sensors

Review Ultrafast Processing of Optical Fibers for Sensing Applications

Stephen J. Mihailov 1,* , Cyril Hnatovsky 1, Nurmemet Abdukerim 2 , Robert B. Walker 1, Ping Lu 1, Yanping Xu 3, Xiaoyi Bao 4, Huimin Ding 1, Manny De Silva 1, David Coulas 1 and Dan Grobnic 1

1 National Research Council Canada, 100 Sussex Drive, Ottawa, ON K1A 0R6, Canada; [email protected] (C.H.); [email protected] (R.B.W.); [email protected] (P.L.); [email protected] (H.D.); [email protected] (M.D.S.); [email protected] (D.C.); [email protected] (D.G.) 2 Infinera Canada Inc., 555 Legget Dr., Ottawa, ON K2K 2X3, Canada; nabdukerim@infinera.com 3 Center for Optics Research and Engineering, Shandong University, Qingdao 266237, China; [email protected] 4 Physics Department, University of Ottawa, 25 Templeton Street, Ottawa, ON K1N 6N5, Canada; [email protected] * Correspondence: [email protected]; Tel.: +1-613-998-2721

Abstract: A review of recent progress in the use of infrared femtosecond to fabricate optical fiber sensors that incorporate fiber Bragg gratings (FBG) and random fiber gratings (RFG) is presented. The important advancements in femtosecond laser writing based on the phase mask technique now allow through-the-coating (TTC) fabrication of Bragg gratings in ultra-thin fiber filaments, tilted fiber Bragg gratings, and 1000 ◦C-resistant fiber Bragg gratings with very strong cladding modes. As an example, through-the-coating femtosecond laser writing is used to manufacture distributed   fiber Bragg grating sensor arrays for oil pipeline leak detection. The plane-by-plane femtosecond laser writing technique used for the inscription of random fiber gratings is also reviewed and novel Citation: Mihailov, S.J.; Hnatovsky, applications of the resultant devices in distributed temperature sensing, fiber lasers and fiber laser C.; Abdukerim, N.; Walker, R.B.; Lu, P.; Xu, Y.; Bao, X.; Ding, H.; De Silva, sensors are discussed. M.; Coulas, D.; et al. Ultrafast Laser Processing of Optical Fibers for Keywords: fiber Bragg gratings; random fiber gratings; femtosecond laser; fiber optic sensor Sensing Applications. Sensors 2021, 21, 1447. https://doi.org/10.3390/ s21041447 1. Introduction Academic Editor: Bernhard High-power near infrared (IR) ultrafast laser systems, such as femtosecond (fs) regen- Wilhelm Roth eratively amplified Ti:sapphire lasers, proved themselves to be effective tools for machining Received: 24 December 2020 of optical fibers for sensing applications [1]. The ultra-high intensity radiation that can Accepted: 17 February 2021 be generated by these laser sources is effective in modifying dielectric materials either Published: 19 February 2021 through ablative processes on the surface or by the induction of large index changes in the bulk. Focused beam intensities of over 1013 W/cm2 are easily realized and are sufficient Publisher’s Note: MDPI stays neutral to initiate nonlinear light absorption in the optical fiber glass during the laser pulse [2,3]. with regard to jurisdictional claims in This highly localized energy deposition produces an electron plasma within the focal published maps and institutional affil- volume which after several picoseconds transfers its energy to the bulk material. This, in iations. turn, leads to permanent material modification such as compaction and/or defect forma- tion, localized melting, and formation of nanogratings [4,5] or voids [6,7]. The specific kind of material modification depends on the intensity of the laser pulse and other laser irradiation conditions. Copyright: © 2021 by the authors. Over the past two decades, fs laser systems have been extensively used to manufacture Licensee MDPI, Basel, Switzerland. temperature and strain sensors based on fiber Bragg gratings (FBG) [8], improved optical This article is an open access article frequency domain reflectometers (OFDR) using fibers with randomly positioned scattering distributed under the terms and sites [9], complex bend sensors based on waveguide inscription in fiber claddings [10,11], conditions of the Creative Commons or for direct machining of innovative biosensors [12]. Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ This review paper will be divided into two broad themes. First, we will summarize 4.0/). recent work from our laboratories on fs laser processing of optical fibers to produce FBGs

Sensors 2021, 21, 1447. https://doi.org/10.3390/s21041447 https://www.mdpi.com/journal/sensors Sensors 2021, 21, 1447 2 of 23

directly through protective polymer coatings of fibers using the phase mask technique and how the resultant devices have been applied for environmental sensing. Second, we will discuss our recent advances in engineering random fiber gratings (RFGs) using fs lasers and the plane-by-plane technique and how these fiber optic devices have been implemented into the design of light sources and sensors.

2. Through-the-Coating Fiber Bragg Gratings 2.1. vs. Infrared Femtosecond Irradiation Optical filter technology based on FBGs is well established in the fields of telecommu- nications and sensing. Originally, FBGs were manufactured by exposing the - doped (Ge-doped) core of silica (SiO2) telecommunications fiber to periodically modulated high intensity ultraviolet (UV) laser radiation. In such cases, the induced index change and modulation pattern in the core of the fiber results from color center formation [13] and localized compaction of the glass matrix [14]. From a manufacturing perspective, grating inscription with UV lasers is limited to Ge-doped fibers that often need to be photosensi- tized by processes such as hydrogen loading (H2-loading), or the presence of extremely high Ge-concentrations in the silica fiber core. Furthermore, because protective polymer coatings on commercially available optical fibers typically absorb UV light, coating removal and reapplication before and after grating inscription, respectively, become necessary pro- cessing steps. Finally, stability of the photo-induced index change has to be assured by annealing the device at temperatures above its normal operating temperature. In this way, unstable color centers that contribute to the overall index change are removed [15]. For fs-laser-written FBGs (fs-FBG) the nature of induced index change is different [4–7]. Gratings can be fabricated with fs lasers in any optical fiber that is transparent to the low-signal IR light and are therefore not reliant on the presence of a specific dopant. The inscription process does not require enhancement of fiber photosensitivity, such as by H2-loading, and can be carried out directly through protective polymer coatings. All of the exotic Bragg grating structures that have been fabricated with UV laser systems in photosensitive telecommunications fibers, such as chirped gratings, phase shifted gratings, apodized gratings, gratings with suppressed cladding modes, and tilted or blazed gratings, can also be fabricated with fs lasers using similar processes.

2.2. Point-by-Point Femtosecond FBG Inscription Process Fs-FBGs have been fabricated by either using the point-by-point (PbP) technique or the phase mask technique. The PbP approach involves the focusing of single fs laser pulses into the core region of the fiber using a high numerical aperture (high-NA) microscope objective. Each pulse makes highly localized changes to the that are seen by the propagating mode(s) in the optical fiber as a FBG ‘plane’. Points are created sequentially in a step-and-repeat fashion by translating the beam using high resolution mechanical translation stages [16]. Through-the-coating (TTC) FBG inscription was first demonstrated using the PbP technique [17]. The advantages of this approach come from the versatility of the grating structure that can be created as it relies solely on the positioning of the focal spot within the fiber and control of the precision translation. Because the fs pulse is highly focused, lower power fs sources can be used, such as high-power oscillators or femtosecond fiber laser sources rather than a regeneratively amplified source. The major disadvantage of this approach is that it is not well-suited for mass production of identical structures.

2.3. Phase Mask Technique for Femtosecond FBG Inscription The phase mask is a diffractive optical element, specifically a transmission grating. It is especially made using microfabrication techniques whereby the grating pattern, produced either holographically or by electron beam lithography, is precisely etched into a silica substrate. To minimize the transmission of zero order diffraction, the etch depth of the grating pattern is approximately equal to the laser that will be used to illuminate the mask and create the Bragg grating pattern in a fiber [18]. Despite Sensors 2021, 21, 1447 3 of 23

its seeming simplicity, the phase mask technique exhibits several characteristic effects that originate from the presence of a strongly dispersive optical element (i.e., the phase mask) in the beam path. Some of these effects will be briefly discussed in the following subsections. The use of a phase mask for FBG inscription using UV lasers, such as KrF systems, has been very successful from an industrial perspective [13]. The phase mask automatically matches path lengths of diffracted interfering beams (±1 diffraction orders) significantly reducing alignment tolerances as compared to bulk interferometers. This aspect is especially important when FBG inscription is performed with (i) excimer laser systems that have spatial coherence on the order of ~100 µm, which requires the path lengths of interfering beams to be matched to that level or (ii) fs lasers, which also requires similar levels of path length matching, e.g., 30 µm for a 100 fs pulse. Even though the phase mask technique generally allows for mass production of identical FBGs, there are several additional factors that need to be considered when fs lasers are used instead of nanosecond or continuous wave UV lasers for FBG inscription. For the FBG inscription process used in our experiments, the laser source was a Coherent Libra Ti:sapphire regenerative amplifier operating at a wavelength λ0 = 800 nm and a repetition rate of 1 kHz. The Fourier transform limited pulse duration of this laser source was 80 fs which corresponds to a spectral bandwidth of ∆λ = 12 nm. The output 2 beam radius (at the 1/e -intensity level) of the laser source was w0 ~3.5 mm. The exposure setup shown schematically in Figure1, used a holographically patterned reactive ion etched silica phase mask that was precision etched to minimize zero order transmission at 800 nm. According to the manufacturer (Ibsen), the mask had a period d = 1.071 µm with a 0.01 nm period accuracy and uniformity. The thickness of the Ibsen mask substrate was t = 2.1 mm. The laser beam was focused with plano-convex acylindrical lenses (from Asphericon) made of OHARA S-LAH64 glass. The focal length of the lenses was either f = 12 mm or f = 15 mm with the respective clear aperture being 15 mm × 15 mm and 18 mm × 18 mm. The curved surface was designed to correct spherical aberration in one dimension. Transmission spectral measurements of fabricated FBGs were taken using a tunable laser and power meter with a spectral resolution of 10 pm.

2.3.1. Longitudinal and Transverse Walk-Off When a fs pulse is focused by a cylindrical lens and then passes through a phase mask −1 at normal incidence, it is diffracted at angles θm = sin (mλ0/d), where λ0 is the central wavelength of the fs pulse, d is the mask pitch and m is the diffraction order number. The phase fronts of the resulting diffracted fs pulses are normal to their propagation direction. The short time duration of the laser pulse results in longitudinal walk-off ∆L [19] of the diffracted pulses belonging to different diffraction orders as they propagate away from the mask, see Figure1[20]. At a distance L from the mask, a pure two-beam interference pattern produced by the +m and −m diffracted orders will be observed when the following condition is satisfied [20]:

 −1  2 cos sin (mλo/d) λo L ≥     (1) ∆λ −1 −1 cos sin ((m − 1)λo/d) − cos sin (mλo/d)

where ∆λ is the FWHM bandwidth of the fs pulse and m is assumed to be positive. Equation (1) can be derived by equating the longitudinal walk-off L of the femtosecond pulses diffracted into different orders and the FWHM of the field autocorrelation function of the pulses. The resulting interference pattern for the ±1 orders has a pitch that is half of that of the phase mask, i.e., d/2. Near the mask, interference of multiple orders (0, ±1, ±2, etc.) creates a Talbot pattern [19,21–23]. There is also transverse walk-off ∆T of the laterally overlapping ±m orders, which at a distance L from the mask is given by ∆T = 2 L tan (θm). Sensors 2021, 21, x FOR PEER REVIEW 4 of 25 Sensors 2021, 21, 1447 4 of 23

Figure 1.Figure Interference 1. Interference of fs pulses of fsdiffracted pulses diffracted by a phase by mask a phase that mask produces that four produces diffraction four diffraction orders orders (m = 0 to( m3).= M 0 todenotes 3). M thedenotes phase the mask, phase CL mask, is theCL cylindricalis the cylindrical lens, ΔT is lens, the ∆transverseT is the transverse walk-off, walk-off, ΔL ∆L is is the longitudinalthe longitudinal walk-off, walk-off, L is theL isdistance the distance from M from to theM toobservation the observation point point(O), l is (O the), l isdistance the distance from from M Mto theto the pulse pulse front front of ofthe the 0th 0thdiffraction diffraction order. order. The The pulse pulse phase phase fronts fronts are are normal normal to the to the propagation propagationdirection direction of the ofrespective the respective diffraction diffraction orders orders [20]. [20].

At2.3.2. a distance Focal L Spot from Minimization the mask, a pure two-beam interference pattern produced by the +m and −Inm diffracted addition toorders the above will be geometrical observed when effects the offollowing the interaction condition between is satisfied the fs pulse [20]: and the phase mask, chromatic diffraction and aberration effects need to be considered, especially in the context2 of tight focusing−1 geometries and small-pitch phase masks. The 휆표 cos(sin (푚휆표⁄푑)) impacts of these퐿 ≥ effects are−1 rigorously analyzed by− Abdukerim1 et al. [20]. It(1 should) be Δ휆 cos(sin ((푚 − 1)휆표⁄푑)) − cos(sin (푚휆표⁄푑)) noted that for the experiments in [20] the authors introduced an interference filter in the where Δbeamλ is the to reduceFWHMthe bandwidth original ∆ofλ thefrom fs pulse 12 nm and to 6m nm. is assumed to be positive. Equa- tion (1) can beThe derived impact by of equating angular the chromatic longitudinal walk-off of theL of broadband the femtosecond fs pulse pulses by the phase diffractedmask into and different chromatic orders aberration and the ofFWHM the cylindrical of the field lens autocorrelation used to focus function the pulse of onto the the fiber pulses. coreThe resulting results in interference an elongation pattern of the for focal the spot ±1 orders along thehas opticala pitchaxis. that Itis washalf shownof that [20] that of the phasethis elongation mask, i.e., (d∆/2.zcm Near) can the be mask, expressed interference as: of multiple orders (0, ±1, ±2, etc.) creates a Talbot pattern [19,21–23]. There is also transverse walk-off ΔT of the laterally 2 overlapping ±m orders, which at a distance L from them maskλ L∆ λis given by ΔT = 2 L tan (θm). ∆z = 0 (2) cm 2 2 2 d − m λ0 2.3.2. Focal Spot Minimization In additionThis to results the above in the geometrical ‘red’ light focus effects appearing of the interaction closer to thebetween phase the mask fs pulse thanthe ‘blue’ and thelight phase focus. mask, The chromatic cylindrical diffraction lens also and introduces aberration focal effects elongation need to but, be inconsidered, this case, the ‘blue’ especiallyspectral in the component context of tight of the focusing pulse is geometries focused closer and tosmall the-pitch mask phase than themasks. ‘red’ The component. impactsThe of these elongation effects of are the rigorously focus after analyzed the phase by mask Abdukerim due to chromaticet al. [20]. aberrationIt should be of the lens noted that(∆z clfor) can the be experiments expressed asin [[20]20,24 the]: authors introduced an interference filter in the beam to reduce the original Δλ from 12 nm to 6 nm.   f cos(θm) dn The impact of angular chromatic∆ dispersionz = − of the broadbandl ∆λ fs pulse by the phase (3) cl n − 1 dλ mask and chromatic aberration of the cylindrical lensl used to focus the pulse onto the fiber core results in an elongation of the focal spot along the optical axis. It was shown [20] that where f is the focal length of the lens and nl is the refractive index of the lens. Thus, ∆zcm this elongation (Δzcm) can be expressed as: can in principle be counteracted by ∆zcl (see Figure2[20]). 2 푚 휆0퐿Δ휆 ∆푧푐푚 = 2 2 2 (2) 푑 − 푚 휆0

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ThisThis results results in the in ‘red’the ‘red’ light light focus focus appearing appearing closer closer to the to phasethe phase mask mask than than the ‘blue’the ‘blue’ lightlight focus. focus. The Thecylindrical cylindrical lens lens also also introduces introduces focal focal elongation elongation but, but, in this in thiscase, case, the ‘blue’the ‘blue’ spectralspectral component component of the of pulsethe pulse is focused is focused closer closer to the to maskthe mask than than the ‘red’the ‘red’ component. component. The Theelongation elongation of the of focusthe focus after after the phasethe phase mask mask due dueto chromatic to chromatic aberration aberration of the of lensthe lens (Δzcl) can be expressed as [20,24]: (Δzcl) can be expressed as [20,24]:

푓 cos(휃푚) 푑푛푙 푓 cos(휃푚) 푑푛푙 Δ푧푐푙Δ=푧 −= − ( () Δ휆) Δ휆 (3) (3) 푐푙 푛푙 − 1 푑휆 푛푙 − 1 푑휆 Sensors 2021, 21, 1447 5 of 23 here f is the focal length of the lens and nl is the refractive index of the lens. Thus, Δzcm w where f is the focal length of the lens and nl is the refractive index of the lens. Thus, Δzcm can in principle be counteracted by Δzcl (see Figure 2 [20]). can in principle be counteracted by Δzcl (see Figure 2 [20]).

Figure 2. Focal elongation caused by chromatic dispersion of the mask Δzcm (a) and chromatic aberration of the cylindrical FigureFigure 2.2. Focal elongation causedcaused byby chromaticchromatic dispersiondispersion ofof thethe maskmask∆ Δzzcmcm (a) and chromatic aberration ofof thethe cylindricalcylindrical lens Δzcl (b). In (a), Δθ1 is the angular spread of the spectrum of the 1st diffraction order corresponding to a pulse bandwidth lens Δzcl (b). In (a), Δθ1 is the angular spread of the spectrum of the 1st diffraction order corresponding to a pulse bandwidth lens ∆zcl (b). In (a), ∆θ1th is the angularst spread of the spectrum of the 1st diffraction order corresponding to a pulse bandwidth Δλ. For clarity, only the 0 andth 1 diffractionst orders are considered. Please note that ‘red’ light is focused closer to M in ∆Δλλ.. For clarity,clarity, onlyonly thethe 0th0 and 1st1 diffraction diffraction orders orders are are considered. considered. Please Please note note that that ‘red’ light is focused closer toto MM inin (a) and(a) andfarther farther from from M in M (b in). (b). (a) and farther from M in (b). In cases where tight focusing of the fs laser beam is required, such as for TTC inscrip- In cases where tight focusing of the fs laser beam is required, such as for TTC inscrip- inscrip- tion of FBGs [25–28], additional effects resulting from conical diffraction of the mask and tion of FBGs [[2525–2828],], additional effects resultingresulting fromfrom conicalconical diffractiondiffraction ofof thethe maskmask andand spherical aberration introduced by the mask substrate need to be considered. spherical aberration introduced byby thethe maskmask substratesubstrate needneed toto bebe considered.considered. Abdukerim et al. showed that the focal elongation due to spherical aberration intro- Abdukerim et al. showed that the focal elongation due to spherical aberration intro- duced by the phase mask substrate can be written after the phase mask as [20]: duced by the phase mask substrate cancan bebe writtenwritten afterafter thethe phasephase maskmask asas [[20]:20]: 2 2 (푛푠 −1)2푡 cos(휃푚)휑 2 (푛푠 −1)푡 cos(휃푚)휑 Δ푧푠푎푠Δ푧= =n2 − t3 (θ ) ϕ 2 (4) (4) 푠푎푠 s 12푛푠cos2푛3 m ∆zsas = 푠 (4) 2n3 where ns is the refractive index of the phase mask substrate,s t is the mask thickness and φ where ns is the refractive index of the phase mask substrate, t is the mask thickness and φ is the angle of focused marginal rays’ incident on the phase mask (see Figure 3). whereis the anglens is theof focused refractive marginal index of rays’ the phaseincident mask on substrate,the phase maskt is the (see mask Figure thickness 3). and ϕ is the angle of focused marginal rays’ incident on the phase mask (see Figure3).

Figure 3. Focal elongation ∆z caused by the plane parallel mask substrate. Please note that Figure 3. Focal elongation Δzsas causedsas by the plane parallel mask substrate. Please note that mar- Figure 3. Focal elongation Δzsas caused by the plane parallel mask substrate. Please note that mar- marginal rays are focused farther from the mask than paraxial rays. ginalginal rays raysare focused are focused farther farther from from the mask the mask than than paraxial paraxial rays. rays. When tight cylindrical focusing of the beam incident on the mask is considered, parax- WhenWhen tight tight cylindrical cylindrical focusing focusing of the of beamthe beam incident incident on the on maskthe mask is considered, is considered, par- par- axialial rays rays lie lie in ina plane a plane that that is perpendicular is perpendicular to the to themask mask grooves grooves (i.e., (i.e., in-plane in-plane diffraction). diffraction). Marginalaxial rays rays,lie in however,a plane that are is no perpendicular longer perpendicular to the mask to grooves the grooves (i.e., of in the-plane mask diffraction). resulting in off-plane or conical diffraction. The result is that for a given diffracted order m, the marginal rays are focused closer to the mask than the paraxial rays. It can be shown that the focal elongation due to conical diffraction can be expressed as [20]:

Lm2λ2 ϕ2 ∆z = 0 (5) cdm 2 2 2 2 d − m λ0

The focal elongation ∆zcdm is depicted schematically in Figure4. As in Figure3, the angle of the marginal rays is denoted by ϕ. In Figure4,F 0,0 denotes the paraxial focus of the 0th diffraction order, Fm,0 and Fm,ϕ respectively denote the paraxial and marginal foci of the mth diffraction order, L and l respectively denote the distance from M and Fm,0 Sensors 2021, 21, x FOR PEER REVIEW 6 of 25

Marginal rays, however, are no longer perpendicular to the grooves of the mask resulting in off-plane or conical diffraction. The result is that for a given diffracted order m, the marginal rays are focused closer to the mask than the paraxial rays. It can be shown that the focal elongation due to conical diffraction can be expressed as [20]:

2 2 2 퐿푚 휆0휑 Δ푧푐푑푚 = 2 2 2 (5) 2(푑 −푚 휆0)

Sensors 2021, 21, 1447 The focal elongation Δzcdm is depicted schematically in Figure 4. As in Figure 3, the 6 of 23 angle of the marginal rays is denoted by φ. In Figure 4, F0,0 denotes the paraxial focus of the 0th diffraction order, Fm,0 and Fm,φ respectively denote the paraxial and marginal foci of the mth diffraction order, L and l respectively denote the distance from M and Fm,0 (obser- vation(observation point O coincides point O coincides with Fm,0) withand the Fm distance,0) and the from distance M to F0,0 from. ForM simplicity,to F0,0. For only simplicity, the 0thonly and the1st diffraction 0th and 1st orders diffraction are considered. orders are Please considered. note that Please the marginal note that focus the marginal(i.e., Fm,φ) focus lies(i.e., closer Fm,ϕ to) lies the closer mask tothan the the mask paraxial than thefocus paraxial (i.e., Fm focus,0). This (i.e., is Foppositem,0). This to is the opposite case of to the sphericalcase of sphericalaberration aberration caused by causedthe phase by mask the phase substrate. mask substrate.

Figure 4. Ray propagation and the focal elongation ∆zcdm caused by conical (off-plane) diffraction. Figure 4. Ray propagation and the focal elongation Δzcdm caused by conical (off-plane) diffraction. Please note that the marginal focus (i.e., Fm,ϕ) lies closer to the mask than the paraxial focus (i.e., Please note that the marginal focus (i.e., Fm,φ) lies closer to the mask than the paraxial focus (i.e., F ). Compare with Figure3. Fm,0m).,0 Compare with Figure 3.

The distance L1 at which chromatic dispersion of the mask is exactly balanced by The distance L1 at which chromatic dispersion of the mask is exactly balanced by chromatic aberration of the cylindrical lens is given by: chromatic aberration of the cylindrical lens is given by:

2 2 2 2 23/ 223/2 −f fdndndl d m−m λ0 LL = l 0 (6) (6) 11 n − 1 dλ 2 m2λ d nl l1 d m 0d 0

whichwhich is isderived derived by byequating equating Δzcm∆ (Equationzcm (Equation (2)) and (2)) Δz andcl (Equation∆zcl (Equation (3)). For (3)).a given For m a and given m λ0and, L1 isλ 0solely, L1 is determined solely determined by the mask by the and mask lens and parameters lens parameters and does andnot depend does not on, depend i.e., on, iti.e., will it be will the besame the for same any for laser any source. laser Similarly, source. Similarly, the distance the L distance2 at whichL 2sphericalat which aber- spherical rationaberration introduced introduced by the mask by the substrate mask substrateis exactly balanced is exactly by balanced conical (off by-plane) conical diffrac- (off-plane) tiondiffraction of the mask of the can mask be derived can be derivedby equating by equating Δzsas (Equation∆zsas (Equation (4)) and Δ (4))zcdm and(Equation∆zcdm (Equation(5)). In(5)). the In3rd- theorder 3rd-order approximation approximation with respect with to respect the focusing to the angle focusing φ (φ angle < 0.3 ϕrad)(ϕ

As it can be seen from Equation (7), L2 does not depend on φ, i.e., it will be the same As it can be seen from Equation (7), L2 does not depend on ϕ, i.e., it will be the same for any focusing cylindrical lens provided that its numerical aperture NA is less than 0.3. for any focusing cylindrical lens provided that its numerical aperture NA is less than 0.3. Thus, there are two independent sets of phenomena that affect the spreading of the focal spot: (i) angular chromatic dispersion originating from the mask (Equation (2)) which

is counteracted by chromatic aberration of the cylindrical focusing lens (Equation (3)) and (ii) spherical aberration caused by the mask substrate (Equation (4)) which is counteracted by conical diffraction (Equation (5)). The interaction of these effects is especially important to consider when TTC inscrip- tion of FBGs is being performed [28]. In such an instance, tight focusing of the fs IR beam is required in order to ensure a large differential in light intensity seen by the fiber core and the fiber coating [25]. Furthermore, the highest reflectivity gratings are created when the resulting grating in the fiber has a period that is at the fundamental Bragg resonance [19], i.e., d/2. Phase masks used to create such a resonance at telecommunications in silica fibers using IR beams have large 1st-order diffraction angles (more than 48◦ for a Sensors 2021, 21, x FOR PEER REVIEW 7 of 25

Thus, there are two independent sets of phenomena that affect the spreading of the focal spot: (i) angular chromatic dispersion originating from the mask (Equation (2)) which is counteracted by chromatic aberration of the cylindrical focusing lens (Equation (3)) and (ii) spherical aberration caused by the mask substrate (Equation (4)) which is counteracted by conical diffraction (Equation (5)). Sensors 2021, 21, 1447 The interaction of these effects is especially important to consider when TTC7 of inscrip- 23 tion of FBGs is being performed [28]. In such an instance, tight focusing of the fs IR beam is required in order to ensure a large differential in light intensity seen by the fiber core and the fiber coating [25]. Furthermore, the highest reflectivity gratings are created when 1.071 µm-pitch mask).the resulting In this grating case, in the the position fiber has a from period the that mask is at wherethe fundamental a distinctive Bragg maxi-resonance mum in the focal[19], peak i.e., intensity d/2. Phase is masks observed used to will create critically such a resonance depend onat telecommunications the mask substrate wave- lengths in silica fibers using IR beams have large 1st-order diffraction angles (more than (thickness, refractive48 for index), a 1.071 focusing μm-pitch mask). cylindrical In this lens case, (focal the position distance, from refractivethe mask where index), a distinctive and diffraction anglemaximum of the mask in the (mask focal period).peak intensity is observed will critically depend on the mask sub- To estimatestrate the quality (thickness, of the refractive focusing index), optics focusing and outputcylindrical beam lens from(focal thedistance, regenerative refractive in- amplifier, 3D-timedex), averaged and diffraction intensity angle distributions of the mask (mask measurements period). about the focal region were performed usingTothe estimate technique the quality described of the focusing in [23]. optics Briefly, and theoutput respective beam from xy-intensity the regenerative distributions withamplifier, a 1 µm 3D separation-time averaged along intensity the z-axis distributions were projected measurements onto about a Complemen- the focal region were performed using the technique described in [23]. Briefly, the respective xy-intensity tary Metal Oxide Semiconductor (CMOS)matrix by means of a high numerical aperture distributions with a 1 μm separation along the z-axis were projected onto a Complemen- (i.e., NA = 0.9) objectivetary Metal lens,Oxide recorded Semiconductor and combined(CMOS)matrix into by 3Dmeans stacks. of a high The numerical yz-intensity aperture distributions shown(i.e., NA in Figure= 0.9) objective5 were lens, obtained recorded by and averaging combined into the 3D values stacks. of The points yz-intensity with dis- fixed (yi, zi)-coordinatestributions along shown the in Figurex-axis 5 andwere projecting obtained by the averaging respective the values mean of valuespoints with onto fixed the yz-plane. Figure(yi, zi5)-a)coordinates shows the along focal the intensityx-axis and pro distributionjecting the respective of the output mean values beam onto in the the yz- yz-plane when theplane. beam Figure is focused 5a) shows with the thefocal 12 intensity mm-focal-length distribution acylindricalof the output beam lens describedin the yz-plane in Section 2.3. Consideringwhen the beam free is space focused Gaussian with the 12 beam mm-focal optics-length only, acylindrical the focal spotlens described line width in Sec- tion 2.3. Considering free space Gaussian beam optics only, the focal spot line width 2w ≈ 2w ≈ 2λ f/πwo, For a collimated beam with diameter, wo = 3.5 mm, λ = 800 nm and 0 2λ0f/πwo, For a collimated beam with diameter, wo = 3.5 mm, λ0 = 0800 nm and f = 12 mm, f = 12 mm, the resultingthe resulting focal focal spot spot would would be be 1.75 1.75µ μm.m. From Figure Figure 5a)5a) the the line line width width of the of focal the spot focal spot is 1.9 ±is 0.11.9 ±µ 0.1m, μ whichm, which is consistentis consistentwith with the Gaussian Gaussian beam beam calculation. calculation.

Figure 5. Focal intensityFigure distributions5. Focal intensity in distributions the yz-plane in ofthe ( ayz)- theplane beam of (a) from the beam the regenerativefrom the regenerative amplifier ampli- fier using the 12-mm-focal-length acylindrical lens whose effective numerical aperture is sin(φ) = using the 12-mm-focal-length0.26 and of (b) acylindrical when the beam lens is focused whose through effective the numerical1.071 μm pitch, aperture 2.1 mmis thick sin( phaseϕ) = 0.26mask. and of (b) when theDistance beam isbetween focused the through focal spot the and 1.071 the phaseµm pitch,mask surface 2.1 mm is 350 thick μm. phase In (a,b mask.), the beam Distance is propa- between the focal spotgating and from the left phase to right. mask [20]. surface is 350 µm. In (a,b), the beam is propagating from left to right. [20]. Considering the laser writing conditions used in Ref. [20] (i.e., λ0 = 800 nm, Δλ = 6 nm, f = 12 mm, nl = 1.776, dnl/dλ = −0.0371 μm−1; d = 1.071 μm, t = 2.1 mm, ns = 1.453). The Considering the laser writing conditions used in Ref. [20] (i.e., λ0 = 800 nm, ∆λ = 6 nm, bandwidth of the 80 fs pulses (i.e.,− 121 nm) was narrowed down to 6 nm by means of a f = 12 mm, nl =narrowband 1.776, dnl/d filter.λ = The−0.0371 minimalµ mfocal; spotd = elongation 1.071 µm, andt = maximum 2.1 mm, peakns = intensity 1.453). oc- The bandwidth ofcurred the at 80 L fs~350 pulses μm from (i.e., the 12 mask nm) and was is shown narrowed in Figure down 5b. The to effect 6 nm at by this means L was very of a narrowbandpronounced filter. The and, minimal for the focalfirst time, spot low elongation-loss FBGs could and maximumbe directly inscribed peak intensity inside a non- occurred at L ~350photosensitizedµm from the polyimide mask and-coated is shown fiber 50 in μm Figure in diameter5b. The (see effect Figure at 6). this Previously,L was the very pronounced and, for the first time, low-loss FBGs could be directly inscribed inside a non-photosensitized polyimide-coated fiber 50 µm in diameter (see Figure6). Previously, the phase mask approach to fs-FBG inscription through polyimide coatings of Ge-doped 50 µm fibers was only possible when the fiber was photosensitized using high-pressure deuterium loading [29]. All in all, the experimental results agree well with the predictions and estimates based on the above analysis, where the chromatic effects are presented in terms of just two different wavelengths (i.e., ‘blue’ and ‘red’) and monochromatic aberrations are introduced as ray optics phenomena. The limitations of the formalism are obvious (i) as it provides only qualitative information about the intensity distribution in the line-shaped focal volume and (ii) neglects temporal pulse distortions caused by the rather complex optical setup consisting of an acylindrical lens, a plane-parallel plate, and a phase mask. To calculate the temporal and spatial distribution of the electric field in the focal volume, diffraction needs to be taken into account. We also note that a fully rigorous treatment of the problem should include the electromagnetic diffraction of light focused through the highly curved cylindrical surface of the fiber, consider residual aberrations of the acylindrical lens, and Sensors 2021, 21, 1447 8 of 23

Sensors 2021, 21, x FOR PEER REVIEW 8 of 25

take into account beam imperfections, which are usually characterized by the beam quality factor (i.e., M2-factor). In this respect, our simple semi-quantitative formalism reinforced by phaseintensity mask distribution approach measurementsto fs-FBG inscription after the maskthrough (Figure polyimide5b) provides coatings a straightforward of Ge-doped 50 μmand fibers highly was intuitive only possible approach when to identifythe fiber optimum was photosensitized laser writing conditions using high to-pressure fabricate deu- teriumFBGs loading using the [29]. phase mask technique.

Figure 6. (a) Reflection spectrumFigure 6. (~6 (a dB) in transmission) spectrum of an (~6 FBG dB written in transmission) in a 50 µm diameter of an FBG fiber written through in the a protective50 μm diameter polyimide coating. (b) Anfiber optical through microscopy the protective image of the polyimide 50 µm fiber coating. containing (b) An the FBG.optical The microscopy refractive index image modulation of the 50 μm fiber of the FBG is ~1.5 × 10−containing4. To visualize the the FBG. FBG, The red refractive light at 637 index nm was modulation coupled into of thethe fiberFBG core is ~1.5 [23]. × 10−4. To visualize the FBG, red light at 637 nm was coupled into the fiber core [23]. 2.3.3. Tilted TTC-FBGs AllTilted in all, FBGs the are experimental Bragg grating results structures agree where well the with grating the planes predictions are not normal and estimates but basedtilted on with the respect above toanalysis, the fiber axis.where Light the propagating chromatic ineffects the guided are presented mode can thenin terms couple of just twointo different backward wavelengths propagating (i.e., cladding ‘blue’ modes and or‘red’) even and radiation monochromatic modes depending aberrations on the tilt are in- troducedangle. Enhancedas ray optics coupling phenomena. to cladding The modes limitations with tilted of the Bragg formalism gratings haveare obvious been used (i) as it providesto fabricate only multi-parameter qualitative information sensors, because about the claddingintensity modes distribution respond in differently the line-shaped to focalfiber volume strain asand compared (ii) neglects to the temporal core mode pulse making distortions a combined caused strain-temperature by the rather sensor complex possible [30]. Until recently [31], tilted FBGs could be inscribed through protective polymer optical setup consisting of an acylindrical lens, a plane-parallel plate, and a phase mask. coatings only using a variation of the PbP technique with fs lasers [32]. In this respect, the To TTCcalculate inscription the temporal of tilted FBGsand spatial using thedistribution phase mask oftechnique the electric would field be in advantageous the focal volume, diffractionfrom a sensor needs manufacturing to be taken into perspective. account. InWe the also absence note ofthat a fiber a fully coating, rigorous fs lasers treatment and of thephase problem masks should were usedinclude to write the electromagnetic tilted FBGs by translating diffraction the of fiber light vertically focused and through along the highlythe fibercurved axis cylindrical simultaneously surface while of thethe fiber fiber, was consider in the beam residual focus aberrations [33]. In this of instance, the acylin- dricallarger lens, pitched and take phase into masks account that produced beam imperfections, higher order Bragg which gratings are usually were used.characterized by the beamThe quality TTC tilted factor FBGs (i.e., were M2 written-factor). using In this the experimentalrespect, our conditionssimple semi given-quantitative in Section for- malism2.3. The reinforced fs laser beam by intensity was expanded distribution along the measurementsx-axis and focused after through the mask the (FigureIbsen mask 5b) pro- (M in Figure7) using an acylindrical lens with a focal length f = 15 mm (CL in Figure vides a straightforward and highly intuitive approach to identify optimum laser writing 7). The linear polarization of the fs laser beam was oriented parallel to the mask grooves. conditionsPolyimide-coated to fabricate Corning FBGs SMF-28using the was phase placed mask along technique. the line-shaped focus and aligned parallel to CL. The fiber was positioned at L ~300 µm away from the phase mask, which 2.3.3.was Tilted the optimal TTC-FBGs distance taking into account diffraction and dispersion effects discussed previously.Tilted FBGs Laser are intensities Bragg grating used resultedstructures in thewhere formation the grating of Type planes I index are change not normal [34]. but tiltedThe with position respect of the to laserthe fiber line focusaxis. Light on the propagating fiber core was in aligned the guided by using mode the can techniques then couple intoof backward nonlinear photoluminescencepropagating cladding microscopy modes andor even dark-field radiation microscopy modes [ 23depending]. The piezo- on the actuated stages for translating CL and the fiber were triggered by the same signal generator tilt angle. Enhanced coupling to cladding modes with tilted Bragg gratings have been used through a variable power splitter to control the translation ratio along the x- and y-axis. to fabricateThe inscription multi set-up-parameter for TTC sensors, tilted gratings because is shownthe cladding in Figure modes7. respond differently to fiber strain as compared to the core mode making a combined strain-temperature sensor possible [30]. Until recently [31], tilted FBGs could be inscribed through protective poly- mer coatings only using a variation of the PbP technique with fs lasers [32]. In this respect, the TTC inscription of tilted FBGs using the phase mask technique would be advanta- geous from a sensor manufacturing perspective. In the absence of a fiber coating, fs lasers and phase masks were used to write tilted FBGs by translating the fiber vertically and along the fiber axis simultaneously while the fiber was in the beam focus [33]. In this in- stance, larger pitched phase masks that produced higher order Bragg gratings were used. The TTC tilted FBGs were written using the experimental conditions given in Section 2.3. The fs laser beam was expanded along the x-axis and focused through the Ibsen mask

Sensors 2021, 21, x FOR PEER REVIEW 9 of 25

(M in Figure 7) using an acylindrical lens with a focal length f = 15 mm (CL in Figure 7). The linear polarization of the fs laser beam was oriented parallel to the mask grooves. Polyimide-coated Corning SMF-28 was placed along the line-shaped focus and aligned parallel to CL. The fiber was positioned at L ~300 μm away from the phase mask, which was the optimal distance taking into account diffraction and dispersion effects discussed previously. Laser intensities used resulted in the formation of Type I index change [34]. The position of the laser line focus on the fiber core was aligned by using the techniques of nonlinear photoluminescence microscopy and dark-field microscopy [23]. The piezo- actuated stages for translating CL and the fiber were triggered by the same signal gener- ator through a variable power splitter to control the translation ratio along the x- and y- axis. The inscription set-up for TTC tilted gratings is shown in Figure 7. Since the fiber itself acts as a cylindrical lens, the of the converging fs laser beam at the fiber surface has to be taken into account when calculating the actual transla- tion range of the focus inside the fiber. For all the tilted FBGs, the vertical displacement ΔL of the fs laser beam along the y-axis was kept at 15 μm to cover the entire core. Under the small-angle approximation, the transverse movement ΔY of the focus inside the fiber is then given by ΔY ≈ ΔL/n (n is the refractive index of the fiber) [31], which results in ΔY ~10 μm. The period of grating planes along the fiber axis is still given by d/2. Hence, tilted FBGs fabricated with different tilt angles are expected to have their main Bragg resonances positioned at the same wavelength. The transmission spectra of tilted FBGs were moni- Sensors 2021, 21, 1447 tored with a spectral resolution of 0.01 nm throughout the writing process using a tunable9 of 23 laser and a power meter.

FigureFigure 7. 7. ExperimentalExperimental setup setup for for writing writing tilted tilted FBGs. FBGs. Since the fiber itself acts as a cylindrical lens, the refraction of the converging fs laser The transmission spectra of TTC-written tilted FBG with different tilt angles up to beam at the fiber surface has to be taken into account when calculating the actual translation 10.3° are shown in Figure 8. In each case, the cladding modes reach ~5 dB in transmission range of the focus inside the fiber. For all the tilted FBGs, the vertical displacement ∆L and gradually shift to shorter wavelengths as the tilt angle increases. The cladding modes of the fs laser beam along the y-axis was kept at 15 µm to cover the entire core. Under appear to have an irregular shape due to the presence of the polyimide coating, which has the small-angle approximation, the transverse movement ∆Y of the focus inside the fiber ais higher then givenrefractive by ∆ indexY ≈ ∆thanL/n silica.(n is theTherefractive slight variation index of of the the Bragg fiber) wavelength [31], which is results caused in by∆ Ythe~10 differenceµm. The in period tension of gratingapplied planeswhile loading along the the fiber fiber axis into is the still fiber given-holding by d/2. jig Hence, and thentilted releasing FBGs fabricated the fiber after with the different inscription. tilt angles It is noted are expected that when to tilt have angles their are main under Bragg 4°, theresonances cladding positionedmodes are atconfined the same to wavelength.within a ~20 The nm transmissionwavelength range spectra near of tiltedthe Bragg FBGs resonance,were monitored allowing with for a spectralthe potential resolution to concatenate of 0.01 nm multiple throughout tilted the FBGs writing in a process distributed using sensinga tunable architecture. laser anda power meter. The transmission spectra of TTC-written tilted FBG with different tilt angles up to 10.3◦ are shown in Figure8. In each case, the cladding modes reach ~5 dB in transmission and gradually shift to shorter wavelengths as the tilt angle increases. The cladding modes appear to have an irregular shape due to the presence of the polyimide coating, which has a higher refractive index than silica. The slight variation of the Bragg wavelength is caused by the difference in tension applied while loading the fiber into the fiber-holding jig and then releasing the fiber after the inscription. It is noted that when tilt angles are under ◦ Sensors 2021, 21, x FOR PEER REVIEW 4 , the cladding modes are confined to within a ~20 nm wavelength range near the10 Braggof 25

resonance, allowing for the potential to concatenate multiple tilted FBGs in a distributed sensing architecture.

FigureFigure 8. Transmission 8. Transmission spectra spectra of tilted of tilted FBGs FBGs written written through through polyimide polyimide coating coating of SMF of SMF-28-28 with with differentdifferent tilt tilt angles angles of of4.6°, 4.6 6.8°,◦, 6.8 8.0°,◦, 8.0 9.0°,◦, 9.0 and◦, and 10.3°. 10.3 ◦.

WithWith only only a thin a thin polyimide polyimide coating coating of of10 10 μm,µm, the the tilted tilted FBGs FBGs can can still still be be used used to todetect detect changeschanges in in the the refractive refractive index ofofthe the environment environment surrounding surrounding the the grating. grating. Figure Figure9 shows 9 showsthe variation the variation in transmission in transmission spectra spectra of a polyimide of a polyimide coated 10.3coated◦ tilted 10.3 FBG tilted as a FBG function as a of functionlocal refractive of local refractive index at room index temperature. at room temperature.

Figure 9. Transformation of the transmission spectra of a 10.3° tilted FBG written through the coat- ing in response to different surrounding refractive indices.

The accuracy of determining the cut-off wavelength is ±0.7 nm within the spectral range of 1460–1510 nm, resulting in the surrounding refractive index sensing accuracy of 2.8 × 10−3. Linear regression based on the cut-off wavelength λc of this TFBG in response to the surrounding refractive index nSRI gives a response function λc = 513 nSRI + 804.5. TFBGs with smaller tilt angles are expected to preserve this response function for spectral intervals centered at shorter wavelengths. The classical approaches of TFBG inscription based on tilting the fiber with respect to the interference fringes cannot be used when it comes to tight focusing geometries that are required for through-the-coating inscription. Indeed, it was analytically shown that rotating either the phase mask or cylindrical lens in the plane of diffraction results in the split of the focal lines [31]. Even though the focal lines can be recombined by counter- rotating the phase mask and cylindrical lens, no tilted grating planes could be achieved inside the fiber core due to the intrinsic orthogonality of the recombined focal line and the interference fringes. In this respect, only ‘dynamic’ laser writing, i.e., writing that requires relative translation of the laser focus and fiber, should be employed for through-the-coat- ing inscription of TFBGs. This is in contrast to the classical approaches that represent ‘static’ laser writing as they do not require any relative translation of the laser focus and fiber.

Sensors 2021, 21, x FOR PEER REVIEW 10 of 25

Figure 8. Transmission spectra of tilted FBGs written through polyimide coating of SMF-28 with different tilt angles of 4.6°, 6.8°, 8.0°, 9.0°, and 10.3°.

With only a thin polyimide coating of 10 μm, the tilted FBGs can still be used to detect changes in the refractive index of the environment surrounding the grating. Figure 9 shows the variation in transmission spectra of a polyimide coated 10.3 tilted FBG as a Sensors 2021, 21, 1447 10 of 23 function of local refractive index at room temperature.

FigureFigure 9. Transformation 9. Transformation of theof transmissionthe transmission spectra of spectra a 10.3◦ tilted of FBGa 10.3° written tilted through FBG the written coating through the coat- ing inin responseresponse to differentto different surrounding surrounding refractive indices. refractive indices. The accuracy of determining the cut-off wavelength is ±0.7 nm within the spectral rangeThe ofaccuracy 1460–1510 nm,of determining resulting in the surroundingthe cut-off refractive wavelength index sensing is ±0.7 accuracy nm within of the spectral −3 range2.8 of× 10 1460. Linear–1510 regression nm, resulting based on thein the cut-off surrounding wavelength λc refractiveof this TFBG index in response sensing accuracy of to the surrounding refractive index nSRI gives a response function λc = 513 nSRI + 804.5. −3 2.8 ×TFBGs 10 . with Linear smaller regression tilt angles are based expected on tothe preserve cut-off this wavelength response function λc forof spectralthis TFBG in response to theintervals surrounding centered at shorterrefractive wavelengths. index nSRI gives a response function λc = 513 nSRI + 804.5. TFBGs withThe classical smaller approaches tilt angles of TFBG are inscriptionexpectedbased to preserve on tilting this the fiber response with respect function for spectral to the interference fringes cannot be used when it comes to tight focusing geometries that intervalsare required centered for through-the-coating at shorter wavelengths. inscription. Indeed, it was analytically shown that rotatingThe classical either the phaseapproaches mask or cylindricalof TFBG lens inscription in the plane based of diffraction on tilting results the in the fiber with respect to thesplit interference of the focal lines fringes [31]. Evencannot though be theused focal when lines canit comes be recombined to tight by focusing counter- geometries that rotating the phase mask and cylindrical lens, no tilted grating planes could be achieved are insiderequired the fiber for core through due to the-the intrinsic-coating orthogonality inscription. of the recombinedIndeed, it focal was line analytically and the shown that rotatinginterference either fringes. the phase In this respect,mask onlyor cylindrical ‘dynamic’ laser lens writing, in the i.e., plane writing of that diffraction requires results in the splitrelative of the translation focal lines of the laser[31]. focus Even and though fiber, should the be focal employed lines for through-the-coatingcan be recombined by counter- inscription of TFBGs. This is in contrast to the classical approaches that represent ‘static’ rotatinglaser writing the phase as they mask do not and require cylindrical any relative translationlens, no oftilted the laser grating focus and planes fiber. could be achieved inside the fiber core due to the intrinsic orthogonality of the recombined focal line and the 2.3.4. FBGs with Ultra-Strong Cladding Modes interference fringes. In this respect, only ‘dynamic’ laser writing, i.e., writing that requires It is not essential that tilted grating planes be inscribed in the fiber in order to create relativestrong translation cladding modes. of the PbP-written laser focus FBGs and whose fiber, grating should points be are employed offset with respect for through-the-coat- ing toinscription the fiber axis, of or TFBGs. core-offset This gratings is in also contrast exhibit strong to the coupling classical of the approaches guided core that represent ‘static’mode laser into claddingwriting modes as they [35,36 do]. It not was require demonstrated any recently relative that translation FBGs with cladding of the laser focus and modes that have a spectral span greater than 250 nm and are 30 dB-strong in transmission fiber.could be written with only a few high intensity fs laser pulses using the phase mask technique [37]. Using the same optical setup and optimal fiber positioning conditions, as discussed previously in this paper, single 800 nm 80 fs laser pulses were used to irradiate the optical fiber using the Ibsen phase mask. The resultant peak intensities within the fiber were kept at roughly two times the intensity threshold for optical breakdown in bulk fused silica [3]. Under these conditions, Abdukerim et al. fabricated FBGs with very strong cladding mode coupling (see Figure 10). Such FBGs can also be easily inscribed through the polyimide coating of the fiber. Because the coating suppresses higher order cladding modes, the FBG spectra presented in Figure 10 were obtained on bare fibers. Sensors 2021, 21, x FOR PEER REVIEW 11 of 25

Sensors 2021, 21, x FOR PEER REVIEW 11 of 25

2.3.4. FBGs with Ultra-Strong Cladding Modes It is not essential that tilted grating planes be inscribed in the fiber in order to create 2.3.4.strong FBGs cladding with Ultramodes.-Strong PbP- writtenCladding FBGs Modes whose grating points are offset with respect to the fiberIt is notaxis, essential or core- thatoffset tilted gratings grating also planes exhibit be strong inscribed coupling in the of fiber the guidedin order core to create mode stronginto cladding cladding modes modes. [35,36]. PbP- writtenIt was demonstrated FBGs whose gratingrecently points that FBGs are offset with claddingwith respect modes to thethat fiber have axis, a spectral or core -spanoffset greater gratings than also 250 exhibit nm and strong are 30coupling dB-strong of the in transmissionguided core mode could intobe written cladding with modes only [35,36]. a few highIt was intensity demonstrated fs laser recently pulses usingthat FBGs the phase with cladding mask technique modes that[37]. have Using a spectral the same span optical greater setup than and 250 optimal nm and fiber are positioning30 dB-strong conditions, in transmission as discussed could bepreviously written with in this only paper, a few single high 800intensity nm 80 fs fs laser laser pulsespulses usingwere usedthe phase to irradiate mask techniquethe optical [37].fiber Using using thethe sameIbsen opticalphase mask. setup The and resultant optimal fiberpeak positioningintensities within conditions, the fiber as discussed were kept previouslyat roughly intwo this times paper, the single intensity 800 thresholdnm 80 fs laser for optical pulses breakdown were used toin irradiatebulk fused the silica optical [3]. fiberUnder using these the conditions, Ibsen phase Abdukerimmask. The resultant et al. fabricated peak intensities FBGs with within very the strongfiber were cladding kept atmode roughly coupling two times (see Figurethe intensity 10). Such threshold FBGs canfor opticalalso be breakdowneasily inscribed in bulk through fused thesilica polyi- [3]. Undermide coatingthese conditions, of the fiber. Abdukerim Because the et coating al. fabricated suppresses FBGs higher with ordervery strongcladding cladding modes, modethe FBG coupling spectra (see presented Figure 10).in Figure Such FBGs10 were can obtained also be easilyon bare inscribed fibers. through the polyi- Sensors 2021, 21, 1447 11 of 23 mide coating of the fiber. Because the coating suppresses higher order cladding modes, the FBG spectra presented in Figure 10 were obtained on bare fibers.

Figure 10. Transmission spectra of FBGs written using a different number of fs laser pulses. (a) laser beam polarization is perpendicular to the fiber axis. (b) laser beam polarization is parallel to the fiber axis. The spectra are plotted with an offset in the vertical axis for clarity. Figure 10. TransmissionFigure spectra 10. of FBGs Transmission written using spectra a different of FBGs number written of fs using laser pulses.a different (a) laser number beam of polarization fs laser pulses. is (a) perpendicular to the fiberlaser axis. beam (b) laser polarization beam polarization is perpendicular is parallel to to the the fiber fiber axis. axis. The (b spectra) laser are beam plotted polarization with an offset is parallel to in the vertical axis for clarity.the fiberAs axis. it can The be spectra seen from are plotted Figure with 10, laseran offset beam in thepolarization vertical axis parallel for clarity. to the fiber axis was more favorable for producing strong cladding modes than the beam polarization perpen- dicularAsAs itto canit the can be fiberbe seen seen axis. from from For Figure Figurelaser 10,beam 10 laser, laser polarization beam beam polarization polarization parallel toparallel the fiber toto the theaxis, fiberfiber the axis axiscladding was was more favorable for producing strong cladding modes than the beam polarization moremodes favorable were at forthe producing level of 7– strong15 dB incladding transmission modes (depending than the beam on thepolarization wavelength) perpen- even perpendicular to the fiber axis. For laser beam polarization parallel to the fiber axis, the in the case of single pulse irradiation, while five pulses with the same light intensity pro- dicularcladding to the modes fiber were axis. at For the levellaser of beam 7–15 dBpolarization in transmission parallel (depending to the fiber on the axis, wavelength) the cladding modesducedeven were incladding the at case the modes of level single inof pulse excess7–15 irradiation, dB of in30 transmission dB. while five pulses(depending with the on same the lightwavelength) intensity even in theproducedAs case shown of cladding single in Figure pulse modes 11,irradiation, in excessthe resulting of 30while dB. devices five pulses are thermally with the samestable light up to intensity 1000 C pro- and, ducedin principle, claddingAs shown can modes in be Figure used in 11 excessas, the a combined resulting of 30 dB. devices temperature/strain are thermally stable sensor up to at 1000 high◦C temperatures and, in [38].principle,As shown can in be Figure used as 11, a combined the resulting temperature/strain devices are thermally sensor at high stable temperatures up to 1000 [38 C]. and, in principle, can be used as a combined temperature/strain sensor at high temperatures [38].

Figure 11. (a) High temperature performance of FBGs written with (a) 1 and (b) 5 pulses (laser beam polarization is parallel to the fiber axis).

2.3.5. TTC-Written FBGs for Environmental Sensing Applications (Optical Trigger)

If a transductive layer or package is applied to an FBG, one that could convert a desirable measurand into a strain, the FBG would then act as a sensor for that measurand. Recently, for example, an FBG was embedded within a magnetostrictive polymer composite comprising epoxy resins and Terfenol D in order to create an FBG sensor sensitive to magnetic fields [39]. The package, upon exposure to a magnetic field, compresses the FBG resulting in a detectable strain-induced Bragg wavelength shift. For environmental applications, FBGs have also been demonstrated for detection of hydrocarbons [40]. FBGs photo-inscribed using a UV laser were packaged in a polymeric material that would act as a transduction element by swelling upon exposure to hydrocarbons. The swelling caused a tensile strain in the fiber which was detected by the FBG. However, the traditional UV photo-inscription procedure requires stripping and recoating of the fiber along with the Sensors 2021, 21, 1447 12 of 23

complex packaging geometry, which significantly reduces the reliability of such a sensor especially when subjected to a tensile strain. On the other hand, TTC-written Type I FBGs can withstand strain levels similar to that of the pristine fiber [25,26]. Here, a FBG array for environmental sensing applications is manufactured in single mode telecommunications optical fiber through the protective polyimide coating using tightly focused fs IR laser pulses. By exploiting the high mechanical reliability of FBGs fabricated using TTC inscription with fs IR lasers, a robust FBG sensor that produces a trigger signal when exposed to hydrocarbons (e.g., crude oil) can be fabricated. The response is much stronger than that produced by thermal or acoustic effects which are normally used for fiber optic sensors applied to oil pipeline leak detection. The method used to create the TTC-FBGs has been described previously [23]. Using the experimental conditions given in Section 2.3, TTC-FBGs were written into polyimide- coated SMF-28-type optical fiber using the Ibsen phase mask and an acylindrical lens with a focal distance f = 15 mm. The interplay of chromatic, aberration and conical diffraction effects caused by the phase mask and the focusing optics was accounted for by placing the fiber at L~300 µm away from the phase mask where the confocal parameter of the laser focus was smallest and, thus, the peak intensity in the focus highest [20]. This also ensured large intensity differentials between the fiber core and the protective coating which are required for TTC inscription of FBGs. Using these exposure conditions, TTC-FBGs were written in the Type I regime [34] where higher mechanical reliability was observed [25,26]. The concept of a leak detection system based on a wavelength demultiplexing ap- proach (WDM) is presented in Figure 12. A commercially available FBG interrogator is used to probe a quasi-distributed FBG array of specially packaged sensor elements. The Sensors 2021, 21, x FOR PEER REVIEW 13 of 25 device under test (DUT) exposed to a liquid hydrocarbon, such as crude oil, undergoes a trigger response leading to a shift of the Bragg wavelength.

Figure 12. Schematic of a WDM-basedWDM-based interrogationinterrogationsystem system used used to to detect detect liquid liquid hydrocarbons hydrocarbons such suchas crude as crude oil. λ 1oil.... λ1λ…n λdenoten denote the the respective respective Bragg Bragg wavelengths wavelengths of theof the DUTs. DUTs.

The packaging geometry considered here is similar toto thatthat of SpirinSpirin etet al.al. [[40].40]. In our case, a polyimide-coatedpolyimide-coated TTC-FBGTTC-FBG with 10% reflectivityreflectivity is packaged with an elastomeric cord (e.g., ethylene propylene diene monomer rubber (EPDM))(EPDM)) thatthat isis end-cappedend-capped withwith thermally moldedmolded polystyrenepolystyrene(PS) (PS) ferrule ferrule anchors anchors to to transfer transfer stress stress caused caused by by swelling swelling in inthe the cord cord to theto the fiber. fiber. EPDM EPDM will will expand expand when when exposed exposed to crude to crude oil butoil but neither neither EPDM EPDM nor norPS will PS will react react upon upon exposure exposure to water. to water. A more A more compact compact configuration configuration of thisof this packaging packaging is isalso also demonstrated demonstrated where where no no PS PS ferrule ferrule anchor anchor is requiredis required and and instead instead the the EPDM EPDM cord cor isd issimply simply glued glued to to the the polyimide polyimide fiber fiber coating coating using using Loctite Loctite 495 495 cyanoacrylate cyanoacrylate glue.glue. WhenWhen either package type is exposed to oil, a positive shift in the Bragg wavelength is observed. Images of both packaging styles are presented in Figure 13.

a) b)

20 mm 20 mm

Figure 13. EPDM TTC-FBG packages (a) with polystyrene anchors (A) and (b) without anchors (B).

Both A and B packaging geometries were tested in crude oil (Access Western Blend) at room temperature. The strain-induced shifts of the Bragg wavelength reflection peaks were measured every 60 s using a Micron Optics SM125 fiber Bragg grating interrogator with a 1 pm wavelength resolution (see Figure 14). The magnitude of the positive Bragg wavelength shift, indicative of a tensile strain applied to the fiber when immersed in oil, was dependent upon the EPDM package diameter and whether or not the PS anchors were present to amplify the tensile strain. As PS is resistant to degradation when exposed to crude oil, it made a suitable anchor material for these tests. For package A with a ~6.4 mm outer diameter of the EPDM package, very large amounts of strain were observed. Maximum wavelength shifts occurred after 30 h of immersion in oil. For the unanchored package B, the time for maximal Bragg wavelength shift was also dependent on the pack- age diameter and occurred after 100 or 300 min for ~1.6 mm and ~3.2 mm cord diameters, respectively.

Sensors 2021, 21, 1447 13 of 23

either package type is exposed to oil, a positive shift in the Bragg wavelength is observed. Images of both packaging styles are presented in Figure 13.

Figure 13. EPDM TTC-FBG packages (a) with polystyrene anchors (A) and (b) without anchors (B).

Both A and B packaging geometries were tested in crude oil (Access Western Blend) at room temperature. The strain-induced shifts of the Bragg wavelength reflection peaks were measured every 60 s using a Micron Optics SM125 fiber Bragg grating interrogator with a 1 pm wavelength resolution (see Figure 14). The magnitude of the positive Bragg wavelength shift, indicative of a tensile strain applied to the fiber when immersed in oil, was dependent upon the EPDM package diameter and whether or not the PS anchors were present to amplify the tensile strain. As PS is resistant to degradation when exposed to crude oil, it made a suitable anchor material for these tests. For package A with a ~6.4 mm outer diameter of the EPDM package, very large amounts of strain were observed. Maximum wavelength shifts occurred after 30 h of immersion in oil. For the unanchored package B, the time for maximal Bragg wavelength shift was also dependent on the Sensors 2021, 21, x FOR PEER REVIEW 14 of 25 package diameter and occurred after 100 or 300 min for ~1.6 mm and ~3.2 mm cord diameters, respectively.

Figure 14. Bragg wavelength shift of EPDM packaged TTC-FBGs vs. time in crude oil. The green Figure 14. Bragg wavelength shift of EPDM packaged TTC-FBGs vs. time in crude oil. The green curvecurve corresponds corresponds to to the the Bragg Bragg wavelength wavelength shift shift of ofpackage package A with A with 6.4 6.4mm mm EPDM EPDM cord cord and andPS PS anchors;anchors; package package B Bsensors sensors with with 1.6 1.6 mm, mm, 2.4 2.4 mm, mm, and and 3.2 3.2 mm mm EPDM EPDM cord cord diameters diameters and and Loctite Loctite adhesiveadhesive only only are are denoted denoted by by the the yellow, yellow, red red and and blue blue traces, traces, respectively. respectively.

◦ TemperatureTemperature sensitivity sensitivity of of the the package package B Btype type sensors sensors were were measured measured from from 24 24°C toC ◦ ◦ 80to1 °C. 80 TheC.The Bragg Bragg wavelength wavelength shifts shifts of the of sensors the sensors were were found found to be to 0.04 be 0.04nm/°C nm/ andC 0.06 and ◦ nm/°C0.06 nm/ for theC for 1.6 the mm 1.6- mm-and 3.2 and mm 3.2 mm-package-package devices, devices, respectively. respectively. As As the the Bragg Bragg wave- wave- lengthlength shifts shifts due due to to temperature temperature or or immersion immersion in in oil oil are are of of the the same same order order of of magnitude, magnitude, anan unpackaged unpackaged grating grating could could be be placed placed adjacent adjacent to to the the EPDM EPDM sensor sensor as as a a temperature temperature reference. No significant variation in the Bragg wavelength was observed in both types of packages when the devices were immersed in water at room temperature for 24 h.

3. Femtosecond Laser-Enhanced Fiber Scattering: Random Fiber Gratings In addition to fabrication of periodic FBG structures, fs lasers can also be used to create quasi-randomly spaced grating planes using a variant of the PbP method known as the plane-by-plane technique [41]. With this approach, random fiber grating structures (RFG) can be created. The concept of the RFG was first theoretically studied by Derevyanko [42] where segmented pseudo-random modulation of the refractive index profile of a fiber Bragg grating resulted in a disordered structure. It was found that if the segments were larger than the correlation length, it would be possible to achieve a flat- top refection spectrum. This concept was experimentally demonstrated by employing phase noise and pseudorandom variations of the refractive index to successfully fabricate a flat-top FBG response [43] Such random fiber gratings (RFG) have been used in distrib- uted temperature measurements [9,44,45], fiber lasers [46–48] and sensors [49– 51] over the past 5 years. The pertinent applications also include structural health moni- toring, harsh environment sensing [45], perimeter intrusion detection and encrypted com- munication [52]. Rayleigh backscattering in optical fibers has been used for fiber sensing and fiber laser applications for decades [53–56,46]. In telecommunications single mode fibers (e.g., SMF-28 from Corning), the Rayleigh backscattering signal is usually very low (−100 dB/mm) as the fiber is designed for long-haul applications with minimized scattering loss. When such fibers are used for distributed sensing, the low backscattering signal level lim- its the sensitivity and spatial resolution of distributed temperature or stain measurements. When fiber with low Rayleigh backscattering is used as the distributed feedback for a random fiber laser application, a long piece of fiber is required resulting in a high lasing threshold and poor stability. In recent years, UV lasers have been used to increase light backscattering in optical fibers for distributed temperature and strain measurements with higher spatial resolution and higher signal-to-noise ratio (SNR) [44,57]. However, H2-

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reference. No significant variation in the Bragg wavelength was observed in both types of packages when the devices were immersed in water at room temperature for 24 h.

3. Femtosecond Laser-Enhanced Fiber Scattering: Random Fiber Gratings In addition to fabrication of periodic FBG structures, fs lasers can also be used to create quasi-randomly spaced grating planes using a variant of the PbP method known as the plane- by-plane technique [41]. With this approach, random fiber grating structures (RFG) can be created. The concept of the RFG was first theoretically studied by Derevyanko [42] where segmented pseudo-random modulation of the refractive index profile of a fiber Bragg grating resulted in a disordered structure. It was found that if the segments were larger than the correlation length, it would be possible to achieve a flat-top refection spectrum. This concept was experimentally demonstrated by employing phase noise and pseudorandom variations of the refractive index to successfully fabricate a flat-top FBG response [43] Such random fiber gratings (RFG) have been used in distributed temperature measurements [9,44,45], fiber lasers [46–48] and fiber laser sensors [49–51] over the past 5 years. The pertinent applications also include structural health monitoring, harsh environment sensing [45], perimeter intrusion detection and encrypted communication [52]. Rayleigh backscattering in optical fibers has been used for fiber sensing and fiber laser applications for decades [46,53–56]. In telecommunications single mode fibers (e.g., SMF-28 from Corning), the Rayleigh backscattering signal is usually very low (−100 dB/mm) as the fiber is designed for long-haul applications with minimized scattering loss. When such fibers are used for distributed sensing, the low backscattering signal level limits the sensitivity and spatial resolution of distributed temperature or stain measurements. When fiber with low Rayleigh backscattering is used as the distributed feedback for a random fiber laser application, a long piece of fiber is required resulting in a high lasing threshold and poor stability. In recent years, UV lasers have been used to increase light backscattering in optical fibers for distributed temperature and strain measurements with higher spatial resolution and higher signal-to-noise ratio (SNR) [44,57]. However, H2-loading of SMF-28 and specialty fibers with high Ge-concentrations are usually required to increase the fiber’s UV photosensitivity. Considering IR lasers, a CO2 laser was used to produce randomly spaced index changes in optical fiber for distributed feedback of fiber lasers with narrower linewidth and lower noise [47,48]. Fs IR lasers were also used to enhance backscattering in optical fiber for high temperature measurement [45]. In these applications, the IR laser-induced very high broadband losses.

3.1. Femtosecond Laser Fabrication of RFGs Recently, we significantly expanded the use of fs IR lasers to fabricate RFGs in stan- dard single mode fiber (SMF-28, Corning) for distributed sensing. The varieties of RFGs include ultra-low insertion loss RFGs for long-haul distributed sensors based on fiber lasers, broadband RFGs for multi-parameter sensing, and strong RFGs for the use in fiber lasers and fiber laser sensor applications. The setup of the plane-by-plane inscription of RFGs is similar to what was shown previously to write standard FBGs [41] (see Figure 15). A fs IR beam from a Ti:sapphire regenerative amplifier (Spitfire, Spectra-Physics) was focused onto the fiber core with a microscope objective (50×, NA = 0.6). To increase the overlap of the laser-induced index change and the modal field in the fiber core, a cylindrical lens with a focal length of either 0.5 m or 1 m was introduced into the laser writing setup before the microscope objective. The cylindrical shape of the focal volume normally produced by the microscope objective alone is instead transformed into a planar strip. The fiber was clamped to a precision air-bearing stage (Aerotech) with a ±10 nm position accuracy. The fs IR laser operated at a central wavelength of λ0 = 800 nm with a repetition rate up to 1 kHz and with a pulse duration of ~120 fs. The microscope objective was mounted on a translation stage (driven by a piezo actuator) that could move the microscope objective back and forth along the fiber by up to 20 µm. The fiber coating was removed so that the laser beam could be easily Sensors 2021, 21, x FOR PEER REVIEW 15 of 25

loading of SMF-28 and specialty fibers with high Ge-concentrations are usually required to increase the fiber’s UV photosensitivity. Considering IR lasers, a CO2 laser was used to produce randomly spaced index changes in for distributed feedback of fiber lasers with narrower linewidth and lower noise [47,48]. Fs IR lasers were also used to enhance backscattering in optical fiber for high temperature measurement [45]. In these applications, the IR laser-induced very high broadband losses.

3.1. Femtosecond Laser Fabrication of RFGs Recently, we significantly expanded the use of fs IR lasers to fabricate RFGs in stand- ard single mode fiber (SMF-28, Corning) for distributed sensing. The varieties of RFGs include ultra-low insertion loss RFGs for long-haul distributed sensors based on fiber la- sers, broadband RFGs for multi-parameter sensing, and strong RFGs for the use in fiber lasers and fiber laser sensor applications. The setup of the plane-by-plane inscription of RFGs is similar to what was shown previously to write standard FBGs [41] (see Figure 15). A fs IR beam from a Ti:sapphire regenerative amplifier (Spitfire, Spectra-Physics) was focused onto the fiber core with a microscope objective (50×, NA = 0.6). To increase the overlap of the laser-induced index change and the modal field in the fiber core, a cylindrical lens with a focal length of either 0.5 m or 1 m was introduced into the laser writing setup before the microscope objective. The cylindrical shape of the focal volume normally produced by the microscope objective alone is instead transformed into a planar strip. The fiber was clamped to a precision air- bearing stage (Aerotech) with a ±10 nm position accuracy. The fs IR laser operated at a central wavelength of λ0 = 800 nm with a repetition rate up to 1 kHz and with a pulse Sensors 2021, 21, 1447 duration of ~120 fs. The microscope objective was mounted on a translation stage (driven15 of 23 by a piezo actuator) that could move the microscope objective back and forth along the fiber by up to 20 μm. The fiber coating was removed so that the laser beam could be easily focused ontoonto thethe fiber fiber core. core. The The fiber fiber was was free-standing, free-standing, with with no index no index matching matching fluid usedfluid betweenused between the fiber the andfiber the and objective. the objective.

Figure 15. A schematic of the setup used to fabricate RFGs.

The plane-by-planeplane-by-plane approach approach has has certain certain advantages advantages over over the point-by-point the point-by-point approach ap- forproach the fabricationfor the fabrication of RFGs andof RFGs FBGs and more FBGs generally. more Forgenerally. the PbP For approach, the PbP the approach, dimensions the ofdimensions the index of change the index of a gratingchange ‘plane’of a grating are typically ‘plane’ are much typically smaller much than thesmaller core than (<1 µ them) resultingcore (<1 μ inm) poor resulting overlap in poor between overlap the guided between mode the guided field propagating mode field along propagating the fiber along core andthe fiber the grating core and structure. the grating To increase structure. the To coupling increase between the coupling the guided between mode the field guided and themode grating, field and either thethe grating, magnitude either ofthe the magnitude index change of the or index its physical change or dimension its physical needs di- tomension be increased. needs to Although be increased. it is straight Although forward it is straight to increase forward the index to increase change the with index the PbPchange approach, with thevery PbP approach, high scattering very high losses scattering are introduced losses are as introduced well. Several as well. approaches Several haveapproaches been reported have been to reported increase to the increase overlap the between overlap thebetween guided the mode guided and mode the gratingand the while producing lower scattering losses. Zhou et al. [58] demonstrated a scanning method to increase the index change dimension by inscribing a line rather than a point across the fiber core. After one line is made, the fiber is moved along the fiber axis and then another line of index change is made. Strong higher order FBGs were made with this technique but with very high scattering losses (~1.2 dB/cm). Williams et al. [59] presented a continuous core-scanning technique where a piezo stage was driven by a sine wave, resulting in a sinusoidal index change across the core. Strong first order FBGs with low induced scattering loss were fabricated with the approach. The fabrication process however is complicated, time consuming when long grating lengths are considered and requires the use of oil-immersion objectives. The use of the long focal length cylindrical lens before the microscope objective, as shown in Figure 15, transforms the cylindrical shape of the focal volume normally produced by the microscope objective into a circular plane. Each plane can be easily inscribed with a single pulse in free-standing fiber without oil-immersion objectives, simplifying the grating fabrication. When intensities are used that result in Type I modification, very long (>250 mm) grating structures can be produced with very low losses (~0.02 dB/cm) [41]. There are two approaches to fabricate RFGs using the setup shown in Figure 15. The selection of the particular approach depends on different application requirements. The first approach requires dithering of the piezo-driven stage along the fiber axis with random displacements while the air-bearing stage moves at a constant velocity and the laser operates at a constant repetition rate. Depending on the piezo stage used, this method can produce RFGs with random grating periods ranging from zero to a few micrometers. The second approach to fabricate RFGs requires the introduction of random changes to the laser repetition rate while the air-bearing stage moves at a constant speed and the piezo actuator is stationary. Details of these two methods are discussed elsewhere [9]. The first method involving the piezo stage is used for fabrication of RFGs with broadband spectral responses of up to a few micrometers which are useful for (i) multi-parameter Sensors 2021, 21, 1447 16 of 23

sensors, (ii) fiber lasers and (iii) fiber laser sensors [49,50,60,61]. The second method, in which the piezo stage is not involved, is used to make (i) RFGs with narrow bandwidths, (ii) RFGs with low insertion losses for long-haul fiber sensor systems [9], and (iii) very strong RFGs for low-threshold fiber lasers to be used in ultrasound sensing with high sensitivity at frequencies in the MHz range [51]. Simulations presented in Figure 16 were performed using coupled mode theory and show the difference in spectral responses of RFGs fabricated using the two above methods. In both simulations, the laser induced index modulation was 1 × 10−6. The total grating length was 100 mm and comprised 4000 sub-gratings, each sub-grating with a uniform pitch that is 25 µm in length but with grating periods that varied randomly. In Figure 16a, the period of each sub-grating was distributed randomly between 0 and 2.5 µm. These conditions corresponded to the case where the air-bearing stage traveled at a constant velocity of 0.5 mm/s, the laser operated at 1 kHz repetition rate, and the piezo stage dithered with random displacements from 0 to 2 µm every 50 ms. In Figure 16b, the grating period of each sub-grating was randomly distributed from 0.5328 to 0.5436 µm, corresponding to the instance where the air-bearing moved at a constant velocity of 0.5382 mm/s and the repetition rate of the laser is randomly tuned every 50 ms from 990 to 1100 Hz (2%).

Figure 16. Simulated back reflection signals of two 100 mm long RFGs. (a) the grating period is randomly distributed from 0 to 2.5 µm and (b) the repetition rate of the fs IR laser is tuned randomly within a 2% range.

3.2. Applications of RFGs Similar to FBGs, RFGs have been used widely in optical fiber communication and sensing applications. Here only the sensing applications of RFGs will be discussed.

3.2.1. Distributed Sensing By using the fs IR laser frequency tuning method, RFGs with low laser-induced losses were fabricated in SMF-28 and used for distributed temperature measurements using the technique of optical frequency domain reflectometry (OFDR) [9]. The backscattering spectrum of the RFG was first measured as a reference, after which temperature-induced variations of the backscattering spectrum were measured and compared to the reference. The distributed spectral shift could then be obtained using a cross-correlation algorithm. To evaluate the sensor performance experimentally, a piece of 100 mm long RFG was sub- merged into a re-circulating chiller/water bath where the water temperature was precisely controlled and maintained at a constant temperature of 20 ◦C ± 0.01 ◦C. The backscattering spectrum of the RFG was repeatedly recorded every minute by an OFDR device (OBR4600, Luna) to monitor the temperature variation of the sensing system (measurement error). For comparison, the temperature measurement error was also simultaneously measured using a length of SMF-28 (see Figure 17). The advantage of using an RFG is obvious. With a gauge length of 10 mm, the standard deviation of the temperature measurement error was Sensors 2021, 21, 1447 17 of 23

Sensors 2021, 21, x FOR PEER REVIEW ◦ ◦ 18 of 25 as low as 0.00085 C in the case of RFG, while it was more than 0.01 C in the case where SMF-28 was used. The laser-induced loss in this RFG is very low (0.08 dB/m), which is desired for long-haul fiber sensing networks.

FigureFigure 17. 17.Variations Variations of temperature of temperature measurement measurement (error) when an (error) RFG and when regular an SMF-28 RFG were and regular SMF-28 were usedused to to measure measure the waterthe water temperature temperature in a re-circulating in a re-circulating chiller/water chiller/water bath where the waterbath where the water tem- temperature was precisely controlled with temperature errors < 0.01 ◦C. perature was precisely controlled with temperature errors < 0.01 °C. 3.2.2. Multi-Parameter Sensing Based on RFGs 3.2.2.RFGs Multi can- beParameter directly used Sensing for multi-parameter Based on sensing RFGs [60]. For this application, an RFG was fabricated in SMF-28 with the piezo stage dithering method and with the fs IR laser pulse energyRFGs above can thebe thresholddirectly of used making for Type multi II FBGs-parameter [34]. Due to sensing the Type II [60]. nature For of this application, an indexRFG changewas fabricated in the fiber, there in SMF is strong-28 couplingwith the between piezo the stage fundamental dithering propagation method and with the fs IR core mode and high-order cladding modes resulting in both a Mach–Zehnder interference (MZI)laser scheme pulse via energy core-cladding above mode the coupling threshold and a Fabry–Pof makingérot interference Type II (FPI)FBGs scheme [34]. Due to the Type II vianature multi-reflected of index core-to-core change modein the coupling. fiber, Thethere core-cladding is strong mode coupling coupling between makes the fundamental thepropagation grating spectral core signature mode sensitive and high to surrounding-order cladding refractive modes index change. resulting Due to in the both a Mach–Zehnder waveguide and material dispersion effects in optical fiber, the grating spectral shifts caused byinterference the changes in(MZI) temperature, scheme strain via and core surrounding-cladding refractive mode coupling index have differentand a Fabry–Pérot interfer- dependenciesence (FPI) onscheme wavelength, via whichmulti can-reflected be applied forcore multi-parameter-to-core mode sensing. coupling. It is not The core-cladding possiblemode coupling to observe spectral makes changes the grating from the spectral entire RFG signature by conventional sensitive peak detection to surrounding refractive methods typically used for FBG interrogation. Instead, a wavelength-division spectral cross-correlationindex change. algorithm Due to is the adopted waveguide to extract the and spectral material shift associated dispersion with different effects in optical fiber, the externalgrating disturbances. spectral shifts An autocorrelation caused by ofthe the changes reflection spectrumin temperature, is performed strain which and surrounding re- createsfractive a correlation index have peak that different is located atdependencies the center of the spectralon wavelength, range. When subjected which can be applied for tomulti an external-parameter parameter sensing. such as It a change is not inpossible temperature, to observe a shift in spectral the correlation changes peak from the entire RFG is observed. In Figure 18, two reflection spectra from the RFG are obtained, one at 27 ◦C (Figureby conventional 18a) and the other peak at detection 83 ◦C (Figure methods 18b). Reflection typically spectra used were for obtained FBG using interrogation. Instead, a anwavelength optical spectrum-division analyzer spectral with a 20 cross pm spectral-correlation resolution. algorithm Autocorrelation is adopted and cross- to extract the spectral correlationsshift associated of the two with reflection different spectra external are presented disturbances. in Figure 18c,d An respectively. autocorrelation of the reflection The cross-correlation peak wavelength is seen to shift with temperature. To simultane- ouslyspectrum measure is multiple performed parameters which different creates wavelength a correlation regions of peak the broad that bandwidth is located at the center of the ofspectral the RFG range. are considered When (see subjected Figure 19 toa). an The external resulting cross-correlationparameter such wavelength as a change in temperature, shiftsa shift have in different the correlation dependencies peak to external is observed. disturbances In due Figure to material 18, and two waveguide reflection spectra from the RFG are obtained, one at 27 C (Figure 18a) and the other at 83 C (Figure 18b). Reflection spectra were obtained using an optical spectrum analyzer with a 20 pm spectral resolu- tion. Autocorrelation and cross-correlations of the two reflection spectra are presented in Figure 18c,d respectively.

Sensors 2021, 21, 1447 18 of 23

Sensors 2021, 21, x FOR PEER REVIEW dispersion of the fiber allowing for the discrimination of changes19 of 25 to temperature, strain and surrounding refractive index (see Figure 19b–d).

FigureFigure 18. Measured 18. Measured reflection spectra reflection of the RFG spectra at (a) a ofreference the RFG temperature at (a) aand reference (b) at an in- temperature and (b) at an creasedincreased temperature; temperature; (c) the auto-correlation (c) the auto-correlation spectrum of (a,d) the spectrum cross-correlation of (a ,spectrumd) the cross-correlation of spectrum of (a,b) (reproduced from [60]). Sensors 2021, 21, x FOR PEER REVIEW 20 of 25 (a,b) (reproduced from [60]). The cross-correlation peak wavelength is seen to shift with temperature. To simulta- neously measure multiple parameters different wavelength regions of the broad band- width of the RFG are considered (see Figure 19a). The resulting cross-correlation wave- length shifts have different dependencies to external disturbances due to material and waveguide dispersion of the fiber allowing for the discrimination of changes to tempera- ture, strain and surrounding refractive index (see Figure 19b–d). According to the error analysis for simultaneous multi-parameter measurements [61], the minimum errors of temperature measurements for the three subsections respec- tively were 0.16 pm/C, 0.16 pm/C and 0.12 pm/C. Similarly the axial strain errors are 0.01, 0.02 and 0.02 pm/με. The minimum errors of the RI measurement were 59.0, 37.7 and 65.8 pm/RIU.

Figure 19. (a) ThreeFigure spectral 19. (a) T regionshree spectral selected regions in selected the reflection in the reflection spectrum spectrum of an ofRFG. an RFG. Calibration Calibration results results based on cross-correlation peak wavelength shift for (b) temperature, (c) strain, and (d) based on cross-correlationrefractive index. peak wavelength shift for (b) temperature, (c) strain, and (d) refractive index.

According to theMulti error-parameter analysis sensing for can simultaneous also be realized multi-parameter by measuring the measurementswavelength shifts of [61 ], the minimum errorsa random of fiber temperature laser where measurements an RFG is used for for distributed the three feedback subsections [49]. Depending respectively on ◦the polarization ◦of the light backscattered◦ from the RFG and the pump current, an RFG- were 0.16 pm/basedC, 0.16 random pm/ fiberC laser and can 0.12 lase pm/ at multipleC. Similarly wavelengths. the The axial lasing strain lines errors have different are 0.01, strain and temperature dependencies due to the different index modifications as well as dispersion effects. By monitoring the shifts of different lasing lines, simultaneous multi- parameter measurements could be achieved with better resolution compared with the sin- gle-pass random grating sensor. Figure 20 shows an experimental setup of a random fiber laser with an RFG incorporated for distributed feedback. Figure 21 shows the correspond- ing laser output with a different number of lasing lines that can be produced by adjusting the two polarization controllers in the setup along with the laser pump current. The num- ber of sensing parameters can be controlled by the number of lasing lines.

Sensors 2021, 21, 1447 19 of 23

0.02 and 0.02 pm/µε. The minimum errors of the RI measurement were 59.0, 37.7 and 65.8 pm/RIU. Multi-parameter sensing can also be realized by measuring the wavelength shifts of a random fiber laser where an RFG is used for distributed feedback [49]. Depending on the polarization of the light backscattered from the RFG and the pump current, an RFG-based random fiber laser can lase at multiple wavelengths. The lasing lines have different strain and temperature dependencies due to the different index modifications as well as dispersion effects. By monitoring the shifts of different lasing lines, simultaneous multi-parameter measurements could be achieved with better resolution compared with the single-pass random grating sensor. Figure 20 shows an experimental setup of a ran- dom fiber laser with an RFG incorporated for distributed feedback. Figure 21 shows the corresponding laser output with a different number of lasing lines that can be produced by

Sensors 2021, 21, x adjustingFOR PEER REVIEW the two polarization controllers in the setup along with the laser pump21 ofcurrent. 25 The number of sensing parameters can be controlled by the number of lasing lines. Sensors 2021, 21, x FOR PEER REVIEW 21 of 25

Figure 20. A schematic diagram of the experimental setup of the RFG-based Erbium-doped fiber Figure 20. A schematic diagram of the experimental setup of the RFG-based Erbium-doped fiber ring laser; the magnified call-out shows a schematic of light backscattering within an RFG. EDFA ring laser; theand magnifiedFigure PC stand 20. call-outAfor schematic Erbium shows-doped diagrama fiber schematic of amplifierthe experimental of and light polarization setup backscattering of the controller. RFG-based within Erbium an RFG.-doped EDFA fiber and PC stand for Erbium-dopedring laser; the magnified fiber amplifier call-out shows and polarizationa schematic of light controller. backscattering within an RFG. EDFA and PC stand for Erbium-doped fiber amplifier and polarization controller.

Figure 21. (a) Lasing thresholds for different numbers of emitted lasing lines as a function of

pump current. Lasing spectra with different input polarizations are shown for (b) one lasing line, Figure 21. (a)( Lasingc) twoFigure lasing thresholds21. (lines,a) Lasing andfor (thresholdsd) three different lasing for differentnumbers lines. numbers of emitted of emitted lasing lasing lines lines as as aa function of of pump pump current. Lasing spectra with different input polarizations are shown for (b) one lasing line, current. Lasing spectra with different input polarizations are shown for (b) one lasing line, (c) two 3.2.3.(c) twoHigh lasing Frequncy lines, Ultrasound and (d) three Sensing lasing lines.Based on RFGs lasing lines, and (d) three lasing lines. In this application, an RFG was not only used as a distributed feedback element for 3.2.3. High Frequncy Ultrasound Sensing Based on RFGs the random fiber laser, but also as a sensing element for ultrasound detection [50]. The RFG as wellIn this as application,a piezoelectric an transducer RFG was not (PZT) only actuator used as were a distributed mounted ontofeedback an aluminum element for plate.the Torandom generate fiber ultrasonic laser, but waves, also as the a PZTsensing actuator element was for driven ultrasound by a function detection generator [50]. The to produceRFG as well Rayleigh as a piezoelectric waves that transducer propagated (PZT) as acoustic actuator surface were mounted waves along onto anthe aluminum alumi- numplate. plate To (see generate Figure ultrasonic 22a). The detewaves,ction the of PZT the ultrasoundactuator was was driven performed by a function by monitoring generator to produce Rayleigh waves that propagated as acoustic surface waves along the alumi- num plate (see Figure 22a). The detection of the ultrasound was performed by monitoring

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3.2.3. High Frequncy Ultrasound Sensing Based on RFGs In this application, an RFG was not only used as a distributed feedback element for the random fiber laser, but also as a sensing element for ultrasound detection [50]. The RFG as well as a piezoelectric transducer (PZT) actuator were mounted onto an aluminum Sensors 2021, 21, x FOR PEER REVIEW 22 of 25 plate. To generate ultrasonic waves, the PZT actuator was driven by a function generator to produce Rayleigh waves that propagated as acoustic surface waves along the aluminum plate (see Figure 22a). The detection of the ultrasound was performed by monitoring the thelaser laser wavelength wavelength shift shift due due to to the the ultrasonic ultrasonic wave, wave, asas shownshown in Figure 22b.22b. The The tunable tunable filterfilter shown shown in in Figure Figure 22a 22 awas was set set to to select select a aspecific specific laser laser line. line. Lasing Lasing of of the the erbium erbium fiber fiber ringring laser laser shown shown in in Figure Figure 22a 22 ais is possible possible at at several several wavelengths wavelengths depending depending on on the the state state ofof polarization polarization of of the the intra intra-cavity-cavity light light and and the the birefringent birefringent properties properties of of the the RFG RFG [48]. [48]. A A tunabletunable filter filter is is introduced introduced toto ensureensure single-wavelength single-wavelength lasing lasing and and the the lasing lasing line line is selected is se- lectedsuch thatsuch the that laser the emissionlaser emission (red line (red in line Figure in Figure 22b) rests 22b) on rests the steepon the slope steep of slope one ofofmany one ofreflectivity many reflectivity peaks generated peaks generated by the by RFG the (black RFG (black line in line Figure in Figure 22b). The22b). dynamic The dynamic strain straingenerated generated by the by PZT the actuatorPZT actuator results results in a shifting in a shifting of the of RFG the reflectionRFG reflection spectrum spectrum which whichcauses causes a modulation a modulation of the of lasing the lasing output output power. power. The The proposed proposed laser laser sensor sensor exhibited exhib- a itedbroadband a broadband ultrasound ultrasound response response within within a 0.8 a MHz 0.8 MHz frequency frequency range range with with a high a high SNR. SNR.

Figure 22. (a) A schematicFigure of the RFG-based 22. (a) A schematic random laserof the sensor RFG- forbased ultrasound random detection.laser sensor (b )for laser ultrasound wavelength detection. shift due (b to) ultrasonic waves. PC1 andlaser PC2 wavelength denote polarization shift due controllers. to ultrasonic waves. PC1 and PC2 denote polarization controllers.

3.2.4.3.2.4. Random Random Fiber Fiber Lasers Lasers BesidesBesides the the numerous numerous applications applications in in sensing, sensing, RFGs RFGs have have also also been been used used to to signifi- signifi- cantlycantly improve improve the the performance performance of of random random fiber fiber lasers lasers resulting resulting in in fiber fiber lasers lasers with with new new features.features. We We will will not not discuss discuss all all the the details details here here but but only only provide provide a abrief brief summary summary of of the the pertinentpertinent results: results: (i) (i) low frequency noisenoise Brillouin Brillouin random random fiber fiber laser laser based based on anon RFGan RFG feed- feedbackback was was demonstrated demonstrated with with a very a very narrow narrow laser laser line line width width (<50 (<50 Hz) Hz) [62], [62], (ii) the (ii) time-delaythe time- delaysignature signature of an of RFG-based an RFG-based fiber fiber laser laser was suppressedwas suppressed to be to as be low as aslow 0.0088 as 0.0088± 0.0015 ± 0.0015 [63 ], [63],which which is of is extremeof extreme importance importance for for real-time real-time physical physical randomrandom bit generation generation [52], [52], (iii) (iii) multimulti-wavelength-wavelength Brillouin Brillouin random random fiberfiber laserslasers [64[64]] and and thermal/acoustic thermal/acoustic noise noise insensitive insensi- tiveBrillouin Brillouin random random fiber fiber lasers lasers [65 ][65] were were realized realized due due to the to the incorporation incorporation of RFGs of RFGs into into their theirdesign. design.

4.4. Conclusions Conclusions InIn this this review, review, we we presented presented recent recent advances advances in in TTC TTC femtosecond femtosecond laser laser inscription inscription of of FBGsFBGs and and how how it itrelates relates to to sensing sensing applications. applications. Namely Namely we we showed showed that that TTC TTC fabrication fabrication ofof distributed distributed FBG FBG arrays arrays in in 50 50 m m diameter diameter fiber fiber filaments filaments becomes becomes possible possible by by using using a a femtosecondfemtosecond laser laser and and the the phase phase mask mask technique technique if ifthe the complex complex diffraction diffraction and and dispersion dispersion effectseffects highlighted highlighted in in this this article article are are properly properly taken taken into into account. account. Such Such FBG FBG sensor sensor arrays arrays cancan be be easily easily integrated integrated into into composite composite materials materials for for structural structural health health monitoring monitoring or or 3D 3D printedprinted components components for for smart smart structures. structures. WeWe also also showed showed thatthat femtosecond femtosecond lasers lasers and the and phasethe phase mask mask technique technique can be can used be usedfor TTC for TTCfabrication fabrication of tilted of tilted or core or- core-offsetoffset gratings gratings for multi-parameter or refractive index sensing. The specific application of a specially pack- aged TTC-written FBG for distributed oil pipeline leak detection is also presented. In addition, this article reviews recent developments in fs laser fabrication of RFGs and applications of the resultant RFGs. More specifically, we demonstrated that the spec- trum of an RFG inscribed using a femtosecond laser and the plane-by-plane technique can

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for multi-parameter or refractive index sensing. The specific application of a specially packaged TTC-written FBG for distributed oil pipeline leak detection is also presented. In addition, this article reviews recent developments in fs laser fabrication of RFGs and applications of the resultant RFGs. More specifically, we demonstrated that the spec- trum of an RFG inscribed using a femtosecond laser and the plane-by-plane technique can be easily tailored for different applications, such as highly accurate distributed tempera- ture/strain measurements, high sensitivity multi-parameter sensing, and high-frequency ultrasound detection.

Funding: This research received no external funding. Conflicts of Interest: The authors declare no conflict of interest.

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