See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/336565866

Enhanced negative group velocity propagation in optical fibers with a hybrid

Brillouin lasing resonator

Article  in  Optics Letters · October 2019

DOI: 10.1364/OL.44.005097

CITATION

1READS

419

4 authors:

Some of the authors of this publication are also working on these related projects:

Slow light and fast light in optical fibers View project

Ultrafast fiber lasers View project

Lirun Gao

Shanghai Jiao Tong University

16 PUBLICATIONS   41 CITATIONS   

SEE PROFILE

Li Zhan

Shanghai Jiao Tong University

186 PUBLICATIONS   2,673 CITATIONS   

SEE PROFILE

Wenyan Zhang

Shanghai Jiao Tong University

15 PUBLICATIONS   37 CITATIONS   

SEE PROFILE

Tianhao Xian

Shanghai Jiao Tong University

16 PUBLICATIONS   37 CITATIONS   

SEE PROFILE

All content following this page was uploaded by Tianhao Xian on 05 January 2020.

The user has requested enhancement of the downloaded file.

Enhanced negative group velocity propagationin optical fibers with a hybrid Brillouin lasingresonatorLIRUN GAO, LI ZHAN,* WENYAN ZHANG, AND TIANHAO XIAN

State Key Lab of Advanced Optical Communication Systems and Networks, Department of Physics and Astronomy,Shanghai Jiao Tong University, Shanghai 200240, China*Corresponding author: lizhan@sjtu.edu.cn

Received 4 June 2019; revised 12 September 2019; accepted 18 September 2019; posted 19 September 2019 (Doc. ID 369234);published 15 October 2019

We report an enhanced scheme to achieve superluminalpropagation at negative group velocity in optical fibers witha hybrid Brillouin lasing cavity. The hybrid cavity was con-structed by introducing a pumped erbium-doped fiber toenhance the Brillouin lasing. Experimental results showthat with the assistance of a hybrid cavity, the thresholdpower of the Brillouin lasing was reduced from 758.7 to235.7 mW, and the time advancement was promoted to444.4 ns after passing through 2 m highly nonlinear fiberat a modulation frequency of 1 MHz, corresponding to agroup index of −44.6 and group velocity of −0.0224c.Moreover, a maximum negative group index of −21, 029was observed at the modulation frequency of 1 kHz, which,to the best of our knowledge, is the highest negative groupindex ever reported in optical fibers via stimulated Brillouinscattering. © 2019 Optical Society of America

https://doi.org/10.1364/OL.44.005097

Superluminal propagation of light, even at negative groupvelocity, has been attracting more and more interest in recentyears [1–3]. To date, this phenomenon was observed in variousmedia, such as optical fibers [2,4–9], crystal [10], atomic vapor[11], molecular gas [12], semiconductor [13], metamaterial[14], and microstructures [15]. Owing to the excellent compat-ibility of telecommunication and fiber sensing systems, theschemes implemented in optical fibers were under particularattention. Specially, stimulated Brillouin scattering (SBS)-basedfast light in optical fiber has been proved to be an excellentcandidate owing to the low threshold, arbitrary wavelength,and room temperature operation [16].

The slow/fast light based on SBS in optical fibers was firstimplemented in Brillouin amplifiers [4,5]. In the case, anoma-lous dispersion was generated by a narrowband resonance,using the narrowband SBS process. The input signal shouldexperience a time advancement when propagating through thisregion [17]. When the advancement exceeds the propagationtime without SBS, the signal seems to be transmitted before

it enters the medium, namely propagating at negative groupvelocity. Subsequently, the employment of Brillouin lasingoscillator greatly promoted the superluminal efficiency[6,18–21]. An advancement time of 221.2 ns and group indexof −6.636 were observed after the signal passed a 10 m single-mode fiber (SMF) [6]. Furthermore, up to 500 m superluminalpropagating in fiber was demonstrated on this basis [18].Besides, in order to further enhance the superluminal effect, spe-cial optical fibers were utilized to provide a higher Brillouin gaincoefficient, such as highly nonlinear fiber (HNLF) [19,20], tel-lurite fiber [21,22], and bismuth-oxide fiber [23]. The reportedbest result was achieved by the tellurite fiber in a ring cavity, themaximum advancement was 385 ns, and the negative groupindex was −17.2 at the modulation frequency of 1 MHz [21].

Various applications of superluminal propagation have beenreported, such as hypersensitive sensing [24,25], gravitationalwave detection [26], quantum correlations and entanglement[27], and light-drag enhancement [28]. In these cases, the sen-sitivity was found to be determined by the value of the negativegroup index in principle, so a critical need is to further increasethis index. However, the schemes of negative group velocity bySBS are facing two obstacles. First, under the same time ad-vancement, shorter fiber length can reduce the passing timeand therefore lead to larger negative group index. But, thismeans less Brillouin gain, which needs a higher pump power,and the system has a very high threshold power of SBS. Second,the saturation effect of the lased Stokes emerges when the pumppower is high enough, which prevents the time advancementfrom further enlarging [19].

In this Letter, to address these obstacles, we propose a modi-fied scheme based on a Brillouin oscillator. We introduced apumped erbium-doped fiber (EDF) to the cavity to enhancethe Stokes light. Experiments show that the threshold powerfor Brillouin lasing was reduced from 758.7 to 235.7 mW.A group velocity of −0.0224c (c is the light speed in vacuum)and group index of −44.6 were obtained. In addition, the maxi-mum negative group index up to −21, 029 was obtained at themodulation frequency of 1 kHz; this is the record of superlu-minal effect ever achieved in optical fibers.

Letter Vol. 44, No. 20 / 15 October 2019 / Optics Letters 5097

0146-9592/19/205097-04 Journal © 2019 Optical Society of America

The experimental configuration of our proposal is given inFig. 1. A tunable laser source (TLS) was utilized to generate thesignal light, as well as the pump wave for the SBS. After modu-lation by the electro-optic modulator (EOM) with a sinusoidalsignal, the signal light was amplified by a high-power erbium-doped fiber amplifier (EDFA), and then the output light servesas the input signal power as well as the Brillouin pump power.Before the signal light was guided into the ring cavity by acirculator, a 3:97 optical coupler (OC) was used to monitorthe signal, and gives the reference signal. The signal lightwas extracted from the cavity by the 1% port of anotherOC, after propagating through a 2 m long HNLF. Betweenport 3 of the circulator and the 99% port of the OC, anEDF with a length of 0.2 m was employed, pumped by a980 nm laser diode (LD) via a wavelength-division multiplexer(WDM). The output signal and the Stokes light were observedby a 2G Hz oscilloscope (R&S, RTO-1022). The measuredtotal loss of the ring cavity was 1.91 dB, and the cavity lengthwas 5.49 m. The HNLF used in the experiment had a mode-field diameter of 4.05 μm, and the nonlinear coefficient was9.1 W−1, which means a higher Brillouin gain coefficient thanthe standard SMF.

According to the theory of the SBS slow/fast light in opticalfiber, after passing through a fiber with the length L, the timedelay of the signal Td can be derived as [6,17]

Td � ngLc

� nf Lc

−g effB LαPStokes

ΔνeffB Aeff

, (1)

where ng is the group index; nf is the effective index of thefiber; α is the amplification coefficient after the EDF; Pstokes

is the Stokes power; geffB and ΔνeffB are the effective Brillouingain factor and the effective bandwidth of the Brillouingain/loss spectrum, respectively; and Aeff is the effective modearea of the fiber. Since the signal light was modulated by theEOM, the effective Brillouin gain factor geffB is decided by theconvolution of the Brillouin gain spectrum and the pumppower spectral density [16]. Due to the group index changeinduced by the SBS resonance, the latter part of Eq. (1) isalways positive. As PStokes increases, Td decreases accordingly,and then the signal wave is advanced in time, correspondingto the fast light effect. If the Stokes power is high enough, theadvancement exceeds the propagation time in the medium, Tdwas reduced to negative, or the signal light propagates at anegative group velocity.

Thanks to the higher Brillouin gain in the HNLF, the SBSin the cavity can generate at a relatively low pump power [17].However, owing to short SBS media length and low outputratio (1%), the Stokes lasing threshold of this cavity is still

relatively high. When the 980 nm pump source is on, the am-plified spontaneous emission (ASE) of the EDF was injected tothe cavity before the SBS took place. When we adjust theEDFA to increase the input signal power, the attendance ofstimulated Stokes results in the most 980 nm pump powertransferred to the Stokes wave, and the ASE was suppressed.The amplified Stokes was brought back to the resonance bythe cavity to further enhance the SBS process. Therefore, thishybrid cavity managed to reduce the threshold of the lasingStokes and to enhance the time delay induced by SBS.

We measured the output power of the signal and the Stokeslight when we increased the output power of the EDFA to themaximum. In Fig. 2, the situation is an equivalent to a normalSBS ring cavity when the 980 nm pump in the cavity wasturned off. The output signal power increases linearly first whilethe Stokes power remains at zero, because the pump power didnot reach the lasing threshold. However, when the signal powerreaches the threshold of 758.7 mW, the signal starts to de-crease, and the Stokes begins to emerge. Due to the short lengthof the HNLF, the threshold power is several times higher thanthe value in the cases of 10 m HNLF [19] and 10 m SMF [6].The output power of the Stokes is 10.05 mW at the pumppower of 2000 mW, and the signal power is 4.61 mW.Then, when we turn on the 980 nm pump and set the poweras 603 mW, the output signal increases linearly as well beforethe output Stokes shows up at 235.7 mW. The signal powercontinues to increase but with a smaller slope, and starts to re-duce after the pump exceeds 692 mW. The lasing thresholdwas reduced to 235.7 mW in the hybrid cavity. The outputsignal power in this situation was measured to be 2.98 mWat the pump power of 2000 mW, while the output Stokes lightwas enlarged to 13.12 mW.

Next, we investigate the effect of the hybrid cavity on thetime advancement of the signal wave. First, we explore themovement of the signal waveforms when the 980 nm pumppower for the EDF was still set as 603 mW. Figure 3 showsthe signal waveforms when the input signal power was in-creased from 100 mW to 2000 mW, and the rightmost signalwas obtained at 100 mW. Compared to the reference signal,the signal was delayed by 14 ns without SBS, which is in goodagreement with the distance of 2.91 m between the ref signalport and the 1% output port. As the input signal powercontinues to increases, and exceeds the threshold, the signalstarts to move backward, or advances in time, as predictedby Eq. (1). Once the advancement is greater than 14 ns,the superluminal effect is established. When the EDFA reaches

Fig. 1. Schematic diagram of the experimental setup. RFG, radiofrequency generator; PC, polarization controller; ISO, isolator.

0 500 1000 1500 2000

0

3

6

9

12

15

980nm pump off 980nm pump on

0

3

6

9

12

15

Fig. 2. Output power of the signal (left) and the Stokes (right) at1 MHz modulation, when the 980 nm pump is off (blue) and on (red).

5098 Vol. 44, No. 20 / 15 October 2019 / Optics Letters Letter

the max input power of 2000 mW, the signal was advanced by444.4 ns in time. The fractional advancement (defined as theratio of the delay time and the period of the signal) is 0.444.Under this circumstance, the group velocity is −0.0224c, andthe calculated negative group index is −44.6. This is the bestrecord of superluminal effect by SBS in optical fibers at themodulation frequency of 1MHz. Compared to previous works,the negative group index was promoted by 1 order of magni-tude than the report in 10 m SMF [6], and almost 5 timeslarger than the value in 10 m HNLF [19,20].

Also, we explore the change of the advance time and thegroup index during the increment of the input signal power.Figure 4(a) shows the change of advancement and group index.When the 980 nm pump was absent, the time advancementwas not observed until the signal power reached the Stokeslasing threshold of 758.7 mW. After a linear increment, themaximum advancement was 384.1 ns under the input powerof 2000 mW. The corresponding group index was −38.15.When we enabled the 980 nm pump power set at603 mW, the signal was advanced, and the group index wasreduced to negative rapidly. As the input signal power increases,the same process is described in Fig. 3. As the Stokes wasamplified by the hybrid cavity, the time advancement of thesignal was enhanced accordingly. Therefore, the thresholdpower to the superluminal propagation was reduced.

Apart from the time advancement, the efficiency to generatefast light is another important parameter. Once the SBS wasstimulated, part of the Brillouin pump power was transferredto the Stokes wave, and the most power was consumed. Thus,the pump loss can characterize the efficiency to generate fast

light. It is decided by the ratio of the Stokes power insidethe cavity and the input signal power. Figure 4(b) depictsthe advancement with respect to the pump loss. A linear fitof 96.07 ns/dB was obtained before the advancement reachedsaturation. The maximum advancement was obtained at thepump loss of 8.17 dB. Considering the cavity loss, the slopeefficiency is higher than the previous works using HNLF[19,20]. The slope efficiency of the advancement to the outputStokes power of 31.5 ns/mW can also be derived from Fig. 2,which is higher than the reported value using SMF [6], too.

Conventionally, the saturation of Brillouin gain/loss is a typ-ical phenomenon when the Stokes power in the cavity is highenough, because most of the pump power was transferred. Thissaturation will cause the saturation of the output Stokes poweras well as the signal advancement. In Fig. 4, the saturation effectstill existed when the SBS pump power was higher than1500 mW, or the pump loss exceeded 5 dB. However, owingto the amplification powered by the EDF, the pump power tothe saturation power in our system is much higher than thevalue in normal ring cavities [18–21].

Figure 5 shows more information about the influence of the980 nm pump inside the cavity. Figure 5(a) describes the spec-tral evolution of the Stokes wave, when the input signal powerwas increased from 0 to 500 Mw, and while the 980 nm powerwas set at 603 mW. During the absence of SBS, the detectedspectrum was a typical spectrum of the EDF ASE. As theBrillouin pump was injected into the cavity, the Stokes was gen-erated by the HNLF. With the increase of the SBS pump, theASE was suppressed, and the 980 nm pump power was trans-ferred to the Stokes light at 1550.46 nm. Furthermore, thegroup velocity manipulation by the 980 nm pump was alsoobserved during this process. Figures 5(b) and 5(c) show thesignal waveforms and the advancement at the input signalpower of 1000 Mw. When we adjust the 980 nm pump powerfrom 0 to 700 mW, the signal was advanced almost proportion-ally to the 980 nm pump power, and the maximum advance-ment was 114.2 ns.

As well known, the transmitted signal undergoes distortionin the process of slow/fast light, especially when the Brillouinpump suffers from apparent pump loss, or when high-order

0 250 500 750 1000

0.0

0.5

1.0pump(mW)

100 200 500 700 800 900 1100 1200 1400 1800 2000

ref signal14ns444.4ns

Fig. 3. Detected output signal waveforms at 1 MHz under differentinput signal powers. The red arrow gives the location of the referencesignal.

0 500 1000 1500 2000

0

150

300

450

600

-45

-30

-15

0

15 (b)980pump off980pump on

(a)

0 2 4 6 8

0

150

300

450

Slope efficiency: 96.07ns/dB

Fig. 4. (a) Advance time (left) and group index (right) of the 1 MHzsignal when the 980 nm pump is off (blue) and on (red).(b) Advancement of the signal with respect to the pump loss.

0 200 400 600

0

25

50

75

100

125 (c)

250 500 750 1000 12500.0

0.5

1.0

1550 1560 1570 1580

-50

0

50

Pow

er (d

Bm

) 1550.46nm 1560nm(a)

114.2ns(b)

Fig. 5. (a) Spectral evolution of the output Stokes when the inputsignal was increased from 0 to 500 mW and the 980 nm pump was setas 603 mW. (b) Detected signals when adjusting the 980 nm pumppower from 0 to 700 mW. The input signal power was set as1000 mW. (c) The time advancement of the signals with respectto the 980 nm pump. The modulation frequency was 1 MHz.

Letter Vol. 44, No. 20 / 15 October 2019 / Optics Letters 5099

Stokes was generated under high pump power [29]. InFig. 5(b), the width of the signal was compressed to 362 nswith the absence of the 980 pump. With the increase of the980 nm pump power, this compression was mitigated accord-ingly. The signal width was broadened to 466 ns at the 980 nmpump power of 700 mW. Figure 3 coincides with this effect,and the pulse shape did not show obvious distortion as theinput signal power increased.

To achieve larger negative group index, one feasible way is toapply lower modulation frequency. Figure 6(a) shows the ex-perimental verification. As the modulation frequency changesfrom 1 to 10 kHz, the time advance and the group index agreewith our speculation. The max time advancement of 204 μswas observed at 1 kHz. With the fractional advancement of0.204, the measured group velocity was −14.26 km∕s, andthe group index was −21, 029.

For signals with different modulation frequencies, the valueof the advancement is determined by the product of the signalperiod and the fractional time delay. These frequencies from1 kHz to 10 kHz did not significantly affect the bandwidthof Brillouin resonance, and thus the fractional time delay isa constant in this case. Therefore, as the frequency was reduced,a bigger signal period caused bigger advancement and negativegroup index. To test this explanation, modulation frequenciesranges from 1 kHz to 15 MHz were further explored inFig. 6(b). Between 10 kHz and 1 MHz, the fractional advance-ment was close to maximum value. However, when the fre-quency was larger than 1 MHz, the interval of the carrierfrequency and sideband frequencies was expanded, and theBrillouin gain of the side band was reduced, so the fractionaladvancement was reduced, too. As to the range between 1 and10 kHz, the result shows a trend of decrease, and the reason liesin the reduction of the response characteristic of the EOM. Infact, the minimum working frequency of the EOM is 1 kHz,and thus, the frequency limit of this scheme was 1 kHz.

The scheme offers an efficient way to achieve large negativegroup index. Moreover, the index change can be further en-hanced if using a shorter fiber to avoid the saturation effectin the SBS process [30]. In addition, the time advancementis sensitive to the cavity loss or the Stokes power, making thisscheme extremely promising for optical fiber sensing. Certainly,due to operating in a hybrid cavity resonator, the input signalshould be limited at the wavelength range to avoid free-runningmode lasing [31].

In conclusion, we proposed an enhanced scheme to achievenegative group velocity propagation in optical fiber. Benefitingfrom the pumped EDF in the hybrid cavity, the Brillouin lasingthreshold power was reduced. At a modulation frequency of

1 MHz, an advancement of 444.4 ns and a group index of−44.6 were observed. Moreover, negative group index up to−21, 029 was obtained at the limited modulation frequencyof 1 kHz. With the advantages of good operability and highefficiency, this proposal offers an effective solution to achievesuperluminal propagation. It may find its potential in applica-tions exploiting the superluminal effect.

Funding. National Natural Science Foundation of China(11874040).

REFERENCES

1. L. J. Wang, A. Kuzmich, and A. Dogariu, Nature 406, 277 (2000).2. G. M. Gehring, A. Schweinsberg, C. Barsi, N. Kostinski, and R. W.

Boyd, Science 312, 895 (2006).3. B. Macke and B. Ségard, Phys. Rev. A 97, 063830 (2018).4. K. Y. Song, M. G. Herráez, and L. Thévenaz, Opt. Express 13, 82

(2005).5. M. González-Herráez, K. Y. Song, and L. Thévenaz, Appl. Phys. Lett.

87, 081113 (2005).6. L. Zhang, L. Zhan, K. Qian, J. Liu, Q. Shen, X. Hu, and S. Luo, Phys.

Rev. Lett. 107, 093903 (2011).7. K. Qian, L. Zhan, L. Zhang, Z. Q. Zhu, J. S. Peng, Z. C. Gu, and Y. X.

Xia, Opt. Lett. 36, 2185 (2011).8. Z. C. Zhuo and B. S. Ham, Eur. Phys. J. D 49, 117 (2008).9. R. T. Glasser, U. Vogl, and P. D. Lett, Phys. Rev. Lett. 108, 173902

(2012).10. M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, Science 301, 200

(2003).11. J. Keaveney, I. G. Hughes, A. Sargsyan, and C. S. Adams, Phys. Rev.

Lett. 109, 233001 (2012).12. B. Ségard and B. Macke, Phys. Lett. A 109, 213 (1985).13. S. Chu and S. Wong, Phys. Rev. Lett. 48, 738 (1982).14. X. Li, C. Xue, L. Fan, S. Zhang, Z. Chen, J. Ding, and H. Zhang, Appl.

Phys. Lett. 108, 231904 (2016).15. P. Chang, X. Li, L. Huang, F. Gao, W. Zhang, F. Bo, G. Zhang, and

J. Xu, Opt. Express 26, 15377 (2018).16. L. Thévenaz, Nat. Photonics 2, 474 (2008).17. G. P. Agrawal, Nonlinear Fiber Optics, 5th ed. (Academic, 2013).18. L. Zhang, L. Zhan, M. Qin, Z. Wang, H. Luo, and T. Wang, Opt. Lett.

40, 4404 (2015).19. L. Zhang, L. Zhan, M. Qin, T. Wang, and J. Liu, Opt. Eng. 53, 102702

(2014).20. D. Deng, W. Gao, M. Liao, Z. Duan, T. Cheng, T. Suzuki, and Y.

Ohishi, Appl. Phys. Lett. 103, 251110 (2013).21. D. Deng, W. Gao, T. Cheng, E. E. Samuel, T. Suzuki, and Y. Ohishi,

IEEE Photon. Technol. Lett. 26, 1758 (2014).22. K. Y. Song, K. S. Abedin, and K. Hotate, Opt. Express 16, 225 (2008).23. C. J. Misas, P. Petropoulos, and D. J. Richardson, J. Lightwave

Technol. 25, 216 (2007).24. H. N. Yum, M. Salit, J. Yablon, K. Salit, Y. Wang, and M. S. Shahriar,

Opt. Express 18, 17658 (2010).25. J. Chen, J. Gan, Z. Zhang, T. Yang, H. Deng, and Z. Yang, Appl. Phys.

Express 7, 012501 (2014).26. M. Salit, G. S. Pati, K. Salit, and M. S. Shahriar, J. Mod. Opt. 54, 2425

(2007).27. R. T. Glasser, U. Vogl, and P. D. Lett, Opt. Express 20, 13702 (2012).28. A. Safari, I. De Leon, M. Mirhosseini, O. S. Magaña-Loaiza, and R. W.

Boyd, Phys. Rev. Lett. 116, 013601 (2016).29. Z. Shi, A. Schweinsberg, J. E. Vornehm, A. M. Gámez, and R. W.

Boyd, Phys. Lett. A 374, 4071 (2010).30. L. Xing, L. Zhan, S. Luo, and Y. Xia, IEEE J. Quantum Electron. 44,

1133 (2008).31. Y. J. Song, L. Zhan, S. Hu, Q. H. Ye, and Y. X. Xia, IEEE Photon.

Technol. Lett. 16, 2015 (2004).

0 2 4 6 8 10

40

80

120

160

200

Ad

van

cem

ent

(µs)

Frequency (KHz)

(a)

-20000

-16000

-12000

-8000

-4000

Gro

up

Ind

ex

Gro

up

Ind

ex

1k 10k 100k 1M 10M0.0

0.2

0.4

0.6 (b)

Fra

ctio

nal

ad

van

ce

Frequency (Hz)

-20000

-15000

-10000

-5000

0

Fig. 6. (a) Dependency of the time advancement and the group in-dex on the modulation frequency. (b) Dependency of the fractionaladvancement and the group index on the modulation frequency.

5100 Vol. 44, No. 20 / 15 October 2019 / Optics Letters Letter

View publication statsView publication stats