Patent Description:
Micro-electromechanical systems (MEMS) and sensors technologies are used in a wide range of applications from optical displays and switches (see, e.g., <NPL>); <NPL>)), to pressure (see, e.g., <NPL>)), inertial guidance (see, e.g., <NPL>)) and biomedical sensors (see, e.g., <NPL>)).

Electronic MEMS sensor technologies mostly based on capacitive (see, e.g., <NPL>) and resistive (see, e.g., Tufte <NUM>)) readout techniques have benefitted from easy scaling for mass production and well-established micro-fabrication techniques to achieve substantial reductions in size, weight, power consumption and fabrication costs, leading to their ubiquitous deployment in billions of everyday devices. However, the same scaling laws set a limit on the sensitivity and sensing resolution of electronic MEMS devices, hindering their use in applications that require high resolution, examples of which include but are not limited to: tactical and strategic-grade navigation, underwater acoustics (see, e.g., <NPL>)), and microbiological applications (see, e.g., <NPL>)).

More recently, optical readout techniques have been integrated with microfabricated mechanical structures, such as diaphragms and mass-spring micro-system, to bridge this resolution gap (see, e.g., <NPL>); <NPL>); <NPL>); O.

Optical interferometric readout techniques can be generally classified in two categories, two-wave and multi-wave interferometers. One common implementation of a multi-wave interferometer is a Fabry-Perot (FP) etalon formed between the end-face of a highly reflective single-mode fiber and that of a compliant diaphragm (see, e.g., Kilic <NUM>; Jo <NUM>; <CIT>). The vibrations of the diaphragm, induced by an incident acoustic pressure, modulate the length of the FP cavity and its resonance frequencies. Laser light launched through the fiber is then used to probe this spectral modulation. For example, if the laser frequency is tuned to a steep portion of a resonance, the cavity length modulation will modulate the intensity of the reflected optical signal. The amplitude and frequency of the acoustic pressure can be inferred by detecting the reflected intensity fluctuations. High-finesse FP-based optical acoustic sensors have been widely reported in the literature (see, e.g., Kilic <NUM>; Jo <NUM>; <CIT>), and can achieve resolutions as low as <NUM>µPa/√Hz between <NUM> to <NUM> (see, e.g., Jo <NUM>; <CIT>). However, to maintain the high sensitivity of the FP to small diaphragm displacements, the probe-light frequency can be locked to the resonance frequency as the latter slowly drifts due to temperature changes (e.g., using a Pound Drexel Hall technique) to make operation of a single FP sensor more complex, and the operation of multiple FP sensors in large arrays more challenging.

<CIT> discloses an acoustic sensor comprising ane optical waveguide configured to emit light in a direction. The sensor further comprises an optical reflector optically coupled to the optical waveguide, the optical reflector is configured to reflect at least a portion of the light. The reflector comprises a first portion configured to reflect a first portion of the light back to the at least one optical waveguide and a second portion configured to reflect a second portion of the light back to the at least one optical waveguide.

According to an aspect of the invention, there is provided an acoustic sensor, as set out in claim <NUM>.

According to another aspect of the invention, there is provided a method of fabricating an acoustic sensor, as set out in claim <NUM>.

Certain implementations described herein build upon a new class of MEMS-based two-wave interferometers, referred to as phase-front modulation (PFM) sensors, which are based on the modulation of the phase of an optical beam (see, e.g., <CIT>; Afshar <NUM>) in which a single-mode fiber is a short distance (about <NUM>-<NUM> micrometers) from a silicon chip containing a compliant spring-loaded diaphragm suspended from a stationary substrate by cantilever springs. In the presence of an acoustic wave, the diaphragm vibrates in and out of the plane of the substrate. The fiber is aligned such that the optical beam is incident on the edge of the diaphragm, with half of the power incident on the diaphragm and the other half on the non-compliant adjacent substrate. Each portion of the optical beam power can be viewed as an arm of a two-wave Michelson interferometer. When exposed to an acoustic wave, the diaphragm vibrates relative to the adjacent substrate, which modulates the phase of the reflected beam. Consequently, the percentage of power in the reflected beam that is re-coupled into the fiber core is modulated, at the acoustic frequency. The amplitude and frequency of the acoustic wave can be inferred by measuring the optical power of the reflected beam.

The sensitivity of such a two-wave interferometer to small diaphragm displacements can be maximized by satisfying two conditions. First, the interferometer can be biased at quadrature (e.g., the diaphragm can be recessed relative to the adjacent substrate by λ/<NUM>, where λ is the laser wavelength, resulting in a π/<NUM> round-trip phase shift between the two arms). Second, the power in the two arms of the interferometer can be substantially equal to one another (e.g., the fiber can be positioned relative to the chip such that the optical power incident on the chip is distributed equally between the diaphragm and the adjacent portion of the substrate. However, satisfying the second condition using conventional techniques would entail a series of manual alignments and epoxy bonding procedures that require micrometer-scale precision to secure the fiber position relative the chip. Such procedures can be time intensive and difficult to mass-produce. Also, because it involves epoxy, over time the fiber position can drift, which can lead to undesirable variations in the acoustic sensitivity.

In certain implementations described herein, an acoustic sensor provides self-alignment of the fiber and the two-wave interferometer using a precise, repeatable and scalable structure. In addition, the fiber alignment is integrated into the micro-fabrication process. In certain implementations, an optical chip houses the optical fiber and a mechanical chip comprises the diaphragm, the optical and mechanical chips fabricated with a set of complementary mating structures (e.g., protrusions; recesses) that, when mated, position the two chips relative to one another such that the fiber is positioned precisely at the boundary between the diaphragm and the substrate. The acoustic sensor can also incorporate a large diaphragm as well as openings in the chips configured to let air/water flow through to reduce (e.g., minimize) squeezed-film damping of the diaphragm, thereby reducing the thermo-mechanical noise of the sensor structure (e.g., self-noise of the sensor limited by the extremely small thermos-mechanical noise induced by air/water molecules striking the diaphragm). Certain implementations described herein comprise a sensor having an air resolution in the sub-µPa/√Hz regime.

<FIG> schematically illustrates a perspective view of a portion of an acoustic sensor <NUM> in accordance with certain implementations described herein. The acoustic sensor <NUM> comprises at least one optical waveguide <NUM> configured to emit an optical beam <NUM>. The sensor <NUM> further comprises a first substrate <NUM> optically coupled to the at least one optical waveguide <NUM> and a second substrate <NUM> (not shown in <FIG>) affixed to the first substrate <NUM> and affixed to the at least one optical waveguide <NUM>. The first substrate <NUM> is configured to be illuminated by the optical beam <NUM> and to reflect at least a portion of the optical beam <NUM> to the at least one optical waveguide <NUM>. The first substrate <NUM> comprises a first substrate portion <NUM> configured to reflect a first portion of the optical beam <NUM> back to the at least one optical waveguide <NUM>. The first substrate <NUM> further comprises a diaphragm <NUM> configured to reflect a second portion of the optical beam <NUM> back to the at least one optical waveguide <NUM>. The diaphragm <NUM> is responsive to a perturbation by moving relative to the first substrate portion <NUM>. The optical beam <NUM> is centered on a region between the first substrate portion <NUM> and the diaphragm <NUM>.

In certain implementations, the at least one optical waveguide <NUM> has a mode-field diameter greater than <NUM> (e.g., greater than <NUM>; greater than <NUM>; greater than <NUM>; in a range between <NUM> and <NUM>; in a range between <NUM> and <NUM>; in a range between <NUM> and <NUM>; in a range between <NUM> and <NUM>). The at least one optical waveguide <NUM> can comprise an optical fiber having an end configured to emit the optical beam <NUM> that propagates towards the diaphragm <NUM>. The light beam can have a divergence angle less than <NUM> degrees (for an LMA fiber) or in a range of <NUM> degrees to <NUM> degrees (for an SMF fiber). The optical fiber can be further configured to receive reflected light from the first substrate portion <NUM> and the diaphragm <NUM>, the reflected light comprising a first reflected portion from the first substrate portion <NUM> and a second reflected portion from the diaphragm <NUM>. In certain implementations, the optical fiber comprises a large mode area (LMA) optical fiber, a tapered optical fiber (e.g., a tapered portion of a single-mode fiber, such as an SMF-<NUM> fiber), and/or a photonic-crystal fiber. Example LMA fibers compatible with certain embodiments described herein can be obtained from Nufern Inc. of East Granby CT, nLIGHT Inc. of Vancouver WA, and NKT Photonics of Denmark. Example photonic-crystal fibers compatible with certain embodiments described herein are available from NKT Photonics of Denmark and Thorlabs of Newton NJ. Example tapered optical fibers compatible with certain embodiments described herein can be made using SMF fiber from Corning Inc. of Corning NY. For example, the LMA fiber can have a numerical aperture of <NUM>, a core radius of <NUM> micrometers, and a cladding radius of <NUM> micrometers. For another example, the photonic-crystal fiber can have a numerical aperture of <NUM>, a core radius of <NUM> micrometers, and a cladding radius of <NUM> micrometers. For another example, the tapered fiber can have a numerical aperture of <NUM>, a core radius of <NUM> micrometers, and a cladding radius of <NUM> micrometers.

In certain implementations, the first substrate <NUM> is substantially planar (e.g., wafer; chip) and is placed a short, non-critical distance (e.g., <NUM> micrometers - <NUM> micrometers) from the end of the optical fiber of the at least one optical waveguide <NUM>. In certain implementations, the first substrate <NUM> comprises at least one of the following materials: silicon, silicon nitride, silicon carbide, graphite, graphene. At least one of the first substrate portion <NUM> and the diaphragm <NUM> can be optically reflective. For example, each of the first substrate portion <NUM> and the diaphragm <NUM> can comprise an optically-reflective material (e.g., a metal layer; a gold layer) or an optically-reflective structure (e.g., a photonic-crystal structure or a dielectric stack).

In certain implementations, a perimeter of the diaphragm <NUM> is substantially surrounded by the first substrate portion <NUM>. For example, as shown in <FIG>, the diaphragm <NUM> can be within a well microfabricated into the first substrate <NUM> (e.g., at a depth h<NUM> below the surface of the first substrate portion <NUM>). In certain implementations, the distance between the top surfaces of the first substrate portion <NUM> and the diaphragm <NUM> (e.g., the depth h<NUM>) is approximately equal to λ/<NUM> (e.g., equal to λ/<NUM> to within ±<NUM>%, ±<NUM>%, or ±<NUM>%), where λ is the wavelength of the optical beam <NUM> (e.g., λ = <NUM> micrometers or other near-infrared wavelength).

In certain implementations, the diaphragm <NUM> is substantially planar and has a shape in a plane parallel to the diaphragm <NUM> that is circular, square, rectilinear, triangular, or another shape. The diaphragm <NUM> can be significantly thinner (e.g., by hundreds of nanometers) than portions of the first substrate <NUM> substantially surrounding the perimeter of the diaphragm <NUM>. In certain implementations, the first substrate <NUM> further comprises a plurality of cantilever springs <NUM> (e.g., <NUM>, <NUM>, <NUM>, <NUM>, <NUM>, <NUM>, <NUM>, <NUM>, or more) that is mechanically coupled to the diaphragm <NUM> such that the diaphragm <NUM> is elastically movable relative to the first substrate portion <NUM> in a direction substantially perpendicular to the diaphragm <NUM> in response to the perturbation. For example, as shown in <FIG>, the diaphragm <NUM> can be substantially circular with substantially identical cantilever springs <NUM> extending radially outward from the diaphragm <NUM>, the cantilever springs <NUM> suspending the diaphragm <NUM> from the substrate <NUM>. In certain implementations, the diaphragm <NUM> and the cantilever springs <NUM> are defined (e.g., separated from the first substrate portion <NUM>) by gaps cut into the first substrate <NUM> (e.g., using microfabrication techniques). The first substrate <NUM> is configured to have the diaphragm <NUM> vibrate by translating in a direction that is generally perpendicular to the diaphragm <NUM> while the diaphragm <NUM> generally retains its shape (e.g., planar), and while the cantilever springs <NUM> elastically stretch and move. The optical beam <NUM> emitted from the at least one optical waveguide <NUM> straddles the first substrate portion <NUM> and the diaphragm <NUM> such that the optical power incident on the first substrate portion <NUM> is substantially equal to the optical power incident on the diaphragm <NUM>. Portions of the optical beam <NUM> are reflected from the first substrate portion <NUM> and the diaphragm <NUM> back to the at least one optical waveguide <NUM>.

The percentage of reflected power recoupled into the at least one optical waveguide <NUM> depends on the relative position of the diaphragm <NUM> to the first substrate portion <NUM>. <FIG> shows plots of the optical power recoupling of a reflected portion of the optical beam <NUM> from the first substrate <NUM> and an optical sensitivity of the acoustic sensor <NUM> as functions of the step height h<NUM> in accordance with certain implementations described herein. <FIG> also shows the field profile of the incident optical beam <NUM> (dashed lines) overlayed with plots of the reflected field profiles (solid lines) for three different step heights h<NUM> = <NUM>, h<NUM> = λ/<NUM>, and h<NUM> = λ/<NUM>, where λ is the wavelength of the incident optical beam <NUM>. The optical beam <NUM> emerging from the end of the optical waveguide <NUM> is incident on the edge of the diaphragm <NUM>, with equal portions of its intensity distributed between the diaphragm <NUM> and the non-compliant, adjacent first substrate portion <NUM>. When the diaphragm <NUM> is at the same plane as the adjacent first substrate portion (e.g., h<NUM> = <NUM>), akin to a flat mirror, both portions of the optical beam <NUM> have the same round-trip phase shift. The reflected portions of the optical beam <NUM>, propagating back towards the optical waveguide <NUM>, maintain a fundamental transverse electromagnetic TEM<NUM> profile (see, solid curve in the top, left plot of <FIG>) and is effectively recoupled back into the optical waveguide <NUM>. However, when the diaphragm <NUM> is displaced by a distance h<NUM> = λ/<NUM> from the first substrate portion <NUM>, where λ is the laser wavelength, the portion of the optical beam <NUM> reflected from the diaphragm <NUM> accumulates an additional π round-trip phase shift relative to the portion of the optical beam <NUM> reflected from the adjacent first substrate portion <NUM>. The reflected field profile at the end of the optical waveguide <NUM> (e.g., calculated by diffraction theory) is no longer a fundamental TEM<NUM> mode but has a two-lobed symmetrical amplitude profile (see, solid curve in the top, right plot of <FIG>) and an asymmetrical phase profile, similar to a TEM<NUM> mode, and is poorly recoupled into the optical waveguide <NUM>. In this configuration, the acoustic sensor <NUM> is a two-wave interferometer, similar to a Michelson interferometer, where the two portions of the intensity illuminating the diaphragm <NUM> and the adjacent first substrate portion <NUM> comprise each arm of the interferometer. To bias the interferometer at the maximum sensitivity to small displacements of the diaphragm <NUM>, the diaphragm <NUM> is recessed below the top surface of the adjacent first substrate portion by λ/<NUM> (e.g., h<NUM> = λ/<NUM> + mλ/<NUM>, where m is an integer) such that the interferometer is biased in quadrature (e.g., π/<NUM> round-trip phase shift), with equal compositions of TEM<NUM> and TEM<NUM> and at maximum sensitivity. The recoupled power dependence on step height (e.g., fiber power recoupling η) is maximized at step heights h<NUM> = <NUM> and λ/<NUM> and minimum at h<NUM> = λ/<NUM> and the slope of the recoupled power dependence on step height is maximized at step heights h<NUM> = λ/<NUM> and minimum at h<NUM> = <NUM>λ/<NUM>.

<FIG> schematically illustrate top views of an example first substrate <NUM> and an example second substrate <NUM>, respectively, in accordance with certain implementations described herein. The first substrate <NUM> is substantially planar (e.g., wafer; chip), the second substrate <NUM> is substantially planar (e.g., wafer; chip), and the second substrate <NUM> is configured to be bonded to the first substrate <NUM> such that the second substrate <NUM> is substantially parallel to the first substrate <NUM>. <FIG> is a photograph of an example acoustic sensor <NUM> comprising an example first substrate <NUM> and an example second substrate <NUM> bonded together in accordance with certain implementations described herein. <FIG> schematically illustrate perspective cross-sectional views of the example first substrate <NUM> and an example second substrate <NUM>, respectively, of <FIG> in accordance with certain implementations described herein. <FIG> also include some example dimensions of various features of the first substrate <NUM> and the second substrate <NUM> in accordance with certain implementations described herein. <FIG> schematically illustrates a perspective cross-sectional view of the example acoustic sensor <NUM> of <FIG> with the first substrate <NUM> and the second substrate <NUM> bonded together in accordance with certain implementations described herein.

As shown in <FIG>, <FIG> and <FIG>, the first substrate <NUM> comprises a compliant, substantially circular diaphragm <NUM> (e.g., at a center of the first substrate <NUM>) suspended by a plurality (e.g., <NUM>) of cantilever springs <NUM> that are substantially identical to one another and extending radially from the diaphragm <NUM>. When an acoustic wave is incident on the diaphragm <NUM>, the diaphragm <NUM> vibrates, in a piston-like motion in a direction substantially perpendicular to the diaphragm <NUM>, relative to the non-compliant (e.g., non-moving) adjacent first substrate portion <NUM>. As shown in <FIG> and <FIG>, the second substrate <NUM> comprises an optical fiber feedthrough hole <NUM> extending through the second substrate <NUM> and configured to receive the optical waveguide <NUM> (e.g., single-mode fiber). The optical waveguide <NUM> can be fixed within the optical feedthrough hole <NUM> by adhesive (e.g., epoxy) such that after the first substrate <NUM> and the second substrate <NUM> are affixed together, an end of the optical waveguide <NUM> is spaced (e.g., by about <NUM> micrometers) from the first substrate <NUM> and positioned such that light emitted from the end of the optical waveguide <NUM> propagates substantially perpendicularly to the first substrate <NUM> and light reflected from the diaphragm <NUM> and the adjacent first substrate portion <NUM> propagates substantially perpendicularly to the first substrate <NUM> back to the end of the optical waveguide <NUM>.

In certain implementations, the first substrate <NUM> and the second substrate <NUM> comprise complementary mating structures configured to facilitate alignment of the optical waveguide <NUM> with the edge of the diaphragm <NUM>. For example, as schematically illustrated by <FIG>, <FIG>, and <FIG>, the first substrate <NUM> can comprise at least one alignment island (e.g., protrusion) <NUM>, and as schematically illustrated by <FIG> and <FIG>, the second substrate <NUM> can comprise at least one alignment well (e.g., recess) <NUM>. The at least one alignment island <NUM> is configured to fit within the at least one alignment well <NUM> (e.g., analogous to LEGO® pieces) to fix (e.g., self-align) the relative positions of the diaphragm <NUM> of the first substrate <NUM> and the feedthrough hole <NUM> of the second substrate <NUM> (e.g., a center of the feedthrough hole <NUM> is aligned with an edge of the diaphragm <NUM>). While <FIG>, <FIG>, <FIG>, <FIG> shown an alignment island <NUM> and an alignment well <NUM> that are substantially circular, other shapes (e.g., oval; square; polygonal; irregular) are also compatible with certain implementations described herein.

In certain implementations, the perimeter of the at least one alignment island <NUM> has a step edge such that the at least one alignment island <NUM> has a height above a surface of a region <NUM> of the first substrate <NUM> substantially surrounding the at least one alignment island <NUM> and the perimeter of the at least one alignment well <NUM> has a depth below a surface of a region <NUM> of the second substrate <NUM> substantially surrounding the at least one alignment well <NUM>. In certain implementations, the width (e.g., diameter) of the at least one alignment island <NUM> has a first width that is less than a second width of the at least one alignment well <NUM>. For example, the height can be less than the depth (e.g., by about <NUM> micrometers) and the first width can be less than the second width (e.g., by about <NUM> micrometers to <NUM> micrometers) such that the top surface of the at least one alignment island <NUM> does not contact the top surface of the at least one alignment well <NUM> when the first substrate <NUM> is mated with the second substrate <NUM> (e.g., the surface of the region <NUM> of the first substrate <NUM> affixed to the surface of the region <NUM> of the second substrate <NUM>) and the at least one alignment island <NUM> is tightly fit into the at least one alignment well <NUM>.

In certain implementations, the at least one alignment island <NUM> comprises at least one alignment ledge <NUM> extending from a perimeter of the at least one alignment island <NUM> and the at least one alignment well <NUM> comprises at least one alignment notch <NUM> extending from a perimeter of the at least one alignment well <NUM>. While <FIG>, <FIG>, and <FIG> show the alignment island <NUM> having a single substantially rectangular alignment ledge <NUM> extending substantially perpendicularly to the perimeter of the alignment island <NUM> and <FIG> and <FIG> show the alignment well <NUM> having four substantially rectangular alignment notches <NUM> (each of which can receive the single alignment ledge <NUM>) positioned equidistantly around the alignment well <NUM>, certain other implementations comprise multiple alignment ledges <NUM> (e.g., positioned equidistantly around the alignment island <NUM>) and/or other shapes, sizes, and arrangements of the at least one alignment ledge <NUM> and/or the at least one alignment notch <NUM>. In certain other implementations, the first substrate <NUM> comprises at least one alignment well and the second substrate <NUM> comprises at least one alignment island configured to fit within the at least one alignment well.

When the first substrate <NUM> is mated with the second substrate <NUM>, the at least one alignment ledge <NUM> can be tightly fit within the at least one alignment notch <NUM>. The at least one alignment notch <NUM> can provide a sufficiently precise fit (e.g., allowing only <NUM> micrometers of misplacement) to provide a sufficiently precise alignment between the center of the feedthrough hole <NUM> and the edge of the diaphragm <NUM>. In addition, the at least one alignment ledge <NUM> and the at least one alignment notch <NUM> can provide redundancy to account for small variations in fabricated dimensions. For example, as shown in <FIG>, the at least one alignment ledge <NUM> can comprise a single ledge <NUM> extending from the alignment island <NUM> and the at least one alignment notch <NUM> can comprises four notches <NUM> arranged equidistantly along and extending from the perimeter of the alignment well <NUM>, such that the first substrate <NUM> of <FIG> and <FIG> can be rotated by <NUM>-degree increments to be fitted to the second substrate <NUM> of <FIG> and <FIG>, respectively, until a minimum misalignment between the center of the feedthrough hole <NUM> and the edge of the diaphragm <NUM> amongst the four possible orientations is achieved. Owing to small variations in fabricated dimensions, not all four orientations provide the same alignment precision. After identifying the orientation having the smallest misalignment, the first and second substrates <NUM>, <NUM> can be placed in the orientations having the smallest misalignment and can be attached to one another in this orientation (e.g., using thermos-compression bonding of gold; see, e.g., <NPL>)).

In certain implementations, the second substrate <NUM> further comprises one or more orifices <NUM> (e.g., squeezed-film damping relief windows 240a, fluid escape windows 240b) configured to allow a fluid medium (e.g., air; water) to flow out from a region between the first substrate <NUM> and the second substrate <NUM> to reduce (e.g., minimize) squeezed-film damping of the diaphragm motion (see, e.g., <NPL>)). For example, as shown in <FIG> and <FIG>, the squeezed-film damping relief window 240a can have a substantially semicircular shape positioned over a majority of the diaphragm <NUM> and the fluid escape windows 240b can comprise multiple (e.g., two; four) substantially symmetrically placed substantially circular windows that are configured to provide additional fluid escape routes. In certain implementations comprising the one or more orifices <NUM>, the acoustic sensor <NUM> can be submerged underwater to be utilized as a hydrophone, without trapping small air pockets within the region between the first substrate <NUM> and the second substrate <NUM>.

In certain implementations, the second substrate <NUM> further comprises one or more trenches <NUM>. For example, the one or more trenches <NUM> of <FIG> include a set of horizontal and curved trenches <NUM> in proximity to the feedthrough hole <NUM> and on an opposite side of the feedthrough hole <NUM> from the squeezed-film damping relief window 240a. Etching of the one or more trenches <NUM> during the fabrication process can facilitate a symmetric and vertical etch profile for the feedthrough hole <NUM>.

<FIG> schematically illustrates an example fabrication process of a first substrate <NUM> in accordance with certain embodiments described herein. This example fabrication process was used at the Stanford Nanofabrication Facility to fabricate <NUM> first substrates <NUM> concurrently on a <NUM>-inch (<NUM> inch equals <NUM>,<NUM>, in the following description the unit inch will be used) silicon-on-insulator wafer with a <NUM>-micrometer optically flat device layer, a <NUM>-micrometer box layer, and a <NUM>-micrometer substrate layer. In certain implementations, the fabrication process of the first substrate <NUM> involves two steps of device thinning by thermal oxidation following a dry etching process (e.g., to define the cantilever springs <NUM> and to release the diaphragm <NUM>). For example, the diaphragm <NUM> can be fabricated on the device layer first by thinning it to a thickness of <NUM> micrometers using thermal oxidation. Local oxidation of silicon (LOCOS) can then be used to create the λ/<NUM> distance between the first substrate portion <NUM> and the diaphragm <NUM>. Using deep reactive ion etch (DRIE), the shape of the diaphragm <NUM> and the alignment island <NUM> can be etched on the device layer. The wafer can then be flipped, and the diaphragm <NUM>, suspended on the SiO<NUM> box layer, can be exposed from the substrate layer using another DRIE step. The box layer can then be removed by vapor hydrofluoric acid to fully release the diaphragm <NUM>. The device layer can be coated with a <NUM>-nanometer-thick chromium adhesion layer, and a <NUM>-nanometer-thick gold layer to increase its power reflectivity to a measured value of about <NUM>%. The completed wafer can contain multiple first substrates <NUM> each with a single diaphragm <NUM> with dimensions summarized in Table <NUM>:.

<FIG> schematically illustrate top views and cross section view of an example second substrate <NUM> at various stages of an example fabrication process in accordance with certain embodiments described herein. This example fabrication process was also used at the Stanford Nanofabrication Facility on a standard <NUM>-micrometer thick, <NUM>-inch silicon wafer to fabricate <NUM> second substrates <NUM> concurrently. Plasma enhanced chemical deposition can be used to deposit <NUM> micrometers of silicon dioxide hard-mask on both surfaces of the Si wafer and a <NUM>-micrometer-thick layer of photoresist (PR) can be spun on the top SiO<NUM> surface of the Si wafer. Structures corresponding to an alignment well <NUM> with four substantially rectangular alignment notches <NUM> can be exposed on the PR and then etched through the SiO<NUM> hard-mask (e.g., with a magnetically-enhanced reactive ion etcher (MERIE)). The exposed regions of the Si wafer, in the shape of the alignment well <NUM> and the four alignment notches can be etched using DRIE to a depth of <NUM> micrometers.

To pattern the backside of the second substrate <NUM>, the Si wafer can be flipped over and attached to a support wafer (e.g., using Crystalbond™ adhesive), and a <NUM>-micrometer-thick layer of PR can be spun on its backside. The PR can be exposed with a pattern including the feedthrough holes <NUM>, squeezed-film damping relief windows 240a, and fluid escape windows 240b.

In certain implementations, rather than exposing the PR to the full window pattern, the PR can be exposed to a pattern comprising lines (e.g., <NUM>-micrometer wide tracks) tracing the perimeters of the windows 240a, 240b, along with the trenches <NUM> (e.g., at an opposite side of the feedthrough hole <NUM> from the squeezed-film damping relief window 240a). The trenches <NUM> are configured to substantially reduce asymmetry in the electric fields at the surface of the oxide hard-mask in the proximity of the feedthrough hole <NUM> that would otherwise occur during a subsequent DRIE step due to etching of the squeezed-film damping relief window 240a in close proximity to the smaller feedthrough hole <NUM> and fluid escape windows 240b. Without the trenches <NUM>, such asymmetrical electric fields can adversely affect the geometry and/or orientation of the etched feedthrough hole <NUM> causing imprecision in the resulting position and/or orientation of the optical waveguide <NUM> within the feedthrough hole <NUM>. By including the trenches <NUM>, certain implementations facilitate a symmetrical charge build up on the oxide hard-mask surface in the proximity of the feedthrough hole <NUM> during the subsequent DRIE step.

After exposing the PR, the backside SiO<NUM> hard-mask can be etched (e.g., using MERIE) through the SiO<NUM> to expose the pattern to the Si wafer. The feedthrough hole <NUM> and the other structures of the pattern can then be etched (e.g., using DRIE) all the way through the Si wafer. The support wafer can be removed (e.g., by dissolving the Crystalbond™ adhesive in acetone) and the SiO<NUM> hard-mask can be etched away (e.g., in a <NUM>% hydrofluoric acid solution). The top surface of the Si wafer can be coated with an adhesion layer of chromium (e.g., <NUM>-nanometers thick) and then gold (e.g., <NUM>-nanometers thick). The resulting second substrates <NUM> are configured to have precise features that complement the features of the first substrates <NUM>.

In certain implementations, fabrication of the acoustic sensor <NUM> comprising a method of aligning and bonding the first substrate <NUM> and the second substrate <NUM> to one another to reduce (e.g., minimize) an offset (e.g., due to fabrication tolerances) between the feedthrough hole <NUM> and the edge of the diaphragm <NUM>. For example, the first and second substrates <NUM>, <NUM> can be mounted on a flip-chip bonder. The method can comprise placing the first and second substrates <NUM>, <NUM> in a first orientation relative to one another in which the at least one alignment ledge <NUM> of the first substrate <NUM> is substantially aligned with the at least one alignment notch <NUM> of the second substrate <NUM> (e.g., with a single alignment ledge <NUM> substantially aligned with a corresponding one of the four alignment notches <NUM> equidistant from one another around the alignment well <NUM>). The method can further comprise substantially aligning a center of the feedthrough hole <NUM> with an edge of the diaphragm <NUM> while the first and second substrates <NUM>, <NUM> are in a first orientation. The method can further comprise measuring a first offset between the center of the feedthrough hole <NUM> and the edge of the diaphragm <NUM> (e.g., using a beam splitter and microscope of the flip-chip bonder) while the first and second substrates <NUM>, <NUM> are in the first orientation. The method can further comprise rotating one of the first and second substrates <NUM>, <NUM> (e.g., by <NUM> degrees in the case of the single alignment ledge <NUM> and the four alignment notches <NUM>) relative to the other of the first and second substrates <NUM>, <NUM> such that the first and second substrates <NUM>, <NUM> are in a second orientation relative to one another in which the at least one alignment ledge <NUM> is substantially aligned with the at least one alignment notch <NUM>. The method can further comprise substantially aligning the center of the feedthrough hole <NUM> with the edge of the diaphragm <NUM> while in the second orientation. The method can further comprise measuring a second offset between the center of the feedthrough hole <NUM> and the edge of the diaphragm <NUM> (e.g., using a beam splitter and microscope of the flip-chip bonder) while the first and second substrates <NUM>, <NUM> are in the second orientation. The method can further comprise further rotations to additional orientations in which the at least one alignment ledge <NUM> is substantially aligned with the at least one alignment notch <NUM>, further substantial alignments of the center of the feedthrough hole <NUM> with the edge of the diaphragm <NUM> while in the additional orientations, and further measuring additional offsets between the center of the feedthrough hole <NUM> and the edge of the diaphragm <NUM> while in the additional orientations.

The method can further comprise comparing the first, second, and any additional offsets to one another and evaluating which of the orientations has the least offset between the center of the feedthrough hole <NUM> and the edge of the diaphragm <NUM>. The method can further comprise substantially realigning the center of the feedthrough hole <NUM> with the edge of the diaphragm <NUM> while in the orientation having the least offset. The method can further comprise bonding (e.g., permanently attaching) the first and second substrates <NUM>, <NUM> to one another while in the orientation having the least offset (e.g., using thermo-compression bonding of gold by pressing the first and second substrates <NUM>, <NUM> together with <NUM> N of force while heating the first and second substrates <NUM>, <NUM> at <NUM> degrees Celsius for <NUM> minutes, forming a metallic bond between the two gold-coated surfaces of the first and second substrates <NUM>, <NUM>; see, e.g., Tsau <NUM>).

In certain implementations, fabrication of the acoustic sensor <NUM> further comprises inserting an end of the optical waveguide <NUM> (e.g., anti-reflection coated bare fiber end of Corning SMF-<NUM> fiber) into the feedthrough hole <NUM> and attaching the optical waveguide <NUM> to the second substrate <NUM>. For example, the bonded assembly can be laid on a flat surface with the second substrate <NUM> facing the optical waveguide <NUM> that is mounted on a three-axis micro-positioner. The end of the optical waveguide <NUM> can be aligned to the center of the feedthrough hole <NUM> and then lowered into the feedthrough hole <NUM> to an operational distance from the first substrate <NUM>. The waveguide-diaphragm distance can be determined by measuring the free spectral range of the weak interferometer formed by the small reflections at the fiber interface and the strong reflections from the first substrate <NUM>. For example, light from a broadband source (e.g., centered at a wavelength of <NUM> micrometers) can be launched into the optical waveguide <NUM> through a circulator and towards the first substrate <NUM> and the reflected light received by the optical waveguide <NUM> from the first substrate <NUM> can be redirected towards an optical spectrum analyzer. The waveguide-diaphragm distance can be adjusted until the measured free spectral range is substantially equal to Δλ = <NUM> nanometers, which corresponds to the end of the optical waveguide <NUM> being <NUM> micrometers away from the diaphragm <NUM>, which can be an optimal distance corresponding to a good compromise between the power recoupled into the waveguide and lateral tolerance in the power-balance of the PFM interferometer. At this position, the optical waveguide <NUM> can be bonded to the second substrate <NUM> (e.g., using about <NUM>µL of a UV curable epoxy). Once cured, this subassembly can be affixed (e.g., clamped) to a housing (e.g., having a <NUM><NUM> back-chamber with two small holes, one to thread the waveguide to the experimental setup and one to reduce sensitivity to static pressure).

<FIG> schematically illustrates an example experimental setup configured to characterize the acoustic sensitivity, noise, and resolution of an acoustic sensor. This example experimental setup was used to characterize acoustic sensors <NUM> in accordance with certain implementations described herein. A superfluorescent fiber source (SFS), with a center wavelength of λ = <NUM> micrometers and a linewidth of Δλ =<NUM> nanometers was used to probe the acoustic sensor <NUM> (e.g., to reduce the coherent noise contributions from the weak fiber-chip interferometer). To suppress the excess noise of the broadband light, a balanced detection scheme was employed. Light from the SFS was split with a <NUM>-<NUM> fiber coupler, <NUM>% of the power was sent through a circulator to the acoustic sensor <NUM>, and the remaining <NUM>% was sent to a variable optical attenuator (VOA) then to one of the photodiodes of a balanced detector. The reflected light from the acoustic sensor <NUM> was directed by the circulator to the second photodiode of the balanced detector. The VOA was adjusted until the same power was incident on both photodiodes. The output of the balanced detector was connected to a <NUM>-bit data acquisition (DAQ) system, which itself was connected to a computer.

The acoustic sensor <NUM> was placed in an anechoic chamber to isolate the acoustic sensor <NUM> from laboratory noise. A reference microphone adjacent to the acoustic sensor <NUM> provided a calibrated measurement of the pressure incident on the acoustic sensor <NUM>. The output of the reference microphone was connected to the DAQ system. The sound measured by both the acoustic sensor <NUM> and the reference microphone was generated by an acoustic source (e.g., speaker) mounted at the back of the anechoic chamber. The acoustic source was excited by a monotonic sinusoidal signal between <NUM> to <NUM> from a function generator controlled by the computer.

Using a detailed model (see, e.g., Afshar <NUM>) of the normalized acoustic sensitivity of the optical microphone, SN, at an acoustic frequency ωa can be defined as the change in the power recoupled into the fiber, Pc, due to a small pressure perturbation, dp, normalized to the input optical power, Pin. The normalized acoustic sensitivity can be expressed as: <MAT> which is composed of the product of three derivatives. The first derivative is the optical sensitivity, Sopt = d(Pc / Pin)/ dh, which is the change in power recoupling coefficient, η = Pc / Pin, induced by a small diaphragm displacement, h. The second derivative is the mechanical compliance, Cm = dh / dPd, which describes the displacement dh induced by a small differential pressure, pd between the diaphragm's front and back surfaces. The third derivative is the acoustic response of the full sensor structure, Ra(ωa) = dpd(ωa) / dp, which is the change in the differential pressure caused by a small change in the incident pressure p at ωa. This third derivative is the only term that depends on the acoustic frequency, and this term defines the shape of the acoustic sensor's spectral response.

The optical sensitivity, Sopt, can be predicted theoretically using diffraction theory (see, e.g., Afshar <NUM>). The optical sensitivity, Sopt, is a function of (i) the optical wavelength λ, (ii) the fiber-to-chip spacing z, (iii) the diaphragm step height h<NUM>, (iv) the lateral misalignment between the center of the beam and the edge of the diaphragm g, and (v) the angular misalignment between the fiber and the mechanical chip αtilt. Under ideal conditions that produce maximum sensitivity (e.g., h<NUM> = λ/<NUM>, g = <NUM> micrometers, and no tilt), at λ = <NUM> micrometers, and z = <NUM> micrometers, the optical sensitivity can be calculated to be <NUM>×<NUM><NUM> m-<NUM> (the maximum value shown in <FIG>). The mechanical compliance Cm is proportional to the surface area of the diaphragm (e.g., scaling the differential pressure pd) and inversely proportional to the flexibility of the cantilever springs supporting the diaphragm (see, e.g., <NPL>)). The expression for the mechanical compliance as a function of the number of cantilevers and their dimensions is provided in Afshar <NUM>. The two sensors described herein were nominally identical. Their parameters are summarized in Table <NUM>, a diaphragm with a radius of <NUM> micrometers and cantilevers with a length of <NUM> micrometers. Their calculated mechanical compliance Cm is <NUM>/Pa. Their acoustic response Ra(ωa) was calculated by treating the full sensor structure including the <NUM>-cm<NUM> back-chamber as a lumped acoustic circuit model (see, e.g., <NPL>)).

<FIG> is a plot of the normalized sensitivity spectrum of an ideal sensor, calculated for these values. The ideal normalized sensitivity exhibits a flat-band sensitivity of <NUM> Pa-<NUM> extending from <NUM> to <NUM> and a fundamental resonance at <NUM>. Beyond the resonance, the sensitivity decreases proportional to ωa-<NUM> associated to the response of a simple harmonic oscillator past its resonance. Below <NUM>, the sensitivity decreases proportional to ωa as the vent holes at the end of the back-chamber leak pressure into the chamber and decrease pd.

<FIG> also plots the normalized sensitivity SN spectra of two assembled sensors measured using the measurement setup of <FIG>. Both sensors exhibit similar sensitivity spectra spanning from <NUM> to <NUM> that closely match the general spectral shape of the modeled sensitivity of the ideal sensor. The measured flat-band sensitivity is <NUM> Pa-<NUM> between <NUM> and <NUM>. The fundamental resonance of the diaphragm structure is at <NUM> for sensor <NUM> and <NUM> for sensor <NUM>. Both sensors exhibit dips in sensitivity between <NUM> and <NUM>, which are caused by small air leaks where the bonded chip sub-assembly sits on the housing of the back-chamber. This dip in sensitivity can be avoided by improving the seal between the chips and the housing.

The agreement (to within <NUM>%) between the ideal and measured resonances (see <FIG>) confirms that the fabricated dimensions of the sensor structure are close to their design values. However, the measured flat-band sensitivity is about <NUM> times smaller than the ideal sensitivity, mainly due to a lower optical sensitivity Sopt. The parameters responsible for the reduction of Sopt were obtained through a least square fit of the modeled wavelength dependence of both η, and SN to their respective measured values, as described herein. A g = <NUM> micrometer lateral offset between the center of the optical beam probing the edge of the diaphragm results in a <NUM>-fold reduction in Sopt. A step height h<NUM> of <NUM> nanometers rather than <NUM> nanometers, is responsible for a further <NUM>-fold reduction. In addition, power losses, such as angular misalignments and connector losses, account for the remaining <NUM>-fold reduction. The path-length mismatch between the two arms of the interferometer is so small (e.g., λ/<NUM>) that a considerable shift in wavelength is used to induce a sizeable change in the interferometer biasing. A ±<NUM>% change in optical wavelength (e.g., ±<NUM> nanometers) will only change the sensitivity by ±<NUM>%. Probing the sensor with any laser wavelength around the designed value will result in a nearly identical sensitivity.

To confirm this feature, the wavelength dependence of the power recoupling and normalized sensitivity were measured. To this end, the broadband SFS in the experimental setup of <FIG> was replaced with a tunable laser with a linewidth of <NUM> femtometer. The probing wavelength was swept from <NUM> nanometers to <NUM> nanometers and the average recoupled power Pc then the sensitivity of sensor <NUM> to a <NUM> mPa acoustic excitation at <NUM> was recorded. <FIG> plots the normalized sensitivity and the power recoupling coefficient of sensor <NUM> measured as a function of the probe wavelength. Varying the wavelength from <NUM> nanometers to <NUM> nanometers (±<NUM>%) resulted in an increase in sensitivity from <NUM> Pa-<NUM> to <NUM> Pa-<NUM>, a ±<NUM>% change only. Similarly, the power recoupling coefficient η increases from <NUM>% to <NUM>%.

The measured η and SN were fitted to their respective models (see, Afshar <NUM>) to infer the values of five sensor parameters: (i) the diaphragm step height h<NUM>, (ii) the lateral misalignment between the beam and the diaphragm g, (iii) the power loss due to the angular misalignment αtilt, (iv) the fiber-to-chip spacing z, and (v) the mechanical response at <NUM> Cm×Ra(<NUM>). There is an excellent agreement between the modeled values (shown as dashed curves) and the measured η and SN (shown as solid curves). As a result, the fitted parameters can be taken as a credible representation of the sensor parameters. The fitted parameters are h<NUM> = <NUM> nanometers (<NUM> nanometers ideally), g = <NUM> micrometers (<NUM> micrometers ideally), αtilt = <NUM> (<NUM> ideally), z = <NUM> micrometers (<NUM> micrometers ideally), and Cm×Ra(<NUM>) = <NUM>/Pa (<NUM>/Pa ideally). The fitted parameters are reasonably close to their targeted ideal values.

The sensors were suspended inside a vacuum chamber and their noise was characterized at <NUM> Torr (<NUM> Torr equals <NUM>,<NUM> Pascal in the following description the unit Torr will be used) and <NUM> Torr. The vacuum chamber offered better acoustic isolation from ambient vibrations compared to the anechoic chamber of <FIG>. <FIG> plot the noise spectral density (in W/√Hz) of sensor <NUM> as a function of acoustic frequency measured at <NUM> Torr and <NUM> Torr, respectively. The measured noise tends to decrease from <NUM> up to <NUM>, then increases in four sets of resonances centered around <NUM>, <NUM>, <NUM>, and <NUM>.

The individual contributions to the total noise of the sensor are detector noise, optical shot noise, thermo-mechanical noise, <NUM>/f electronic noise and the ambient noise leaking into the chambers. The detector noise was measured to be <NUM> pW/√Hz from <NUM> to <NUM>. The optical shot noise was calculated to be <NUM> pW/√Hz based on an average detected power of <NUM>µW incident on each of the two diodes of the balanced detector. <FIG> also plot the Euclidean sum of the shot and detector noises and a <NUM>/f electronic noise of the detector that is manifested as <NUM>/√f in the plot of optical power density. The ambient noise leaking into the chamber is hard to incorporate as a model and inferred by comparing the measured noise of sensor <NUM> at the two static pressures of <NUM> Torr (<FIG>) and <NUM> Torr (<FIG>). The only other remaining noise contribution is the thermo-mechanical noise.

The thermo-mechanical noise is the stochastic vibrations of the diaphragm structure due to its thermodynamic interaction with the surrounding medium to reach thermal equilibrium (see, e.g., <NPL>)). These random diaphragm vibrations modulate the phase of light reflected from the diaphragm that result in an intensity modulation of the recoupled light into the fiber. A simple model of the thermo-mechanical noise can be considered where the diaphragm structure is modeled as a multi-mode harmonic oscillator with orthogonal resonant modes ψi. Fluctuation-dissipation theorem can be applied to each resonant mode and the overall thermo-mechanical noise can be calculated as the Euclidean sum of the thermal noise in each orthogonal mode (see, e.g., Saulson <NUM>): <MAT> where KB is the Boltzmann's constant, T is ambient temperature, m is the mass of the diaphragm, ωi is the ith resonance mode of the diaphragm with a displacement mode ψi at the edge where the fiber is probing its motion, and ci is the damping coefficient of the ith resonance mode. The displacement mode ψi is normalized such that <ψi|ψj> = δij. The modeled thermo-mechanical noise of sensor <NUM> is plotted in <FIG>, incorporating the first three resonances of the diaphragm structure at <NUM>, <NUM>, and <NUM>. The mass of the diaphragm was calculated based on its physical dimensions. The displacement ratio ψi for each resonance mode was modeled numerically. The only remaining unknown parameters were the damping coefficients ci. The damping coefficient of the fundamental resonance mode, c<NUM>, was inferred by fitting the measured sensitivity spectrum of <FIG> with the model of a simple harmonic oscillator. The remaining values of ci were inferred based on the width of the subsequent resonance modes of the measured noise spectrum.

<FIG> also plot the total expected noise of sensor <NUM>. The measured noise is in good agreement with the expected noise above <NUM>, where it is predominantly limited by the calculated thermo-mechanical noise. Between <NUM> to <NUM>, the measured noise is on average nine times higher than the expected noise and likely dominated by ambient acoustic vibrations leaking into the chamber. To confirm the sensor is limited by ambient noise and not by internal thermal noises, the pressure inside the vacuum chamber was reduced to <NUM> Torr. Doing so reduces the transmission of the acoustic noise by the ratio of the two pressures (about <NUM>) without substantially reducing damping around the spring-loaded diaphragm, which depends weakly on pressure, near atmospheric pressures (see, e.g., <NPL>)).

<FIG> demonstrates the measured and calculated noise spectra of sensor <NUM> at <NUM> Torr to be in good agreement from <NUM> to <NUM>. Between <NUM> to <NUM>, the measured noise is eight times lower than the noise at <NUM> Torr, and the fitted damping coefficients and thermo-mechanical noise (<NUM> pW/√Hz) are within <NUM>% of their respective values at <NUM> Torr (<NUM> pW/√Hz). Thus, all noises are accounted for and the sensor is ambient-noise limited at <NUM> Torr.

The minimum detectable pressure (MDP), equivalent to a signal-to-noise ratio of unity, can be calculated by dividing the measured noise spectrum at <NUM> Torr (normalized by the input power) by the sensitivity spectrum. <FIG> plots the measured MDP of sensor <NUM> for an input power of <NUM> mW. The MDP decreases from <NUM>µPa/√Hzto <NUM> nPa/√Hz between <NUM> and <NUM>, followed by two hikes to <NUM>µPa/√Hzbetween <NUM> and <NUM>, and increases beyond <NUM>. The average measured MDP between <NUM> and <NUM> is <NUM>µPa/√Hz and the minimum measured MDP of the sensor is <NUM> nPa/√Hz at <NUM> and <NUM>. The measured MDP is limited by ambient noise of the chamber and is not a true reflection of the sensor's self-noise. The expected MDP based on the sensor self-noise can be calculated as the ratio of the total expected noise (e.g., plotted in <FIG>) to the measured sensitivity (e.g., plotted in <FIG>). For sensor <NUM>, the average expected MDP is <NUM> nPa/√Hz between <NUM> and <NUM> reaching a minimum of <NUM> nPa/√Hz at <NUM>.

Although commonly used terms are used to describe the systems and methods of certain implementations for ease of understanding, these terms are used herein to have their broadest reasonable interpretations. Although various aspects of the disclosure are described with regard to illustrative examples and implementations, the disclosed examples and implementations should not be construed as limiting. Conditional language, such as, among others, "can," "could," "might," or "may," unless specifically stated otherwise, or otherwise understood within the context as used, is generally intended to convey that certain implementations include, while other implementations do not include, certain features, elements and/or steps. Thus, such conditional language is not generally intended to imply that features, elements and/or steps are in any way required for one or more implementations or that one or more implementations necessarily include logic for deciding, with or without user input or prompting, whether these features, elements and/or steps are included or are to be performed in any particular implementation. In particular, the terms "comprises" and "comprising" should be interpreted as referring to elements, components, or steps in a non-exclusive manner, indicating that the referenced elements, components, or steps may be present, or utilized, or combined with other elements, components, or steps that are not expressly referenced.

It is to be appreciated that the implementations disclosed herein are not mutually exclusive and may be combined with one another in various arrangements. In addition, although the disclosed methods and apparatuses have largely been described in the context of various devices, various implementations described herein can be incorporated in a variety of other suitable devices, methods, and contexts.

Language of degree, as used herein, such as the terms "approximately," "about," "generally," and "substantially," represent a value, amount, or characteristic close to the stated value, amount, or characteristic that still performs a desired function or achieves a desired result. For example, the terms "approximately," "about," "generally," and "substantially" may refer to an amount that is within ± <NUM>% of, within ± <NUM>% of, within ± <NUM>% of, within ± <NUM>% of, or within ± <NUM>% of the stated amount. As another example, the terms "generally parallel" and "substantially parallel" refer to a value, amount, or characteristic that departs from exactly parallel by ± <NUM> degrees, by ± <NUM> degrees, by ± <NUM> degrees, by ± <NUM> degree, or by ± <NUM> degree, and the terms "generally perpendicular" and "substantially perpendicular" refer to a value, amount, or characteristic that departs from exactly perpendicular by ± <NUM> degrees, by ± <NUM> degrees, by ± <NUM> degrees, by ± <NUM> degree, or by ± <NUM> degree. The ranges disclosed herein also encompass any and all overlap, sub-ranges, and combinations thereof. Language such as "up to," "at least," "greater than," less than," "between," and the like includes the number recited. As used herein, the meaning of "a," "an," and "said" includes plural reference unless the context clearly dictates otherwise. Also, as used in the description herein, the meaning of "in" includes "into" and "on," unless the context clearly dictates otherwise.

While the methods and systems are discussed herein in terms of elements labeled by ordinal adjectives (e.g., first, second, etc.), the ordinal adjective are used merely as labels to distinguish one element from another (e.g., one signal from another or one circuit from one another), and the ordinal adjective is not used to denote an order of these elements or of their use.

The invention described and claimed herein is not to be limited in scope by the specific example implementations herein disclosed, since these implementations are intended as illustrations, and not limitations, of several aspects of the invention.

Claim 1:
An acoustic sensor (<NUM>) comprising:
an optical waveguide (<NUM>) configured to emit an optical beam (<NUM>);
a substantially planar first substrate (<NUM>) optically coupled to the optical waveguide, the first substrate configured to be illuminated by the optical beam and to reflect at least a portion of the optical beam to the optical waveguide, the first substrate comprising:
a first substrate portion (<NUM>) configured to reflect a first portion of the optical beam back to the optical waveguide; and
a diaphragm (<NUM>) configured to reflect a second portion of the optical beam back to the optical waveguide, the diaphragm responsive to a perturbation by moving relative to the first substrate portion, the optical beam centered on a region between the first substrate portion and the diaphragm; and
a substantially planar second substrate (<NUM>) affixed to the first substrate and affixed to the optical waveguide, the second substrate substantially parallel to the first substrate,
characterized in that
the second substrate comprises a feedthrough hole (<NUM>) extending through the second substrate and configured to receive the optical waveguide.