Superluminal signal conversion in stimulated Brillouin scattering via an optical fiber ring resonator

Transcription

1 Suerluminal signal conversion in stimulated rillouin scattering via an otical fiber ring resonator Liang Zhang, Li Zhan *, Jinmei Liu, Gaomeng Wang, Fangying Tao, Taohu Xu,Qishun Shen Deartment of Physics, Key Laboratory for Laser Plasmas (Ministry of Education), State Key Lab of Advanced Otical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai, , China *Corresonding author, We reort the suerluminal henomenon of both Stokes and um light in stimulated rillouin scattering (SS) via an otical-fiber ring lasing resonator. In our exeriment, the suerluminal generation of Stokes light firstly delayed with ns and then roagated with the advancement of ns within an 8-m single mode fiber (SMF), when the um ower increased from the SS threshold to a higher ower. This roves the first evidence that the otical interaction is determined by the grou velocity even at the negative grou velocity suerluminal roagation. It is imortant that, this imlies the ossibility of suerluminal information interchange because the results also indicate that the signal conversion between different wavelengths can be realized at the negative grou velocity roagation. PACS numbers: s, Es, Wd, Qb, Lm To date, many exeriments have demonstrated the ossibility to control the grou velocity of light, resulting in slow, fast or even suerluminal light 1-2. Slow light has been demonstrated with very small grou velocity 3-5 and even stoed light 6-7. Meanwhile, suerluminal or even negative grou velocity roagation has been demonstrated by recent exeriments Here, the anomalous disersion is generated to result in light roagation with the negative grou velocity in material. In such cases, the light ulse aears to exit the medium before entering, which seems at odds with causality. However, a direct consequence of classical interference between light ulse s different frequency comonents results in the observed suerluminal roagation in an anomalous disersion region Slow/fast light is initially demonstrated by exloiting narrow sectral gain/loss resonances, tyically created by electromagnetically induced transarency 4 or coherent oulation oscillation 9. Within the gain/loss resonance, the light ulse exeriences the normal/anomalous disersion, which comlies with the Kramers-Kronig relations 13. The grou velocity υ g = c/ ng = c/( n+ ωdn/ dω) (c is the light seed in vacuum; n is the refractive index; a ositive or negative value of dn / dω is referred to as normal or anomalous disersion.) can be smaller/larger than the hase velocity c/ n in medium. Thus, suerluminal light aears when the grou velocity exceeds c if the anomalous disersion is large enough. Generally, gain resonance results in normal disersion and slow-light effect, and the deleted wave undergoes loss resonance and fast-light effect. The SS aroach has been roved as a flexible mechanism to realize the fast/slow light in otical fibers 3, Within the gain band at the Stokes frequency, the light signal is slowed and its delay agumentes as the um ower increases. On the contrary, the attenuated um light exeriences fast-light effect. The ossibility of suerluminal roagation via SS has been demonstrated in fibers 17-19, but the light usually exeriences tremendous absortion. However, our recent work demonstrated the low-loss suerluminal roagation in fibers by emloying the rillouin lasing cavity, which rovides a simle but ractical latform for studying the suerluminal hysics 20. In all revious exeriments, the Stokes wave in SS rocess exhibits slow light and the um wave shows fast light. This is the certain conclusion from the Kramers-Kronig relations. Usually, suerluminal effect leads to the controversies of the definition of the information velocity and relativistic causality However, recent exeriments demonstrated that the suerluminal transfer of information is consistent with the concet of Einstein causality It has been demonstrated that the eak of the ulse does roagate backward inside the fiber when the ulse roagates with suerluminal or even negative grou velocity, whereas the energy flow is in the forward direction 17. Although many secial roerties surrounding the suerluminal effect have been studied, the signal conversion has not yet been exerimentally demonstrated under the suerluminal roagation. Esecially, a fundamental question still should be addressed: Can the light signal convert to the other wavelength at the negative grou velocity roagation? In this case, the energy flow asses in the oosite direction to the signal. In the resent work, we show that the Stokes light is generated with suerluminal roagation via a fiber ring rillouin resonator. Thanks to the owerful enhancement of lased Stokes wave, the um aears low-loss suerluminal roagation. Such large advancement of the grou velocity, in turn, makes an ignorable influence towards the Stokes light. The results firstly demonstrated the otical interaction between the um and Stokes wave is not definitely determined by the hase velocity but by the grou velocity, which is still consistent with suerluminal henomenon even at negative grou velocity. SS is a well known nonlinear effect. When um light with the frequency ω roagates in a fiber, Stokes light is backward generated with a downshifted frequency ω s = ω Ω ( Ω is the Stokes shift). The um exeriences an absortion and anomalous disersion while the Stokes wave exeriences a gain and normal disersion, which results in fast/slow light effect. With the slowly varying envelo aroximation, the grou index via SS is given by 25 2 gcp 1 δ g g0 2 2 Aeff (1 δ ) n = n + ( ), (1) Γ +

2 where, n g 0 is the grou index in the absence of SS gain, g is the eak value of gain, Γ is the gain linewidth, P is the um ower, A eff is the effective core area of fiber, and δ = 2( ω ωs Ω) / Γ is the normalized detuning. After roagating the distance L, slow/fast light can be determined by considering the relative advancement Δ T = Lng / c Ln/ c. Δ T =0 if no slow/fast light effect. It erforms slow light if Δ T < 0. Otherwise, fast light aears if ΔT is ositive. Negative grou velocity roagation aears when ΔT is larger than Ln / c, which seems that the light has exited in the medium before its entering. FIG. 1. Exerimental setu to observe the suerluminal effect of Stokes light via a fiber ring rillouin resonator. A tunable laser source (TLS) modulated by an electro-otic modulator (EOM) is to roduce a sinusoidal um at 1550 nm. The sinusoidal signal is set at 1-MHz frequency by adjusting the function generator. After boosted by an erbium-doed fiber amlifier (EDFA), the um light is injected into the SMF to generate SS and create the backward Stokes wave. Here, 90% of Stokes light is circulated for lasing. In exerimental setu (Fig. 1), we choose a 10-m SMF as the SS medium in the ring lasing resonator. 90% of backward Stokes light is served to roduce SS-induced loss resonance of the um light, and 10% ower as the outut lasing ower is detected at ort 2. The outut um light is observed at ort 3. The temoral traces of the um light are monitored by an oscilloscoe with hoto detectors. Norm. Amlitude ns 48.6ns Inut signa Outut signals a different outu Stokes owers 05mW 08mW 16mW 97mW 0.367mW 17mW 1.249mW 2.948mW 3.724mW 3.922mW 5.416mW 6.721mW 7.729mW 8.989mW 12mW 12.42mW sinusoidal signal of 1 MHz by the EOM. When the inut ower is below the SS threshold, the delay of um wave is 48.6 ns after assing through 10-m SMF. Suerluminal roagation of um wave aears when the inut ower reached mw. However, in Fig. 2, it is surrised that the Stokes light roagates with advancement as the Stokes lasing ower increased. The largest advancement of 97.2 ns is observed and exceeds the roagating time of ~50 ns through 10-m SMF. This means that the Stokes light also erforms suerluminal roagation. Here, the Stokes ower in the ring cavity is as 10 times as the outut lasing ower, which is determined by the otical couler ratio. According to Kramers-Kronig relations, the Stokes wave should be slow light, and its delay should increase with the um ower increasing. However, the observed result is oosite to this. To understand the origination of this surrising henomenon, we change the couler ratio for 2:8 and choose a shorter fiber of 8-m SMF to observe the slow-light effect of Stokes light. The Stokes ower within the cavity and the cavity loss are determined by the couler ratio. The couler ratio of 2:8 makes a higher cavity loss and a lower Stokes ower which ostones the fast light effect on um light. If the fast-light effect on Stokes light results from the signal conversion of the suerluminal um signal, we believe that the Stokes wave should erform slow light at the beginning of lasing. It is reasonable that the um signal is advanced in time as the um ower is increased. Without fast-light effect, the time delay after assing through an 8-m SMF is ~40 ns. In Fig 3, the advancement of 115ns exceeds the normal roagating time and reaches suerluminal roagation at negative grou velocity which rovides a recondition to observe the suerluminal Stokes wave. Norm. Aml. 115 ns Advance Inut Pum 162.0mW 192.9mW 224.8mW 25mW 276.9mW 290.5mW 323.8mW 357.4mW Norm. Amlitude 97.2 ns Outut Stokes lasing ower 1.388mW 3.388mW 4.898mW 6.018mW 7.898mW 9.48 mw 1 mw 12.8 mw 13.8 mw Advancement /ns FIG. 2. Waveforms of inut signal and outut um signal after roagating through the 10-m SMF, Waveforms of generated Stokes wave after anticlockwise assing through the SMF, for different outut Stokes lasing owers. As shown in Fig. 2, the um light is modulated to a Loss /d FIG. 3. Waveforms of outut um signal after roagating through an 8-m SMF. The maximum advancement is 115ns. The advancement as a function of the loss through the SMF. The advancement varies linearly with the rillouin loss, and the results show a linear fit with sloes of 23 ns/d. In Fig. 4, it is clearly observed that the Stokes wave

3 roagates as slow light when the inut um ower range from mw to mw. In this range, the delay of Stokes light increases with the um ower. However, the Stokes wave advances when the um ower exceeds mw. The largest advancement of ns is observed and has exceeded the round-tri roagating time (~40 ns) through the 8-m fiber resonator, which means that the Stokes wave erforms negative grou velocity suerluminal roagation as well as the um light. medium even earlier than the initial seed ulse eak for the grou velocity transition. Suerluminal signal conversion from the um signal results in the fast-light effect on Stokes light. The Stokes light comounds these two effects, and finally may exhibit fast light or even suerluminal effect, as shown in Fig 5. Imortantly, the Stokes ower in the lasing cavity can exceed the um ower, which is very different from the conventional SS rocess ns Inut um 186.7mW 192.9mW 205.4mW Norm. Amlitude Delay Norm. Amlitude ns Advance Inut um 205.4mW 224.8mW 25mW 263.8mW 276.9mW 323.8mW FIG. 4. Waveforms of generated Stokes wave after anticlockwise assing through an 8-m SMF. Slow-light effect of Stokes wave at the beginning of SS rocess. Fast-light effect of Stokes wave when the um ower exceeds mw. In tyical SS rocess 3, 14, the um and Stokes wave erform fast and slow light resectively, as shown in Fig. 5. However, for its low efficiency, the velocity change of both um and Stokes wave is small comared with the light seed. In addition, the Stokes ower is always lower than the um ower. Otical Frequency rillouin shift Amlified Stokes Time domain SS signal conversion Otical Frequency lased Stokes rillouin shift Time domain FIG. 5. Schematic illustration. Fast and slow light in tyical SS amlifier system. Suerluminal light roagation of um and generated Stokes wave in the rillouin lasing resonator. Nevertheless, the advancement of um light is greatly enhanced but it is low loss when assing through a rillouin lasing oscillator 20. The seeded Stokes ulse always obtains a gain and exhibits slow-light effect. Here, the Stokes signal is converted from the modulated um signal. When the um light roagates with a grou velocity that is larger than c, the generated Stokes ulse eak may exit the FIG. 6. Outut um/stokes ower versus different inut um owers and the advancement of outut um and Stokes wave as a function of inut ower. The um level is divided into three areas: (i) no SS effect area (below the threshold); (ii) SS slow light area (the Stokes ower in the cavity is lower than the um); (iii) SS fast light area (the Stokes ower in the cavity is higher than the um). Corresondingly, the slow/fast light turn oint aears at the turn oint of ower level between um and Stokes light. The Stokes ower in the cavity is as 4 times as the outut lasing ower. Above the SS threshold of mw, the outut Stokes lasing ower increases raidly and then exceeds the outut um ower, which means the Stokes ower is larger than the um ower within the resonator. In rincile, the SS rocess is governed by the couled mode equations 25. The Stoke wave exits the fiber with a delay time after assing through a length L of the fiber. Whenδ << 1, the relative delay time can be written as Lg P Δ T = Ln / 0 / d g c Lng c =. (2) Γ Aeff SS fast-light for um is mathematically described as the same as the case for Stokes light, but the only difference is the negative sign of rillouin gain in the couling wave equation. Thus, the relative advanced time Δ Ta for the um wave after roagating through the fiber is Lg Ps Δ Ta = Lng / c Lng0 / c =. (3) Γ A Considering the generation of Stokes wave and the grou velocity change of um light in the SMF, the Stokes wave also obtains a time boost as the um light. ased on a basic assumtion that the otical interaction is determined by the grou velocity even at the negative grou velocity suerluminal roagation, the time delay or advancement Δ T s of Stokes light is determined by eff

4 Lg Ps Lg P Lg Δ Ts = Δ Ta + ( Δ Td) = = ( Ps P) (4) Γ Aeff Γ Aeff Γ Aeff Corresonding to this assumtion, the combined slowand fast-light effects are observed, as shown in Fig. 6. When the um ower is below the SS threshold, there is no Stokes light. As the inut ower exceeds the threshold of mw, the generated Stokes light obtains a rillouin gain at first and erforms slow light. The slow/fast light turnning oint aears at the reversed oint of the ower level of um and Stokes light, which confirms with Eq. (4). The Stokes wave erforms slow light effect because of the gain, and the maximum delay is ns when the inut ower is mw. As the um ower is increasing, the Stokes wave turns to advance in the time domain. With the mW um ower, the ns advancement is beyond the ~40-ns transmission time of the 8-m SMF, which means the Stokes light roagates with a negative grou velocity. Clearly, the Stokes ower results in suerluminal roagation of um light. Then, the um light in turn converts the suerluminal grou velocity to the Stokes via SS rocess. However, in usual SS amlifier structure, the Stokes ower is always lower than the um one which means the fast-light advancement of Stokes is smaller than delay time. However, the Stokes ower in a lasing resonator can exceed the um ower, which is essential in observing the fast light effect of Stokes wave. This roves that the suerluminal Stokes light accomanies the suerluminal roagation of um light when the um signal converts into the Stokes light. esides, we insert two bidirectional 1:99 otical coulers in the rillouin laser resonator (at oint A and in Fig. 1) in order to measure the grou velocity and energy flow in different oints within the suerluminal roagation. It s observed that the eak of a suerluminal ulse roagates in backward at a negative grou velocity. Even though energy flow is always forward signal of um light also converts to the oosite-roagating Stokes light within the otical fibers. Moreover, all these effects are initiated by the far leading edge of the ulse and are consistent with the causality. Finally, we note that the mechanism of the observed suerluminal light via a rillouin fiber ring resonator differs from the revious slow/fast-light exeriments associated with a rillouin amlifier. In the resent exeriments, the lased Stokes light within the cavity makes the grou velocity of um wave a tremendous change and suerluminal roagation. Combined with the SS slow-light effect and otical interaction, the Stokes wave erforms from slow light to fast and suerluminal roagation by increasing the inut um ower. The results rove the first evidence that the otical interaction is determined by the grou velocity even at the negative grou velocity roagation. The Stokes waves are generated from the um waves with the wavelength conversion of ~10-GHz frequency shift. It imlies that the signal conversion can be realized at the negative grou velocity suerluminal roagation and the ossibility of suerluminal information interchange. To date, ultra dense wavelength-division-multilexed (DWDM) otical transmission around 10-GHz sacing has been reorted. The develoment of ultra DWDM makes the ossibility of SS suerluminal signal conversion. Also, it allows large suerluminal effects that lead to a new examination of the suerluminal hysics imlied by secial relativity. We believe that it may lay an imortant role in the imlementation of all-otical communication system, interconnection in suer comuter, otical buffering, high sensitivity sensing, and data synchronization. This work was suorted by the National Natural Science Foundation of China (Grants / ), and the key roject of the Ministry of Education of China (Grant ). 1. L. 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