 3123. [8] Y. Okawachi, M.S. Bigelow, J.E. Sharping, Z. Zhu, A. Schweinsberg, D.J. Gauthier, R.W. Boyd, A.L. Gaeta, Phys. Rev. Lett. 94 (2005) 153902.
Contents lists available at ScienceDirect
Optical Materials journal homepage: www.elsevier.com/locate/optmat
Slow-light generation through Brillouin scattering in As2S3 fibers C. Florea a,*, M. Bashkansky b, J. Sanghera b, I. Aggarwal b, Z. Dutton c a
Global Strategies Group, Crofton, MD 21114, United States US Naval Research Lab, Washington, DC 20375, United States c BBN Technologies, Cambridge, MA 02138, United States b
a r t i c l e
i n f o
Article history: Received 19 February 2009 Received in revised form 13 July 2009 Accepted 4 September 2009 Available online 6 October 2009
a b s t r a c t We demonstrate efficient generation of slow-light in As2S3 single-mode fibers through stimulated Brillouin scattering using a 1548 nm DFB laser. Sinusoidal pulses with a 40-ns period have been delayed 19 ns with only 31 mW of launched power in 10 m of fiber. Ó 2009 Elsevier B.V. All rights reserved.
PACS: 42.65.Es 42.81.Cn Keywords: Chalcogenide fiber Stimulated Brillouin scattering Slow-light
1. Introduction The slow-light technique based on stimulated Brillouin scattering (SBS) in optical fibers has recently attracted interest as it allows a very simple and robust implementation of tunable optical pulse delays, using mostly standard telecom components. Especially important are non-silica-based fibers with higher nonlinearity since these require lower powers and shorter lengths for practical implementations. To date there have been reports of slow-light generation in Bioxide high-nonlinearity fiber [1], telluride fiber [2] and of very efficient slow and fast light generation in As2Se3 chalcogenide fiber [3]. Additionally, the SBS process has been studied in As2S3 glass fibers [4]. In this paper we demonstrate for the first time, to the best of our knowledge, slow-light generation in As2S3 fiber. This is important since the As2S3 fiber is a more robust and exhibits lower losses than the As2Se3 fiber which otherwise would be the ideal system for this type of applications. Due to better drawing parameters for example, the slope of gain versus launched pump power is higher than the best result previously obtained in As2Se3 fiber [2], as expected from the analysis of the SBS figure of merit in these fibers [4]. We, therefore, demonstrate 19 ns delay with only
* Corresponding author. Tel.: +1 202 404 2306. E-mail address: catalin.fl[email protected] (C. Florea). 0925-3467/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.optmat.2009.09.002
31 mW of launched pump power in 10 m of fiber. We also measure the critical power, the Brillouin shift and its linewidth. This paper continues with Section 2 in which we give details on the experimental setup, and Section 3 in which we present new data on Brillouin scattering parameters characterizing the As2S3 fiber. Section 4 contains the actual gain and delay data, while the last section, Section 5, contains brief analysis and conclusions. 2. Experimental setup The experimental setup is detailed in Fig. 1. The components contained within the dashed contour lines were only employed for the delay measurements. We used the typical approach of splitting the output of a DFB laser (at 1548 nm, in our case) in two components, one which will serve as a pump while the other will serve as a counter-propagating signal. The signal component is frequency shifted by a certain amount (fm) such as to match the Brillouin shift. Using a LiNbO3 modulator and a Wiltron 68147B Sweep Generator we generate two sidebands which are then separated by using a fiber Bragg grating (FBG) filter, custom made by Advanced Optics Solutions Gmbh. We used the FBG filter in reflection mode and hence a circulator was needed in front of the filter. The center frequency is suppressed through DC biasing. For the gain measurements, the signal is coupled into the chalcogenide fiber and the output is monitored with an OSA. For the delay measurements, the signal, prior to being
C. Florea et al. / Optical Materials 32 (2009) 358–361
359
Fig. 1. Experimental setup used for gain and delay (dashed contour line) measurements. Abbreviations: LD, laser diode; EOM, electrooptical modulator; FBG, fiber Bragg grating filter; EDFA, Er-doped fiber amplifier; VOA, variable optical attenuator; fPD, fast photodiode; Amp, electrical amplifier.
coupled into the fiber, is modulated (sine wave at 25 MHz) with a LiNbO3 modulator and a DS345 signal generator. The output is then passed through a variable optical attenuator (VOA) and detected with a fast photodiode and an amplifier on an oscilloscope. The VOA allowed us to control the signal on the detector such that we maintained the same signal (as low as possible) throughout the gain measurement to avoid any electronics-induced time response. The pump is amplified with a standard EDFA and passed through a circulator before being coupled into the chalcogenide fiber, counter-propagating with the signal. The circulator allows us to pick off the signal and send it to the detector. Coupling efficiency in excess of 60% was achieved for the pump. 3. Brillouin scattering parameters The in-house drawn fiber used in this work was similar to the one used in previous work [4] but this time the fiber was cabled and both ends were antireflection coated. The core and clad compositions are As39S61 and As38S62, respectively. The fiber had a core of 5.2 lm diameter1 and a clad of 150 lm diameter, while the loss at 1550 nm was measured to be 0.138 m1 (0.6 dB m1). We measured the effective area of the fundamental mode and have also determined the critical power, Pcr, for a 10-m length of fiber, directly from the variation, with pump power, of the counter-propagating signal generated through Brillouin scattering. We did so in order to check our previous estimate of the gB coefficient [4], which was obtained by rather qualitatively analyzing the spectral changes of signal. By using Aeff and Pcr to determine gB as detailed below, we are following the approach used in previous work [3,5] although a more exact analysis was proposed elsewhere [6]. The effective area (Aeff) was measured by imaging the fiber output on a vidicon camera using an appropriate microscope objective. We decided to actually measure the Aeff rather than to use a theoretical estimate [3] due to the fact that our fiber had a very high NA (greater than 0.30) making it possible for a second, higher order mode to contribute to the fundamental mode field. Our measuring system was calibrated by also imaging a patch of SMF28 fi1 The core diameter is found to vary slightly along the fiber within 5% of the quoted value.
ber with well-known mode-field diameter (MFD) of 10.4 ± 0.8 lm at 1550 nm. The two images are shown side by side in Fig. 2. The MFD for the chalcogenide fiber was thus determined to be 5.2 ± 0.4 lm. The critical power was measured by monitoring the intensity of the Brillouin scattered signal versus the launched, counter-propagating pump power.2 A more precise analysis is usually performed in silica fibers [7]. The pump source was a DFB laser amplified with an EDFA which was launched into the chalcogenide fiber using a free-space system (imaging lenses and alignment stage). The coupling efficiency was estimated from fiber throughput measurements. The reflected signal was collected using a circulator, and the values of the Brillouin peak were read directly from the optical spectrum analyzer (OSA). Several measurements were made which yielded an average Pcr of 29 ± 6 mW, which is close to the previously reported value [4] of 27 ± 3 mW. A typical data set is shown in Fig. 3. Using Eq. (1), in which a is the fiber loss and L is the fiber length, we estimate an effective fiber length (Leff) of 5.4 m. Finally, one can use these values for Aeff, Pcr, and Leff, to estimate the Brillouin scattering coefficient using Eq. (2), where k is a constant which reflects whether the polarization is maintained constant throughout the interaction (k = 1) or not (k = 0.5, our case). Using proper error analysis, we have determined the Brillouin scattering coefficient to be (5.7 ± 2.0) 109 m W1 for the As2S3 fiber used.
Leff ¼
1
a
P cr ffi 21
1 eaL
Aeff Leff g B k
ð1Þ
ð2Þ
Additionally, we have performed a linewidth measurement of the Brillouin signal using a small probe (8 lW) launched counter-propagating through the fiber. We manually tuned the microwave generator while monitoring the variation of the signal peak, as read from the OSA. The Brillouin shift was identified to be 7.96 GHz while the linewidth of the Brillouin shift was found to be 31 MHz, with typical data being represented in Fig. 4. The 2
There was no external signal launched into the fiber for this measurement.
360
C. Florea et al. / Optical Materials 32 (2009) 358–361
Fig. 2. Near-field imaging of the fiber output for the fibers: (a) SMF28 and (b) As2S3.
sine wave was read from the oscilloscope. Typical set of traces is shown in Fig. 5. We were limited in the observable gain and delay by the damage threshold of the AR coating, which unfortunately was lower than the threshold for the bare As2S3 glass. A slow variation of the amplified signal was observed which perhaps was due to the lack of polarization control in the setup. The overall results are represented in Fig. 6.
5. Analysis and conclusions
Fig. 3. Brillouin scattered signal in As2S3 fiber versus launched pump power.
We have characterized the Brillouin scattering process in As2S3 fiber and we have found that the Brillouin gain coefficient is (5.7 ± 2.0) 109 m W1, the frequency shift is 7.96 GHz, and the linewidth of the Brillouin shift if 31 MHz. The slope of gain-versus-power is twice as large as the best previously reported result [2]. This was expected based on the analysis of the figure of merit (FOM) for the SBS process in these fibers [3,4]. However, the gain slope we have obtained falls short of the theoretical estimate. Using the undepleted pump approximation, the small-signal gain is given theoretically by Eq. (3) (see [3,4]):
Gth ½dB ¼ 4:34
g B k Leff P Aeff
ð3Þ
Using the experimentally determined values for the involved parameters along with the associated uncertainties, Eq. (3) gives us a slope in the range [1.8, . . ., 5.0] dB mW1.
Fig. 4. Typical linewidth data at low pump power.
linewidth was measured at low pump powers.3 Linewidth narrowing was observed for higher powers with linewidths as small as 19 MHz being recorded. 4. Gain and delay data Gain and delay measurements using a small signal (8 lW) were performed in the chalcogenide fiber. For the gain measurement, the signal peak values were read from the OSA for different pump powers. For the delay measurement, the relative shift of the 3
A calibration of coupling efficiency for this measurement was not performed.
Fig. 5. Typical waveforms showing the delay for different pump powers.
C. Florea et al. / Optical Materials 32 (2009) 358–361
361
Fig. 6. Gain (a) and pulse delay (b) measurements in 10-m long As2S3 fiber at 1548 nm.
The inhomogeneity in the fiber core diameter which we have noticed, the potential presence of a second mode and the pump depletion approximation can be viewed as factors contributing to the discrepancy. The same factors can also influence the delay data. Once again we can predict theoretically how much the peak of the signal pulse would be delayed (Dt) by assuming an undepleted pump. The group velocity (given by vg = c/ng, c – speed of light, ng – total fiber group index) determines the time that a given pulse will take to travel the effective length of fiber. In the presence of the pump, the group velocity at the peak of the Brillouin gain will be modified according to Eq. (4) [8], where Dm is the linewidth (full-width halfmaximum) of the Brillouin shift:
G=Leff 1 nfg ¼ þ vg c 2 p Dm
References
ð4Þ
For a narrow linewidth pulse the delay, that is difference between the transit times required by the pulse with and without the pump, will then be given by Eq. (5) [8]:
Dt
g k Leff G ¼ B P 2p Dm Aeff 2p Dm
While in practical terms we obtained a 19 ns delay for only 31 mW of pump power, which is marginally better than the result in the As2Se3 fiber [2], these experimental values fall short of the theoretical expectations. The choice of the 25 MHz frequency for modulation of the signal was unfortunate since it turned out to be too close to the Brillouin linewidth, especially at low powers. Future work will try different modulation parameters and will also provide a study to gain an insight into the nature and origin of fiber imperfections and the role of polarization which can negatively influence the performance of this system. This understanding will pave the way forward for delays of the order of 20 ns with as little as 10 mW of launched power.
ð5Þ
Using the experimentally determined values for the involved parameters along with the associated uncertainties, Eq. (5) gives us a slope in the range [2.1, . . ., 5.9] ns mW1. For this type of fiber, Eq. (5) indicates theoretically that delays on the order of 100 ns or more can be obtained for reasonable powers.
[1] C. Jáuregui, H. Ono, P. Petropoulos, D.J. Richardson, OFC, Paper PDP2, 2006. [2] K.S. Abedin, G.-W. Lu, T. Miyazaki, Electron. Lett. 44 (2008) 16. [3] K.Y. Song, K.S. Abedin, K. Hotate, M.G. Herráez, L. Thévenaz, Opt. Exp. 14 (2006) 5860. [4] C.M. Florea, M. Bashkansky, Z. Dutton, J. Sanghera, I. Aggarwal, Opt. Exp. 14 (2006) 12063. [5] K.S. Abedin, Opt. Exp. 13 (2006) 10266. [6] K. Ogusu, IEEE Photon. Technol. Lett. 14 (2002) 947. [7] See, for example, A.B. Roffin, in: NIST Symposium on Optical Fiber Measurements, Technical Digest, 2004, pp. 23–28; A.B. Ruffin, M.-J. Li, X. Chen, A. Kobyakov, F. Annunziata, Opt. Lett. 30 (2005) 3123. [8] Y. Okawachi, M.S. Bigelow, J.E. Sharping, Z. Zhu, A. Schweinsberg, D.J. Gauthier, R.W. Boyd, A.L. Gaeta, Phys. Rev. Lett. 94 (2005) 153902.