1. INTRODUCTION

Optical fibers are an excellent platform for sensing because they support measurement over hundreds of kilometers, are simply embedded within the structures under test, provide comparative immunity to electromagnetic interference, and are suitable for harsh and hazardous environments [1,2]. The detection and analysis of chemicals are among the main objectives of optical fiber sensors. Such sensors, however, face an inherent challenge: Standard optical fibers guide light at an inner core that is isolated from its surrounding, whereas a substance under test typically lies outside a much larger cladding. Guided light is often insensitive to the presence and properties of media outside the cladding boundaries. The difficulty is increased further by coating layers outside the cladding, which are mandatory for nearly all applications of fibers outside the research laboratory. Many optical fiber sensors of chemicals therefore rely on nonstandard fiber geometries [3–6], fibers with core and/or cladding made of specialty materials that react with target media [7,8], or structural modifications to standard fibers such as etching [9], tapering [10], cleaving of facets [11], or drilling of holes [12].

A promising strategy for chemical sensing relies on the coupling of guided light to the cladding modes of standard fibers [13–15]. The transverse profiles of cladding modes span the entire cross-section of the fiber cladding and reach its outer boundary. The evanescent tails of cladding mode profiles may overlap with an outside substance under test, and their propagation can be affected by the optical properties of that substance [13–15]. Cladding mode fiber sensors have been widely studied and employed for more than 30 years [13–15]. The coupling of light to or from cladding modes typically relies on the inscription of permanent gratings [16,17]. The gratings restrict the operation of the sensors to point measurements in a predetermined, discrete set of locations only, and the extension of the sensors toward spatially distributed analysis of outside conditions is difficult. In addition, the refractive indices of most standard coating materials exceed that of the silica cladding, and consequently suppress the guiding of the cladding modes. Certain types of coatings are also absorbing. Cladding mode sensors are often restricted to operation in bare fibers, and their practical value is significantly diminished.

In this work, we report the spatially distributed analysis of coupling spectra to the cladding modes of a standard, off-the-shelf, coated single-mode fiber. The inscription of gratings, the removal of the coating, or any other structural modifications are not required. The refractive index of the specific fluoroacrylate coating is lower than that of silica [18], so the guiding of cladding modes is supported. Light is coupled to the cladding modes using Brillouin dynamic gratings [19–22]: Two counter-propagating optical pump waves stimulate longitudinal acoustic waves in the core of the fiber through a standard, backward Brillouin scattering process [19–22]. The same acoustic wave, in turn, can couple a probe wave from the core mode to a cladding mode of the coated fiber. Coupling takes place at specific optical frequencies of the probe wave, which are determined by the effective indices of the core and cladding modes [22]. The frequencies of maximum coupling are sensitive to the properties of media outside the cladding.

Spatially distributed measurements are obtained using time-domain principles: pulse modulation of one of the pump waves and time-of-flight analysis of the output probe wave [23,24]. The spatial resolution of the measurement is one meter. The protocol is demonstrated over a range of five meters; however, it is scalable to a range of hundreds of meters. The acquisition duration is several minutes. The measurements identify local changes in the index difference between core and cladding modes, to the sixth decimal point.

The measurements identify the local immersion of a meter-long coated fiber in acetone. The coupling spectra to the cladding modes change within minutes following immersion and continue to evolve over hours. The observations are supported by control experiments using a thin film of the same polymer and by monitoring the elastic properties of the immersed coating through opto-mechanical analysis [25,26]. The presence of acetone could not be identified in Brillouin scatting measurements in the core mode only. The results extend upon our previous study of distributed cladding mode sensors [22], in two significant respects: the introduction of time-domain distributed analysis and the use of coated fibers. The experiments demonstrate the potential of the proposed technique toward distributed analysis of media outside fibers that is practical, sensitive, specific, and convenient. Preliminary results were presented at a recent conference [27].

2. PRINCIPLE OF OPERATION

A. Brillouin Optical Time-Domain Analysis of Coupling to the Cladding Modes of Coated Fibers

Figure 1(a) shows a schematic cross-section of the single-mode fiber used in this work [26]. The fiber was provided by OFS, a unit of Furukawa Electric Co. It was drawn from an SMF-28-compatible, G.652 preform, and had a germanium-doped silica core and a pure silica cladding with a 125 µm diameter. The field diameter of the single core mode was taken as 10.4 µm, according to specifications. The fiber was coated at production by a fluoroacrylate polymer layer with an outer diameter of 136 µm. The coating is designed for an index of 1.405 refractive index units (RIUs), which is lower than that of silica (1.45 RIUs). Fluoroacrylate layers often serve as light-guiding claddings in specialty fibers [18]. Due to the low index of the polymer layer, the coated fiber supports the propagation of a discrete set of cladding modes. Figure 1(b) presents the calculated transverse profile of the electromagnetic intensity in the 11th cladding mode. The effective index of that mode is 1.442 RIUs. An evanescent tail of the modal profile is exponentially decaying into the coating layer.

 

Fig. 1. (a) Schematic cross-section of the single-mode fiber used in this work [26]. The fiber is drawn from an SMF-28-compatible, G.652 preform. It consists of a germanium-doped silica core, a pure silica cladding of 125 µm outer diameter, and a fluoroacrylate polymer coating with an outer diameter of 136 µm. (b) Calculated normalized transverse profile of electromagnetic intensity in the 11th cladding mode of the coated fiber shown in (a). The effective index of that mode is 1.442 RIU.

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Light is coupled between the core mode and the cladding modes of the fiber using Brillouin dynamic gratings [19–22]. Let ${E_{\rm pump1}}$ denote the field of a first optical pump wave of frequency ${\omega _{\rm pump1}}$, propagating in the positive $\hat z$ direction. A second pump field ${E_{\rm pump2}}$ is counter-propagating in the $-\hat z$ direction. The optical frequency of the second pump wave is ${\omega _{\rm pump2}} = {\omega _{\rm pump1}} - {{\Omega}}$, where the offset ${{\Omega}}$ is chosen near the Brillouin frequency shift of the fiber ${{{\Omega}}_B}$. Both pump waves propagate in the single core mode of the fiber. The two pumps generate an acoustic wave of frequency ${{\Omega}}$, through a backward stimulated Brillouin scattering process [19–22]. The acoustic wave co-propagates with the first pump wave in the positive $\hat z$ direction.

Consider next an optical probe wave of frequency ${\omega _{{\rm probe}}} \gt {\omega _{\rm pump1}}$, which is launched alongside ${E_{\rm pump1}}$ to the core mode in the positive $\hat z$ direction. The stimulated acoustic wave may partially couple the probe to a cladding mode of integer order $m$, in the opposite, $-\hat z$ direction [22]. The coupling induced by the acoustic wave is analogous to that of a short period fiber Bragg grating [17,22]. Brillouin dynamic gratings are most often used to couple between Brillouin scattering processes along the principal axes of polarization-maintaining fibers [19–21]. However, the concept is also applicable to different spatial modes of few-order-mode fibers [28], and we have recently introduced it to the coupling of light between core and cladding modes [22].

Figure 2(a) illustrates the dispersion relations between temporal frequencies and axial wavenumbers of modal solutions for guided waves in the fiber: the optical core mode, an optical cladding mode, and a dilatational axial acoustic mode. Each dashed line represents one such mode. The solid arrows represent specific choices of frequency and wavenumber for fields taking part in the interaction. The acoustic coupling to a cladding mode of order $m$ is wavenumber matched for a specific optical frequency of the probe wave, $\omega _{{\rm opt}}^{(m)}$ [22]:

 

Fig. 2. Coupling between the core mode and a cladding mode through a Brillouin dynamic grating [27]. (a) Illustration of the dispersion relations for the core mode of the fiber in both directions, a cladding mode in one direction, and a longitudinal acoustic wave in silica. A Brillouin dynamic grating (black) is stimulated by the two pump waves (blue and red). The probe wave (green) is coupled into the cladding mode (purple) by the dynamic grating [22]. (b) Top: Two counterpropagating pump waves in the core mode (red and blue) with frequency difference of ${{{\Omega}}_B}$ stimulate a Brillouin dynamic grating (black). The intensity of one of the pump tones is modulated by isolated pulses, and therefore the dynamic grating also propagates as a pulse perturbation. Bottom: A probe wave in the core mode (green), with frequency offset ${{\Delta}}\omega$ with respect to the pumps, is scattered by the Brillouin dynamic grating to the cladding mode (purple). Local coupling to the cladding mode can be monitored by observation of the output probe power (green) as a function of time.

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Here, ${n_{{\rm{core}}}}$ and $n_{{\rm clad}}^{(m)}$ denote the effective indices of the core mode and the $m$th order-cladding mode, respectively. The difference ${{\Delta}}\omega _{{\rm opt}}^{(m)}$ between the frequency of the pump and the optimal probe frequency $\omega _{{\rm opt}}^{(m)}$ is given by

The wavenumber-matching condition is therefore highly sensitive to the difference in effective indices $\Delta n^{(m)}=n_{\rm core}-n_{\rm clad}^{(m)}$ between the core and cladding modes. For example, a difference in indices at the second decimal point corresponds to ${{\Delta}}\omega _{{\rm opt}}^{(m)}$ of hundreds of GHz, or to a wavelength offset of several nanometers. Conditions that affect the indices of both modes in a similar manner have a lesser effect on ${{\Delta}}\omega _{{\rm opt}}^{(m)}$.

The relative fraction of optical power that is coupled from the core mode probe to the $m$th cladding mode, over a uniform fiber section of length ${{\Delta}}L$ at position $z$, is given by [22]

In Eq. (3), ${P_{1,2}}(z)$ denote the local power levels [${{W}}$] of the first and second pump waves, respectively, ${g_B}$ ${\sim}\;{0.1}\;{{\rm{W}}^{- 1}} \times {{\rm{m}}^{- 1}}$ is the coefficient of backward stimulated Brillouin scattering in standard single-mode fibers, ${{{\Omega}}_B}$ is again the Brillouin frequency shift, and ${{{\Gamma}}_B}$ ${\sim}\;{{2}}\pi \times {{30}}\;{\rm{MHz}}$ is the linewidth of that process. The mismatch $\Delta k^{(m)}$ of the modal wavenumbers is [22]

The reflectivity of the probe depends on the spatial overlap between the optical modes involved and the acoustic mode. In Brillouin dynamic gratings over polarization-maintaining fibers, the probe is launched in the optical core mode and back-reflected within that same mode. The overlap between the core mode and the acoustic mode, which is also confined to the core, is comparatively large. In this work, the spatial overlap between the core mode, cladding mode, and acoustic mode is smaller and degrades the probe wave reflectivity. We quantify the reduced reflectivity due to the mismatch in spatial profiles by the unitless inefficiency penalty ${| {{\eta ^{(m)}}} |^2}$, which is cladding-mode specific. The penalty is derived in detail in [22], and it assumes a value of unity in core-mode Brillouin dynamic gratings of polarization-maintaining fibers. For the coated fiber used in this work, ${| {{\eta ^{(m)}}} |^2}$ is 0.025 at most, as shown in Fig. 3.

 

Fig. 3. Calculated relative efficiency ${| {{\eta ^{(m)}}} |^2}$ of the dynamic grating coupling between the core mode and cladding modes of the fiber under test, as a function of the necessary wavelength offset between pumps and probe waves [22]. The highest relative efficiency of 2.5% is predicted for cladding modes that require an offset of 3 nm.

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The dependence of the reflectivity spectrum on the frequencies of the pumps and probe is separable. The spectrum varies with the difference ${{\Omega}}$ between the pump waves according to the Lorentzian lineshape of Brillouin scattering, and with the choice of probe frequency due to wavenumber matching considerations. The former term describes the stimulation of the Brillouin dynamic grating, whereas the latter quantifies the photoelastic scattering by the same grating. The spectral bandwidth with respect to the offset between the pumps is given by ${{{\Gamma}}_B}$. The bandwidth for the probe frequency is inversely proportional to the length of the fiber section $\Delta L$: It is expected to be on the order of 100 MHz for a meter-long fiber, but it may be broadened due to nonuniformities in the cladding or coating within that section length. For pump power levels of several Watts and a meter-long fiber section, the peak values of ${R^{(m)}}$ are expected to be between 10–100 parts per million (ppm). Such a weak coupling between the core and cladding modes is nevertheless measurable.

 

Fig. 4. Schematic illustration of the experimental setups [27]. (a) Nondistributed coupling of an optical probe wave to the cladding modes of a standard, coated fiber using Brillouin dynamic gratings. (b) Extension of the setup to spatially distributed analysis. BPF, tunable optical bandpass filter; SSB, single-sideband electro-optic modulator; EDFA, erbium-doped fiber amplifier; and EOM, electro-optic Mach–Zehnder intensity modulator.

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Spatially distributed mapping is realized using time-of-flight principles, which is similar to the standard Brillouin optical time-domain analysis (BOTDA) protocols. The first pump wave is continuous, whereas the second one is modulated by short pulses of duration ${{\Delta}}\tau$ and a low duty cycle [23,24]. The Brillouin dynamic grating therefore propagates in the $-\hat z$ direction in the form of pulsed perturbation, as shown in Fig. 2(b) [20]. The optical power of the probe wave is monitored at its output end of the fiber as a function of time [20]. The output probe power observed $\tau$ seconds following the launch of the pump pulse is related to the coupling losses to the cladding mode at a distance $z = {v_g}\tau /2$ from the input end of the pulse. Here, ${v_g}$ is the group velocity of light in the core mode. The spatial resolution of the analysis is ${{\Delta}}z=v_{g}\cdot \Delta \tau/2$.

B. Performance Limitations

The pulse duration in backward Brillouin scattering processes is limited by the lifetime of acoustic waves stimulation, on the order of 5–10 ns. The corresponding ${{\Delta z}}$ is about 1 meter. Numerous protocols have successfully brought down the resolution of BOTDA sensors in the core mode to several centimeters [29].

The interaction between the two pump waves may lead to the depletion or amplification of the pulsed pump over the entire length $L$ of a fiber under test. To avoid excessive depletion of the pulses pump wave ${E_{\rm pump2}}$, the coupling of optical power between the two pump waves must be restricted to [30]

Here, ${C_{{\rm dep}}}$ is a numerical factor that is application specific. This requirement restricts the power ${P_1}$ of the continuous pump wave ${E_{\rm pump1}}$. The depletion limitations of the proposed protocol are not as severe as those of standard Brillouin fiber sensors since the quantitative reconstruction of Brillouin gain spectra is not necessary. Nevertheless, excessive pumps depletion would reduce the magnitude of the stimulated dynamic gratings and should be avoided. We consider below ${C_{{\rm dep}}}\sim \,1$. This limitation on ${P_1}$ is more stringent than the restriction imposed by the possible onset of amplified spontaneous Brillouin scattering.

In addition to depletion considerations, the power ${P_2}$ of the pulsed pump wave is limited by the onset of modulation instability via the Kerr effect [31,32]:

In Eq. (6), ${\gamma _{{\rm Kerr}}}$ ${\sim}\;{1.3}\;{{\rm{W}}^{- 1}} \times {\rm{k}}{{\rm{m}}^{- 1}}$ is the coefficient of Kerr nonlinearity in standard, single-mode fiber, and ${C_{{\rm Kerr}}}$ denotes an application-specific constant that is again on the order of unity. Substituting Eqs. (5) and (6) into Eq. (3), we find that the maximum fraction of the optical probe power that may be coupled to a cladding mode via Brillouin dynamic gratings is bound by

Here, $N=\Delta L/L$ is the number of spatial resolution points. The maximum fraction of the probe power that may be coupled to the cladding modes within limits of depletion and modulation instability scales inversely with ${N^2}$. Given the above values of ${C_{{\rm dep}}}$, ${C_{{\rm Kerr}}}$, ${g_B}$, ${\gamma _{{\rm Kerr}}}$, and ${\eta ^{(m)}}$, we estimate the following upper bound:

The result of Eq. (8) sets the limit on the coupling signal that may be obtained for a given number of resolution points. That limitation, in turn, determines the number of averages over repeating acquisitions that is necessary to obtain a target SNR and measurement precision [33]. For a given detector noise level and precision requirements, the number of necessary averages would scale with ${N^4}$.

3. EXPERIMENTAL SETUP AND RESULTS

A. Coupling to the Cladding Modes of a Coated Fiber

Schematic illustrations of the experimental setups are shown in Fig. 4. The two pump waves were drawn from a common laser diode of 1563.3 nm wavelength. The exact optical frequency of the source was fine-tuned in a suppressed-carrier single-sideband (SC-SSB) electro-optic modulator, driven by a microwave generator. The small-scale frequency offsets adjusted the difference between the optical frequencies of the pump waves and the probe field. The pump light was split into two branches. The wave in one branch, ${E_{\rm pump1}}$, was amplified by an erbium-doped fiber amplifier (EDFA) to 30 dBm power and launched into one end of the fiber under test. The frequency of the pump wave ${E_{\rm pump2}}$ in the other branch was downshifted using a second SC-SSB modulator, driven by a sine wave from a second microwave generator. The difference frequency $\Omega$ between the pump waves was chosen to match the Brillouin frequency shift ${{{\Omega}}_B}{{\approx}}\;{{2}}\pi \times {10.890}\;{\rm{GHz}}$ of the fiber under test. The second pump wave was amplified by another EDFA to 27 dBm power and launched from the opposite end of the fiber under test.

 

Fig. 5. (a) Measured (blue) and calculated (red) normalized spectra of coupling from the core mode to cladding modes in the coated fiber under test, as functions of the probe wavelength. Coupling was achieved using Brillouin dynamic gratings. The pumps wavelength is noted in black. Discrete peaks correspond to specific cladding modes. Agreement between the model and measurements is good. (b)–(c) Magnified views of the experimental trace in (a). The spectral bandwidths of coupling to the specific two cladding modes are 115 MHz and 136 MHz for (b) and (c), respectively. The bandwidths agree with expectations.

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A continuous probe wave of 13 dBm power was provided by another laser diode. Its wavelength could be tuned in 8 pm increments (1 GHz frequency steps), over several nanometers. Combined with the small-scale frequency offsets of the pumps source, the difference between the pump and probe frequencies could be adjusted over a broad range and with high accuracy. The probe was launched into the fiber under test in the same direction as ${E_{\rm pump1}}$. The Brillouin dynamic grating stimulated by the two pumps could couple light from the probe wave into counter-propagating cladding modes, as described above. The probe wave was detected by a photoreceiver at its output end of the fiber. A tunable optical bandpass filter blocked off the pump waves from reaching the detector.

Initially, the coupling to the cladding modes of the fiber under test was characterized over a meter of fiber in a nondistributed manner. To that end, ${E_{\rm pump2}}$ was amplitude-modulated by a sine wave of 50 kHz frequency from a lock-in amplifier, as shown in Fig. 4(a). The strength of the stimulated Brillouin dynamic gratings was therefore modulated at the same rate. The dynamic grating coupling imposed a weak modulation at 50 kHz rate on the detected power of the output probe wave. The received signal was monitored by the lock-in amplifier.

The blue trace in Fig. 5(a) shows the measured magnitude of the lock-in signal as a function of the probe wavelength. Multiple peaks, corresponding to the coupling of the probe wave to a discrete set of cladding modes, are readily observed. A predicted spectrum (red), obtained through numerical calculations of the cladding mode profiles in the coated fiber and their effective indices, is presented for comparison. Agreement between the measured and predicted wavelengths of the peak coupling is very good. The coupling of light to the cladding modes of a coated fiber is successfully demonstrated through Brillouin dynamic gratings, without inscription of permanent gratings or other structural modifications. Figures 5(b) and 5(c) present magnified views of the coupling spectra to two specific cladding modes. The spectral widths are 115 MHz and 136 MHz, respectively. The widths agree with the expectations for a meter long fiber (see Section 2).

B. Spatially Distributed, Brillouin Optical Time-Domain Analysis of Cladding Modes

Next, spatially distributed analysis of coupling to the cladding modes has been realized. To that end, lock-in modulation and detection were disconnected. Instead, the pump wave ${E_{\rm pump2}}$ was intensity modulated by repeating pulses of 10 ns duration and 200 ns period [Fig. 4(b)]. The average power levels of the continuous and pulsed pump waves were 29 dBm and 27 dBm, respectively. The baseline pumps wavelength in this experiment was changed to 1534.4 nm. In addition, the probe power was raised to 19 dBm. The output probe was sampled by a real-time digitizing oscilloscope at 2 GS/s and observed as a function of time. The difference in wavelengths between the pumps and probe was scanned over 20–30 picometers, in 0.08 pm increments. Temporal traces were averaged over 4,096 repeating pulses. The measurement duration was few minutes, limited by the latencies of standard laboratory equipment. Five sections of the coated fiber under test, each 1 meter long, were connected in a series. Adjacent sections were separated by 20 cm long single-mode fiber segments with standard, dual-layer acrylate coating. The sections under test were taken from different locations along a continuous 100-meter fiber reel.

 

Fig. 6. (a) Detected voltage of the output probe wave as a function of fiber position and fine tuning of the pump wavelength offset. The baseline difference between the pump and probe wavelengths was 2.4 nm. Coupling to a cladding mode is observed in five sections of fiber coated with a fluoroacrylate layer, each 1 meter long, separated by connectors with standard acrylate coating in which cladding modes are not guided. Coupling manifests in local dips in the output power of the probe wave in the core mode. The differences among the pump wavelength offsets of peak coupling in the five sections reach 6 pm. (b) Same as (a), with the baseline difference between pump and probe wavelengths increased to 4.4 nm. Coupling to higher-order cladding modes is observed. Differences among the pump wavelength offsets of peak coupling in the five sections are increased to 18 pm. Splitting is observed in some of the fiber sections.

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Figures 6(a) and 6(b) show maps of the detected output voltage $V$ as a function of position $z$ and the relative fine-tuning offset $\Delta \lambda$ of the pump wavelength from a reference value. Power transfer from the core-mode probe to the cladding modes manifests as local dips in the measured voltage. The baseline wavelength differences between the pumps and probe in the two panels were 2.4 nm and 4.4 nm, respectively. The traces present coupling to two different cladding modes. The five sections of fluoroacrylate-coated fiber are identified, and the gaps between them correspond to the acrylate-coated connectors in which cladding modes are not guided. The pump wavelength offsets of peak coupling differ among sections, within a range of 6 pm (18 pm) in Figs. 6(a) and 6(b), respectively. The differences among the local spectra are consistent between the two figures, and they are likely due to submicron variations in the exact local cladding diameter [22,34]. The signals in Fig. 6(b) are weaker, due to the smaller spatial overlap between the Brillouin dynamic grating and the higher-order cladding mode [22]. Splitting of the coupling spectra to the higher-order cladding mode is observed in some of the sections in Fig. 6(b) and is possibly due to the nonuniformity of the silica cladding diameter within specific sections. Simulations suggest that cladding diameter variations of a few tens of nanometers can account for the observed differences in the wavelength offsets of the peak coupling. Variations in the diameter require pre-calibration of the coupling spectra.

The experimental uncertainty was estimated through repeating acquisitions of the coupling spectra over an entire day. While the absolute wavelengths of maximum coupling drifted due to temperature variations and sources instabilities, the differences among those wavelengths in the five fiber sections remained consistent to within ${{\pm}}\;{0.25}\;{\rm{pm}}$ (${{\pm}}\;{{30}}\;{\rm{MHz}}$). That wavelength uncertainty corresponds to an experimental error of ${{\pm}}\;{{5}} \times {{1}}{{{0}}^{- 7}}\;{\rm{RIU}}$ in the effective indices difference $\Delta n^{(m)}=n_{\rm core}-n_{\rm clad}^{m}$. That difference, in turn, is equivalent to a modification of the coating refractive index by ${{\pm}}\;{{8}} \times {{1}}{{{0}}^{- 4}}\;{\rm{RIU}}$. In the sensing demonstrations reported below, a first fiber section was kept outside the media under test and served as a reference to calibrate common drifts such as temperature changes (see Sections 3C and 4). Changes in $\Delta n^{(m)}$ due to the environmental conditions in the other fiber locations, with respect to the reference section, could be spatially mapped with meter resolution and sixth decimal point accuracy.

C. Spatially Distributed Detection of Acetone Outside Coated Fiber

The BOTDA technique of coupling to the cladding modes is suitable for distributed detection of chemicals based on induced modifications to the polymer coating layer, even when the silica fiber itself is unaffected. To demonstrate this approach, two sections of the fluoroacrylate-coated fiber under test were connected in a series as above. Each section was 1 meter long. The first fiber section only was immersed in liquids, whereas the second served as a reference.

Figures 7(a) and 7(b) show maps of the detected output voltage $V$ as a function of fiber position and the pumps wavelength offset $\Delta \lambda$, at the output of the two sections. The baseline wavelength difference between the pumps and probe was 2.4 nm. Figures 7(a) and 7(b) present measurements taken before and few minutes after the immersion of the first fiber section in acetone, respectively. The refractive index of acetone at 1550 nm wavelength is 1.3483 RIU [35]. Coupling to the cladding mode is observed in both panels and in both fiber sections. The quantity observed in subsequent data analysis is the difference between the optimal values $\Delta\lambda^{(m)}_{\textit{opt}}$ in the two sections. That difference was ${-}{{4}}\;{\rm{pm}}$ in Fig. 7(a), prior to immersion, and was changed to ${-}{{1.25}}\;{\rm{pm}}$ following immersion, as shown in Fig. 7(b). The 2.75 pm change corresponds to an increase in $\Delta n^{(m)}$ of the immersed fiber section by ${5.3} \times {{1}}{{{0}}^{- 6}}\;{\rm{RIU}}$. That variation, in turn, suggests a decrease in the coating index by 0.009 RIU following immersion in acetone.

 

Fig. 7. Detected voltage of the output probe wave as a function of position and fine-tuning offset of the pump wavelength. The baseline difference between the pump and probe wavelengths was 2.4 nm. Coupling to a cladding mode is observed in two sections of fiber under test coated with a fluoroacrylate layer, each 1 meter long. (a) Both sections were kept in air. The difference between the wavelength offsets of maximum coupling in the two sections is ${-}{{4}}\;{\rm{pm}}$. (b) Few minutes following the immersion of the first fiber section only in the acetone. The difference in peak wavelengths is changed to ${-}{1.25}\;{\rm{pm}}$. This variation corresponds to a decrease in the local index of the coating layer by 0.009 RIU. (c) Same as (b), 6 hours after immersion. The coupling spectrum to the cladding mode in the immersed section is split in two peaks, separated by 9.35 pm (difference of 0.047 RIU in the index outside the cladding). (d) Same as (c), 24 hours after immersion. The coupling spectrum in the immersed section is entirely shifted to the second, upper peak of panel (c). The wavelength separation between the peaks in the two sections is 8.8 pm. (e) Same as (d), a few minutes after the removal of the first fiber section from the acetone. The spectrum remains similar to that of panel (d). The wavelength difference between the peaks of the two fiber sections increased to 10.4 pm. (f) Same as panel (e), 40 minutes after removal from the acetone. The fiber section was blown dry by compressed (E)-1,3,3,3-tetrafluoropropene gas (Thorlabs CA6-EU). The original peak of panel (b) is restored, whereas the second peak of the immersed section in (d) vanishes. The difference between the pump wavelength offsets of maximum coupling in the two fiber sections is ${-}{{3}}\;{\rm{pm}}$.

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The local spectra of coupling to the cladding mode were monitored every 15 minutes for 24 hours. Figure 7(c) shows a measurement taken after six hours. The coupling peak to the cladding mode in the immersed fiber section was split in two: A second peak appeared at $\Delta \lambda_{\rm opt}^{(m)}$ 9.3 pm higher than the original one (difference in $\Delta n^{(m)}$ of ${1.7} \times {{1}}{{{0}}^{- 5}}\;{\rm{RIU}}$). The difference in $\Delta \lambda_{\rm opt}^{(m)}$ between the two peaks is 35 times larger than the experimental uncertainty. The splitting suggests that the coating along parts of the meter long fiber section switched to a different state, whereas other parts remained unchanged. The difference in $\Delta n^{(m)}$ between the two states corresponds to a further decrease in the refractive index immediately outside the silica cladding by 0.047 RIU, down to 1.358 RIU. That estimated index is within 0.01 RIU only of the index of acetone itself. It is therefore possible that the acetone penetrated the thin coating layer and came into contact with the fiber cladding.

Following 24 hours in acetone, the original coupling peak vanished entirely and only the second offset peak remained, as shown in Fig. 7(d). The results suggest that the cladding interface has been modified by the acetone over the entire length of the immersed section. The wavelength difference between the peaks in the two fiber sections in Fig. 7(d) was 8.8 pm. The effect of acetone on the interface is binary: The coupling to the cladding mode is switched from one peak wavelength to another. At all times, no coupling was observed in the range of wavelengths in between the two, as shown in Fig. 8(a). The orange trace in Fig. 8(b) shows the relative weight of the new, offset spectral peak ${S_2}/({{S_1} + {S_2}})$. Here, ${S_1}$ is the area $\int V(\Delta \lambda){\rm d}\Delta \lambda$ of the original coupling peak near $\Delta \lambda_{\rm opt}^{(m)}$ of ${-}{{4}}\;{\rm{pm}}$, as shown in Figs. 7(c) and 8(a), whereas ${S_2}$ denotes the corresponding area for the new coupling peak near ${+}{{5}}\;{\rm{pm}}$ wavelength offset. The relative weight changed from 0 to 1 over the course of eight hours. Standard BOTDA of the two pump waves could not identify the immersion of the fiber section in the acetone.

 

Fig. 8. (a) Schematic illustration of the evolution of the coupling spectrum to the cladding mode of a coated fiber under test, along a specific fiber section, at different times following its immersion in the acetone. The local spectrum initially consists of a single peak, that of the coated fiber in air (illustration 1). The strength of that peak diminishes over time following immersion (illustrations 1 through 5). A new peak, at a different wavelength offset between pumps and probe, builds up over time. At all times, no coupling is observed at the range of wavelengths between the two peaks. (b) Changes in the elastic and optical properties of the fluoroacrylate coating layer as functions of time following immersion in the acetone. The orange trace shows the relative fraction of the coupling signal to the cladding mode that is offset from the original spectral peak to the new, offset one, as shown in (a) and also in Fig. 7(c). Immediately following immersion, coupling takes place only at the initial pump wavelength offset of the fiber in air; however, coupling is gradually switched to the new wavelength over the course of hours. The blue solid trace shows the FWHM of a guided radial acoustic mode of the coated fiber. The spectrum of the guided acoustic mode was obtained using a forward Brillouin scattering experiment [36]. The modal linewidth is 4.8 MHz with the coated fiber in air [green trace in (c))]. It changes to 6 MHz following immersion of the fiber in the acetone [blue trace in (c)], due to modifications to the acoustic boundary condition at the outer edge of the coating. The linewidth continuously decreases to 3.3. MHz over the course of hours, due to a gradual change in the elastic properties of the immersed coating. Examples of the acoustic mode spectra following 5 hours and 10 hours of immersion are shown in (c) (see legend). The dynamics of changes in the elastic properties of the coating corroborate the cladding mode results. (d) Measured changes in the refractive index of a 320 µm thick film of the fluoroacrylate polymer used in the fiber coating. The film was measured before immersion in the acetone for 30 minutes, and over 21 hours following removal from the acetone. Immediately following removal, the film index was 0.0103 RIU lower than the reference value before immersion. The result supports the estimate of the cladding mode analysis. The film index gradually returns to within 0.0033 RIU of its initial value after 21 hours.

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Figure 7(e) presents a measurement taken a few minutes after the first fiber section was taken out of the acetone. The spectrum remained similar to that shown in Fig. 7(d). The wavelength separation between the peaks of the two sections increased to 10.4 pm. The fiber section was blown dry with compressed (E)-1,3,3,3-tetrafluoropropene gas (Thorlabs CA6-EU), 40 minutes after removal from the acetone, as shown in Fig. 7(f). At that stage, the spectrum returned to its original shape, with a single peak located 3 pm below that of the reference section.

In a control experiment, a 320 µm thick film of the same fluoroacrylate polymer used in the fiber coating was cured using UV light. The refractive index of the film in air at 1538 nm wavelength was measured using a prism coupler, and the result served as a reference value. The film was then immersed in the acetone for 30 minutes. Following removal from the acetone, the film was reinstalled in the prism coupler and its refractive index was measured repeatedly over 21 hours. Figure 8(d) presents the difference between the film index and the reference value as a function of time following its removal from the acetone. Immediately after its removal, the film index was lower than the reference value by 0.0103 RIU. This observation corroborates the estimate of the cladding modes experiment, as shown in Figs. 7(a) and 7(b), and their analysis above. The index change is associated with the penetration of the acetone into the film. The index gradually increased with time, and after 21 hours, it reached 0.0033 RIU below the reference. The recovery of the film index was slower than that of the fiber coating: The film was 50 times thicker, it was not blown dry, and was kept between the prism coupler and a mounting holder.

As a second control experiment, the elastic properties of the fluoroacrylate coating layer before, during, and following immersion in the acetone were also monitored. The measurement was carried out using an opto-mechanical fiber sensing protocol, based on forward Brillouin scattering [25,26,36]. In this protocol, pump pulses stimulate a packet of radial-guided acoustic modes that propagate outward from the fiber core toward the edge of the cladding and the coating layer. The acoustic wave packet is partially reflected at the boundary between the cladding and coating, and again at the outer boundary of the coating layer. Reflections from multiple delayed echoes of the acoustic wave packet across the fiber core. These echoes are monitored, in turn, through the photoelastic phase modulation of an optical probe wave [37].

The analysis of the photoelastic modulation traces in the time or frequency domain can retrieve the elastic properties of the coating layer, such as acoustic velocity, stiffness, or mechanical impedance [25,26]. We have recently employed this technique to monitor the effects of temperature on the acoustic velocities in various coatings [25], and in the quantitative estimate of gamma radiation dosage [26]. Here, we track the effect of acetone on the spectrum of forward Brillouin scattering in the coated fiber and compare the observations with those of optical cladding mode analysis. A fiber under test that had a length of five meters was taken from the same reel of fiber used in cladding mode experiments. A detailed description of the forward Brillouin scattering measurement protocol can be found in [25,26,36].

Figure 8(c) shows several examples of forward stimulated Brillouin scattering spectra through one guided acoustic mode, with a resonance frequency of 320 MHz [38]. The modal linewidth prior to immersion in acetone was 4.8 MHz. The linewidth was broadened to 6.0 MHz immediately following immersion, due to modifications to the elastic boundary condition at the outer edge of the coating [39,40]. The blue trace in Fig. 8(b) presents the measured linewidth as a function of time following the immersion of the fiber in the acetone. The results are drawn alongside those of the cladding mode experiment, as shown by the orange trace in Fig. 8(b). The initial change in acoustic linewidth is followed by a continuous decrease over several hours. Examples of forward Brillouin scattering spectra taken at 5 hours and 10 hours following immersion are shown in Fig. 8(c). The gradual changes in the optomechanical linewidth corroborate the observed variations in the spectrum of coupling to the cladding mode.

As shown in Fig. 8(b), both the optical and elastic properties of the coating layer were successfully monitored with no structural modification or the inscription of gratings, even though all optical signals were launched and detected only in the single core mode. The optical and elastic properties were retrieved using backward and forward Brillouin scattering processes, respectively. Both protocols are scalable to spatially distributed mapping: The time domain analysis of cladding mode spectra was shown here, whereas a distributed optomechanical analysis was reported in a series of recent works by our group and others [41–44]. Together, the two techniques constitute a powerful fiber sensing toolset.

4. DISCUSSION

The spatially distributed mapping of coupling spectra to the cladding modes of standard, coated fiber was demonstrated using BOTDA principles. The commercially available, off-the-shelf fiber under test was coated with a polymer layer with a refractive index below that of silica. The inscription of gratings, removal of the coating, or structural modifications to the fiber were not required. The observed coupling spectra agree with predictions. The measured spectra identify local changes to the difference in effective indices between the core and cladding modes, in the sixth decimal point. The spatial resolution of the measurement was 1 meter. The acquisition duration was a few minutes.

The results successfully identified the local immersion of a one-meter-long fiber section in the acetone, and the continued effect of the acetone on the cladding interface over the course of hours. The observations are supported by a control experiment using a film of the same polymer and by measurements of the opto-mechanical properties of the coated fiber. The results extend our previous study of spatially distributed cladding mode sensors in two significant respects [22]: A coated fiber is used instead of a bare fiber, and correlation domain analysis is replaced with time domain analysis, which is much faster and scales to longer reaches.

Optical fiber point sensors of various chemicals are sensitive, selective, and fast [45–47]. However, a network of such sensors is, at best, quasi-distributed. Several groups demonstrated spatially distributed analysis of chemicals using forward Brillouin scattering [41–44]; however, the sensitivity of these protocols is considerably inferior to that of distributed cladding mode analysis. In addition, the spatial resolution of the cladding mode analysis can be an order of magnitude higher (see [22] and discussion below).

The effect of temperature variations on the protocol is twofold. First, the stimulation of the acoustic waves by the two pump waves might be degraded. The difference ${{\Omega}}$ between the two pump frequencies is set to the Brillouin frequency shift ${{{\Omega}}_B}$. Since ${{{\Omega}}_B}$ is temperature dependent, the frequencies offset ${{\Omega}}$ might become suboptimal when the temperature changes. Such drift would degrade the magnitude of the stimulated acoustic wave and the reflectivity of the probe wave, according to Eq. (3). However, the dependence of the reflectivity on the offset ${{\Omega}}$ is separable from its dependence on the frequency difference between the pump and probe. Therefore, quantitative cladding mode sensing of the outside index may still take place following temperature drifts, albeit with a reduced signal. That loss of signal would only become appreciable when ${{{\Omega}}_B}$ had drifted by the Brillouin linewidth ${{{\Gamma}}_B}$. Such drifts require temperature variations on the order of 30°K. Even then, drifts in ${{{\Omega}}_B}$ may be readily identified through the detection of the pump waves, and the value of the frequencies offset ${{\Omega}}$ can be corrected accordingly.

Temperature variations may also give rise to cross-sensitivity through the thermo-optic dependence of the effective indices of the core and cladding modes. The thermo-optic coefficient of polymers is typically on the order of ${{100}}\;{\rm{ppm}}\;{\rm{per\,}}^{\circ}{\rm K}$ [48], an order of magnitude larger than in silica; hence, the difference $\Delta n^{(m)}$ between the effective indices of the core and cladding modes might change with the temperature. However, the cladding modes used in this work are 99.8% confined to the silica cladding. Therefore, the temperature dependence of $\Delta n^{(m)}$ is reduced to an order of only ${0.1}\;{\rm{ppm}}\;{\rm{per\,}}^{\circ}\rm K$. The corresponding spectral offsets in coupling to the cladding modes would exceed the measurement uncertainty only for temperature drifts beyond 10°K. With knowledge of the temperature drifts through the monitoring of ${{{\Omega}}_B}$ [23,24], the necessary corrections can be made in the data analysis.

The spatial resolution of the standard BOTDA protocols was successfully enhanced to few centimeters using double pulse, pre-excitation, and other methods [49–52]. These techniques are directly applicable toward similar resolution enhancement in the time-domain analysis of coupling to cladding modes proposed in this work. The measurement range is scalable to hundreds of meters, limited eventually by the modulation instability of the pulsed pump wave [31,32], excessive depletion or amplification of that wave [30], and the amplified spontaneous Brillouin scattering of the continuous pump wave [53], as discussed in Section 2B. Longer reaches would require weaker pump power levels, with a compromise in the sensitivity and/or acquisition duration. These can be compensated in turn using coded sequences of pulses, as routinely employed in traditional Brillouin fiber sensors [54].

The immersion of a fiber section in the acetone was identified after a few minutes. The measurement duration was limited by the latencies of standard laboratory equipment, and it is not fundamental. The time required to identify a chemical would eventually depend on the kinetics of its reactions with the polymer coating chosen. Specific coatings and functionalization protocols might be considered and developed to make such reactions faster. Functionalization could also support target-specific, selective sensing. Variations in the diameter of the silica fiber cladding induce frequency shifts in the coupling spectra that exceed the experimental measurement uncertainty. Local reference spectra of coupling to the cladding modes must be obtained as pre-calibration prior to the sensor deployment. Since the local cladding diameters are fixed in time, their variations would not limit the sensor performance following such calibration.

The cladding modes used in this work decay evanescently in the coating layer and do not reach its outer boundary. Sensing applications using these modes are based on chemical modifications to the coating, and do not probe the media outside the coating directly. Variations to the diameter of the polymer coating do not affect the spectra of coupling to these modes. Additional cladding modes, with effective indices lower than that of the polymer coating, also can be potentially addressed. The transverse profiles of these modes oscillate within the coating and reach its outer edge, and they would exhibit even more sensitive measurements of refractive index variations in the coating and its surroundings. The lower the modal effective index, the more sensitive it becomes to changes in external conditions. On the other hand, higher-order cladding modes of lower effective indices are in smaller spatial overlap with the core mode and would provide less efficient coupling and inferior SNRs in measured spectra.

In conclusion, this work established a spatially distributed, cladding mode optical fiber sensor that we believe is more practical and suitable than previous configurations for deployment outside the research laboratory. The proposed protocol can be used for the detection and sensing of chemicals based on modifications to the polymer coating of standard, unmodified fiber, even when the silica fiber itself is unaffected. Future work will address higher-order cladding modes, extending the measurement range, the detection of other chemicals, and the monitoring of additional conditions such as ionizing radiation.