Classifications

• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01D—MEASURING NOT SPECIALLY ADAPTED FOR A SPECIFIC VARIABLE; ARRANGEMENTS FOR MEASURING TWO OR MORE VARIABLES NOT COVERED IN A SINGLE OTHER SUBCLASS; TARIFF METERING APPARATUS; MEASURING OR TESTING NOT OTHERWISE PROVIDED FOR
  • G01D5/00—Mechanical means for transferring the output of a sensing member; Means for converting the output of a sensing member to another variable where the form or nature of the sensing member does not constrain the means for converting; Transducers not specially adapted for a specific variable
  • G01D5/26—Mechanical means for transferring the output of a sensing member; Means for converting the output of a sensing member to another variable where the form or nature of the sensing member does not constrain the means for converting; Transducers not specially adapted for a specific variable characterised by optical transfer means, i.e. using infrared, visible, or ultraviolet light
  • G01D5/32—Mechanical means for transferring the output of a sensing member; Means for converting the output of a sensing member to another variable where the form or nature of the sensing member does not constrain the means for converting; Transducers not specially adapted for a specific variable characterised by optical transfer means, i.e. using infrared, visible, or ultraviolet light with attenuation or whole or partial obturation of beams of light
  • G01D5/34—Mechanical means for transferring the output of a sensing member; Means for converting the output of a sensing member to another variable where the form or nature of the sensing member does not constrain the means for converting; Transducers not specially adapted for a specific variable characterised by optical transfer means, i.e. using infrared, visible, or ultraviolet light with attenuation or whole or partial obturation of beams of light the beams of light being detected by photocells
  • G01D5/353—Mechanical means for transferring the output of a sensing member; Means for converting the output of a sensing member to another variable where the form or nature of the sensing member does not constrain the means for converting; Transducers not specially adapted for a specific variable characterised by optical transfer means, i.e. using infrared, visible, or ultraviolet light with attenuation or whole or partial obturation of beams of light the beams of light being detected by photocells influencing the transmission properties of an optical fibre
  • G01D5/35303—Mechanical means for transferring the output of a sensing member; Means for converting the output of a sensing member to another variable where the form or nature of the sensing member does not constrain the means for converting; Transducers not specially adapted for a specific variable characterised by optical transfer means, i.e. using infrared, visible, or ultraviolet light with attenuation or whole or partial obturation of beams of light the beams of light being detected by photocells influencing the transmission properties of an optical fibre using a reference fibre, e.g. interferometric devices
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
  • G01C19/00—Gyroscopes; Turn-sensitive devices using vibrating masses; Turn-sensitive devices without moving masses; Measuring angular rate using gyroscopic effects
  • G01C19/58—Turn-sensitive devices without moving masses
  • G01C19/64—Gyrometers using the Sagnac effect, i.e. rotation-induced shifts between counter-rotating electromagnetic beams
  • G01C19/72—Gyrometers using the Sagnac effect, i.e. rotation-induced shifts between counter-rotating electromagnetic beams with counter-rotating light beams in a passive ring, e.g. fibre laser gyrometers
  • G01C19/721—Details, e.g. optical or electronical details
• • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
  • Y10—TECHNICAL SUBJECTS COVERED BY FORMER USPC
  • Y10T—TECHNICAL SUBJECTS COVERED BY FORMER US CLASSIFICATION
  • Y10T29/00—Metal working
  • Y10T29/49—Method of mechanical manufacture
  • Y10T29/49826—Assembling or joining

Definitions

• the present application relates generally to optical sensors, and more specifically to fiber optic sensors. Description of the Related Art
• an optical sensor comprises at least one optical coupler and an optical waveguide in optical communication with the at least one optical coupler.
• the optical waveguide is configured to receive a first optical signal from the at least one optical coupler.
• the first optical signal has a group velocity and a phase velocity while propagating through at least a portion of the optical waveguide, the group velocity less than the phase velocity.
• An interference between the first optical signal and a second optical signal is affected by perturbations to at least a portion of the optical sensor.
• an optical sensor comprises at least one optical coupler and an optical waveguide configured to receive a first optical signal and a second optical signal from the at least one optical coupler.
• Light propagates through at least a portion of the optical waveguide with a group velocity and a phase velocity, the group velocity less than the phase velocity.
• the optical waveguide is configured to move along a first direction while the first optical signal propagates through the optical waveguide in the first direction and the second optical signal propagates through the optical waveguide in a second direction generally opposite to the first direction.
• An interference between the first optical signal and the second optical signal is affected by perturbations to at least a portion of the optical sensor.
• an optical sensor comprises a fiber coupler configured to receive light from a light source and to transmit light to a light detector.
• the optical sensor further comprises a fiber coil optically coupled to the fiber coupler. At least a portion of the fiber coil comprises an optical fiber through which light propagates with a group velocity and a phase velocity, the group velocity less than the phase velocity.
• At least one of the fiber coil and the fiber coupler is configured to move relative to the other such that a first optical pathlength between a first portion of the fiber coil and the fiber coupler increases and a second optical pathlength between a second portion of the fiber coil and the fiber coupler decreases.
• a first portion of the light received by the fiber coupler from the light source propagates from the fiber coupler, through the fiber coil in a first direction, and back to the fiber coupler and a second portion of the light received by the fiber coupler from the light source propagates from the fiber coupler, through the fiber coil in a second direction opposite to the first direction, and back to the fiber coupler.
• the first portion of the light and the second portion of the light propagate to the light detector and interfere with one another, wherein the interference between the first portion of the light and the second portion of the light is indicative of the movement of the fiber coil relative to the fiber coupler.
• a method fabricates an optical sensor having a first sensitivity to changes of a first measurand and a second sensitivity to changes of a second measurand.
• the method comprises providing an optical waveguide through which light is configured to propagate with a group velocity and a phase velocity, the group velocity less than the phase velocity.
• a first enhancement of the first sensitivity is dependent on a group index of the optical waveguide and a second enhancement of the second sensitivity is dependent on the group index.
• the method further comprises selecting the group index such that the first enhancement is greater than the second enhancement.
• Figure 1 schematically illustrates an interferometric fluid velocity sensor.
• Figure 2 schematically illustrates an interferometric tangential velocity sensor.
• Figure 3 schematically illustrates an example optical sensor in accordance with certain embodiments described herein.
• FIG 4 schematically illustrates a conventional fiber optic gyroscope (FOG).
• FOG fiber optic gyroscope
• Figure 5 schematically illustrates a fiber optic gyroscope with stationary source and detector.
• Figure 6 schematically illustrates a fiber optic gyroscope with a stationary source, detector, and coupler.
• Figure 7A schematically illustrates an example fiber optic gyroscope in accordance with certain embodiments described herein.
• Figure 7B schematically illustrates a reciprocal configuration of the fiber optic gyroscope of Figure 7A in accordance with certain embodiments described herein.
• Figure 7C schematically illustrates another reciprocal configuration of the fiber optic gyroscope of Figure 7A utilizing a circulator in accordance with certain embodiments described herein.
• Figure 8 A schematically illustrates another example fiber optic gyroscope in accordance with certain embodiments described herein with a prism coupler and a rotating fiber coil.
• Figure 8B schematically illustrates the example fiber optic gyroscope of Figure 8A in a reciprocal configuration in accordance with certain embodiments described herein.
• Figure 8C schematically illustrates another reciprocal configuration of the fiber optic gyroscope of Figure 8A utilizing a circulator in accordance with certain embodiments described herein.
• Figure 9 schematically illustrates an example optical sensor having a Mach-Zehnder configuration in accordance with certain embodiments described herein.
• Figure 10 is a plot of the calculated normalized phase changes due to changing the temperature of a solid-core fiber with a mean refractive index of 1.45.
• Figure 11 is a plot of the calculated normalized phase changes due to changing the strain in the solid-core fiber of Figure 10.
• Figure 12 is a plot that compares the strain and thermal sensitivities of the solid-core fiber of Figure 10 as its group index is varied.
• Figure 13 is a plot of the ratio of the phase sensitivity to changes of strain and temperature for the solid-core fiber of Figure 10.
• the sensitivity of an optical fiber sensor is proportional to the group index of the optical fiber (or, equivalently, inversely proportional to the group velocity of light propagating through the optical fiber), which allows for greater sensitivity to be achieved when using slow light to probe the optical fiber sensor.
• group index of the optical fiber or, equivalently, inversely proportional to the group velocity of light propagating through the optical fiber
• sensitivity has its broadest reasonable interpretation, including but not limited to, a quantity proportional to the reciprocal of the minimum detectable signal.
• the slow light is generated by using one of the existing techniques referenced above, or any technique to be developed.
• the slow light is generated using a Bragg fiber (see, e.g., C. Lin, W. Zhang, Y. Huang, and J. Peng, "Zero dispersion slow light with low leakage loss in defect Bragg fiber " Appl. Phys. Lett., Vol. 90, 031109 (2007), incorporated in its entirety by reference herein) or by a photonic-bandgap fiber.
• the optical waveguide has a group index n g and a phase index n p
• the slow light has a group velocity v g and a phase velocity v p
• the group velocity v g is less than the phase velocity v p
• This condition can be expressed by a slow-down factor which is defined as the ratio v p lv g or as the ratio n s ln p and for slow light, the slow-down factor is greater than one ⁇ e.g., greater than 1.2, greater than 1.5, greater than 2, greater than 5, greater than 10, greater than 15, greater than 20).
• the group index n g of the material through which the slow light propagates is significantly greater than one (e.g., greater than 2, greater than 5, greater than 10, greater than 15, or greater than 20).
• the group velocity is less than 50% the speed of light in vacuum, hi certain embodiments, the group velocity is less than 20% the speed of light in vacuum, hi certain embodiments, the group velocity is less than 10% the speed of light in vacuum, hi certain such embodiments, the group velocity is between one-eleventh and one-tenth the speed of light in vacuum, hi certain embodiments, the group velocity is between 0.01 and 0.2 times the speed of light in vacuum.
• A is the area of the gyro coil.
• This result is independent of both the group and phase index of refraction of the fiber used to make the gyro. ⁇ See, e.g., HJ. Arditty and H.C. Lefevre, "Sagnac effect in fiber gyroscopes," Opt. Lett. , Vol. 6, No. 8, 401 (1981), incorporated in its entirety by reference herein).
• the sensitivity to rotation of a conventional FOG cannot be improved by utilizing slow light.
• V ph,l ⁇ 'v a' (l —r + - 1 ⁇ J ⁇ — ) (2) n( ⁇ L y n( ⁇ L )
• Equation (2) n g ( ⁇ ) is the group index of the material at the frequency of the light measured in the laboratory frequency, hi both Equation (1) and Equation (2), the ⁇ symbol is taken as + if the material and the light are moving in the same direction, and - if they are moving in opposite directions. Equations (1) and (2) are equivalent; the difference between them only comes from the reference frame in which the light frequency is measured. Equation (1) gives the phase velocity in the laboratory frame in terms of the light frequency measured in the material's reference frame. Equation (2) gives the phase velocity in the laboratory frame in terms of the light frequency measured in the laboratory reference frame. Both Equation (1) and Equation (2) express the concept that the phase velocity depends on the velocity of the moving object, hi other words, light can be described as being "dragged" by the moving material.
• the output signal depends on the relative phase of the two signals that are being interfered.
• this phase depends on the velocity of some object through which light is propagating.
• Using the Fresnel-Fizeau drag formula for phase velocity it is possible to find the time delays (and hence the phase delays) between the two signals being interfered in different interferometer configurations.
• FIG. 1 schematically illustrates an interferometric fluid velocity sensor 10 in which a fluid 12 (e.g., a liquid or gas) of index n flows in a closed path (e.g., ring) at constant velocity v.
• a fluid 12 e.g., a liquid or gas
• Light 14 from the light source S e.g., laser
• an optical coupler 16 e.g., a beamsplitter
• mirrors 18 e.g., by mirrors 18
• a portion of the light 14 e.g., a first signal
• a second portion of the light 14 e.g., a second signal
• the time delay between the two signals reaching the optical detector D e.g., photodiode
• P is the perimeter of the path followed by the light 14.
• the time delay depends on a ', which, for large values of the group index n g , is proportional to n g /n, the ratio of the group index to the phase index, as expressed in Equation (2).
• the sensitivity of interferometric fluid velocity sensors having the configuration of Figure 1 is proportional to At, and is proportional to the reciprocal of the velocity of the light traveling through it. Consequently, for interferometric fluid velocity sensors 10 which utilize slow light, the slower the light, the higher its sensitivity to the velocity of the fluid flowing through the closed path.
• Figure 2 schematically illustrates an interferometric tangential velocity sensor 30 having a disc 32 of radius R and index n rotating relative to a fixed laboratory frame at some angular frequency ⁇ which is inserted into a Sagnac interferometer used in its reciprocal configuration.
• the same analysis can be made for other kinds of interferometers, including, but not limited to, Mach-Zehnder and Michelson interferometers.
• Note that the physics of the interferometric tangential velocity sensor 30 schematically illustrated by Figure 2 is exactly the same as that of the interferometric fluid velocity sensor schematically illustrated by Figure 1, and this configuration was also predicted by Fizeau.
• Such as sensor can be made of all free-space components, or can incorporate optical fibers, in particular to replace the portions of light traveling between the source S and point A and between the detector D and point B.
• a Mach-Zehnder-type Sagnac interferometer having the general configuration of Figure 2 has been proposed and analyzed (see, M.S. Shahriar, G.S. Pati, R. Tripathi, V. Gopal, M. Messall, and K. Salit, "Ultrahigh enhancement in absolute and relative rotation sensing using fast and slow light " Phys. Rev. A, Vol. 75, 053807 (2007).
• FIG. 3 schematically illustrates an example optical sensor 40 in accordance with certain embodiments described herein.
• the optical sensor 40 utilizes slow light to measure the linear velocity of a material ⁇ e.g., an optical waveguide 42).
• the optical sensor 40 comprises at least one optical coupler 46 and an optical waveguide 42 in optical communication with the at least one optical coupler 46.
• the optical waveguide 42 is configured to receive a first optical signal from the at least one optical coupler 46.
• the first optical signal has a group velocity and a phase velocity while propagating through at least a portion of the optical waveguide 42.
• the group velocity is less than the phase velocity.
• An interference between the first optical signal and a second optical signal is affected by perturbations to at least a portion of the optical sensor 40.
• the at least one optical coupler 46 can comprise a beamsplitter, hi addition, the at least one optical coupler 46 can comprise a plurality of mirrors 18.
• the portion of the optical waveguide 42 comprises a Bragg fiber, a photonic-bandgap fiber, or a multilayer film stack inserted into a Sagnac interferometer operated in its reciprocal configuration, hi certain embodiments, the group velocity is less than 20% of the speed of light in vacuum, while in certain other embodiments, the group velocity is less than 10% of the speed of light in vacuum, hi certain embodiments, the portion of the optical waveguide 42 is solid, while in certain other embodiments, the portion of the optical waveguide 42 comprises a fluid (e.g., a hollow-core optical fiber with a gas or liquid within the core).
• the portion of the optical waveguide 42 is homogeneous, while in certain other embodiments, the portion of the optical waveguide 42 is inhomogeneous. hi certain embodiments, the portion of the optical waveguide 42 has a refractive index greater than 1.
• the perturbations to at least a portion of the optical sensor 40 comprise a movement of the optical waveguide 42 relative to another portion of the optical sensor 40 (e.g., to the at least one optical coupler 46).
• the movement comprises a translation of the optical waveguide 42 and the interference is indicative of a velocity of the optical waveguide 42.
• the optical waveguide 42 is configured to receive the first optical signal and the second optical signal from the at least one optical coupler 46.
• the optical waveguide 42 of certain embodiments is configured to move along a first direction while the first optical signal propagates through the optical waveguide 42 in the first direction and the second optical signal propagates through the optical waveguide 42 in a second direction generally opposite to the first direction.
• the optical sensor 40 of Figure 3 is different from the two sensors of Figures 1 and 2 discussed above, because the end points of the moving optical waveguide 42 in the optical sensor 40 of Figure 3 are not stationary in the laboratory frame. At least a portion of the optical waveguide 42 has an index n and length L and is moving at velocity v. A Doppler shift component must then be taken into account to calculate the time delay between the two signals counter-propagating through the sensor 40. A careful analysis of this time delay gives At « - a') - ll/ c 2 . hi the limit n g » n (slow light), this time delay is proportional to the ratio n g /n, indicating that the sensitivity of this optical sensor 40 is also enhanced by the use of slow light. Unlike the tangential velocity sensor 30 described above with regard to Figure 2, the physics of the optical sensor 40 schematically illustrated by Figure 3 is not equivalent to that of the configuration of Figure 1.
• the optical sensor 40 schematically illustrated by Figure 3 senses the linear velocity of the optical waveguide 42.
• the first optical signal traveling along the first optical path (e.g., clockwise through the interferometer of Figure 3) propagates through the optical waveguide 42 in a direction generally parallel to the linear velocity of the optical waveguide 42 and the second optical signal traveling along a second optical path (e.g., counterclockwise through the interferometer of Figure 3) propagates through the optical waveguide 42 in a direction generally opposite to the linear velocity of the optical waveguide 42.
• the linear movement of the optical waveguide 42 modifies the interference between the first optical signal and the second optical signal detected by the detector D.
• the optical sensor 40 has a sensitivity to the velocity of the optical waveguide 42 which is dependent on the group velocity (e.g., is inversely proportional to the group velocity).
• the optical sensor 40 can be used in any system in which velocity is to be measured, and in certain embodiments, the optical sensor 40 can be formed in a microelectromechanical system (MEMS) configuration.
• MEMS microelectromechanical system
• the FOG 50 comprises a fiber coil 52 (e.g., having a plurality of loops), a light source S, a detector D, and at least one optical coupler 54.
• the at least one optical coupler 54 comprises a first beam splitter or fiber coupler to couple the optical signals from the source S into the coil 52, and a second beam splitter or fiber coupler to tap the optical signals returning from the coil 52 to the detector D.
• the source S sends two counter-rotating signals into the coil 52, which, after traveling around the coil 52, are recombined at the detector D.
• the FOG 50 schematically illustrated by Figure 4
• everything inside the dashed box can rotate at the same rate ⁇ about the main symmetry axis of the coil 52, and everything else is stationary with respect to the fixed laboratory frame.
• the two counter- rotating signals accumulate different phase shifts via the nonreciprocal Sagnac effect, which leads to interference between the two optical signals at the detector D.
• the interference affects the detected power, which is indicative of (e.g., depends on) ⁇ .
• phase index of the light propagating in the coil 52 changes ⁇ e.g., increases
• two opposing effects take place.
• One effect is that the phase increases proportionally to the phase index.
• increases of the phase index results in increases of the differential phase change due to rotation between the two counter-propagating waves.
• the other effect is that the light traveling in the direction of the rotation gets dragged by the Fresnel-Fizeau drag effect and travels a little faster, while light traveling against the direction of the rotation is dragged with the opposite sign, so it travels a little slower.
• the differential phase change due to rotation between the two counter-propagating waves decreases.
• the FOG 50 of Figure 4 is sensitive to absolute rotation of the FOG 50, and it is used in commercial applications for inertial navigation ⁇ e.g., in aircraft). As described with regard to the examples below, in certain embodiments, gyroscope configurations slightly different from the one in Figure 4 are considered.
• different parts of the FOG can rotate relative to one another, unlike in a conventional FOG 50, in which typically the whole device rotates, hi these other configurations, the FOG has a sensitivity to relative rotation ⁇ e.g., rotation of one part of the device relative to another) Certain such embodiments are advantageously used for applications in which only extremely small rotations are applied to a portion of the FOG (unlike inertial navigation of an airplane or automobile, in which the FOG is routinely called to make full turns about at least one rotation axis).
• the sensitivity of a conventional FOG 50 is not changed by slow light, whereas the sensitivity of the optical velocity sensor 40 discussed above can be made proportional to the group velocity v g or the group index n g .
• a two- wave interferometer has a sensitivity which is affected by slow light when the frequencies of the two waves are different when measured in the material's frame of reference.
• the optical sensor of certain embodiments described herein has one or more optical pathlengths which change in response to the perturbations applied to the optical sensor.
• certain embodiments described herein exhibit a Doppler shift of frequencies between two optical signals.
• FIG. 5 schematically illustrates an FOG 60 having a coil 62 and at least one optical coupler 64.
• the source S and the detector D are fixed in an inertial reference frame, and the rest of the FOG 60 rotates at a rate ⁇ . As the rotation occurs, the pathlengths between the at least one optical coupler 64 and the source S and the detector D do not change (e.g., the optical waveguides are merely deflected).
• the FOG 60 behaves exactly like the conventional FOG 50 shown in Figure 4. There is no Doppler shift in the configuration of Figure 5, and the at least one optical coupler 64 serves as the effective light source for the FOG 60. This FOG 60 does not have a sensitivity which benefits from slow light.
• FIG. 6 schematically illustrates an FOG 70 having a coil 72 and at least one optical coupler 74.
• the at least one optical coupler 74 is moved outside the dotted box, indicating that the at least one optical coupler 74 is stationary as well as the source S and the detector D.
• the pathlengths between the at least one optical coupler 74 and the coil 72 do not change (e.g., the optical waveguides are merely deflected).
• the FOG 70 also behaves in the same way as the two FOGs 50, 60 of Figures 4 and 5.
• the light coming out of the at least one optical coupler 74 has the same frequency measured at either point A or point B, which means that this FOG 70 behaves just as if the at least one optical coupler 74 were co-rotating with the loop 72.
• the sensitivity of the FOG 70 is independent of the group velocity and the group index, and it does not benefit from the use of slow light.
• FIG. 7A schematically illustrates an example FOG 80 in accordance with certain embodiments described herein.
• the FOG 80 comprises an optical waveguide 82 (e.g., a fiber coil comprising a plurality of loops) and at least one optical coupler 84 (e.g., a 3- dB fiber coupler).
• the optical waveguide 82 is in optical communication with the at least one optical coupler 84.
• the optical waveguide 82 is configured to receive a first optical signal from the at least one optical coupler 84.
• the first optical signal has a group velocity and a phase velocity while propagating through at least a portion of the optical waveguide 82, with the group velocity less than the phase velocity. Interference between the first optical signal and a second optical signal is affected by perturbations to at least a portion of the FOG 80.
• the optical waveguide 82 is in a coiled configuration with a plurality of loops (e.g., 100 or more loops) which are generally parallel with one another. At least a portion of the optical waveguide 82 supports slow light propagation (e.g. , at least a portion of the optical waveguide 82 comprises a Bragg fiber or a photonic-bandgap fiber), and in certain embodiments, the optical waveguide 82 supports slow light propagation along its entire length.
• the FOG 80 further comprises a light source S and a light detector D.
• the source S, detector D, and the at least one optical coupler 84 of certain embodiments are stationary, and the optical waveguide 82 is configured to move relative to the stationary source S, detector D, and at least one optical coupler 84.
• the perturbations comprise a rotation of the optical waveguide 82 relative to another portion of the FOG 80 (e.g., the source S, the detector D, and the at least one optical coupler 84). In certain embodiments, the rotation is about an axis of symmetry of the coiled optical waveguide 82.
• the at least one optical coupler 84 is mechanically decoupled from the optical waveguide 82 such that the at least one optical coupler 84 and the optical waveguide 82 can be moved relative to one another.
• the optical waveguide 82 is configured to move along a first direction (e.g., rotated clockwise about a symmetry axis of the coiled optical waveguide 82), as schematically illustrated by Figure 7.
• the first optical signal from the at least one optical coupler 84 propagates through the optical waveguide 82 in the first direction (e.g., clockwise through the coiled optical waveguide 82) and the second optical signal from the at least one optical coupler 84 propagates through the optical waveguide 82 in a second direction generally opposite to the first direction (e.g., counterclockwise through the coiled optical waveguide 82).
• the at least one optical coupler 84 comprises a first port 85 and a second port 86
• the coiled optical waveguide 82 comprises a first end 87 and a second end 88.
• the first port 85 is optically coupled to the first end 87 and the second port 86 is optically coupled to the second end 88.
• the FOG 80 comprises a first gap between the first port 85 and the first end 87 such that optical signals traveling between the first port 85 and the first end 87 propagate in free space.
• the FOG 80 of certain such embodiments comprises a second gap between the second port 86 and the second end 88 such that optical signals traveling between the second port 86 and the second end 88 propagate in free space
• the FOG 80 comprises a first lengthwise stretchable optical waveguide (e.g., a waveguide comprising a polymer material) between the first port 85 and the first end 87, and a second lengthwise stretchable optical waveguide between the second port 86 and the second end 88.
• the FOG 80 can be used as a practical rotation sensor in applications where the applied rotation has a finite excursion, for example to detect flexing of large structures such as sea platforms or buildings, or to detect movement of mechanical parts, such as mirrors in a bulk-optic interferometer.
• a first optical pathlength between the first port 85 of the at least one optical coupler 84 and the first end 87 of the coiled optical waveguide 82 changes and a second optical pathlength between the second port 86 of the at least one optical coupler 84 and the second end 88 of the coiled optical waveguide 82 changes.
• the FOG 80 is responsive to changes of the first optical pathlength, the second optical pathlength, or both the first and second optical pathlengths.
• Figure 7B schematically illustrates a reciprocal configuration of the FOG 80 of Figure 7A utilizing at least one optical coupler comprising a first fiber coupler 84a and a second fiber coupler 84b.
• Figure 7C schematically illustrates another reciprocal configuration of the FOG 80 of Figure 7A utilizing at least one optical coupler 84 comprising a first fiber coupler 84a and a three-port circulator 84c having ports pi, p2, and p3.
• Other configurations of optical couplers are also compatible with various embodiments described herein.
• FIG. 8A schematically illustrates another example FOG 90 in accordance with certain embodiments described herein.
• the FOG 90 of Figure 8A comprises a coiled optical waveguide 92 (e.g., at least a portion of which comprising a Bragg fiber or a photonic-bandgap fiber) and at least one optical coupler 94 which is evanescently coupled to the optical waveguide 92 (e.g., a prism coupler), with the coiled optical waveguide 92 rotating relative to the at least one optical coupler 94.
• the FOG 90 is analogous to the optical sensor 10 depicted in Figure 1, with the flowing fluid 12 replaced by the rotating optical waveguide 92, and the fixed beam splitter 16 replaced with the at least one optical coupler 94 (e.g., prism coupler).
• the interferometric fluid velocity sensor 10 has a sensitivity which depends on the group index of the fluid, and the use of slow light provides enhancements of the sensitivity.
• the FOG 90 of Figure 8 A has a sensitivity which depends on the group index or group velocity of light in the optical waveguide 92, and the use of slow light provides enhancements of the sensitivity.
• Figure 8B schematically illustrates the FOG 90 in a reciprocal configuration in which the at least one optical coupler 94 comprises a first coupler 94a and a second coupler 94b.
• the light returning from the Sagnac loop is collected at the reciprocal output port, which is the port into which light is launched into the loop.
• This can be accomplished in a straightforward manner by placing a coupler ⁇ e.g., a fiber coupler) on the light input port, and collecting the return light at the fourth port of the coupler, as schematically illustrated in Figure 8B.
• Figure 8C schematically illustrates another reciprocal configuration of the FOG 90 of Figure 8A utilizing at least one optical coupler 94 comprising a first fiber coupler 94a and a three- port circulator 94c having ports pi, p2, and p3.
• Other configurations of optical couplers are also compatible with various embodiments described herein.
• the FOG 90 of Figures 8A-8C can have the same kind of applications as does the FOG 80 of Figures 7A-7C.
• the at least one optical coupler 94 rotates about an axis generally perpendicular to the optical waveguide 92 such that the at least one optical coupler 94 and the optical waveguide 92 move relative to one another.
• the FOG 90 is responsive to relative rotations between the at least one optical coupler 94 and the optical waveguide 92.
• an optical waveguide e.g., fiber
• AL ⁇ Lo. Neither of these effects depends on the group index or the group velocity, so while an optical sensor can be responsive to changes of the length of the waveguide, the sensitivity of the optical sensor to such changes is not enhanced by the use of slow light.
• a waveguide mode has an effective index n( ⁇ ).
• the transverse dimension of the waveguide is scaled uniformly (e.g., as occurs due to either a strain or a change in temperature) by a factor (1 + ⁇ )
• the effective index of the mode is scaled as well: it becomes n eff ( ⁇ (l + ⁇ )) . That is, the mode of the scaled waveguide has the same effective index at wavelength (1 + ⁇ ) ⁇ as the original waveguide had at wavelength ⁇ .
• This means that even if the signal frequency is constant, the effective (normalized) frequency of the signal is changed due to the change in the waveguide's transverse dimension. This causes the group index to appear in the effective index: An eff (n g - n eff ) ⁇ and hence
• FIG. 9 schematically illustrates an example optical sensor 100 having a Mach-Zehnder configuration in accordance with certain embodiments described herein.
• the optical sensor 100 comprises at least one optical coupler (e.g., a first optical coupler 102 and a second optical coupler 104) and an optical waveguide 106 (e.g., in a sensing arm 108 of the optical sensor 100) in optical communication with the at least one optical coupler.
• the optical waveguide 106 is configured to receive a first optical signal (e.g., a first portion of an optical signal received by the first optical coupler 102 from the source S) from the at least one optical coupler.
• the first optical signal has a group velocity and a phase velocity while propagating through at least a portion of the optical waveguide 106, with the group velocity less than the phase velocity.
• An interference between the first optical signal and a second optical signal is affected by perturbations (e.g., change of longitudinal strain, changes of temperature) applied to the optical waveguide 106.
• the second optical signal comprises a second portion of the optical signal received by the first optical coupler 102 from the source S.
• the second optical signal propagates through a conventional optical waveguide 110 (e.g., having a group velocity equal to the phase velocity) in a reference arm 112 of the optical sensor 100.
• the first optical signal and the second optical signal are received by the second optical coupler 104 and interference between the first and second optical signals is detected by the detector D.
• the sensitivity of the optical sensor 100 to the perturbations is inversely proportional to the group velocity.
• An optical fiber is in general composed of several materials, each with different mechanical and thermal properties.
• the core, the cladding, and the jacket all have different mechanical and thermal properties.
• the core, the lattice, the silica cladding, and the acrylate jacket have different properties.
• a Bragg fiber which is made of materials with dissimilar properties.
• the longitudinal component of the strain is slightly greater than that of a conventional fiber (having the same cladding thickness and material).
• the transverse component of the strain is a more complex function of temperature due to the more complex and heterogeneous nature of the fiber cross-section.
• this transverse component of the strain was not included in the modeling described herein due to its complexity. However, it was calculated for an air-core photonic-bandgap fiber (PBF) by Dangui et ah, cited above, and it is slightly weaker. A similar trend is expected towards a slight reduction in the case of an air-core Bragg fiber. In addition, in an air-core Bragg fiber, the thermo-optic term is much lower because the thermo-optic coefficient of air is much lower than that of a solid. This result is independent of the group velocity of the light.
• PPF photonic-bandgap fiber
• the application of a strain causes a change in the fiber index, which changes the effective mode index in the fiber.
• the effect of strain in a conventional single-mode solid-core fiber can be considered ⁇ see, e.g., G.B. Hocker, "Fiber-optic sensing of pressure and temperature," Appl. Opt., Vol. 18, No. 19, 1445 (1979), incorporated in its entirety by reference herein). While there are no known ways at present to induce slow light in a conventional fiber, this analysis is still informative to derive general trends.
• An eff ⁇ n g ln eff ) ⁇ tsn from above, the change in the effective index in a solid-core fiber can be calculated for various values of rieff and ng.
• FIG. 10 plots the normalized phase changes that result from changing the temperature of this fiber.
• the solid line is the phase change caused by the thermo-optic effect
• the dashed line is the phase change due to transverse expansion of the fiber
• the dotted line is the phase change from the longitudinal expansion of the fiber, hi accordance with the above derivations, both the thermo-optic and transverse expansion phase delays exhibit enhancement when n g is large.
• Figure 11 plots the normalized phase changes that result from changing the strain applied to the same fiber as used for Figure 10.
• the solid curve is the phase change caused by the elasto-optic effect
• the dashed curve is due to changes in transverse dimension of the fiber
• the dotted curve is the phase change from the longitudinal expansion of the fiber.
• the absolute value of each phase change is plotted, although they do not all have the same sign.
• the terms plotted in Figure 11 which are due to change in index and transverse dimension also exhibit enhancement with increasing n g when n g is large.
• Figure 12 is a plot that compares the strain and thermal sensitivities of the solid-core fiber as its group index is allowed to vary. Both the strain response (solid line) and the tempeature response (dashed line) show increasing sensitivity as the group index is increased.
• Figure 13 is a plot of the ratio of the phase sensitivities to strain and to temperature. As shown in Figure 13, the ratio of strain to thermal sensitivity is minimized for ng between about 10 and 11, and the ratio of the two sensitivities becomes constant as n g gets larger than this range (slower light), since the terms proportional to n g dominate.
• the group index is selected to provide a predetermined ratio of the strain sensitivity to the temperature sensitivity.
• Air-core fibers including air-core Bragg fibers, are expected to exhibit similar behavior (although the actual group index values will be different than those discussed above with regard to solid- core fibers) such that the group index can be selected to provide a predetermined ratio of the strain sensitivity to the temperature sensitivity.
• an optical sensor having a first sensitivity to changes of a first measurand ⁇ e.g., strain) and a second sensitivity to changes of a second measurand (e.g., temperature) is fabricated.
• the method comprises providing an optical waveguide through which light is configured to propagate with a group velocity and a phase velocity, the group velocity less than the phase velocity.
• a first enhancement of the first sensitivity and a second enhancement of the second sensitivity are both dependent on the group index of the optical waveguide.
• the method further comprises selecting the group index such that the first enhancement is greater than the second enhancement.
• an optical sensor using slow light to enhance the sensitivity to a measurand other than temperature advantageously corrects or otherwise reduces the effects of the increase in temperature sensitivity using one of the many existing techniques ⁇ e.g., maintaining a stable temperature of the optical sensor, particularly of the optical waveguide through which the slow light propagates) or techniques to be developed.
• the sensitivity to strain increases with the slowness of light in the same way as does the sensitivity to temperature.
• a very sensitive temperature sensor with a slow-light fiber can beneficially be made.
• the optical sensor of certain embodiments uses a solid-core fiber which has a group index between approximately 10 and 11, thereby increasing the sensitivity to temperature with comparatively reduced strain sensitivity.
• it is desirable to control the effects of strain since sensitivity to strain would also be enhanced, using one of the many existing techniques ⁇ e.g., mounting the optical sensor, particularly the portion of the optical sensor through which the slow light propagates, on a material having a low coefficient of thermal expansion so that induced changes of strain are reduced) or techniques to be developed.

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