Brillouin scattering behavior in acoustically guiding single-mode optical fibers with different core diameters

Journal Pre-proof Brillouin scattering behavior in acoustically guiding single-mode optical fibers with different core diameters Li Jiang, Yingying Wang, Peilong Yang, Lei Zang, Lingling Yang, Shixun Dai, Cibo Lou

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S0030-4018(19)31081-8 https://doi.org/10.1016/j.optcom.2019.125040 OPTICS 125040

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Optics Communications

Received date : 22 October 2019 Revised date : 23 November 2019 Accepted date : 28 November 2019 Please cite this article as: L. Jiang, Y. Wang, P. Yang et al., Brillouin scattering behavior in acoustically guiding single-mode optical fibers with different core diameters, Optics Communications (2019), doi: https://doi.org/10.1016/j.optcom.2019.125040. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.

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Brillouin scattering behavior in acoustically guiding single-mode optical fibers with different core

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diameters

Li Jiang a, b, Yingying Wang c, Peilong Yang a, *, Lei Zang d, Lingling Yang a, Shixun Dai a, *, Cibo Lou b, *

Laboratory of Infrared Material and Devices, The Research Institute of Advanced Technologies, Ningbo University, Ningbo 315211, China

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a

b

School of Physical Science and Technology, Ningbo University, Ningbo 315211, China

c

State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai 200240, China

d

R&D Center, Yangtze Optical Fiber and Cable Company Ltd, Wuhan 430073, China

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*Corresponding author. E-mail address: [email protected]; [email protected]; [email protected]. Abstract The Brillouin scattering behaviors in three kinds of acoustically guiding single-mode silica fibers with different core diameters of 8.8 m, 5 m, and 3 m were characterized, including the Brillouin scattering spectrum, the stimulated Brillouin scattering (SBS) threshold power, the amount of Brillouin frequency shift (BFS), and the Brillouin linewidth. The experimental results demonstrate that with the same fiber length (~10 km), the SBS threshold of the fiber with core

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diameter of 3 m is approximately one sixth of that of standard G652 fiber, which has a core diameter of 8.8 m. In combination with numerically studies, it is found that small-core fiber with high NA has a distinct advantage in relatively short fiber lengths in terms of reducing SBS threshold. In addition, the amounts of BFS are influenced by both the fiber core diameter and specially the fiber core dopants. Finally, we have also experimentally confirmed that reduced fiber core diameter would lead to the Brillouin linewidth broadening. We believe that these new results provide valuable reference for Brillouin fiber laser. Keywords: Nonlinear optics, Brillouin scattering behavior, acoustically guiding fiber, core diameter. 1. Introduction

Stimulated Brillouin scattering (SBS) is a typical nonlinear optical phenomenon with many evident advantages, such as low threshold power, ultra-narrow gain linewidth, and extremely high conversion efficiency [1,2]. It has been widely used in narrow linewidth fiber lasers [2-4], fiber amplifiers [5-7], narrow-band optical filters [8-10], and slow light modulators [11-13]. There are numerous factors that can affect this nonlinear scattering process, including the nonlinearity of the medium, the light source characteristics etc. [14,15]. In addition to the abovementioned factors, the waveguide structure will also have significant impact on the behavior of the optical and acoustic mode transmission, especially in optical fibers. Optical fiber has strong light field constraint ability and high nonlinearity. It is well know that, the geometrical structure of an optical fiber can affect the behavior of the optical and acoustic

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modes transmission greatly, and could further affect the Brillouin scattering properties (i.e., SBS threshold, amount of Brillouin frequency shift (BFS), and Brillouin linewidth). For example, Shiraki et al. used a nonuniform fiber to suppress the SBS threshold level and obtained an adjustable range of the amount of BFS [16]. Jeong et al. demonstrated that a silica hollow fiber waveguide structure could regulate the amount of BFS in the fiber, in which the amount of BFS increases as the hollow fiber core radius increases [17]. Cherif et al. adjusted the acousto-optic overlap area and acoustic velocity by optimizing the fiber microstructure, thus affecting its SBS threshold and amount of BFS [18]. However, it is noticed that contrary conclusions have been obtained when same parameters of fiber structure were changed. For example, Beugnot et al. reported decreasing BFS by using tapered fiber [19]. While, Zou et al. obtained an increasing BFS using the same method [20]. This is because of the fact that the transverse acoustic velocity distribution characteristics are different with each other. The fiber in [19] is acoustically anti-guided where the acoustic velocity is higher in the core than that in the cladding, while the one in [20] is acoustically guided where the acoustic velocity is lower in the core than that in the cladding. The transverse acoustic properties of fiber also have an apparent effect on the Brillouin scattering behavior. For example, Yu et al. [21] designed two types of double-clad fibers with different acoustic velocity distributions, and observed the variation of BFS with core size by adjusting its inner cladding acoustic velocity. Mermelstein et al. [22] proved that the acoustically anti-guiding fiber is superior to the acoustically guiding fiber in term of SBS threshold suppression levels and Brillouin gain spectrum (BGS) broadening. Therefore, three kinds of acoustically guiding fibers are employed in this work for comparison to eliminate these effects. In addition, in order to remove the influences of high order modes, such as BGS broadening [23], threshold increases [24] etc., thus, three single-mode optical fibers were selected. In this work, the acoustically guiding single-mode silica fibers with a standard core diameter of 8.8 m and two kinds of fibers with small core diameters of 5 m, 3 m were used. For each fiber, the Brillouin scattering behavior, including the Brillouin scattering spectra, SBS threshold power, the amount of BFS, and Brillouin linewidth were characterized experimentally. In addition, we also numerically calculated the influence of the related parameters (Aeff, I, Gth), on SBS threshold levels. 2. Theory

For single-mode silica fibers, the Brillouin linewidth approximately varies from 20 MHz to 100 MHz [25]. When the linewidth of pump light is relatively narrow (≤1 MHz), the SBS threshold can be expressed as [26]

Pth 

Gth  Aeff

K  Leff  g B  I

(1)

where Leff is the effective length of the fiber, gB is the gain coefficient, and K is the polarization correlation factor, of which the value is 2/3 for low birefringence fiber [27], I is the acousto-optic overlap integral, Gth is the threshold exponential gain, which is not a constant, and can be expressed as [28]

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G th  ln[

4 Aeff  f B  Gth

3/2

  1/2

g B  k  T   f p  Leff

(2)

]

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where fB is BFS, k is the Boltzmann constant, T is the absolute temperature,  is the phonon decay rate, and fP is the frequency of the pump light. The acousto-optic overlap integral can be expressed as I = Aeff / Aao, where Aeff is the effective area of optical mode and Aao is the effective area of the fundamental acoustic mode, which are given by

(  E dxdy)2

Aeff 



(  E dxdy )2

(  E u dxdy ) 2

(3)

E dxdy

2

Aao 

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2

*

2

u

2

dxdy

(4)

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where E is optical mode field, u is longitudinal acoustic mode field. To obtain these two parameters, the finite element method (FEM) is used to solve the optical wave equation and the displacement distribution equation of acoustic wave, and the specific equations can be given by

t2 E  (

2



t2u  (

)(n 2  neff ) E  0

a2   a2 )u  0 2

(5) (6)

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where  is the pump wavelength, n and neff are the refractive index and effective refractive index of the fundamental optical mode, respectively, a is the angular frequency of the acoustic wave,  is the acoustic velocity of the longitudinal mode, and a is the propagation constant of acoustic mode. The backscattered SBS is generated only when the phase matching condition a = 2opt is satisfied, and opt = 2neff /  is the propagation constant of the optical mode. 3. Experimental setup

The schematic diagram of the experimental setup for measuring Brillouin scattering spectra, SBS threshold, and BGS is shown in Fig. 1. A distributed feedback laser (DFB, SPL-1550-10-2-1-1-B, FiberLake), with a linewidth of 1 MHz and an output power of 10 mW operating at 1.55 m, was used as the seed source. The DFB laser was amplified by an erbium-doped fiber amplifier (EDFA, EDFA-BA-25-B, Fsphotonic) with a maximum output power of 300 mW. A polarization controller (PC) was used to optimize the backscattered power and beat signal. A variable optical attenuator (VOA) was used to adjust the pump power into the fibers under test (FUT). The amplified light was launched into the FUT through port 1 of an optical circulator, whereas the backscattered light was measured through port 3. The Aeff of these small-core fibers do not match with that of the standard single-mode fiber (~80 m2). Hence, two kinds of mode field adapters (MFA) with an insertion loss of < 0.2 dB were used, which could reduce the losses of light in two opposite directions simultaneously and increase the stability of scattered light. The backscattered Brillouin power and spectra were acquired by a power meter (PM) and an optical spectrum analyzer (OSA, AQ6317B, Yokogawa) with a high resolution of

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0.01 nm, respectively. In addition, heterodyne measurement was performed to characterize the BGS with a high resolution. The beating results of backscattered light detected by a PD were amplified by low-noise amplifier (LNA) and sent to a high-performance spectrum analyzer (PSA, E4448A, Agilent). The PSA has a resolution bandwidth of 100 kHz. Meanwhile, the LNA was used to amplify electrical signals and reduce spontaneous emission noise. Fibers were angle cleaved to reduce the influence of Fresnel reflection when the SBS threshold was characterized, while the fibers were flat cleaved to enhance the beat frequency effects in the BGS characterization process. All tests were carried out with the same experimental conditions, such as same bending radius and surrounding temperature, etc., to compare the Brillouin scattering behavior of these fibers.

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Two acoustically guiding single-mode silica fibers with small-core diameters of 5 m (Fiber II) and 3 m (Fiber III) and a G652 fiber (Fiber I) with a core diameter of 8.8 m were used. The special fibers were provided by Yangtze Optical Fiber and Cable Company. Table 1 summarizes the detailed acousto-optic parameters of each fiber.

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Fig. 1. Experimental setup used for observation of Brillouin scattering behavior in small-core fibers. The port A is used for measurement for Brillouin scattering spectrum and SBS threshold; the port B is used for measurement for BGS spectra by performing a heterodyne detection. DFB: distributed feedback laser, EDFA: erbium-doped fiber amplifier, PC: polarization controller, VOA: variable optical attenuator, MFA: mode field adapters, FUT: fibers under test, PM: power meter, OSA: optical spectrum analyzer, PD: photodiode, LNA: low-noise amplifier, PSA: high-performance spectrum analyzer. Table 1 The parameters of small-core fibers at 1.55 m. Parameter

Core diameter Ge /F-core doped Transmission loss Numerical aperture, NA Effective mode area, Aeff Acoustic velocity,  Density, 

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4. Results and discussion

Units

m wt% dB · km−1 m2 m · s−1 kg · m−3

Fiber I (G652)

Fiber II

Fiber III

8.8 4/0 0.2 0.13 77.3 5772 2216

5 6/0.3 0.29 0.17 42.8 5639 2284

3 19/0.4 0.48 0.27 16.9 5087 2466

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4.1. Brillouin scattering spectra and threshold Pth of Fiber I-III

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Figure 2 shows the evolution of Brillouin scattering spectra under various input power levels in Fiber I-III. It can be seen that there are three peaks in the backscattered spectra, corresponding to the anti-Stokes peaks, Rayleigh scattering peaks, and the Stokes peaks from left to right. The Rayleigh scattering is a non-frequency-shifting scattering caused by nonpropagating density fluctuations, and its wavelength is the same with the pump wavelength [29]. In comparison, the Stokes (anti-Stokes) components are generated by the down- (up-) frequency-shift caused by Brillouin scattering. For Fiber I-III, the amount of wavelength shift of Stokes and anti-Stokes are approximately 0.085, 0.083, and 0.078 nm, respectively.

Fig. 2. Brillouin scattering spectra evolution in Fiber I-III with core diameters of 8.8, 5, and 3 m for various input power levels. From Fig. 2, we can see that the Stokes growth trend is more obvious when the input power exceeds a threshold value. Generally, the input power, where the backscattered power is of 1% of it, can be defined as the Pth [30]. This physical definition is reasonable because it marks the transition of the SBS interaction from a small signal to a pump depletion state [31]. The measured power of the backscattered light as the function of input power is shown in Fig. 3(a), and the 1% of input power is represented by the green dot line. When the input power increases, the backscattered light power in Fiber I-III grows exponentially. The Pth of Fiber I-III are approximately 11.53, 4.98, and 2.04 mW, respectively. So the Pth in Fiber III with a core diameter of 3 m is about one sixth of that in Fiber I with a core diameter of 8.8 μm. In addition, Fig. 3(b) shows the measured Pth of fibers with 8.8 μm-core-diameter under five different lengths. The measured Pth values are approximately 55.70, 25.98, 11.53, 7.87, and 6.21 mW for fiber lengths of 1.55, 4, 10, 16, and 20 km, respectively.

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Fig. 3. Backscattered power as a function of input power. (a) Fibers with different core diameters of 8.8 m, 5 m, and 3 m and the same fiber length of 10 km; (b) Fibers with different fiber lengths of 1.55 km (violet solid line), 4 km (orange solid line), 10 km (blue solid line), 16 km (red

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solid line), and 20 km (black solid line)) and the same core diameter of 8.8 m. To understand the influence of the core diameter on the SBS threshold, the parameters (Aeff, I) affecting the SBS threshold are simulated. These acousto-optic parameters are numerically calculated using a finite element method (COMSOL). The variation of Aeff and Aao with the core size is shown in Fig. 4(a). As we can see, the variation of Aeff and Aao shows a similar trend as the fiber core diameter changes. The Aeff and Aao decrease with increasing numerical aperture (NA) when the fiber core diameter is fixed. This is because for a silica fiber with doped Ge or F, the acoustic index N (ratio of acoustic velocity of cladding and core) is proportional to the NA [32]. The fiber with a large NA has a strong ability to simultaneously confine the optical and acoustic mode in the core. For fibers with three kinds of NAs, the Aeff and Aao decrease initially to a certain value with fiber core diameter decreases. When the core diameter is further reduced, light will leak into the cladding, resulting in increasing Aeff and Aao. In this work, the simulated values of Aeff and Aao are 76.16, 77.76 m2 for Fiber I, 37.16, 40.24 m2 for Fiber II, and 15.34, 16.91 m2 for Fiber III, respectively. Figure 4(b) shows energy distributions for both fundamental optical mode and acoustic mode of Fibers I–III.

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Fig. 4. (a) Optical and acoustic effective areas versus core diameter under three NA values. (b) The energy distributions for both fundamental optical mode and acoustic mode of Fiber I-III. Figure 5 shows the relationship between the acousto-optic overlap integral I and the core

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diameter of fibers with three kinds of NAs. The acousto-optic overlap integrals for fibers with three different NAs show a monotonically decreasing trend with the reduction of fiber core diameters because of the difference in the confinement degree of optical and acoustic mode. Due to the well confinement of both optical and acoustic mode in the core, I is always close to 1. For a fiber with NA of 0.13, the I can even be reduced to <0.3 when the core diameter is 3 μm. For Fiber I-III, the I are calculated to be 0.979, 0.923, and 0.907, respectively. Although the differences among them are relatively small, the SBS threshold, which is inversely proportional to I according to Eq. (1), can also be affected to some extent.

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Fig. 5. Acousto-optic overlap integral as a function of the core diameter under three kinds of NA values. The Brillouin gain coefficient gB of Fiber I-III can be obtained by substituting the measured Pth and the expression of threshold exponential gain Gth into Eq. (1), and the corresponding values are 2.55 × 10-11, 3.61 × 10-11, and 4.08 × 10-11 m · W−1, respectively. The reason for this may be, that acoustically guiding single-mode small-core fiber has a higher nonlinearity due to its smaller Aeff than others fibers, thereby further obtaining a higher Brillouin gain coefficient. The variation of Gth and Pth with fiber length in three different fiber core diameters can be deduced from Eqs. (1) and (2). As shown in Fig. 6(a), the curves represent the simulated Gth values as functions of fiber length. With the increase of fiber length (0.1–20 km), the Gth of fibers decreases from 21.77, 20.77, and 19.87 to 16.89, 16.06, and 15.48, for Fiber I, Fiber II and Fiber III individually. In addition, at the same fiber length, relatively low Gth is found in small-core fiber. Figure 6(b) shows simulated Pth values as functions of fiber length in three fibers with different core diameters. These dots represent the measured Pth of Fiber I with different lengths. Thanks to the rationality of the simulated parameters, the simulated results agree well with measured ones. Pth of the Fiber III is always smaller than that of the Fiber I, especially under the scenario with relatively short lengths. This is because, in comparison, the Pth sensitivity to the fiber length in the smaller core fiber will be lower, resulting in an increase of the Pth difference at relatively short lengths in these fibers.

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Fig. 6. Simulated variation of (a) threshold exponential gain Gth and (b) SBS threshold with fiber length under three kinds of core diameters.

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4.2. The BFS spectra of Fiber I-III

Figure 7 shows the normalized beat spectra of Fiber I-III performed by the heterodyne detection. For Fiber I-III, the BFS are 10.72, 10.5, and 9.71 GHz, respectively. Previous literature has reported that when the acoustically guiding condition is satisfied, the mode field diameter of nonuniform fiber varies from 8.11 m to 6.93 m along its length, and the BFS is only increased by 49 MHz [16]. However, in this work, the BFS is reduced by approximately 1 GHz when the

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core diameter decreases from 8.8 to 3 m. The reason is that the BFS is not only related to the core diameter but also to the core dopants. The core doped with Ge or F can decrease the acoustic velocity, which will further decrease the BFS. The frequency shift coefficient of the fiber doped with Ge is approximately 89 MHz/wt% [33], and it will be higher while doped with F [34]. Hence, we can see that the method of core doping has a greater influence on the BFS than the core diameter.

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Fig. 7. Normalizing Brillouin gain spectra of Fiber I-III with the same fiber length of 10 km.

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4.3. Brillouin linewidth versus input power for Fiber I-III

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Figure 8 shows the measured Brillouin linewidth for the three different core diameter fibers versus the input power. At a relatively low input power, the spontaneous Brillouin linewidths of Fiber I-III are 29.4, 44.4, and 80.9 MHz, respectively. When the input power reaches the threshold, the stimulated Brillouin linewidths are 8.9, 9.2, and 10.9 MHz, respectively. With further increase in pump power, the linewidth changes slowly and approaches a stable value about 10 MHz finally. The cease of linewidth narrowing is due to the pump power depletion [35]. And the changes in the corresponding Brillouin linewidth are approximately 21.54, 36.45, and 72.12 MHz, respectively. Obviously, a smaller-core fiber with higher spontaneous and stimulated Brillouin linewidth and its variation of Brillouin linewidth is greater than that in a fiber with a larger core. The reason for this case may be that the shear acoustic wave cannot be ignored, which broadens the Brillouin linewidth, in such small core size fiber [36].

Fig. 8. Brillouin linewidth as a function of input power for Fiber I-III with the same fiber length of 10 km. 5. Conclusions To summarize, we studied the SBS behavior in three acoustically guiding single-mode fibers with different core diameters numerically and experimentally, including the Brillouin scattering spectrum, the threshold power, the amount of BFS, and the Brillouin linewidth. The reduction in the BFS and the linewidth broadening were also reported in small-core fiber, where the reduction in the BFS was mainly due to the method of doping in fiber core area. We also experimentally demonstrate that the SBS threshold of 3 m-core fiber is one sixth that of standard G652 fiber under the same fiber length (~10 km). In combination with our numerically studies, we found that small-core fiber with high NA has a distinct advantage in relatively short lengths in terms of reducing SBS threshold. This work will lay a solid foundation for some low-threshold single-frequency Brillouin lasers.

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Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant No. 61875094) and by K.C. Wong Magna Fund in Ningbo University.

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*Author Contributions Section

Author contributions:

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Li Jiang, Yingying Wang, Shixun Dai participated in the conception and design of this work. Li Jiang, Yingying Wang, Peilong Yang, Shixun Dai, and Cibo Lou participated in the data acquisition, analysis or interpretation of this work. Lei Zhang provided the experimental fibers and parameters of this work. Li Jiang, Lingling Yang participated in the experimental process of this work. All authors contributed to the critical revision of the manuscript and approved the final version submitted for publication.