Superluminal propagation through 500 m opticalfiber via stimulated Brillouin scatteringLIANG ZHANG, LI ZHAN,* MINGLEI QIN, ZHIQIANG WANG, HAO LUO, AND TANTAN WANG

Department of Physics and Astronomy, State Key Lab of Advanced Optical Communication Systems and Networks,Key Laboratory for Laser Plasmas (Ministry of Education), Shanghai Jiao Tong University, Shanghai 200240, China*Corresponding author: lizhan@sjtu.edu.cn

Received 10 June 2015; revised 19August 2015; accepted 19 August 2015; posted 20August 2015 (Doc. ID 242728); published 18 September 2015

We have experimentally demonstrated superluminal propa-gation through a 500 m optical fiber using stimulatedBrillouin scattering (SBS), which is the longest superlumi-nal propagating distance reported so far, to the best of ourknowledge. Brillouin-induced loss resonance for fast lightgeneration of pump signals is achieved in a single frequencyBrillouin lasing oscillator with a highly nonlinear fiber asthe SBS medium. The single frequency operation is realizedby embedding the saturable absorber fiber loop with an un-pumped erbium-doped fiber. Consequently, signals with apulse width of 710 ns experience a maximum advancementof 1330 ns. Furthermore, the effects of pulse width and theduty cycle of pump signals are also investigated. © 2015Optical Society of America

OCIS codes: (060.4370) Nonlinear optics, fibers; (290.5900)

Scattering, stimulated Brillouin; (350.5500) Propagation.

http://dx.doi.org/10.1364/OL.40.004404

During the past decades, impressive progress in controlling thegroup velocity of light by creating sharp spectral resonance indispersive media has been reported [1–5]. Slow light and fastlight offer potential applications for optical variable delaylines [6], optical signal processing [7], optical communications[8], light–matter interaction enhancement [9], microwavephotonics filters, and temporal cloaks [6–10]. Recently, it hasbeen shown that a rotation sensor based on fast-light technol-ogy exhibits enhanced sensitivity by a factor of 106 [11], whichmay bring benefits to detecting the gravitational frame-drag-ging effect [12]. Also, various approaches have been proposedto study fast-light ring laser gyroscopes [13–16].

Slow/fast light based on stimulate Brillouin scattering (SBS)has become an effective way to engineer the group index[17,18]. However, because it operates on a strong absorptionband, the propagating distance and the time advancement offast light is severely restricted. Although superluminal propaga-tion based on a gain-assisted scheme has been demonstrated,the transmission distance of signals is extremely limited bythe length of the ultracold atomic vapor [2]. Coherent popu-lation oscillation (CPO) [19] and cross gain modulation(XGM) [20] can be implemented to generate superluminal

propagation in erbium-doped fibers. However, the dependenceon a well-defined modulation frequency of light renders suchschemes impractical. Recent research has reported low-losssuperluminal propagation in optical fibers via Brillouin lasingoscillation [21,22]. Owing to the perfect self-adaptation [23]and the linewidth narrowing [24] of the lasing Stokes, thisscheme shows strong robustness and inherent stability inachieving anomalous dispersion at the frequency of the pumplight. Highly nonlinear fiber (HNLF) has been applied to en-hance the time advancement [22,25]. Nevertheless, the super-luminal propagating distance could not be extended by simplyincreasing fiber length since enough signal advancement is alsorequired to support a group velocity larger than the speed oflight in vacuum. To date, the distances of superluminal propa-gation in previous works have been limited to the order of 10 m[2,19–22]. However, long-distance superluminal propagationis expected for gravitational wave detection [12].

The Brillouin gain can be enhanced by using a medium witha high gain coefficient [26]. However, longer fibers easily leadto saturation of the Brillouin gain [27], and result in a limitedBrillouin-induced delay or advancement. Therefore, the signaladvancement and transmission distance of fast light based onBrillouin lasing oscillation was not intended to be significantlyimproved through simply using a longer fiber instead of 10 msingle-mode fiber (SMF) in previous schemes [21]. On theother hand, a Brillouin fiber laser (BFL) with a longer-than-10-m cavity essentially results in multiple-longitudinal-mode(MLM) oscillation. This greatly broadens the Brillouin-induced loss bandwidth at the pump light. The signal advance-ment is thus degraded since the advancement is inverselyproportional to the bandwidth [26]. Consequently, the preser-vation of single-frequency lasing operation turns out to be acritical issue for long-distance superluminal propagation.

In this Letter, Brillouin-induced superluminal propagationof ultralong distance in optical fiber was experimentally dem-onstrated. In our scheme, a 500 m HNLF is used as the SBSmedium in the BFL cavity. A saturable absorber (SA) fiber loopwith an unpumped erbium-doped fiber (EDF) is utilized toguarantee single-longitudinal-mode (SLM) operation of the las-ing Stokes wave. In our experiment, the pump signal experien-ces an advancement of 1330 ns and the group velocity is 1.48c(c is the speed of light in vacuum) in passing through the

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HNLF, which is the longest distance of superluminal propaga-tion reported so far, to the best of our knowledge.

According to the Kramers–Kronig relation, the SBS gain/loss process can introduce a change of the refractive indexand thus manipulate the group velocity of the light. In aBrillouin fiber ring cavity, the circulating Stokes wave introdu-ces a Brillouin-induced loss spectral resonance at the pumplight. Consequently, the pump signals exhibit fast light propa-gation and the advancement is proportional to the circulatingStokes power (Pcs) in the cavity. Usually, a BFL with a shorter-than-10-m cavity operates in excellent SLM status since thecorresponding free spectral range is less than the Brillouin gainbandwidth (20–30 MHz) in silica fibers [28]. However, theBFL with a longer-than-10-m cavity is supposed to generatea MLM oscillation. The MLM oscillation actually broadensthe bandwidth of Brillouin-induced loss resonance and hencedegrades signal advancement. Thus, SLM operation is a keyissue in overcoming the fundamental limitation of superlumi-nal propagating distance based on Brillouin lasing oscillation.The utilization of an SA fiber loop with unpumped EDF pro-vides an effective tool to realize SLM operation [29,30]. Alongthe EDF in the loop, a standing wave is established by twocounterpropagating light waves. The spatial periodic distribu-tion of the light intensity introduces a periodic variation of therefractive index [31]. Finally, a dynamic Bragg grating (DBG) isformed as an autotracking narrowband filter, which can be usedto suppress the MLM operation.

The experimental setup for long-distance superluminalpropagation in an SLM BFL is illustrated in Fig. 1. Theincident light from a distributed feedback (DFB) laser(λ � 1550 nm) is modulated through a Mach–Zehndermodulator (MZM) driven by a function generator. The signalamplitude and DC bias for the MZM are properly adjusted toobtain an incompletely modulated pump signal, which is ben-eficial to Stokes generation and then improves advancementefficiency [21]. The modulation depth is only 10% of thepump signal amplitude. Here, the Gaussian pulse signal withfull width at half-maximum (FWHM) of 710 ns andrepetition rate of 500 kHz is generated. Then, the signals areamplified by an erbium-doped fiber amplifier (EDFA) andlaunched as the SBS pump into the BFL, which is composedof an optical circulator (CIR-1), a SBS medium, and a 10/90optical coupler (OC-1). The circulating Stokes power in thecavity is 10 times larger than the output Stokes lasing power.SLM operation is maintained by an intracavity fiber loop con-sisting of a CIR-2, a 50/50 OC-2, polarization controllers(PCs), and an SA of unpumped EDF (400 parts per million Erion concentration). The output Stokes from the OC-1 is de-tected by a photodetector (PD) and an electrical spectrum ana-lyzer (ESA) at Port 2. The output pump signals are visualizedon an oscilloscope triggered by the same function generator.

A tunable optical filter (TOF) is used to suppress the amplifiedspontaneous emission noise of the EDFA before detection.

To verify the importance of SLM operation on Stokes lasing,we carried out an experiment with a piece of 50 m standardSMF embedded between points A and B as the Brillouinmedium. The total cavity of the BFL is 52.6 m, correspondingto a longitudinal mode space of 3.8 MHz. The RF spectra ofthe output lasing Stokes is monitored by the ESA as the outputlaser power remains 10 mW. When the laser turns off, the re-sponse of the PD is regarded as the reference in each measure-ment. In Fig. 2(a), without the SA fiber loop, the output Stokeslaser works on MLM operation and we observe strong periodicbeat signals with a space of 3.8 MHz. When using the intra-cavity SA loop with 3 m EDF, high-order longitudinal modesare greatly suppressed. A longer EDF could offer a narrower-bandwidth DBG. However, more attenuation would be intro-duced owing to the absorption of the EDF. In our experiment,an SA loop with an 8 m unpumped EDF provides satisfactoryperformance on the SLM operation. In Fig. 2(b), the outputsignals in all cases experience temporal boosts above the thresh-old. The signal advancement without the SA turns out to besaturated and even degraded when Pcs exceeds 50 mW. Byembedding the 3 m EDF SA loop, the advancement is extendedto 280 ns at 110 mW Pcs. A longer unpumped EDF of 8 mleads to stronger MLM suppression. Signal advancement isachieved with a maximum advancement of 395 ns underPcs of 210 mW. Clearly, SLM operation in BFLs overcomesthe distance limitation of fast light propagation.

Compared with the SMF, the HNLF has a smaller modefield area and a larger Brillouin gain coefficient. Here, a500 m HNLF with a mode field diameter of 4.0 μm and anonlinear coefficient of 9.1 W−1 is used as the SBS medium.An SA loop with 8 m EDF is embedded to suppress MLMoperation. Figure 3(a) shows output pump signals under differ-ent Pcs in the cavity. Advancements of 340 and 900 ns are ob-served under Pcs of 1 and 2 mW, respectively. As Pcs increasesto 5 mW, signal advancement of 1210 ns can be found.Because the CPO works at the frequency of the order of kilo-hertz because of the relaxation time of Er ions (∼10.5 ms),there is no noticeable delay or advancement from the CPOeffect in the EDFA. Since the limited loss spectral resonancecauses different frequency components to experience differenttransmission phases and amplitude responses, output signalswith steeper leading edges and longer trailing edges can be

Fig. 1. Experimental setup for long-distance superluminal propaga-tion via a BFL by employing an SA fiber loop.

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found under Pcs of 1 and 2 mW. However, less pulse distortionis observed as Pcs reaches above 5 mW. This is mainly causedby linewidth broadening of the lasing Stokes under the higherpower. The effective Brillouin gain distribution corresponds tothe convolution of the natural narrowband Brillouin gain spec-trum with the normalized pump power spectrum [17], whichalso applies for Brillouin-induced loss resonance [21]. The line-width broadening under the high circulating Stokes powercould broaden the effective loss bandwidth for the pumpsignals. Therefore, the pulse distortion of output signals is alle-viated when Pcs > 5 mW. The disadvantage is that the broad-ening also results in saturation of the advancement. As shownin Fig. 3(b), signal advancement cannot be effectively improvedby increasing Pcs beyond 5 wM. The advancement is found tohave a maximum of 1330 ns, corresponding to a fractional ad-vancement of 1.87. The group velocity of the HNLF is givenby 0.67c when the refractive index is typically 1.47, withoutany nonlinear effect. Considering the transmission distanceof 500 m HNLF, the maximum group velocity is 1.48c withPcs of 10 mW, while the minimum group index is 0.67. It isworth mentioning that the utility of the HNLF instead of theSMF reduces power requirements for the desired advancementsby 1–2 orders of magnitude.

In Fig. 4, the RF spectra of the output lasing Stokes ismeasured to clarify the longitudinal mode feature. Withoutthe SA loop, obvious MLM operation is observed when Pcs

is 10 mW. By using the SA loop, a suppression of 20.7 dBof MLM operation is found. Moreover, the longitudinal modesincrease as Pcs varies from 5 to 10 mW. A higher optical powerin the SA fiber loop results in a larger index change in the EDF[31], degrading MLM suppression. The MLM lines broadened

the effective loss bandwidth at the pump light and thusdegraded the advancement.

A single-shot experiment is also implemented to verify thefast light effect in this scheme. The pulse separation of modu-lated pump signals is set to be larger than the propagating timeof 2.5 μs through the 500 m HNLF. Completely modulatedpulses of different widths are injected into the cavity. InFig. 5(a), the measured advancement of the pulses increasesas Pcs varies from 0 to 2.5 mW. In particular, the signals withthe wider pulse width exhibit a larger advancement under thesame Pcs since pump signals with wide pulse width are expectedto experience multiple Stokes lasing round trips. In Figs. 5(b)and 5(c), the signals with the pulse widths of 0.5 and 5 μsundergo the fast light effect as Pcs increases. The advancementand pulse distortion of the 0.5 μs width signals are relativelysmall. However, the 5 μs width signals experience larger ad-vancement and suffer from worse pulse distortion.

Moreover, the impact of the duty cycle for the advancementis investigated, as shown in Fig. 6. Pump signals with pulsewidth of 0.49 μs and different duty cycles of 20% and 50%are launched into the fiber cavity. As Pcs increases, the advance-ments go up with a slope of 27.4 ns/mW under the 50% dutycycle and 4.7 ns/mW under the 20% duty cycle. This indicatesthat signal pulses with large duty cycles can enhance signal

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advancement since the pregenerated circulating Stokes light canprovide multiple SBS interactions for successive signal pulses.It is worth mentioning that incompletely modulated pumpsignals with strong DC components can greatly enhance thelasing Stokes generation and advancement efficiency, becausethe Stokes light always circulates in the cavity [21].Therefore, we use weakly modulated pump signals in the aboveexperiment to obtain advancement of 1330 ns.

Along the optical fiber, most of the power transfer in theSBS process occurs within the first 20% of the fiber length[32]. This indicates that most of the advancement occurs inthe first 20% of the length. For application, the fiber lengthand the advancement in our scheme require precise design.For instance, the sensitivity enhancement in a superluminalring laser gyroscope can be obtained if the group delay is opti-mized [16]. Note that the utilization of a unidirectional attenu-ator/amplifier in the junction of the fiber segments couldprovide a solution to the gain/loss saturation along the longfiber [33].

Additionally, MLM operation of Stokes lasing under highpower could lead to instability of the system, which rendersthe scheme impractical for applications. However, combina-tion with other SLM techniques, such as sub-ring resonators[34], should provide further optimization. Another main limi-tation involves generation of the second Stokes, which couldreduce the power of the first Stokes. Although the nonreso-nance pump scheme [28] avoids second Stokes lasing oscilla-tion, the high-power first Stokes can even generate the secondone when the pump power increases to ∼400 mW in ourexperiment.

In conclusion, we have demonstrated superluminal propa-gation through the ultralong distance of 500 m based on SLMBrillouin lasing oscillation. SLM operation in a long-cavity BFLis achieved by utilizing an intracavity SA. Maximum advance-ment of 1330 ns and fractional advancement of 1.87 have beenobserved. Although the restriction of the delay–bandwidthproduct still applies in the proposed scheme, the scheme offersadvantages of extended advancement, scalable propagation dis-tance, and low-power operation, which suggests possible appli-cations in hypersensitive sensing, gravitational wave detection,temporal cloaks [35], and others.

Funding. National Natural Science Foundation of China(NSFC) (11274231, 61178014).

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Letter Vol. 40, No. 19 / October 1 2015 / Optics Letters 4407