- Email: [email protected]
Demonstration of slow light propagation in an optical fiber under dual pump light with co-propagation and counter-propagation
Optics Communications 413 (2018) 207–211
Contents lists available at ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Demonstration of slow light propagation in an optical fiber under dual pump light with co-propagation and counter-propagation Wei Qiu *, Jianjun Liu, Yuda Wang, Yujing Yang, Yuan Gao, Pin Lv, Qiuli Jiang Department of Physics, Liaoning University, Shenyang 110036, China
a r t i c l e
i n f o
Keywords: Er3+ -doped optical fiber The time delay Dual frequency pumping light Counter-propagation Co-propagation
a b s t r a c t In this paper, a general theory of coherent population oscillation effect in an Er3+ -doped fiber under the dualfrequency pumping laser with counter-propagation and co-propagation at room temperature is presented. Using the numerical simulation, in case of dual frequency light waves (1480 nm and 980 nm) with co-propagation and counter-propagation, we analyze the effect of the pump optical power ratio (M) on the group speed of light. The group velocity of light can be varied with the change of M. We research the time delay and fractional delay in an Er3+ -doped fiber under the dual-frequency pumping laser with counter-propagation and co-propagation. Compared to the methods of the single pumping, the larger time delay can be got by using the technique of dual-frequency laser pumped fiber with co-propagation and counter-propagation. © 2017 Elsevier B.V. All rights reserved.
1. Introduction The group velocity of light pulses can be dramatically modified in a material with a steep variation in frequency-dependent optical properties [1–5]. Hau et al. [6] decelerated the group velocity of a light pulse to 17 ms in an ultracold gas of sodium atoms by using the electromagnetically induced transparency EIT effect in which the narrow transparency resonance was accompanied by a steep slope in the refractive-index dispersion. In view of practical applications, the focus of observation of slow light has been shifted to solid-state materials and room temperatures. In 2010, R. Lauro et al. observed slow light phenomenon in a Tm3+-doped yttrium-aluminum-garnet crystal [7]. Melle et al. studied on both 1550 nm and 980 nm laser into an erbium-doped fiber amplifier to observe slow light and superluminal propagation in 2010 [8]. In 2013, slow and fast light via two-wave mixing in ytterbiumdoped fiber at 1064 nm are investigated in detail [9]. Qian proposed and experimentally demonstrated the propagation of slow/fast light in an erbium-doped fiber (EDF) using mutually modulated cross-gain modulation. The group velocity of the light signal can be manipulated by the effect of gain cross-saturation modulation by saturating light at an arbitrary wavelength in the gain bandwidth of the EDF [10]. In 2014, Than Singh Saini et al. simulated two different types of tellurite fibers for tunable slow light generation based on SBS [11]. Their simulated results indicate that (i) Brillouin gain up to ∼91 dB and maximum time delay of 140 ns can be achieved using 2-m long
Er-doped tellurite fiber with maximum allowable pump power of 1100 mW and (ii) Brillouin gain up to ∼86 dB and maximum time delay of 227 ns can be achieved from 100 m undoped tellurite fiber with 23 mW pump power. Rim Cherif et al. reported a detailed implementation of a two-dimensional finite element method that was applied to calculate the stimulated SBS characteristics in highly nonlinear tellurite PCF in 2015 [12]. In 2016, Varsha Jain et al. reported two different kinds of photonic crystal fiber for tunable slow-light generation based on stimulated Brillouin scattering. PCF characteristics for slow light, such as maximum allowable pump power, Brillouin gain, and time delay for both types of PCF, were simulated [13]. Compared to previous research methods [14,15], the technique of dual-frequency laser pumped fiber with co-propagation and counterpropagation is more controllable. This method is desirable for practical applications. The output signal power can be increased by using this method. The signal noise can be decreased and the deformation of the light pulse can be improved. We can increase the time delay and fraction delay under dual-frequency laser pumped single fiber with copropagation and counter-propagation. 2. Analysis model In the paper, we utilize Er3+− doped fiber of a three-level system, see Fig. 1. When |1⟩ is the fundamental energy level, |2⟩ and |3⟩ represent
* Corresponding author.
E-mail address: [email protected] (W. Qiu). https://doi.org/10.1016/j.optcom.2017.12.057 Received 11 October 2017; Received in revised form 28 November 2017; Accepted 20 December 2017 0030-4018/© 2017 Elsevier B.V. All rights reserved.
W. Qiu et al.
Optics Communications 413 (2018) 207–211
We have defined ( ) 𝛿1𝑎 + 𝛿1𝑒 𝛿 𝑁 𝐵1 = 𝛤1 𝐶1 = 1𝑎 𝛤1 𝐴 𝐴 𝛿2𝑎 𝛿2𝑎 𝐵2 = 𝛤2 𝐶2 = 𝛤 𝐴 2 (𝐴 ) 𝛿𝑠𝑒 + 𝛿𝑠𝑎 𝛿 𝑁 𝛤𝑆 𝐶s = 𝑠𝑎 𝛤𝑠 𝐵𝑠 = 𝐴 𝐴 In case of the steady state 𝑁20 = 3+
Fig. 1. The three level energy of an Er
ion.
+
𝑃2 (0)𝐵2 h𝜈21
+
+
𝑃𝑠 (0)𝐶s h𝜈s1
𝑃𝑠 (0)𝐵s h𝜈s1
+
(6)
1 𝜏21
Using trigonometric function formula, we can obtain the expression of the output signal power, [ ( )] 𝑝𝑠 (𝐿, 𝑡) = 𝑃𝑠0 (𝐿) 1 + 𝑚′𝑠 cos 𝑤𝑡 + 𝜃𝑠 √( )2 ( )2 𝑚𝑠 + 𝐵𝑠 𝑁20 𝛿 cos 𝜙 + 𝐵𝑠 𝑁20 𝛿 sin 𝜙 , Thus, 𝑚′𝑠 = tan 𝜃𝑠 =
(1)
We set
(2)
−
(9)
𝑚𝑠 + 𝐵𝑠 𝑁20 𝛿 cos 𝜙
𝐵𝑠 [𝑃𝑠 (𝐿)−𝑃𝑠 (0)] ℎ𝑣𝑠1
= 𝑄, as a result, the time delay is equal to
( 0 )2 𝑃 0 (0) exp(𝐵1 𝑁2 −𝐶1 ) 𝑃 (𝐿) 𝑃𝑠0 (𝐿) 1 𝜔2 + ℎ𝜈 + 2 + ℎ𝜈 + 𝜏1 ℎ𝜈 11
21
𝑠1
21
𝑄
) ( ) 𝑑𝑛2 ( = 𝑊𝑠𝑎 + 𝑊1𝑎 𝑛1 − 𝐴21 + 𝑊1𝑒 + 𝑊𝑠𝑒 𝑛2 + 𝑊2𝑎 𝑛1 (3) 𝑑𝑡 Here 𝑊𝑗𝑎 𝑊𝑗𝑒 represent the absorption rate and the emission rate of the 𝑗 pumping light, in addition, 𝐴21 = 𝜏1 .
(8)
𝐵𝑠 𝑁20 𝛿 sin 𝜙
1 arctan 2𝜋𝜔
𝛥t =
Because of 𝐴31 ≪ 𝐴32 , 𝐴32 ≫ 𝑇1 , we can easily in a generally accepted approximation 𝑛3 ≈ 0 , 𝑊2𝑎 𝑛1 = 𝐴32 𝑛3 . As a result, the rate equations is equal to
𝜔 +
(10)
𝑃10 (𝐿) ℎ𝜈11
+
𝑃20 (0) exp(𝐵1 𝑁2 −𝐶1 ) ℎ𝜈21
+
𝑃𝑠0 (𝐿) h𝜈𝑠1
+
1 𝜏21
2.2. Theoretical model of dual-frequency pumping laser with counterpropagation In the case of negligible loss, the transmission equation along 𝑧 is can be expressed as
2.1. Theoretical model of dual-frequency pumping laser with co-propagation
( ) 𝑑𝑃1 = −𝑃1 𝛿1𝑎 𝑛1 − 𝛿1𝑒 𝑛2 𝛤1 𝑑𝑧 𝑑𝑃2 (11) = 𝑃2 𝛿2𝑎 𝑛1 𝛤2 𝑑𝑧 ( ) 𝑑𝑃𝑠 = −𝑃𝑠 𝛿𝑠𝑎 𝑛1 − 𝛿𝑠𝑒 𝑛2 𝛤3 𝑑𝑧 We can determine the output signal light and the output pump power equation by the use of Eq. (12) ( ) 𝑃1 (𝐿) = 𝑃1 (0) exp 𝐵1 𝑁2 − 𝐶1 𝑃2 (𝐿) ( ) = 𝑃2 (0) exp −𝐵2 𝑁2 + 𝐶2 𝑃s (𝐿) ( ) = 𝑃𝑠 (0) exp 𝐵𝑠 𝑁2 − 𝐶𝑠 (12)
In the case of negligible loss, the transmission equation along 𝑧 can be expressed as ( ) 𝑑𝑃1 = −𝑃1 𝛿1𝑎 𝑛1 − 𝛿1𝑒 𝑛2 𝛤1 𝑑𝑧 𝑑𝑃2 (4) = −𝑃2 𝛿2𝑎 𝑛1 𝛤2 𝑑𝑧 ( ) 𝑑𝑃𝑠 = −𝑃𝑠 𝛿𝑠𝑎 𝑛1 − 𝛿𝑠𝑒 𝑛2 𝛤3 𝑑𝑧 Here 𝜎𝑠𝑒 is stimulated absorption cross section of the 𝑗 pumping light, 𝜎𝑠𝑎 is stimulated emission cross section of the 𝑗 pumping light, those are 𝛿1𝑒 = 0.42 × 10−25 𝛿2a = 1.29 × 10−25 𝛿2e = 1.86 × 10−25 , and 𝛿sa 𝛿se is stimulated absorption cross section and emission cross section of signal light, respectively representing 2.85 × 10−25 , 5.03 × 10−25 . Where 𝐴 indicates the effective cross-sectional area of the core. 𝜎𝑗𝑎 𝑃𝑗 𝛤𝑗 Compared with 𝑊𝑗𝑎 = ℎ𝜈 and 𝑁𝑖 = 𝑛𝑖 𝐴𝐿 𝑗1 𝐴 We can determine the output signal light and the output pump power equation by the use of Eq. (5) ( ) 𝑃1 (𝐿) = 𝑃1 (0) exp 𝐵1 𝑁2 − 𝐶1 ( ) 𝑃2 (𝐿) = 𝑃2 (0) exp 𝐵2 𝑁2 − 𝐶2
𝑃1 (0)𝐵1 h𝜈11
𝑃2 (0)𝐶2 h𝜈21
+
= 0, we can obtain
Introducing a power with cosines variation as modulation of the signal ( ) 𝑃s (0, 𝑡) = 𝑃𝑠 (0) 1 + 𝑚𝑠 cos 𝑤𝑡 (7) 0 𝑁2 (0, 𝑡) = 𝑁2 [1 + 𝛿 cos (𝑤𝑡 + 𝜙)]
the up energy of pumping light of 1480 nm and 980 nm, respectively. A spatially selective saturation of the optical transition between the fundamental energy level 4 𝐼15∕2 and the meta-stable level 4 𝐼11∕2 of the corresponding Er3+ ion. The population decay from this level within a few picoseconds to the meta-stable 4 𝐼13∕2 levels and eventually returns to fundamental energy level 4 𝐼15∕2 with a decay time of a few milliseconds, so the two level system is inverted in case of owing the stronger pumping power. We set 𝑛𝑖 = 𝑛𝑖 (𝑟, 𝜙, 𝑧, 𝑡) 𝑖 = 1, 2, 3, respectively the population density of each level and 𝑁 is the total population. 𝑁0 𝑁1 𝑁2 𝑁3 represent the corresponding population of each energy level. Due to energy transition of the Er3+ ion, the rate equations can be obtained ) ( ) 𝑑𝑛2 ( = 𝑊𝑠𝑎 + 𝑊1𝑎 𝑛1 − 𝐴21 + 𝑊1𝑒 + 𝑊𝑠𝑒 𝑛2 + 𝐴32 𝑛3 𝑑𝑡 d𝑛3 = 𝑊2𝑎 𝑛1 − (𝑊2𝑎 + 𝐴31 + 𝐴32 )𝑛3 𝑑𝑡
𝑃1 (0)𝐶1 h𝜈11
𝑑𝑁2 𝑑𝑡
The time delay is equal to 𝛥t ′ = −
1 arctan 2𝜋𝜔
( 0 )2 𝑃 (𝐿) 𝑃 0 (0) exp(−𝐵2 𝑁2 +𝐶2 ) 𝑃𝑠0 (𝐿) 1 𝜔2 + ℎ𝜈 + 2 + ℎ𝜈 + 𝜏1 ℎ𝜈 11
21
𝑠1
𝑄
21
𝜔 +
𝑃10 (𝐿) ℎ𝜈11
+
𝑃20 (0) exp(−𝐵2 𝑁2 +𝐶2 ) ℎ𝜈21
+
𝑃𝑠0 (𝐿) ℎ𝜈𝑠1
+
1 𝜏21
(13) 3. Theoretical calculation
(5)
Considering to the above analysis model and the pump ratio 𝑀 (𝑀 = 𝑃 1 : 𝑃 2 (𝑃1480 :𝑃 980 )), 𝑀 varies with 𝑃1, and 𝑃2 is fixed to 0.001w. We debate time delay and fractional delay with different direction of
( ) 𝑃s (𝐿) = 𝑃𝑠 (0) exp 𝐵𝑠 𝑁2 − 𝐶𝑠 208
W. Qiu et al.
Optics Communications 413 (2018) 207–211
delay can be increased by 2.17 times under dual-frequency pump laser with co-propagation. Compared to previous research methods for slow light propagation [14–16], dual-frequency laser pumped fiber with copropagation and counter-propagation are very promising in practical applications. From Fig. 3, we can see that the group velocity of signal pulse propagation in an Er3+ -doped optical fiber under dual-frequency laser pumping with counter-propagation is significantly reduced. From above theoretical analysis, the factor of 𝑀 has a great effect on the slow light propagation in an Er3+ -doped optical fiber under dual-frequency laser pumping. We simulate time delay as a function of modulation frequency with different 𝑀 in Fig. 4. From Fig. 4, we are able to demonstrate how pulses can transition from slow light to fast light group velocities with increasing the value of M. The time delay or advancement is larger at lower frequency range. With the increasing of M, the time delay is reduced until it reaches negative, namely, the light speed is changing from slow to advancement. Therefore, by adding an additional pump excitation light source to change the absorption state of the medium, the transmission speed of the optical pulse signal in the erbium-doped fiber can be effectively controlled. For the Fig. 4(a) and Fig. 4(b), when 𝑀 is 7, the group velocity of signal light in an optical fiber under the dualfrequency pump laser with co-propagation is fast light propagation. However, when 𝑀 is 7, the group velocity of signal light in an optical fiber under the dual-frequency pump laser with counter-propagation is slow light propagation. We can conclude that the larger time delay can be got by using the technique of dual-frequency pump laser with counter-propagation and the conversion from slow to fast light is more controllable by using the technique of dual-frequency pump laser with co-propagation. It is possible for the optical delay line to be applied in optical communication system. Thus we can select the optimization of 𝑀 to obtain appropriate time delay and the slowdown of group velocity. In an Er3+ -doped optical fiber, the fractional delay is defined as 𝐹 = 𝑡𝑑 𝑓𝑚 , where 𝑡𝑑 is the time delay, and 𝑓𝑚 is the modulation frequency. The fractional delay represents the size of the medium’s storage capacity for optical information. The large fractional delay is desirable for the application of slow light delay lines. In order to demonstrate the influence of 𝑀 on the fractional delay and slow light propagation, we simulate the fractional delay as a function of modulation frequency for 𝑀 of 2, 5 and 7. The simulation results are shown in Fig. 5. When the medium is pumped with a strong light and the second beam of light to detect, the coherent oscillatory quantum effect leads to reduce the absorption of the probe light and there will appear hole burning in the absorption lines of the probe light. Fig. 5(a) shows the fractional delay under the dual-frequency pumping laser with copropagation for 𝑀 of 2, 5and 7. As shown in Fig. 5(a), the larger 𝑀 is, the smaller the fractional delay is. We also observe that the peak position of the maximum fractional delay moves to low frequency with increasing the value of 𝑀. When 𝑀 is equal to 7, the group
Fig. 2. Recording of the G by the dual-frequency laser with co-propagation and the dualfrequency laser with counter-propagation.
dual-frequency pumping laser(co-propagation, the forward(1480 nm) and the backward(980 nm)). We defined 𝐺 as factor of gain, and gain factor as a function of 𝑀 are shown in Fig. 2. Making use of coherent population oscillation effect, we can observe optical pulse delay and advancement propagation with the increase of 𝑀 in an Er3+ doped optical fiber under dualfrequency pumping laser with co-propagation and counter-propagation. From Fig. 2, when the Gain is smaller than 0, the oscillation leads to the pulse experiencing absorption saturation and propagation delay, and the light is slow transmission. If the Gain is bigger than 0, this effect induces the pulse experiencing gain saturation and propagation advance, and the light is super transmission. Dual-frequency pumping an Er3+ doped optical fiber with co-propagation is easy to achieve the change of slow and fast light propagation in Fig. 2. In the theoretical simulation, the data used for the calculation are 𝐿 = 10 m, 𝑝s =4 mW,and the ion density of the Er3+ doped optical fiber 𝑐 = 3.0 × 1024 m−3 , the time delay as a function of the modulation frequency under the dual-frequency pumping laser with co-propagation and counter-propagation directions are shown in Fig. 3(a) and (b). Compared slow light propagation under the single-pumping light, larger time delay of slow light propagation can be obtained under dualfrequency pump laser with co-propagation and counter-propagation. We can get the maximum time delay of 0.79 ms under dual-frequency pump laser with counter-propagation. The maximum time delay of 0.63 ms can be obtained under dual-frequency pump laser with copropagation. However, the maximum time delay of 0.29 ms can be obtained under single-pumping light. According to the comparisons, the maximum time delay can be increased by 2.72 times under dualfrequency pump laser with counter-propagation. The maximum time
Fig. 3. The time delay as a function of modulation frequency for the 𝑀 = 0.1. (a) The solid curve represents the time delay under dual-frequency pumping laser with co-propagation. (b) The solid curve presents the time delay under the dual-frequency pumping laser with counter-propagation. The insert in (a) and (b) show the time delay under the single pumping laser.
209
W. Qiu et al.
Optics Communications 413 (2018) 207–211
Fig. 4. The time delay with respect to 𝑀 as a function of the modulation frequency. (a) The solid curves represent the time delay under the dual-frequency pumping laser with co-propagation. (b) The solid curves represent the time delay under dual-frequency pumping laser with counter-propagation.
Fig. 5. The fractional delay as function of modulation frequency for different 𝑀. (a) The fractional delay under the dual-frequency pumping laser with co-propagation for 𝑀 of 2, 5 and 7. (b) The fractional delay under the dual-frequency pumping laser with counter-propagation for 𝑀 of 2, 5 and 7.
Fig. 6. The fractional delay as function of modulation frequency for different 𝑀. (a) The fractional delay under the dual-frequency pumping laser with co-propagation for 𝑀 of 20, 50 and 100. (b) The fractional delay under the dual-frequency pumping laser with counter-propagation for 𝑀 of 20, 50 and 100.
velocity of probe pulse is fast light propagation. Fig. 5(a) shows the fractional delay under the dual-frequency pumping laser with counterpropagation for 𝑀 of 2, 5 and 7. We can obtain the larger by using smaller M. We get the maximum fractional delay is 6.75×10−2 under the dual-frequency pumping laser with counter-propagation for 𝑀 of 2. The larger fractional delay can be got by using the technique of dualfrequency pump laser with counter-propagation and the conversion from slow to fast light is more controllable by using the technique of dual-frequency pump laser with co-propagation. Furthermore, we confirm that the fractional delay can be increased using dual-frequency pump laser with counter-propagation.
Fig. 6(a) shows the fractional delay under the dual-frequency pumping laser with co-propagation for 𝑀 of 20, 50and 100. Fig. 6(b) shows the fractional delay under the dual-frequency pumping laser with counter-propagation for 𝑀 of 20, 50 and 100. When 𝑀 is larger than 20, both using the technique of dual-frequency pump laser with counterpropagation and using the technique of dual-frequency pump laser with co-propagation, superluminal transmission has been achieved. According to the analysis of gain theory, the absorption or gain of medium depends on the pump ratio M. The coherent population oscillation leads the pulse to experience absorption saturation and propagation delay in a medium with absorption. And this effect induces the pulse to experience 210
W. Qiu et al.
Optics Communications 413 (2018) 207–211
gain saturation and propagation advance in a medium with gain. We can see that there is a saturation effect of fast light in low frequency region, but the fast light is enhanced with the pump ratio 𝑀 increasing in high frequency region.
[4] Y.N. Zhang, Y. Zhao, Q. Wang, Optimizing the slow light properties of slotted photonic crystal waveguide and its application in a high sensitivity gas sensing system, Meas. Sci. Technol. 24 (10) (2013) 105109–105116. [5] Y. Zhang, Y. Zhao, Q. Wang, Improved design of slow light interferometer and its application in FBG displacement sensor, Sensors Actuators A 214 (2014) 717–732. [6] L.V. Hau, S.E. Harris, Z. Dutton, C.H. Behroozi, Light speed reduction to 17 metres per second in an ultracold atomic gas, Nature (London) 397 (6720) (1999) 594–598. [7] R. Lauro, T. Chaneliere, J.L. Le Gouet, Slow light using spectral hole burning in a tm3+-doped yttrium-aluminum-garnet crystal, Phys. Rev. A 79 (2009) 063844–1–6. [8] M. Sonia, M. Marcelo, Group velocity coupling and synchronization-like phenomena on of two light beams based on coherent population oscillations, J. Phys. B: At. Mol. Opt. Phys. 43 (2010) 215401–215410. [9] G.P. Enrique, P.S. Marcos, S. Serguei, Slow and fast light via two-wave mixing in ytterbium-doped fiber at 1064 nm, Opt. Commun. 300 (2013) 45–50. [10] K. Qian, L. Zhan, Z.Q. Zhu, et al., Group velocity manipulation in active fibers using mutually modulated cross-gain modulation: from ultraslow to superluminal propagation, Opt.Lett. 36 (12) (2011) 2185–2187. [11] Than Singh Saini, Ajeet Kumar, Ravindra Kumar Sinha, Slow light generation in single-mode tellurite fibers, J. Modern Opt. 62 (7) (2015) 508–513. [12] Rim Cherif, Amine Ben Salem, Than Singh Saini, Ajeet Kumar, Ravindra K. Sinha, Mourad Zghal, Design of small core tellurite photonic crystal fiber for slow-lightbased application using stimulated Brillouin scattering, Opt. Eng. 54 (7) (2015) 075101 –075101–6. [13] Varsha Jain, Shubham Sharma, Than Singh Saini, Ajeet Kumar, Ravindra Kumar Sinha, Design and analysis of single-mode tellurite photonic crystal fibers for stimulated brillouin scattering based slow-light generation, Appl. Opt. 55 (25) (2016) 6791–6796. [14] A. Schweinsberg, N.N. Lepeshkin, M.S. Bigelow, R.W. Boyd, S. Jarabo, Observation of superluminal and slow light propagation in erbium-doped optical fiber, Europhys. Lett. 73 (2) (2006) 218–222. [15] Wei Qiu, Bo Gao, Peng Lin, Jia Li, Jingting Zhou, Qiuli Jiang, Maximum fractional delay achievable on slow light propagation through an erbium-doped optical fiber, Opt. Commun. 326 (2014) 100–104. [16] A.Y. Francisco, C.G. Eduardo, M.E. Jose, et al., Pulse-width-dependent subluminal and superluminal propagation in highly doped erbium fibers, J. Opt. Soc. Amer. B. 28 (5) (2011) 1172–1179.
4. Conclusion In this article, a general theory of coherent population oscillation effect in an Er3+ -doped fiber under the dual-frequency pumping laser with counter-propagation and co-propagation at room temperature is presented. The larger time delay and fractional delay can be got by using the technique of dual-frequency pump laser with counter-propagation and the conversion from slow to fast light is more controllable by using the technique of dual-frequency pump laser with co-propagation. We can get the maximum time delay of 0.79 ms under dual-frequency pump laser with counter-propagation. The maximum time delay of 0.63 ms can be obtained under dual-frequency pump laser with co-propagation. However, the maximum time delay of 0.29 ms can be obtained under single-pumping light. Dual-frequency laser pumped fiber with counterpropagation and co-propagation is more controllable. It is possible for the optical delay line to be applied in optical communication system. References [1] Zhou Zhang, Hau-Feng Xu, Jun Qu, Wei Huang, Radiation forces of highly focused radially polarized hollow sinh-Gaussian beams on a Rayleigh metallic particle, J. Mordern Opt. 62 (9) (2015) 754–760. [2] Zhaoming Zhou, Daniel J. Gauthier, Yoshitomo Okawachi, Jay E. Sharping, Alexander L. Gaeta, Robert W. Boyd, Alan E. Willner, Numerical study of all-optical slowlight delays via stimulated Brillouin scattering in an optical fiber, J. Opt. Soc. Amer. B 22 (11) (2005) 2378–2384. [3] R. Pant, A. Byrnes, C.G. Poulton, E. Li, D.Y. Choi, S. Madden, B. Luther-Davies, B.J. Eggleton, Photonic-chip-based tunable slow and fast light via stimulated Brillouin scattering, Opt. Lett. 37 (5) (2012) 969–971.
211
Contents lists available at ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Demonstration of slow light propagation in an optical fiber under dual pump light with co-propagation and counter-propagation Wei Qiu *, Jianjun Liu, Yuda Wang, Yujing Yang, Yuan Gao, Pin Lv, Qiuli Jiang Department of Physics, Liaoning University, Shenyang 110036, China
a r t i c l e
i n f o
Keywords: Er3+ -doped optical fiber The time delay Dual frequency pumping light Counter-propagation Co-propagation
a b s t r a c t In this paper, a general theory of coherent population oscillation effect in an Er3+ -doped fiber under the dualfrequency pumping laser with counter-propagation and co-propagation at room temperature is presented. Using the numerical simulation, in case of dual frequency light waves (1480 nm and 980 nm) with co-propagation and counter-propagation, we analyze the effect of the pump optical power ratio (M) on the group speed of light. The group velocity of light can be varied with the change of M. We research the time delay and fractional delay in an Er3+ -doped fiber under the dual-frequency pumping laser with counter-propagation and co-propagation. Compared to the methods of the single pumping, the larger time delay can be got by using the technique of dual-frequency laser pumped fiber with co-propagation and counter-propagation. © 2017 Elsevier B.V. All rights reserved.
1. Introduction The group velocity of light pulses can be dramatically modified in a material with a steep variation in frequency-dependent optical properties [1–5]. Hau et al. [6] decelerated the group velocity of a light pulse to 17 ms in an ultracold gas of sodium atoms by using the electromagnetically induced transparency EIT effect in which the narrow transparency resonance was accompanied by a steep slope in the refractive-index dispersion. In view of practical applications, the focus of observation of slow light has been shifted to solid-state materials and room temperatures. In 2010, R. Lauro et al. observed slow light phenomenon in a Tm3+-doped yttrium-aluminum-garnet crystal [7]. Melle et al. studied on both 1550 nm and 980 nm laser into an erbium-doped fiber amplifier to observe slow light and superluminal propagation in 2010 [8]. In 2013, slow and fast light via two-wave mixing in ytterbiumdoped fiber at 1064 nm are investigated in detail [9]. Qian proposed and experimentally demonstrated the propagation of slow/fast light in an erbium-doped fiber (EDF) using mutually modulated cross-gain modulation. The group velocity of the light signal can be manipulated by the effect of gain cross-saturation modulation by saturating light at an arbitrary wavelength in the gain bandwidth of the EDF [10]. In 2014, Than Singh Saini et al. simulated two different types of tellurite fibers for tunable slow light generation based on SBS [11]. Their simulated results indicate that (i) Brillouin gain up to ∼91 dB and maximum time delay of 140 ns can be achieved using 2-m long
Er-doped tellurite fiber with maximum allowable pump power of 1100 mW and (ii) Brillouin gain up to ∼86 dB and maximum time delay of 227 ns can be achieved from 100 m undoped tellurite fiber with 23 mW pump power. Rim Cherif et al. reported a detailed implementation of a two-dimensional finite element method that was applied to calculate the stimulated SBS characteristics in highly nonlinear tellurite PCF in 2015 [12]. In 2016, Varsha Jain et al. reported two different kinds of photonic crystal fiber for tunable slow-light generation based on stimulated Brillouin scattering. PCF characteristics for slow light, such as maximum allowable pump power, Brillouin gain, and time delay for both types of PCF, were simulated [13]. Compared to previous research methods [14,15], the technique of dual-frequency laser pumped fiber with co-propagation and counterpropagation is more controllable. This method is desirable for practical applications. The output signal power can be increased by using this method. The signal noise can be decreased and the deformation of the light pulse can be improved. We can increase the time delay and fraction delay under dual-frequency laser pumped single fiber with copropagation and counter-propagation. 2. Analysis model In the paper, we utilize Er3+− doped fiber of a three-level system, see Fig. 1. When |1⟩ is the fundamental energy level, |2⟩ and |3⟩ represent
* Corresponding author.
E-mail address: [email protected] (W. Qiu). https://doi.org/10.1016/j.optcom.2017.12.057 Received 11 October 2017; Received in revised form 28 November 2017; Accepted 20 December 2017 0030-4018/© 2017 Elsevier B.V. All rights reserved.
W. Qiu et al.
Optics Communications 413 (2018) 207–211
We have defined ( ) 𝛿1𝑎 + 𝛿1𝑒 𝛿 𝑁 𝐵1 = 𝛤1 𝐶1 = 1𝑎 𝛤1 𝐴 𝐴 𝛿2𝑎 𝛿2𝑎 𝐵2 = 𝛤2 𝐶2 = 𝛤 𝐴 2 (𝐴 ) 𝛿𝑠𝑒 + 𝛿𝑠𝑎 𝛿 𝑁 𝛤𝑆 𝐶s = 𝑠𝑎 𝛤𝑠 𝐵𝑠 = 𝐴 𝐴 In case of the steady state 𝑁20 = 3+
Fig. 1. The three level energy of an Er
ion.
+
𝑃2 (0)𝐵2 h𝜈21
+
+
𝑃𝑠 (0)𝐶s h𝜈s1
𝑃𝑠 (0)𝐵s h𝜈s1
+
(6)
1 𝜏21
Using trigonometric function formula, we can obtain the expression of the output signal power, [ ( )] 𝑝𝑠 (𝐿, 𝑡) = 𝑃𝑠0 (𝐿) 1 + 𝑚′𝑠 cos 𝑤𝑡 + 𝜃𝑠 √( )2 ( )2 𝑚𝑠 + 𝐵𝑠 𝑁20 𝛿 cos 𝜙 + 𝐵𝑠 𝑁20 𝛿 sin 𝜙 , Thus, 𝑚′𝑠 = tan 𝜃𝑠 =
(1)
We set
(2)
−
(9)
𝑚𝑠 + 𝐵𝑠 𝑁20 𝛿 cos 𝜙
𝐵𝑠 [𝑃𝑠 (𝐿)−𝑃𝑠 (0)] ℎ𝑣𝑠1
= 𝑄, as a result, the time delay is equal to
( 0 )2 𝑃 0 (0) exp(𝐵1 𝑁2 −𝐶1 ) 𝑃 (𝐿) 𝑃𝑠0 (𝐿) 1 𝜔2 + ℎ𝜈 + 2 + ℎ𝜈 + 𝜏1 ℎ𝜈 11
21
𝑠1
21
𝑄
) ( ) 𝑑𝑛2 ( = 𝑊𝑠𝑎 + 𝑊1𝑎 𝑛1 − 𝐴21 + 𝑊1𝑒 + 𝑊𝑠𝑒 𝑛2 + 𝑊2𝑎 𝑛1 (3) 𝑑𝑡 Here 𝑊𝑗𝑎 𝑊𝑗𝑒 represent the absorption rate and the emission rate of the 𝑗 pumping light, in addition, 𝐴21 = 𝜏1 .
(8)
𝐵𝑠 𝑁20 𝛿 sin 𝜙
1 arctan 2𝜋𝜔
𝛥t =
Because of 𝐴31 ≪ 𝐴32 , 𝐴32 ≫ 𝑇1 , we can easily in a generally accepted approximation 𝑛3 ≈ 0 , 𝑊2𝑎 𝑛1 = 𝐴32 𝑛3 . As a result, the rate equations is equal to
𝜔 +
(10)
𝑃10 (𝐿) ℎ𝜈11
+
𝑃20 (0) exp(𝐵1 𝑁2 −𝐶1 ) ℎ𝜈21
+
𝑃𝑠0 (𝐿) h𝜈𝑠1
+
1 𝜏21
2.2. Theoretical model of dual-frequency pumping laser with counterpropagation In the case of negligible loss, the transmission equation along 𝑧 is can be expressed as
2.1. Theoretical model of dual-frequency pumping laser with co-propagation
( ) 𝑑𝑃1 = −𝑃1 𝛿1𝑎 𝑛1 − 𝛿1𝑒 𝑛2 𝛤1 𝑑𝑧 𝑑𝑃2 (11) = 𝑃2 𝛿2𝑎 𝑛1 𝛤2 𝑑𝑧 ( ) 𝑑𝑃𝑠 = −𝑃𝑠 𝛿𝑠𝑎 𝑛1 − 𝛿𝑠𝑒 𝑛2 𝛤3 𝑑𝑧 We can determine the output signal light and the output pump power equation by the use of Eq. (12) ( ) 𝑃1 (𝐿) = 𝑃1 (0) exp 𝐵1 𝑁2 − 𝐶1 𝑃2 (𝐿) ( ) = 𝑃2 (0) exp −𝐵2 𝑁2 + 𝐶2 𝑃s (𝐿) ( ) = 𝑃𝑠 (0) exp 𝐵𝑠 𝑁2 − 𝐶𝑠 (12)
In the case of negligible loss, the transmission equation along 𝑧 can be expressed as ( ) 𝑑𝑃1 = −𝑃1 𝛿1𝑎 𝑛1 − 𝛿1𝑒 𝑛2 𝛤1 𝑑𝑧 𝑑𝑃2 (4) = −𝑃2 𝛿2𝑎 𝑛1 𝛤2 𝑑𝑧 ( ) 𝑑𝑃𝑠 = −𝑃𝑠 𝛿𝑠𝑎 𝑛1 − 𝛿𝑠𝑒 𝑛2 𝛤3 𝑑𝑧 Here 𝜎𝑠𝑒 is stimulated absorption cross section of the 𝑗 pumping light, 𝜎𝑠𝑎 is stimulated emission cross section of the 𝑗 pumping light, those are 𝛿1𝑒 = 0.42 × 10−25 𝛿2a = 1.29 × 10−25 𝛿2e = 1.86 × 10−25 , and 𝛿sa 𝛿se is stimulated absorption cross section and emission cross section of signal light, respectively representing 2.85 × 10−25 , 5.03 × 10−25 . Where 𝐴 indicates the effective cross-sectional area of the core. 𝜎𝑗𝑎 𝑃𝑗 𝛤𝑗 Compared with 𝑊𝑗𝑎 = ℎ𝜈 and 𝑁𝑖 = 𝑛𝑖 𝐴𝐿 𝑗1 𝐴 We can determine the output signal light and the output pump power equation by the use of Eq. (5) ( ) 𝑃1 (𝐿) = 𝑃1 (0) exp 𝐵1 𝑁2 − 𝐶1 ( ) 𝑃2 (𝐿) = 𝑃2 (0) exp 𝐵2 𝑁2 − 𝐶2
𝑃1 (0)𝐵1 h𝜈11
𝑃2 (0)𝐶2 h𝜈21
+
= 0, we can obtain
Introducing a power with cosines variation as modulation of the signal ( ) 𝑃s (0, 𝑡) = 𝑃𝑠 (0) 1 + 𝑚𝑠 cos 𝑤𝑡 (7) 0 𝑁2 (0, 𝑡) = 𝑁2 [1 + 𝛿 cos (𝑤𝑡 + 𝜙)]
the up energy of pumping light of 1480 nm and 980 nm, respectively. A spatially selective saturation of the optical transition between the fundamental energy level 4 𝐼15∕2 and the meta-stable level 4 𝐼11∕2 of the corresponding Er3+ ion. The population decay from this level within a few picoseconds to the meta-stable 4 𝐼13∕2 levels and eventually returns to fundamental energy level 4 𝐼15∕2 with a decay time of a few milliseconds, so the two level system is inverted in case of owing the stronger pumping power. We set 𝑛𝑖 = 𝑛𝑖 (𝑟, 𝜙, 𝑧, 𝑡) 𝑖 = 1, 2, 3, respectively the population density of each level and 𝑁 is the total population. 𝑁0 𝑁1 𝑁2 𝑁3 represent the corresponding population of each energy level. Due to energy transition of the Er3+ ion, the rate equations can be obtained ) ( ) 𝑑𝑛2 ( = 𝑊𝑠𝑎 + 𝑊1𝑎 𝑛1 − 𝐴21 + 𝑊1𝑒 + 𝑊𝑠𝑒 𝑛2 + 𝐴32 𝑛3 𝑑𝑡 d𝑛3 = 𝑊2𝑎 𝑛1 − (𝑊2𝑎 + 𝐴31 + 𝐴32 )𝑛3 𝑑𝑡
𝑃1 (0)𝐶1 h𝜈11
𝑑𝑁2 𝑑𝑡
The time delay is equal to 𝛥t ′ = −
1 arctan 2𝜋𝜔
( 0 )2 𝑃 (𝐿) 𝑃 0 (0) exp(−𝐵2 𝑁2 +𝐶2 ) 𝑃𝑠0 (𝐿) 1 𝜔2 + ℎ𝜈 + 2 + ℎ𝜈 + 𝜏1 ℎ𝜈 11
21
𝑠1
𝑄
21
𝜔 +
𝑃10 (𝐿) ℎ𝜈11
+
𝑃20 (0) exp(−𝐵2 𝑁2 +𝐶2 ) ℎ𝜈21
+
𝑃𝑠0 (𝐿) ℎ𝜈𝑠1
+
1 𝜏21
(13) 3. Theoretical calculation
(5)
Considering to the above analysis model and the pump ratio 𝑀 (𝑀 = 𝑃 1 : 𝑃 2 (𝑃1480 :𝑃 980 )), 𝑀 varies with 𝑃1, and 𝑃2 is fixed to 0.001w. We debate time delay and fractional delay with different direction of
( ) 𝑃s (𝐿) = 𝑃𝑠 (0) exp 𝐵𝑠 𝑁2 − 𝐶𝑠 208
W. Qiu et al.
Optics Communications 413 (2018) 207–211
delay can be increased by 2.17 times under dual-frequency pump laser with co-propagation. Compared to previous research methods for slow light propagation [14–16], dual-frequency laser pumped fiber with copropagation and counter-propagation are very promising in practical applications. From Fig. 3, we can see that the group velocity of signal pulse propagation in an Er3+ -doped optical fiber under dual-frequency laser pumping with counter-propagation is significantly reduced. From above theoretical analysis, the factor of 𝑀 has a great effect on the slow light propagation in an Er3+ -doped optical fiber under dual-frequency laser pumping. We simulate time delay as a function of modulation frequency with different 𝑀 in Fig. 4. From Fig. 4, we are able to demonstrate how pulses can transition from slow light to fast light group velocities with increasing the value of M. The time delay or advancement is larger at lower frequency range. With the increasing of M, the time delay is reduced until it reaches negative, namely, the light speed is changing from slow to advancement. Therefore, by adding an additional pump excitation light source to change the absorption state of the medium, the transmission speed of the optical pulse signal in the erbium-doped fiber can be effectively controlled. For the Fig. 4(a) and Fig. 4(b), when 𝑀 is 7, the group velocity of signal light in an optical fiber under the dualfrequency pump laser with co-propagation is fast light propagation. However, when 𝑀 is 7, the group velocity of signal light in an optical fiber under the dual-frequency pump laser with counter-propagation is slow light propagation. We can conclude that the larger time delay can be got by using the technique of dual-frequency pump laser with counter-propagation and the conversion from slow to fast light is more controllable by using the technique of dual-frequency pump laser with co-propagation. It is possible for the optical delay line to be applied in optical communication system. Thus we can select the optimization of 𝑀 to obtain appropriate time delay and the slowdown of group velocity. In an Er3+ -doped optical fiber, the fractional delay is defined as 𝐹 = 𝑡𝑑 𝑓𝑚 , where 𝑡𝑑 is the time delay, and 𝑓𝑚 is the modulation frequency. The fractional delay represents the size of the medium’s storage capacity for optical information. The large fractional delay is desirable for the application of slow light delay lines. In order to demonstrate the influence of 𝑀 on the fractional delay and slow light propagation, we simulate the fractional delay as a function of modulation frequency for 𝑀 of 2, 5 and 7. The simulation results are shown in Fig. 5. When the medium is pumped with a strong light and the second beam of light to detect, the coherent oscillatory quantum effect leads to reduce the absorption of the probe light and there will appear hole burning in the absorption lines of the probe light. Fig. 5(a) shows the fractional delay under the dual-frequency pumping laser with copropagation for 𝑀 of 2, 5and 7. As shown in Fig. 5(a), the larger 𝑀 is, the smaller the fractional delay is. We also observe that the peak position of the maximum fractional delay moves to low frequency with increasing the value of 𝑀. When 𝑀 is equal to 7, the group
Fig. 2. Recording of the G by the dual-frequency laser with co-propagation and the dualfrequency laser with counter-propagation.
dual-frequency pumping laser(co-propagation, the forward(1480 nm) and the backward(980 nm)). We defined 𝐺 as factor of gain, and gain factor as a function of 𝑀 are shown in Fig. 2. Making use of coherent population oscillation effect, we can observe optical pulse delay and advancement propagation with the increase of 𝑀 in an Er3+ doped optical fiber under dualfrequency pumping laser with co-propagation and counter-propagation. From Fig. 2, when the Gain is smaller than 0, the oscillation leads to the pulse experiencing absorption saturation and propagation delay, and the light is slow transmission. If the Gain is bigger than 0, this effect induces the pulse experiencing gain saturation and propagation advance, and the light is super transmission. Dual-frequency pumping an Er3+ doped optical fiber with co-propagation is easy to achieve the change of slow and fast light propagation in Fig. 2. In the theoretical simulation, the data used for the calculation are 𝐿 = 10 m, 𝑝s =4 mW,and the ion density of the Er3+ doped optical fiber 𝑐 = 3.0 × 1024 m−3 , the time delay as a function of the modulation frequency under the dual-frequency pumping laser with co-propagation and counter-propagation directions are shown in Fig. 3(a) and (b). Compared slow light propagation under the single-pumping light, larger time delay of slow light propagation can be obtained under dualfrequency pump laser with co-propagation and counter-propagation. We can get the maximum time delay of 0.79 ms under dual-frequency pump laser with counter-propagation. The maximum time delay of 0.63 ms can be obtained under dual-frequency pump laser with copropagation. However, the maximum time delay of 0.29 ms can be obtained under single-pumping light. According to the comparisons, the maximum time delay can be increased by 2.72 times under dualfrequency pump laser with counter-propagation. The maximum time
Fig. 3. The time delay as a function of modulation frequency for the 𝑀 = 0.1. (a) The solid curve represents the time delay under dual-frequency pumping laser with co-propagation. (b) The solid curve presents the time delay under the dual-frequency pumping laser with counter-propagation. The insert in (a) and (b) show the time delay under the single pumping laser.
209
W. Qiu et al.
Optics Communications 413 (2018) 207–211
Fig. 4. The time delay with respect to 𝑀 as a function of the modulation frequency. (a) The solid curves represent the time delay under the dual-frequency pumping laser with co-propagation. (b) The solid curves represent the time delay under dual-frequency pumping laser with counter-propagation.
Fig. 5. The fractional delay as function of modulation frequency for different 𝑀. (a) The fractional delay under the dual-frequency pumping laser with co-propagation for 𝑀 of 2, 5 and 7. (b) The fractional delay under the dual-frequency pumping laser with counter-propagation for 𝑀 of 2, 5 and 7.
Fig. 6. The fractional delay as function of modulation frequency for different 𝑀. (a) The fractional delay under the dual-frequency pumping laser with co-propagation for 𝑀 of 20, 50 and 100. (b) The fractional delay under the dual-frequency pumping laser with counter-propagation for 𝑀 of 20, 50 and 100.
velocity of probe pulse is fast light propagation. Fig. 5(a) shows the fractional delay under the dual-frequency pumping laser with counterpropagation for 𝑀 of 2, 5 and 7. We can obtain the larger by using smaller M. We get the maximum fractional delay is 6.75×10−2 under the dual-frequency pumping laser with counter-propagation for 𝑀 of 2. The larger fractional delay can be got by using the technique of dualfrequency pump laser with counter-propagation and the conversion from slow to fast light is more controllable by using the technique of dual-frequency pump laser with co-propagation. Furthermore, we confirm that the fractional delay can be increased using dual-frequency pump laser with counter-propagation.
Fig. 6(a) shows the fractional delay under the dual-frequency pumping laser with co-propagation for 𝑀 of 20, 50and 100. Fig. 6(b) shows the fractional delay under the dual-frequency pumping laser with counter-propagation for 𝑀 of 20, 50 and 100. When 𝑀 is larger than 20, both using the technique of dual-frequency pump laser with counterpropagation and using the technique of dual-frequency pump laser with co-propagation, superluminal transmission has been achieved. According to the analysis of gain theory, the absorption or gain of medium depends on the pump ratio M. The coherent population oscillation leads the pulse to experience absorption saturation and propagation delay in a medium with absorption. And this effect induces the pulse to experience 210
W. Qiu et al.
Optics Communications 413 (2018) 207–211
gain saturation and propagation advance in a medium with gain. We can see that there is a saturation effect of fast light in low frequency region, but the fast light is enhanced with the pump ratio 𝑀 increasing in high frequency region.
[4] Y.N. Zhang, Y. Zhao, Q. Wang, Optimizing the slow light properties of slotted photonic crystal waveguide and its application in a high sensitivity gas sensing system, Meas. Sci. Technol. 24 (10) (2013) 105109–105116. [5] Y. Zhang, Y. Zhao, Q. Wang, Improved design of slow light interferometer and its application in FBG displacement sensor, Sensors Actuators A 214 (2014) 717–732. [6] L.V. Hau, S.E. Harris, Z. Dutton, C.H. Behroozi, Light speed reduction to 17 metres per second in an ultracold atomic gas, Nature (London) 397 (6720) (1999) 594–598. [7] R. Lauro, T. Chaneliere, J.L. Le Gouet, Slow light using spectral hole burning in a tm3+-doped yttrium-aluminum-garnet crystal, Phys. Rev. A 79 (2009) 063844–1–6. [8] M. Sonia, M. Marcelo, Group velocity coupling and synchronization-like phenomena on of two light beams based on coherent population oscillations, J. Phys. B: At. Mol. Opt. Phys. 43 (2010) 215401–215410. [9] G.P. Enrique, P.S. Marcos, S. Serguei, Slow and fast light via two-wave mixing in ytterbium-doped fiber at 1064 nm, Opt. Commun. 300 (2013) 45–50. [10] K. Qian, L. Zhan, Z.Q. Zhu, et al., Group velocity manipulation in active fibers using mutually modulated cross-gain modulation: from ultraslow to superluminal propagation, Opt.Lett. 36 (12) (2011) 2185–2187. [11] Than Singh Saini, Ajeet Kumar, Ravindra Kumar Sinha, Slow light generation in single-mode tellurite fibers, J. Modern Opt. 62 (7) (2015) 508–513. [12] Rim Cherif, Amine Ben Salem, Than Singh Saini, Ajeet Kumar, Ravindra K. Sinha, Mourad Zghal, Design of small core tellurite photonic crystal fiber for slow-lightbased application using stimulated Brillouin scattering, Opt. Eng. 54 (7) (2015) 075101 –075101–6. [13] Varsha Jain, Shubham Sharma, Than Singh Saini, Ajeet Kumar, Ravindra Kumar Sinha, Design and analysis of single-mode tellurite photonic crystal fibers for stimulated brillouin scattering based slow-light generation, Appl. Opt. 55 (25) (2016) 6791–6796. [14] A. Schweinsberg, N.N. Lepeshkin, M.S. Bigelow, R.W. Boyd, S. Jarabo, Observation of superluminal and slow light propagation in erbium-doped optical fiber, Europhys. Lett. 73 (2) (2006) 218–222. [15] Wei Qiu, Bo Gao, Peng Lin, Jia Li, Jingting Zhou, Qiuli Jiang, Maximum fractional delay achievable on slow light propagation through an erbium-doped optical fiber, Opt. Commun. 326 (2014) 100–104. [16] A.Y. Francisco, C.G. Eduardo, M.E. Jose, et al., Pulse-width-dependent subluminal and superluminal propagation in highly doped erbium fibers, J. Opt. Soc. Amer. B. 28 (5) (2011) 1172–1179.
4. Conclusion In this article, a general theory of coherent population oscillation effect in an Er3+ -doped fiber under the dual-frequency pumping laser with counter-propagation and co-propagation at room temperature is presented. The larger time delay and fractional delay can be got by using the technique of dual-frequency pump laser with counter-propagation and the conversion from slow to fast light is more controllable by using the technique of dual-frequency pump laser with co-propagation. We can get the maximum time delay of 0.79 ms under dual-frequency pump laser with counter-propagation. The maximum time delay of 0.63 ms can be obtained under dual-frequency pump laser with co-propagation. However, the maximum time delay of 0.29 ms can be obtained under single-pumping light. Dual-frequency laser pumped fiber with counterpropagation and co-propagation is more controllable. It is possible for the optical delay line to be applied in optical communication system. References [1] Zhou Zhang, Hau-Feng Xu, Jun Qu, Wei Huang, Radiation forces of highly focused radially polarized hollow sinh-Gaussian beams on a Rayleigh metallic particle, J. Mordern Opt. 62 (9) (2015) 754–760. [2] Zhaoming Zhou, Daniel J. Gauthier, Yoshitomo Okawachi, Jay E. Sharping, Alexander L. Gaeta, Robert W. Boyd, Alan E. Willner, Numerical study of all-optical slowlight delays via stimulated Brillouin scattering in an optical fiber, J. Opt. Soc. Amer. B 22 (11) (2005) 2378–2384. [3] R. Pant, A. Byrnes, C.G. Poulton, E. Li, D.Y. Choi, S. Madden, B. Luther-Davies, B.J. Eggleton, Photonic-chip-based tunable slow and fast light via stimulated Brillouin scattering, Opt. Lett. 37 (5) (2012) 969–971.
211