Abstract:
The theory, design, fabrication, and characterization of MEMS (micro electrical mechanical system) Fabry-Perot diaphragm-fiber optic microphone are described in the present invention. By using MEMS technology in processing and packaging, a square 1.9 mm×1.9 mm, 2 μ thick SiO 2  diaphragm with a 350 μ square embossed center of silicon is mechanically clamped to the ferrule of a single mode fiber to keep its closeness (5 μ) and perpendicular orientation with respect to the diaphragm. Static measurement of optical output power versus the pressure on membrane reveals more than one period of Fabry-Perot interference, thereby generating a Fabry-Perot diaphragm-fiber interferometer device accurately reproducing audible acoustic wave.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
   This application claims the benefit of U.S. Provisional Application No. 60/801,910 entitled “MEMS Fiber Optic Microphone” filed May 19, 2006 which is incorporated by reference herein in its entirety and U.S. Provisional Application No. 60/801,943 entitled “Aligned Embossed Diaphragm Based Fiber Optic Sensor” filed May 19, 2006 which is incorporated herein by reference in its entirety. 

   FIELD OF THE INVENTION 
   This invention involves the design and fabrication of a new Fabry-Perot diaphragm-fiber optic microphone by using MEMS technology in processing and packaging. The currently described microphone permits direct amplification of audible signal without requiring modulation or demodulation. 
   BACKGROUND OF THE INVENTION 
   Commercially available microphones or acoustic sensors in the audible frequency range (20-20,000 Hz) convert mechanical pressure wave to electrical signal (current or voltage). Fiber optic microphones have been proposed [1-3] however, they are non-functional or ineffective because they are either interference based, utilizing a piece or coil of optical fiber as the sensing element, or intensity based, using a diaphragm as the pressure wave sensing element. Sensors with diaphragm-fiber for acoustic signal sensing or pressure sensing, especially under high temperature, were inaccurately reported as Fabry-Perot type interferometer devices. As Fabry-Perot multiple beam interference is a static phenomenon, static dependence of output optic power versus applied pressure follows the Airy function, which is approximated by a harmonic function, to confirm that the observed pressure or pressure wave sensing is indeed due to Fabry-Perot interference, not due to intensity modulation or due to diaphragm tilting. By using MEMS technology in sensor processing and packaging, a truly Fabry-Perot sensor working as an acoustic sensor in the audible range has been demonstrated. 
   SUMMARY OF THE INVENTION 
   The present invention is a Fabry-Perot diaphragm fiber optic microphone, which was fabricated with MEMS (micro electric mechanical system) technology. In one embodiment, the microphone contains a diaphragm which is clamped to the ferrule of the single mode fiber. The diaphragm structure may contain three thicknesses which control various frequency responses. The inner area can be embossed to minimize the interference gap width between the diaphragm and the fiber endface as well as ensure proper alignment between the fiber and the diaphragm. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     To assist those of ordinary skill in the relevant art in making and using the subject matter hereof, reference is made to the appended drawings, wherein: 
       FIG. 1  is a drawing illustrating the design of a broadband Fabry-Perot Diaphragm-Fiber Optic Microphone. 
       FIGS. 2 and 2A  are drawings illustrating the details of the Diaphragm of Fiber Optic Microphone, wherein a=3.5 mm, a′=3.4 mm, b=1.9 mm, c=350 μ, u=200 μ, d=80 μ, g (interference gap width L)=5 μ, t=2 μ. 
       FIG. 3  is a micrograph of the diaphragm of a MEMS Fiber Optic Microphone. 
       FIG. 4  a graphical representation of the static measurement of output optic intensity as a function of pressure. The pressure is in units of centimeter of water column, and the optical output power is in arbitrary units. 
       FIG. 5  represents the frequency response of the microphone with 2 μ thick diaphragm and 5 μ gap. 
   

   DETAILED DESCRIPTION OF THE INVENTION 
   Definition Of Symbols 
   
       
       V FP  the output voltage of the DFOS 
       V FPo  the maximum of output voltage of the DFOS 
       n refractive index of the medium; for air n˜1 
       λ wavelength of the light used for the DFOS 
       L the width of the narrow gap between the back of the diaphragm and the end surface of the single mode optic fiber 
       L o  the equilibrium width of the narrow gap diaphragm and the optic fiber 
       φ o  the Q-point phase factor determined by the equilibrium width of the interference gap 
       E Young&#39;s modulus of the material of the diaphragm 
       ν Poisson coefficient of the material of the diaphragm 
       η the constant of proportionality in the equation of displacement versus pressure, which is dependent on the geometric shape of the diaphragm 
       u the thickness of the silicon wafer (or other material) used for the fabrication of the DFOS diaphragm 
       t the thickness of the diaphragm of the DFOS 
       a the square silicon chip (or other material) size of the DFOS 
       b the size or length of the square diaphragm of the DFOS 
       c the size of the embossed square center 
       e the length of the microchannel 
       f the width of the microchannel 
       f′ the width of the narrow bottleneck of the microchannel 
       D out  the external diameter of the stainless steel tube for the assembling of the DFOS 
       D in  the internal diameter of the stainless steel tube for the assembling of the DFOS, which is equal to the diameter of the ferrule 
       P 0  the pressure needed for the diaphragm to bend ⅛ of the wavelength of the light λ/n 
       P atm  the atmospheric pressure 
       P a  the maximum pressure of the acoustic wave 
       P f  the pressure at the front side of the diaphragm of the DFOS 
       P b  the pressure at the back side of the diaphragm of the DFOS 
       P l  the pressure at the lateral side of the diaphragm of the DFOS 
       P cap  capillary pressure of the liquid in the microchannel 
       P 1  the initial air pressure of the cavity, or at the backside of the diaphragm before the DFOS is immersed in the liquid 
       P 2  the final air pressure of the cavity, or at the backside of the diaphragm after the DFOS is immersed in the liquid 
       V 1  the initial air volume of the cavity or the backside of the diaphragm before the DFOS is immersed in the liquid 
       V 2  the final air volume of the cavity or at the backside of the diaphragm after the DFOS is immersed in the liquid 
       ρ the density of the liquid the DFOS is immersed in 
       g gravitational acceleration, ˜9.8 m/s 2    
       h the depth of the liquid 
       NA numerical aperture of the fiber 
       θ beam  angle of spreading of the Gaussian beam 
       w o  waist of the Gaussian beam 
       z o  Rayleigh length of the Gaussian beam 
       R wave front radius of the Gaussian beam 
       n f  refractive index of the core of the step-index fiber 
       n c  refractive index of the cladding of the step-index fiber 
     
  
   The present invention is a Fabry-Perot diaphragm fiber optic microphone, which was fabricated with MEMS (micro electric mechanical system) technology.  FIG. 1  is one embodiment of the overall structure of the microphone. In this embodiment, diaphragm  102  is clamped to the stainless steel ferrule  104  of the single mode fiber  106  (which is enclosed by zinconia ferrule  107 ) by a washer  108 , disk spring  110 , and window cap  112 . The detailed structure of the three thicknesses of the diaphragm is shown in  FIG. 2  (and a side view,  FIG. 2A ). The outer area 3.4 mm×3.4 mm (the length of one edge of the outer area is indicated by a′) is responsible for higher frequency response. It has a thickness of 280 μ (see thickness u in  FIG. 2A ) which is almost the same as the clamped area (one edge of the clamped area is indicated by a). The middle area 1.9 mm×1.9 mm is extremely thin (one edge of the middle area is indicated by b), only 2 μ thick (see thickness t in  FIG. 2A ), where the diaphragm&#39;s intrinsic frequency is about 150 Hz. The center square of 350 μ×350 μ (one edge of the center square is indicated by c) is the embossed center to keep the interference gap width between the diaphragm and the fiber endface as small as 5 μ. The embossed center also helps keep the fiber and diaphragm properly aligned. The effect of the embossing on the microphone&#39;s frequency response is negligible.  FIG. 3  is the optical micrograph of the diaphragm of this embodiment of the MEMS Fabry-Perot fiber optic microphone. Note that the 2 μ thick middle area  302  is transparent. Multiple light sources are compatible with the present invention. One embodiment includes using a DFB single mode laser. Another embodiment uses a lower cost light emitting diode (LED) as the light source. 
   Using the plane wave Airy function of Fabry-Perot interferometry as an approximation of multiple interference of the light in the gap between the diaphragm and the fiber endface [1] 
                   I     (   o   )       =         F   ⁢           ⁢     sin   2     ⁢     δ   2         1   +     F   ⁢           ⁢     sin   2     ⁢     δ   2           ⁢     I     (   i   )                 (   1   )               
where I (i)  is the intensity of the incident light, and δ the phase dependent on the optic path or interference gap width L.
 
                 δ   =         4   ⁢   n   ⁢           ⁢   π       λ   ⁢               ⁢   L             (   2   )               
F is the finesse, defined by
 
                 F   =       4   ⁢   R         (     1   -   R     )     2               (   3   )               
where R is the reflectance of the air-silicon oxide interface. For a microphone or diaphragm-fiber optic acoustic sensor according to the invention
 
                 R   =       r   2     =         (         n   ′     -   n         n   ′     +   n       )     2     =   0.035               (   4   )               
where n′=1.46 for silicon oxide at both sides of the gap, and n=1 for air. Substituting (3) to (2) yields F=0.15. When F is smaller than 0.2, equation (1) can be approximated as [1]
 
                       I     (   o   )         I     (   i   )         ≈     F   ⁢           ⁢     sin   2     ⁢     δ   2         =         F   2     ⁢     (     1   -     cos   ⁢           ⁢   δ       )       =       F   2     ⁡     [     1   +     sin   ⁡     (           4   ⁢   π   ⁢           ⁢   n     λ     ⁢   L     +     ϕ   o       )         ]                 (   5   )               
where φ o , a phase factor related to the equilibrium gap width, determines the so-called Q-point. When φ o =0, the sensor has the highest sensitivity. Note that (5) depicts I (o)  as a harmonic function of L, with low optical efficiency F/2 but high visibility or contrast defined as
 
   
     
       
         
           
             
               
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                 ( 
                 6 
                 ) 
               
             
           
         
       
     
   
   With the well known linear dependence of ΔL, small center deflection of an edge clamped diaphragm [2], on pressure P applied on the diaphragm 
                   Δ   ⁢           ⁢   L     =     α   ⁢           ⁢       b   4     D     ⁢   P             (   7   )               
where α is a constant depending on the shape and boundary conditions of the plate or diaphragm, being 0.00126 for square shape and 0.000977, b the lateral size of the edge clamped diaphragm, and D the flexural rigidity of the diaphragm, defined by
 
                 D   =       Eh   3       12   ⁢     (     1   -     ν   2       )                 (   8   )               
h is the thickness of the diaphragm, E Young&#39;s modulus, and ν Poisson coefficient of the diaphragm material.
 
   
     
       
             
             
             
             
             
           
             
             
             
             
             
           
         
             
                 
                 
             
             
                 
               Si (100) 
               Poly Si 
               SiO 2  Quartz 
               Amorph. SiO2 
             
             
                 
                 
             
           
           
             
                 
             
           
        
         
             
               E (10 9  Pa) 
               130 
               160 
               72 
               69 
             
             
               v 
               0.28 
               0.2 
               0.16 
               0.17 
             
             
               E/12(1 − v 2 ) (10 9  Pa) 
               11.8 
               13.9 
               6.17 
               5.92 
             
             
               Circular ΔL/P (10 −13 /Pa) 
               0.828 b 4 /h 3   
               0.703 b 4 /h 3   
               1.58 b 4 /h 3   
               1.65 b 4 /h 3   
             
             
               Square ΔL/P (10 −13 /Pa) 
                1.07 b 4 /h 3   
               0.906 b 4 /h 3   
               2.04 b 4 /h 3   
               2.13 b 4 /h 3   
             
             
                 
             
           
        
       
     
   
   Substituting (7) to (5), it follows that 
                     I     (   o   )         I     (   i   )         ≈       F   2     ⁡     [     1   +     sin   ⁡     (           4   ⁢   π   ⁢           ⁢   n     λ     ⁢     S   S     ⁢   P     +     ϕ   o       )         ]               (   9   )               
where static sensitivity S S  in this work is 0.347 μ/Pa. When acoustic wave is detected, the dynamic sensitivity of the diaphragm S D  is &gt;&gt;S S .
 
   The approximately harmonic dependence of optical power output I (o)  on pressure P as depicted by equation (9) is experimentally verified ( FIG. 4 ). The present embodiment that generated the experimental results is a pure Fabry-Perot interferometer device with the diaphragm-fiber structure. 
   The intrinsic fundamental mode frequency of the diaphragm is [3] 
                   f   o     =         2   ⁢     λ   2         π   ⁢           ⁢     b   2         ⁢       D     ρ   p                   (   10   )               
where λ is the eigen value depending on the shape and boundary condition of the diaphragm, b the lateral size of the diaphragm, ρ p  the plate mass density, equal to ρh, ρ being the density of material of the plate. Therefore
 
   
     
       
         
           
             
               
                 
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                 ( 
                 11 
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   For this embodiment of the fabricated microphone, by controlling the time of silicon oxidation, the thickness of the diaphragm can be varied while keeping the lateral size a constant so that the same mask set can be used. Therefore, the frequencies of the fundamental and higher order modes of the diaphragm can meet the need. The experimental results of frequency response for this embodiment are as shown in  FIG. 5 . 
   Applicant has attempted to disclose all embodiments and applications of the disclosed subject matter that could be reasonably foreseen. However, there may be unforeseeable, insubstantial modifications that remain as equivalents. While the present invention has been described in conjunction with specific, exemplary embodiments thereof, it is evident that many alterations, modifications, and variations will be apparent to those skilled in the art in light of the foregoing description without departing from the spirit or scope of the present disclosure. Accordingly, the present disclosure is intended to embrace all such alterations, modifications, and variations of the above detailed description. 
   REFERENCES 
   
       
       [1] M. Born and E. Wolf,  Principles of Optics , p. 327, 6 th  Edition, Pergamon Press, (1980). 
       [2] S. Timoshenko,  Strength of Materials , Part II, 3rd Edition, p. 97, D. Van Nostrand Co., 1956. 
       [3] A. W. Leissa,  Vibration of Plates , Chapter 2 and 4, Scientific and Technical Information Division, Washington, D.C., 1969.