coatings
Article Temperature Sensing Utilizing Stimulate Brillouin Scattering Fast Light in Liquid-Filled Photonic Crystal Fibers
Jingli Lei, Shuaibin Niu, Shanglin Hou *, Daobin Wang and Xiaoxiao Li
School of Science, Lanzhou University of Technology, Lanzhou 730050, China; [email protected] (J.L.); [email protected] (S.N.); [email protected] (D.W.); [email protected] (X.L.) * Correspondence: [email protected]; Tel.: +86-138-9369-7556
Received: 17 October 2020; Accepted: 18 November 2020; Published: 20 November 2020
Abstract: A novel temperature sensor designed on stimulate Brillouin scattering fast light in liquid-filled photonic crystal fibers is proposed. The time advancement and the Brillouin frequency shift of fast light are simulated according to the three-wave coupling equations of stimulate Brillouin scattering, and the temperature sensing characteristics of the fast light in liquid-filled hexagonal photonic crystal fibers with three different air filling factors are simulated from 20 ◦C to 70 ◦C by using the full-vector finite element method. The alcohol-filled photonic crystal fibers exhibit rather sensitive responses to temperature. With temperature varying from 20 ◦C to 70 ◦C, the variation of the effective mode area is 2.75 µm at the air filling factor of 0.6, the Brillouin frequency shift is about 11 GHz and its average modification is 1.15 MHz. The time advancement increases with the rise of temperature, its increment can reach up to 4.53 ns at the air filling factor of 0.6 and the pump power of 60 mW, the temperature sensitivity of the time advancement is 0.272 ns/◦C.
Keywords: stimulate Brillouin scattering; photonic crystal fiber; fast light; temperature; sensor
1. Introduction Stimulate Brillouin scattering (SBS), a nonlinear interaction between light wave and acoustic wave, can induce Stocks wave and anti-Stocks wave during transmission [1]. Controlling group velocity of the light wave via SBS has attracted much attention in optical societies during recent decades and much promising research has also been reported [2]. A series of applications in both academia and industry have been implemented, such as slow and fast light generator [3], fiber amplifier [4], optical fiber lasers [5] and special optical fiber sensors [6]. Meanwhile, compared with conventional optical fiber, photonic crystal fiber (PCF) [7] exhibits more flexibility on designing optical components or sensors because of its special structure, and PCF also exhibits unique optical features, such as adjustable dispersion, endless single mode transmission, large mode area and high nonlinearity. In recent years, various ways to realize the slow or fast light in optical fibers have been exploited at room temperature, for example, coherent population oscillation (CPO) [8], stimulated Raman scattering (SRS), stimulated Brillouin scattering (SBS), optical parametric amplification (OPA) [9], and fiber Bragg grating (FBG) [10]. The fast or slow light technology based on SBS has attracted more interest due to it occurring at room temperature, operating at any wavelength, having a simple compact structure and being compatible with the existing communication system. Confining light into a tiny core of PCF enhances the interaction between the light wave and the acoustic wave. This leads to extremely high nonlinearity and the SBS occurs easily. So, the fast or slow light via SBS can be realized in a relative short fiber, which can be used for sensing by adjusting the structure or filling gas or liquid or solid into the air holes of the PCF. Steinvurzel et al. [11] filled acrylate
Coatings 2020, 10, 1123; doi:10.3390/coatings10111123 www.mdpi.com/journal/coatings Coatings 2020, 10, 1123 2 of 11 liquid mixture into the fiber air holes to design an adjustable grate filter in 2005. In 2010, Han et al. [12] used liquid-filled PCF to design an intensity modulation temperature sensor. Geng et al. [13] used liquid-filled PCF to design a high-sensitivity temperature sensor based on a Mach–Zednder interferometer in 2014: the temperature sensitivity reached 1.83 nm/ C. Monfared Y.E. et al. [14] − ◦ analyzed the SBS slow light by filling liquid into a PCF core in 2016. Sanggwon Song et al. [15] reported systematic experimental characterizations of the SBS in passive 1060 nm SMFs using a highly sensitive optical heterodyne method with a narrow linewidth CW (continuous wave) laser operating at a wavelength of 1064 nm. It can be seen from this literature that the research on SBS temperature sensing is mainly based on refractive index of PCF, because the transmission characteristics of light changes with the various refractive indexes of the filled liquid induced by varying temperature, and the previous research focused on SBS slow light. Up to now, the research on temperature sensing utilizing the SBS fast light in liquid-filled PCF has not been reported yet. In this paper, we proposed an index-guided PCF filled with alcohol and an experimental configuration. The temperature-sensing characteristics of the SBS fast light were simulated by the full vector finite element method, and the dependence of temperature response of the SBS fast light on the effective mode area, the effective refractive index, the Brillouin frequency shift, the time advancement, the pulse broadening factor, the group velocity of signal light and the threshold pump power were investigated. This research will provide a valuable theoretical reference for designing novel temperature sensors based on fast light via SBS in optical fibers.
2. Theoretical Analysis Generally, the dynamics of SBS can be described by the following Equations [16,17]:
∂Ep ng ∂Ep α γeωp + = Ep + i Esρ − ∂z c ∂t − 2 2ngcρ0 ∂Es ng ∂Es α γeωp + = Es + i Epρ∗ (1) ∂z c ∂t 2 2ngcρ0 h − i 2 ∂ρ ΓB γeq ε0 + i(ΩB Ω) ρ = i EpE∗ ∂t 2 − − 8ΩB s where Ep, Es and ρ are the amplitudes of the pump wave, the stokes wave and the acoustic wave respectively, ng is the group refractive index, c is the speed of light in vacuum, α is the attenuation coefficient of the PCF, γe is the electrostriction constant, ωp and Ω are the angular frequencies of the pump wave and the acoustic wave respectively, ΓB is the full width at half maximum of Brillouin absorption spectra or gain spectra and is the reciprocal of the photon life, ΩB is the Brillouin frequency shift which is the frequency difference between the pump wave and the Stokes light, ε0 is the dielectric constant in vacuum. Under the condition of small signal steady-state solution, the Equation (1) can be solved to obtain the time advancement as follow
2 G 1 [2(∆ω ΩB)/ΓB] ∆T = − − (2) n o2 ΓBAe f f 2 1 + [2(∆ω ΩB)/ΓB] − where ∆T is the time difference corresponding to the maximum point of the output signal shape with or without SBS, ∆ω is the frequency difference between the pump wave and the signal wave, G is the SBS loss and expressed as G = gBLe f f P, gB is the SBS absorption coefficient and which equals to the gain coefficient, L is the effective fiber length and expressed as L = 1 e(αL) /α, L is the fiber e f f e f f − length and P is the pump power. Ae f f is the effective mode field area and expressed as
R 2 2 ( ∞ E(x, y) dxdy) A = −∞ (3) e f f R 4 ∞ E(x, y) dxdy −∞ Coatings 2020, 10, 1123 3 of 11
The phase relationship of the pump wave, the anti-Stokes wave and the acoustic wave is described as ωas = ωp + ΩB, where ωas is the anti-Stokes angular frequency. Because ωas is at the range of the Brillouin absorption spectrum, the group velocity of the anti-Stokes wave is greater than the velocity of light in vacuum which is regarded as the fast light. When the center frequency of the signal wave is at the peek value of the absorption spectrum, the frequency difference between the signal wave and the pump wave equals to the Brillouin frequency shift (∆ω = ΩB), then the signal pulse can be maximally advanced and the time advancement is expressed as follow
gBLe f f P ∆T = (4) ΓBAe f f
The pulse broadening factor B is written as [18]
1/2 τout 16(ln 2)G B = = 1 (5) τ − 2 2 in τinΓBAe f f where τin and τout are the full widths at half maximum of the input and output signal wave respectively. Longitudinal acoustic waves in optical fibers contain many different modes, according to the phase matching condition, the Brillouin frequency shift takes the form
ωa,i 2ne f f vi ΩB,i = = (6) 2π λp where ωa,i is the angular frequency of the i-order acoustic mode, vi is the effective sound velocity of the i-order acoustic mode and vi = ωa,i/βa, here βa is the longitudinal transmission constant of the acoustic wave and βa = 2βo, here βo is the transmission constant of the optical wave and βo = 2πne f f /λp, λp is the wavelength of the pump wave. The nonlinear coupling effect between the optical fundamental mode and the i-order acoustic mode can be expressed by the following overlap integral
R 2 2 E ui∗dxdy Ii = R | | R (7) E 4dxdy u 2dxdy | | | i| The relationship between the Brillouin absorption spectrum and the absorption coefficient can be expressed as 2 g0,iIi(ΓB/2) g (Ω) = (8) B,i 2 2 (Ω ΩB) + (ΓB/2) − where g0,i is the absorption coefficient of the i-order acoustic mode. The effective transmission length of the signal wave is L, and according to the Equation (4) the fast light group velocity can be figured out as
Lc vg = (9) Ln c∆T eff − where neff is the effective refractive index of the fiber. For simplicity, the main acoustic modes are taken into account and the Brillouin absorption coefficient of the i-order acoustic mode when Ω ΩB is expressed as [19,20] − 8 2 4πne f f p12 g = I (10) B,i 3 i cλpρ0ΓBΩB,i · Coatings 2020, 10, 1123 4 of 11
where p12 = 0.270 is the elasto-optical coefficient of the fiber and ρ0 is the density of the medium. The full width at half maximum ΓB of acoustic modes approximately equals 20 MHz [21,22]. Then the Equation (10) is substituted into the Equation (4), and the relationship between the time advancement and the Brillouin absorption coefficient can be obtained. When the value of the pump power is between the maximum pump power Pmax and the minimum pump power Pmin [23], the time advancement can be tailored by the pump power. Pmax and Pmin can be written as 21Ae f f Pmax = (11) gBLe f f
21Ae f f Pmin = α (12) gBLe f f where the absorption coefficient approximately keeps constant of 0.2 dB/km because of the narrow temperature range. The function of refractive index of liquid with temperature is
n(T) = n β(T T ) (13) 0 − − 0 where n0 is the refractive index of liquid at temperature T0, β is the thermo-sensitivity coefficient of liquid and for alcohol β is 3.94 10 4/ C, the refractive index n is 1.352 at the wavelength of 1550 nm × − ◦ 0 and temperature T0 = 20 ◦C, so the refractive index n(T) of alcohol for different temperature can be achieved. The longitudinal sound velocity vl can be expressed as s M(1 γ) v = − (14) l (1 + γ)(1 2γ)ρ − where M and γ respectively are the Young modulus and the Poisson ratio of materials, ρ is the density of fiber, these parameters and the refractive index n both are relate to material and temperature. When temperature changes from 20 ◦C to 70 ◦C, the relationships between M, γ, ρ and T satisfy the following Equation set (15) [24]. According to Equations (14) and (15), the longitudinal sound velocity can be obtained. 3 7 2 3 ρ = 2200.1704 4.0358 10− T + 3.86 10− T kg/m − × × M = 7.253 + 1.35 10 3T 1010 Pa − (15) × 5 × 8 2 γ = 0.169 + 4.515 10− T 0.65 10− T × − × n = 1.4435 + 2.1233 10 5T + 0.6 10 8T2 × − × − 3. Proposed Experimental Setup An experimental setup is proposed as shown in Figure1. The distributed feedback laser (DFB) is modulated by an electro-optical modulator (EOM) which works at the modulating ratio-frequency signal produced by signal generator, then the modulated signal pulse is amplified by the erbium-doped fiber amplifier (EDFA) and filtered by the fiber Bragg grating (FBG). One thousand of the filtered signal pulses output as the reference light by the optical coupler (OC), and the residual signal pulse is rejected into the SBS oscillation cavity through the circulator and induces the occurring of SBS in liquid-filled PCF, then the backward Stokes light occurs and propagates counterclockwise in the oscillation cavity. Here the frequency of the signal light is higher than the that of Stokes light and matches with ωas = ωp + ΩB, thus the Stokes light can be regarded as the pump light and the signal light acts as the anti-Stokes light whose pulse is advanced when transmitting along the liquid-filled PCF. The time advancement of the signal pulse can be obtained and measured by comparing the 10% output signal light from the OC-2 with the 1‰ input signal from the OC-1. The polarization of the signal light and the Stokes light are controlled by the polarization controller (PC) so as to achieve the Coatings 2020, 10, x FOR PEER REVIEW 5 of 12
（2200.1704 4.0358 103TT 3.86 10 7 2）kg/m 3
3 10 M 7.253 1.35 10T 10 Pa (15) 0.169 4.515 105TT 0.65 10 8 2 5 8 2 n1.4435 2.1233 10 T 0.6 10 T
3. Proposed Experimental Setup An experimental setup is proposed as shown in Figure 1. The distributed feedback laser (DFB) is modulated by an electro-optical modulator (EOM) which works at the modulating ratio-frequency signal produced by signal generator, then the modulated signal pulse is amplified by the erbium- doped fiber amplifier (EDFA) and filtered by the fiber Bragg grating (FBG). One thousand of the filtered signal pulses output as the reference light by the optical coupler (OC), and the residual signal pulse is rejected into the SBS oscillation cavity through the circulator and induces the occurring of SBS in liquid-filled PCF, then the backward Stokes light occurs and propagates counterclockwise in the oscillation cavity. Here the frequency of the signal light is higher than the that of Stokes light and
matches with ωasω p B , thus the Stokes light can be regarded as the pump light and the signal light acts as the anti-Stokes light whose pulse is advanced when transmitting along the liquid-filled
CoatingsPCF. The2020 ,time10, 1123 advancement of the signal pulse can be obtained and measured by comparing the5 of 10% 11 output signal light from the OC-2 with the 1‰ input signal from the OC-1. The polarization of the signal light and the Stokes light are controlled by the polarization controller (PC) so as to achieve the maximummaximum time time advancement advancement of of the the signal signal light. light. Due Due to the to dithefferent different refractive refractive index index of the of liquid-filled the liquid- PCFfilled at diPCFfferent at different temperatures, temperatures, the effective the mode effective field mode areas field and the areas Brillouin and the absorption Brillouin coe absorptionfficient arecoefficient different, are thus different, leading to thus the di leadingfferent time to the advancement different time of the advancement signal light, so of temperature the signal sensinglight, so cantemperature be implemented sensing by can varying be implemented the time advancement by varying the of the time signal advancement light. of the signal light.
Figure 1. The proposed experimental setup. DFB: distributed feedback laser; EDFA: erbium-doped fiberFigure amplifier; 1. The proposed OC: optical experimental coupler. setup. DFB: distributed feedback laser; EDFA: erbium-doped fiber amplifier; OC: optical coupler. 4. Numerical Simulation Results 4. NumericalThis section Simulation may be divided Results by subheadings. It should provide a concise and precise description of the experimentalThis section results, may be their divided interpretation by subheadings. as well asIt should the experimental provide a concise conclusions and thatprecise can description be drawn. of the experimental results, their interpretation as well as the experimental conclusions that can be 4.1. The Mode Field Distribution Coatingsdrawn. 20 20, 10, x FOR PEER REVIEW 6 of 12 The cross profile of the PCF which has four hexagonal rings of air-holes is shown in Figure2. d is the air filling factor (AFF). In this paper is 2.3 μm and d / is set as 0.6, 0.7 and 0.8 the4.1. air-hole The Mode diameter, Field DistributionΛ is the distance between adjacent two air-holes and d/Λ is defined as the air fillingrespectively factor (AFF).for different In this d. paper We setΛ is the2.3 pumpµm and powerd/Λ aiss set20 mW, as 0.6, the 0.7 pulse and 0.8width respectively of the signal for di wavefferent is The cross profile of the PCF which has four hexagonal rings of air-holes is shown in Figure 2. d d.200 We ns, set and the the pump wavelength power as of 20 the mW, pump the pulse wave width is 1550 of nm. the signalDue to wave the melting is 200 ns, point and the(−114 wavelength.3 °C ) and theis the boiling air-hole point diameter, (78.4 °C ) of aislcohol, the distance the sensing between temperature adjacent istwo set air between-holes and 20 °C d and/ 70 is °C defined for this as of the pump wave is 1550 nm. Due to the melting point ( 114.3 ◦C) and the boiling point (78.4 ◦C) of alcohol -filled fiber, and some key parameters for SBS fast −light are described at this temperature range alcohol, the sensing temperature is set between 20 ◦C and 70 ◦C for this alcohol-filled fiber, and some keyin this parameters paper. for SBS fast light are described at this temperature range in this paper.
FigureFigure 2.2. The cross profileprofile ofof thethe photonicphotonic crystalcrystal fiberfiber (PCF).(PCF). Figures3 and4 depict the fundamental mode distribution of optical field and acoustic field in the Figures 3 and 4 depict the fundamental mode distribution of optical field and acoustic field in filled and unfilled PCF when d/Λ is 0.8 and the sensing temperature is 20 C. It can be seen that the the filled and unfilled PCF when d / is 0.8 and the sensing temperature◦ is 20 °C. It can be seen filled and unfilled PCF have a greater difference on the distribution of the optical field and the acoustic that the filled and unfilled PCF have a greater difference on the distribution of the optical field and field, this is because the optical field is confined in the core of the PCF due to the index difference with the acoustic field, this is because the optical field is confined in the core of the PCF due to the index the air-holes. The acoustic field is confined in the core of the PCF. When the air-holes are filled with difference with the air-holes. The acoustic field is confined in the core of the PCF. When the air-holes are filled with alcohol, the index of the air-holes increases so the index difference between the core and the cladding decreases, then the restrictions on the optical field is reduced, so the optical field distribution in filled PCF is larger than that of the unfilled PCF.
(a) (b)
Figure 3. Distribution of optical fundamental mode in the proposed (a) filled and (b) unfilled PCF at 20 °C .
Coatings 2020, 10, x FOR PEER REVIEW 6 of 12 the air filling factor (AFF). In this paper is 2.3 μm and d / is set as 0.6, 0.7 and 0.8 respectively for different d. We set the pump power as 20 mW, the pulse width of the signal wave is 200 ns, and the wavelength of the pump wave is 1550 nm. Due to the melting point (−114.3 °C ) and the boiling point (78.4 °C) of alcohol, the sensing temperature is set between 20 °C and 70 °C for this alcohol-filled fiber, and some key parameters for SBS fast light are described at this temperature range in this paper.
Figure 2. The cross profile of the photonic crystal fiber (PCF).
Figures 3 and 4 depict the fundamental mode distribution of optical field and acoustic field in the filled and unfilled PCF when d / is 0.8 and the sensing temperature is 20 °C. It can be seen thatCoatings the2020 filled, 10, and 1123 unfilled PCF have a greater difference on the distribution of the optical field6 and of 11 the acoustic field, this is because the optical field is confined in the core of the PCF due to the index difference with the air-holes. The acoustic field is confined in the core of the PCF. When the air-holes arealcohol, filled the with index alcohol, of the the air-holes index of increases the air- soholes the increases index diff erenceso the index between difference the core between and the claddingthe core anddecreases, the cladding then the decreases, restrictions then on the opticalrestrictions field on is reduced,the optical so thefield optical is reduced, field distribution so the optical in filledfield distributionPCF is larger in than filled that PCF of is the larger unfilled than PCF. that of the unfilled PCF.
(a) (b)
Figure 3. DistributionDistribution of of optical optical fundamental fundamental mode mode in in the the proposed proposed ( (aa)) filled filled and and ( (b)) unfilled unfilled PCF at Coatings 2020, 10, x FOR PEER REVIEW 7 of 12 2200 °C◦C..
(a) (b)
Figure 4. Distribution ofof acousticacoustic fundamentalfundamental modemode in in the the proposed proposed (a ()a filled) filled and and (b ()b unfilled) unfilled PCF PCF at
at20 2◦0C. °C .
The variation of the effective effective refractive index of the the PCF PCF with with different different temperature temperature and different different AFF is shown in in Fig Figureure 55a.a. The The effective e ffective refractive refractive index index reduces reduces when when dd//Λ increasesincreases atat aa given temperature. Compared Compared to to the the change change of of quartz quartz index index with with different different temperature, the alcohol index changes largely and thus induce inducess varying of the difference difference of the eeffectiveffective refractive index for the differentdifferent temperatures.temperatures. FigureFigure5 b5b shows shows the the e ffeffectiveective mode mode field field area area varying varying with with temperature temperature in the in thefilled filled PCF. PCF. It can It be can seen be that seen the that larger the the largerd/Λ theis, thed / smaller is, the the e smallerffective mode the effective field becomes, mode field and whenbecomes, temperature and when goes temperature up the eff ectivegoes up mode the effecti field areave mode gradually field shrinksarea gradually because shrinks of the reducing because of the alcoholreducing index of the with alcohol temperature index with rising. temperature The effective rising. mode The field effective area variation mode field reaches area to variation2.75 µm whilereachesd/ toΛ is2.75 0.6 atμm the while temperature d / rangeis 0.6 ofat 20–70the temperature◦C. range of 20–70 °C .
16
1.426 15 d/=0.8
)
2 d/=0.7 14 d/=0.6
1.424 μm ( 13
1.422 12
11
1.420 10
1.418 d/=0.8 9 d/=0.7 8 d/=0.6 1.416 7
Effective mode area Effective refractive index 1.414 6 20 30 40 50 60 70 20 30 40 50 60 70 Temperature （℃） Temperature （℃）
(a) (b) Figure 5. (a) the effective refractive index and (b) the effective mode area vary with temperature.
4.2. The Brillouin Frequency Shift Figure 6 shows the variation of the effective acoustic velocity and the Brillouin frequency shift with temperature. It can be seen from Figure 6a that the effective acoustic velocity increases gradually with the rising of temperature, and there is a larger effective acoustic velocity corresponding with high , this is because the effective refractive index decreases with the rising of temperature or with the increasing of . Meanwhile these result in a small Brillouin frequency shift, which can also be seen from Figure 6b. The Brillouin frequency shift is different at about 11 GHz and the average difference per unit temperature is 1.15 MHz.
Coatings 2020, 10, x FOR PEER REVIEW 7 of 12
(a) (b)
Figure 4. Distribution of acoustic fundamental mode in the proposed (a) filled and (b) unfilled PCF at 20 °C .
The variation of the effective refractive index of the PCF with different temperature and different AFF is shown in Figure 5a. The effective refractive index reduces when d / increases at a given temperature. Compared to the change of quartz index with different temperature, the alcohol index changes largely and thus induces varying of the difference of the effective refractive index for the different temperatures. Figure 5b shows the effective mode field area varying with temperature in the filled PCF. It can be seen that the larger the d / is, the smaller the effective mode field becomes, and when temperature goes up the effective mode field area gradually shrinks because of the reducing of the alcohol index with temperature rising. The effective mode field area variation Coatings 2020, 10, 1123 7 of 11 reaches to 2.75 μm while d / is 0.6 at the temperature range of 20–70 °C .
16
1.426 15 d/=0.8
)
2 d/=0.7 14 d/=0.6
1.424 μm ( 13
1.422 12
11
1.420 10
1.418 d/=0.8 9 d/=0.7 8 d/=0.6 1.416 7
Effective mode area Effective refractive index 1.414 6 20 30 40 50 60 70 20 30 40 50 60 70 Temperature （℃） Temperature （℃）
(a) (b) Figure 5. (a) the effective refractive index and (b) the effective mode area vary with temperature. Figure 5. (a) the effective refractive index and (b) the effective mode area vary with temperature.
4.2.4.2. TheThe BrillouinBrillouin FrequencyFrequency ShiftShift FigureFigure6 6shows shows the the variation variation of of the the e effectiveffective acoustic acoustic velocity velocity andand thethe Brillouin Brillouin frequencyfrequency shiftshift withwith temperature. temperature. It It cancan bebe seenseen fromfrom FigureFigure6 6aa that that the the e effectiveffective acousticacoustic velocityvelocity increasesincreases graduallygradually withwith the the rising rising of of temperature, temperature, and and there there is ais larger a larger effective effect acousticive acoustic velocity velocity corresponding corresponding with highwith dhigh/Λ, this is because, this is thebecause effective the effective refractive refractive index decreases index decreases with the risingwith the of temperaturerising of temperature or with the or increasingwith the increasing of d/Λ. Meanwhile of . theseMeanwhile result inthese a small result Brillouin in a small frequency Brillouin shift, frequency which canshift, also which be seen can fromalso be Figure seen6 fromb. The Fig Brillouinure 6b. The frequency Brillouin shift frequency is di fferent shift at is aboutdifferent 11 GHzat about and 11 the GHz average and the diff averageerence Coatings 2020, 10, x FOR PEER REVIEW 8 of 12 perdifference unit temperature per unit temperature is 1.15 MHz. is 1.15 MHz.
6060
11.10 d/=0.8 6050 d/=0.8 d/=0.7 d/=0.7 d/=0.6 11.08 d/=0.6 6040
11.06
6030
11.04
6020
11.02
Effective velocity (m/s) 6010 11.00
Brillouin frequency shift (GHz)
6000 20 30 40 50 60 70 20 30 40 50 60 70 Temperature (℃) Temperature (℃)
(a) (b)
FigureFigure 6. 6.( a(a)) the the e effectiveffective velocity velocity ( b(b)) the the Brillouin Brillouin frequency frequency shift shift vary vary with with temperature. temperature.
4.3.4.3. The The Brillouin Brillouin Threshold Threshold BecauseBecause the the Brillouin Brillouin absorption absorption coeffi cient coefficient of the filled of the PCF filled is di fferent PCF at is di differentfferent temperatures, at different thetemperature Brillouin thresholds, the Brillouin value at threshold different temperatures value at different can be obtained temperature froms thecan Equations be obtained (11) andfrom (12). the Figure7 depicts the changes of Pmax and Pmin at different d/Λ and temperature. When d/Λ increases, Equations (11) and (12). Figure 7 depicts the changes of Pmax and Pmin at different d / and both Pmax,Pmin and their modifications reduce. Since larger d/Λ confine the transmission light into smallertemperature. regions When to reduce SBS increases, occurring inboth the area in, the PCF,and their and formodifications the same reason, reduce. the Since SBS occurs larger easily due confine to the the shrinking transmission of the light effective into modesmaller field regions area asto thereduce temperature SBS occurring rises. in The the simulation area in the resultPCF， showsand for that the the same range reason, of Pmax theis SBS from occurs 913 mW easily to 1137 due mWto the and shrinking the range of of thePmin effectiveis from mode 0.18 mWfield toarea 0.23 as mW the whiletemperature the effective rises. transmissionThe simulation length result is shows 10 m and thatd /theΛ isrange 0.6. of is from 913 mW to 1137 mW and the range of is from 0.18 mW to 0.23 mW while the effective transmission length is 10 m and is 0.6.
1200 0.24
d/=0.8 d/=0.8 1100 d/=0.7 0.22 d/=0.7 d/=0.6 d/=0.6 1000 0.20
900 0.18
(mw)
(mw)
min max 800 0.16
P
P
700 0.14
600 0.12
20 30 40 50 60 70 20 30 40 50 60 70 Temperature (℃) Temperature (℃)
(a) (b)
Figure 7. (a) Pmax and (b) Pmin vary with temperature.
4.4. The Temperature Response of the Fast Light The variations of the time advancement, the pulse broadening factor, the velocity and the time advancement sensitivity of the signal light are shown in Figure 8. From Figure 8a it can be seen that the time advancement of the signal light increases with higher temperature and larger AFF. When temperature rises and AFF becomes larger, the effective mode field area shrinks, more light beams are confined in the fiber core, and then the SBS is enhanced. As is 0.8, 0.7 and 0.6, the corresponding time advancement modifications of the signal light are 3.98 ns, 4.12 ns and 4.53 ns respectively. Obviously it is more sensitive for the time advancement modifications with the changes
Coatings 2020, 10, x FOR PEER REVIEW 8 of 12
6060
11.10 d/=0.8 6050 d/=0.8 d/=0.7 d/=0.7 d/=0.6 11.08 d/=0.6 6040
11.06
6030
11.04
6020
11.02
Effective velocity (m/s) 6010 11.00
Brillouin frequency shift (GHz)
6000 20 30 40 50 60 70 20 30 40 50 60 70 Temperature (℃) Temperature (℃)
(a) (b)
Figure 6. (a) the effective velocity (b) the Brillouin frequency shift vary with temperature.
4.3. The Brillouin Threshold Because the Brillouin absorption coefficient of the filled PCF is different at different temperatures, the Brillouin threshold value at different temperatures can be obtained from the
Equations (11) and (12). Figure 7 depicts the changes of Pmax and Pmin at different d / and temperature. When increases, both , and their modifications reduce. Since larger confine the transmission light into smaller regions to reduce SBS occurring in the area in the PCF，and for the same reason, the SBS occurs easily due to the shrinking of the effective mode field area as the temperature rises. The simulation result shows that the range of is from 913 mW to 1137 mW and the range of is from 0.18 mW to 0.23 mW while the effective transmission length Coatingsis 10 m2020 and, 10 , 1123 is 0.6. 8 of 11
1200 0.24
d/=0.8 d/=0.8 1100 d/=0.7 0.22 d/=0.7 d/=0.6 d/=0.6 1000 0.20
900 0.18
(mw)
(mw)
min max 800 0.16
P
P
700 0.14
600 0.12
20 30 40 50 60 70 20 30 40 50 60 70 Temperature (℃) Temperature (℃)
(a) (b)
Figure 7. (a) Pmax and (b) Pmin vary with temperature. Figure 7. (a) Pmax and (b) Pmin vary with temperature.
4.4.4.4. The The Temperature Temperature Response Response of of the the Fast Fast Light Light TheThe variations variations of of the the time time advancement, advancement, the the pulse pulse broadening broadening factor, factor, the the velocity velocity and and the the time time advancementadvancement sensitivity sensitivity of of the the signal signal light light are are shown shown in in Figure Figure8. 8. From From Figure Figure8a 8a it canit can be be seen seen that that thethe time time advancement advancement of of the the signal signal light light increases increases with with higher higher temperature temperature and and larger larger AFF. AFF. When When temperaturetemperature rises rises and and AFF AFF becomes becomes larger, larger, the the effective effective mode mode field field area area shrinks, shrinks, more more light light beams beams are confinedare confined in the fiberin the core, fibe andr core, then and the SBSthen is the enhanced. SBS is enhanced. As d/Λ is 0.8, As 0.7 and 0.6,is 0.8, the 0.7corresponding and 0.6, the timecorresponding advancement time modifications advancement of modifications the signal light of the are signal 3.98 ns, light 4.12 are ns 3.98 and ns, 4.53 4.12 ns ns respectively. and 4.53 ns Obviouslyrespectively. it is moreObviously sensitive it is formore the sensitive time advancement for the time modifications advancement with modifications the changes with of temperature the changes d d when the /Λ is small, but the time advancement is inferior to that of the fast light for large /Λ. The time advancement goes up to 36.52 ns at 70 ◦C while the d/Λ is 0.8. In Figure8b, the pulse broadening factor decreases with temperature increasing. Fast light transmission means the attenuation of the signal pulse: the more obvious the fast light is, the greater the pulse attenuation becomes. Figure8c shows the changes of the group velocity of the fast light with temperature. The group velocity gradually increases with the increase of temperature, and the variation range of the group velocity becomes larger for larger d/Λ. The figure shows the variation range is from 6.83 108 m/s to × 9.40 108 m/s while the d/Λ is 0.8, and it is from 3.45 108 m/s to 4.09 108 m/s while the d/Λ is × × × 0.6. This is because different d/Λ results in different effective refractive index and causes different group velocity. The sensitivity of the time advancement on temperature for different pump power is shown in Figure8d. It can be seen that the time advancement is linearly related to pump power, and as mentioned above, the more sensitive the time advancement becomes, the smaller the d/Λ is, as well as the higher the pump power is. As shown in this figure, the sensitivity of the time advancement is only 0.045 ns/◦C for the d/Λ of 0.6 and the pump power of 10 mW, but the sensitivity of the time advancement reaches to 0.272 ns/◦C at a pump power of 60 mW, so it is feasible to enhance the sensitivity of the time advancement by increasing pump power.
4.5. The Shape of the Output Signal Pulse Figure9 describes the normalized signal pulse shape of the fast light. The black curve illustrates the pulse of the input signal light whose width is 200 ns. It can be seen that the shapes of the output signal pulses are narrower than the input pulse shape. Because the signal pulses are compressed in the fast light process, and the compression is more easily distinguished because of the larger time advancement due to higher temperature in alcohol-filled PCF. The signal pulses at different temperature are nearly overlapped in unfilled PCF as shown in Figure9a, however they are clearly separated in the filled PCF as shown in Figure9b. Coatings 2020, 10, x FOR PEER REVIEW 9 of 12
of temperature when the d / is small, but the time advancement is inferior to that of the fast light for large . The time advancement goes up to 36.52 ns at 70 °C while the is 0.8. In Figure 8b, the pulse broadening factor decreases with temperature increasing. Fast light transmission means the attenuation of the signal pulse: the more obvious the fast light is, the greater the pulse attenuation becomes. Figure 8c shows the changes of the group velocity of the fast light with temperature. The group velocity gradually increases with the increase of temperature, and the variation range of the group velocity becomes larger for larger . The figure shows the variation range is from 6.83 × 108 m/s to 9.40 × 108 m/s while the is 0.8, and it is from 3.45 × 108 m/s to 4.09 × 108 m/s while the is 0.6. This is because different results in different effective refractive index and causes different group velocity. The sensitivity of the time advancement on temperature for different pump power is shown in Figure 8d. It can be seen that the time advancement is linearly related to pump power, and as mentioned above, the more sensitive the time advancement becomes, the smaller the is, as well as the higher the pump power is. As shown in this figure, the sensitivity of the time advancement is only 0.045 ns/°C for the of 0.6 and the pump power of 10 mW, but the sensitivity of the time advancement reaches to 0.272 ns/°C at a pump power of 60 mW, so it is Coatings 2020, 10, 1123 9 of 11 feasible to enhance the sensitivity of the time advancement by increasing pump power.
0.88 38 d/=0.8 d/=0.8 0.86 36 d/=0.7 d/=0.7 d/=0.6 34 0.84 d/=0.6
32 0.82
30 0.80
28
0.78 26 0.76 24 0.74 22
Pulse broading factor B
Time advancement (ns) 0.72 20
18 0.70
20 30 40 50 60 70 20 30 40 50 60 70 Temperature (℃) Temperature (℃)
(a) (b)
10 0.30
)
d/=0.8 ℃ d/=0.8 9 d/=0.7 0.25 d/=0.6 d/=0.7 8 d/=0.6 0.20
(m/s)
8
10 7
0.15
6
0.10 5
0.05
Group velocity 4
3 0.00 20 30 40 50 60 70 Time advancement sensitivity (ns/ 10 20 30 40 50 60 Temperature (℃) Pump power (mw)
Coatings 2020, 10, x FOR PEER( cREVIEW) (d) 10 of 12 FigureFigure 8. 8.( a()a) Time Time advancement, advancement, ( b(b)) pulse pulse broadening broadening factor factor and and ( c()c) group group velocity velocity of of signal signal light light temperaturevariesvaries with with are temperature. nearlytemperature. overlapped (d ()d Time) Time advancementin advancement unfilled PCF sensitivity sensitivity as shown varies varies in withFig withure pump pump 9a, power.however power. they are clearly separated in the filled PCF as shown in Figure 9b. 4.5. The Shape of the Output Signal Pulse Figure 9 describes the normalized signal pulse shape of the fast light. The black curve illustrates the pulse of the input signal light whose width is 200 ns. It can be seen that the shapes of the output signal pulses are narrower than the input pulse shape. Because the signal pulses are compressed in the fast light process, and the compression is more easily distinguished because of the larger time advancement due to higher temperature in alcohol-filled PCF. The signal pulses at different
(a) (b)
Figure 9. The output waveformwaveform ofof pulsepulse signal signal for for di differentfferent temperature temperature in in (a )(a ethanol-unfilled) ethanol-unfilled and and (b) (ethanol-filledb) ethanol-filled PCF. PCF.
5. Conclusion Conclusionss The sensing characteristics of of the the SBS fast light in liquid liquid-filled-filled PCF for different different temperaturestemperatures (20(20–70–70 ◦C)°C ) are are theoretically theoretically analyzed, analyzed, an index-guided an index-guided hexagonal hexagonal PCF is proposed PCF is and proposed an experimental and an experimentalsetup is proposed setup to is eproposedffectively to realize effectively temperature realize temperature sensing. From sensing. simulated From resultssimulated we knowresults that we knowthe liquid-filled that the liquid PCF-filled is more PCF sensitive is more tosensitive temperature to temperature than the unfilledthan the PCF. unfilled The PCF main. T reasonhe main is reasonthe temperature is the temperature sensitivity sensitivity on the refractive on the index refractive of liquid index which of liquid causes which remarkable causes remarkable changes of changesthe effective of the refractive effective index refractive of the index whole of PCF.the whole Some PCF. parameters Some parameters including the including effective the mode effective area, mode area, the Brillouin frequency shift, the SBS threshold value pump power and the SBS fast light parameters such as the time advancement, the pulse broadening factor and the group velocity are simulated for different temperature and different AFF in filled PCF. When the temperature rises from 20 °C to 70 °C , the Brillouin frequency shift, the time advancement and the group velocity of the signal light increase meanwhile the effective mode area and the pulse broadening factor decrease, and the variations of these parameters with temperature are similar to that with the AFF but opposite for the Brillouin frequency shift. The modification of the effective mode area with temperature is 2 2.72 μm when d / is 0.6. The Brillouin frequency shift is about 11 GHz within the temperature range of 20–70 °C and the average difference per unit temperature is 1.15 MHz. The effective transmission length is 10 m and is 0.6, the range of Pmax is from 913 mW to 1137 mW and the range of Pmin is from 0.18 mW to 0.23 mW, and the variation range of the group velocity is from 3.45 × 108 m/s to 4.09 × 108 m/s, meanwhile the modification of the time advancement is 4.53 ns, and while the is 0.8 the time advancement reaches to 36.52 ns at 70 °C . These results are of importance for designing fast-light temperature sensors, and future work will be focused on the investigation of larger time advancement and more sensitive sensing efficiency of SBS fast light by optimizing the structure of PCF or by filling other liquids with a bigger temperature coefficient in PCF.
Author Contributions: Conceptualization, J.L., S.N., and S.H.; methodology, J.L. and S.N.; validation, J.L. and S.N.; formal analysis, J.L.; investigation, J.L., S.N., and D.W.; writing—original draft preparation, S.N.; writing— review and editing, J.L. and S.H.; supervision, S.H.; project administration, X.L.; funding acquisition, S.H. All authors have read and agreed to the published version of the manuscript.
Funding: This work was supported in part by the National Natural Science Foundation of China (No. 61665005) and the HongLiu First-class Disciplines Development Program of Lanzhou University of Technology.
Conflicts of Interest: The authors declare no conflict of interest.
Coatings 2020, 10, 1123 10 of 11 the Brillouin frequency shift, the SBS threshold value pump power and the SBS fast light parameters such as the time advancement, the pulse broadening factor and the group velocity are simulated for different temperature and different AFF in filled PCF. When the temperature rises from 20 ◦C to 70 ◦C, the Brillouin frequency shift, the time advancement and the group velocity of the signal light increase meanwhile the effective mode area and the pulse broadening factor decrease, and the variations of these parameters with temperature are similar to that with the AFF but opposite for the Brillouin frequency shift. The modification of the effective mode area with temperature is 2.72 µm2 when d/Λ is 0.6. The Brillouin frequency shift is about 11 GHz within the temperature range of 20–70 ◦C and the average difference per unit temperature is 1.15 MHz. The effective transmission length is 10 m and d/Λ is 0.6, the range of Pmax is from 913 mW to 1137 mW and the range of Pmin is from 0.18 mW to 0.23 mW, and the variation range of the group velocity is from 3.45 108 m/s to 4.09 108 m/s, × × meanwhile the modification of the time advancement is 4.53 ns, and while the d/Λ is 0.8 the time advancement reaches to 36.52 ns at 70 ◦C. These results are of importance for designing fast-light temperature sensors, and future work will be focused on the investigation of larger time advancement and more sensitive sensing efficiency of SBS fast light by optimizing the structure of PCF or by filling other liquids with a bigger temperature coefficient in PCF.
Author Contributions: Conceptualization, J.L., S.N. and S.H.; methodology, J.L. and S.N.; validation, J.L. and S.N.; formal analysis, J.L.; investigation, J.L., S.N. and D.W.; writing—original draft preparation, S.N.; writing—review and editing, J.L. and S.H.; supervision, S.H.; project administration, X.L.; funding acquisition, S.H. All authors have read and agreed to the published version of the manuscript. Funding: This work was supported in part by the National Natural Science Foundation of China (No. 61665005) and the HongLiu First-class Disciplines Development Program of Lanzhou University of Technology. Conflicts of Interest: The authors declare no conflict of interest.
References
1. Hau, L.V.; Harris, S.E.; Dutton, Z.; Behroozi, C.H. Light speed reduction to 17 metres per second in an ultracold atomic gas. Nature 1999, 397, 594–598. [CrossRef] 2. Kash, M.M.; Sautenkov, V.A.; Zibrov, A.S.; Hollberg, L.; Welch, G.R.; Lukin, M.D.; Rostovtsev, Y.; Fry, E.S.; Scully, M.O. Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas. Phys. Rev. Lett. 1999, 82, 5229–5232. [CrossRef] 3. Chu, S.; Wong, S. Linear pulse propagation in an absorbing medium. Phys. Rev. Lett. 1982, 48, 738–741. [CrossRef] 4. Stenner, M.D.; Gauthier, D.J.; Neifeld, M.A. The speed of information in a ‘fast-light’optical medium. Nature 2003, 425, 695–698. [CrossRef] 5. Sharping, J.E.; Okawachi, Y.; Gaeta, A.L. Wide bandwidth slow light using a Raman fiber amplifier. Opt. Express 2005, 13, 6092–6098. [CrossRef][PubMed] 6. Okawachi, Y.; Bigelow, M.S.; Sharping, J.E.; Zhu, Z.; Schweinsberg, A.; Gauthier, D.J.; Boyd, R.W.; Gaeta, A.L. Tunable All-Optical Delays via Brillouin Slow Light in an Optical Fiber. Phys. Rev. Lett. 2005, 94, 153902. [CrossRef] 7. Dahan, D.; Eisenstein, G. Tunable all optical delay via slow and fast light propagation in a Raman assisted fiber optical parametric amplifier: A route to all optical buffering. Opt. Express 2005, 13, 6234–6249. [CrossRef]
8. Sinha, R.K.; Kumar, A.; Saini, T.S. Analysis and Design of Single-Mode As2Se3-Chalcogenide Photonic Crystal Fiber for Generation of Slow Light with Tunable Features. IEEE J. Sel. Top. Quantum Electron. 2015, 22, 287–292. [CrossRef] 9. Hassani, A.; Dupuis, A.; Skorobogatiy,M. Low loss porous terahertz fibers containing multiple subwavelength holes. Appl. Phys. Lett. 2008, 92, 071101. [CrossRef] 10. Pisco, M.; Ricciardi, A.; Campopiano, S.; Caucheteur, C.; Mégret, P.; Cutolo, A.; Cusano, A. Fast and slow light in optical fibers through tilted fiber Bragg gratings. Opt. Express 2009, 17, 23502–23510. [CrossRef] 11. Steinvurzel, P.; Eggleton, B.; De Sterke, C.M.; Steel, M.J. Continuously tunable bandpass filtering using high-index inclusion microstructured optical fibre. Electron. Lett. 2005, 41, 463. [CrossRef] Coatings 2020, 10, 1123 11 of 11
12. Han, T.; Liu, Y.; Wang, Z.; Zou, B.; Tai, B.; Liu, B. Avoided-crossing-based ultrasensitive photonic crystal fiber refractive index sensor. Opt. Lett. 2010, 35, 2061–2063. [CrossRef] 13. Geng, Y.; Li, X.; Tan, X.; Deng, Y.-L.; Hong, X. Compact and Ultrasensitive Temperature Sensor with a Fully Liquid-Filled Photonic Crystal Fiber Mach–Zehnder Interferometer. IEEE Sens. J. 2013, 14, 167–170. [CrossRef] 14. Monfared, Y.E.; Ponomarenko, S.A. Slow light generation via stimulated Brillouin scattering in liquid-filled photonic crystal fibers. Optik 2016, 127, 5800–5805. [CrossRef] 15. Song, S.; Jung, A.; Oh, K. High-Temperature Sensitivity in Stimulated Brillouin Scattering of 1060 nm Single-Mode Fibers. Sensors 2019, 19, 4731. [CrossRef] 16. Kalosha, V.P.; Chen, L.; Bao, X. Slow and fast light via SBS in optical fibers for short pulses and broadband pump. Opt. Express 2006, 14, 12693–12703. [CrossRef] 17. Kalosha, V.P.; Chen, L.; Bao, X. Slow light of subnanosecond pulses via stimulated Brillouin scattering in nonuniform fibers. Phys. Rev. A 2007, 75, 021802. [CrossRef] 18. Qin, G.; Sotobayashi, H.; Tsuchiya, M.; Mori, A.; Suzuki, T.; Ohishi, Y. Stimulated Brillouin Scattering in a Single-Mode Tellurite Fiber for Amplification, Lasing, and Slow Light Generation. J. Lightwave Technol. 2008, 26, 492–498. [CrossRef] 19. Cheng, T.; Liao, M.; Gao, W.; Duan, Z.; Suzuki, T.; Ohishi, Y. Suppression of stimulated Brillouin scattering in all-solid chalcogenide-tellurite photonic bandgap fiber. Opt. Express 2012, 20, 28846–28854. [CrossRef] 20. Dasgupta, S.; Poletti, F.; Liu, S.; Petropoulos, P.; Richardson, D.J.; Grüner-Nielsen, L.; Herstrøm, S. Modeling Brillouin Gain Spectrum of Solid and Microstructured Optical Fibers Using a Finite Element Method. J. Light. Technol. 2010, 29, 22–30. [CrossRef] 21. Hou, S.; Wen, B.; Li, H.; Liu, Y.; Wang, D.; Li, X.; Lei, J. Effects of SBS slow light on super-Gaussian pulses in fibers. Opt. Commun. 2014, 323, 13–18. [CrossRef] 22. Huang, M.; Huang, J. Temperature Dependence of Brillouin Scattering Spectrum for High Nonlinear Photonic Crystal Fiber. Opto Electron. Eng. 2011, 38, 6–10. 23. Jain, V.; Sharma, S.; Saini, T.S.; Kumar, A.; Sinha, R.K. Design and analysis of single-mode tellurite photonic crystal fibers for stimulated Brillouin scattering based slow-light generation. Appl. Opt. 2016, 55, 6791. [CrossRef][PubMed] 24. Zhao, L. Influence of environment temperature wide-range variation on Brillouin shift in optical fiber. Acta Phys. Sin. 2010, 59, 6219–6223.
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