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Fibre Bragg Gratings in Embedded Microstructured Optical Fibres Allow Distinguishing between Symmetric and Anti-Symmetric Lamb Waves in Carbon Fibre Reinforced Composites

Conventional contact sensors used for Lamb wave-based ultrasonic inspection, such as piezo-electric transducers, measure omnidirectional strain and do not allow distinguishing between fundamental symmetric and anti-symmetric modes. In this paper, we show that the use of a single fibre Bragg grating created in a dedicated microstructured optical fibre allows one to directly make the distinction between these fundamental Lamb wave modes. This feature stems from the different sensitivities of the microstructured fibre to axial and transverse strain. We fabricated carbon fibre-reinforced polymer panels equipped with embedded microstructured optical fibre sensors and experimentally demonstrated the strain waves associated with the propagating Lamb waves in both the axial and transverse directions of the optical fibre.


Introduction
Lamb wave-based ultrasonic inspection for damage identification in engineering structures is considered to be an attractive alternative for conventional and time-consuming point-by-point ultrasonic inspection techniques, mainly because Lamb waves can travel long distances across the structure and therefore allow for inspecting fairly large areas. Such Lamb waves can be excited and detected in various manners depending on the size and material of the structure under test [1][2][3]. In the aerospace industry, for example, the most common technique to both excite and detect Lamb waves in plate-like composite components uses piezo-electric transducers (PZTs). Such transducers feature a small size and low power consumption. The main disadvantages of PZTs in Lamb wave-based inspection are twofold. First, each PZT requires being individually connected, which calls for dealing with a multitude of wires when using arrays of transducers. Second, PZTs exhibit unselective sensitivity in the sense that Lamb waves propagating along different directions in the plane of a panel are all picked up with the same sensitivity. Critical directions, corresponding to, for example, a defect in the panel, are recorded simultaneously and with the same sensitivity as every other direction. It is thus challenging to identify the result of a defect in a panel on Lamb waves propagating in this structure and, therefore, it is difficult to locate and assess the size of the defect. Optical fibre Bragg gratings (FBGs) have already been proposed to detect Lamb waves in order to cope with the aforementioned

MOFBG Sensors and Measurement Strategy
MOFBGs can exhibit peculiar characteristics that cannot be achieved using conventional optical fibre technology. More specifically, the design flexibility of such microstructured fibres (MOFs) allows for the development of sensors that exhibit selective sensitivities to e.g., axial strain, transverse strain, or even shear strain, whilst being negligibly cross-sensitive to temperature changes. Examples of MOF-based sensors have been reviewed in several research papers [12][13][14][15][16][17][18][19][20]. In this paper, we use a specific microstructured fibre design which we refer to as a 'butterfly' MOF [17][18][19][20]. Figure 1a shows an SEM image of the cross-section of the butterfly MOF [18]. The peculiar microstructure induces a high level of birefringence in the optical fibre. When this MOF is equipped with an FBG, the latter reflects two Bragg wavelengths corresponding to the two orthogonal polarised propagation modes. The Bragg wavelengths (or peaks) will shift with the same amount when an axial load is applied to the optical fibre, but will move in opposite ways when a transverse load (parallel to axis 'S') is applied. The absolute and relative position of the Bragg peaks therefore encodes axial strain as well as transverse strain, respectively, into the reflection spectrum of the MOFBG. This principle is summarised in Figure 1b. (b) Response of a fibre Bragg grating (FBG) created in the butterfly MOF: axial strain corresponds to both peaks moving in the same way, whilst transverse strain (applied parallel to axis 'S') corresponds to the peaks moving in opposite directions [18].
The selective sensitivity of a single MOFBG to axial and transverse strain can be exploited to differentiate between the S0 and A0 modes. This stems from the nature of the induced strain distribution (or strain mode shape) in the axial and transverse directions of a plate-like structure, which is different for these modes. Owing to the anti-symmetric shape of the A0, the associated strain amplitude in the transverse direction is close to zero near the mid-plane of the panel [21]. The symmetry of the S0 mode, on the other hand, results in an increase of the strain amplitude at that location. Consequently, an MOFBG embedded for example at a depth of ¼ (or equivalently ¾) of the thickness of a plate-like structure will be able to pick up both the S0 and A0 mode in the axial direction, but mostly the S0 mode in the transverse direction, as depicted in Figure 2, which illustrates typical strain mode shapes in the lateral direction of a plate-like structure. At ¼ or ¾ of the thickness, the A0 wave as well as the S0 wave will still exhibit some transverse strain components, but given the contrast with the axial strain components, the MOFBG allows distinguishing between the two parties. Note that the actual measured strain amplitude of both the S0 and A0 modes also depends on the transfer of the strain induced in the material by the Lamb waves to the optical fibre and on the excitation amplitude and attenuation of each mode. Illustration of strain mode shapes of both S0 and A0 waves in the lateral direction of a platelike structure. The strain induced by an A0 wave close to the mid-thickness tends to be zero, in contrast to the induced strain of the S0 wave, which increases at the same depth. An MOFBG embedded at a depth of, for example, ¼ of the panel thickness, that is sensitive to both axial and transverse strain, can exploit this difference to distinguish between the S0 and A0 modes [18,21]. (b) Response of a fibre Bragg grating (FBG) created in the butterfly MOF: axial strain corresponds to both peaks moving in the same way, whilst transverse strain (applied parallel to axis 'S') corresponds to the peaks moving in opposite directions [18].
The selective sensitivity of a single MOFBG to axial and transverse strain can be exploited to differentiate between the S 0 and A 0 modes. This stems from the nature of the induced strain distribution (or strain mode shape) in the axial and transverse directions of a plate-like structure, which is different for these modes. Owing to the anti-symmetric shape of the A 0 , the associated strain amplitude in the transverse direction is close to zero near the mid-plane of the panel [21]. The symmetry of the S 0 mode, on the other hand, results in an increase of the strain amplitude at that location. Consequently, an MOFBG embedded for example at a depth of 1 ⁄4 (or equivalently 3 ⁄4) of the thickness of a plate-like structure will be able to pick up both the S 0 and A 0 mode in the axial direction, but mostly the S 0 mode in the transverse direction, as depicted in Figure 2, which illustrates typical strain mode shapes in the lateral direction of a plate-like structure. At 1 ⁄4 or 3 ⁄4 of the thickness, the A 0 wave as well as the S 0 wave will still exhibit some transverse strain components, but given the contrast with the axial strain components, the MOFBG allows distinguishing between the two parties. Note that the actual measured strain amplitude of both the S 0 and A 0 modes also depends on the transfer of the strain induced in the material by the Lamb waves to the optical fibre and on the excitation amplitude and attenuation of each mode. The selective sensitivity of a single MOFBG to axial and transverse strain can be exploited to differentiate between the S0 and A0 modes. This stems from the nature of the induced strain distribution (or strain mode shape) in the axial and transverse directions of a plate-like structure, which is different for these modes. Owing to the anti-symmetric shape of the A0, the associated strain amplitude in the transverse direction is close to zero near the mid-plane of the panel [21]. The symmetry of the S0 mode, on the other hand, results in an increase of the strain amplitude at that location. Consequently, an MOFBG embedded for example at a depth of ¼ (or equivalently ¾) of the thickness of a plate-like structure will be able to pick up both the S0 and A0 mode in the axial direction, but mostly the S0 mode in the transverse direction, as depicted in Figure 2, which illustrates typical strain mode shapes in the lateral direction of a plate-like structure. At ¼ or ¾ of the thickness, the A0 wave as well as the S0 wave will still exhibit some transverse strain components, but given the contrast with the axial strain components, the MOFBG allows distinguishing between the two parties. Note that the actual measured strain amplitude of both the S0 and A0 modes also depends on the transfer of the strain induced in the material by the Lamb waves to the optical fibre and on the excitation amplitude and attenuation of each mode. Illustration of strain mode shapes of both S0 and A0 waves in the lateral direction of a platelike structure. The strain induced by an A0 wave close to the mid-thickness tends to be zero, in contrast to the induced strain of the S0 wave, which increases at the same depth. An MOFBG embedded at a depth of, for example, ¼ of the panel thickness, that is sensitive to both axial and transverse strain, can exploit this difference to distinguish between the S0 and A0 modes [18,21].

Figure 2.
Illustration of strain mode shapes of both S 0 and A 0 waves in the lateral direction of a plate-like structure. The strain induced by an A 0 wave close to the mid-thickness tends to be zero, in contrast to the induced strain of the S 0 wave, which increases at the same depth. An MOFBG embedded at a depth of, for example, 1 ⁄4 of the panel thickness, that is sensitive to both axial and transverse strain, can exploit this difference to distinguish between the S 0 and A 0 modes [18,21].
To demonstrate the capability of an MOFBG to distinguish between S 0 and A 0 modes using the approach outlined above, we fabricated a 250 mm by 25 mm carbon fibre-reinforced polymer (CFRP) panel made from Hexcel M21/T800S prepreg, with a lay-up of (45/−45/0 2 /90/0) s . The thickness of each ply is close to 0.184 mm, resulting in an overall thickness of 2.21 mm. We embedded an MOFBG between the third and fourth laminar layers (i.e., at 1 4 of the thickness of the panel) and aligned the optical fibre with the 0 • orientation of the plies (i.e., parallel with the carbon fibres in the plane of the laminate plies) to minimize the effect of the embedding and, in particular, to avoid the creation of resin pockets [7]. We positioned the MOFBG at the half-length of the panel and angularly oriented the MOFBG such that the peak separation was essentially sensitive to the out-of-plane transverse load. To do so, we rotated the fibre about its axis (i.e., changed the roll angle) so that the butterfly axis (referred to as 'S' in Figure 1a) was aligned with the desired axis of the CFRP panel. To obtain the desired orientation of the microstructured optical fibre, we relied on our technique described in Reference [18], which yields angular accuracies of the roll angle of the fibre with respect to the instrumented structure close to ±8 • . We have previously determined that such a tolerance on the roll angle guarantees a sensitivity to loads along the desired CFRP panel axis of well beyond 85% of the sensitivity achieved when the fibre's microstructure is perfectly aligned along the desired axis [19]. This is not only sufficient for the demonstration purpose reported in this paper, but also allows one to envisage its implementation in practical applications. To excite the Lamb waves in the fabricated panel, we surface-mounted a disk-shaped PZT of type PIC255 (PI Ceramic GmbH, Lederhose, Germany) with a diameter of 10 mm on one extremity. One important remark here is that the distance between the PZT and the MOFBG is only 10 cm, and is thus typically insufficient for the A 0 and S 0 modes to fully separate owing to their different propagation velocities (in the used material). More specifically, we observed from the experimentally and numerically determined dispersion curves of our setup that the delay between the A 0 and S 0 waves was only about 18 µs. For the frequency-thickness used in this paper, the measured phase velocities of the S 0 and A 0 waves were close to 4.5 m/ms and 2.8 m/ms, respectively. A schematic of the experimental setup is depicted in Figure 3. We controlled the PZT using a waveform generator that generates five-cycle tonebursts with a Hanning filter applied at a preset frequency. The response of the FBG to the impinging Lamb waves was measured using the so-called edge filtering method [22], in which the output wavelength of a tunable laser is tuned to the wavelength where the slope of the Bragg peak is steepest. A shift of the Bragg peak resulting from a passing strain wave is then recorded as a change of optical intensity by a fast photodetector (Thorlabs PDA20CS). Note that the birefringence in the MOFBG produces two Bragg peaks (see Figure 1), meaning that a total of four slopes (two ascending and two descending) can be used. To demonstrate the capability of an MOFBG to distinguish between S0 and A0 modes using the approach outlined above, we fabricated a 250 mm by 25 mm carbon fibre-reinforced polymer (CFRP) panel made from Hexcel M21/T800S prepreg, with a lay-up of (45/−45/02/90/0)s. The thickness of each ply is close to 0.184 mm, resulting in an overall thickness of 2.21 mm. We embedded an MOFBG between the third and fourth laminar layers (i.e., at ¼ of the thickness of the panel) and aligned the optical fibre with the 0° orientation of the plies (i.e., parallel with the carbon fibres in the plane of the laminate plies) to minimize the effect of the embedding and, in particular, to avoid the creation of resin pockets [7]. We positioned the MOFBG at the half-length of the panel and angularly oriented the MOFBG such that the peak separation was essentially sensitive to the out-of-plane transverse load. To do so, we rotated the fibre about its axis (i.e., changed the roll angle) so that the butterfly axis (referred to as 'S' in Figure 1a) was aligned with the desired axis of the CFRP panel. To obtain the desired orientation of the microstructured optical fibre, we relied on our technique described in Reference [18], which yields angular accuracies of the roll angle of the fibre with respect to the instrumented structure close to ±8°. We have previously determined that such a tolerance on the roll angle guarantees a sensitivity to loads along the desired CFRP panel axis of well beyond 85% of the sensitivity achieved when the fibre's microstructure is perfectly aligned along the desired axis [19]. This is not only sufficient for the demonstration purpose reported in this paper, but also allows one to envisage its implementation in practical applications. To excite the Lamb waves in the fabricated panel, we surface-mounted a disk-shaped PZT of type PIC255 (PI Ceramic GmbH, Lederhose, Germany) with a diameter of 10 mm on one extremity. One important remark here is that the distance between the PZT and the MOFBG is only 10 cm, and is thus typically insufficient for the A0 and S0 modes to fully separate owing to their different propagation velocities (in the used material). More specifically, we observed from the experimentally and numerically determined dispersion curves of our setup that the delay between the A0 and S0 waves was only about 18 µs. For the frequencythickness used in this paper, the measured phase velocities of the S0 and A0 waves were close to 4.5 m/ms and 2.8 m/ms, respectively. A schematic of the experimental setup is depicted in Figure 3. We controlled the PZT using a waveform generator that generates five-cycle tonebursts with a Hanning filter applied at a preset frequency. The response of the FBG to the impinging Lamb waves was measured using the so-called edge filtering method [22], in which the output wavelength of a tunable laser is tuned to the wavelength where the slope of the Bragg peak is steepest. A shift of the Bragg peak resulting from a passing strain wave is then recorded as a change of optical intensity by a fast photodetector (Thorlabs PDA20CS). Note that the birefringence in the MOFBG produces two Bragg peaks (see Figure 1), meaning that a total of four slopes (two ascending and two descending) can be used.

MOFBGs Allow Distinguishing between A0 and S0 Waves
Using the setup described above, we excited the fundamental S0 and A0 modes in the fabricated panel by actuating the PZT with a 20 Vpp five-cycle toneburst at 250 kHz with the amplitude modulated using a Hanning filter, and we measured the response with the embedded MOFBG. To

MOFBGs Allow Distinguishing between A 0 and S 0 Waves
Using the setup described above, we excited the fundamental S 0 and A 0 modes in the fabricated panel by actuating the PZT with a 20 Vpp five-cycle toneburst at 250 kHz with the amplitude modulated using a Hanning filter, and we measured the response with the embedded MOFBG. To improve the signal-to-noise ratio, each measurement was repeated 1000 times and averaged. The measured wavelength shifts as a function of time for the four slopes of the MOFBG are shown in Figure 4a. The average wavelength shift of the four measurements is proportional to the axial strain applied to the MOFBG, while the shift in spectral distance between the first and third slopes or between the second and fourth slopes is proportional to the transverse strain applied to the MOFBG. The resulting wavelength shifts corresponding to the axial (in black) and transverse (in red) directions are shown in Figure 4b. Although the sensitivity in the transverse direction is not as high as that in the axial direction [18][19][20], we observed a clear difference in the obtained signals. In particular, the signal measured in the axial direction proved to be more responsive to an impinging A 0 wave (because the PZT excitation of A 0 is more pronounced), while the signal measured in the transverse direction was more responsive to the S 0 wave. improve the signal-to-noise ratio, each measurement was repeated 1000 times and averaged. The measured wavelength shifts as a function of time for the four slopes of the MOFBG are shown in Figure 4a. The average wavelength shift of the four measurements is proportional to the axial strain applied to the MOFBG, while the shift in spectral distance between the first and third slopes or between the second and fourth slopes is proportional to the transverse strain applied to the MOFBG. The resulting wavelength shifts corresponding to the axial (in black) and transverse (in red) directions are shown in Figure 4b. Although the sensitivity in the transverse direction is not as high as that in the axial direction [18][19][20], we observed a clear difference in the obtained signals. In particular, the signal measured in the axial direction proved to be more responsive to an impinging A0 wave (because the PZT excitation of A0 is more pronounced), while the signal measured in the transverse direction was more responsive to the S0 wave. The identification of both types of waves is confirmed by the time-of-arrival of both the wave packets that arrive first as well as the wave packets returning after a reflection at the extremity of the panel (see also Section 3.3). The results therefore evidence that a single embedded MOFBG, sensitive to both axial and transverse strains, allows distinguishing between the A0 and S0 Lamb waves propagating through the CFRP panel.

Selection of Preferential Directions Allow Filtering out Undesired Edge Reflections
The directional sensitivity of the MOFBG can bring an additional advantage to Lamb wavebased ultrasonic inspection. In a geometry similar to the CFRP panel explained in the previous section, the response of a PZT sensor surface mounted at the position of the embedded MOFBG would be significantly influenced by the multitude of reflections. Such a situation would make it very challenging to distinguish the A0 and S0 waves from PZT recordings, since a PZT is sensitive to all incident directions and the reflected Lamb waves arrive at the sensor quasi-simultaneous. The key feature of MOFBGs is that they are essentially sensitive to two perpendicular directions (one axial and one transverse to the optical fibre), which allowed us to choose, by carefully angularly orienting the MOFBG, to filter out part of the edge reflections. To demonstrate this, we fabricated a second CFRP panel with the same geometry as before and with the MOFBG embedded at the same location. In this panel, however, we angularly oriented the MOFBG (i.e., adjusted the roll angle of the fibre to align the axis 'S' of the butterfly structure) so that to the peak separation is essentially sensitive to the transverse in-plane load. We repeated the measurement procedure and we separated again the axial load and transverse loads, as performed for the previous panel. Figure 5 shows the results. The The identification of both types of waves is confirmed by the time-of-arrival of both the wave packets that arrive first as well as the wave packets returning after a reflection at the extremity of the panel (see also Section 3.3). The results therefore evidence that a single embedded MOFBG, sensitive to both axial and transverse strains, allows distinguishing between the A 0 and S 0 Lamb waves propagating through the CFRP panel.

Selection of Preferential Directions Allow Filtering out Undesired Edge Reflections
The directional sensitivity of the MOFBG can bring an additional advantage to Lamb wave-based ultrasonic inspection. In a geometry similar to the CFRP panel explained in the previous section, the response of a PZT sensor surface mounted at the position of the embedded MOFBG would be significantly influenced by the multitude of reflections. Such a situation would make it very challenging to distinguish the A 0 and S 0 waves from PZT recordings, since a PZT is sensitive to all incident directions and the reflected Lamb waves arrive at the sensor quasi-simultaneous. The key feature of MOFBGs is that they are essentially sensitive to two perpendicular directions (one axial and one transverse to the optical fibre), which allowed us to choose, by carefully angularly orienting the MOFBG, to filter out part of the edge reflections. To demonstrate this, we fabricated a second CFRP panel with the same geometry as before and with the MOFBG embedded at the same location. In this panel, however, we angularly oriented the MOFBG (i.e., adjusted the roll angle of the fibre to align the axis 'S' of the butterfly structure) so that to the peak separation is essentially sensitive to the transverse in-plane load. We repeated the measurement procedure and we separated again the axial load and transverse loads, as performed for the previous panel. Figure 5 shows the results. The reflections from the long edges are more clearly observed than in the previous composite panel, as shown in Figure 5a, using a measurement on a single slope. Similar to the previous panel, we noticed a more significant response to the S 0 wave than to the A 0 mode in the transverse direction and vice versa in the axial direction. Therefore, carefully aligning the butterfly structure by adjusting the roll angle of the MOFBG during mounting allows for the selection or elimination of certain directions of strain and, hence, potentially accounts for undesired effects resulting from Lamb wave reflections from the edges of a panel under test.
Sensors 2017, 17,1948 6 of 9 reflections from the long edges are more clearly observed than in the previous composite panel, as shown in Figure 5a, using a measurement on a single slope. Similar to the previous panel, we noticed a more significant response to the S0 wave than to the A0 mode in the transverse direction and vice versa in the axial direction. Therefore, carefully aligning the butterfly structure by adjusting the roll angle of the MOFBG during mounting allows for the selection or elimination of certain directions of strain and, hence, potentially accounts for undesired effects resulting from Lamb wave reflections from the edges of a panel under test.

Consequences for Impact Damage Detection in CFRP
The demonstrated ability to resolve the two components of Lamb waves is also beneficial when Lamb waves are used to detect damage in a structure. In most experiments involving Lamb wave-based damage detection, the signals of an undamaged structure are compared to the signals of the damaged structure [23][24][25]. Damage in the structure will cause propagating Lamb waves to reflect and refract, yielding an alteration in the recorded Lamb waves. In general, one can distinguish between two situations.
First, the damage can be on the direct path between the actuator and the sensor. In this case, the fraction of the Lamb waves that are influenced (because of reflection, refraction, attenuation, etc.) will alter the energy contained in the wave packets that are picked up by the sensor [25]. As an example of such a situation, we experimentally mimicked an impact damage by applying a dot of synthetic rubber adhesive with a diameter of about 5 mm to the CFRP panel described in Section 3.1, and we recorded Lamb waves with the embedded MOFBG. We show the result in Figure 6, in which we have plotted the wavelength shifts corresponding to strains in the axial and transverse directions. The dashed lines in the figure indicate the pristine situation, while the solid lines correspond to the damaged situation. Since the simulated damage is located on the direct path between the PZT actuator and the MOFBG sensor, a fraction of the Lamb waves will be attenuated, yielding less energetic strain waves to be transmitted and thus smaller recorded wavelength shifts. The latter can be clearly seen in both the axial and transverse directions when the first wave packets arrive at the MOFBG. In addition, due to the additional attenuation which is possibly accompanied with partial mode conversion from A0 to S0, the second wave packet shows a significantly larger amplitude compared to the undamaged state in the transverse direction. In the described situation, we observed an increase of the amplitude of the second wave packet of more than a factor of 2. Recall, however, that for the used setup the excitation of the A0 mode is more pronounced compared to the S0 mode. Nevertheless, our approach illustrates the potential benefits of using MOFBGs as sensors in Lamb

Consequences for Impact Damage Detection in CFRP
The demonstrated ability to resolve the two components of Lamb waves is also beneficial when Lamb waves are used to detect damage in a structure. In most experiments involving Lamb wave-based damage detection, the signals of an undamaged structure are compared to the signals of the damaged structure [23][24][25]. Damage in the structure will cause propagating Lamb waves to reflect and refract, yielding an alteration in the recorded Lamb waves. In general, one can distinguish between two situations.
First, the damage can be on the direct path between the actuator and the sensor. In this case, the fraction of the Lamb waves that are influenced (because of reflection, refraction, attenuation, etc.) will alter the energy contained in the wave packets that are picked up by the sensor [25]. As an example of such a situation, we experimentally mimicked an impact damage by applying a dot of synthetic rubber adhesive with a diameter of about 5 mm to the CFRP panel described in Section 3.1, and we recorded Lamb waves with the embedded MOFBG. We show the result in Figure 6, in which we have plotted the wavelength shifts corresponding to strains in the axial and transverse directions. The dashed lines in the figure indicate the pristine situation, while the solid lines correspond to the damaged situation. Since the simulated damage is located on the direct path between the PZT actuator and the MOFBG sensor, a fraction of the Lamb waves will be attenuated, yielding less energetic strain waves to be transmitted and thus smaller recorded wavelength shifts. The latter can be clearly seen in both the axial and transverse directions when the first wave packets arrive at the MOFBG. In addition, due to the additional attenuation which is possibly accompanied with partial mode conversion from A 0 to S 0 , the second wave packet shows a significantly larger amplitude compared to the undamaged state in the transverse direction. In the described situation, we observed an increase of the amplitude of the second wave packet of more than a factor of 2. Recall, however, that for the used setup the excitation of the A 0 mode is more pronounced compared to the S 0 mode. Nevertheless, our approach illustrates the potential benefits of using MOFBGs as sensors in Lamb wave-based damage detection owing to their ability to discern between the strains recorded in the axial and transverse directions.
Sensors 2017, 17, 1948 7 of 9 wave-based damage detection owing to their ability to discern between the strains recorded in the axial and transverse directions. Second, the damage can be off the direct path between the actuator and sensors. In such a situation, Lamb waves altered from the damage will yield wave packets arriving at the sensor at different times. In this case, the ability to determine the time-of-arrival of wave packets is crucial [23,24]. Thus, to illustrate the potential of the MOFBGs in time-of-arrival damage detection, we experimentally determined the dispersion curve of the Lamb waves generated in the CFRP panel which also relies on accurate measurements of the time-of-arrival of the wave packets. Recall that the distance between the actuator and sensor is only 10 cm, which is typically insufficient for the A0 and S0 waves to separate. The result is shown in Figure 7, in which the dots represent the phase velocity determined from the observed time-of-arrival for a certain excitation frequency. We determined the time-of-arrival of both the first wave packet as well as the first reflected wave packet. The solid lines in Figure 7 show the dispersion curves calculated using the material parameters and the panel geometry (detailed in Section 2). We conclude that there is good agreement between the calculated and observed values, as we observed no discrepancies exceeding 10% except the second lowest frequency-thickness tested (at 0.1105 MHz·mm) for the A0 mode, which differed by 14%. Using the propagation velocities, we can calculate the distance required for the five-cycle wave packets of A0 and S0 to separate, which is about 18 cm for the frequency-thickness of 0.221 MHz·mm.  Second, the damage can be off the direct path between the actuator and sensors. In such a situation, Lamb waves altered from the damage will yield wave packets arriving at the sensor at different times. In this case, the ability to determine the time-of-arrival of wave packets is crucial [23,24]. Thus, to illustrate the potential of the MOFBGs in time-of-arrival damage detection, we experimentally determined the dispersion curve of the Lamb waves generated in the CFRP panel which also relies on accurate measurements of the time-of-arrival of the wave packets. Recall that the distance between the actuator and sensor is only 10 cm, which is typically insufficient for the A 0 and S 0 waves to separate. The result is shown in Figure 7, in which the dots represent the phase velocity determined from the observed time-of-arrival for a certain excitation frequency. We determined the time-of-arrival of both the first wave packet as well as the first reflected wave packet. The solid lines in Figure 7 show the dispersion curves calculated using the material parameters and the panel geometry (detailed in Section 2). We conclude that there is good agreement between the calculated and observed values, as we observed no discrepancies exceeding 10% except the second lowest frequency-thickness tested (at 0.1105 MHz·mm) for the A 0 mode, which differed by 14%. Using the propagation velocities, we can calculate the distance required for the five-cycle wave packets of A 0 and S 0 to separate, which is about 18 cm for the frequency-thickness of 0.221 MHz·mm. wave-based damage detection owing to their ability to discern between the strains recorded in the axial and transverse directions. Second, the damage can be off the direct path between the actuator and sensors. In such a situation, Lamb waves altered from the damage will yield wave packets arriving at the sensor at different times. In this case, the ability to determine the time-of-arrival of wave packets is crucial [23,24]. Thus, to illustrate the potential of the MOFBGs in time-of-arrival damage detection, we experimentally determined the dispersion curve of the Lamb waves generated in the CFRP panel which also relies on accurate measurements of the time-of-arrival of the wave packets. Recall that the distance between the actuator and sensor is only 10 cm, which is typically insufficient for the A0 and S0 waves to separate. The result is shown in Figure 7, in which the dots represent the phase velocity determined from the observed time-of-arrival for a certain excitation frequency. We determined the time-of-arrival of both the first wave packet as well as the first reflected wave packet. The solid lines in Figure 7 show the dispersion curves calculated using the material parameters and the panel geometry (detailed in Section 2). We conclude that there is good agreement between the calculated and observed values, as we observed no discrepancies exceeding 10% except the second lowest frequency-thickness tested (at 0.1105 MHz·mm) for the A0 mode, which differed by 14%. Using the propagation velocities, we can calculate the distance required for the five-cycle wave packets of A0 and S0 to separate, which is about 18 cm for the frequency-thickness of 0.221 MHz·mm.

Conclusions
In conclusion, we demonstrated, for the first time to our knowledge, the use of MOFBG-based sensors embedded within a composite panel to measure Lamb waves. Until now, mostly surface-mounted FBGs have been used for this purpose. The MOFBGs used in this paper exhibit selective sensitivity to axial and transverse strains, which allows distinguishing between the two fundamental Lamb wave modes. The ability of our sensing scheme to successfully discern between the two fundamental Lamb wave modes offers perspectives for detecting higher order modes as well. In addition, the orientation of the MOFBG (by adjusting the roll angle and aligning the fibre axis 'S') allows for the selection of preferential directions of strain. In this manner, directions corresponding to critical locations in a structure can be promoted while undesired reflections impinging from other directions can be impeded. Furthermore, we illustrated in two scenarios the ability to discern the axial and transverse directions with the intention to improve and simplify Lamb wave-based damage detection with the damage located either on or off the direct path between the actuator and sensor. We showed that the ability to make the distinction between the axial and transverse strain directions is clearly beneficial in the former case, as the distinction between the S 0 and A 0 waves allowed for the individually evaluation of additional losses and for the observation of partial mode conversion. The latter situation was exemplified by determining the time-of-arrival and associated dispersion of the two fundamental Lamb wave modes for a range of frequencies. Despite the small dimensions of the tested panel, we were able to determine the dispersion curve using an embedded MOFBG with an accuracy essentially exceeding 90%. The results summarised above evidence the added value of using MOFBG sensors in Lamb wave detection-based applications.