hv photonics

Communication Femtosecond Fabricated Apodized Fiber Bragg Gratings Based on Energy Regulation

Qi Guo 1, Zhongming Zheng 2, Bo Wang 1, Xuepeng Pan 1, Shanren Liu 1, Zhennan Tian 1, Chao Chen 2 and Yongsen Yu 1,*

1 State Key Laboratory of Integrated Optoelectronics, College of Electronic Science and Engineering, Jilin University, 2699 Qianjin Street, Changchun 130012, China; [email protected] (Q.G.); [email protected] (B.W.); [email protected] (X.P.); [email protected] (S.L.); [email protected] (Z.T.) 2 Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China; [email protected] (Z.Z.); [email protected] (C.C.) * Correspondence: [email protected]

Abstract: In this paper, an energy regulation method based on the combination of a half-wave plate (HWP) and a polarization beam splitter (PBS) is proposed for the fabrication of apodized fiber gratings, which can effectively improve the side lobe suppression ratio of high-reflectivity fiber Bragg gratings (FBGs) fabricated by femtosecond laser. The apodized FBGs prepared by this method has good repeatability and flexibility. By inputting different types of apodization functions through the program, the rotation speed of the stepping motor can be adjusted synchronously, and then the position of the HWP can be accurately controlled so that the laser energy can be distributed as an apodization function along the axial direction of the fiber. By using the energy apodization method, the gratings with a reflectivity of 75% and a side lobe suppression ratio of 25 and 32 dB are

 fabricated in the fiber with a core diameter of 9 and 4.4 µm, respectively. The temperature and strain  sensitivities of the energy-apodized fiber gratings with a core diameter of 4.4 µm are 10.36 pm/◦C µε Citation: Guo, Q.; Zheng, Z.; Wang, and 0.9 pm/ , respectively. The high-reflectivity gratings fabricated by this energy apodization B.; Pan, X.; Liu, S.; Tian, Z.; Chen, C.; method are expected to be used in high-power narrow-linewidth and division Yu, Y. Femtosecond Laser Fabricated multiplexing (WDM) systems. Apodized Fiber Bragg Gratings Based on Energy Regulation. Photonics 2021, Keywords: half-wave plate; polarization beam splitter; apodized fiber gratings; energy apodization 8, 110. https://doi.org/10.3390/ photonics8040110

Received: 17 March 2021 1. Introduction Accepted: 5 April 2021 Fiber grating is a kind of grating formed by the axial periodic modulation Published: 7 April 2021 of the of the fiber core through a certain method, and it is a passive filter device [1]. Fiber Bragg grating (FBG) is a typical reflective device with wavelength Publisher’s Note: MDPI stays neutral selectivity. As an all-fiber device, FBG has been widely studied and applied due to its with regard to jurisdictional claims in advantages of low cost, fiber compatibility, and easy integration [2]. The uniform-period published maps and institutional affil- FBG, commonly called FBG, is one of the earliest and most widely used gratings. The iations. modulation depth of the refractive index and the grating period are constant, and the wave vector direction of the grating is consistent with the axial direction of the fiber [3,4]. This kind of gratings has an important application value in fiber lasers, fiber sensors, a dense wavelength division multiplexing (DWDM) system, and a high-speed fiber sensing Copyright: © 2021 by the authors. demodulation system [5–9]. There are many side lobes on both sides of the reflection Licensee MDPI, Basel, Switzerland. spectrum of a uniform FBG with high reflectivity, which is caused by Fabry–Perot cavity This article is an open access article resonance formed by an abrupt change of the refractive index at both ends of the grating. distributed under the terms and The existence of side lobes greatly reduces the wavelength selectivity of the FBG. At the conditions of the Creative Commons Attribution (CC BY) license (https:// same time, large side lobes in multiwavelength systems will cause crosstalk between creativecommons.org/licenses/by/ adjacent channels, reduce the side lobe suppression ratio, and require large wavelength 4.0/). intervals in channels. If the time delay oscillation is too large, the compensation

Photonics 2021, 8, 110. https://doi.org/10.3390/photonics8040110 https://www.mdpi.com/journal/photonics Photonics 2021, 8, 110 2 of 9

is not good, which will restrict the application of the fiber grating. In order to suppress the side lobes in the reflection spectrum and reduce the time delay oscillation, the refractive index modulation amplitude can be changed. The apodization method is adopted to make the refractive index modulation amplitude conform to the distribution effect of the apodization function, which can effectively suppress the side lobes and improve the side lobe suppression ratio [10]. Using an apodized phase mask to make apodized fiber gratings is the most traditional method for fabricating apodized fiber gratings [11,12]. This method is relatively simple, but it is difficult to make phase masks, different apodization gratings need different phase masks, and the cost is high. At the same time, the average refractive index modulation coefficient of the fiber gratings produced in this way is not constant, and the short-wave oscillation effect will appear. Femtosecond laser has the advantages of ultrashort pulse width and high peak power, which can be used as an excellent optical micro-nano processing method [13–15]. Based on the principle of multiphoton absorption, femtosecond laser can induce a permanent change of the refractive index in the transparent material [16,17], so the type II fiber gratings prepared by femtosecond laser have good temperature stability [18]. Femtosecond laser has important applications in the fabrication of high-temperature fiber gratings of quartz fiber and sapphire fiber [19,20]. The femtosecond laser point-by-point method has good flexibility and can be used to fabricate different types of gratings in different fibers [21–23]. Williams et al. proposed an oblique apodization method for preparing apodized FBGs, which was obtained by controlling the moving track of the fiber and changing the transverse position of the laser pulse modulation [24]. In this method, the refractive index modulation region is distributed obliquely in the core by using the point-by-point method, and the coupling efficiency at different positions of the core is adjusted to achieve the effect of apodization distribution of coupling strength. In this paper, a new method for preparing apodized FBGs by femtosecond laser is proposed. In this method, the energy of the femtosecond laser pulse can be adjusted in real time by combining a half-wave plate (HWP) and polarization beam splitter (PBS). By controlling the rotation angle and speed of the stepping motor through the program, and then adjusting the position of the HWP, the laser pulse energy can be accurately controlled, and the refractive index modulation amplitude can conform to the apodization function distribution so as to achieve the effect of apodized FBGs. This method is flexible in design and not limited by core diameter and grating length, and can be used to design and fabricate apodized FBGs with different parameters.

2. Principle and Methods The optical apodization of an FBG means that the amplitude of the photoinduced refractive index modulation in the grating is distributed along the axis of the fiber as a bell function. The coupling coefficient of this apodization envelope function is the largest at the center of the grating, and gradually decreases toward both ends, so that the refractive index variation amplitude at both ends of the FBG gradually tends to zero, which weakens the Fabry–Perot cavity resonance effect and reduces the side lobes of the FBG reflection spectrum. The FBG can be considered a periodic refractive index modulation region in the axial direction of the fiber under the action of periodic laser pulses. The photoinduced refractive index change ∆n inside the fiber core can be expressed by the following formula [25]:

2π ∆n = ∆n(z){1 + νcos[ z + ϕ(z)]} (1) Λ where ∆n(z) is the envelope function of refractive index change, ν is the fringe visibility of the index change, Λ is the grating period, and ϕ(z) describes the phase change of the grating. Photonics 2021, 8, x FOR PEER REVIEW 3 of 9

Photonics 2021, 8, 110 3 of 9 where ∆n(z) is the envelope function of refractive index change, ν is the fringe visibility of the index change, Λ is the grating period, and φ(z) describes the phase change of the grat- ing. TypicalTypical envelope envelope functions include include the the Gaussian Gaussian distribution distribution function, function, the the superGaus- super- Gaussiansian distribution distribution function, function, the rising the rising cosine cosine function, function and the, and Cauchy the Cauchy distribution distribution function. function.In this experiment, In this experiment, the Gaussian the Gaussian distribution distribution function function is taken asis taken an example as an example to make theto makecore refractivethe core refractive index modulation index modulation amplitude amplitude conform to conform the Gaussian to the distribution Gaussian distribu- function, tionand function, apodized and FBGs apodized are prepared. FBGs Theare prepared. Gaussian distributionThe Gaussian function distribution can be function expressed can by bethe expressed following by formula the following [25]: formula [25]:

2 −42ln4ln z2z2 ∆nn(z()()) z = ∆ n n expexp( ) (2(2)) e f feffe eff f f FWHMFWHM2 2 wherewhere FWHMFWHM isis full full width width at at half half maximum. maximum. AA device device diagram of of apodized apodized fiber fiber gratings gratings prepared prepared by the by femtosecondthe femtosecond laser laserpoint- pointby-point-by-point method method based based on energy on energy regulation regulation is shown is shown in Figure in Figure1. The 1. femtosecondThe femtosecond laser laser(light-conversion (light-conversion Pharos) Pharos) emits emits 1030 nm1030 laser nm with laser a with pulse a width pulse of width 290 fs of and 290 a repetitionfs and a repetitionfrequency frequency of 200 kHz. of 200 The kHz. 1030 The nm 1030 femtosecond nm femtosecond laser is frequency-doubled laser is frequency-doubled to a 515 nmto afemtosecond 515 nm femtosecond laser by alaser nonlinear by a nonlinear crystal (β -BaBcrystal2O 4(β) (BBO).-BaB2O The4) (BBO) 515 nm. The femtosecond 515 nm femto- laser secondis focused laser through is focused a 60 ×throughhigh numerical-aperture a 60× high numerical oil-immersion-aperture oil objective-immersion lens (Olympus,objective lensNA (Olympus, = 1.42) on NA the = center 1.42) on of the the center fiber coreof the placed fiber core on the placed five-dimensional on the five-dimensional processing processingplatform (Aerotech). platform (Aerotech).

FigureFigure 1. 1. SchematicSchematic diagram diagram of ofthe the device device for forfabricating fabricating apodized apodized FBGs FBGs based based on energy on energy regulation regula- method.tion method.

InIn this this way, way, the laserlaser pulsespulses can can be be focused focused on on a smallera smaller focal focal point, point, which which can can improve im- provethe processing the processing accuracy. accuracy. The laser The energylaser energy regulation regulation device device is included is included in the opticalin the opti- path. calThe path. HWP The is HWP fixed onis fixed the rotating on the r bracketotating ofbracket the stepping of the stepping motor controlled motor controlled by the program, by the program,and the laserand the polarization laser polarization can be changedcan be changed in real time.in real The time. laser The pulse laser energypulse energy can be canprecisely be precisely controlled controlled by the by combination the combination of the of PBS the withPBS with a high a high extinction extinction ratio. ratio. The laserThe laserpulse pulse energy energy corresponding corresponding to different to different angles angles of the HWPof the canHWP be accuratelycan be accurately calibrated cali- by brateda laser by power a laser meter power (OPHIR meter 10A-P). (OPHIR By inputting 10A-P). By an apodizationinputting an function apodization model function through modelthe program, through thethe laserprogram, pulse the energy laser canpulse be energy distributed can be as distributed a Gaussian as function a Gaussian along func- the tionfiber along axis. the The fiber rotating axis. speed The rotating of the stepping speed of motor the stepping can be synchronized motor can be with synchronized the moving withspeed the of moving the processing speed of platform the processing so that theplatform refractive so that index the modulationrefractive index amplitude modulation will be amplitudedistributed will as anbe apodizationdistributed as function an apodization in the middle function of the in fiberthe middle core, and of apodizedthe fiber core, FBGs andwith apodiz differented FBGs parameters with different can be flexiblyparameters prepared. can be flexibly prepared. 3. Design Results and Discussion 3. Design Results and Discussion 3.1. Spectral Comparison 3.1. Spectral Comparison The FBG phase matching condition is as follows [26]: The FBG phase matching condition is as follows [26]:

mλB = 2ne f f Λ (3)

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mnB2 eff (3)

where Λ is the grating period, neff is the effective refractive index, λB is the wavelength, where Λ is the grating period, neff is the effective refractive index, λB is the wavelength, and mandis them is grating the grating order. order. A second-order A second apodized-order apodized FBG is fabricatedFBG is fabricated in a 9 µm in core a 9 diameterμm core fiberdiameter with fiber a grating with perioda grating of 1.071periodµ mof and1.071 a μm central and wavelength a central wavelength of 1550 nm. of An1550 apodized nm. An FBGapodized is fabricated FBG is fabricated in a 4.4 µ min corea 4.4 diameterμm core diameter fiber with fiber a grating with a period grating of period 1.064 µofm 1.064 and aμm center and a wavelength center wavelength of 1030 nm.of 1030 Because nm. Because the center the wavelengthcenter wavelength is short, is theshort, grating the grat- is a third-ordering is a third apodized-order apodized FBG. FBG. The micrographs of apodized FBGs prepared byby oblique oblique apodization apodization and energy energy apodization methods are shown in Figure2 2.. FigureFigure2 a,b2a,b shows shows micrographs micrographs of of apodized apodized fiberfiber gratings prepared by different methods in the fiber fiber with a core diameter of 9 μm.µm. Figure2 2cc,d,d showsshows micrographsmicrographs ofof apodizedapodizedfiber fibergratings gratingsprepared prepared by by different different methods methods in the fiberfiber withwith a corecore diameterdiameter ofof 4.44.4 µμm.m. InIn orderorder toto makemake aa clearclear comparisoncomparison betweenbetween the two methods, thethe gratinggrating lengthlength isis selectedselected asas 5050 µμm.m. It can be seen from FigureFigure2 2 that that femtosecond laser pulses with ultrahigh peak power are focused on the fiberfiber corecore byby thethe point-by-pointpoint-by-point method to form a periodicperiodic refractiverefractive indexindex modulationmodulation region.region. The laserlaser spot size is aboutabout 500500 nm.nm. Figure 22aa,c,c presentspresents apodizedapodized FBGsFBGs preparedprepared byby anan oblique oblique apodization method, which keeps the laser energy unchanged and changes the transverse position of the laser pulse modulation by controlling the moving track of the the optical . fiber. Figure2 2bb,d,d showsshows apodizedapodized FBGs FBGs prepared prepared by by an an energy energy regulation regulation method. method. In In this this method, the laser pulsepulse energy needsneeds toto be adjusted in real time so that the refractive index modulation amplitude is distributed asas anan apodizationapodization functionfunction alongalong thethe fiberfiber axis.axis.

Figure 2. (a,b) shows micrographs of apodized fiber gratings fabricated by different methods in a Figure 2. (a,b) shows micrographs of apodized fiber gratings fabricated by different methods in a fiberfiber withwith aa corecorediameter diameter of of 9 9µ m.μm. (c (,cd,)d shows) shows micrographs micrographs of of apodized apodized fiber fiber gratings gratings fabricated fabricated by differentby different methods methods in ain fiber a fiber with with a core a core diameter diameter of 4.4 of µ4.4m. μm.

When preparing FBGs with the same reflectivity,reflectivity, thethe maximummaximum single-pulsesingle-pulse energyenergy required forfor preparingpreparing apodizedapodized FBGsFBGs isis largerlarger thanthan thatthat forfor uniformuniform FBGs.FBGs. ThisThis isis because the refractiverefractive indexindex modulationmodulation amplitudeamplitude of thethe apodizedapodized gratinggrating decreasesdecreases graduallygradually along bothboth endsends of of the the grating, grating, which which leads leads to theto the decrease decrease of the of averagethe average coupling coupling efficiency effi- ofciency the grating. of the grating. Therefore, Therefore, in order in to obtainorder to FBGs obtain with FBGs the samewith reflectivity,the same reflectivity, the maximum the single-pulsemaximum single energy-pulse needed energy to needed prepare to apodized prepare apodized FBGs will FBGs be higher. will be The higher. single-pulse The sin- energiesgle-pulse needed energies for needed preparing for prepa uniformring FBGs uniform and apodizedFBGs and FBGs apodized with FBGs a 75% with reflectivity a 75% arereflectivity 90 and 100are nJ90 (maximumand 100 nJ single-pulse(maximum single energy),-pulse respectively. energy), respectively. The length ofThe all length gratings of preparedall gratings is 4prepared mm. The is moving 4 mm. speedThe moving of the processing speed of the platform processing is 0.4284 platform mm/s, is and 0.4284 the timemm/s required, and the is time about required 10 s. is about 10 s. Three differentdifferent typestypes of of FBGs FBGs are are prepared prepared in ain single-mode a single-mode fiber fiber (Corning, (Corning, SMF-28e), SMF- and28e), a and spectral a spectral comparison comparison is shown is shown in Figure in Figure3a. The 3a. sideThe lobeside suppressionlobe suppression ratios ratio of thes of threethe three FBGs FBGs are 10, are 16, 10, and 16, 25and dB. 25 The dB. apodized The apodi gratingzed grating with a with higher a sidehigher lobe side suppression lobe sup- ratiopression is fabricated ratio is fabricated by an energy by an regulationenergy regulation method. method. The reflectivity The reflectivity and FWHM and FWHM of the apodizedof the apodized grating grating are 75% are and 75% 0.31 and nm, 0.31 respectively. nm, respectively. Figure Figure3b shows 3b shows the preparation the prepara- of apodizedtion of apodized FBG with FBG higher with reflectivityhigher reflectivit (>99%).y (>99%). The side The lobe side suppression lobe suppression ratios (SLSR) ratios before(SLSR) andbefore after and apodization after apodization are 8 and are 8 18 and dB, 18 respectively. dB, respectively. It can It be can seen be seen that that with with the increasethe increase of reflectivity, of reflectivity, the effectthe effect of side of side lobe lobe suppression suppression will bewill reduced. be reduced.

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(a) (b)

Figure 3. ((a)) Comparison Comparison of of a uniform uniform FBG spectrum spectrum and an apodized apodized FBG spectrum with a reflectivity reflectivity of 75% fabricated by two methods in fibers fibers with a core diameter of 9 μmµm.. ( b) Comparison of a uniform FBG spectrum and an apodized FBG spectrum with a reflectivityreflectivity of 99% fabricated by an energyenergy regulationregulation methodmethod inin fibersfibers withwith aa corecore diameterdiameter ofof 99µ μm.m.

ComparedCompared with with a a standard standard single single-mode-mode fiber, fiber, a thin core fiber fiber has a smaller cut-offcut-off wavelength andand cancan supportsupport shorter-wavelength shorter-wavelength light light to to realize realize single-mode single-mode transmission, transmis- sion,so it hasso it a has good a applicationgood application value invalue short-wavelength in short-wavelength laser. However, laser. However, the core the diameter core di- of ametera thin core of a fiber thin iscore small, fiber so is it issmall, more so challenging it is more tochallenging prepare apodized to prepare FBGs apodized with different FBGs withparameters. different FBGs parameters. have important FBGs have applications important in applications fiber lasers [ 27in, 28fib],er and lasers the [27,28] wavelength, and theof 1030 wavelength nm is a commonof 1030 nm laser is wavelength.a common laser As shownwavelength. in Figure As4 showna, three in different Figure 4a, types three of differentFBGs are types prepared of FBGs in a 4.4 areµ preparedm core diameter in a 4.4 fiber μm (Nuferncore diameter 780-HP) fiber by an(Nufern energy 780 regulation-HP) by anmethod. energy The regulation reflectivity method. of the The three reflectivity FBGs is 75%, of the and three the sideFBGs lobe is 75%, suppression and the ratiosside lobe are suppression10, 20, and 32 ratio dB,s respectively. are 10, 20, and The 32 FWHM dB, respectively. of the FBG The prepared FWHM by of thethe energyFBG prepared regulation by themethod energy is 0.18regulation nm. Figure method3b shows is 0.18 the nm. preparation Figure 3b shows of an apodized the preparation FBG with of aan reflectivity apodized FBGof over with 99%. a reflectivity The side lobeof over suppression 99%. The ratios side lobe before suppression and after ratio apodizations before areand 7 after and apodization22 dB, respectively. are 7 and 22 dB, respectively. Due to the smaller core diameter of a thin core fiber, the energy density of the optical field in the core is higher, and the coupling efficiency will be higher. Compared with the standard single-mode fiber, when the grating with the same reflectivity is prepared, the laser pulse energy needed to prepare the grating with the same reflectivity will be smaller. In the fiber with a core diameter of 4.4 µm, the single pulse energies required to prepare uniform FBGs and apodized FBGs with a reflectivity of 75% are 60 and 70 nJ (maximum single pulse energy), respectively. The length of all gratings prepared is 4 mm. The moving speed of the processing platform is 0.4256 mm/s, and the time required is about 10 s.

(a) (b) Figure 4. (a) Comparison of a uniform FBG spectrum and an apodized FBG spectrum with a reflectivity of 75% fabricated by two methods in fibers with a core diameter of 4.4 μm. (b) Comparison of a uniform FBG spectrum and an apodized FBG spectrum with a reflectivity of 99% fabricated by an energy regulation method in fibers with a core diameter of 4.4 μm.

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(a) (b) Figure 3. (a) Comparison of a uniform FBG spectrum and an apodized FBG spectrum with a reflectivity of 75% fabricated by two methods in fibers with a core diameter of 9 μm. (b) Comparison of a uniform FBG spectrum and an apodized FBG spectrum with a reflectivity of 99% fabricated by an energy regulation method in fibers with a core diameter of 9 μm.

Compared with a standard single-mode fiber, a thin core fiber has a smaller cut-off wavelength and can support shorter-wavelength light to realize single-mode transmis- sion, so it has a good application value in short-wavelength laser. However, the core di- ameter of a thin core fiber is small, so it is more challenging to prepare apodized FBGs with different parameters. FBGs have important applications in fiber lasers [27,28], and the wavelength of 1030 nm is a common laser wavelength. As shown in Figure 4a, three different types of FBGs are prepared in a 4.4 μm core diameter fiber (Nufern 780-HP) by an energy regulation method. The reflectivity of the three FBGs is 75%, and the side lobe suppression ratios are 10, 20, and 32 dB, respectively. The FWHM of the FBG prepared by

Photonics 2021, 8, 110 the energy regulation method is 0.18 nm. Figure 3b shows the preparation of an apodized6 of 9 FBG with a reflectivity of over 99%. The side lobe suppression ratios before and after apodization are 7 and 22 dB, respectively.

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Due to the smaller core diameter of a thin core fiber, the energy density of the optical field in the core is higher, and the coupling efficiency will be higher. Compared with the standard single-mode fiber, when the grating with the same reflectivity is prepared, the

laser pulse energy needed to prepare the grating with the same reflectivity will be smaller. (a) (b) In the fiber with a core diameter of 4.4 μm, the single pulse energies required to prepare Figure 4. (a) Comparison of uniform a uniform FBGs FBG spectrumand apodized and an FBGs apodized with FBG a reflectivity spectrum with of 75% a reflectivityreflectivity are 60 and of 75% 70 fabricatednJ (maximum by twotwo methodsmethods inin fibers fibers with withsingle a a core core pulse diameter diameter energy), of of 4.4 4.4 µresm. μm.pectively. (b )( Comparisonb) Comparison The length of aof uniform a of uniform all FBGgratings FBG spectrum spectrum prepared and anand is apodized 4an mm. apodized The FBG mov- spectrumFBG spectrum with awith reflectivity a reflectivitying of 99% speed of fabricated 99% of fabricated the byprocessing an energyby an energyplatform regulation regulation is method 0.425 method6 inm fibersm/s in, and withfibers the a corewith time diametera corerequired diameter of 4.4 is aboutµ m.of 4.4 10 s. μm. 3.2. Apodized FBG Temperature TestingTesting TheThe temperaturetemperature andand strainstrain characteristicscharacteristics ofof apodizedapodized FBGsFBGs preparedprepared inin anan opticaloptical fiberfiber withwith a corecore diameterdiameter of 4.4 µμmm areare testedtested byby combiningcombining a spectrometerspectrometer (Yokogawa,

AQ6370D),AQ6370D), broadbandbroadband light light source source (NKT (NKT Photonics), Photonics) and, and customized customized optical optical fiber fiber coupler. cou- First,pler. First, the grating the grating is annealed is annealed in a tube in a furnacetube furnace at 800 at◦ C800 for °C 3 h,for then 3 h, cooledthen cooled to room to room tem- perature,temperature, in order in order to eliminate to eliminate the internal the internal stress stress and unstable and unstable structure structure after femtosecond after femto- lasersecond processing. laser processing. Then, theThen, apodized the apodized grating grating is tested is againtested fromagain room from temperatureroom tempera- to 800ture◦ toC 800 with °C an with interval an interval of 100 of◦C. 100 Each °C . temperatureEach temperature point point is kept is kept for 30 for min, 30 min and, and the correspondingthe corresponding spectral spectral data data are are recorded. recorded. The The drift drift curve curve of of the the resonance resonance wavelengthwavelength withwith temperaturetemperature is is shown shown in in Figure Figure5. With5. With the the increase increase of temperature, of temperature, it shows it shows red shift red characteristics,shift characteristics, which which is consistent is consistent with thewith characteristics the characteristics of quartz of quartz FBGs. FBGs.

Figure 5.5. The reflectionreflection spectrumspectrum of of an an apodized apodized FBG FBG with with a corea core diameter diameter of of 4.4 4.4µm μm varies varies with with tem- perature.temperature.

The measured data are fitted linearly, and the fitting curve is shown in Figure 6. The temperature sensitivity of the apodized FBG is 10.36 pm/°C. The experimental results show that the apodized FBG has good temperature stability and can work stably at 800 °C.

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Photonics 2021, 8, x FOR PEER REVIEW The measured data are fitted linearly, and the fitting curve is shown in Figure6. The7 of 9 Photonics 2021, 8, x FOR PEER REVIEW ◦ 7 of 9 temperature sensitivity of the apodized FBG is 10.36 pm/ C. The experimental results show that the apodized FBG has good temperature stability and can work stably at 800 ◦C.

Figure 6.6. TheThe relationshiprelationship between between the the resonant resonant wavelength wavelength of of an an apodized apodized FBG FBG with with a core a core diameter diam- Figureeter of 6.4.4 The μm relationship and temperature. between the resonant wavelength of an apodized FBG with a core diam- of 4.4 µm and temperature. eter of 4.4 μm and temperature. 3.3. Apodized FBG Strain Testing 3.3. Apodized FBG Strain Testing The apodized apodized FBG FBG is is placed placed on on a stress-testing a stress-testing device device (WDW-100) (WDW- to100) prepare to prepare for strain for testing.strainThe testing. The apodized apodized The apodized FBG FBG is is placed FBG clamped is on clamped aon stress the testingon-testing the machinetesting device machine by (WDW the fiber -by100) the clamps, to fiber prepare andclamps, the for strainstressand the testing. applied stress Theapplied by theapodized testingby the FBGtesting machine is clampedmachine is controlled onis controlled the bytesting the by program.machine the program. by The the maximumThe fiber maximum clamps, test andstresstest thestress is stress 1 N,is 1 and appliedN, and the stresstheby the stress test testing intervaltest machineinterval is 0.1 is is N. 0.1controlled When N. When the by spectrumthe the spectrum program. is stable, is The stable, maximum record record the testcorrespondingthe correspondingstress is 1 N, spectral and spectral the data. stress data. The test The drift interval drift curve curve is of0.1 theof N. the resonanceWhen resonance the wavelengthspectrum wavelength is stable, with with stress record stress is theshownis shown corresponding in in Figure Figure7. spectral7. data. The drift curve of the resonance wavelength with stress is shown in Figure 7.

Figure 7. The reflection spectrum of an apodized FBG with a core diameter of 4.4 µm varies Figure 7. The spectrum of an apodized FBG with a core diameter of 4.4 μm varies with with strain. Figurestrain. 7. The reflection spectrum of an apodized FBG with a core diameter of 4.4 μm varies with strain. With thethe increaseincrease ofof stress,stress, thethe spectrumspectrum isis red-shifted.red-shifted. AxialAxial strainstrain εε cancan bebe obtainedobtained by thetheWith followingfollowing the increase formula:formula of stress,: the spectrum is red-shifted. Axial strain ε can be obtained by the following formula: ε = F/πr2E (4)   F/ π r2 E (4)   F/ π r2 E (4) where F is the axial stress, r is the fiber radius (r = 62.5 μm), and E is Young’s modulus (E where= 73 GPa). F is the The axial linear stress, relationship r is the fiber between radius the (r = resonance 62.5 μm), andwavelength E is Young and’s modulusstrain of (anE =apodized 73 GPa). FBG The is linear fitted relationship in Figure 8, andbetween the strain the resonance sensitivity wavelength is 0.9 pm/με. and strain of an apodized FBG is fitted in Figure 8, and the strain sensitivity is 0.9 pm/με.

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where F is the axial stress, r is the fiber radius (r = 62.5 µm), and E is Young’s modulus Photonics 2021, 8, x FOR PEER REVIEW 8 of 9 (E = 73 GPa). The linear relationship between the resonance wavelength and strain of an apodized FBG is fitted in Figure8, and the strain sensitivity is 0.9 pm/ µε.

Figure 8. The relationship between the resonant wavelength of an apodized FBG with a core diameter Figure 8. The relationship between the resonant wavelength of an apodized FBG with a core diam- of 4.4 µm and strain. eter of 4.4 μm and strain. 4. Conclusions 4. Conclusions In conclusion, a flexible and efficient method for fabricating apodized FBGs is pro- posed,In whichconclusion, is to controla flexible energy and efficient through method the combination for fabricating of an apodized HWP and FBGs PBS. is Thepro- steppingposed, which motor is isto controlledcontrol energy by a through program, the and combination the position of an of theHWP HWP and isPBS. rotated The step- syn- chronouslyping motor tois adjustcontrolled the energyby a program, size. In differentand the position core diameter of the fibers,HWP theis rotated point-by-point synchro- methodnously isto used adjust to make the energy the core size. refractive In different index modulation core diameter distributed fibers, the as anpoint apodization-by-point function.method is The used spectral to make effects the ofcore apodized refractive fiber index gratings modulation fabricated distributed by oblique as apodizationan apodiza- andtion energyfunction. apodization The spectral methods effects areof apodized compared. fiber When gratings the energy fabricated apodization by oblique method apodi- is usedzation to and fabricate energy apodized apodization fiber gratings, methods it are does compared. not need to When change the the energy processing apodiza trajec-tion torymethod obliquely, is used so to the fabricate design apodized is more flexible fiber gratings, and better it does spectral not qualityneed to canchange be obtained. the pro- Incessing particular, trajectory apodized obliquely, FBGs so with the adesign 75% reflectivityis more flexible and aand 32 dBbetter side spectral lobe suppression quality can ratiobe obtained. are fabricated In particular, in a 4.4 µapodizedm core diameter FBGs with fiber. a The75% temperaturereflectivity and sensitivity a 32 dB and side strain lobe sensitivitysuppression are ratio 10.36 are pm/ fabricated◦C and in 0.9 a 4.4 pm/ μmµε core, respectively. diameter fiber. The The apodized temperature fiber gratingssensitiv- fabricatedity and strain by thissensitivity method are have 10.36 potential pm/°C and applications 0.9 pm/με in, respectively. high-power The narrow-linewidth apodized fiber lasersgratings and fabricated wavelength by this division method multiplexing have potential (WDM) applicat systems.ions in high-power narrow-lin- ewidth lasers and wavelength division multiplexing (WDM) systems. Author Contributions: Conceptualization, Q.G. and Z.Z.; methodology, Q.G.; software, Q.G. and X.P.; formalAuthor analysis, Contribution C.C. ands: Conceptualization, Z.T.; data curation, Q.G.,Q.G. and S.L. andZ.Z.; B.W.; methodology, writing—original Q.G.; software, draft preparation, Q.G. and Q.G.;X.P.; f writing—reviewormal analysis, C.C. and and editing, Z.T.; Y.Y. data All curation, authors Q.G., have readS.L. and and B.W.; agreed w toriting the— publishedoriginal draft version prep- of thearation, manuscript. Q.G.; writing—review and editing, Y.Y. All authors have read and agreed to the published version of the manuscript. Funding: National Natural Science Foundation of China (91860140, 62090064, 61874119); Science and TechnologyFunding: National Development Natural Project Science of JilinFoundation Province of (20180201014GX). China (91860140, 62090064, 61874119); Science and Technology Development Project of Jilin Province (20180201014GX). Institutional Review Board Statement: Not applicable. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: The data presented in this study are available on request from the correspondingData Availability author. Statement: The data presented in this study are available on request from the corresponding author. Acknowledgments: This work is supported by the National Natural Science Foundation of China (91860140,Acknowledgments: 62090064, 61874119)This work and is supported the Science by and the Technology National Natural Development Science Project Foundation of Jilin Provinceof China (20180201014GX).(91860140, 62090064, 61874119) and the Science and Technology Development Project of Jilin Prov- ince (20180201014GX). Conflicts of Interest: The authors declare no conflict of interest. Conflicts of Interest: The authors declare no conflicts of interest.

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Photonics 2021, 8, 110 9 of 9

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