Classifications

• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01H—MEASUREMENT OF MECHANICAL VIBRATIONS OR ULTRASONIC, SONIC OR INFRASONIC WAVES
  • G01H9/00—Measuring mechanical vibrations or ultrasonic, sonic or infrasonic waves by using radiation-sensitive means, e.g. optical means
  • G01H9/004—Measuring mechanical vibrations or ultrasonic, sonic or infrasonic waves by using radiation-sensitive means, e.g. optical means using fibre optic sensors
• • G—PHYSICS
  • G02—OPTICS
  • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
  • G02B6/00—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings
  • G02B6/24—Coupling light guides
  • G02B6/26—Optical coupling means
  • G02B6/262—Optical details of coupling light into, or out of, or between fibre ends, e.g. special fibre end shapes or associated optical elements
• • G—PHYSICS
  • G02—OPTICS
  • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
  • G02B6/00—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings
  • G02B6/24—Coupling light guides
  • G02B6/26—Optical coupling means
  • G02B6/32—Optical coupling means having lens focusing means positioned between opposed fibre ends
• • G—PHYSICS
  • G02—OPTICS
  • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
  • G02B6/00—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings
  • G02B6/10—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings of the optical waveguide type
  • G02B6/12—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings of the optical waveguide type of the integrated circuit kind
  • G02B2006/12133—Functions
  • G02B2006/12138—Sensor
• • 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

• This application relates generally to acoustic sensor systems, and more particularly to optical-fiber-compatible acoustic sensor systems.
• PCSs Photonic-crystal slabs
• a PCS exhibits guided resonance optical modes that are strongly confined within the PCS, but are coupled to incident radiation through a phase matching mechanism due to the periodically varying refractive index.
• These guided resonance modes are typically manifest in transmission or reflection spectra as sharp Fano lineshapes superimposed on a smoothly varying background. See, e.g., M. Kanskar et al., "Observation of leaky slab modes in an air-bridged semiconductor wavegiride with a two-dimensional photonic lattice," Appl. Pbys. Lett., vol. 70, page 1438 (1997); V.N.
• an acoustic sensor comprises a diaphragm comprising a reflective element.
• the sensor also comprises an optical fiber positioned relative to the reflective element such that light emitted from the optical fiber is reflected by the reflective element.
• a first end of the optical fiber and the reflective element forms an optical cavity therebetween.
• the sensor further comprises a structural element mechanically coupling the diaphragm and the optical fiber.
• the structural element of certain embodiments comprises a material having a coefficient of thermal expansion substantially similar to the coefficient of thermal expansion of the optical fiber.
• the structural element of certain embodiments comprises silica.
• the light reflected by the reflective element can propagate into the optical fiber.
• the first end of the optical fiber can comprise a second reflective element.
• the second reflective element and the reflective element can form a Fabry-Perot cavity therebetween.
• the optical fiber can comprise fused silica and the structural element can comprise fused silica.
• the reflective element can comprise a photonic-crystal structure.
• the diaphragm of some embodiments can comprise silica.
• the diaphragm of the acoustic sensor can have a thickness approximately equal to a distance between the first end of the optical fiber and the reflective element.
• the acoustic sensor can further comprise a compensating element comprising silica.
• the compensating element can be spaced from the diaphragm and positioned within the optical cavity.
• the diaphragm of certain embodiments can have a lateral dimension and a ratio of the lateral dimension to the optical fiber diameter can be in a range between 1.2 and 8.
• the diaphragm can have a movable portion having an area and a ratio of the area to a cross-sectional area of the optical fiber can be in a range between 1.4 and 64.
• the diaphragm can comprise one or more fluid conduits.
• One or more fluid conduits can be separate from the reflective element.
• the optical cavity can comprise a liquid.
• the acoustic sensor can further comprise at least one generally compressible and generally elastic element to increase sensitivity. At least one generally compressible and generally elastic element can be a gas bubble.
• an acoustic sensor comprises a reflective element.
• the sensor further comprises an optical fiber positioned relative to the reflective element such that light emitted from the optical fiber is reflected by the reflective element.
• the first end of the optical fiber and the reflective element form an optical cavity therebetween.
• the optical cavity comprises a medium having a refractive index change with temperature.
• an element within the optical cavity has a coefficient of thermal expansion and thickness that compensate the refractive index change with temperature.
• the medium can be water.
• the element within the optical cavity can comprise silica and can have a thickness approximately equal to a distance between the first end of the optical fiber and the reflective element.
• the element within the optical cavity can be a diaphragm mechanically coupled to the reflective element.
• the element within the optical cavity can also be mechanically coupled to the optical fiber.
• a method of fabricating an acoustic sensor comprises providing a diaphragm.
• the diaphragm comprises a reflective element.
• the method further comprises positioning an optical fiber relative to the reflective element such that light emits from the optical fiber and is reflected from the reflective element.
• Positioning the optical fiber relative to the reflective element comprises forming an optical cavity therebetween.
• the method further comprises mechanically coupling the diaphragm to the optical fiber with a structural element.
• the structural element comprises a material having a coefficient of thermal expansion similar to the coefficient of thermal expansion of the optical fiber.
• the structural element can comprise silica.
• providing a diaphragm comprising a reflective element can include providing a photonic-crystal structure as the reflective element.
• providing a photonic-crystal structure can comprise providing a photonic- crystal structure fabricated by photolithography.
• the method of fabricating an acoustic sensor can further comprise silicate bonding the diaphragm to the structural element.
• the method of fabricating an acoustic sensor can further comprise employing an element comprising silica with the optical cavity.
• the method can further comprise selecting a thickness for the element comprising silica approximately equal to a distance between the first end of the optical fiber and the diaphragm.
• the method of certain embodiments can comprise selecting a diaphragm diameter to increase mechanical compliance.
• the method can further comprise selecting a diaphragm cross-sectional area to increase mechanical compliance.
• the method can further comprise employing one or more fluid conduits separate from the reflective element.
• the method can further comprise employing at least one generally compressible and generally elastic element to increase sensitivity.
• At least one generally compressible and generally elastic element can be a gas bubble.
• FIGS 1A-1B schematically illustrate examples of acoustic sensors compatible with certain embodiments described herein.
• Figure 2 is a plot of a portion of the response of an example acoustic sensor as a function of wavelength for various temperatures.
• Figure 3 is an example plot of the calculated resonance wavelength change as a function of temperature for a Fabry-Perot sensor comprising silica compared to one comprising silicon.
• Figures 4A-4B schematically illustrate examples of acoustic sensors compatible with certain embodiments described herein.
• Figure 5 is a graph showing the variation of the temperature sensitivity of the optical path length with respect to different thicknesses of a fused silica diaphragm in accordance with certain embodiments described herein.
• Figure 6 shows the reflection spectrum calculated for an example photonic-crystal having a square pattern of holes with diameters of 800 nm and a period of 900 nm, fabricated on a silicon diaphragm of thickness 450 nm.
• Figure 7 shows the calculated change in reflectivity at 1550 nm as a function of temperature for an example sensor in accordance with certain embodiments described herein.
• Figure 8 illustrates the contribution to the resonance wavelength change as a function of temperature from various factors.
• Figure 9 schematically illustrates an example of an acoustic sensor with fluid conduits in accordance with certain embodiments described herein.
• Figure 10 shows the finesse of a fiber Fabry-Perot calculated for varying reflectivities and cavity lengths in accordance with certain embodiments described herein.
• FIGS 11A-11B schematically illustrate example focusing elements in accordance with certain embodiments described herein.
• Figure 12 schematically illustrates an example of an acoustic sensor compatible with certain embodiments described herein.
• Figure 13 A is an example response curve exhibiting cross-coupling for a first sensor in parallel with a second sensor.
• Figure 13B is an example response curve exhibiting cross-coupling for a second sensor in parallel with a first sensor.
• Figure 14A is an example response curve exhibiting a reduced or substantially eliminated cross-coupling for a first sensor in parallel with a second sensor in accordance with certain embodiments described herein.
• Figure 14B is an example response curve exhibiting a reduced or substantially eliminated cross-coupling for a second sensor in parallel with a first sensor in accordance with certain embodiments described herein.
• Figure 15 schematically illustrates an example photolithography fabrication process in accordance with certain embodiments described herein.
• Figure 16 schematically illustrates an example fabrication process for producing a backside pattern in accordance with certain embodiments described herein.
• Figures 17A-17C schematically illustrate example portions of three individual wafers and their patterns of holes to be used as building blocks of the silica structural element in accordance with certain embodiments described herein.
• Figure 18 schematically illustrates the wafers after they have been bonded together and attached to the photonic-crystal structure and the optical fiber to form the sensor head in accordance with certain embodiments described herein.
• Figure 19 schematically illustrates the forces due to phenyl benzoate in accordance with certain embodiments described herein.
• Figures 20A-20B schematically illustrate structures used in a method that reduces the arc current used to obtain a good bond between the two elements in accordance with certain embodiments described herein.
• Figure 21 is a flowchart of an example method of fabricating an acoustic sensor in accordance with certain embodiments described herein.
• Figure 22 schematically illustrates an example acoustic sensor fabricated and assembled in accordance with certain embodiments described herein.
• Figure 23A shows a scanning electron micrograph of a top view of a fabricated photonic-crystal mirror in accordance with certain embodiments described herein.
• Figure 23B shows a scanning electron micrograph of an angled view of a fabricated photonic-crystal mirror in accordance with certain embodiments described herein.
• Figure 23C is a photograph of a fabricated sensor in accordance with certain embodiments described herein.
• Figure 24 schematically illustrates an acoustic characterization setup to test example sensors.
• Figure 25 shows the measured coherence between a calibrated reference microphone and an example acoustic sensor.
• Figure 26 shows the measured frequency response of an example sensor.
• Figure 27 shows the measured noise (top curve), optoelectronic noise (middle curve), and the noise due to detection electronics (bottom curve) for an example sensor.
• Figure 28 shows the measured minimum detectable pressure (MDP) of an example sensor with the frequency response shown in Figure 26.
• Figure 29 shows the measured thermal stability of the resonance wavelengths for a silicon sensor (top curve) and an example silica sensor (bottom curve).
• Figure 30 shows an example optical acoustic sensor system for ocean acoustics in accordance with certain embodiments described herein.
• Figure 31 schematically illustrates an example fabrication process for producing a sensor system in accordance with certain embodiments described herein
• Figure 32 shows an optical profilometry measurement on an example diaphragm in accordance with certain embodiments described herein.
• Figure 33 shows a photograph of an example packaged sensor system in accordance with certain embodiments described herein.
• Figure 34 shows an example equivalent circuit formed by various lumped elements describing sensor system acoustics and the interfacing with optoelectronics in accordance with certain embodiments described herein.
• Figure 35 A shows an example calculated response curve of a first sensor as a function of frequency calculated with the lumped-element model.
• Figure 35B shows the calculated noise spectrum (solid line) transferred to an example diaphragm showing contributions from radiation resistance (dashed line), hole resistance (dotted line), and channel resistance (dash-dotted line).
• Figure 35C shows the calculated noise spectrum (solid line) showing contributions from the noise coupling from a second sensor (dashed line) and a third sensor (dotted line), and optoelectronic noise (dash-dotted line) in an example sensor system in accordance with certain embodiments described herein.
• Figure 36A shows the calculated minimum detectable pressure (MDP) as a function of frequency on an example diaphragm in accordance with certain embodiments with the minimum ambient noise in the sea shown for reference.
• Figure 36B shows the minimum detectable pressure as a function of frequency when two parallel sensors are non-operational.
• Figure 37A shows the calculated linearity as a function of diaphragm displacement, showing the normalized linearities of the diaphragm displacement (solid line), Fabry-Perot response (dashed line), and power coupled back into the optical fiber (dotted line).
• Figure 37B shows the total harmonic distortion (THD) as a function of pressure amplitude for a first sensor (solid line), a second sensor (dashed line), and a third sensor (dotted line) in a sensor system in accordance with certain embodiments described herein.
• Figure 38 show Reynolds number as a function of frequency for annular channels for a first sensor (solid line), a second sensor (dashed line), and a third sensor (dotted line) in a sensor system in accordance with certain embodiments described herein.
• Figure 39 schematically illustrates an example setup to characterize example sensor systems in accordance with certain embodiments described herein.
• Figure 40 shows the coherence between a reference sensor system and an example sensor system in accordance with certain embodiments described herein.
• Figure 41 A shows the measured frequency response for an example sensor system (solid line) and a theoretical fit (dashed line).
• Figure 4 IB shows the measured minimum detectable pressure (MDP) for an example sensor system (solid line) and a theoretic fit (dashed line).
• Figure 42 shows the measure power spectrum of an example sensor system in accordance with certain embodiments described herein.
• Optical acoustic sensing has various important applications. For example, for structural health monitoring, acoustic sensors can monitor the health of massive aerospace and wind-energy structures. Acoustic sensors can also provide mobile detection, tracking, and reporting of submarine contacts at long range in defense applications. As a further example, the production from wells and zones within a well in oil and gas applications can be monitored and controlled. In yet another example, acoustic sensing can measure the pressure of any bodily fluid, used in many medical applications, including life-support devices.
• Certain embodiments described herein include structures, elements, or features which advantageously address one or more issues arising from previously-disclosed acoustic sensors which utilize a mechanical diaphragm, a first reflective element, and a second reflective element (e.g., one or more photonic-crystal slabs) to produce a Fabry-Perot sensor with optical properties which are responsive to acoustic waves (e.g., acoustic waves incident on the sensor from the ambient environment or acoustic waves generated within the sensor).
• acoustic waves e.g., acoustic waves incident on the sensor from the ambient environment or acoustic waves generated within the sensor.
• Certain embodiments described herein can be practiced by appropriate modification of these previously-disclosed acoustic sensors. Examples of such previously-disclosed acoustic sensors are described in U.S. Pat. No.
• FIGS 1A-1B schematically illustrate example acoustic sensors 10 in accordance with certain embodiments described herein.
• the acoustic sensor 10 comprises a diaphragm 20 comprising a reflective element 22.
• the diaphragm 20 is deflectable by acoustic waves 400 and can comprise silicon, as is typically used in acoustic sensors.
• the diaphragm 20 can advantageously comprise silica as will be discussed in more detail below.
• the diaphragm 20 can comprise silicon nitride. Other materials are possible.
• the reflective element 22 of certain embodiments can be positioned (e.g., deposited) on the diaphragm 20.
• the reflective element 22 can be bonded directly onto the diaphragm 20 (e.g., through thermal bonding). In certain embodiments, the reflective element 22 is positioned (e.g., deposited or bonded) on a surface of the diaphragm 20 facing away from the optical fiber 30, as shown in Figures 1 A- IB. However, in other embodiments, the reflective element 22 can be positioned (e.g., deposited or bonded) on a surface of the diaphragm 20 facing towards the optical fiber 30. In still other embodiments, the reflective element 22 can be positioned (e.g., found) within the diaphragm 20. In various embodiments, the diaphragm 20 comprises a reflective element 22 comprising a photonic-crystal structure.
• the reflective element 22 comprises a metallic mirror structure (e.g., one or more layers of gold, silver, aluminum, chromium, or combinations thereof).
• chromium e.g., about 2 to about 5 nm thickness, can be used as an adhesion layer beneath the reflective element 22.
• the chromium can be relatively absorptive at certain wavelengths of interest.
• the reflective element 22 can further comprise a thin (e.g., between about 10 nanometers to about 100 nanometers thick) layer of silicon oxide to protect the metal surface against oxidation and scratching.
• the reflective element 22 comprises a dielectric mirror (e.g., multilayer structure comprising a plurality of transparent dielectric layers with selected thicknesses and refractive indices to provide a predetermined reflectivity).
• the dielectric mirror can have a thickness between 1 micron and 5 microns, and can have an area on the order of square inches (e.g., a film stretched across a frame).
• dielectric materials compatible with certain embodiments described herein include, but are not limited to, silicon dioxide, magnesium fluoride, silicon monoxide, and tantalum oxide.
• the reflective element 22 comprises at least a portion of a photonic crystal structure.
• the photonic crystal structure of certain embodiments comprises one or more photonic crystal slabs.
• a dielectric layer such as silicon or silicon nitride is deposited on the outer surface of the diaphragm 20, and is subsequently patterned with holes going through the dielectric layer.
• the acoustic sensor 10 further comprises an optical fiber 30 positioned relative to the reflective element 22 such that light emitted from the optical fiber 30 is reflected by the reflective element 22.
• the optical fiber 30 of certain embodiments is a single-mode fiber. Examples compatible with certain embodiments described herein include, but are not limited to, silica-based fiber, SMF-28® fiber available from Corning Incorporated of Corning, New York, cutoff shifted fiber, low-water-peak fiber, dispersion-shifted fiber, non-zero dispersion-shifted fiber, and non-standard microstructured fiber (e.g., photonic crystal fiber).
• the optical fiber 30 comprises a reflective element 32 (e.g., the first end 32 of the optical fiber 30), and the reflective element 22 and the reflective element 32 of the optical fiber 30 form an optical cavity 40 therebetween.
• the reflective element 32 of the optical fiber 30 and the reflective element 22 are spaced from one another in certain embodiments by a distance between 500 nanometers and 50 microns.
• sensors 10 with a smaller optical cavity 40 can have a more advantageous thermal stability.
• the optical cavity 40 comprises a gas (e.g., air), while in certain other embodiments, the cavity 40 comprises a liquid (e.g., water).
• the optical fiber 30 transmits light from a light source to irradiate at least a portion of the reflective element 22.
• light sources compatible with certain embodiments described herein include, but are not limited to, monochromatic sources (e.g., laser, laser diode), broadband sources (e.g., incandescent lamp, light-emitting diode), and tunable sources (e.g., tunable laser).
• the reflective element 32 of the optical fiber 30 comprises a metal layer at or on a first end of the optical fiber 30 which is partially reflective and partially transmissive to light emitted from the optical fiber 30.
• the metal layer comprises multiple sublayers of various materials, examples of which include, but are not limited to, chromium, gold, silver, aluminum, and combinations thereof.
• the metal layer further comprises a thin (e.g., between about 10 nanometers to about 100 nanometers thick) layer of silicon oxide to protect the metal surface against oxidation and scratching.
• the metal layer has a thickness in a range between 1 nanometer and 50 nanometers.
• the reflective element 32 of the optical fiber 30 comprises a dielectric mirror at or on the first end of the optical fiber 30 comprising a plurality of dielectric material layers.
• dielectric materials compatible with certain embodiments described herein include, but are not limited to, magnesium fluoride, zinc sulfide, silicon dioxide, titanium dioxide, and tantalum pentoxide.
• the reflective element 32 of the optical fiber 30 comprises a photonic crystal structure at or on the first end of the optical fiber 30. [0076] In embodiments where the reflective element 32 of the optical fiber 30 comprises a partially reflective end of the optical fiber 30, the end of the optical fiber 30 and the reflective element 22 of the diaphragm 20 define a Fabry-Perot optical cavity 40 therebetween.
• one or more factors can induce a frequency shift in the Fabry-Perot spectrum, and therefore an error in the measured acoustic pressure can occur.
• the temperature of the Fabry-Perot optical cavity 40 slowly increases, the material surrounding the Fabry-Perot optical cavity 40 can expand.
• the spacing of the Fabry-Perot optical cavity 40 can increase, and the reflection spectrum can slowly shift.
• this frequency shift can be indistinguishable from a slow change in acoustic pressure.
• the responsivity of certain embodiments of the acoustic sensor 10 to a given displacement of the reflective element 22 can also change.
• FIG. 2 plots a portion of the response (reflected power/incident power) of an example acoustic sensor 10 as a function of wavelength for various temperatures.
• the operating (or bias) point at the laser wavelength which is fixed
• the scale factor of the acoustic sensor 10 which is proportional to the slope of the curve, decreases, e.g., the calibration of the sensor response to an acoustic field decreases.
• the acoustic sensor 10 comprises a structural element 50 mechanically coupling the diaphragm 20 and the optical fiber 30 and surrounding the optical cavity 40, wherein the structural element 50 advantageously comprises a material having a similar coefficient of thermal expansion as the optical fiber 30.
• the structural element 50 can include a plurality of elements. Additionally, in certain embodiments as will be described more fully below, the structural element 50 can include one or more holes, fluid conduits, or channels 55.
• the acoustic sensor 10 is rendered substantially insensitive to variations in ambient temperature.
• the optical fiber 30 can be inserted within a capillary tube.
• the capillary tube can advantageously comprise a material having a similar coefficient of thermal expansion as the optical fiber 30.
• the material can be silica.
• the acoustic sensor 10 of certain embodiments further comprises a housing 60 substantially surrounding the diaphragm 20 comprising a reflective element 22, the structural element 50, the optical cavity 40, and the optical fiber 30.
• the housing 60 can comprise a plurality of elements, e.g., a protective membrane 61 and a backchamber housing 62.
• the protective membrane 61 can keep the reflective element 22 and the optical cavity 40 isolated from the environment, e.g., to keep contaminants away and to prevent corrosion.
• the protective membrane 61 can be configured to allow acoustic waves 400 to propagate across the membrane 61 to deflect the diaphragm 20 (e.g. the membrane 61 can comprise a flexible, polymeric material).
• the backchamber housing 62 can surround a backchamber or reservoir 65 that is in fluidic communication with the optical cavity 40. It can be mechanically coupled to both the structural element 50 and the optical fiber 30, as shown in Figure IB.
• the backchamber housing 62 comprises brass or aluminum.
• the backchamber housing 1 advantageously comprises a material with a similar coefficient of thermal expansion as the optical fiber 30 and/or structural element 50 for similar reasons discussed above.
• the backchamber housing 62 can comprise silica.
• Figure 3 is an example plot of the resonance wavelength change as a function of temperature for a Fabry-Perot sensor 10 with a sensor head comprising silica in accordance with certain embodiments described herein compared to one comprising silicon, using a probing wavelength of 1550 nm.
• the all-silica sensor 10 e.g., silica fiber 30, silica capillary tube, and silica structural element 50
• the all-silica sensor 10 offers a substantial enhancement in thermal stability as compared to the sensor comprising the silica fiber and the silicon sensor head.
• the effects of thermal expansion on the sensitivity of the acoustic sensor 10 are at least a factor of 10 smaller than other effects on the sensitivity of the acoustic sensor 10. Simulations show that with suitable design, the sensitivity of certain embodiments of the acoustic sensor 10 does not change by more than 10% for a temperature variation of greater than 100°C. Assuming that the Fabry-Perot cavity 40 is filled with air, for a Fabry-Perot cavity 40 with a 10- ⁇ mirror spacing and a finesse of 30, the temperature change that changes the sensitivity of the sensor 10 by 10% is 300°C.
• the temperature change is approximately inversely proportional to the finesse, so that, e.g., a sensor 10 having an air-filled Fabry-Perot cavity 40 with a mirror spacing of 10 ⁇ and a finesse of 300 can tolerate a maximum temperature change of around 30°C for a sensitivity variation of no more than 10%.
• the Fabry-Perot cavity 40 is filled with water.
• This water can be either the ambient water in which the sensor 10 or hydrophone head is immersed, or a separate reservoir of water isolated from the ambient water by an enclosure, such as the protective membrane 61.
• the refractive index of water varies with temperature, more so than does the refractive index of air, and its effect on the thermal sensitivity of the sensor 10 is about one order of magnitude larger than the effect of the thermal expansion of silica (the dn/dT coefficient of water is -11.8x10 ⁇ 6 /°C for optical wavelengths around 1550 nm).
• the maximum tolerable temperature change for a cavity filled with water is generally smaller by a factor of 15 than the maximum tolerable temperature change for a cavity filled with air.
• the temperature change which changes the sensitivity of the sensor 10 by 10% is only 20°C.
• This temperature change is approximately inversely proportional to the finesse, so that, e.g., a sensor 10 having a cavity 40 with a finesse of 300 can tolerate a maximum temperature change of only 2°C for a sensitivity variation of no more than 10%.
• FIG 4A schematically illustrates an example of an acoustic sensor 10 compatible with certain embodiments described herein.
• the acoustic sensor 10 comprises a reflective element 22.
• the acoustic sensor 10 further comprises an optical fiber 30 positioned relative to the reflective element 22 such that light emitted from the optical fiber 30 is reflected by the reflective element 22.
• the reflective element 32 of the optical fiber 30 and the reflective element 22 define an optical cavity 40 therebetween.
• the optical cavity 40 comprises a medium having a refractive index change with temperature.
• the acoustic sensor 20 further comprises a compensating element 25 positioned within the optical cavity 40 and having a coefficient of thermal expansion and thickness.
• the coefficient of thermal expansion and the thickness are selected such that the compensating element 25 compensates the refractive index change with temperature of the medium. In certain such embodiments, this compensation is sufficient for the optical sensor to have reduced thermal variation in performance as compared to an optical sensor without the compensating element.
• the compensating element 25 can comprise one or more pieces of material that are selected to provide a coefficient of thermal expansion and total thickness so that the sensor 10 has a reduced sensitivity to temperature variations.
• the compensating element 25 within the optical cavity 40 comprises of material spaced away from the diaphragm 20.
• Such a material can be part of the first end 32 of the optical fiber 30.
• the material can be attached to the reflective end of the optical fiber 30 before the optical fiber 30 is inserted into the sensor head.
• the compensating element 25 can comprise the portion of the optical fiber 30 between the reflective element 32 and the end of the optical fiber 30.
• At least a portion of the compensating element 25 can be formed by micro- fabrication such that it is positionable partway between the reflective element 32 of the optical fiber 30 and the reflective element 22.
• at least a portion of the compensating element 25 can be on the diaphragm 20 facing the optical fiber 30 (or can be mechanically coupled to another portion of the optical sensor 10 (e.g., the structural element 50).
• the diaphragm 20 can serve as the compensating element 25 within the optical cavity 40.
• the compensating element 25 within the optical cavity 40 has a thickness (labeled S in Figure 4B) substantially equal to the spacing between the fiber end 32 and the diaphragm 20 (labeled W in Figure 4B).
• the reflective element 22 can be a material coated or fabricated on the diaphragm 20. The spacing volume is filled with water, and light is reflected from the reflective element 22 on the side of the diaphragm 20 facing away from the optical fiber 30. As discussed above, the reflective element 22 can comprise layers of metals, dielectrics, or photonic-crystal structure formed, deposited, or bonded on the diaphragm 20.
• the refractive index of fused silica changes by approximately the same magnitude as for water, but in the opposite direction (the dn/dT coefficient of fused silica is about +12.8xlO "6 /°C for optical wavelengths around 1550 nm while dn/dT for water is about -12.8xl0 ⁇ 6 /°C for these optical wavelengths). Therefore, in certain such embodiments, when light propagates by approximately equal distances through water and silica, the temperature effect on the refractive index of water is effectively cancelled out by the temperature effect on the refractive index of silica.
• Figure 5 is a graph showing the variation of the temperature sensitivity of the optical path length (physical length multiplied by the refractive index) with respect to different thicknesses of the fused silica diaphragm 20.
• the absolute value of the temperature sensitivity of the optical path length the light travels in the cavity versus diaphragm thickness is significantly below the absolute value of the temperature sensitivity for a non-silica diaphragm (shown in Figure 5 as the dash-dot line) and is below a maximum practical temperature sensitivity (shown in Figure 5 as the dotted line) for the entire range of diaphragm thicknesses between about 6.15 ⁇ and 10 ⁇ .
• a minimum temperature sensitivity is observed for a diaphragm thickness of about 8.15 ⁇ , corresponding to a sensor 10 in which the refractive index variations and material expansions compensate each other, such that the sensor 10 is rendered substantially insensitive to temperature variations.
• a sensor 10 or hydrophone having a water-filled cavity and employing a silica diaphragm 20 is even less sensitive to temperature than is the sensor 10 upon having an air- filled cavity (shown in Figure 5 as the dashed line).
• the relationship between the temperature sensitivity dn dT of the optical path length with respect to different thicknesses for the compensating element can be determined for other materials for the compensating element and for other media for the optical cavity.
• the diaphragm thickness is selected to render a sensor with a water-filled cavity substantially insensitive to thermal effects.
• the diaphragm thickness is in a range between about 5 ⁇ and about 12 ⁇ , between about 7 ⁇ and about 10 ⁇ , or between about 8 ⁇ and about 9 ⁇ .
• the ratio of the thickness of the diaphragm 20 to the cavity size between the diaphragm 20 and the optical fiber 30 is in a range between about 0.5 and about 1.2, between about 0.7 and about 1, or between about 0.8 and about 0.9.
• the value of the diaphragm thickness of 8.15 ⁇ denoted in Figure 5 for the 10- ⁇ water-filled cavity is based on an assumption that the light is directly reflected from the reflective element 22 on the outer surface of the diaphragm 20. This assumption is accurate for certain embodiments when metal layers are used as the reflective element 22.
• dielectric mirrors or photonic crystals which can range in thickness approximately from 0.5 ⁇ to 5 ⁇
• light travels beyond the outer surface of the diaphragm 20 into the reflective element 22 before it is reflected. Therefore, to compensate for thermal expansion and refractive index changes with temperature of the reflective element 22, the diaphragm thickness can be adjusted to obtain the optimum temperature insensitivity for a given reflective element 22.
• the thermal response of the photonic-crystal mirror is another factor that affects the thermal stability of the sensor 10.
• the refractive index of the materials of the photonic-crystal mirror change, and so do its physical dimensions, (e.g., the thicknesses of the materials, and the periodicity and the diameter of the periodic structures, such as holes). Since all of these parameters affect the reflection spectrum of the photonic-crystal mirror, as these parameters change, the spectrum also changes.
• the finesse of the Fabry-Perot optical cavity 40 changes, and so does the slope of its reflection spectrum, in particular at the optimum bias point shown in Figure 2, and the scale factor of the sensor 10.
• FIG. 6 shows the reflection spectrum calculated for an example photonic-crystal structure having a square pattern of holes with diameters of 800 nm and a period of 900 nm, fabricated on a silicon diaphragm 20 of thickness 450 nm. These parameters were selected to obtain a high reflection at 1550 nm, a convenient target wavelength for this type of sensor.
• This photonic-crystal design provides ⁇ 99 % reflectivity at 1550 nm and a bandwidth of 48 nm for 99 % reflectivity.
• the spectrum of the same photonic-crystal structure can be simulated at different temperatures, taking into account the changes in refractive index, in hole radius, in period, and in thickness of the diaphragm.
• Figure 7 shows the calculated change in reflectivity at 1550 nm as a function temperature for a sensor 10 in accordance with certain embodiments described herein.
• the reflectivity remains within 0.02 % of its value at 20 °C.
• the bandwidth of the photonic- crystal structure for 99 % reflectivity, not shown in Figure 7, remains within 2.1 % over this temperature range.
• the reflectivity remains within 0.03 %, 0.04 %, 0.05 %, 0.08 %, or 0.10 % of its value at 20 °C over a range of temperature of about 20 °C to about 80 °C.
• the result of this small variation in the photonic-crystal reflectivity is that the resonance wavelength of the sensor remains within 0.02 nm over a 400 °C temperature range assuming a 90 % reflectivity for the reflecting element 32 at the end 32 of the optical fiber 30, which translates into a nominal finesse for the Fabry-Perot optical cavity of 96.
• thermally induced variations in the refractive index of the optical cavity 40 e.g., the intra-cavity medium.
• this medium is air, as in the case of a microphone for example, this contribution can be negligible.
• water as may be the case in a hydrophone, a change in this refractive index can induce an additional shift in the resonance of magnitude:
• the shift in resonance wavelength due to this effect stays within ⁇ 1 nm, thus provides enough stability over ⁇ 100 °C before the maximum responsivity drops by more than 10 % for a Fabry-Perot cavity of length 10 ⁇ . This shift can be acceptable for many applications.
• Figure 8 illustrates the contribution from each individual factor described above: thermal expansion of silica (TE), thermally induced variation of the intra-cavity medium refractive index (RIM), and thermally induced variation in the spectral response of the photonic-crystal mirror (PC).
• Figure 8 also shows the resonance wavelength change with temperature resulting from the sum of these three effects.
• the intra-cavity medium is taken to be water in this analysis, and because water has a negative thermo-optic coefficient, the contribution of the intra-cavity medium refractive index can be negative, e.g., its sign is opposite that of the other two contributions, hence it partially cancels them.
• a different choice of materials and/or design parameters could tailor the amount of cancellation and total contribution.
• the material for the medium of the optical cavity 40 can be advantageously selected for improved thermal stability.
• the thermal modulation of the refractive index of the medium of the optical cavity 40 also can contribute to the thermal stability of the sensor 10. For example, (2)
• na Si0i —— > ⁇ 3 ⁇ 4— -—
• L is the length of the optical cavity 40
• n is the refractive index of the cavity medium
• cisi0 2 is the thermal expansion coefficient of silica.
• this effect can be exploited for thermal stability.
• the effect of the thermal expansion of the silica structural element 40 and the refractive index modulation of the medium of the optical cavity 40 cancel each other if the right material is selected for the cavity medium.
• the medium for the optical cavity 40 can be selected for improved thermal stability.
• a thicker diaphragm 20 is generally mechanically less compliant than is a thinner diaphragm 20.
• one of the strongest damping effects that can limit the sensitivity of the sensor 10 is squeeze-film damping, which is due to the water forced out of the cavity 40 by the moving diaphragm 20, as is described more fully in U.S. Pat. No. 7,526,148, U.S. Pat. No. 7,630,589; U.S. Pat. No. 7,809,219, U.S. Pat. No. 7,881 ,565, and U.S. Pat. Appl. Publ. No. 201 1/0041616, each of which is incorporated in its entirety by reference herein.
• Certain embodiments described herein restore the compliance of the diaphragm 20 by increasing the diaphragm diameter (e.g., by approximately a factor of 5) or the diaphragm area (e.g., by approximately a factor of 25). Such a significant increase in the diaphragm diameter or area also reduces the squeeze-film damping significantly (e.g., by approximately a factor of 25), since the relative area of the end face of the optical fiber 30 to the area of the diaphragm 20 is reduced.
• the ratio of the diaphragm diameter to the end diameter of the optical fiber 30 is in a range between 1.2 and 8, in a range between 1.5 and 6, or in a range between 2 and 5.
• the ratio of the diaphragm area to the area of the end face of the optical fiber 30 is in a range between 1.4 and 64, in a range between 2.35 and 36, or in a range between 4 and 25.
• the diameter ratio is about 2.4 and the area ratio is about 5.76.
• the diameter ratio is about 4.8 and the area ratio is about 23, resulting in a reduction of the squeeze-film damping by about a factor of 23.
• the diaphragm diameter or area is limited by the desired resonance frequency of the diaphragm 20.
• the diaphragm diameter is less than 1 mm.
• the use of the diaphragm diameter in describing this feature is not intended to indicate that the diaphragm shape is limited to solely generally circular diaphragms.
• Other diaphragms having other shapes e.g., oval, square, octagon, or other polygonal or irregular shapes
• the diaphragm 20 has a lateral dimension and the compliance of the diaphragm 20 can be restored by increasing the diaphragm lateral dimension as described above.
• the compliance of the diaphragm 20 can be restored by increasing the cross sectional area of the diaphragm 20.
• the reflective element 22 (e.g., a reflective surface on the outside of the diaphragm 20) of certain embodiments can be a dielectric- or metal-based mirror, or a photonic-crystal reflector.
• a photonic- crystal mirror reflector can also serve as the mechanical diaphragm 20 comprising a reflective element 22.
• the holes extending through the diaphragm 20 in certain such embodiments can serve as pressure-equalization channels as well, to allow the hydrostatic pressures between the outside and inside of the sensor 10 to equalize.
• the mechanical compliance of the diaphragm 20, and the acoustic response of the sensor 10 at low frequencies can create challenges in designing the optimum sensor 10 for a given application.
• a set of one or more fluid conduits is formed (e.g., by etching or drilling) in the sensor 10 to allow fluid flow from one side of the diaphragm 20 to the other for pressure equalization across the diaphragm 20.
• one or more of the fluid conduits 55 can be through the diaphragm 20.
• the one or more fluid conduits 55 can be through a diaphragm 20 sufficiently thick to reduce the sensitivity to thermal effects as described above, or through a thicker diaphragm 20 that is mechanically less compliant as described above.
• one or more of the fluid conduits 55 are separate from the photonic-crystal structures of the diaphragm 20 (e.g., holes in a thick diaphragm 20 as described above) which affect the optical properties of the reflector or reflective element 22.
• one or more of the fluid conduits 55 are located in a portion of the diaphragm 20 which does not contribute to the optical properties of the Fabry-Perot cavity 40, e.g., separate from the reflective element 22.
• one or more of the fluid conduits 55 are separate from the diaphragm 20 (e.g., conduits through or along a portion of the structural element 50).
• the sensor 10 can include one or more fluid conduits 55 in both the diaphragm 20 and the structural element 50.
• the total cross-sectional area of the set of one or more fluid conduits is in a range between about 1 ⁇ 2 and about 50 ⁇ 2 .
• the total cross-sectional area of the one or more fluid conduits is sufficiently small such that, at the desired operational acoustic frequency range, the fluid (e.g., water) preferably moves through the one or more fluid conduits rather than through the photonic-crystal structures (e.g., holes).
• Certain embodiments described herein allow the optical and acoustic design constraints to be separately satisfied, thereby allowing better sensor optimization.
• one or more fluid conduits 55 which are separate from the photonic- crystal holes which provide the optical properties of the photonic-crystal reflective element 22
• other photonic-crystal reflector structures can be used which do not provide a fluid conduit for fluid flow across the diaphragm 20 (e.g., photonic-crystal structures with protrusions rather than holes, or photonic-crystal structures with holes that do not go through the full thickness of the diaphragm 20).
• This method of separating the optical, mechanical, and acoustical design is not specific to a thick diaphragm 20, and can also be employed for thinner diaphragms 20, whenever it is desired to decouple the mechanical and acoustical functions from the optical function of the photonic-crystals structures (e.g. holes).
• the thicker diaphragm 20 described above can result in an increase of the optical path length between the first end 32 of the optical fiber 30 and the reflective element 22, which can cause additional diffraction loss. Unless counteracted in some way, this additional diffraction loss can reduce the reflectivity, and hence the sensitivity of the sensor 10.
• Figure 10 shows the finesse of a fiber Fabry-Perot cavity 40 (e.g., as depicted in Figure 4B) as a function of reflectivity and for various cavity lengths in accordance with certain embodiments described herein.
• the finesse of the fiber Fabry-Perot cavity 40 which can be termed the "effective finesse," includes the effect of diffractive loss of energy which is not coupled back into the optical fiber 30.
• the curves of Figure 10 were calculated for a Fabry-Perot cavity 40 formed by an SMF-28 single-mode fiber 30 and a reflective element 22, and by varying both the cavity length 40 and the reflectivities of the reflective element 22.
• the solid line of Figure 10 corresponds to the calculated finesse as a function of reflectivity for a standard Fabry-Perot cavity between two planar and infinite reflective surfaces.
• the finesse is dominated by diffraction loss, and is therefore not affected much by the reflectivities of the reflective element 22 (see, e.g., the lines corresponding to cavity lengths of 8 ⁇ and 16 ⁇ ).
• the sensor 10 comprises a focusing element 70 (e.g., a lens or curved mirror) as part of the optical path of the Fabry-Perot cavity 40 in order to reduce diffraction loss.
• a focusing element 70 e.g., a lens or curved mirror
• Figures 11A-11B schematically illustrate two example focusing elements 70 in accordance with certain embodiments described herein.
• Figure 11A schematically illustrates a diaphragm 20 comprising a lens structure 70 (e.g., a curved surface fabricated as at least a part of the surface of the diaphragm 20 facing towards the optical fiber 30).
• Figure 1 IB schematically illustrates a diaphragm 20 comprising a curved reflective surface or layer 70 (e.g., a curved mirror fabricated as at least a part of the surface of the diaphragm 20 facing away from the optical fiber 30).
• the curvatures of either the lens structure or the reflective surface of layer 70 can be chosen so that the mode-field diameter of the light beam reflected back to the fiber's end face is matched to the mode-field diameter of the fiber mode, such that the diffraction loss can be substantially reduced or eliminated.
• the radius of curvature of either the lens structure or the reflective surface of layer 70 is in a range between about 0.1 mm and about 0.6 mm.
• the focusing element 70 (e.g., the lens and/or curved mirror) of certain embodiments is a part of the diaphragm 20.
• the focusing element 70 is separate from the diaphragm 20 but is still part of the optical path of the Fabry-Perot cavity 40.
• the focusing element 70 can comprise a separate slab or structure spaced away from the diaphragm 20 (e.g., a lens structure between the diaphragm 20 and the optical fiber 30 or a structure positioned on the optical fiber 30).
• Other configurations are also compatible with certain embodiments described herein.
• FIG 12 schematically illustrates an example of an acoustic sensor system 100 having a plurality of sensors compatible with certain embodiments described herein. Scanning electron micrographs of an example backside wafer, diaphragm 20, and frontside wafer are shown beneath the schematic.
• the structural element 50 (comprising the backside wafer and the frontside wafer) is fabricated with silicon, and the reflective element 22 of the diaphragm 20 comprises photonic-crystal mirrors positioned to form optical cavities with the two single-mode optical fibers 30.
• channels 90 e.g., diaphragm-sized channels, can be fabricated around the fibers to allow water to flow out of the optical cavity 40 and to allow the diaphragm 20 to move.
• the diaphragm-sized channels 90 are between about 0.1mm and about 0.4mm in diameter, between about 0.15mm and about 0.35mm in diameter, or between about 0.2mm and about 0.3mm in diameter.
• the diaphragm-size channels 90 define the diameters of the diaphragms 20 and provide a connection around the optical fibers 30 to expanded channels 92.
• the expanded channels 92 can further lead to a backchamber channel 95.
• the expanded channels 92 are larger than the diaphragm-sized channels 90 to reduce flow resistance within the expanded channels 92.
• the backchamber channel 95 can be a large hole at the center of the structural element 50. In certain embodiments, the backchamber channel 95 is between about 1mm and 2mm in diameter, e.g., about 1.5mm in diameter.
• two or more sensors 101, 102 that are responsive to different acoustic signal levels can be used in parallel with one another to improve the dynamic range of the sensor system 100.
• the plurality of parallel sensors 101, 102 are placed close to each other, so that they are exposed to approximately the same acoustic signal.
• the first sensor 101 can be used to measure weak acoustic signals
• the second sensor 102 can be used to measure stronger signals. In this way, the total dynamic range of sensor system 100 with the two combined sensors 101, 102 is larger than the dynamic range of either sensor 101 or 102 alone.
• At least one sensor of the plurality of sensors can measure stronger signals, but has a reduced sensitivity, as compared to the other sensors (e.g., the first sensor 101) of the plurality of sensors.
• the sensitivity of at least one sensor is reduced by various methods, techniques, or modifications.
• the finesse of the Fabry-Perot cavity 40 of the at least one sensor e.g., the second sensor 102
• Such modifications of the Fabry-Perot cavity 40 cause a higher diffraction loss and thereby reduce the finesse of the Fabry-Perot cavity 40.
• the mechanical compliance of the diaphragm 20 in the at least one sensor can be reduced as compared to the other sensors (e.g., the first sensor 101).
• a thicker diaphragm 20, and/or a diaphragm 20 with a smaller diameter, and/or a diaphragm 20 made of a less compliant material can be used to reduce the mechanical compliance of the diaphragm 20.
• At least one sensor can utilize an optical detection scheme different than that of a Fabry-Perot cavity 40.
• at least one sensor can comprise a bare fiber 30 (e.g., a fiber 30 without any reflective element 32 on its end), such that there is no significant reflection from its end face (since silica-water interface reflection is less than 0.3%).
• the motion of the diaphragm 20 in certain such embodiments only affects the amount of light coupled back into the optical fiber 30, since the coupling is dependent on the spacing between the diaphragm 20 and the fiber end.
• the coupled signal consequently, can be used in the same way the Fabry-Perot signal is used to measure the acoustic signal.
• a reservoir referred to as the backchamber 65
• the backchamber 65 comprises a volume of water (e.g., a few cubic millimeters in size) that is in fluidic communication with the optical cavity 40.
• FIGS. 13A and 13B are plots of the example responses of a first sensor
• the first sensor 101 has a 0.5- ⁇ - ⁇ 1 ⁇ diaphragm 20 with a diameter of 200 ⁇ , and the resonance of the first sensor 101 is at 18 kHz
• the second sensor 102 has a diaphragm 20 with the same thickness as the first sensor 101, but with a 180 ⁇ m-diameter and a resonance at 21 kHz
• the backchamber 65 is a cylindrical volume with a radius of 3 mm and a length of 5 mm, and it has a Helmholtz resonance of 82 kHz.
• the two sensors 101, 102 couple to each other, and introduce additional resonant features.
• the arrow of Figure 13 A points to a resonance feature in the response of the first sensor 101 due to coupling from the signal of the second sensor 102
• the arrow of Figure 13B points to a resonance feature in the response of the second sensor 102 due to coupling from the signal of the first sensor 101.
• This cross-coupling can be detrimental, in certain embodiments, to the sensor performance, since it complicates the response and couples noise between sensors 101, 102, so that the noise floor for each sensor 101, 102 is increased.
• Certain embodiments described herein advantageously eliminate cross- coupling between the two or more parallel sensors 101, 102.
• the Helmholtz resonance of the backchamber 65 and the sensor resonances are tailored so that they are substantially equal in frequency with one another.
• the impedance of the backchamber 65 is zero such that the two parallel sensors 101, 102 are acoustically grounded, hence uncoupled.
• Certain such embodiments advantageously eliminate or reduce cross-coupling between the two or more sensors 101, 102, as illustrated in Figures 14A and 14B.
• the backchamber length is increased to 23 mm, such that its Helmholtz resonance becomes 18 kHz. In this way, the sensor resonances are very close to the backchamber Helmholtz resonance, and cross-coupling between the first sensor 101 and the second sensor
• the Helmholtz resonance of the backchamber 65 and the sensor resonance are less than 1%, less than 2%, less than 3%, less than 5%, less than 8%, or less than 10% from each other. While the response curves of Figures 14A and 14B are plotted for the case when there is a first sensor 101 and a second sensor 102 in parallel, the curves substantially match the curve for an individual sensor, with no other sensor parallel to it. Thus, optimizing the Helmholtz resonance in certain embodiments can be an effective way to reduce or completely eliminate cross-coupling. Air bubbles to increase sensitivity
• a sensor 10 For a sensor 10 generally assembled in air, when it is immersed into water, water will gradually fill the sensor 10, which can provide insensitivity to hydrostatic pressure. Sometimes, however, some amount of air may remain inside the sensor 10 and one or more gas or air bubbles (ranging in size between about 0.1 mm and about 2 mm diameter) can be trapped inside the sensor 10. It is possible to generally avoid such gas or air bubbles by putting a surfactant into the water, such as a standard dish soap detergent, so that the surface tension of water is reduced, and water can flow easily into the sensor 10. In certain embodiments, however, it is beneficial to keep the one or more gas or air bubbles inside the sensor 10, or to introduce one or more gas or air bubbles deliberately into the sensor 10. In certain embodiments, the one or more gas or air bubbles advantageously generally increase the sensitivity of the sensor 10, while reducing its frequency bandwidth.
• the presence of a small air bubble in the backchamber 65 has a negligible effect on the acoustic mass.
• the stiffness of the backchamber 65 can be dominated by the compressibility of the air bubble.
• the overall stiffness of the diaphragm 20 and backchamber 65 system can therefore be reduced in certain embodiments, which decreases the resonance frequency.
• the reduction in resonance frequency in certain embodiments is not strongly dependent on the size of the air bubble (as long as it is larger than approximately 100 ⁇ ), since the mass is generally dominated by water, and the compressibility is generally dominated by air.
• the senor 10 can advantageously measure pressures as low as 3.5 ⁇ 8/ ⁇ 1/2 in a frequency range of 100Hz to 10kHz. This enhanced minimum detectable pressure can be provided by the increased compressibility in the backchamber 65 caused by the trapped air. In certain embodiments, the sensor 10 can advantageously measure pressures less than 10 ⁇ 112 , less than 9 ⁇ / ⁇ . ⁇ ⁇ 2 , less than 8 ⁇ ⁇ 1 , less than 7 ⁇ / ⁇ , less than 6 ⁇ / ⁇ , less than 5 ⁇ ⁇ , less than 4 ⁇ 3/ ⁇ 1 2 , or less than 3 ⁇ 3/ ⁇ 1/2 .
• the one or more gas or air bubbles may be used where sensitivity is more significant for the application of the sensor 10, and bandwidth can be sacrificed.
• the one or more gas or air bubbles serve as a generally compressible (e.g., more compressible than water) and generally elastic element within the sensor 10 which substantially dominates the compressibility of the contents of the sensor 10.
• the fabrication process of the acoustic sensor 10 involves silicon microfabrication techniques.
• Figure 15 schematically illustrates an example fabrication process in accordance with certain embodiments described herein. Other techniques are possible.
• a silicon-on-insulator (SOI) wafer includes a silicon substrate 510, a buried oxide layer 520 having a thickness of approximately 1 ⁇ , and a silicon device layer 530 having a thickness of approximately 450 nm.
• a low temperature oxide (LTO) layer 540 is deposited on the SOI waiter, as shown in (a) of Figure 15. Then, the wafer is coated with photoresist 550 and exposed using photolithography, e.g. using a photolithography mask 560, as shown in (b) of Figure 15.
• LTO low temperature oxide
• the LTO layer 540 is then etched with plasma etch to form the structure shown in (c) of Figure 15.
• This patterned LTO layer 540 is used as a hard mask to etch the silicon layer 530 underneath, as shown in (d) of Figure 15.
• the back side is patterned to release the photonic-crystal structure of the silicon device layer 530.
• FIG. 16 schematically illustrates an example fabrication process for producing a backside pattern in accordance with certain embodiments described herein.
• a low temperature silicon oxide (LTO) layer 540 is deposited on the silicon substrate 510 (e.g., the silicon substrate 510 resulting from the process described above in conjunction with Figure 15).
• a LTO layer 540 can be deposited on each of both sides of the silicon substrate.
• one or more nitride layers e.g., S13N4 not shown
• S13N4 can be deposited on each of the LTO layers 540. These nitride layers can help compensate for residual stresses in the silicon layer 530.
• Si 3 N 4 is deposited under tensile stress, which can compensate for the compressive stress due to the silica (Si0 2 ) films.
• the LTO layer 540 on the surface of the silicon substrate 510 opposite to the silicon device layer 530 is patterned using reactive ion etching as shown in (b) of Figure 16. At least a portion of the silicon substrate 510 on the backside is removed (e.g., using tetramethylammonium hydroxide (TMAH) wet etch), as shown in (c) of Figure 16.
• TMAH tetramethylammonium hydroxide
• the body of the sensor 10, e.g. the structural element 50 can be fabricated of a plurality of elements.
• the structural element 50 can be fabricated by bonding together several wafer portions (e.g., portions of 4"-diameter fused silica wafers), each of which has a different pattern of holes, e.g., pressure equalization channels as discussed above.
• Figures 17A-17C schematically illustrate example portions of three individual wafers 50a, 50b, 50c and their patterns of holes to be used as building blocks of the silica structural element 50 in accordance with certain embodiments described herein.
• Figures 17A-17C are generally circular, other shapes of holes (e.g., square, rectangular, triangular, polygonal, oval, or irregular) may also be used.
• the diameters of the example holes are 0.3 mm, 2 mm, and 0.2 mm for 50a, 50b, and 50c of Figures 17A-17C, respectively.
• the diameters of the holes can be tailored to other diameters.
• Figure 18 schematically illustrates example locations of the wafers 50a, 50b, 50c of Figures 17A-17C being bonded together and attached to the photonic-crystal structure of the diaphragm 20 and the optical fiber 30 to form the sensor head in accordance with certain embodiments described herein.
• the photonic-crystal structure serves as the reflective element 22 of the diaphragm 20.
• the wafer thicknesses in certain embodiments are 0.5 mm. In other embodiments, the wafer thicknesses can be between about 0.3 mm and 0.7 mm, or between about 0.4 mm and 0.6 mm. Both sides of each wafer (e.g., 50a, 50b, 50c of Figures 17A-17C) can be polished for bonding purposes.
• a two-dimensional array of circular holes can be etched through each wafer with the pattern or array comprising a plurality of cells with each cell corresponding to one sensor head.
• Figures 17A-17C only show one cell of this pattern for the three wafers 50a, 50b, 50c with the one cell utilized to form one sensor head.
• the hole closest to the diaphragm 20 defines the dimension over which the diaphragm 20 of the acoustic sensor 10 will be allowed to flex, which affects the acoustic sensitivity of the final device (e.g., the larger the diaphragm 20, the more sensitive the sensor 10).
• the second and third layers e.g., shown in Figure 17B and Figure 17C of certain embodiments define the channels for the water flow from the diaphragm 20 to the backchamber 65 shown in Figure 18 (e.g., in the case of a hydrophone).
• silica wafers produced at Valley Design of Santa Cruz, California and patterned by Mindrum Precision of Rancho Cucamonga, California can be utilized.
• the silicon-on-insulator (SOI) wafer is bonded to the silica wafers using a technique called silicate bonding (hydroxide-catalysis bonding as described in the Laser Interferometer Gravitational-Wave Observatory (LIGO) project).
• silicate bonding hydroxide catalyzes the silica surface by hydration and dehydration. Because the surfaces are desired to be in close contact to bond, a flatness of 1/10 or better is used on the surfaces in certain embodiments.
• hydrophilic surfaces with a high density of Si-OH groups are utilized for a successful bonding.
• the procedure applied to achieve the bonding in certain embodiments includes rinsing the substrates under de-ionized (DI) water to wash off any particles, and wiping the surface with methanol to dry.
• DI de-ionized
• approximately 5 ml from a sodium silicate solution are drawn with a pipette, and DI water is transferred to the sodium silicate solution to obtain approximately 25 ml (1:4) of bonding solution.
• Approximately 1.0 ml of this bonding solution is extracted using a fresh pipette, and dispensed onto the glass. Then, the two surfaces to be bonded are brought together into contact with pressure.
• this process is utilized to bond the SOI wafers having the diaphragms to the silica wafers, each of which are again bonded to another silica wafer using the same silicate bonding technique.
• two silica wafers e.g., 50b shown in Figure 17B and 50c shown in Figure 17C
• another silica wafer e.g., 50a shown in Figure 17A
• the SOI wafer is bonded to wafer 50a.
• the alignments utilized during this example process to center the corresponding holes can be performed under a microscope. This stack comprising four 4" wafers, and the 2D array of sensors can be diced into individual cells to obtain the individual sensors. Bonding can be done using silicate bonding, or thermal bonding, as examples.
• the sensor 10 is further assembled.
• the sensor 10 assembly process of certain embodiments comprises holding the sensor head fixed with a vacuum chuck and moving an optical fiber 30 with a reflective element 32 (e.g., at the tip of the optical fiber 30) in close proximity to the diaphragm 20. During this process, the reflection spectrum can be monitored, with the cavity length 40 inferred from a classic measurement of the Fabry-Perot cavity free spectral range. Once the correct cavity length 40 is achieved, the optical fiber 30 can be bonded to the structural element 50.
• the fabrication process can be used to bond entire wafers together, then to dice into individual structural elements 50, as described above.
• the wafers can be diced first, then bonded into individual structural elements 50 one at a time.
• the optical fiber 30 can be mounted after dicing the wafers. In other embodiments, the optical fiber 30 can be mounted before dicing the wafers.
• the method used to bond the optical fiber 30 to the structural element 50 advantageously provides a Fabry-Perot cavity 40 with a reproducible cavity length, e.g., a resonance wavelength that substantially does not change during the bonding process, during the curing process if the bonding requires curing, and over time after the device assembly is completed.
• a reproducible cavity length e.g., a resonance wavelength that substantially does not change during the bonding process, during the curing process if the bonding requires curing, and over time after the device assembly is completed.
• it also advantageously yields a bond that substantially does not produce a change in the cavity length 40 as temperature varies. This goal can be met using a number of techniques, e.g., phenyl benzoate, arc splicing, or C0 2 -laser fusion.
• two through holes 85 of diameters 0.75 mm are drilled symmetrically on the sides of a silica capillary tube 80 of internal diameter close to that of the optical fiber 30 (for example, a diameter of 127 ⁇ for a standard fiber, which typically have a diameter of 125 ⁇ ).
• the outside diameter of the capillary tube 80 is not critical; a value of 1.8 mm can be used.
• the holes 85 provide channels for the bonding material to reach and hold the optical fiber 30 inside the capillary tube 80.
• Phenyl benzoate (Ci 3 Hio0 2 ), which is a powder at room temperature, is a bonding material which is compatible with certain embodiments described herein.
• the optical fiber 30 of certain embodiments is inserted into the capillary tube 80 to form a Fabry-Perot cavity 40 with the reflective element 20 of the diaphragm 20.
• the optical spectrum of the sensor 10 is monitored with an optical spectrum analyzer while the fiber end is brought in close proximity to the diaphragm 20 by a high- accuracy mechanical positioner. Once the correct cavity length is achieved, phenyl benzoate is applied through the holes 85, then heated above the melting point of phenyl benzoate (phenyl benzoate melts at 68°C-70°C).
• the molten phenyl benzoate flows into the holes 85, the heat source is removed, and the phenyl benzoate cools down and crystallizes as it solidifies and bonds the optical fiber 30 to the capillary tube 80.
• the output spectrum can be reexamined in certain embodiments. If a deviation is observed in the Fabry-Perot cavity length from the target value due to the bonding process, the phenyl benzoate can be reheated, at which point the optical fiber 30 is free to move, the cavity length is adjusted, and the spacing is measured again. The process can be repeated a few times until the desired cavity length is achieved.
• One further advantage of this example method is that because the side holes 85 are symmetrically located, the bonding material exerts equal forces on the optical fiber 30 (see Figure 19), which would otherwise result in a shift in the cavity length.
• an electric arc (for example from a commercial fiber splicer) is used to attach the optical fiber 30 to the silica capillary tube 80.
• Figures 20A-20B schematically illustrate structures used in a method that reduces the arc current used to obtain a good bond between the two elements in accordance with certain embodiments described herein.
• the capillary tube 80 of certain such embodiments is tapered at one end 81.
• the optical fiber 30 is inserted in the capillary tube 80, and the whole assembly is placed in a conventional arc splicer. With suitable choice of the arc current and arc duration, the optical fiber 30 is fused to the silica capillary tube 80.
• a similar goal can be met using a C0 2 laser.
• the untapered, large area side 82 of the silica capillary tube 80 is bonded to the side of the silica structural element 50 where the diaphragm 20 does not exist (e.g., side 82 shown in Figure 20A is bonded to side 51 of the structural element 50 shown in Figure 20B, which is not to scale).
• this bond can be achieved by silicate bonding, which works successfully for silica surface bonding purposes as described previously.
• FIG. 21 is a flowchart of an example method 1000 of fabricating an acoustic sensor 10 in accordance with certain embodiments described herein.
• the method 1000 comprises providing a diaphragm 20 comprising a reflective element 22, as shown in operational block 1010 of Figure 21.
• the method 1000 also comprises positioning an optical fiber 30 relative to the reflective element 22 such that light emits from the optical fiber 30 and is reflected from the reflective element 22, as shown in operational block 1020.
• Positioning the optical fiber 30 relative to the reflective element 22 comprises forming an optical cavity 40 therebetween.
• the method 1000 further comprises, as shown in operational block 1030, mechanically coupling the diaphragm 20 to the optical fiber 30 with a structural element 50.
• the structural element 50 comprises silica.
• providing a diaphragm 20 comprising a reflective element 22, as shown in operational block 1010 comprises providing a photonic-crystal structure as the reflective element 22.
• Providing a photonic-crystal structure can comprise providing a photonic-crystal structure fabricated by photolithography.
• the method 1000 further comprises silicate bonding the diaphragm 20 to the structural element 50.
• the method 1000 further comprises employing an element 25 comprising silica within the optical cavity 40.
• the method 1000 can further comprise selecting a thickness for the element 25 comprising silica approximately equal to a distance between the first end 32 of the optical fiber 30 and the diaphragm 20.
• the method 1000 can further comprise selecting a diaphragm diameter to increase mechanical compliance and/or selecting a diaphragm cross- sectional area to increase mechanical compliance.
• the method 1000 can also include employing one or more fluid conduits 55 separate from the reflective element 22 positioned on the diaphragm 20.
• the method 1000 can also include employing at least one generally compressible and generally elastic element within the optical cavity 40 to increase sensitivity.
• FIG. 22 schematically illustrates an example acoustic sensor 10 fabricated and assembled in accordance with certain embodiments described herein.
• the sensor 10 comprises a deflectable diaphragm 20 comprising a 450 nm thick single-crystal silicon photonic-crystal structure placed in close proximity (approximately 25 ⁇ ) to the stationary tip 32 of a single-mode fiber 30 coated with 15 nm of gold serving as the reflective element 32 of the optical fiber 30.
• the photonic-crystal structure is a square 300 ⁇ on each side.
• the photonic-crystal structure has a square lattice of 800 nm diameter holes on a 900 nm pitch, e.g., a minimum wall thickness on the order of 100 nm.
• the sensor 10 was fabricated using the photolithography and silicate bonding methods described herein.
• Figure 23A shows a scanning electron micrograph of a top view of the fabricated photonic- crystal structure of the diaphragm 20.
• Figure 23B shows a scanning electron micrograph of an angle view of the fabricated photonic-crystal structure of the diaphragm 20. Shown in Figure 23C, the fabricated sensor 10 is 5x5x5 mm in dimension. Further miniaturization is possible.
• the example fiber acoustic sensor 10 was tested in an acoustically isolated enclosure using a conventional calibrated microphone as a reference.
• a schematic of the acoustic characterization setup is shown in Figure 24.
• the sensor 10 was interrogated with a 15-kHz linewidth, low-noise, 1550-nm laser diode.
• the laser light was coupled into the sensor 10 via an optical circulator, and the light reflected by the sensor 10 was detected with a PIN photodiode.
• the electrical outputs of the calibrated reference microphone and the acoustic sensor 10 were connected to a dynamic signal analyzer (DSA), which measured the frequency response and noise spectrum of the two sensors, and the coherence between them.
• DSA dynamic signal analyzer
• Coherence is a measure of the degree of linear correlation between two signals. When two signals are uncorrelated, such as if one is dominated by noise, the coherence value is zero. In the case of complete correlation, the coherence value is one.
• the electrical signal from the reference microphone was used as a feedback signal on the DSA to adjust the output of the acoustic source such that a constant pressure of 1 Pa was incident on the sensors at all frequencies. The measurements were conducted up to an acoustic frequency of 30 kHz, which is the frequency band that the calibrated reference microphone is specified and measured to have a flat frequency response.
• Figure 25 shows that there is a strong coherence ( ⁇ 1) between the two sensor outputs for frequencies higher than -700 Hz, which establishes that the data in this frequency band is accurate.
• the low coherence at lower frequency might be because one or both of the sensors has a signal-to-noise lower than unity.
• Figure 26 shows the measured frequency response of the example fiber acoustic sensor 10, which is the ratio of the power spectrum of the acoustic fiber sensor 10 (in volts V) and the power spectrum of the reference microphone (in Pascals Pa).
• This sensor 10 has a measured finesse of -6.
• the other small resonances above -700 Hz are mainly due to residual resonances in the acoustic chamber.
• Figure 27 plots three example noise curves, measured on a different example sensor 10 with the same apparatus as Fig. 24 but in the absence of acoustic signal.
• noise can be measured between about 10 "4 and about 10 "7 V/Hz 1/2 .
• the top curve is the noise of the sensor 10.
• the middle curve is the noise measured when replacing the acoustic fiber sensor 10 with a reflector. The lowest curve was measured when the laser was off. It represents the noise due to the detection electronics (photodetector plus DSA).
• the middle curve represents the optoelectronic noise: it includes the detection electronics and the laser noise.
• the sensor 10 noise (top curve) is a little larger than the optoelectronic noise; this increase can be assigned to thermo-mechanical noise of the sensor 10, as well as conversion of laser phase noise into intensity noise.
• Figure 28 shows the minimum detectable pressure (MDP) of the sensor 10 with the frequency response shown in Figure 26. This spectrum was obtained by dividing the noise spectrum of this sensor 10 by its frequency response. The data below -700 Hz is again not accurate because of the low coherence of the measurement. From ⁇ 700 Hz to 8.6 kHz, the MDP is in the range of -180 to -27 ⁇ 3 ⁇ / ⁇ . Above 8.6 kHz the MDP improves as the frequency approaches the device's main mechanical resonances, and becomes as low as about 5.6 ⁇ 3 ⁇ / ⁇ at 12.5 kHz.
• MDP minimum detectable pressure
• the average MDP over the frequency band of 1 kHz to 30 kHz is about 33 This result demonstrates that certain embodiments as described herein are capable of providing the sensitivity and bandwidth performance desired for implementation in, e.g., Navy acoustic systems.
• these MDP values are limited in part by the optoelectronic noise, and they can be further reduced with straightforward improvements in the detection electronics.
• the acoustic noise of the laboratory environment can also be responsible for some degradation in the MDP observed during measurements.
• the measured value is higher mostly because of the silicate-bonding material.
• this result constitutes a major step towards highly stable acoustic sensors, and it is more than adequate for larger-scale sensor networks.
• Figure 30 is an example optical acoustic sensor system 200 for ocean acoustics. See also O. Kilic, M. Digonnet, G. Kino, and O. Solgaard, "Photonic-crystal- diaphragm-based fiber-tip hydrophone optimized for ocean acoustics " Proc. of SPEE, vol. 7004, 700405 (2008).
• the sensor system 200 comprises a face 210 of the sensor head.
• the face 210 of the sensor head can comprise a reflective element 22 of a diaphragm 20 and a structural element 50 in accordance with certain embodiments described above.
• the sensor system 200 in this embodiment can comprise a plurality 230 of optical fibers 30, each having a reflective element 32 on the end of the optical fiber 30.
• the sensor 200 can further comprise a backchamber housing 260.
• a cross-section of the sensor system 200 is similar to the sensor system 100 shown in Figure 12.
• the reflective element 20 can comprise a photonic- crystal reflective element 22 micro-machined on a silicon structural element 50.
• the plurality 230 of optical fibers 30 can comprise four SMF-28 fibers, each one transmitting and returning a different optical signal. In other embodiments, more than four optical fibers 30 can be used.
• three of the four optical fibers 30 can lead to the photonic-crystal reflective elements 22 of the diaphragm 20 placed at the face of the sensor head.
• the photonic-crystal structures are reflective elements 22 with high reflectivity (>95%).
• each optical fiber 30 can be coated with a reflective element 32, so that when placed in close proximity (-20 ⁇ ) with the photonic-crystal reflective elements 22, they each form a Fabry-Perot optical cavity 40.
• a reflective element 32 By deforming the compliant diaphragm 20, an incident acoustic signal 400 can modulate the spacings of the optical cavities 40, giving rise to a change in the power of the laser light reflected back into the optical fibers 30.
• the three sensors of the sensor system 200 shown in Figure 30 can be localized in a region of about 2.5-mm diameter which is approximately an order of magnitude smaller than one of the shortest acoustic wavelengths of interest (15 mm at 100 kHz), so they can be exposed to approximately the same acoustic amplitude. In other embodiments, the sensor system 200 can be localized in a region of about 2mm to about 3mm in diameter.
• the three diaphragms 20 can have different diameters (e.g., 150 ⁇ , 212 ⁇ , and 300 ⁇ ) and hence different compliances (relative compliances are, e.g., xl, x4, and xl6, respectively).
• the diaphragms 20 can have diameters between about 100 ⁇ and about 400 ⁇ , between about 150 ⁇ and about 350 ⁇ , or between about 200 ⁇ and about 300 ⁇ .
• each of the three sensors can address a different range of pressures to increase the dynamic range of the sensor 200 head over that of a single sensor. Calculations show that this range can span pressures as low as the ocean's ambient thermal noise ( ⁇ 10 ⁇ 3/ ⁇ 1 2 ) all the way up to 160 dB larger signals.
• the fourth fiber can be connected to a reference reflective element for calibration purposes in sensor-array applications.
• the sensor system 200 can comprise diaphragm-sized channels 90, expanded channels 92, and a backchamber channel 95.
• the sensor system 200 can be fabricated using silicon micro-fabrication techniques, for example, as shown in Figure 31.
• the fabrication can include the following steps: (a)-(c) etching the diaphragm-sized channels 90 and expanded channels 92, (d) bonding the backside wafer, (d) defining the photonic-crystal reflective elements 22, and (e) etching the backchamber channels 95 and fiber alignment channels 97.
• a 2 ⁇ m-thick low-temperature silicon oxide (LTO) layer 610 is deposited using low-pressure chemical- vapor deposition (LPCVD) on both sides of a 400 ⁇ m-thick silicon wafer 620.
• the wafer 620 can be between about 300 ⁇ m-thick and about 700 ⁇ m-thick, between about 350 ⁇ m-thick and about 650- ⁇ - ⁇ , or between about 400 ⁇ m-thick and about 600 ⁇ m-thick.
• LTO instead of thermally grown silicon-oxide, has a low stress, which can be advantageous in later fabrication steps.
• the LTO layer 610 on the backside is subsequently patterned using a wet oxide etch (buffered hydrofluoric acid). This step defines the shapes of the expanded channels 92.
• the backside Before etching the expanded channels 92 into the wafer 620, the backside is covered with a thick (>10 ⁇ ) photoresist (not shown) and is patterned with shapes defining the diaphragm-size channels 90 as shown in (b) of Figure 31. This step also determines the diameters of each of the three diaphragms 20.
• the next step involves etching the backside using deep-reactive ion-etching (DRIE). The etch can be timed so that the diaphragm-size channels 90 are only etched partially into the wafer 620.
• DRIE deep-reactive ion-etching
• the LTO layer 610 on the backside is stripped off using a timed hydrofluoric-acid etch, while protecting the front side of the wafer 620 with photoresist.
• a second 400 ⁇ -thick silicon wafer 620 is bonded to the backside of the first wafer 620 at 1000 °C.
• the second wafer 620 can be between about 300 ⁇ m-thick and about 700 ⁇ m-thick, between about 350 ⁇ m-thick and about 650- ⁇ -thick, or between about 400 ⁇ m-thick and about 600 ⁇ m-thick.
• the diaphragm layer 630 comprising of a 450-nm polysilicon layer sandwiched between two 25-nm silicon nitride layers.
• the total diaphragm can be between about 400 ⁇ m-thick and about 700 ⁇ m-thick, or between about 450 ⁇ m-thick and about 650 ⁇ m-thick.
• the thin nitride layers can serve to compensate for the residual stress in the polysilicon layer. See, e.g., S. Kim, S. Hadzialic, A. Sudbo, and O.
• Figure 32 shows an optical profilometry measurement on a mid-sized diaphragm (e.g., 212 ⁇ diameter) comprising of a 450-nm polysilicon layer sandwiched between two 25-nm silicon nitride layers, without any oxide underneath.
• the measurement indicates that the diaphragm 20 is elevated from the surface of the wafer 620 by a relatively small amount of about 300 nm.
• the top region is flat within about 10 nm in a 130- ⁇ diameter central region.
• the diaphragm layer 630 is deposited, it is patterned with a photonic- crystal mirror pattern.
• a relatively thin (e.g., between about 100 nm and about 200 nm, here, about 150 nm) LTO layer 610 is deposited to serve as an etch mask (not shown).
• a polymethylmethacrylate (PMMA) resist layer is spun on the LTO layer 610 and is patterned with e-beam lithography. Other method of patterning are possible, e.g., photolithography.
• the holes of the photonic-crystal reflective elements 22 are then etched into the LTO layer 610 using magnetically-enhanced reactive-ion etching (MERIE), and then into the diaphragm layer 630 through subsequent MERE etches.
• MIE magnetically-enhanced reactive-ion etching
• the various channels are etched into the silicon wafer 620 anisotropically through a series of alternating passivation and isotropic-etch steps, which can create scalloping on the sidewalls with a mean depth of -0.25 ⁇ (or between about 0.15 ⁇ and about 0.35 ⁇ or between about 0.2 ⁇ and about 0.3 ⁇ ).
• a plasma conformally deposits a layer of a PTFE-like fluorocarbon polymer. This polymer protects the sidewalls from etching, and remains there after the etch is completed.
• the hydrophobic nature of this passivation film combined with the scalloping geometry of the sidewalls, makes the wetting of the DRIE etched channels substantially low.
• the sidewall polymers can be removed, in some embodiments completely removed, after the DRIE steps.
• Employing an asher that etches organics away with an oxygen plasma, followed by a hot Piranha wet etch (9:1 sulfuric acid:hydrogen peroxide) is sufficient in certain embodiments for stripping off the sidewall polymers in the wafers 620.
• the reflective elements 32 on each of the optical fibers 30 within the plurality 230 of fibers 30 can be deposited using e-beam evaporation on cleaved SMF-28 fibers.
• the reflective elements 22 in the example embodiment comprised of a 4-nm chrome adhesion layer, followed by a 20-nm gold reflection layer, and finally a 15-nm magnesium fluoride protection layer.
• the chrome layer can be between about 2-nni and about 5-nm thick.
• the gold reflection layer can be between about 15-nm and about 25- nm or between about 18-nm and about 22-nm thick.
• the protection layer can be between about 10-nm and about 20-nm or between about 18-nm and about 22-nm thick. Other dimensions are possible. Gold is advantageous because of its low absorption and superior reflective properties at wavelengths around 1550 nm, the operation wavelength of the laser to address the sensor system 200.
• the characteristic sensor system dimensions are substantially smaller than the acoustic wavelengths of interest. In other embodiments, the sensor system dimensions can be between about 1.5 mm and about 2 mm. Therefore, it is possible to approximate spatially distributed elements with a single lumped elment to model the noise of the sensor system 200 and thermal-mechanical noise. See, e.g., T. B. Gabrielson, "Mechanical thermal noise in micromachined acoustic and vibration sensors " IEEE Trans. Electron Devices, vol. 40, pages 903-909 (1993). In this lumped model, the distributed potential and kinetic energies in the sensor system 200 are described through a single acoustic compliance C and acoustic mass M , respectively. Likewise, the dissipation in the sensor system 200 is modeled with a single acoustic resistance ⁇ .
• the incident acoustic signal is represented by a pressure source (P !n ).
• the acoustic signal can travel to the optical cavity 40 through two pathways, either as a volume flow through the holes of the photonic-crystal reflective elements 22 (the path M hole - R hole ), or through a motion of the compliant diaphragm 20.
• the signal Once the signal reaches the optical cavity 40, it is transmitted through the diaphragm-sized channel 90 around the optical fiber 30 leading to the backchamber 65.
• the small volume of the optical cavity 40 makes its acoustic compliance low, which means that the water is not compressed between the optical fiber 30 and the diaphragm 20 but is forced to flow into the backchamber 65.
• this equivalent-circuit model can be used to calculate the fraction of incident pressure that drops across the diaphragm compliance to obtain the sensor response.
• the amount of noise transferred to the diaphragm compliance from dissipative elements can be calculated using this equivalent-circuit model to obtain the thermal-mechanical noise limitation of the sensor system 200.
• ⁇ is the residual stress
• D is the flexural rigidity, defined as ⁇ ⁇ 12 ⁇ ⁇ ⁇ v with E being Young's modulus, and ⁇ Poisson's ratio.
• Equation (5) can be solved analytically to obtain expressions for the resonance frequencies and mode profiles.
• the bending profile for a diaphragm 20 with low residual stress e.g., a 2 ho «D
• u(r,t) u 0 e Jwt (t- r 2 /a 2 ) 2 ( 6 )
• c m a 4 /64D is the mechanical compliance (the inverse of stiffness) of the diaphragm 20.
• the mechanical resonances of the diaphragm 20 can be disregarded, since the impedance of water dominates the diaphragm mechanics. Therefore, Eq.
• Equation (5) models a solid diaphragm, hence does not account for the effects of the holes of the photonic-crystal reflective element 22 on the diaphragm's mechanical properties.
• the perforations make the elasticity of the diaphragm 20 highly anisotropic, which complicates the mechanical modeling. Nonetheless, it is possible to approximate the structure as a homogenous diaphragm by using modified elastic constants.
• the effective elastic constants of the photonic-crystal reflective element 22 are found by equating the strain energy of a perforated diaphragm to the one of an equivalent solid diaphragm.
• a perforated plate can be modeled as a solid isotropic plate with modified elastic constants.
• the effective elastic constants are found by equating the strain energy of the two plates, yielding the following material constants: (9)
• Eqs. (8) and (9) together to calculate the effective Young's modulus E', and the effective Poisson's ratio ⁇ '.
• Eq. (9) yields the effective flexural rigidity D'
• ⁇ ⁇ 0-50 is the fill factor, defined as the ratio of the open area to the total area of the photonic-crystal reflective element 22.
• the composite diaphragm is assumed equivalent to a uniform diaphragm with an effective flexural rigidity D" satisfying approximately v u aa v — u v .
• a single density p" is employed.
• D effective flexural rigidity
• p 0.70/J
• the acoustic mass of the diaphragm 20 is determined by calculating the kinetic energy (U k ) of the diaphragm 20, then equating it to an equivalent system including of a lumped mass (M dia ) with a single speed (it ), defined as ⁇ - I ° iir)2mdr corresponding to the volumetric flow rate.
• U k kinetic energy
• M dia lumped mass
• ⁇ - I ° iir2mdr corresponding to the volumetric flow rate.
• the compliance of the diaphragm 20 is of particular importance, because it determines the displacement of the diaphragm 20 as a function of pressure. Since the optical part of the sensor 10 only senses the diaphragm displacement, the main purpose of the lumped model is to calculate the pressure (P dja ) and noise across this particular compliance. Radiation Impedance of the Diaphragm
• the ambient fluid plays an important role in the overall mechanics of the sensor 10, and necessitates modeling of other acoustic masses and compliances that have a significant effect on the sensor dynamics.
• the presence of the fluid also creates dissipation, causing thermal-mechanical noise, which also utilizes modeling the loss through an acoustic resistance.
• thermal-mechanical noise which also utilizes modeling the loss through an acoustic resistance.
• the effective acoustic mass of the diaphragm 20 in water is more than one order of magnitude larger than the acoustic mass in vacuum. This is because the fluid moves with the diaphragm 20 when it oscillates. Therefore, a mass term can be included to account for the moving fluid, referred to as the radiation mass (M rad ).
• the oscillating diaphragm 20 also radiates part of its energy into the fluid, creating a channel of dissipation. To account for this radiative loss, an acoustic radiation resistance (R rad ) can be included.
• the radiation mass and resistance can be calculated by approximating the diaphragm as a rigid piston mounted in an infinite baffle, yielding:
• an infinite baffle approximation is too simplistic, considering that the sensor-head size is sub-wavelength over most of the frequency range of interest. Since the sensor desirably has a self noise that can be limited by radiation loss above 30 kHz, where the ocean noise is dominated by the Brownian motion of water molecules, the accurate modeling of the radiation loss can be significant in certain embodiments.
• a finite closed baffle may be a better description of the structure in certain embodiments. Modeling a finite baffle can be rather challenging, but the results can be summarized as follows: At low frequencies, the sensor acts like a piston at the end of an infinite tube, such that the radiation loss is approximately half of the value for an infinite baffle.
• the sensor 10 is mounted on a larger structure.
• the theoretical treatment based on the size, shape, and rigidity of such actual baffle structures can be too complicated. Nonetheless, based on the fact that these baffles are usually larger than the wavelengths above 30 kHz ( ⁇ 5 cm), the infinite baffle model in Eqs. (14) and (15) can be assumed sufficient in the modeling of certain embodiments of the sensor 10. If a more elaborate baffle model were to be used, the thermal noise contribution to the ambient sea noise can be adjusted to reflect the minimum noise level such a sensor-baffle structure is exposed to.
• an effective thickness 8 hok can be employed. This modified thickness can be used to make corrections for the effect of the hole end, when the hole radius a hole and the thickness h are comparable. See, e.g., D. Homentcovschi and R. N. Miles, "Viscous damping of perforated planar micromechanical structures," Sensors and Actuators A, vol. 119, pages 544-552 (2005).
• the radiation resistance of the holes can be insignificant compared to the flow resistance and is not included in the modeling.
• the acoustic mass of the hole can also be considered, and taken as: ( 18)
• an effective thickness n can be defined. Since the holes in certain embodiments provide parallel channels, the overall hole impedance can be reduced by a factor equal to the hole number.
• a bc and L are the radius and length of the backchamber 65, respectively. See, e.g., L. L. Beranek, Acoustics (American Institute of Physics, New York, 1986); and M. Rossi, Acoustics and Electroacoustics (Artech House, Inc., 1988).
• the cavity compliance can be ignored in the calculations because its reactance is very large in the frequency range of interest, due to the small cavity volume.
• the relatively large volume of the backchamber 65 includes its acoustic mass: See, e.g., id. In certain embodiments, the reactance of this mass is small for low frequencies but can dominate the backchamber impedance above the Helmholtz frequency of 27 kHz.
• the optical fiber 30 and the diaphragm-size channel 90 through which it passes defines an annular opening that connects the optical cavity 40 to the backchamber 65.
• the resistance and acoustic mass of these annular channels can be included in the modeling of the sensor 10. Calculations yield expressions similar to Eqs. (17) and (18):
• ⁇ is the length of the annular channel.
• R chan ⁇ r f R ( £ ) > Whete f R ( £ ) ⁇
• the surface of the optical fiber 30 can be considered perfectly smooth, as mentioned earlier the silicon sidewalls etched with DRIE can have a scalloping structure with a mean height of -0.25 ⁇ .
• Such a rough surface can increase the flow resistance, which can be modeled through an increase in the viscosity of water or a decrease in the channel diameter.
• the response of a first sensor (e.g., 300- ⁇ - diameter diaphragm) over the frequency range of 1 Hz-100 kHz calculated with the lumped- element model is shown in Figure 35 A.
• the structural parameters of the first sensor design are summarized in Table I.
• Table I Structural dimensions of an example sensor within the sensor system
• the shared backchamber 65 allows cross coupling between sensors within the sensor system 200.
• This frequency corresponds to the resonance of the second sensor (e.g., 212 ⁇ diameter), and hence the resonant feature is a result of cross coupling from this sensor.
• the third sensor e.g., 150 ⁇ diameter
• Such resonances can be reduced by similar methods used in loudspeaker enclosures: e.g., by lining the backchamber 65 with sound absorbing or impedance matching layers, so that standing waves are suppressed.
• the methods may be modified due to the small size of the backchamber 65 relative to typical loudspeaker enclosures.
• Figure 35B shows the total thermal noise (at 20 °C) transferred to the diaphragm 20, along with contributions from several dissipation channels, which are radiation loss (dashed line), flow through the holes of the photonic-crystal reflective element 22 (dotted line), and flow through the optical cavity 40 and annular channels (dash-dotted line).
• dissipation channels which are radiation loss (dashed line), flow through the holes of the photonic-crystal reflective element 22 (dotted line), and flow through the optical cavity 40 and annular channels (dash-dotted line).
• the highly dissipative flow through the small holes of the photonic- crystal reflective element 22 can dominate the noise floor.
• the flow through the holes of the photonic-crystal reflective element 22 can be reduced substantially, so that the dissipation through the annular channels can dominate the noise.
• FIG. 35C shows the total noise, along with the contributions from the second sensor (dashed line), and the third sensor (dotted line).
• the noise contribution from the second and third sensors is minimum at about 27 kHz, because the backchamber 65 is at its Helmholtz resonance, and prevents cross coupling between sensors, as explained above.
• a typical optoelectronic noise spectrum encountered in actual measurements is shown (dash-dotted line) for an optical finesse of ⁇ 10.
• the noise has a white-noise component dominated by the relative intensity noise (RTN) of the laser (-155 dB/Hz), and by a 1/f-noise component below 1 kHz.
• the noise on the diaphragm 20 normalized to the response yields the minimum detectable pressure (MDP) shown in Figure 36 A.
• MDP minimum detectable pressure
• the MDP curve shows that there is substantially no resonance in the sensitivity in certain embodiments. Resonance effects can be cancelled out, other than the small resonant feature due to crosstalk. Because the noise floor is set by the thermal-mechanical noise of the sensor (self noise), the noise at resonance can be amplified too.
• the compliance of the sensor system 200 can be adjusted to a high value, so that self noise is dominant over optoelectronic noise. Although increasing the compliance makes the sensor system 200 more susceptible to Brownian motion, it increases the signal too.
• the SNR signal-to-noise ratio
• the fundamental limit of the SNR can be reached by employing this method.
• the sensitivity of the sensor system 200 is increased by making the sensor system 200 noisier. Since in this case the signal and noise are from the same source (acoustic), the resonances in the noise and signal cancel out, so that no peak in the MDP is observed in Figure 36A.
• the MDP curve was optimized to match the minimum ambient noise level of the ocean by tuning various parameters such as the channel lengths, backchamber volume, and number of holes in the photonic-crystal structure (see Table I).
• the largest diaphragm 20 (e.g., 300 ⁇ diameter) is generally the most fragile one. Therefore, the pressure range of safe operation for the sensor system 200 may be limited by the fracture strength of this diaphragm 20.
• the maximum pressures the sensor system 200 can be exposed to without damaging the diaphragm 20 is -lMPa (240 dB re. 1 ⁇ &), for a 1 GPa yield strength, (see, e.g., W. N. Sharpe, Jr., K. Jackson, K. J. Hemker, and Z. Xie, "Effect of specimen size on Young's modulus and fracture strength of polysilicon," J. Micromech.
• cavitation effects may also damage the sensor system 200 at lower pressures than the fracture limit of the diaphragm 20, reducing the maximum safe pressure.
• cavitation can occur at pressures as low as about 0.18 MPa (measured at about 10 kHz at a depth of 10 m). See, e.g., V. A. Akulichev and V. I. IPichev, "Acoustic cavitation thresholds of sea water in different regions of the world ocean,” Acoust. Phys., vol. 51, pages 128-138 (2005).
• the maximum safe pressure can be reduced to -220 dB.
• the limiting factor in the dynamic range may be the linearity of the sensor system response.
• Figure 37A shows the calculated linearity of the optical signal and the diaphragm displacement. Because the values are normalized, they are independent of the diaphragm size.
• the plot in Figure 37A assumes an optical finesse of -10 (referring to the finesse of a fiber Fiber-Fabry interferometer, which is different from the finesse of a free- space Fabry-Perot cavity. See, e.g., O. Kilic, M. Digonnet, G. Kino, and O. Solgaard, "Asymmetrical spectral response in fiber Fabry-Perot interferometers," J. Lightwave Technol., vol. 28, pages 5648-5656 (2009). Although Fabry-Perot detection provides the high displacement sensitivity to detect small pressure amplitudes, its linearity may be limited.
• the linearity of the Fabry-Perot optical cavity 40 can drop to 90%. Such a nonlineanty in certain embodiments can cause harmonic distortion in the sensor system signal.
• the sensor system dynamic range for certain embodiments disclosed herein is calculated for a total harmonic distortion (THD) of about - 30 dB.
• THD total harmonic distortion
• the amplitude of a pure sine wave is distorted with the linearity curves of Figure 37 A.
• a Fourier transform of this distorted wave yields the power spectrum of the harmonics.
• the THD is calculated by dividing the total power in higher harmonics to the power in the fundamental harmonic.
• a pressure amplitude of about 0.6 Pa introduces a THD of about -30 dB as shown in Figure 37B.
• the minimum pressure the first sensor can detect in a 1-Hz bandwidth is ⁇ 10 ⁇ Pa (20 dB). Therefore, the first sensor can address pressures limited to the range of about 20 dB to 115 dB.
• it is possible to increase this dynamic range by utilizing a second sensor and a third sensor. Although all three sensors within the sensor system 200 measure the same acoustic signal, they are optically decoupled. Therefore, the optical parameters, such as finesse, can be varied for the second and third sensors without compromising the high sensitivity of the first sensor.
• the optical finesse of the second sensor can be reduced to ⁇ 1, corresponding essentially to two-beam interference.
• the smaller compliance and reduced finesse allow detection of larger signals at the expense of sensitivity, providing a pressure range of about 35 dB to 140 dB for this sensor.
• the optically decoupled sensors within the sensor system 200 allow even greater freedom in tailoring the optical detection schemes.
• the third sensor does not require a high displacement sensitivity, since it is designed to measure large signals. Therefore, as described herein, another optical detection scheme that has less sensitivity but more linearity than the Fabry- Perot detection can be employed.
• an optical fiber without a reflective element on its end is used, so that there is no significant reflection from its end face (silica-water interface reflection is less than 0.3%). In this embodiment, optical interference is prevented.
• the diaphragm displacement is detected instead by measuring the optical power coupled back into the fiber.
• This coupling changes with the spacing of the optical cavity 40 because of the diffraction of the light emerging from the tip of the optical fiber 30. See, e.g., O. Kilic, M. Digonnet, G. Kino, and O. Solgaard, "Asymmetrical spectral response in fiber Fabry-Perot interferometers " J. Lightwave Technol., vol. 28, pages 5648-5656 (2009).
• the limiting factor can be the linearity of the diaphragm displacement, as shown in Figure 37 A.
• the minimum displacement that the third sensor can measure is limited by the RIN. This is in contrast to the Fabry-Perot detection employed in the first sensor and the second sensor, where the limitation is mainly the self noise of the sensor.
• the third sensor within the sensor system 200 can detect pressures in the range of about 80 dB to 180 dB. Therefore, this example demonstrates as disclosed herein, with the utilization of parallel sensors, the sensor system 200 can be capable of a dynamic range of about 160 dB (20 dB to 180 dB), limited in certain embodiments, only by the linearity of the diaphragm displacement with pressure.
• the dynamic ranges of the first sensor and the third sensor can overlap by about 35 dB (80 dB to 115 dB). Therefore, in certain embodiments, the second sensor may not be utilized for applications utilizing a THD of -30 dB. However, for THD levels below -65 dB, the dynamic ranges of the first sensor and the third sensor may not overlap at all because the slopes of the THD curves as shown in Figure 37B for the first sensor and the third sensor are substantially different.
• the change in THD with respect to the pressure amplitude may be twice as fast as for the Fabry-Perot-detection (about 30 dB/16 dB vs.
• the second sensor within the sensor system 200 can be used so that there is sufficient overlap between the dynamic ranges.
• the dynamic ranges for a -70 dB THD are about 20 dB-75 dB, about 35 dB-100 dB, and about 80 dB-160 dB for the first sensor, the second sensor, and the third sensor, respectively.
• the lower and upper limits of the pressure ranges can be different. For the lower limits, a 1-Hz detection bandwidth can be assumed. Therefore, for larger bandwidths, the MDP for each sensor can be increased, hence the dynamic range can be reduced. This reduction also can reduce the overlap in the pressure ranges of the parallel sensors within the sensor system 200. As an example, even for a large measurement bandwidth of about 100 Hz, there is still an overlap of about 15 dB between the first sensor and the third sensor in a -30 dB THD regime. However, for a slightly more stringent THD of better than -40 dB, the overlap may not be sufficient so that the second sensor can be used also to cover the complete dynamic range.
• Turbulent flow can occur in microfluidic channels for Reynolds numbers (Re) larger than ⁇ 1500.
• Re Reynolds numbers
• K.V. Sharp and R.J. Adrian "Transition from laminar to turbulent flow in liquid filled microtubes " Exp. Fluids, vol. 36, pages 741-747 (2004); and C. Rands, B. W. Webb, and D. Maynes, "Characterization of transition to turbulence in microchannels " Int. J. Heat Mass Transfer, vol. 49, pages 2924-2930 (2006).
• An advantage of the analytical model described herein is that it allows the calculation of the flow rate through each diaphragm-sized channel 90. Since the Reynolds numbers are proportional to the flow rate, it is possible to analyze various parts of the sensor system 200 to obtain the flow characteristics.
• the first places for turbulent flow to set on are the annular channels (e.g., diaphragm-size channels 90), because they can accommodate all the flow (unlike, e.g., the optical cavity 40) despite their relatively small hydraulic diameters.
• Figure 38 shows the Reynolds number for the three flow channels 90 for a constant pressure of about 180 dB incident on the third sensor of the sensor system 200. The Reynolds numbers were calculated at different frequencies, and the incident pressure was varied so that the pressure on the smallest diaphragm (e.g., 150 ⁇ diameter) was constant at the maximum assumed range of the sensor system 200 (about 180 dB).
• the results shown in Figure 38 indicate that within the dynamic range of the sensor system 200 no turbulent flow is expected, hence the laminar- flow model and the upper limits of the pressure ranges it predicts are valid.
• the dynamic range cannot be increased substantially because of turbulence. Even with more linear diaphragm structures and displacement sensing mechanisms, the dynamic range can be ultimately limited by turbulent flow.
• the example optical sensor system 200 was characterized inside a container filled with distilled water, in the setup shown in Figure 39.
• the optical sensor system 200 was interrogated by a fiber-coupled laser with a wavelength of ⁇ 1550 nm.
• the laser light first passed through an optical circulator, which fed the light to the optical sensor system 200 and directed the reflected light from the sensor system 200 to a photoreceiver (e.g., New Focus 2053-FC).
• the photoreceiver consisted of an indium-gallium-arsenide PIN photodiode, a gain stage set to 10, and a high-pass filter set to 10 Hz.
• the optical sensor system 200 was calibrated with a reference sensor system (e.g., Celesco LC-10).
• the reference sensor system had a lead-zirconate-titanate reflective element 22, with a calibrated sensitivity of about 39.8 ⁇ /Pa in a wide frequency range of about 0.1 Hz to 120 kHz.
• the reference sensor system 200 was connected to a low- noise preamplifier (e.g., Ithaco 1201) with a gain of about 10 and a high-pass cutoff of about 10 Hz.
• a low- noise preamplifier e.g., Ithaco 1201
• the electrical outputs of the two sensor systems were connected to a dynamic signal analyzer (DSA) (e.g., HP 3562A), which converted the raw signal into various data such as frequency response, coherence, noise spectrum, and total-harmonic distortion.
• DSA dynamic signal analyzer
• HP 3562A a dynamic signal analyzer
• the DSA also had a built-in signal source that was used to drive the sound source.
• the drive signal from the DSA was fed to a wideband power amplifier (e.g., Krohn-Hite 7500) connected to the sound source.
• the sound source was an acoustic projector consisting of a rigid circular piston (e.g., USRD CI 00) with a diameter matching the container diameter of 20 cm. Sound was generated by moving the water column in the cylinder-shaped container up and down.
• the measured signal from the reference sensor system was fed through an internal feedback circuit in the DSA to the signal source to continuously adjust the output of the sound source. This was done to keep the pressure amplitude incident on the sensor systems at a constant 1 Pa throughout the frequency range. A constant incident pressure provided a smoother frequency response for both sensor systems, yielding a more accurate calibration of the optical sensor system 200.
• the two sensor systems were mounted on a vibration-isolation stage that comprised of a metal plate resting on a slightly deflated air- filled rubber cushion with a torus shape.
• the metal container was in the form of a plane-wave tube with a height of about 56 cm.
• the cutoff frequency of the first cross mode was expected to be ⁇ 4 kHz. Therefore, standing- wave resonances were present in the tube above this frequency. Any effect these resonances could have on the calibration process was suppressed in two ways:
• the two sensor systems were mounted close to each other ( ⁇ 1 cm distance), and for higher frequencies, an additional metal tube with a smaller diameter of 2.5 cm was used in the setup.
• the tube was covered on the outside with a standard pipe-heat isolation material consisting of 0.95-cm-thick polyethylene with closed air pockets.
• the isolation material provided a good acoustic isolation from the container resonances, due to the large impedance mismatch between air pockets and water.
• the smaller diameter of the tube provided a higher cross- mode cutoff of ⁇ 35 kHz, yielding a smoother response for frequencies above about 1 kHz.
• Figure 40 The coherence between the reference and optical sensor system spectra, measured with the DSA, is shown in Figure 40.
• Figure 40 indicates that the two sensor system signals are strongly correlated from ⁇ 150 Hz to ⁇ 15 kHz. The weak correlation above ⁇ 10 kHz suggests that the optical sensor system signal is dominated by noise.
• Figure 41 A shows the measured frequency response of the optical sensor system 200. The frequency response is calculated by the DSA by dividing the power spectrum of the optical sensor system 200 (in units of V), to the power spectrum of the calibrated reference sensor system (in units of Pa). The response has a resonance at -2.2 kHz. Above the resonance frequency, the response gradually drops, approaching the noise level above -10 kHz, so that the coherence degrades.
• the resonance for the sensor system 200 occurs at a rather low frequency, deviating from the calculated values (2.2 kHz instead of 10 kHz).
• an important reason as described herein is trapped air in the backchamber 65.
• the exact size of the air bubble was not measured, but visually estimated to be on the order of about 1-2 mm through a semitransparent part of the sensor head.
• the theoretical fit in Figure 41 A was obtained with the analytical model for an air bubble with an equivalent radius of 1 mm.
• Figure 41 B shows the experimental MDP of the sensor system 200 with a theoretical fit also obtained with the model.
• the sensor system 200 is able to measure pressures as low as 3.5 / ⁇ 1/2

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