Scattering array interferometers

Abstract

Disclosed are various embodiments for scattering array interferometers. In one embodiment, an optical medium comprises one or more scattering array interferometers in the optical medium. Each of the scattering array interferometers includes a respective array or other spatial distribution of scatterers / reflectors comprising at least two scatterers / reflectors that are uniformly sized and spaced according to a corresponding pitch. The respective array or other spatial distribution of scatterers / reflectors is configured to cause coherent light interference when a light source is applied to the optical medium.

Description

SCATTERING ARRAY INTERFEROMETERSCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to, and the benefit of, US Provisional Patent Application No. 63 / 515,381, entitled “SCATTERING ARRAY INTERFEROMETERS,” and filed on July 25, 2023, which is incorporated herein by reference in its entirety.BACKGROUND

[0002] Optical interferometers are precision instruments used for measuring the wave properties of light by exploiting the principle of interference. The fundamental working principle involves splitting a single light beam into two or more beams that travel along different paths and then recombining them. When these beams overlap, they create an interference pattern due to the differences in their optical path lengths. This pattern is analyzed to extract information about the optical paths the beams traveled, which can be related to various physical quantities such as distance, refractive index, or surface topology.

[0003] Optical interferometers have wide-ranging applications across various fields of science and engineering. In metrology, they are used for precise distance and displacement measurements, surface profiling, and material characterization. In astronomy, interferometers enable the measurement of stellar diameters, the study of binary star systems, and the imaging of distant astronomical objects with unprecedented resolution. In telecommunications, interferometric techniques are employed in fiber optic sensors and coherent communication systems.BRIEF SUMMARY

[0004] One general aspect includes an optical medium. The optical medium also includes one or more scattering array interferometers in the optical medium, each of the scattering array interferometers including a respective array or other spatial distribution of scatter er s / reflectors that has at least two scatterers / reflectors uniformly sized and spaced according to a corresponding pitch, the respective array or other spatial distribution of scatterers / reflectors being configured to cause coherent light interference when a light source is applied to the optical medium.

[0005] Implementations may include one or more of the following features. The optical medium where at least one scatterer / reflector of the one or more scattering arrayinterferometers differs in size from the at least two scatterers / reflectors or is not spaced according to the corresponding pitch. The optical medium may include any optical waveguide, including, but not limited to: a silica fiber, a sapphire fiber, an yttrium aluminum garnet (YAG) fiber, a polymer fiber, a rear earth-doped optical fiber, a silicate fiber, or an integrated photonic waveguide. The optical medium may include an optical wafer or substrate. The optical medium may include a plurality of scattering array interferometers, each of the plurality of scattering array interferometers being spaced in different regions of the optical medium, and each of the respective array of scatterers / reflectors of the plurality of scattering array interferometers has a different spatial distribution. The optical medium is formed of an environmentally sensitive material, and the refractive index modulation of the respective array of scatterers / reflectors differs based at least in part on an environmental change that affects the optical medium. The respective array of scatterers / reflectors is created in the optical medium using a spatially or temporally controlled fabrication method. The respective array of scatterers / reflectors is created in the optical medium by methods including but not limited to: laser inscription, chemical deposition, 3D printing, mechanical processing, thermal processing, mechanical machining, thin film deposition, chemical etching, or three-dimensional printing on an optical waveguide. The corresponding pitch is between 0.1 micrometer and 10 millimeters, and the respective array or other spatial distribution of scatterers / reflectors includes at least two scatter er s / refl ectors .

[0006] One general aspect includes a system for multi-point optical medium sensing. The system also includes an optical medium having a first end and a second end and may include a plurality of scattering array interferometers, each of the plurality of scattering array interferometers including a respective array of scatterers / reflectors with at least one pair of scatterers / reflectors that are uniformly sized and spaced according to a corresponding pitch, each of the plurality of scattering array interferometers being at a corresponding location in the optical medium. The system also includes an interrogation light source coupled to the first end of the optical medium. The system also includes a detector coupled to the optical medium and configured to detect a respective interference signal produced by each of the plurality of scattering array interferometers using refractive index modulation, where the detector may include a spectrometer, a spectrum analyzer, a photodiode, a charge coupled device (CCD), or a complementary metaloxidesemiconductor (CMOS) array.

[0007] Implementations may include one or more of the following features. The system where the respective interference signal changes based at least in part on a respective temperature of the corresponding location of the optical medium. The respective interferencesignal changes based at least in part on actions including but not limited to respective rotation, stress, bending, refractive index change, or strain applied to the corresponding location of the optical medium. The corresponding pitch is between 0.1 micrometer and 10 millimeters. The optical medium may include a sapphire fiber. Each respective array of scatterers / reflectors may include a plurality of periodic scatterer lines arranged in parallel.

[0008] One general aspect includes a method for fabrication of a multi-point sensor in an optical medium. The method also includes inscribing a first array of scatterers / reflectors at a first location in the optical medium, at least two scatterers / reflectors of the first array of scatterers / reflectors being uniformly sized and spaced according to a first pitch. The method also includes inscribing a second array of scatterers / reflectors at a second location in the optical medium, at least two scatterers / reflectors of the second array of scatterers / reflectors being uniformly sized and spaced according to a second pitch differing from the first pitch.

[0009] Implementations may include one or more of the following features. The method where the optical medium may include a sapphire fiber. The method may include inscribing a third array of scatterers / reflectors at a third location in the optical medium, at least two scatterers / reflectors of the third array of scatterers / reflectors being uniformly sized and spaced according to a third pitch differing from the first pitch and the second pitch. All the pitches may be between 0.1 micrometer and 10 millimeters. The first array of scatterers / reflectors and the second array of scatterers / reflectors may include a plurality of periodic scatterer lines arranged in parallel.BRIEF DESCRIPTION OF THE DRAWINGS

[0010] Many aspects of the present disclosure can be better understood with reference to the following drawings. The components in the drawings are not necessarily to scale, with emphasis instead being placed upon clearly illustrating the principles of the disclosure. Moreover, in the drawings, like reference numerals designate corresponding parts throughout the several views.

[0011] FIG. 1 is an illustration showing one example of a scattering array interferometer (SAI).

[0012] FIG. 2 is a micrograph showing one example of an SAI sensor with a laser inscription point array.

[0013] FIG. 3 is an illustration showing one example of an SAI sensor with scatter er / reflector lines.

[0014] FIG. 4 is a graph of an example spectrum for the signal of a SAI sensor in optical fibers.

[0015] FIG. 5A is a graph of the interference signal fast-Fourier transform (FFT) spectrum comparing an SAI signal with a background signal.

[0016] FIG. 5B is an illustration showing one example of a laser fabrication system that uses an optical shutter or chopper to block part of the incident laser pulses in fabrication of an SAI sensor.

[0017] FIG. 5C is a graph showing the signal of an SAI sensor when periodicity is broken in the SAI sensor according to one example.

[0018] FIG. 6 is a graph showing optical path length difference (OPD) response of different harmonics in an SAI sensor over time based on temperature change.

[0019] FIG. 7 is a diagram showing a cascade of SAI sensors in an optical fiber according to one example.

[0020] FIG. 8 is a graph showing calibration curves of three cascaded SAI sensors according to one example.

[0021] FIG. 9 illustrates the design and fabrication of one example of the sapphire fiber SAI, where (a) illustrates the working principle of the sensor, (b) illustrates the laser point-by- point inscription procedure, and (c) is a micrograph of the sapphire fiber SAI, where A and Ax indicate pitch and lateral offset between adjacent periodic scatterer lines, respectively.

[0022] FIG. 10 illustrates spectra of one example of the sapphire fiber SAI, where (a) is a graph that shows the signal of a sapphire fiber SAI, and (b) is a graph that illustrates signal enhancement of each harmonic during thermal annealing.

[0023] FIG. 11 illustrates properties of the SAI signal, where (a) is a graph of a comparison of SAI signals in silica and sapphire fibers, and (b) is a graph of the temperature response of the sapphire fiber SAI at different harmonics.

[0024] FIG. 12 illustrates calibration and performance of one example of the cascaded sapphire fiber SAI sensor, where (a) is a graph showing calibration of the three sapphire fiber SAIs, (b) is a graph showing hysteresis of the SAI B, and (c) is a graph showing multipoint temperature sensing.

[0025] FIG. 13 is a flowchart illustrating one example method for fabrication of the SAI sensor in an optical medium.DETAILED DESCRIPTION

[0026] Optical interferometers are widely utilized in optical sensing systems because they can provide outstanding sensitivity and are insensitive to spectral fluctuations. The optical path length difference (OPD) is demodulated in such sensors through the carrier frequency analysis of the interference signal, where high signal -to-noise ratio (SNR) can be achieved with fast Fourier transform (FFT) analysis. With the help of several interferogram signal -processing algorithms, deep sub-nanometer resolution can be achieved.

[0027] The present disclosure introduces a structure for coherent sensing and / or three- dimensional (3D) optical engineering called scattering array interferometers (SAIs). As shown in FIG. 1, an example of SAI is composed of one pair or a series of scatter er s / reflectors in the optical fiber or other optical media, which may have uniform shapes and may be separated with the same pitch. An SAI can also be a 3D distribution of scatter ers / reflectors that can modify and manipulate optical fields in a designed way.

[0028] FIG. 1 shows one example of the interference of the optical field from the infiber reflectors. The scatterers / reflectors can be formed by laser inscription, mechanical machining, thin film deposition, chemical etching, and three-dimensional (3D) printing on optical waveguides or during the fabrication of optical waveguides. The scatterers / reflectors can have a regular shape, for example, cylindrical, spherical, polygonal, and helical shapes, which can introduce refractive index (RI) modulation of the optical fiber / optical media. The SAI sensors may be used to sense various environmental parameters such as temperature, strain, stress, bending, shape changing, rotation, and so on. Multi-point sensing within an optical medium may be achieved through different SAIs having different pitches at corresponding locations in the optical medium. Applications of SAI sensors may include endoscopy, magnetic field sensing, load cells, and so on. Sensitivity may be at the nanometer to picometer level.

[0029] FIG. 2 shows an SAI sensor with a laser inscription point array. The number of the scatterers / reflectors can be from one pair to multiple, or a great number to increase the scattering strength / reflectivity, such as in FIG. 2. There are multiple other methods to increase the RI modulation volume to increase the sensor’s signal intensity, such as laser point-by-point inscription, laser filamentation, laser line-by-line inscription, fabrication of multiple layers of scatterers / reflectors at different depths, and parallelly inscription.

[0030] FIG. 3 shows one example of an SAI sensor with scatterer / reflector lines. The scatterers / reflectors can be formed separately (one-by one) or simultaneously (in pairs or in multiple lines), which may be achieved via laser point-by-point inscription, laser line-by-linescanning (as in FIG. 3), laser beam shaping, laser holographic shaping, fabrication with phase masks, laser direct writing, laser beam splitting with Wollaston prism, laser beam scanning by moving stage, or galvanometers, or actuators, laser pulse selections and modulations by adding temporal controls or modulators such as optical shutters, optical modulators, or optical choppers.

[0031] The optical fibers or other optical media here include all kinds of optical waveguides with various structures, shapes or materials. The optical fibers include but not limited to silica fibers, sapphire fibers, yttrium aluminum garnet (YAG) fibers, polymer fibers, rear earth-doped optical fibers, silicate fibers or fibers with specific dopants. The fiber types include but not limited to single mode fibers, two / few mode fibers, multimode fibers, multicore fibers, and photonic crystal fibers. Apart from optical fibers, the SAIs can also be fabricated in other non-waveguiding optical media including but not limited to wafers / slabs / rods made of optical materials.

[0032] FIG. 4 shows an example spectrum for the signal of a SAI sensor in optical fibers. The SAI signal 403 is shown by comparison to a background signal 406, with wavelength and corresponding intensity. Because of optical interference, spectral modulation is created on its spectrum. However, the signal may not be identifiable since the reflectivity is not sufficiently high. Therefore, an FFT transform can be applied to the spectrum to pick out the interference signal, as demonstrated in FIG. 5A, which shows the interference signal FFT spectrum, with the SAI signal 503 compared to the background signal 506. Then, by spectral analysis, carrier frequency analysis or total phase evaluation, the OPD can be demodulated.

[0033] As shown in FIG. 5A, if more than one pair of scatterers / scatterers / reflectors are constructed in fibers, not only the interference signal corresponding to the OPD of the adjacent scatterers / scatterers / reflectors will appear, high order harmonics, which are from the non-adjacent scatterers / scatterers / reflectors but have fixed pitches, will also appear. Due to the larger pitch sizes, these higher harmonics have a higher response to OPD changes.

[0034] In various embodiments, the array can be periodic or not periodic, which can include multiple scatter er s / reflectors with the same pitches, or with different pitches. Periodicity can generate harmonics, and an array that breaks periodicity is not limited by high order harmonics. The periodicity of the scatterers or reflectors can be broken by adding temporal or spatial modulations or controls during the fabrication. The periodicity is not necessarily maintained between all scatterers or reflectors; in some cases, only some of these scatterers or reflectors have the designed periodicity, and separations of other scatterers or reflectors can be random to break the periodicity of the whole scatterer / reflector array. Forexample, FIG. 5B presents a laser fabrication system that uses an optical shutter or chopper to block part of the incident laser pulses, then separate scatter er / reflector pairs are formed (such as the scatterer / reflector pair between point 1 and 2, and point 5 and 6 as shown in FIG. 5B). Consequently, the periodicity of the whole periodic scatterer line (PSL) is broken.

[0035] As shown in FIG. 5C, although the periodicity of the whole scatterer / reflector line is broken, the optical scattering / reflections in the scatterer / reflector pairs can still form the SAI signal. The scatterer / reflector pairs may also avoid the formation of high order harmonics and achieve higher multiplexity.

[0036] FIG. 6 shows the OPD response of different harmonics over time based on temperature change. In FIG. 6, a first harmonic 603, a second harmonic 606, a third harmonic 609, and a fourth harmonic 612 are shown. As shown in FIG. 6, under the same temperature change, the higher order harmonics of the SAI signal has larger OPD change, but also has worse OPD stability due to the lower signal amplitude.

[0037] FIG. 7 is a diagram showing a cascade of SAI sensors in an optical fiber. As shown in FIG. 7, multipoint sensing can be achieved by constructing several fiber SAI sensors in a single optical fiber. By separating the OPDs of each SAI sensors with sufficient OPD difference and avoid signal overlap in FFT spectrum, multiplexed sensing can be achieved. As an example, a cascaded sapphire fiber SAI sensor is shown in FIG. 7, which is composed of three SAIs in a single sapphire fiber. The pitch sizes of SAI A, SAI B and SAI C are 13 pm, 20 pm, and 32 pm, respectively. The calibration curves of the three cascaded SAI sensors are shown in FIG. 8, which shows the temperature response with different pitches. Curve 803 corresponds to SAI A, curve 806 corresponds to SAI B, and curve 809 corresponds to SAI C. All of them follow a nonlinear relationship between OPD and temperature due to the thermal expansion and thermo-optics effect. With a larger pitch size, the OPD change is larger under the same temperature change.

[0038] Sapphire fiber-based sensors may be used in harsh environment sensing because of their ultrahigh working temperature and excellent chemical, mechanical and optical stability. Among others, sapphire fiber Bragg gratings (FBGs) and sapphire fiber Fabry -Perot interferometers (FPIs) are the two most common structures using optical coherence to provide sensitive and reliable sensing signals. Sapphire FBGs are sometimes preferred because of their simple wavelength-tracing demodulation and multiplexing capability, but they also suffer from limitations. The wavelength-dependent demodulation is sensitive to spectral fluctuations of the light source and / or external factors such as blackbody radiation, which may impair measurement sensitivity and accuracy. Additionally, when multiplexed, each of the FBGsrequires relatively wide and high-intensity spectral band without overlapping with others. The total number of multiplexed sensors is thus limited by the bandwidth of the light source.

[0039] On the other hand, sapphire fiber FPIs have better stability and sensitivity than sapphire FBGs. Unlike the wavelength-tracing method, the OPD of an interferometer is demodulated through carrier frequency analysis of its interference spectrum, where the Cramer-Rao bound of detection can be achieved. Using several interferogram signalprocessing algorithms, deep sub-nanometer resolution can be reached. Since the interference signal is independent of the source envelope and other slowly varying spectral background signals, the accuracy and sensitivity of the OPD demodulation is insensitive to their fluctuation and deformation. Moreover, interferometers with different carrier frequencies can be readily multiplexed to share the entire source spectrum while cleanly separated in the FFT spectrum, even when source bandwidth is limited.

[0040] Several extrinsic sapphire fiber FPIs have been developed. Such sensors are usually constructed by an air gap or a sapphire wafer. Multiplexed high temperature sensors have been demonstrated with extrinsic sapphire FPIs, where air gaps with different OPDs are formed with sapphire fiber segments inserted in zirconia tubes. However, the diameter mismatch between the tubes and sapphire fibers causes misalignment and the degradation of fringe visibility due to reduced parallelism and light coupling, and sensor reliability is compromised because of material mismatch. Wafer-based sapphire fiber FPIs usually function better than air-gap ones due to the simplicity in the generation of high-quality interference fringes. However, most wafer-based sapphire fiber FPI sensors use high temperature adhesive to fix the wafer, which reduces the sensor stability due to the presence of exotic material that hampers the uniformity of sensor response. Although all-sapphire wafer-based FPI sensors have been demonstrated through carbon dioxide laser direct welding, the fabrication procedure is complicated, and its extrinsic nature is incompatible with multiplexing. Multiplexable intrinsic sapphire fiber interferometers are thus of significant interest, especially in industrial applications, but they have yet to be demonstrated.

[0041] Various embodiments of the present disclosure introduce an intrinsic sapphire fiber SAI that is composed of periodic scattering points inscribed by a femtosecond (fs) laser. The point-by-point inscription technique produces excellent uniformity in the morphology and pitch of the inscription points. This is essential in generating sufficient mutual coherence and interference visibility between these points, even in a fully multimode sapphire fiber system. Parallel inscription and thermal annealing are applied to further improve signal-to-noise ratio (SNR), forming a sapphire fiber SAI sensor. High order harmonics from non-adjacentscattering points are observed and compared with that of silica multimode fibers (MMFs) to examine the coherence properties of sapphire fibers. Then, cascaded SAI sensors may be fabricated on a single sapphire fiber and interrogated using a low cost fully multimode spectral- domain system. Reliable multipoint temperature sensing up to 1500° Celsius (C) is demonstrated.

[0042] The inscription points formed by fs laser point-by-point fabrication often possess excellent uniformity, and thus can be treated as identical scatterers for optical interference. However, because of their limited refractive index (RI) modulation volume and the low spatial coherence in sapphire fibers, a single pair of inscription points suffer from low scattering strength and cannot provide sufficient interference intensity. Therefore, as demonstrated in FIG. 9(a), a line of periodic scattering points (periodic scatterer line, PSL) is designed to significantly increase the number of scatterers and thus the interference strength. In the meantime, excessive number of scattering points may result in an extremely long PSL and reduce the spatial resolution of the sensor. In some embodiments, parallel PSLs are fabricated to balance between sensor size and signal intensity. Periodic structures, such as FBGs or long period-gratings, are designed with specific pitches to couple selected modes at certain wavelengths, while the pitch of the proposed structure can be rather arbitrary.

[0043] The PSLs may be fabricated using a fs laser inscription system. As shown in FIG. 9(b), the fabrication in one non-limiting example starts along the center axis of a c-axis single crystal sapphire fiber with a diameter of 75 micrometers (pm). In the example, the laser may be set to an average output power of 75 microwatts (pW) and a repetition rate of 125 Hertz (Hz), corresponding to a single pulse energy of 600 nanojoules (nJ). In the example, the sapphire fiber may be mounted on an air-bearing stage with a moving speed of 1.25 millimeters per second (mm / s) to inscribe a single 5 mm-long PSL with a pitch of 10 pm. After the fabrication of one line, the laser focus is laterally shifted by 3 pm toward the fiber boundary and another identical PSL is fabricated parallel to the prior one. The 3 pm separation is sufficient to minimize possible coherent interaction between adjacent PSLs in the multimode setting. After the inscription of ten parallel PSLs on one side of the first line, another ten lines may be fabricated on the other side. The set of all 21 parallel PSLs forms one sapphire fiber SAI sensor as shown in FIG. 9(c). It should be noted that due to the air-bearing stage movement and the asynchronized laser shutter delay, the axial locations of the individual PSLs may be aligned randomly.

[0044] The sapphire fiber SAI may be fabricated 250 mm away from the input end of the sapphire fiber, with its reflection spectrum shown in the inset of FIG. 10(a), where a 600-nanometer (nm) light emitting diode (LED) may be used as the light source. As shown in FIG. 10(a), the interference cannot be visualized with a single PSL due to the low scattering strength. After the fabrication of the SAI, although the interference fringes can be barely seen from the spectrum, its signal can be clearly identified from the FFT spectrum with an SNR of approximately 11 decibels (dB) at an OPD of 36.2 pm, corresponding to its first harmonic or the 10 pm pitch in sapphire fiber. To further enhance signal intensity, thermal annealing (for example, 1200°C for four hours) may be conducted. The annealing may improve the surface quality, morphology and consistency of the laser inscription points, thus enhancing the coherence of the waves scattered from the inscription points. Consequently, the SNR of the 10 pm SAI signal is effectively enhanced to approximately 20 dB, as shown with the SAI signal before annealing 1003 as compared to the SAI signal after annealing 1006. Moreover, with the enhancement of coherent scattering, interference signals at OPD of 72.3 pm, 107.6 pm, 142.9 pm, and 179.0 pm can also be observed in FIG. 10(a), corresponding to pitch sizes of 20 pm, 30 pm, 40 pm, and 50 pm (namely, the 2nd, 3rd, 4th and 5th harmonics), respectively. These additional peaks indicate that the interference can be formed not only between adjacent laser inscription points, but also between pairs of longer separation, albeit with reduced coherence that depends on the coherence of light source and modal volume / mixing of fiber.

[0045] Furthermore, the SNR change of the first four harmonics is plotted in FIG. 10(b), with the first harmonic signal 1009 (10 pm pitch), the second harmonic signal 1012 (20 pm pitch), the third harmonic signal 1015 (30 pm pitch), and the fourth harmonic signal 1018 (40 pm pitch). The SNR does not show much enhancement before reaching 1200°C. Then, significant SNR rise is observed in the first hour at the annealing temperature and reaches the maxima at approximately 2.5 hours. Further extension of the annealing time may not facilitate further SNR improvement. This result indicates that a reduced annealing time of approximately 2.5 hours may be sufficient to achieve optimal SNR for the sapphire fiber SAIs. It should be noted that additional SNR rise can be observed when the sensor is cooled to room temperature, which is likely related to mode mixing and sensitive coherence response to thermal expansion and RI change. Moreover, by analyzing the evolution of the peak intensity change with different harmonics (and different effective OPD), the coherence property of the waveguide can be evaluated.

[0046] In the FFT spectrum of sapphire fiber SAI after thermal annealing, there is a similar number of scattering point pairs, and the intensity of the interference harmonics decreases as the OPD increases, indicating the degradation of coherence with larger scattering point separation. The coherence is dependent on properties such as modal volume andnumerical aperture (NA) of the waveguide, which is vague for sapphire fibers and is critical in the SAI sensor design. To assist the evaluation, a SAI with the same number of inscription points may be fabricated in a silica step-index multimode fiber. In one non-limiting example, the pitch of the silica multimode fiber (MMF) SAI may be set to be 12.08 pm to match with the OPD of the 10-pm sapphire fiber SAI. The FFT spectra of the two SAIs are shown in FIG. 11(a), with the silica SAI evolution trend 1103 contrasting with the sapphire SAI evolution trend 1106. As shown in the FIG. 11(a), the silica MMF SAI peaks generally have higher amplitude than that of the sapphire fiber SAI, which is attributed to a higher coherence because of lower modal volume in silica MMFs. Meanwhile, with the increment of OPD, although both SAIs suffer from the peak amplitude degradation, the amplitude decreases faster in silica MMFs at shorter OPD and then gradually reaches similar amplitude in both fibers beyond approximately 150 pm. That harmonics in silica MMF degrade faster than those in sapphire fiber indicates different coherence properties, which could be related to mode mixing behaviors. In silica fibers, mode mixing is negligible over short distance due to smooth boundary geometry, but sapphire fibers suffer from strong mode mixing due to their rough surface.

[0047] With the sapphire fiber SAI heated from room temperature to 155°C, the OPD evolutions of the first four harmonics of the sapphire fiber SAI sensor are demodulated with the Type II algorithm and shown in FIG. 11(b), with the first harmonic 1109, the second harmonic 1112, the third harmonic 1115, and the fourth harmonic 1118. Larger OPD changes are observed for larger harmonics, with proportionally higher temperature responses as listed in FIG. 11(b). However, the stability of the measurement becomes worse at high-order harmonics, which is a result of lower SNR due to the increment of OPD. This indicates that a trade-off between temperature response and measurement resolution may be a factor in SAI design in selecting a suitable pitch size for the optimal sensing performance.

[0048] To demonstrate the sensing capability of the sapphire fiber SAIs, a fully multimode multipoint temperature sensing system is designed. The interrogator in one nonlimiting example includes a 600-nm LED light source, a charge coupled device (CCD)-based spectrometer as the detector, and a 105 / 125 pm multimode fiber coupler. In one example, the sensing probe may have three SAIs fabricated with a separation of 80 mm on a 450-mm-long sapphire fiber fusion-spliced to the interrogator (FIG. 7). To avoid signal overlap in the FFT spectrum while maintaining adequate SNR, the pitch sizes of the three SAIs in this example may be set to be 13 pm (SAI A), 20 pm (SAI B), and 32 pm (SAI C), with a length of 5.2 mm, 8.0 mm, and 10.2 mm, respectively. All three SAIs may be fabricated on the same azimuthalplane of the fiber to simplify the fabrication procedure. The sapphire fiber end may be polished to 30° in this example to suppress end reflection, thus maximizing sensor signal on the spectrometer and improving SNR. After thermal annealing, the FFT spectrum of the cascaded SAI sensors at room temperature (TO) may have three SAI peaks observed at the OPD of 47.1 pm, 72.3 pm, and 115.3 pm, with an SNR of 12.1 dB, 14.7 dB, and 8.6 dB, respectively. Although the high order harmonics of SAI A and SAI B exist, the crosstalk is avoided by the sufficient OPD separation between the SAIs.

[0049] The change of the FFT spectra with temperature increment is also seen, where SAI A is at room temperature (TO), heated to 531°C (Tl), 1111°C (T2), and 1350°C (T3), and SAI B and SAI C are at lower temperatures. Although SAI peak shifts can be observed as temperature rises, the signals of the three SAIs have no overlaps and maintain desirable SNR for OPD demodulation for multipoint temperature sensing.

[0050] The impact of blackbody radiation at high temperature is also examined. The spectra of TO and T3 show significant spectral deformation at T3 due to the raised background from blackbody radiation. Such deformation will cause severe errors in wavelength-tracing- based signal demodulation such as in FBG sensors. However, this significant background is a slowly varying function and is thus located around DC and away from the sensor peaks in the FFT spectrum. Its influence can be negligible in the SAI signal demodulation.

[0051] The sapphire sensor may then be placed in a programmable furnace for temperature sensing tests with a B-type thermocouple for calibration. The OPD changes with temperature for each SAI sensor are demodulated with the same Type II demodulation algorithm, as demonstrated in FIG. 12(a). FIG. 12(a) shows three response curves: an SAI A curve 1203, an SAI B curve 1206, and an SAI C curve 1209. All three response curves follow similar parabolic trend with temperature up to 1500°C as a result of thermal expansion and thermo-optic effect, and the range of OPD change increases for larger pitch of SAI.

[0052] The measurements of SAI B are plotted in FIG. 12(b) for a complete temperature change cycle. Parabolic curve fitting is applied to the temperature rise and drop separately and matches well with the measurements. A mismatch less than 0.006 pm is obtained, corresponding to a hysteresis of less than 4°C, which is likely caused by the thermal hysteresis of the testing apparatuses during the thermal cycles.

[0053] The sensing performance of the cascaded SAI probe is evaluated in FIG. 12(c). With SAI B placed in the center of the furnace’s heating area and SAI A and SAI C away from the center, the three SAIs experience different temperatures. Based on the calibration curve, temperature changes at the three SAIs are demodulated. As shown in the figure, all three curvesfollow stepwise temperature changes, as programmed for the furnace. The temperature ranges are from room temperature to 1176°C, 1471°C, and 1364°C, with a stability of 0.6°C, 0.5°C, and 0.6°C for SAI A, SAI B, and SAI C, respectively, confirming the multiplexed sensing capability.

[0054] FIG. 13 is a flowchart providing one example of a method for fabrication of an SAI sensor in an optical medium. At 1303, a first array of scatterers / reflectors is inscribed at a first location in an optical medium. Two or more of the scatterers / reflectors may be uniformly sized and spaced according to a first pitch. At 1306, a second array of scatterers / reflectors is inscribed at a second location in the optical medium. Two or more of the scatterers / reflectors may be uniformly sized and spaced according to a second pitch that differs from the first pitch. At 1309, a third array of scatterers / reflectors is inscribed at a third location in the optical medium. Two or more of the scatterers / reflectors may be uniformly sized and spaced according to a third pitch that differs from the first and second pitches.

[0055] In summary, a fabrication of an intrinsic sapphire fiber SAI sensor through the fs laser point-by-point inscription technique is described. The excellent uniformity and large number of the scattering points facilitate desirable coherent interaction and enable robust interference. With the help of parallel inscription and thermal annealing, interference signal with an SNR of ~20 dB can be achieved with a 10-pm-pitch sapphire fiber SAI. A multipoint high temperature sensor may be fabricated with three cascaded SAIs on a single sapphire fiber. With a low-cost, fully multimode interrogator composed of a visible-band LED and a CCDbased fast spectrometer, reliable multipoint temperature sensing up to 1500°C is demonstrated.

[0056] The SAI introduces a novel interferometric mechanism to achieve robust optical interference signal with fully in-fiber structures, which is particularly desirable for sapphire fiber sensors because of its simplicity and the anticipated high survivability in harsh sensing environment. Meanwhile, the existence of high order harmonic signals may cause crosstalk between multiplexed SAIs. However, by proper OPD management, scattering intensity enhancement, and interrogation light modification, such limitations can be effectively mitigated to achieve more densely multiplexed sensing. The discussion of the multiple harmonic signals offers insights into the coherence properties of sapphire fibers, which has a complex relationship with its high modal volume, dynamic mode mixing, and increased scattering loss at the surface.

[0057] Embodiments of the present disclosure may be described by one or more of the following clauses:

[0058] Clause 1. An optical medium, comprising: one or more scattering array interferometers in the optical medium, each of the scattering array interferometers including a respective array or other spatial distribution of scatterers / reflectors that are uniformly sized and spaced according to a corresponding pitch, the respective array or other spatial distribution of scatterers / reflectors being configured to cause coherent light interference when a light source is applied to the optical medium.

[0059] Clause 2. The optical medium of clause 1, wherein at least one scatter er / reflector of the one or more scattering array interferometers differs in size from a size of the at least two scatterers / reflectors or is not spaced according to the corresponding pitch.

[0060] Clause 3. The optical medium of clauses 1 to 2, wherein the optical medium comprises at least one of a silica fiber, a sapphire fiber, an yttrium aluminum garnet (YAG) fiber, a polymer fiber, a rear earth-doped optical fiber, a silicate fiber, or an integrated photonic waveguide.

[0061] Clause 4. The optical medium of clauses 1 to 3, wherein the optical medium comprises an optical wafer or substrate.

[0062] Clause 5. The optical medium of clauses 1 to 4, wherein the optical medium comprises a plurality of scattering array interferometers, each of the plurality of scattering array interferometers being spaced in different regions of the optical medium, and each of the respective array of scatterers / reflectors of the plurality of scattering array interferometers has a different spatial distribution.

[0063] Clause 6. The optical medium of clauses 1 to 5, wherein the optical medium is formed of an environmentally sensitive material, and the refractive index modulation of the respective array of scatterers / reflectors differs based at least in part on an environmental change that affects the optical medium.

[0064] Clause 7. The optical medium of clauses 1 to 6, wherein the respective array of scatterers / reflectors is created in the optical medium using a spatially or temporally controlled fabrication method.

[0065] Clause 8. The optical medium of clauses 1 to 7, wherein the respective array of scatterers / reflectors is created in the optical medium by at least one of laser inscription, chemical deposition, 3D printing, mechanical processing, thermal processing, mechanical machining, thin film deposition, chemical etching, or three-dimensional printing on an optical waveguide.

[0066] Clause 9. The optical medium of clauses 1 to 8, wherein the corresponding pitch is between 0.1 micrometer and 10 millimeters, and the respective array or other spatial distribution of scatterers / reflectors includes at least two scatterers / reflectors.

[0067] Clause 10. A system for multi-point optical medium sensing, comprising: an optical medium having a first end and a second end and comprising a plurality of scattering array interferometers, each of the plurality of scattering array interferometers including a respective array of scatterers / reflectors that include at least two scatterers / reflectors that are uniformly sized and spaced according to a corresponding pitch, each of the plurality of scattering array interferometers being at a corresponding location in the optical medium; an interrogation light source coupled to the first end of the optical medium; and a detector coupled to the optical medium and configured to detect a respective interference signal produced by each of the plurality of scattering array interferometers using refractive index modulation, wherein the detector comprises a spectrometer, a spectrum analyzer, a photodiode, a charge coupled device (CCD), or a complementary metal-oxide-semiconductor (CMOS) array.

[0068] Clause 11. The system of clause 10, wherein the respective interference signal changes based at least in part on a respective temperature of the corresponding location of the optical medium.

[0069] Clause 12. The system of clauses 10 to 11, wherein the respective interference signal changes based at least in part on at least one of a respective rotation, stress, bending, refractive index change, or strain applied to the corresponding location of the optical medium.

[0070] Clause 13. The system of clauses 10 to 12, wherein the corresponding pitch is between 0.1 micrometer and 10 millimeters.

[0071] Clause 14. The system of clauses 10 to 13, wherein the optical medium comprises a sapphire fiber.

[0072] Clause 15. The system of clauses 10 to 14, wherein each respective array of scatterers / reflectors comprises a plurality of periodic scatterer lines arranged in parallel, at a different depth, or at different lateral positions in the optical medium.

[0073] Clause 16. A method for fabrication of a multi-point sensor in an optical medium, comprising: inscribing a first array of scatterers / reflectors at a first location in the optical medium, at least two scatterers / reflectors of the first array of scatterers / reflectors being uniformly sized and spaced according to a first pitch; and inscribing a second array of scatterers / reflectors at a second location in the optical medium, at least two scatterers / reflectorsof the second array of scatterers / reflectors being uniformly sized and spaced according to a second pitch differing from the first pitch.

[0074] Clause 17. The method of clause 16, wherein the optical medium comprises a sapphire fiber.

[0075] Clause 18. The method of clauses 16 to 17, further comprising inscribing a third array of scatterers / reflectors at a third location in the optical medium, at least two scatterers / reflectors of the third array of scatterers / reflectors being uniformly sized and spaced according to a third pitch differing from the first pitch and the second pitch.

[0076] Clause 19. The method of clauses 16 to 18, wherein the first pitch and the second pitch are between 0.1 micrometer and 10 millimeters.

[0077] Clause 20. The method of clauses 16 to 19, wherein the first array of scatterers / reflectors or the second array of scatterers / reflectors comprise a plurality of periodic scatterer lines arranged in parallel, at a different depth, or at different lateral positions in the optical medium.

Claims

CLAIMS1. An optical medium, comprising: one or more scattering array interferometers in the optical medium, each of the scattering array interferometers including a respective array or other spatial distribution of at least two scatterers / reflectors that are uniformly sized and spaced according to a corresponding pitch, the respective array or other spatial distribution of scatterers / reflectors being configured to cause coherent light interference when a light source is applied to the optical medium.

2. The optical medium of claim 1, wherein at least one reflector of the one or more scattering array interferometers differs in size from the at least two scatterers / reflectors or is not spaced according to the corresponding pitch.

3. The optical medium of claim 1, wherein the optical medium comprises at least one of: a silica fiber, a sapphire fiber, an yttrium aluminum garnet (YAG) fiber, a polymer fiber, a rear earth-doped optical fiber, a silicate fiber, or an integrated photonic waveguide.

4. The optical medium of claim 1, wherein the optical medium comprises an optical wafer or substrate.

5. The optical medium of claim 1, wherein the optical medium comprises a plurality of scattering array interferometers, each of the plurality of scattering array interferometers being spaced in different regions of the optical medium, and each of the respective array of scatterers / reflectors of the plurality of scattering array interferometers has a different spatial distribution.

6. The optical medium of claim 1, wherein the optical medium is formed of an environmentally sensitive material, and the refractive index modulation of the respective array of scatterers / reflectors differs based at least in part on an environmental change that affects the optical medium.

7. The optical medium of claim 1, wherein the respective array of scatterers / reflectors is created in the optical medium using a spatially or temporally controlled fabrication method comprising at least one of: laser point-by-point inscription, laser line-by-line scanning, laser beam shaping, fabrication with phase masks, laser direct writing, laser beam separation with a Wollaston prism, laser holographic shaping, laser beam scanning by moving stage, or galvanometers, or actuators, laser pulse selections and modulations by adding temporal controls or modulators such as optical shutters, optical modulators, or optical choppers.

8. The optical medium of claim 1, wherein the respective array of scatter er s / reflectors is created in the optical medium by at least one of: laser inscription, chemical deposition, 3D printing, mechanical processing, thermal processing, mechanical machining, thin film deposition, chemical etching, or three-dimensional printing on an optical waveguide.

9. The optical medium of claim 1, wherein the corresponding pitch is between 0.1 micrometer and 10 millimeters, and the respective array or other spatial distribution of scatter er s / reflectors includes at least two scatterers / reflectors.

10. A system for multi-point optical medium sensing, comprising: an optical medium having a first end and a second end and comprising a plurality of scattering array interferometers, each of the plurality of scattering array interferometers including a respective array of scatterers / reflectors including at least two scatterers / reflectors that are uniformly sized and spaced according to a corresponding pitch, each of the plurality of scattering array interferometers being at a corresponding location in the optical medium; an interrogation light source coupled to the first end of the optical medium; and a detector coupled to the optical medium and configured to detect a respective interference signal produced by each of the plurality of scattering array interferometers using refractive index modulation, wherein the detector comprises a spectrometer, a spectrum analyzer, a photodiode, a charge coupled device (CCD), or a complementary metal-oxide- semiconductor (CMOS) array.

11. The system of claim 10, wherein the respective interference signal changes based at least in part on a respective temperature of the corresponding location of the optical medium.

12. The system of claim 10, wherein the respective interference signal changes based at least in part on at least one of a respective rotation, stress, bending, refractive index change, or strain applied to the corresponding location of the optical medium.

13. The system of claim 10, wherein the corresponding pitch is between 0.1 micrometer and 10 millimeters.

14. The system of claim 10, wherein the optical medium comprises a sapphire fiber.

15. The system of claim 10, wherein each respective array of scatterers / reflectors comprises one or more periodic scatterer lines arranged in parallel, at a different depth, or at different lateral positions in the optical medium.

16. A method for fabrication of a multi-point sensor in an optical medium, comprising: inscribing a first array of scatterers / reflectors at a first location in the optical medium, at least two scatterers / reflectors of the first array of scatterers / reflectors being uniformly sized and spaced according to a first pitch; and inscribing a second array of scatterers / reflectors at a second location in the optical medium, at least two scatterers / reflectors of the second array of scatterers / reflectors being uniformly sized and spaced according to a second pitch differing from the first pitch.

17. The method of claim 16, wherein the optical medium comprises a sapphire fiber.

18. The method of claim 16, further comprising inscribing a third array of scatterers / reflectors at a third location in the optical medium, at least two scatterers / reflectors of the third array of scatterers / reflectors being uniformly sized and spaced according to a third pitch differing from the first pitch and the second pitch.

19. The method of claim 16, wherein the first pitch and the second pitch are between0.1 micrometer and 10 millimeters.

20. The method of claim 16, wherein the first array of scatterers / reflectors or the second array of scatterers / reflectors comprise one or more periodic scatterer lines arranged in parallel, at a different depth, or at different lateral positions in the optical medium.

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