Patent Publication Number: US-8994955-B2

Title: Fabry-Perot interferometer

Description:
CROSS REFERENCE TO RELATED APPLICATION 
     This application is based on Japanese Patent Application No. 2012-137237 filed on Jun. 18, 2012, the disclosure of which is incorporated herein by reference. 
     TECHNICAL FIELD 
     The present disclosure relates to a Fabry-Perot interferometer. 
     BACKGROUND 
     JP 2008-134388 A (corresponding to U.S. Pat. No. 7,733,495 B2) discloses a Fabry-Perot interferometer. The Fabry-Perot interferometer includes a pair of mirrors. Each mirror includes a pair of high-refractive layers each of which having a high refractive index and a low-refractive layer having a low refractive index. The pair of high-refractive layers is provided by semiconducting films made of silicon, germanium or the like. The low-refractive layer, which actually is a space layer, is selectively arranged between the pair of high-refractive layers. The pair of mirrors arranged facing each other via an air gap. Each mirror includes a bridge part that crosses the air gap. One of the bridge parts of the mirrors provides a membrane, which is movable. The bridge part includes a transmission portion in which the low-refractive layer is sandwiched by the pair of high-refractive layers and a periphery portion arranged around the transmission portion. The transmission portion at least includes one mirror element in which the low-refractive layer is sandwiched by the pair of high-refractive layers. The pair of transmission portions, respectively, included in the pair of bridge parts are arranged facing each other. 
     In the above Fabry-Perot interferometer, the mirror includes optical multiple layers including the space layer. With this configuration, a wide high-reflectance band is provided and, accordingly, a wide spectroscopy band is provided. However, a mechanical strength of each mirror having the space layer is low. Thus, a warpage may occur on the high-refractive layer arranged on the space layer. In order to secure the mechanical strength, a ratio of the space layer to the transmission portion may be reduced. That is, a width of the mirror element may be reduced. 
     Absorption wavelengths of normal gas and normal liquid, such as gasoline, water, alcohol, for example, ethanol, acetic acid, carbon dioxide, carbon monoxide, nitrogen oxide (NOx), sulfur dioxide are within a range of 2 micrometers (μm) to 10 μm, which is approximately equal to a mid-wavelength infrared range. Thus, the above-described Fabry-Perot interferometer may be used in an infrared light detector or may configure an infrared light absorption sensor together with an infrared light source. The infrared light detector and the infrared light absorption sensor may be used to detect compositions and concentration of a gas or a liquid. 
     However, when the width of the mirror element is reduced in order to improve the mechanical intensity, the mirror functions as a slit within the mid-wavelength infrared range and a diffraction occurs to a transmission light passing through the mirror. When the diffraction occurs, not only a rectilinear propagation light but also a diffraction light, which is slanted by the diffraction, resonate by the mirrors. When passing through the gap, an optical path length of the rectilinear propagation light is different from an optical path length of the diffraction light. Thus, a full width at half maximum (FWHM) of the transmission light, which passes through the Fabry-Perot interferometer, is increased. That is, a resolution of the infrared light absorption sensor to differentiate compositions is reduced. This conclusion is found by inventors of the present disclosure. 
     SUMMARY 
     In view of the foregoing difficulties, it is an object of the present disclosure to provide a Fabry-Perot interferometer, which is appropriate to detect compositions of a gas or a liquid having a wavelength within a mid-wavelength infrared range. 
     According to an aspect of the present disclosure, a Fabry-Perot interferometer includes an input mirror arranged at an input side of a light, and an output mirror arranged at an output side of the light. The output mirror faces the input mirror in a first direction via a gap. Each of the input mirror and the output mirror includes a pair of high-refractive layers and a space layer arranged selectively between the pair of high-refractive layers. Each of the pair of high-refractive layers has a refractive index larger than a refractive index of the space layer. In the input mirror, the pair of high-refractive layers and the space layer provide an input-side bridge part that crosses the gap defined between the input mirror and the output mirror. In the output mirror, the pair of high-refractive-layers and the space layer provide an output-side bridge part that crosses the gap defined between the input mirror and the output mirror. At least one of the input-side bridge part and the output-side bridge part is movable in the first direction as a membrane. Each of the input-side bridge part and the output-side bridge part includes a transmission portion and a periphery portion arranged around the transmission portion. Each of the transmission portions includes a mirror element in which the space layer is sandwiched by the pair of high-refractive layers. The transmission portion of the input mirror is arranged facing the transmission portion of the output mirror. The light output from the output mirror is referred to as a transmission light. In a second direction perpendicular to the first direction, the mirror element of the input mirror has a width larger than seven times of a maximum wavelength of the transmission light, and functions as a diffraction restriction mirror. 
     In the above Fabry-Perot interferometer, the width of the mirror element of the input mirror is set larger than the width of the mirror element of the output mirror. Thus, an increase of the FWHM of the transmission light, which is caused by the diffraction, is restricted. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The above and other objects, features and advantages of the present disclosure will become more apparent from the following detailed description made with reference to the accompanying drawings. In the drawings: 
         FIG. 1  is a diagram showing a single slit diffraction; 
         FIG. 2  is a diagram showing a relationship between a wavelength λ of an incident light and a parameter D 2 /λ for each mirror element width D; 
         FIG. 3  is a diagram showing a Fresnel diffraction range and a Fraunhofer diffraction range; 
         FIG. 4  is a diagram showing a relationship between a diffraction angle θd and a standardized light energy SLE for each mirror element width D when an incident light has a wavelength λ of 10 micrometers (μm); 
         FIG. 5  is a diagram showing a relationship between a mirror element width D and a half value diffraction angle θdh when the incident light has the wavelength λ of 10 μm; 
         FIG. 6  is a diagram showing a relationship between a diffraction angle θd and a standardized light energy SLE for each mirror element width D when an incident light has a wavelength λ of 2 μm; 
         FIG. 7  is a diagram showing a relationship between a mirror element width D and a half value diffraction angle θdh when the incident light has the wavelength λ of 2 μm; 
         FIG. 8  is a diagram showing a relationship between a diffraction angle θd and a standardized light energy SLE for each mirror element width D when an incident light has a wavelength λ of 6 μm; 
         FIG. 9  is a diagram showing a relationship between a mirror element width D and a half value diffraction angle θdh when the incident light has the wavelength λ of 6 μm; 
         FIG. 10  is a diagram showing a diffraction occurred in the Fabry-Perot interferometer; 
         FIG. 11  is a diagram showing an analysis model of the diffraction occurred in the Fabry-Perot interferometer having multiple layers; 
         FIG. 12  is a diagram showing a relationship between a wavelength WL of a transmission light and a transmittance T for each incident angle when an incident light has a wavelength λ of 10 μm; 
         FIG. 13  is a diagram showing a relationship among an incident angle θi, a peak transmittance Tp, and a FWHM when the incident light has the wavelength λ of 10 μm; 
         FIG. 14  is a diagram showing a relationship between a wavelength WL of a transmission light and a transmittance T for each incident angle when an incident light has a wavelength λ of 2 μm; 
         FIG. 15  is a diagram showing a relationship among an incident angle θi, a peak transmittance Tp, and a FWHM when the incident light has the wavelength λ of 2 μm; 
         FIG. 16  is a diagram showing a relationship between a wavelength WL of a transmission light and a transmittance T for each incident angle when an incident light has a wavelength λ of 6 μm; 
         FIG. 17  is a diagram showing a relationship among an incident angle θI, a peak transmittance Tp, and a FWHM when the incident light has the wavelength λ of 6 μm; 
         FIG. 18  is a plan view showing a configuration of a Fabry-Perot interferometer according to a first embodiment of the present disclosure; 
         FIG. 19  is a cross-sectional view of the Fabry-Perot interferometer taken along line XIX-XIX in  FIG. 18 ; 
         FIG. 20  is a plan view showing a configuration of a Fabry-Perot interferometer according to a second embodiment of the present disclosure; 
         FIG. 21  is a cross-sectional view of the Fabry-Perot interferometer taken along line XXI-XXI in  FIG. 20 ; 
         FIG. 22  is a plan view showing a configuration of a Fabry-Perot interferometer according to a third embodiment of the present disclosure; 
         FIG. 23  is a cross-sectional view of the Fabry-Perot interferometer taken along line XXIII-XXIII in  FIG. 22 ; 
         FIG. 24  is a plan view showing a configuration of a Fabry-Perot interferometer according to a fourth embodiment of the present disclosure; 
         FIG. 25  is a cross-sectional view of the Fabry-Perot interferometer taken along line XXV-XXV in  FIG. 24 ; 
         FIG. 26  is a plan view showing a configuration of a Fabry-Perot interferometer according to a fifth embodiment of the present disclosure; and 
         FIG. 27  is a cross-sectional view of the Fabry-Perot interferometer taken along line XXVII-XXVII in  FIG. 26 . 
     
    
    
     DETAILED DESCRIPTION 
     The following will describe embodiments of the present disclosure with reference to the drawings. In each of the following embodiments, the same reference number is added to the same or equivalent parts in the drawings. Hereinafter, a direction in which a pair of mirrors facing each other is referred to as a first direction. The pair of mirrors is arranged via an air gap, which is referred to as gap hereinafter. Further, a direction along a plane that is perpendicular to the first direction is referred to as a second direction, and a length of a mirror element in the second direction is referred to as a width of the mirror element or a mirror element width. 
     Before describing the embodiments of the present disclosure, a development to create the present disclosure will be described. 
     The applicant of the present disclosure proposed variety of improvements for a Fabry-Perot interferometer disclosed in JP 2008-134388 A. The Fabry-Perot interferometer disclosed in JP 2008-134388 A includes a pair of mirrors arranged facing each other via a gap. Each mirror includes a pair of high-refractive layers made of, such as polysilicon, and a low-refractive layer selectively arranged between the pair of high-refractive layers. The low-refractive layer is actually provided by a space layer. In the above Fabry-Perot interferometer, each mirror includes a bridge part that crosses the gap. At least one of the bridge parts functions as a membrane, which is movable in the first direction. The bridge part includes a transmission portion in which the low-refractive layer is sandwiched by the pair of high-refractive layers and a periphery portion arranged around the transmission portion. In the periphery portion, the pair of high-refractive layers is contacted with each other without the low-refractive layer. The transmission portion includes at least one mirror element in which the low-refractive layer is sandwiched by the pair of high-refractive layers. The pair of transmission portions, respectively, included in the pair of bridge parts are arranged facing each other. 
     The Fabry-Perot interferometer having has a low mechanical strength due to the space layer include in the mirror. In order to secure the mechanical strength, a ratio of the space layer to the transmission portion may be reduced. The transmission portion includes at least one mirror element that selectively transmits the infrared lights. That is, a width of the mirror element is reduced in order to secure a mechanical strength. When the width of the mirror is reduced, diffraction of light easily occurs within the mid-wavelength infrared range (2 μm to 10 μm). As well known, absorption wavelengths of normal gas and normal liquid, such as gasoline, water, alcohol, for example, ethanol, acetic acid, carbon dioxide, carbon monoxide, nitrogen oxide (NOx), sulfur dioxide are within the mid-wavelength infrared range (2 μm to 10 μm). 
     Regarding the above-described difficulty, the inventors of the present disclosure studied on an effect of the diffraction on light amount of the transmission light passing through the Fabry-Perot interferometer by simulations.  FIG. 1  shows a diffraction of a light when the light passes through a single slit  100 . Hereinafter, the infrared light is also referred to as light for convenience. The single slit  100  corresponds to one of the mirrors of the Fabry-Perot interferometer arranged on an incidence side. A screen  101  arranged apart from the single slit  100  by a distance R in a z-direction corresponds to an infrared light detector. The single slit  100  has a width of D. That is, the mirror element has a width of D. 
     When R&lt;D 2 /λ, that is in a range where the distance R is smaller than the mirror element width D and larger than the wavelength λ, a Fresnel diffraction occurs. When R&gt;D 2 /λ, that is in a range where the distance R is larger than the mirror element width D and smaller than the wavelength λ, a Fraunhofer diffraction occurs.  FIG. 2  shows a relationship between the wavelength λ of an incident light and a parameter D 2 /λ for each mirror element width D. In  FIG. 2 , a unit of the mirror element width D is meter (m). That is, the value 1×10 −2  of the mirror element width D indicates 10 millimeters (mm). The above-described Fabry-Perot interferometer is manufactured by a micro electro mechanical systems (MEMS) technology. In order to secure a mechanical strength, a maximum value of the mirror element width D is approximately 150 μm. Accordingly, as shown in  FIG. 2 , within the mid-wavelength infrared range of 2 μm to 10 μm, the parameter D 2 /λ is smaller than 1×10 −2  m (D 2 /λ&lt;1×10 −2  m). 
       FIG. 3  shows a range of the Fresnel diffraction and a range of the Fraunhofer diffraction. In the above-described Fabry-Perot interferometer, the distance R from the mirror, which is arranged at the incidence side, to the infrared light detector is normally set equal to or larger than 10 mm considering a mounting of the Fabry-Perot interferometer and the infrared light detector. In  FIG. 3 , a region that satisfies the distance R is equal to or larger than 10 mm and the parameter D 2 /λ is smaller than 10 mm is shown by hatched lines. Thus, Fraunhofer diffraction is taken into consideration. 
     In the Fraunhofer diffraction, an amplitude u p  of the diffraction light is calculated by expression 1 showing below. Further, light energy I is calculated by expression 2 showing below. The light energy I indicates amount of the lights. In expression 1, A′ is a related constant. The related constant A′ is related to an amplitude, a wavelength of an incident light, and a detection distance. Further, in expression 1, k indicates a wave number, x 0  indicates a position of a point P along X 0  direction in  FIG. 1 . 
     
       
         
           
             
               
                 
                   
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     Further, a diffraction angle θ in  FIG. 1  is calculated by expression 3 showing below. In order to differentiate with other angles, which will be described later, the diffraction angle θ is also referred to as θd. 
     
       
         
           
             
               
                 
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       FIG. 4  shows a relationship between the diffraction angle θd and a standardized light energy (SLE) of the diffraction light. The standardized light energy has an arbitrary unit (a. u.). The standardized light energy of the diffraction light is standardized with the light energy of the rectilinear propagation light as one. In  FIG. 4 , the relationship between the diffraction angle θd and the standardized light energy of the diffraction light is based on the wavelength λ of the incident light is equal to 10 μm and the distance R from the mirror to the detector is equal to 10 mm (λ=10 μm, R=10 m). As shown in  FIG. 4 , when the mirror element width D decreases, a ratio of the diffraction lights having relatively large diffraction angles θd to the whole transmission lights increases. 
       FIG. 5  shows a relationship between the mirror element width D and the diffraction angle θd when the standardized light energy of the diffraction light is equal to half of the light energy of the rectilinear propagation light (shown by a dashed line H in  FIG. 4 ). When the standardized light energy of the diffraction light is equal to half of the light energy of the rectilinear propagation light, the diffraction angle θd is also referred to as a half value diffraction angle θdh. As shown in  FIG. 5 , when the mirror element width D is smaller than 1×10 −4  m, that is 100 μm, the half value diffraction angle θdh sharply increases with a slight decrease in the mirror element width D. When the mirror element width D is equal to or larger than 100 μm to the wavelength λ of 10 μm, that is the mirror element width D is equal to or larger than ten times of the wavelength λ (D&gt;=10λ), the half value diffraction angle θdh is decreased. 
     The inventors performed similar simulations to incident lights having different wavelengths within the mid-wavelength infrared range.  FIG. 6  shows a relationship between the diffraction angle θd and a standardized light energy (SLE) of the diffraction light when the wavelength λ of the incident light is equal to 2 μm and the distance R is equal to 10 mm (λ=2 μm, R=10 mm).  FIG. 7  is a diagram showing a relationship between the mirror element width D and the half value diffraction angle θdh based on  FIG. 6 .  FIG. 8  shows a relationship between the diffraction angle θd and a standardized light energy (SLE) of the diffraction light when the wavelength λ of the incident light is equal to 6 μm and the distance R is equal to 10 mm (λ=2 μm, R=10 mm).  FIG. 9  is a diagram showing a relationship between the mirror element width D and the half value diffraction angle θdh based on  FIG. 8 . 
     As shown in  FIG. 6  and  FIG. 8 , when the mirror element width D decreases, a ratio of the diffraction lights having relatively large diffraction angles θd to the whole transmission lights increases. As shown in  FIG. 7 , when the mirror element width D is smaller than 2×10 −5  m, that is 20 μm, the half value diffraction angle θdh sharply increases with a slight decrease in the mirror element width D. Thus, when the mirror element width D is equal to or larger than 20 μm to the wavelength λ of 2 μm, that is the mirror element width D is equal to or larger than ten times of the wavelength λ (D&gt;=10λ), the half value diffraction angle θdh can be decreased. Similarly, as shown in  FIG. 9 , when the mirror element width D is smaller than 6×10 −5  m, that is 60 μm, the half value diffraction angle θdh sharply increases with a slight decrease in the mirror element width D. Thus, when the mirror element width D is equal to or larger than 60 μm to the wavelength λ of 6 μm, that is the mirror element width D is equal to or larger than ten times of the wavelength λ (D&gt;=10λ), the half value diffraction angle θdh can be decreased. 
     As described above, the inventors of the present disclosure found that within the mid-wavelength infrared range (2 μm to 10 μm), when the mirror element width D is equal to or larger than ten times of the wavelength λ (D&gt;=10λ), the half value diffraction angle θdh can be decreased. That is, the inventors obtained a first learning that the full width at half maximum (FWHM) of the transmission light can be decreased when the mirror element width D is equal to or larger than ten times of the wavelength λ (D&gt;=10λ). 
     The inventors of the present disclosure further studied on an effect of the diffraction on a wavelength of the transmission light that passes through the mirror and an effect of the diffraction on a transmittance by simulations.  FIG. 10  shows that an incident light enters the gap AG of the Fabry-Perot interferometer along the first direction. As shown in  FIG. 10 , the Fabry-Perot interferometer includes an input-side mirror element M 1 , an output-side mirror element M 2 , a pair of high-refractive layers  31 ,  32  included in the input-side mirror element M 1 , a space layer  33  included in the input-side mirror element M 1 , a pair of high-refractive layers  51 ,  52  included in the output-side mirror element M 2 , and a space layer  53  included in the output-side mirror element M 2 . Further, the input-side mirror element M 1  and the output-side mirror element M 2 , which are paired with each other, are arranged via the gap AG. The Fabry-Perot interferometer further includes a substrate  20  that supports the output-side mirror element M 1 . The substrate  20  includes a semiconductor substrate  21  and an insulation film  22  arranged on the semiconductor substrate  21 . 
     As shown in  FIG. 10 , in the Fabry-Perot interferometer, an incident light passes through the high-refractive layer  52 , the space layer  53 , and the high-refractive layer  51  in order along the first direction. The transmission light passes through the input-side mirror element M 2 , and enters the gap AG. A part of the transmission light diffracts at an angle of θ. 
     The diffraction occurred at a boundary surface between the high-refractive layer  51  and the gap AG is reproduced in  FIG. 11  regarding multi layer analysis, and the effect of the diffraction on the wavelength of the transmission light and the transmittance are studied. Specifically, as shown in  FIG. 11 , the incident light having an incident angle of θi enters the high-refractive layer  52  of the input-side mirror element M 2 . The incident angle θi is set equal to the diffraction angle θd shown in  FIG. 10 . That is, the incident light is slanted with respect to the first direction and the second direction. The slanted incident light refracts when entering the high-refractive layer  52 . Then, when the incident light enters the space layer  53 , the angle between the incident light and the first direction returns to θ. Further, the incident light refracts again when entering the high-refractive layer  51 . Then, when the incident light enters the gap AG, the angle between the incident light and the first direction returns to θ. Thus, performing transmission simulations to the incident light having incident angle θi, the effect of the diffraction on the wavelength of the transmission light and the effect of the diffraction on the transmittance can be known. 
     For example, when the incident light has a wavelength λ of 10 μm (λ=10 μm), parameters of the layers configuring the input-side mirror element M 2 , a parameter of the gap AG, and parameters of the layers configuring the output-side mirror element M 1  are set as below. The high-refractive layer  52  is provided by a non-doped polysilicon having a thickness of 440 nanometers (nm), the space layer  53  has a thickness of 2040 nm, and the high-refractive layer  51  is provided by a non-doped polysilicon having a thickness of 440 nm. Further, the gap AG has a thickness of 5500 nm. The high-refractive layer  32  is provided by a non-doped polysilicon having a thickness of 440 nanometers (nm), the space layer  33  has a thickness of 2040 nm, and the high-refractive layer  31  is provided by a non-doped polysilicon having a thickness of 440 nm. Further, the insulation film  22  is provided by a silicon dioxide film having a thickness of 880 nm, and the semiconductor substrate  21  has a thickness of 400 μm. 
       FIG. 12  shows a relationship between the wavelength (WL) of the transmission light and the transmittance (T) when the incident light has a wavelength of 10 μm. In this case, the incident light is slanted to the first direction and the second direction. As shown in  FIG. 12 , when the incident angle θi increases, the wavelength of the transmission light shifts to a short-wavelength side. The wave number k is calculated by expression 4 showing below. In expression 4, I indicates a wave number of a standing wave, n indicates a refractive index of the gap AG sandwiched by the pair of mirrors, d indicates a distance between the pair of mirrors, θ indicates the incident angle, which is equal to the diffraction angle. 
     
       
         
           
             
               
                 
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     In expression 4, the wave number k increases with an increase in the incident angle θi. Further, the wavelength λ decreases with an increase in the wave number k. Thus, it is known from expression 4 that when the incident angle θi increases, the wavelength of the transmission light shifts to the short-wavelength side. 
     Further, when the incident angle θi, which is equal to the diffraction angle θd, is equal to or larger than 20 degrees, a width of the FWHM of the transmission light increases with an increase in the incident angle θi. However, when the incident angle θi is equal to or larger than 20 degrees, a split occurs to the transmission light. That is, multiple peaks of transmittance are confirmed at multiple wavelengths with respect to certain incident angle θi. A rise and fall of the transmittance is deemed as a peak of the transmittance. Specifically, split is not occurred to the transmission light having the incident angle θi of 0 degree, 5 degrees, 10 degrees, 12 degrees, 14 degrees, 15 degrees, 16 degrees, 18 degrees, or 19 degrees. Further, split is occurred to the transmission light having the incident angle θi of 20 degrees or 22 degrees. As shown in  FIG. 5 , in a case where the wavelength of the incident light is equal to 10 μm (λ=10 μm), the diffraction angle θd (half value diffraction angle θdh) is smaller than 20 degrees when the mirror element width D is larger than 70 μm. That is, it is known that when the mirror element width D is larger than seven times of the wavelength λ (D&gt;7λ), the split is restricted and the increase in the FWHM is restricted. 
     Further,  FIG. 13  shows a relationship among the incident angle θi, a peak transmittance (Tp) for each incident angle θi, and the FWHM of the transmission light when the incident light has the wavelength λ of 10 μm based on  FIG. 12 . In  FIG. 13 , a line connected by solid squares indicates the peak transmittance for each incident angle θi, and a line connected by hollow triangles indicates the FWHM of the transmission light. As shown in  FIG. 13 , when the incident angle θi is equal to or smaller than 12 degrees, the peak transmittance is maintained around 32% and the FWHM is maintained around 125 nm. Further, when the incident angle θi is larger than 12 degrees, the peak transmittance sharply decreases and the FWHM sharply increases with an increase in the incident angle θi. As shown in  FIG. 5 , in a case where λ=10 μm, when the mirror element width D is larger than 50 μm, the diffraction angle θd (half value diffraction angle θdh) becomes smaller than 12 degrees. That is, it is known that when the mirror element width D is equal to or larger than fifteen times of the wavelength λ (D&gt;=15λ), the peak transmittance is maintained at a high level and the FWHM is further reduced. 
     The inventors performed similar simulations to an incident light having a different wavelength within the mid-wavelength infrared range.  FIG. 14  shows a relationship between the wavelength (WL) of the transmission light and the transmittance (T) when the wavelength λ of the slanted incident light is equal to 2 μm.  FIG. 15  shows a relationship of the incident angle θi, the peak transmittance (Tp), and the FWHM of the transmission light, which is obtained based on  FIG. 14 . In  FIG. 15 , a line connected by solid squares indicates the peak transmittance for each incident angle θi, and a line connected by hollow triangles indicates the FWHM of the transmission light.  FIG. 16  shows a relationship between the wavelengths (WL) of the transmission light and the transmittance (T) when the wavelength λ of the slanted incident light is equal to 6 μm.  FIG. 17  shows a relationship of the incident angle θi, the peak transmittance (Tp), and the FWHM of the transmission light, which is obtained based on  FIG. 16 . In  FIG. 17 , a line connected by solid squares indicates the peak transmittance for each incident angle θi, and a line connected by hollow triangles indicates the FWHM of the transmission light. 
     Similar to  FIG. 12 ,  FIG. 14  shows that when the incident angle θi increases, the wavelength of the transmission light shifts to a short-wavelength side. Further, as shown in  FIG. 14 , when the incident angle θi, which is equal to the diffraction angle θd, is equal to or larger than 22 degrees, a width of the FWHM of the transmission light increases with an increase in the incident angle θi. However, when the incident angle θi is equal to or larger than 22 degrees, a split occurs to the transmission light. Specifically, split is not occurred to the transmission light having the incident angle θi of 0 degree, 10 degrees, 15 degrees, 18 degrees, 19 degrees, 20 degrees, or 21 degrees. Further, split is occurred to the transmission light having the incident angle θi of 22 degrees, 23 degrees, or 25 degrees. As shown in  FIG. 7 , in a case where λ=2 μm, the diffraction angle θd (half value diffraction angle θdh) is smaller than 22 degrees when the mirror element width D is larger than 14 μm. That is, it is known that when the mirror element width D is larger than seven times of the wavelength λ (D&gt;7λ), the split is restricted and the increase in the FWHM is restricted. 
     As shown in  FIG. 15 , when the incident angle θi is equal to or smaller than 10 degrees, the peak transmittance is maintained around 65% and the FWHM is maintained around 35 nm. Further, when the incident angle θi is larger than 10 degrees, the peak transmittance sharply decreases and the FWHM sharply increases with an increase in the incident angle θi. As shown in  FIG. 7 , in a case where λ=2 μm, when the mirror element width D is larger than 30 μm, the diffraction angle θd (half value diffraction angle θdh) becomes smaller than 10 degrees. That is, it is known that when the mirror element width D is equal to or larger than fifteen times of the wavelength λ (D&gt;=15λ), the peak transmittance is maintained at a high level and the FWHM is further reduced. 
     Similar to  FIG. 12 ,  FIG. 16  shows that when the incident angle θi increases, the wavelength of the transmission light shifts to a short-wavelength side. Further, as shown in  FIG. 16 , when the incident angle θi, which is equal to the diffraction angle θd, is equal to or larger than 18 degrees, a width of the FWHM of the transmission light increases with an increase in the incident angle θi. However, when the incident angle θi is equal to or larger than 18 degrees, a split occurs to the transmission light. Specifically, split is not occurred to the transmission light having the incident angle θi of 0 degree, 5 degrees, 7 degrees, 8 degrees, 9 degrees, 10 degrees, 12 degrees, 14 degrees, or 16 degrees. Further, split is occurred to the transmission light having the incident angle θi of 18 degrees or 20 degrees. As shown in  FIG. 9 , in a case where λ=6 μm, the diffraction angle θd (half value diffraction angle θdh) is smaller than 18 degrees when the mirror element width D is larger than 40 μm. That is, it is known that when the mirror element width D is larger than seven times of the wavelength λ (D&gt;7λ), the split is restricted and the increase in the FWHM is restricted. 
     As shown in  FIG. 17 , when the incident angle θi is equal to or smaller than 10 degrees, the peak transmittance is maintained around 55% and the FWHM is maintained around 50 nm. Further, when the incident angle θi is larger than 10 degrees, the peak transmittance sharply decreases and the FWHM sharply increases with an increase in the incident angle θi. As shown in  FIG. 9 , in a case where λ=6 μm, the diffraction angle θd (half value diffraction angle θdh) is smaller than 10 degrees when the mirror element width D is larger than 90 μm. That is, it is known that when the mirror element width D is equal to or larger than fifteen times of the wavelength λ (D&gt;=15λ), the peak transmittance is maintained at a high level and the FWHM is further reduced. 
     As described above, the inventors of the present disclosure found that within the mid-wavelength infrared range (2 μm to 10 μm), when the mirror element width D is larger than seven times of the wavelength λ (D&gt;7λ), the split is restricted and an increase in the FWHM is restricted as a second learning. Further, the inventors of the present disclosure found that within the mid-wavelength infrared range (2 μm to 10 μm), when the mirror element width D is equal to or larger than fifteen times of the wavelength λ (D&gt;=15λ), the peak transmittance is increased and the FWHM is further reduced as a third learning. 
     The present disclosure is based on the foregoing learnings obtained by the inventors of the present disclosure, and the following will describe embodiments of the present disclosure with reference to the drawings. 
     First Embodiment 
     A Fabry-Perot interferometer according to the present embodiment is similar to the Fabry-Perot interferometer disclosed in JP 2008-134388 A, which is filed by the applicant of the present disclosure. Thus, description of similar parts of the Fabry-Perot interferometer will be omitted. 
     The following will describe a configuration of the Fabry-Perot interferometer  10  with reference to  FIG. 18  and  FIG. 19 . 
     As shown in  FIG. 18  and  FIG. 19 , the Fabry-Perot interferometer  10  includes a substrate  20 , a first mirror  30 , a spacer  40 , and a second mirror  50 . In the present embodiment, the second mirror  50  is arranged at an input side from which a light enters the Fabry-Perot interferometer  10  as shown by an arrow IN in  FIG. 19 , and the first mirror  30  is arranged at an output side from which the light exits from the Fabry-Perot interferometer  10  as shown by an arrow OUT in  FIG. 19 . Thus, the second mirror  50  is also referred to as an input mirror  50 , and the first mirror  30  is also referred to as an output mirror  30 . The output mirror  30  is paired with the input mirror  50 . 
     The substrate  20  includes a semiconductor substrate  21  made of single crystal silicon and an insulation film  22  arranged on the semiconductor substrate  21 . The insulation film  22  is made of silicone oxide film or silicon nitride film. The output mirror  30  is arranged on the insulation film  22  of the substrate  20 . The substrate  20  has a first surface on which the insulation film  22  is arranged and a second surface that is opposite to the first surface. The second surface of the substrate is etched so that a through hole  23  is defined through the substrate  20 . By etching the second surface of the substrate  20 , a transmission portion S 1  of the output mirror  30  is provided. The transmission portion S 1  also functions as a first membrane MEM 1 , which is movable in the first direction. A part of the output mirror  30  that crosses the gap AG is defined as a bridge part  34 . The bridge part of the output mirror  30  is also referred to as an output-side bridge part. The bridge part  34  includes the transmission portion S 1  and a periphery portion T 1  arranged around the transmission portion S 1 . 
     The output mirror  30  includes a pair of high-refractive layers that is arranged on the insulation film  22  of the substrate  20 . The pair of high-refractive layers includes a first high-refractive layer  31  arranged on the insulation film  22  of the substrate  20  and a second high-refractive layer  32  arranged on an opposite side of the first high-refractive layer  31  from the insulation film  22 . Each of the first high-refractive layer  31  and the second high-refractive layer  32  is made of a material having a refractive index larger than air. For example, each of the first high-refractive layer  31  and the second high-refractive layer  32  may be provided by a semiconducting film, which is made of at least one of silicon material or germanium material. In the present embodiment, both the first high-refractive layer  31  and the second high-refractive layer  32  are made of polysilicon. 
     The output mirror  30  includes the transmission portion S 1 , which is provided by a part of the first high-refractive layer  31 , a part of the second high-refractive layer  32 , and a space layer  33  sandwiched between the first high-refractive layer  31  and the second high-refractive layer  32  as a low-refractive layer. A structure in which the space layer  33  is sandwiched by the high-refractive layers  31 ,  32  provide a mirror element M 1 . The mirror element M 1  has an optical multiple layer structure. The transmission portion S 1  may have at least one mirror element M 1 .  FIG. 19  shows an example in which the transmission portion S 1  has multiple mirror elements M 1  as a mirror element group. As shown in  FIG. 18  and  FIG. 19 , each mirror element M 1  of the output mirror  30  is arranged facing to a mirror element M 2  of the input mirror  50 . Similar to the output mirror  30 , the input mirror  50  may have one mirror element M 2  or multiple mirror elements M 2  as a mirror element group. The mirror element M 2  of the input mirror  50  is arranged at a central region of a second membrane MEM 2  of the input mirror  50 . The membrane MEM 2  of the input mirror  50  approximately has a circular plate shape, and is movable in the first direction. Within a range of the transmission portion S 1  of the output mirror  30 , the second high-refractive layer  32  includes a floating section  32   a  and a supportive section  32   b . The floating section  32   a  is arranged apart from the first high-refractive layer  31 , and the space layer  33  is sandwiched between the floating section  32   a  and the first high-refractive layer  31 . The supportive section  32   b , a part of which is contacted with the first high-refractive layer  31 , supports the floating section  32   a  to be located above the first high-refractive layer  31  via the space layer  33 . The supportive section  32   b  includes a first sub-section that supports a side surface of the space layer  33  and a second sub-section that is contacted with the first high-refractive layer  31 . In the present embodiment, the supportive section  32   b  is arranged along a periphery portion of the mirror element. M 1 , and defines a shape of the mirror element M 1 . The space layer  33  is divided by the supportive section  32   b  into multiple space elements  33  so that the multiple mirror elements M 1  are provided within the transmission portion S 1 . In the present embodiment, the multiple mirror elements M 1  are arranged in a honeycomb manner. The multiple mirror elements M 1  of the output mirror  30  have the same dimensions, and configure the transmission portion S 1  of the output mirror  30 . A minimum width of an upper surface of each space element  33  is defined as a width D 1  of the mirror element M 1 , and a direction along the width D 1  of the mirror element M 1  is defined as the second direction. 
     In the periphery portion T 1  of the output mirror  30 , the first high-refractive layer  31  is contacted with the second high-refractive layer  32 . In the output mirror  30 , the periphery portion T 1  and an outer portion arranged around outside of the periphery portion T 1  are supported by the substrate  20 . The bridge part  34  is arranged facing a bridge part  54  of the input mirror  50 . The bridge part  54  of the input mirror  50  functions as a second membrane MEM 2 , which is movable in the first direction. 
     As shown in  FIG. 19 , through holes  35  are defined by each of the first high-refractive layer  31  and the second high-refractive layer  32 . The space layer  33  and the gap AG are formed by etching from the second surface of the substrate  20  through the through holes  35 . Each of the first high-refractive layer  31  and the second high-refractive layer  32  includes an electrode  36 , which is formed by implanting p-type impurity ions. Each of the electrodes  36  is arranged such that a part of the electrode  36  of the output mirror  30  faces a part of an electrode  56  of the input mirror  50 . The output mirror  30  further includes a pad  37  arranged on the second high-refractive layer  32 . In the present embodiment, the pad  37  is made of Ag—Cu alloy, and is in an ohmic contact with the electrode  36 . 
     The Fabry-Perot interferometer  10  according to the present embodiment further includes a spacer  40  arranged between the input mirror  50  and the output mirror  30 . Specifically, the spacer  40  is arranged on a predetermined region of the second high-refractive layer  32  of the output mirror  30  other than a region on which the bridge part  34 , the pad  37  are arranged. The spacer  40  supports the input mirror  50  above the output mirror  30  so that the gap AG is defined between the input mirror  50  and the output mirror  30 . In the present embodiment, the spacer  40  is made of silicon dioxide. A middle portion of the spacer  40  corresponding to the bridge part  34  and the bridge part  54 , which will be described later, are hollowed out so that the gap AG is defined between the input mirror  50  and the output mirror  30 . In the spacer  40 , an opening  41  is defined corresponding to the pad  37  so that the pad  37  is exposed to outside. 
     The input mirror  50  includes a pair of high-refractive layers including a first high-refractive layer  51  and a second high-refractive layer  52 . The first high-refractive layer  51  is arranged on a surface of the spacer  40  so that the gap AG is defined between the first high-refractive layer  51  of the input mirror  50  and the second high-refractive layer  32  of the output mirror  30 . The second high-refractive layer  52  is arranged on the first high-refractive layer  51 . Each of the first high-refractive layer  51  and the second high-refractive layer  52  is made of a material having a refractive index larger than air. For example, each of the first high-refractive layer  51  and the second high-refractive layer  52  may be provided by a semiconducting film, which is made of at least one of silicon material or germanium material. In the present embodiment, both the first high-refractive layer  51  and the second high-refractive layer  52  are made of polysilicon. A part of the input mirror  50  that crosses the gap AG is defined as the bridge part  54 . The bridge part  54  of the input mirror  50  is also referred to as an input-side bridge part. The bridge part  54  includes a transmission portion S 2  and a periphery portion T 2  arranged around the transmission portion S 2 . 
     The transmission portion S 2  is provided by a part of the first high-refractive layer  51 , a part of the second high-refractive layer  52 , and a space layer  53  as a low-refractive layer. The space layer  53  is sandwiched between the first high-refractive layer  51  and the second high-refractive layer  52 . A structure in which the space layer  53  is sandwiched by the high-refractive layers  51 ,  52  provide a mirror element M 2 . The mirror element M 2  has an optical multiple layer structure. The transmission portion S 2  may have at least one mirror element M 2 .  FIG. 19  shows an example in which the transmission portion S 2  has multiple mirror elements M 2  as a mirror element group. As shown in  FIG. 18  and  FIG. 19 , the mirror elements M 2  are arranged at the central region of the second membrane MEM 2  of the input mirror  50 , which has the circular plate shape. Within a range of the transmission portion S 2  of the input mirror  50 , the second high-refractive layer  52  includes a floating section  52   a  and a supportive section  52   b . The floating section  52   a  is arranged apart from the first high-refractive layer  51 , and the space layer  53  is sandwiched between the floating section  52   a  and the first high-refractive layer  51 . The supportive section  52   b , a part of which is contacted with the first high-refractive layer  51 , supports the floating section  52   a  to be located above the first high-refractive layer  51  via the space layer  53 . The supportive section  52   b  includes a first sub-section that supports a side surface of the space layer  53  and a second sub-section that is contacted with the first high-refractive layer  51 . In the present embodiment, the supportive section  52   b  is arranged along a periphery portion of the mirror element M 2 , and defines a shape of the mirror element M 2 . The space layer  53  is divided by the supportive section  52   b  into multiple space elements  53  so that the multiple mirror elements M 2  are provided within the transmission portion S 2 . In the present embodiment, the multiple mirror elements M 2  of the input mirror  50  are arranged in a honeycomb manner corresponding to the multiple mirror elements M 1  of the output mirror  30 . The multiple mirror elements M 2  have the same dimensions, and configure the transmission portion S 2  of the input mirror  50 . A minimum width of an upper surface of each space element  53  is defined as a width D 2  of the mirror element M 2 . In the present embodiment, the mirror elements M 1  of the output mirror  30  are arranged corresponding to respective mirror elements M 2  of the input mirror  50 . Each mirror element M 1  and a corresponding mirror element M 2  have the same pattern and dimensions. The width D 1  of the mirror element M 1  is the same with the width D 2  of the mirror element M 2 . 
     In the periphery portion T 2  of the input mirror  50 , the first high-refractive layer  51  is contacted with the second high-refractive layer  52 . In the input mirror  50 , an outer portion arranged around outside of the periphery portion T 2  are supported by the spacer  40 . 
     As shown in  FIG. 19 , multiple through holes  55  are defined by the first high-refractive layer  51 . The space layer  53  is formed by etching from the gap AG through the through holes  55 . Each of the first high-refractive layer  51  and the second high-refractive layer  52  includes an electrode  56 , which is formed by implanting p-type impurity ions. The input mirror  50  further includes a pad  57  arranged on the second high-refractive layer  52 . In the present embodiment, the pad  57  is made of Ag—Cu alloy, and is in an ohmic contact with the electrode  56 . 
     With above-described configuration, when a driving voltage is applied between the electrodes  36 ,  56  via the respective pads  37 ,  57 , the first membrane MEM 1  of the output mirror  30  and the second membrane MEM 2  of the input mirror  50  move in the first direction toward each other due to an electrostatic force generated between the electrodes  36 ,  56 . When the first membrane MEM 1  and the second membrane MEM 2  move toward each other, a distance between the mirror element M 1  and the mirror element M 2  changes. Thus, infrared lights are selectively transmitted through the Fabry-Perot interferometer  10  based on the wavelength. 
     The high-refractive layers  31 ,  32 ,  51 ,  52  are made of polysilicon. Thus, the high-refractive layers  31 ,  32 ,  51 ,  52  are appropriate to the infrared lights having a wavelength of 2 μm to 10 μm. Further, the high-refractive layers  31 ,  32 ,  51 ,  52  may be provided by semiconducting films including at least one of polygermanium, polysilicon-germanium, silicon, or germanium so that the high-refractive layers  31 ,  32 ,  51 ,  52  are appropriate to the infrared lights having a wavelength of 2 μm to 10 μm. 
     As described above, the space layers  33 ,  53  are employed as the low-refractive layers of the mirror elements M 1 , M 2 . Thus, a refractive index ratio n 1 /n 2  of the refractive index n 1  of the high-refractive layer  31 ,  32 ,  51 ,  52  to the refractive index n 2  of the low-refractive layer  33 ,  53  can have a relatively large value. For example, the refractive index of silicon is 3.45, and the refractive index of germanium is 4, while the refractive index of air is 1. Thus, the refractive index ratio n 1 /n 2  can have a value larger than 3.3. With this configuration, the infrared light having a wavelength within a range of 2 μm to 10 μm transmits through the Fabry-Perot interferometer  10 . Thus, a cost reduction is achieved with the Fabry-Perot interferometer  10  according to the present embodiment. 
     The transmission portion S 1  includes multiple mirror elements M 1 , and the transmission portion S 2  includes multiple mirror elements M 2 . Thus, when an area of the transmission portion S 1  and an area of the transmission portion S 2  are constant, the multiple mirror element structure increase a mechanical strength compared with a structure in which single mirror is provided within each of the transmission portion S 1  and the transmission portion S 2 . Further, the supportive sections  32   b ,  52   b  are provided by respective second high-refractive layers  32 ,  52 . Thus, the structure of the Fabry-Perot interferometer  10  is simplified compared with a case in which the floating sections  32   a ,  52   a  are supported by separate components. 
     Further, the substrate  20  defines the through hole  23  corresponding to the transmission portion S 1 . Thus, the infrared lights are restricted to be absorbed by the substrate  20 . That is, a loss of the infrared lights is restricted. 
     The following will describe features of the Fabry-Perot interferometer  10  according to the present embodiment. 
     As shown in  FIG. 19 , the arrows IN and the arrow OUT indicate a transmission direction of the light. Based on the above-described second learning by the inventors of the present disclosure, all of the mirror elements M 2  of the input mirror  50  have respective widths D 2 , which are larger than seven times of a maximum value of a mid-wavelength infrared range. Hereinafter, the mirror element M 2  of the input mirror  50  having the width D 2  larger than seven times of the maximum value of a mid-wavelength infrared range is also referred to as a diffraction restriction mirror. As described above, the mid-wavelength infrared range is from 2 μm to 10 μm. Thus, the width D 2  of each mirror element M 2  is larger than 70 μm, which is seven times of 10 μm (D 2 &gt;70 μm). The mirror element M 2  having the width D 2  larger than 70 μm is also referred to as a diffraction restriction mirror. With this configuration, the transmission light passing through the input mirror element M 2  are not split within the mid-wavelength infrared range. Thus, a difficulty in correctly detecting a peak transmittance of compositions in a composition analysis due to the split is restricted. Further, the diffraction angle θd is reduced compared with a case in which the split occurs. Thus, the FWHM of the transmission light is reduced. As described above, the Fabry-Perot interferometer  10  without split occurrence is more appropriate to detect compositions of gas and liquid, whose absorption wavelength lay within the mid-wavelength infrared range compared with a conventional Fabry-Perot interferometer  10  in which the split occurs. In the present embodiment, each mirror element M 1  of the output mirror  30  also has a width D 1  larger than seven times of the maximum value of mid-wavelength infrared range. That is, the width D 1  of each output mirror element M 1  is larger than 70 μm (D 1 &gt;70 μm). 
     Further, based on the second learning, the width D 2  of each mirror element M 2  of the input mirror  50  is set at least equal to or larger than ten times of the maximum value of the mid-wavelength infrared range. That is, the width D 2  of each mirror element M 2  of the input mirror  50  is equal to or larger than 100 μm (D 2 &gt;=100 μm). With this configuration, the half value diffraction angle θdh can be reduced within the mid-wavelength infrared range. Thus, the FWHM of the transmission light is further reduced within the mid-wavelength infrared range. 
     Based on the above-described third learning, at least the width D 2  of each mirror element M 2  of the input mirror  50  is set equal to or larger than fifteen times of the maximum value of the mid-wavelength infrared range. That is, the width D 2  of each mirror element M 2  of the input mirror  50  is set equal to or larger than 150 μm (D 2 &gt;=150 μm). With this configuration, the FWHM of the transmission light is further reduced within the mid-wavelength infrared range, and the peak transmittance of the transmission light at peak wavelength is increased. Thus, the FWHM of the transmission light within the mid-wavelength infrared range is further reduced. The mirror elements M 1 , M 2  include the space layers  33 ,  53 , respectively, as the low-refractive layers. Thus, maximum values of the widths D 1 , D 2  of respective mirror elements M 1 , M 2  are around 150 μm considering the mechanical strength of the mirror elements M 1 , M 2 . Thus, when at least the width D 2  of the mirror element M 2  of the input mirror  50  is set as 150 μm, the FWHM of the transmission light within the mid-wavelength infrared range is further reduced. 
     In the present embodiment, the first membrane MEM 1  of the output mirror  30  is provided by the transmission portion S 1 . Further, the first membrane MEM 1  of the output mirror  30  may be provided by the whole bridge part  34  of the output mirror  30  similar to the second membrane MEM 2  of the input mirror  50 . Further, the width D 1  of the mirror element M 1  of the output mirror  30  may be set smaller than the width D 2  of the mirror element M 2  of the input mirror  50 . In the present embodiment, the light enters the Fabry-Perot interferometer  10  from the second mirror  50 , and exits from the first mirror  30 . Thus, the second mirror  50  is defined as the input mirror, and the first mirror  30  is defined as the output mirror. Further, the light may pass through the Fabry-Perot interferometer  10  in an opposite direction from the direction described in the present embodiment. That is, the light may enter the Fabry-Perot interferometer  10  from the first mirror  30 , and exits from the second mirror  50 . In this case, the first mirror  30  functions as the input mirror  30 , and the second mirror  50  functions as the output mirror  50 . 
     In the present embodiment, the supportive sections  32   b ,  52   b  is provided by a part of the second high-refractive layer  32 ,  52 . Further, the supportive sections  32   b ,  52   b  may be provided by a separate component other than the part of the second high-refractive layer  32 ,  52 . 
     In the present embodiment, each mirror element M 1 , M 2  has multiple layers including the space layer  33 ,  53 . With this configuration, a refractive index ratio of the refractive index of the high-refractive layer  31 ,  32 ,  51 ,  52  to the refractive index of the low-refractive layer  33 ,  53  provided by the space layer  33 ,  53  can have a relatively large value. Thus, a wide high-reflectance band is provided and, accordingly, a wide spectroscopy band is provided. 
     Further, based on the studies performed by the inventors of the present disclosure, the inventors found that when the diffraction angle θd is larger than a predetermined value, the FWHM of the transmission light increases with an increase of the diffraction angle θd and a split occurs in the transmission light. That is, multiple peak transmittance occurs at multiple wavelengths. Based on the learnings obtained by the studies, the width D 2  of the mirror element M 2  of at least the input mirror  50  is set larger than seven times of a maximum wavelength of the transmission light, which have a wavelength range of 2 μm to 10 μm. In this case, the input mirror  50  functions as a diffraction restriction mirror. With this configuration, the split is not occurred to the transmission light within the mid-wavelength infrared range. Thus, a difficulty in correctly detecting a peak transmittance of compositions in a composition analysis due to the split is restricted. Further, the diffraction angle θd in the present embodiment is smaller than a predetermined angle at which the split occurs. Thus, the FWHM of the transmission light is reduced. As described above, the Fabry-Perot interferometer  10  without split occurrence is more appropriate to detect compositions of gas and liquid, whose absorption wavelength lay within the mid-wavelength infrared range compared with a conventional Fabry-Perot interferometer  10  in which the split occurs. 
     In the present embodiment, the width of the diffraction restriction mirror is set equal to or larger than ten times of the maximum wavelength of the transmission light. 
     Based on the studies performed by the inventors, when the width of the mirror decreases, the diffraction angle θd increases and an energy ratio of the diffraction light to the transmission light increases. As described above, when the standardized light energy of the diffraction light is equal to half of the light energy of the rectilinear propagation light, the diffraction angle θd is referred to as a half value diffraction angle θdh. The inventors obtained from the studies that in a relationship between the minimum width of the mirror element M 1 , M 2  and the half value diffraction angle θdh, an inflection point exists, and when the minimum width of the mirror element M 1 , M 2  is smaller than a width corresponding to the inflection point, half value diffraction angle θdh sharply increases. 
     In the present embodiment, the second mirror  50  arranged on an input side of the light is set as the diffraction restriction mirror. Thus, the minimum width of the input mirror  50  is larger than a width corresponding to the inflection point so that the half value diffraction angle θdh is reduced. Thus, the FWHM of the transmission light within the mid-wavelength infrared range is reduced. 
     In the present embodiment, the width of the diffraction restriction mirror is further set equal to or larger than fifteen times of the maximum wavelength of the transmission light. 
     Based on the studies performed by the inventors, the FWHM of the transmission light and the peak transmittance are maintained around a predetermined level when the diffraction angle θd is equal to or smaller than a predetermined angle. When the diffraction θd is larger than the predetermined angle, the FWHM of the transmission light increases sharply and the peak transmittance decreases sharply. 
     In the present embodiment, based on the above-described learning, the mirror arranged at the input side of the light is set as the diffraction restriction mirror. With this configuration, within the mid-wavelength infrared range, the FWHM of the transmission light is reduced and the peak transmittance of the transmission light is increased. Accordingly, within the mid-wavelength infrared range, the FWHM of the transmission light is further reduced. 
     Second Embodiment 
     The following will describe a Fabry-Perot interferometer  10  according to a second embodiment of the present disclosure. In the present embodiment, same or equivalent parts of the Fabry-Perot interferometer  10  with the first embodiment will be omitted. 
     As shown in  FIG. 20  and  FIG. 21 , the light enters the first mirror  30  arranged adjacent to the substrate  20 , and exits from the mirror second  50  arranged apart from the substrate  20 . Thus, in the present embodiment, the first mirror  30  is referred to as an input mirror, and the second mirror  50  is referred to as an output mirror. As shown in  FIG. 21 , in the present embodiment, the through hole  23  is not defined in the substrate  20 . Thus, the input mirror  30  does not include the movable first membrane MEM 1 . Further the width D 1  of the mirror element M 1  of the input mirror  30  is larger than the width D 2  of the mirror element M 2  of the output mirror  50 . Further, in the output mirror  50 , through holes  55  are defined in a part of a high-refractive layer  52 , which is included in the mirror element M 2 . Further, in the output mirror  50 , through holes are further defined in the high-refractive layers  51 ,  52 , which provide a part of the periphery portion T 2 . The through holes  55  are defined so that the space layer  53  and the gap AG are formed by etching through the through holes  55 . Further, in the mirror elements M 1  of the input mirror  30 , through holes  35  are defined in the high-refractive layer  32  so that the space layer  33  is formed by etching through the through holes  55 ,  35 . Other parts of the Fabry-Perot interferometer  10  according to the present embodiment are similar to the Fabry-Perot interferometer  10  according to the first embodiment. 
     Similar to the first embodiment, at least the width D 1  of each mirror element M 1  of the input mirror  30  is set larger than seven times of the maximum value of the mid-wavelength infrared range. That is, the width D 1  of each mirror element M 1  of the input mirror  30  is set larger than 70 μm (D 1 &gt;70 μm). Further, the width D 1  of each mirror element M 1  of the input mirror  30  may be set equal to or larger than ten times of the maximum value of the mid-wavelength infrared range. That is, the width D 1  of each mirror element M 1  of the input mirror  30  may be set equal to or larger than 100 μm (D 1 &gt;=100 μm). Furthermore, the width D 1  of each mirror element M 1  of the input mirror  30  may be set equal to or larger than fifteen times of the maximum value of the mid-wavelength infrared range. That is, the width D 1  of each mirror element M 1  of the input mirror  30  may be set equal to or larger than 150 μm (D 1 &gt;=150 μm). With the above-described configuration, advantages similar to the first embodiment are provided by the Fabry-Perot interferometer  10  according to the present embodiment. 
     Further, in the present embodiment, the width D 1  of each mirror element M 1  of the input mirror  30  is set larger than the width D 2  of each mirror element M 2  of the output mirror  50 . Thus, an increase of the FWHM of the transmission light is restricted compared with a case in which the width D 1  and the width D 2  are the same or the width D 2  is larger than the width D 1 . 
     Further, in the present embodiment, the first mirror  30 , which has no membrane MEM 1 , functions as the input mirror  30 . Further, the width D 1  of each mirror element M 1  of the input mirror  30  is larger than the width D 1  of each mirror element M 2  of the output mirror  50 . Since the input mirror  30  does not include the first membrane MEM 1 , the width of D 1  of each mirror element M 1  of the input mirror  30  can be easily set larger than the width D 2  of each mirror element M 2  of the output mirror  50 . Further, the output mirror  50  includes the second membrane MEM 2 . Thus, the width D 2  of each mirror element M 2  of the output mirror  50  can be decreased in order to increase a ratio of the supportive section  52   b  to the transmission portion S 2 . With this configuration, the mechanical strength of the output mirror  50  is secured. As described above, in the Fabry-Perot interferometer  10  according to the present embodiment, the FWHM of the transmission light is reduced and the mechanical strength is improved. Further, the width D 2  of each mirror element M 2  of the output mirror  50  is not limited to a predetermined range when the width D 2  of each mirror element M 2  of the output mirror  50  is smaller than the width D 1  of each mirror element M 1  of the input mirror  30 . 
     Third Embodiment 
     The following will describe a Fabry-Perot interferometer  10  according to a third embodiment of the present disclosure. Same or equivalent parts of the Fabry-Perot interferometer  10  with the foregoing embodiments will be omitted. In the present embodiment, the light may enter the Fabry-Perot interferometer  10  from any one of the first mirror  30  and the second mirror  50 . 
     As shown in  FIG. 22  and  FIG. 23 , the transmission portion S 1  of the first mirror  30  has only one mirror element M 1 , and the transmission portion S 2  of the second mirror  50  has only one mirror element M 2 . Further, the mirror element M 1  and the mirror element M 2  have the same formation pattern and the same dimension. That is, the width D 1  of the mirror element M 1  is the same with the width D 2  of the mirror element M 2 . Other parts of the Fabry-Perot interferometer  10  according to the present embodiment are similar to the Fabry-Perot interferometer  10  according to the second embodiment. 
     For example, when the second mirror  50  function as the input mirror  50  and the first mirror  30  functions as the output mirror  30  similar to the first embodiment, at least the width D 2  of the mirror element M 2  of the input mirror  50  is set larger than seven times of the maximum value of the mid-wavelength infrared range. That is, the width D 2  of the mirror element M 2  of the input mirror  50  is set larger than 70 μm (D 2 &gt;70 μm). Further, the width D 2  of the mirror element M 2  of the input mirror  50  may be set equal to or larger than ten times of the maximum value of the mid-wavelength infrared range. That is, the width D 2  of the mirror element M 2  of the input mirror  50  may be set equal to or larger than 100 μm (D 2 &gt;=100 μm). Furthermore, the width D 2  of the mirror element M 2  of the input mirror  50  may be set equal to or larger than fifteen times of the maximum value of the mid-wavelength infrared range. That is, the width D 2  of the mirror element M 2  of the input mirror  50  may be set equal to or larger than 150 μm (D 2 &gt;=150 μm). With this configuration, advantages similar to the first embodiment are provided by the Fabry-Perot interferometer  10  according to the present embodiment. 
     Further, in the present embodiment, the transmission portion S 2  of the input mirror  50  has only one mirror element M 2 . Thus, interference of light is restricted compared with a structure in which the input mirror  50  includes multiple mirror elements M 2 , each of which functions as a slit. Thus, the FWHM of the transmission light is reduced in the Fabry-Perot interferometer  10  according to the present embodiment. 
     Fourth Embodiment 
     The following will describe a Fabry-Perot interferometer  10  according to a fourth embodiment of the present disclosure. Same or equivalent parts of the Fabry-Perot interferometer  10  with the foregoing embodiments will be omitted. 
     Similar to the first embodiment, the through hole  23  is defined in the substrate  20  corresponding to the transmission portion S 1 . Different from the first embodiment, in the present embodiment, the transmission portion S 2  of the input mirror  50  has only one mirror element M 2 , and the transmission portion S 1  of the output mirror  30  has multiple mirror elements M 1 . 
     In the present embodiment, at least the width D 2  of the mirror element M 2  of the input mirror  50  is set larger than seven times of the maximum value of the mid-wavelength infrared range. That is, the width D 2  of the mirror element M 2  of the input mirror  50  is set larger than 70 μm (D 2 &gt;70 μm). Further, the width D 2  of the mirror element M 2  of the input mirror  50  may be set equal to or larger than ten times of the maximum value of the mid-wavelength infrared range. That is, the width D 2  of the mirror element M 2  of the input mirror  50  may be set equal to or larger than 100 μm (D 2 &gt;=100 μm). Furthermore, the width D 2  of the mirror element M 2  of the input mirror  50  may be set equal to or larger than fifteen times of the maximum value of the mid-wavelength infrared range. That is, the width D 2  of the mirror element M 2  of the input mirror  50  may be set equal to or larger than 150 μm (D 2 &gt;=150 μm). With the above-described configuration, advantages similar to the first embodiment are provided by the Fabry-Perot interferometer  10  according to the present embodiment. 
     In the present embodiment, the substrate  20  defines the through hole  23  corresponding to the transmission portion S 1 . Thus, the infrared lights are restricted to be absorbed by the substrate  20 . That is, a loss of the infrared lights is restricted. 
     In the present embodiment, the transmission portion S 2  of the input mirror  50  has only one mirror element M 2 . Thus, interference of light is restricted compared with a structure in which the input mirror  50  includes multiple mirror elements M 2 , each of which functions as a slit. With this configuration, the FWHM of the transmission light is reduced. 
     Further, in the present embodiment, the width D 2  of the mirror element M 2  of the input mirror  50  is set larger than the width D 1  of the mirror element M 1  of the output mirror  30 . Thus, an increase of the FWHM of the transmission light due to the diffraction is restricted. Further, the width D 1  of each mirror element M 1  of the output mirror  30  is set relatively small so that a ratio of the supportive section  32   b  to the transmission portion S 1  is increased. By this configuration, the mechanical strength of the first membrane MEM 1  is increased. Further, when the width D 1  of each mirror element M 1  of the output mirror  30  is smaller than the width D 2  of the mirror element M 2  of the input mirror  50  (D 1 &lt;D 2 ), the width D 1  is not limited to a predetermined range. 
     In the present embodiment, the second mirror  50  is referred to as the input mirror  50 , the first mirror  30  is referred to as the output mirror  30 , the transmission portion S 2  has only one mirror element M 2 , and the transmission portion S 1  has multiple mirror elements M 1 . Further, the first mirror  30  may function as the input mirror, the second mirror  50  may function as the output mirror, the transmission portion S 1  may have only one mirror element M 1 , and the transmission portion S 2  may have multiple mirror elements M 2 . 
     Fifth Embodiment 
     The following will describe a Fabry-Perot interferometer  10  according to a fifth embodiment of the present disclosure. Same or equivalent parts of the Fabry-Perot interferometer  10  with the foregoing embodiments will be omitted. 
     As shown in  FIG. 26  and  FIG. 27 , the Fabry-Perot interferometer  10  according to the present embodiment has similar configurations to the Fabry-Perot interferometer  10  according to the third embodiment. In the present embodiment, in the first mirror  30 , a supportive section  32   c , which is provided by a part of the second high-refractive layer  32 , is arranged on the first high-refractive layer  31 . Thus, the floating section  32   a  of the second high-refractive layer  32  is supported by the supportive section  32   c  above the first high-refractive layer  31 . The supportive section  32   c  is in contact with the first high-refractive layer  31  in an overlapped manner within the transmission portion S 1  of the first mirror  30 . Similarly, in the second mirror  50 , a supportive section  52   c , which is provided by a part of the second high-refractive layer  52 , is arranged on the first high-refractive layer  51 . Thus, the floating section  52   a  of the second high-refractive layer  52  is supported by the supportive section  52   c  above the first high-refractive layer  51 . The supportive section  52   c  is in contact with the first high-refractive layer  51  in an overlapped manner within transmission portion S 2  of the second mirror  50 . In the present embodiment, the supportive section  32   c ,  52   c  does not define a shape of the mirror element M 1 , M 2 . Specifically, the supportive section  32   c  does not divide the mirror element M 1  into multiple mirror elements M 1 , and the supportive section  52   c  does not divide the mirror element M 2  into multiple mirror elements M 2 . In the present embodiment, as shown in  FIG. 26 ,  FIG. 27 , the supportive sections  32   c  is arranged in a central portion of the mirror element M 1  having a circular shape, and the supportive section  52   c  is arranged in a central portion of the mirror element M 2  having a circular shape. Thus, the mirror element M 1  and the mirror element M 2  are maintained as a single mirror. With this configuration, a mechanical strength of the mirror element M 1 , M 2  improved. 
     In the present embodiment, the second mirror  50  function as the input mirror  50  and the first mirror  30  functions as the output mirror  30  similar to the first embodiment. Then, at least the width D 2  of the mirror element M 2  of the input mirror  50  is set larger than seven times of the maximum value of the mid-wavelength infrared range. That is, the width D 2  of the mirror element M 2  of the input mirror  50  is set larger than 70 μm (D 2 &gt;70 μm). Further, the width D 2  of the mirror element M 2  of the input mirror  50  may be set equal to or larger than ten times of the maximum value of the mid-wavelength infrared range. That is, the width D 2  of the mirror element M 2  of the input mirror  50  may be set equal to or larger than 100 μm (D 2 &gt;=100 μm). Furthermore, the width D 2  of the mirror element M 2  of the input mirror  50  may be set equal to or larger than fifteen times of the maximum value of the mid-wavelength infrared range. That is, the width D 2  of the mirror element M 2  of the input mirror  50  may be set equal to or larger than 150 μm (D 2 &gt;=150 μm). With this configuration, advantages similar to the first embodiment are provided by the Fabry-Perot interferometer  10  according to the present embodiment. 
     In the present embodiment, the transmission portion S 2  of the input mirror  50  has only one mirror element M 2 . Thus, interference of light is restricted compared with a structure in which the input mirror  50  includes multiple mirror elements M 2 , each of which functions as a slit. By this configuration, the FWHM of the transmission light is reduced. 
     Further, the mirror element M 1 , M 2  may include more than one supportive sections  32   c ,  52   c . In the present embodiment, the supportive sections  32   c ,  52   c  is provided by a part of the second high-refractive layer  32 ,  52 . Further, the supportive sections  32   c ,  52   c  may be provided by a separate component other than the part of the second high-refractive layer  32 ,  52 . 
     Other Embodiments 
     In the present embodiment, the substrate  20  includes the semiconductor substrate  21  and the insulation film  22  arranged on a surface of the semiconductor substrate  21 . Further, an insulated substrate, such as a glass substrate, may be employed as the substrate  20 . When the substrate  20  is provided by the glass substrate, the insulation film  22  is not necessary. 
     In the present embodiment, the second mirror  50  is supported via the spacer  40  above the first mirror  30 . Further, a part of the second mirror  50  that is arranged at an outer side than the second membrane MEM 2  (bridge part  54 ) may be extended and contacted with the first mirror  30  in order to support the second membrane MEM 2 . In this configuration, the spacer  40  is not additionally necessary. In this structure, the spacer  40  is arranged on a part of the high-refractive layer  32  of the first mirror  30  corresponding to the second membrane MEM 2 . Then, the second mirror  50  is arranged such that the second mirror  50  covers the spacer  40 . Then, the whole spacer  40  is removed by performing etching so that the gap AG is defined. 
     In the present embodiment, the distance between the mirror element M 1  and the mirror element M 2  is changed based on the electrostatic force generated between the electrodes  36 ,  56 . Further, a piezoelectric effect may be used instead of the electrostatic force. For example, the distance between the mirror element M 1  and the mirror element M 2  may be changed by extending or contracting the spacer  40 . Further, the mirrors  30 ,  50  may employ a structure that is deformable by heat, such as a bimorph structure, so that the distance between the mirror element M 1  and the mirror element M 2  is changed. Further, the distance between the mirror element M 1  and the mirror element M 2  may be changed by an electromagnetic force. 
     While only the selected exemplary embodiments have been chosen to illustrate the present disclosure, it will be apparent to those skilled in the art from this disclosure that various changes and modifications can be made therein without departing from the scope of the disclosure as defined in the appended claims. Furthermore, the foregoing description of the exemplary embodiments according to the present disclosure is provided for illustration only, and not for the purpose of limiting the disclosure as defined by the appended claims and their equivalents.