Patent Publication Number: US-2021181103-A1

Title: Optical densitometer and optical waveguide

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     The present application claims priority to and the benefit of Japanese Patent Application No. 2019-224937 filed Dec. 12, 2019, Japanese Patent Application No. 2019-224818 filed Dec. 12, 2019, and Japanese Patent Application No. 2019-224941 filed Dec. 12, 2019, the entire contents of which are incorporated herein by reference. 
     TECHNICAL FIELD 
     The present disclosure relates to an optical densitometer and an optical waveguide. 
     BACKGROUND 
     When the refractive index of a material forming a structure, such as a thin film formed by crystals or the like, is greater than the refractive index of the material outside the structure, light propagating through the structure progresses while repeatedly undergoing total reflection at the boundary between the structure and the outside of the structure. When the light propagating through the structure is totally reflected at the boundary, the light extends to the outside, which has a smaller refractive index. Such an extension is referred to as an evanescent wave (see  FIG. 14 ). An evanescent wave EW may be absorbed by a substance  52  adjacent to the structure  51  while light L is propagating. This enables detection and identification of the substance  52  in contact with the structure  51  based on a change in the intensity of the light L propagating through the structure  51 . An analytical technique employing the above-described principle of evanescent waves EW is referred to as an attenuated total reflection (ATR) technique and is used to analyze the chemical composition of the substance  52 , for example. Typically, infrared radiation is used as the light to be propagated. Substances have the property of selectively absorbing infrared radiation of particular wavelengths. A substance of interest can therefore be analyzed or sensed by causing infrared radiation corresponding to the absorption spectrum of the substance to be propagated. 
     Patent literature (PTL) 1 proposes an optical waveguide sensor in which the ATR technique is applied to a sensor. This optical waveguide sensor has a core layer formed on a substrate, allows light to pass through the core layer, and uses an evanescent wave to detect a substance in contact with the core layer. 
     CITATION LIST 
     Patent Literature 
     PTL 1: JP2005-300212A 
     SUMMARY 
     A sensor employing the ATR technique requires a location for introducing light from a light source into a core layer of an optical waveguide, as well as a location for extracting light from the core layer of the optical waveguide towards a photodetector. A diffraction grating portion for bending the optical axis of the light is therefore often provided as a part of the core layer in each of the location for introducing light from the light source into the core layer of the optical waveguide and the location for extracting the light from the core layer of the optical waveguide towards the photodetector. Such diffraction grating portions are required to be structured so as to suit the sizes and shapes of the light source and the photodetector in view of efficient light inputs to the optical waveguide or efficient light outputs from the optical waveguide. 
     Further, in a diffraction grating portion for extracting light from the core layer, as illustrated in  FIG. 15A , when light propagating through the core layer is diffracted toward the external side D 1 , the diffracted light has light component La that is bent from a diffraction grating region  331  toward the external side D 1  (the surface side in the thickness direction), as well as light component Lb that is bent toward the substrate side D 2  in the thickness direction of the optical waveguide. After the light component Lb thus bent toward the substrate side D 2  reaches the boundary with (surface of) the substrate  39 , it may be reflected at the boundary back to the diffraction grating region  331 . As a result, the light component Lb reflected back to the diffraction grating region  331  may interfere with the light component La extracted from the diffraction grating region  331  to the external side D 1  without being reflected, in the diffraction grating region  331 . Thus, in order to efficiently extract light from the diffraction grating region  331  to the external side D 1 , it is important to control the phase difference between the reflected light component Lb and the non-reflected light component La, in other words, to control the distance L 1  between the diffraction grating region  331  and the substrate  39  to a certain value. 
     In the meantime, in such a sensor, the light introduced into the core layer needs to extend from a light propagation portion as an evanescent wave and be absorbed by the external substance of interest, as described above. It is thus preferable to increase the propagation distance of light through the light propagation portion (propagation channel), and to cause more evanescent waves to extend, for the purpose of improving the sensitivity of a sensor. In the case where the substrate of the optical waveguide, however, is in immediate proximity to the light propagation portion, an evanescent wave extending from the light propagation portion may reach the substrate, and a part of light propagating through the light propagation portion may leak to the substrate. In order to suppress leakage of evanescent waves to the substrate to thereby improve the propagation efficiency, it is thus important to control the distance between the light propagation portion and the substrate to a certain value, as in the distance between the diffraction grating region and the substrate. 
     In such a sensor, the diffraction grating portions and the light propagation portion are provided as the core layer. The required functions, shape, size, and material of the diffraction grating portions, however, differ from the functions required for the light propagation portion. Further, it is required to design the distance between the diffraction grating region and the substrate and the distance between the light propagation portion and the substrate by taking into consideration the diffraction efficiency of the diffraction grating region and the propagation efficiency of the light propagation portion in the optical waveguide. 
     In a conventional optical waveguide, however, because a light propagation portion and a diffraction grating region are formed on a flat support layer as a single core layer on a silicon-on-insulator (SOI) substrate or the like. It is thus difficult to optimize the shape, size, and material of the diffraction grating portions independently from those of the light propagation portion. In a conventional optical waveguide, it is also difficult to optimize the distance between the light propagation portion and the substrate and the distance between the diffraction grating region and the substrate independently from each other. It has thus been difficult to fabricate a sensor provided with a diffraction grating portion and a light propagation portion both exhibiting high performances. 
     It thus would be helpful to provide an optical densitometer and an optical waveguide provided with a diffraction grating portion and a light propagation portion both exhibiting high performances as a core layer. 
     To achieve the above, an aspect of the present disclosure is an optical densitometer for measuring a density of a gas or liquid of interest, the optical densitometer comprising: 
     a light source capable of introducing light into a core layer; 
     a detector capable of receiving the light that has propagated through the core layer; and 
     an optical waveguide, the optical waveguide comprising:
         a substrate; and   the core layer comprising a light propagation portion capable of propagating the light in an extending direction of the light propagation portion, and a diffraction grating portion,       

     the diffraction grating portion comprising a diffraction grating region and an extension region connected to the diffraction grating region, and 
     a first optical coupling region included in the extension region and a second optical coupling region included in the light propagation portion being optically coupled with respect to the light propagating through the core layer. 
     Further, to achieve the above, another aspect of the present disclosure is an optical waveguide for use in an optical densitometer for measuring a density of a gas or liquid of interest, the optical waveguide comprising: 
     a substrate; and 
     a core layer comprising a light propagation portion capable of propagating light in an extending direction of the light propagation portion, and a diffraction grating portion, 
     the diffraction grating portion comprising a diffraction grating region and an extension region connected to the diffraction grating region, and 
     a first optical coupling region included in the extension region and a second optical coupling region included in the light propagation portion being optically coupled with respect to the light propagating through the core layer. 
     The present disclosure can provide an optical densitometer and an optical waveguide provided with a diffraction grating portion and a light propagation portion both exhibiting high performances as a core layer. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       In the accompanying drawings: 
         FIG. 1  illustrates the schematic configuration of an optical densitometer and an optical waveguide according to first and second embodiments of the present disclosure; 
         FIG. 2  is a schematic plan view illustrating the optical waveguide in  FIG. 1  from a light source side or a photodetector side; 
         FIG. 3A  is a schematic plan view illustrating a part of a first diffraction grating portion and a propagation channel of the optical waveguide in  FIG. 1 ; 
         FIG. 3B  is a cross-sectional view illustrating a cross section along the line A-A; 
         FIG. 4  is a cross-sectional view partially illustrating an optical waveguide main portion to illustrate a method of manufacturing the optical waveguide used in the optical densitometer according to the first and second embodiments of the present disclosure; 
         FIG. 5  is a cross-sectional view partially illustrating the optical waveguide main portion to illustrate the method of manufacturing the optical waveguide used in the optical densitometer according to the first and second embodiments of the present disclosure; 
         FIG. 6  is a cross-sectional view partially illustrating the optical waveguide main portion to illustrate the method of manufacturing the optical waveguide used in the optical densitometer according to the first and second embodiments of the present disclosure; 
         FIG. 7  is a cross-sectional view partially illustrating the optical waveguide main portion to illustrate the method of manufacturing the optical waveguide used in the optical densitometer according to the first and second embodiments of the present disclosure; 
         FIG. 8  is a cross-sectional view partially illustrating the optical waveguide main portion to illustrate the method of manufacturing the optical waveguide used in the optical densitometer according to the first and second embodiments of the present disclosure; 
         FIG. 9  is a cross-sectional view partially illustrating the optical waveguide main portion to illustrate the method of manufacturing the optical waveguide used in the optical densitometer according to the first and second embodiments of the present disclosure; 
         FIG. 10  is a cross-sectional view partially illustrating the optical waveguide main portion to illustrate the method of manufacturing the optical waveguide used in the optical densitometer according to the first and second embodiments of the present disclosure; 
         FIG. 11  is a cross-sectional view partially illustrating the optical waveguide main portion to illustrate the method of manufacturing the optical waveguide used in the optical densitometer according to the first and second embodiments of the present disclosure; 
         FIG. 12  is a schematic plan view illustrating an optical waveguide used in an optical densitometer according to a third embodiment of the present disclosure from a light source side or a photodetector side; 
         FIG. 13A  is a schematic plan view illustrating a part of a first diffraction grating portion and a propagation channel of the optical waveguide in  FIG. 12 ; 
         FIG. 13B  is a cross-sectional view illustrating a cross section along the line B-B; 
         FIG. 14  illustrates an evanescent wave of light propagating through an optical waveguide; and 
         FIGS. 15A and 15B  are diagrams for illustrating interference of light that may occur in a diffraction grating region. 
     
    
    
     DETAILED DESCRIPTION 
     Embodiments of the present disclosure are now described, but the following embodiments do not limit the claimed subject matter. Furthermore, not all combinations of features described in the embodiments are necessarily essential to the solution to the problem of the present disclosure. 
     &lt;Optical Densitometer&gt; 
     An optical densitometer according to an embodiment of the present disclosure includes an optical waveguide, described below, according to an embodiment of the present disclosure, a light source capable of introducing light into a core layer, and a detector capable of receiving light propagating through the core layer. 
     The elements of the optical densitometer are described below with references to an example. 
     &lt;Optical Waveguide&gt; 
     An optical waveguide according to an embodiment of the present disclosure is an optical waveguide for use in an optical densitometer for measuring the density of a gas or liquid of interest. The optical waveguide includes a substrate, and a core layer including a light propagation portion through which light propagates in an extending direction of the light propagation portion, and a diffraction grating portion. Further, in the optical waveguide, the diffraction grating portion includes a diffraction grating region and an extension region connected to the diffraction grating region, and a first optical coupling region included in the extension region and a second optical coupling region included in the light propagation portion are optically coupled with respect to the light propagating through the core layer. Further, at least a portion of the diffraction grating portion may be spatially separated from the light propagation portion. 
     The optical waveguide according to the present embodiment enables the diffraction grating portion and the light propagation portion as the core layer to be formed in sizes and shapes, and from materials suited to their respective functions. In this configuration, the first optical coupling region included in the extension region and the second optical coupling region included in the light propagation portion are optically coupled with respect to the light propagating through the core layer. Accordingly, light introduced from the light source by the diffraction grating portion can be guided from the diffraction grating portion to the light propagation portion, or the light propagating through the light propagation portion can be introduced from the light propagation portion to the diffraction grating portion. In the first optical coupling region and the second optical coupling region, light propagating through the core layer optically couples from the first optical coupling region to the second optical coupling region, or from the second optical coupling region to the first optical coupling region. 
     In the present embodiment, the extending direction refers to at least one direction in which an object extends. For example, in a three-dimensional structure, the path of shortest distance from one end to another end (or any one point to any other point) while in contact with the three-dimensional structure is the extending direction. Alternatively, the direction that minimizes the change in cross-sectional area from one end to another end (or any one point to any other point) may be the extending direction. The extending direction need not be linear and may be curved. 
     Further, in the present embodiment, the extension region includes a portion which extends in the extending direction of the second optical coupling region which is included in the light propagation portion capable of propagating light. Specifically, one end thereof is connected to the diffraction grating region and the other end (end portion) is terminated without being connected to another core layer. The extension region connected to the diffraction grating region refers to the state in which the extension region and the diffraction grating region are formed of the same material as at least one of the materials of the layers forming the diffraction grating region, and is continuous with the at least one layer without being interrupted. The extension region is made from the material of that connecting portion inside the extension region. 
     Further, in the present embodiment, at least a portion of the diffraction grating portion is spatially separated from the light propagation portion means that a material (including the air) having a relatively lower refractive index than that of the core layer is interposed between the at least a portion of the diffraction grating portion and the light propagation portion. 
     Further, in the present embodiment, the diffraction grating portion including the extension region and the light propagation portion can be formed from any material. The diffraction grating portion and the light propagation portion may be formed from the same or different materials, but it is often preferable that they are formed from different materials. The reason is that in cases such as when the portion of the core layer separated from the diffraction grating portion is formed as a light propagation portion, the functions required for the diffraction grating portion differ from the functions required for the light propagation portion. Hence, forming these components from different materials enables materials to be chosen to suit the function required for each component and also allows the optical waveguide of the present embodiment to be manufactured more easily. 
     In the present disclosure, different materials refer not only to materials containing different elements, but also to materials in different crystalline state of the same element. This is because, in optical terms, light propagation phenomena differ if the crystal state differs, even if the constituent elements of the materials are the same. 
     In the present embodiment, the first optical coupling region included in the extension region and the second optical coupling region included in the light propagation portion are optically coupled with respect to light propagating through the core layer means that, when the light which has propagated to the extension region or the light propagation portion proceeds from the first optical coupling region to the second optical coupling region or from the second optical coupling region to the first optical coupling region, the light transitions to one to the other by using an evanescent wave or by causing the first optical coupling region and the second optical coupling region to come in direct contact with one another. 
     In the present embodiment, how the coupling of the first optical coupling region included in the extension region and the second optical coupling region included in the light propagation portion is established is not limited as long as they are optically coupled. Nevertheless, it is preferable that the propagation direction of the light propagating through the core layer does not substantially changes before and after the transition from the first optical coupling region to the second optical coupling region, and/or before and after the transition from the second optical coupling region to the first optical coupling region. In other words, in the present embodiment, the first optical coupling region and the second optical coupling region preferably function as a directional coupler for light propagating through the core layer. The first optical coupling region and the second optical coupling region functioning as a directional coupler can establish an ideal optical coupling with an efficiency of 100%. The first optical coupling region and the second optical coupling region functioning as a directional coupler refers to an optical coupled state in which light transitions from one to the other using an evanescent wave such that the propagation direction of light does not change before and after the transition. 
     In the present embodiment, the at least a portion of the diffraction grating portion may take any positional relationship with the light propagation portion as long as the first optical coupling region of the extension region and the second optical coupling region of the light propagation portion are optically coupled. For example, the extension region and the light propagation portion may be disposed in the optical waveguide so as to be adjacent to each other in the direction orthogonal to the extending direction of the light propagation portion (second optical coupling region). Alternatively, both at least a portion of the extension region and at least a portion of the light propagation portion may be disposed so as to be included in one plane orthogonal to the extending direction of the at least a portion of the light propagation portion. Further, in the case where the extension region and the light propagation portion are disposed so as to be adjacent to each other in the direction orthogonal to the extending direction of the light propagation portion, they may be disposed in the optical waveguide so as to be in the same position in the thickness direction, or so as to be in different positions in the thickness direction. 
     Among them, in the present embodiment, it is preferable the extension region and the light propagation portion are disposed so as to be adjacent to each other in the direction orthogonal to the extending direction of the light propagation portion, and to be separated in different positions in the thickness direction. 
     In the present embodiment, by separating the at least a portion of the diffraction grating portion and the light propagation portion from each other in the thickness direction, the diffraction grating portion and the light propagation portion having different functions will be located in different layers. In this structure, the diffraction grating portion and the light propagation portion can be efficiently subjected to processing suited to their respective functions. Further, it is possible to save the area in an efficient manner by grade-separating the diffraction grating portion and the light propagation portion. Further, even in the case where the at least a portion of the diffraction grating portion and the light propagation portion are provided so as to be separated from each other in the plane direction and to be disposed at the same portion in the thickness direction, the diffraction grating portion including the diffraction grating region and the extension region and the light propagation portion can be formed in different layers. This enables the diffraction grating portion and the light propagation portion to be subjected to processing suited to their respective functions. 
     Further, in the present embodiment, the distance between the first optical coupling region and the second optical coupling region is preferably equal to or smaller than the distance given by the following Expression (1): 
     
       
         
           
             
               
                 
                   
                     3 
                      
                     
                       λ 
                       0 
                     
                   
                   
                     2 
                      
                     π 
                      
                     
                       
                         
                           n 
                           coup 
                           2 
                         
                         - 
                         
                           n 
                           mid 
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   Expression 
                    
                   
                       
                   
                    
                   
                     ( 
                     1 
                     ) 
                   
                 
               
             
           
         
       
     
     where λ 0  represents the average wavelength, in vacuum, of light propagating through the core layer, n coup  represents the refractive index of the material forming the first optical coupling region or the second optical coupling region, and n mid  represents the refractive index of a material present in the portion sandwiched between the first optical coupling region and the second optical coupling region. In the case where a plurality of materials are present in the portion sandwiched between the first optical coupling region and the second optical coupling region, the largest refractive index among the refractive indices of the plurality of materials is used as n mid . This distance specifies a value three times the commonly-defined extending distance of evanescent light. The extending distance of the evanescent light refers to the distance, from the surface of the portion of the core layer in the thickness direction, of the position where the energy of light diminishes to 1/e from the energy value at the surface of the portion of the core layer. Therefore, the distance defined herein indicates the distance, from the surface of the portion of the core layer, of the position where the energy of light diminishes to (1/e) 3  or less from the energy value at the surface of the portion of the core layer. A distance between the first optical coupling region and the second optical coupling region of equal to or smaller than the distance given by above Expression (1) enables the first optical coupling region and the second optical coupling region to be optically coupled in no small extent. As the distance between the first optical coupling region and the second optical coupling region reduces, they can be coupled efficiently with a smaller area. 
     Note that the distance between the first optical coupling region and the second optical coupling region refers to the shortest distance among distances from points at the outer surface of the first optical coupling region facing the second optical coupling region, to the outer surface of the second optical coupling region. The lower limit of the distance between the first optical coupling region and the second optical coupling region is not particularly limited, and the first optical coupling region and the second optical coupling region may be in contact with each other. In the case where the first optical coupling region and the second optical coupling region are in direct contact with each other, n mid  cannot be defined. In this case, the distance between the first optical coupling region and the second optical coupling region is 0 μm, which is regarded to be included in the range of equal to or smaller than the distance given by the above Expression (1). 
     Further, the distance between the first optical coupling region and the second optical coupling region is preferably 0.7 μm or smaller. For example, in an optical densitometer for detecting CO 2 , which is a gas typically present in the environment, infrared radiation with a wavelength of approximately 4.3 μm in vacuum is typically used as the light to propagate through the core layer. In this case, the most common combination of materials forming the optical waveguide is a combination of silicon for the core layer and a silicon oxide film for the portion sandwiched between the first optical coupling region and the second optical coupling region. In this case, n coup  is about 3.4, n mid  is about 1.4, giving the value by the above Expression (1) of about 0.66 μm. In other words, the distance between the first optical coupling region and the second optical coupling region is 0.7 μm or smaller. For a more efficient optical coupling between the first optical coupling region and the second optical coupling region, the distance between the first optical coupling region and the second optical coupling region may be 0.4 μm or smaller, more preferably 0.2 μm or smaller, and even more preferably 0.1 μm or smaller. Alternatively, a silicon nitride film or any other material may be used as the material forming the portion sandwiched between the first optical coupling region and the second optical coupling region. In the case where a silicon nitride film is used, for example, n mid  is about 2.0. 
     In the present embodiment, the refractive indices of the first optical coupling region and the second optical coupling region may have any values. Nevertheless, the equivalent refractive index of the first optical coupling region is preferably from 0.7 times to 1.3 times, more preferably from 0.8 times to 1.2 times, and even more preferably from 0.9 times to 1.1 times of the equivalent refractive index of the second optical coupling region, with respect to the light propagating through the core layer. When the equivalent refractive index of the first optical coupling region is from 0.7 times to 1.3 times of the equivalent refractive index of the second optical coupling region with respect to the light propagating through the core layer, the efficiency of the optical coupling improves as their equivalent refractive indices are closer. 
     Additionally, in the present embodiment, the refractive index of the material forming the first optical coupling region is preferably from 0.9 times to 1.1 times and more preferably from 0.95 times to 1.05 times of the refractive index of the material forming the second optical coupling region. When the refractive index of the material forming the first optical coupling region is from 0.9 times to 1.1 times of the refractive index of the material forming the second optical coupling region, the equivalent refractive index of the first optical coupling region becomes more likely to match the equivalent refractive index of the second optical coupling region with respect to the light propagating through the core layer as the refractive index of the material forming the first optical coupling region is closer to that of the material forming the second optical coupling region. This improves the efficiency of the optical coupling. 
     In the present embodiment, the film thickness of the first optical coupling region is preferably from 0.7 times to 1.3 times, more preferably from 0.8 times to 1.2 times, and even more preferably from 0.9 times to 1.1 times of the film thickness of the second optical coupling region. When the film thickness of the first optical coupling region is from 0.7 times to 1.3 times of the film thickness of the second optical coupling region, the equivalent refractive index of the first optical coupling region becomes more likely to match the equivalent refractive index of the second optical coupling region with respect to the light propagating through the core layer as the film thickness of the first optical coupling region is closer to that of the second optical coupling region. This improves the efficiency of the optical coupling. 
     In the present embodiment, the film thickness of the first optical coupling region and film thickness of the second optical coupling region refer to the respective film thicknesses of the first optical coupling region and the second optical coupling region in the region with the smallest distance between the first optical coupling region and the second optical coupling region in the case where the film thickness of the first optical coupling region varies in the first optical coupling region or the film thickness of the second optical coupling region varies in the second optical coupling region. 
     In the present embodiment, the width of the first optical coupling region is preferably from 0.7 times to 1.3 times, more preferably from 0.8 times to 1.2 times, and even more preferably from 0.9 times to 1.1 times of the width of the second optical coupling region. When the width of the first optical coupling region is from 0.7 times to 1.3 times of the width of the second optical coupling region, the equivalent refractive index of the first optical coupling region becomes more likely to match the equivalent refractive index of the second optical coupling region with respect to the light propagating through the core layer as the width of the first optical coupling region is closer to that of the second optical coupling region. This improves the efficiency of the optical coupling. 
     In the present embodiment, the width of the first optical coupling region and width of the second optical coupling region refer to the respective widths of the first optical coupling region and the second optical coupling region in the region with the smallest distance between the first optical coupling region and the second optical coupling region in the case where the width of the first optical coupling region varies in the first optical coupling region or the width of the second optical coupling region varies in the second optical coupling region. 
     In the present embodiment, preferably, the extension region is made from at least one of the materials forming the diffraction grating region, and is continuously connected to the diffraction grating region. Such a structure can prevent unintentional loss of light inside the diffraction grating portion. 
     Further, in the present embodiment, at least a portion of the light propagation portion is separated from the extension region preferably at a distance of greater than the distance between the first optical coupling region and the second optical coupling region, and more preferably at a distance greater than the distance given by the following Expression (2) or a distance greater than 0.7 μm: 
     
       
         
           
             
               
                 
                   
                     3 
                      
                     
                       λ 
                       0 
                     
                   
                   
                     2 
                      
                     π 
                      
                     
                       
                         
                           n 
                           pro 
                           2 
                         
                         - 
                         
                           n 
                           gap 
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   Expression 
                    
                   
                       
                   
                    
                   
                     ( 
                     2 
                     ) 
                   
                 
               
             
           
         
       
     
     where λ 0  represents the average wavelength, in vacuum, of light propagating through the core layer, n pro  represents the refractive index of the material forming the light propagation portion or the extension region, and n gap  is the refractive index of the material present in the portion sandwiched between the at least a portion of the light propagation portion and the extension region. 
     If the light propagation portion is in close proximity to the extension region except in the second optical coupling region, unintentional optical coupling occurs between the extension region and the light propagation portion. This unintentional optical coupling causes a transition from the extension region to the light propagation portion or a transition from the light propagation portion to the extension region, which results in loss of light. Thus, when at least a portion of the light propagation portion is separated from the extension region at a distance greater than the distance between the first optical coupling region and the second optical coupling region, unintentional optical coupling between the light propagation portion and the extension region is less likely to occur. Further, when the at least a portion of the light propagation portion is separated from the extension region at a distance greater than the distance given by Equation (2) or a distance greater than 0.7 μm, unintentionally optical coupling between the light propagation portion and the extension region is even less likely to occur. The reason why the distance with a smaller likelihood of optical coupling is specified by the Expression (2) is similar to the reason why the Expression (1) specifies the distance between the first optical coupling region and the second optical coupling region, and a detailed description thereof is omitted. The distance between the at least a portion of the light propagation portion and the extension region is defined as the shortest distance among distances between the outer surface of the at least a portion of the light propagation portion and the outer surface of the extension region. 
     Further, in the present embodiment, at least one of the light propagation portion and the extension region may include an end portion, and the distance between the end portion of the light propagation portion and the diffraction grating portion and/or the distance between the end portion of the extension region and the light propagation portion are preferably greater than the distance given by Expression (2) or greater than 0.7 μm. Here, n gap  shall be replaced with the refractive index of the material present in the portion sandwiched between the end portion of the light propagation portion and the diffraction grating portion, or the material present in the portion sandwiched between the end portion of the extension region and the light propagation portion. In the case where a plurality of materials are present in the portion sandwiched between the end portion of the light propagation portion and the diffraction grating portion or the portion sandwiched between the end portion of the extension region and the light propagation portion, the largest refractive index among the refractive indices of the plurality of materials is used as n gap . 
     If the end portion of the light propagation portion is disposed in the vicinity of the diffraction grating portion, light which has propagated through the diffraction grating portion would encounter an abrupt change in the equivalent refractive index of the diffraction grating portion while it passes through the vicinity of the end portion of the light propagation portion, resulting in disturbances, such as reflection and scattering, of the light propagating through the diffraction grating portion. Similarly, if the end portion of the extension region is disposed in the vicinity of the light propagation portion, light which has propagated through the light propagation portion would encounter an abrupt change in the equivalent refractive index of the light propagation portion while it passes through the vicinity of the end portion of the extension region, resulting in disturbances, such as reflection and scattering, of the propagating light. Because these disturbances cause unintentional losses of the propagating light, the end portion of the light propagation portion and the diffraction grating portion, and/or the end portion of the extension region and the light propagation portion are preferably separated from each other at a certain distance. When the distance defined by Expression (2) or the distance of 0.7 μm is ensured, an evanescent wave of light propagating through the core layer of one of the light propagation portion and the diffraction grating portion is less likely to optically couple to the core layer of the other. The distance between the end portion of the light propagation portion and the diffraction grating portion is defined as the shortest distance among distances between the outer surface of the end portion of the light propagation portion and the outer surface of the diffraction grating portion. The distance between the end portion of the extension region and the light propagation portion is defined as the shortest distance among distances between the outer surface of the end portion of the extension region and the outer surface of the light propagation portion. 
     Further, in the present embodiment, in the region where the diffraction grating portion and the light propagation portion overlap in plan view, a first distance modification region may be provided in which the distance between the diffraction grating portion and the light propagation portion reduces in the direction approaching from the diffraction grating region toward the first optical coupling region. Further, the first distance modification region may have a portion in which the distance from the light propagation portion gradually changes from a distance greater than the distance given by Expression (2) or a distance greater than 0.7 μm, to a distance equal to or smaller than the distance given by Expression (1) or a distance of 0.7 μm or smaller. Here, n gap  shall be replaced with the refractive index of the material present in the portion sandwiched between the light propagation portion and the at least a portion of the diffraction grating portion. In the case where a plurality of materials are present in the portion sandwiched between the light propagation portion and the at least a portion of the diffraction grating portion, the largest refractive index among the refractive indices of the plurality of materials is used as n gap . Further, the maximum angle of the first distance modification region relative to the light propagation portion is preferably 45° or less. 
     In the region where the diffraction grating portion and the light propagation portion overlap in plan view, the first distance modification region in which the distance between the diffraction grating portion and the light propagation portion reduces in the direction approaching from the diffraction grating region toward the first optical coupling region provides a structure where the at least a portion of the diffraction grating portion approaches the light propagation portion gradually. This prevents propagating light from encountering an abrupt change in the equivalent refractive index of the at least a portion of the diffraction grating portion and the light propagation portion, thereby achieving an efficient optical coupling between the diffraction grating portion and the light propagation portion via the first optical coupling region and the second optical coupling region. Further, because the distance between the at least a portion of the diffraction grating portion and the light propagation portion gradually changes in the first distance modification region from a distance greater than the distance given by Expression (2) or a distance greater than 0.7 μm, to a distance equal to or smaller than the distance given by Expression (1) or a distance of 0.7 μm or smaller, an efficient optical coupling can be established between the first optical coupling region and the second optical coupling region while preventing unintentional optical coupling except in the first optical coupling region and the second optical coupling region. The distance between the at least a portion of the diffraction grating portion and the light propagation portion in the first distance modification region refers to the shortest distance among distances from points at the outer surface of the diffraction grating portion to the outer surface of the light propagation portion, in the first distance modification region. 
     Further, for achieving a reduction in loss of light in the first distance modification region, the maximum angle of the first distance modification region relative to the light propagation portion is preferably 45° or less and is more preferably 30° or less. If this angle is too small, on the other hand, the first distance modification region needs to be large (or long) for ensuring an appropriate distance between the at least a portion of the diffraction grating portion and the light propagation portion. Thus, the maximum angle of the first distance modification region relative to the light propagation portion is preferably 10° or more and more preferably 15° or more. 
     Further, in the optical waveguide, the substrate and the core layer may be separated from each other, and the distance L 1  between the diffraction grating region and the substrate may differ from the distance L 2  between the light propagation portion and the substrate. 
     In a conventional optical waveguide in which the distance L 1  between the diffraction grating region and the substrate equals the distance L 2  between the light propagation portion and the substrate, the optical waveguide is difficult to be designed to suppress leakage of an evanescent wave extending from the light propagation portion to the substrate while improving the diffraction efficiency of light in the diffraction grating region. According to the optical waveguide according to the present embodiment, the substrate and the core layer are separated from each other, and the distance L 1  between the diffraction grating region and the substrate differs from the distance L 2  between the light propagation portion and the substrate. It is thus possible to improve both the diffraction efficiency of light in the diffraction grating region and the propagation efficiency in the light propagation portion. Further, the distance L 1  between the diffraction grating region and the substrate more preferably differs from the distance L 2  between the light propagation portion and the substrate throughout the diffraction grating region. 
     Although the present embodiment is structured so that the first optical coupling region included in the extension region and the second optical coupling region included in the light propagation portion are optically coupled with respect to the light propagating through the core layer, the first optical coupling region and the second optical coupling region are not essential for controlling the distance L 1  between the diffraction grating region and the substrate and the distance L 2  between the light propagation portion and the substrate to differ from each other. Accordingly, the diffraction grating portion and the light propagation portion may be continuous so that no boundary can be distinguishable between the diffraction grating portion and the light propagation portion, as long as the distance L 1  between the diffraction grating region and the substrate differs from the distance L 2  between the light propagation portion and the substrate. 
     Further, in the present embodiment, the substrate and the core layer are separated means that a material (including the air) having a relatively lower refractive index than that of the core layer is interposed between the substrate and the core layer. 
     Further, in the present embodiment, the distance L 1  between the diffraction grating region and the substrate refers to the length, measured in the thickness direction, from the surface of the diffraction grating region on the substrate side in the thickness direction, to the surface of the substrate on the diffraction grating region side in the thickness direction. The distance L 2  between the light propagation portion and the substrate refers to the length, measured in the thickness direction, from the surface of the light propagation portion on the substrate side in the thickness direction, to the surface of the substrate on the light propagation portion side in the thickness direction. 
     Further, in the present embodiment, a support layer for supporting the core layer is preferably provided between the substrate and the core layer. The optical waveguide provided with the supporting layer can effectively separate the substrate and the core layer from each other. 
     In the present embodiment, the distance L 2  between the light propagation portion and the substrate is preferably equal to or greater than a distance given by the following Expression (3): 
     
       
         
           
             
               
                 
                   
                     6 
                      
                     
                       λ 
                       0 
                     
                   
                   
                     2 
                      
                     π 
                      
                     
                       
                         
                           n 
                           pro 
                           2 
                         
                         - 
                         
                           n 
                           
                             L 
                              
                             
                                 
                             
                              
                             2 
                           
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   Expression 
                    
                   
                       
                   
                    
                   
                     ( 
                     3 
                     ) 
                   
                 
               
             
           
         
       
     
     where λ 0  represents the average wavelength, in vacuum, of light propagating through the core layer, n pro  represents the refractive index of the material forming the light propagation portion, and n L2  represents the refractive index of the material present in the portion sandwiched between the light propagation portion and the substrate. In the case where a plurality of materials are present in the portion sandwiched between the light propagation portion and the substrate, the largest refractive index among the refractive indices of the plurality of materials is used as n L2 . This distance specifies a value six times the aforementioned extending distance of evanescent light. Therefore, the distance as specified herein specifies the distance, from the surface of the portion of the core layer, of the position where the energy of light diminishes to (1/e) 6  or less from the energy value at the surface of the portion of the core layer. The aforementioned maximum value of the distance between the first optical coupling region and the second optical coupling region has been specified to a value three times of the extending distance of evanescent light for achieving an optical coupling efficiently in a short distance. In contrast, the lower limit of the distance L 2  between the light propagation portion and the substrate is for preventing an optical coupling between the light propagation portion and the substrate while light propagates over a long distance, and is thus specified to a value six times of the extending distance of evanescent light. If the distance L 2  between the light propagation portion and the substrate is less than the value given by the above Expression (3), the light propagation portion and the substrate would be optically coupled relatively strongly. In a light propagation portion having a long propagation distance of several centimeters or longer, the amount of light leaking to the substrate generally tends to increase, which leads to a decrease in the propagation efficiency of the light propagation portion. By setting the distance L 2  to be equal to or greater than the value given by the above Expression (3), leakage of an evanescent wave extending from the light propagation portion to the substrate can be suppressed to a sufficiently low level, thereby further improving the propagation efficiency of the light propagation portion. 
     The distance L 2  between the light propagation portion and the substrate refers to the shortest distance among distances from points at the outer surface of the light propagation portion facing the substrate to the outer surface of the substrate. 
     The distance L 2  between the light propagation portion and the substrate is preferably 1.3 μm or greater. For example, in an optical densitometer for detecting CO 2 , which is a typical gas present in the environment, it is common to use an infrared radiation having a center wavelength of about 4.3 μm in vacuum as the light to propagate through the core layer. In this case, the most common combination of materials forming the optical waveguide is a combination of silicon for the core layer and the air for the portion sandwiched between the light propagation portion and the substrate. In this case, n pro  is about 3.4, n L2  is about 1.0, and the above Expression (3) gives a value of about 1.26 μm. Thus, 1.3 μm is the value equal to or greater than the value calculated from the above Expression (3). For more efficiently suppressing leakage of light propagating through the light propagation portion to the substrate, the distance L 2  between the light propagation portion and the substrate may be 2.0 μm or greater, more preferably 2.5 μm or greater, and even more preferably may be 3.0 μm or greater. Alternatively, in the case where a silicon oxide film is used as the material forming the portion sandwiched between the light propagation portion and the substrate, n L2  of about 1.4 is given. 
     In the present embodiment, in the case where the material forming a separation portion between the substrate and the diffraction grating region has a refractive index smaller than the refractive index of the substrate, the distance L 1  between the diffraction grating region and the substrate preferably satisfies the following Expression (4): 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             
                               ( 
                               
                                 
                                   2 
                                    
                                   m 
                                 
                                 - 
                                 1 
                               
                               ) 
                             
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                               λ 
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                             4 
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                               n 
                               gr 
                             
                              
                             
                               t 
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                           4 
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                             n 
                             
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                                
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                             n 
                             
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                             n 
                             
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                   ; 
                 
               
               
                 
                   Expression 
                    
                   
                       
                   
                    
                   
                     ( 
                     4 
                     ) 
                   
                 
               
             
           
         
       
     
     more preferably satisfies the following formula (5): 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             
                               ( 
                               
                                 
                                   2 
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                               L 
                                
                               
                                   
                               
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                   ; 
                 
               
               
                 
                   Expression 
                    
                   
                       
                   
                    
                   
                     ( 
                     5 
                     ) 
                   
                 
               
             
           
         
       
     
     and even more preferably satisfies the following formula (6) 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             
                               ( 
                               
                                 
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                   , 
                 
               
               
                 
                   Expression 
                    
                   
                       
                   
                    
                   
                     ( 
                     6 
                     ) 
                   
                 
               
             
           
         
       
     
     where λ 0  represents the average wavelength, in vacuum, of light propagating through the core layer, n L1  represents the refractive index of the material forming the separation portion between the substrate and the diffraction grating region, t g r represents the effective film thickness of the diffraction grating region of the diffraction grating portion, n gr  represents the refractive index of the material forming the diffraction grating region of the diffraction grating portion, and m is a natural number. In the case where a plurality of materials are present for forming the separation portion between the substrate and the diffraction grating region, the effective value calculated as {Σ(n L1i   2 ×A L1i )} 1/2  is used as n L1 , where n L1i  represents the refractive index of each material forming the isolation portion between the substrate and the diffraction grating region, and A L1i  represents the occupation ratio of the each material between the substrate and the diffraction grating region. Further, the effective film thickness of the diffraction grating region of the diffraction grating portion is defined as a sum of the film thickness of the core layer in recessed portions of the diffraction grating region, and a half the film thickness difference of the core layer between recessed portions and protruding portions of the diffraction grating region. Further, in the case where a plurality of materials are present for forming the diffraction grating region of the diffraction grating portion, the effective value calculated as {Σ(n gri   2 ×A gri )} 1/2  is used as n gr , where n gri  is the refractive index of each material forming the core layer in recessed portions of the diffraction grating region, and A gri  represents the occupation ratio of the each material in the recessed portions of the diffraction grating region. 
     Light returns to its original phase when it travels an optical distance equivalent to an integer multiple of the wavelength of the light. Thus, when the distance L 1  between the diffraction grating region and the substrate is an odd multiple of ¼ the wavelength, in the medium of the separation portion (between the substrate and the diffraction grating region), of light propagating through the core layer, the light that has taken one round trip of the distance L 1  (i.e., light that is reflected by the surface of the substrate) can constructively interfere with light that has not traveled by the distance L 1 . It is presumed that the phase is displaced by half the wavelength when the light is reflected by the surface of the substrate. This phenomenon is described in R. M. Emmons and D. G. Hall, “Buried-Oxide Silicon-on-Insulator Structures II: Waveguide Grating Couplers”,  IEEE JOURNAL OF QUANTUM ELECTRONICS , VOL. 28, NO. 1, January 1992, pp. 164-175, for examples, as a technique to increase the efficiency of light extraction in a diffraction grating region. For extracting light to the outside by the diffraction grating region, however, a change in phase caused by propagation of light within the core layer forming the diffraction grating region also needs be taken into consideration. When such a phase change taken into consideration, the efficiency of light extraction to the outside by the diffraction grating region is maximized (details will be described below) when the distance L 1  between the diffraction grating region and the substrate equals the distance given by the following Expression (7): 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           ( 
                           
                             
                               2 
                                
                               m 
                             
                             - 
                             1 
                           
                           ) 
                         
                          
                         
                           λ 
                           0 
                         
                       
                       - 
                       
                         4 
                          
                         
                           n 
                           gr 
                         
                          
                         
                           t 
                           gr 
                         
                       
                     
                     
                       4 
                        
                       
                         n 
                         
                           L 
                            
                           
                               
                           
                            
                           1 
                         
                       
                     
                   
                   . 
                 
               
               
                 
                   Expression 
                    
                   
                       
                   
                    
                   
                     ( 
                     7 
                     ) 
                   
                 
               
             
           
         
       
     
     In other words, the distance L 1  between the diffraction grating region and the substrate has the optimum value at a period of a half the wavelength, in the medium of the separation portion (between the substrate and the diffraction grating region) (i.e., λ 0 /n L1 ), of light propagating through the core layer. Conversely, the efficiency reduces to the lowest when the value of L 1  is the midpoint between the optimum value and the next optimum value, i.e., a distance at +/−¼ times of the wavelength, in the medium of the separation portion, of light propagating through the core layer with respect to the value given by the above Expression (7). It is thus possible to prevent the efficiency from reducing to the lowest by controlling the distance L 1  to a distance within +/− 3/16 times of the wavelength, in the medium of the separation portion, of light propagating through the core layer, with respect to the distance given by the above Expression (7). The distance L 1  is controlled more preferably to a distance within +/−⅛ times of the wavelength, in the medium of the separation portion, of light propagating through the core layer, with respect to the distance given by the above Expression (7). The distance L 1  is even more preferably controlled to a distance within +/− 1/16 times of the wavelength, in the medium of the separation portion, of light propagating through the core layer, with respect to the distance given by the above Expression (7). By controlling the distance L 1  to fall within one of the above ranges, the diffraction efficiency of light by the diffraction grating region can be maintained to a high level. Although the description has been given with reference to the case of extracting light to the outside in the diffraction grating region, the above principle is similarly applicable for cases of introducing light from the outside by the diffraction grating region. 
     Next, the elements of the optical waveguide are described below with references to examples. 
     &lt;&lt;Core Layer&gt;&gt; 
     In the present disclosure, the core layer includes a light propagation portion through which light propagates in an extending direction of the light propagation portion, and a diffraction grating portion. 
     The core layer is capable of propagating light in an extending direction of the core layer. 
     Any material may be used in the core layer. Examples of materials included in the core layer include monocrystalline silicon and polycrystalline silicon, amorphous silicon, silicon nitride, silicon germanium, germanium, gallium arsenide, indium phosphide, indium antimony, indium gallium arsenide, indium gallium phosphide, indium fluoride, diamond, sapphire, lithium niobate, and chalcogenide glass. The core layer may be a single-layered film or may be a multilayer film. 
     At least a portion of the diffraction grating portion may be formed from a material different from the material of the light propagation portion. In this case, the material forming the light propagation portion is preferably a monocrystalline material, and the material forming the diffraction grating portion preferably includes a polycrystalline or amorphous material. Most preferably, the material forming the light propagation portion is monocrystalline silicon, and the material forming the diffraction grating portion includes polycrystalline silicon or amorphous silicon. 
     By forming the respective core layers in the diffraction grating portion and the light propagation portion from different materials, the optimal core layers can be formed with the shapes, sizes, refractive indices, surface roughness, and the like, suited to the functions required for each core layer. Further, by forming the respective core layers in the diffraction grating portion and the light propagation portion from different materials, it is possible to independently process each core layer, and to process one core layer without being limited to conditions for the other core layer, which improves the degree of freedom of the processing. 
     More specifically, in the light propagation portion which is a portion for detecting the substance of interest, for example, the core layer is preferably formed so as to have a film thickness sufficiently smaller than the wavelength (the wavelength in the core layer) of light propagating through the core layer for increasing evanescent waves extending from the core layer. Additionally, a long propagation distance of light is required for improving the detection sensitivity of the substance of interest. In the light propagation portion intended to propagate light over a long distance, a monocrystalline material having a small surface roughness is preferred for the core layer for minimizing the propagation loss. The monocrystalline material which is the most common and is easy to process as the material of the core layer is monocrystalline silicon. Thus, the light propagation portion can be suitably formed at the lowest cost by forming the light propagation portion to include monocrystalline silicon. 
     On the other hand, in the diffraction grating portion which is a portion for introducing light from the light source into the core layer, the core layer preferably has a film thickness comparable to the wavelength (the wavelength in the core layer) of light propagating through the core layer for increasing the efficiency of entry of light. If the diffraction grating portion is too thin, entry of light into the core layer becomes extremely difficult. Additionally, the surface of the diffraction grating region of the diffraction grating portion is preferably provided with fine random irregularities (roughness). The reason is that the optical densitometer in the present embodiment detects the substance of interest by causing propagation of light with a wavelength band corresponding to the absorption spectrum of the substance of interest. The wavelength band of light to be propagated preferably matches a wavelength band in the absorption spectrum of the substance of interest. For example, when the diffraction grating region is formed to have a highly precise periodic pattern, light closer to single-wavelength light is selected by the diffraction grating region and the spectrum approaches a line spectrum. In other words, the selected wavelength band becomes narrower to approach a line spectrum, as the diffraction grating region is formed more precisely. The wavelength range of light absorption by a substance, however, has a certain width, and is not a strictly single wavelength. For example, a representative absorption wavelength of CO 2 , which is a gas present in the environment, is distributed over a relatively wide range of approximately 4.20 μm to 4.35 μm. In other words, if light is excessively selected to the point of a strictly single wavelength, a wavelength effective for a density measurement is wasted. This is not preferable for an optical densitometer. In particular, the optical densitometer according to the present embodiment, as will be described later, can use an incoherent light source such as an LED as a light source. From the viewpoint of effectively utilizing light having a certain wavelength range (wavelength band) from an incoherent light source, the wavelength band selected by the diffraction grating region preferably has a certain width. In particular, in the present embodiment, the fine random irregularities (roughness) provided to the surface of the diffraction grating region of the diffraction grating portion increases the efficiency of coupling between the light-emitting element and the optical waveguide. By using a polycrystalline or amorphous material for the core layer forming the diffraction grating portion, provision of appropriate roughness on the surface of the core layer is facilitated. The polycrystalline or amorphous material which is the most common and easy to be processed for the core layer is polycrystalline silicon or amorphous silicon. Thus, by forming the diffraction grating portion so as to include polycrystalline silicon or amorphous silicon, the diffraction grating portion can be suitably formed at the lowest cost. Note that fine random irregularities (roughness) formed on the surface of the diffraction grating region are different from the periodic unevenness which define the diffraction grating region to be described later. 
     Furthermore, a cross-section orthogonal to the extending direction of the core layer at an arbitrary position along the extending direction may, for example, have a shape in which the distance from the center of the core layer to the outer surface in the cross-section varies, such as a rectangle, or a shape in which the distance from the center of the core layer to the outer surface in the cross-section does not vary, i.e. a circle. 
     In the present embodiment, at least a portion of the core layer may be exposed or covered by a thin film. Consequently, the portion of the core layer that is exposed or covered can come into direct contact with a gas or liquid of interest, or can come into contact with the gas or liquid of interest with the thin film interposed therebetween. This enables interaction between an evanescent wave and the gas or liquid of interest, thereby enabling measurement of the density of the gas or liquid of interest. In the present embodiment, the thin film is preferably thinner than ¼ the wavelength, in vacuum, of the light propagating through the core layer. 
     In the present embodiment, the light propagating through the core layer may be infrared radiation serving as an analog signal. Infrared radiation serving as an analog signal does not refer to determining the change in the energy of light to be one of two values, i.e. 0 (low level) or 1 (high level), but rather to a signal that carries the magnitude of change in the energy of light. The optical waveguide according to the present embodiment can therefore be used in sensors or analyzers. In this case, the wavelength, in vacuum, of the infrared light may be from 2 μm or greater to smaller than 12 μm. This is a wavelength band absorbed by gases (CO 2 , CO, NO, N 2 O, SO 2 , CH 4 , H 2 O, C 2 H 6 O, and the like) that are typically present in the environment. This enables the optical waveguide according to each embodiment to be used as a gas sensor. 
     The core layer may include a portion extending in a curved shape. This enables the aspect ratio of the profile of the core layer to approach 1 in plan view of the entire core layer, enabling miniaturization of the optical waveguide and the optical densitometer. 
     Furthermore, as described above, the diffraction grating portion of the optical waveguide can include a first diffraction grating portion that receives light from a light source and guides the light towards the light propagation portion, and a second diffraction grating portion that receives the light from the light propagation portion and outputs the light to the detector. 
     In the present embodiment, as described above, the diffraction grating portion includes the diffraction grating region and the extension region, and a first optical coupling region included in the extension region and a second optical coupling region included in the light propagation portion are optically coupled with respect to the light propagating through the core layer. In the present embodiment, however, as long as one of the first diffraction grating portion and the second diffraction grating portion includes the diffraction grating region which is connected to the extension region including the first optical coupling region as described above, the other may be configured arbitrary, for example, so as not to include a diffraction grating region connected to the extension region including the first optical coupling region. Further, in the case where a plurality of diffraction grating regions are present in the first diffraction grating portion or a plurality of diffraction grating regions are present in the second diffraction grating portion, at least one of these the diffraction grating regions may be connected to the extension region including the first optical coupling region and the remaining diffraction grating regions may not be connected to the extension region including the first optical coupling region. 
     &lt;&lt;&lt;Light Propagation Portion&gt;&gt;&gt; 
     In the present embodiment, the light propagation portion has a propagation channel capable of propagating light in the extending direction of the light propagation portion. A cross-section orthogonal to the extending direction of the propagation channel at an arbitrary position along the extending direction may, for example, have a shape in which the distance from the center of the core layer to the outer surface in the cross-section varies, such as a rectangle, or a shape in which the distance from the center of the core layer to the outer surface in the cross-section does not vary, i.e. a circle. 
     The propagation channel in the present embodiment may have a substantially uniform film thickness in the extending direction. A substantially uniform film thickness refers, for example, to the height difference in the film thickness being 200 nm or smaller. The propagation channel may have a portion with a different width along the extending direction. In the case where the light propagation portion includes a plurality of propagation channels, the propagation channels may have different film thicknesses or widths. The film thickness of the core layer may or may not be uniform throughout the light propagation portion. 
     Further, the light propagation portion may be a multilayer film, but the light propagation portion preferably a single-layered film. This is because propagation loss may be increased in the light propagation portion which is a multilayer film because of a transition of light from one layer to another layer or conversion between propagation modes. 
     &lt;&lt;&lt;Diffraction Grating Portion&gt;&gt;&gt; 
     In the present embodiment, the diffraction grating portion can include a first diffraction grating portion that receives light from a light source and guides the light towards the light propagation portion, and a second diffraction grating portion that receives the light from the light propagation portion and outputs the light to the detector. 
     In the present embodiment, the first diffraction grating portion may include a light diffraction grating region that causes light from the outside to enter the core layer, and the second diffraction grating portion may include a light diffraction grating region that extracts light to outside the core layer. In the present embodiment, these light diffraction grating regions may be portions where an unevenness is formed on the surface over a particular period (or a plurality of periods). Alternatively, in a cross-sectional view of the optical waveguide including a plane having recessed portions and protruding portions, the recessed portions of the unevenness may become deep grooves, separating the core layer. In this configuration, the protruding portions are formed discontinuously. 
     The diffraction grating region can be provided so that, in plan view, unevenness is formed in parallel patterns extending as lines or arcs, but the unevenness may extend in any shape. Note that the diffraction grating region provided in the diffraction grating portion is partitioned as a region having the unevenness formed therein. In particular, the diffraction grating region provided in the diffraction grating portion is the region inside the portion between the outermost wall surfaces of at least either of the outer walls defining the protruding portions and the inner walls defining the recessed portions. 
     Further, in the present embodiment, the diffraction grating region may have any shape in plan view, and may have a shape having a portion which widens from the extension region side of the diffraction grating region toward the distal end opposite to the extension region, for example. Specific examples include a fan shape which has the center within the extension region of the diffraction grating portion and widens toward the distal end opposite to the extension region. The shape of the diffraction grating region preferably is line-symmetric relative to a virtual line extending from the extension region side towards the distal end. 
     In the present embodiment, the structure of the second diffraction grating portion may be the same structure as the first diffraction grating portion or a converted structure from the first diffraction grating portion. The converted structure from the first diffraction grating portion refers to that the shape, configuration, arrangement, and the like, of the diffraction grating region included in the second diffraction grating portion is a form with rotation, enlargement, reduction, translation, line symmetry, or point symmetry relative to the shape, configuration, arrangement, and the like, of the diffraction grating region included in the first diffraction grating portion. Noted that a difference between these structures within the wavelength, in vacuum, of light propagating through the core layer, preferably a difference of 1 μm or smaller, is tolerated. When the structure of the second diffraction grating portion is the same structure as the first diffraction grating portion or a converted structure from the first diffraction grating portion, the wavelength selectivity in the first diffraction grating portion and the wavelength selectivity in the second diffraction grating portion can be made substantially equivalent. This can avoid light loss occurring when the wavelength selectivities differ between the first diffraction grating portion and the second diffraction grating portion. 
     &lt;&lt;Substrate&gt;&gt; 
     The substrate in the present embodiment may be any substrate on which the core layer can be formed. The below-described support layer can also be formed on the substrate. Specific examples of the substrate include a silicon substrate and a GaAs substrate. 
     &lt;&lt;Support Layer&gt;&gt; 
     Any support layer may be provided in the present embodiment. The support layer connects at least a portion of the substrate and at least a portion of the core layer. The support layer may be any material capable of joining the substrate and the core layer but is preferably a material that has a smaller refractive index than that of the core layer with respect to light of any wavelength or light propagating through the core layer. Examples of the material forming the support layer include SiO 2 . The support layer is not an essential element in the present disclosure. The core layer may be joined to the substrate by the support layer, or the core layer may be formed directly on the substrate. The support layer may be discontinuous, and at least a portion of the core layer may be free-standing, without being joined to the support layer. In other words, a space is provided between the substrate and the core layer except in a region where the support layer is provided in an optical waveguide configured in this way. The extent of the interaction between the evanescent wave and the substance of interest can be increased by causing a portion of the core layer to be free-standing. This can increase sensor sensitivity. 
     An example of a method of forming the support layer in the present embodiment is to etch a buried oxide (BOX) layer (SiO 2  layer) of an SOI substrate, thereby forming a structure in which the BOX layer supports the core layer (Si layer) with respect to the substrate (Si layer). 
     &lt;Light Source&gt; 
     The light source may be any light source capable of introducing light into the core layer. An incandescent bulb, a ceramic heater, a micro electro mechanical systems (MEMS) heater, an infrared light-emitting diode (LED), or the like can be used as the light source in the case of using infrared radiation to measure a gas. In other words, the light source may be an incoherent light source. The light source may be arranged in any way that allows an optical coupling. For example, the light source may be arranged adjacent to the optical waveguide in the same part as the optical waveguide or may be arranged in a separate part separated from the optical waveguide at a certain distance. A mercury lamp, an ultraviolet LED, or the like can be used as the light source in the case of using ultraviolet rays to measure a gas. 
     The light propagating through the core layer of the optical waveguide provided in the optical densitometer may be infrared radiation serving as an analog signal. Infrared radiation serving as an analog signal does not refer to determining the change in the energy of light to be one of two values, i.e. 0 (low level) or 1 (high level), but rather to a signal that carries the magnitude of change in the energy of light. The optical densitometer can therefore be applied to sensors or to analyzers. In this case, the wavelength of the infrared light may be from 2 μm or greater to smaller than 12 μm. This is a wavelength band absorbed by gases (CO 2 , CO, NO, N 2 O, SO 2 , CH 4 , H 2 O, C 2 H 6 O, and the like) that are typically present in the environment. This makes the optical densitometer of the present embodiment to be used as a gas sensor. 
     &lt;Detector&gt; 
     The detector may be any detector capable of receiving the light that has propagated through the core layer of the optical waveguide. A thermal infrared sensor such as a pyroelectric sensor, a thermopile, or a bolometer; a quantum infrared sensor such as a diode or a phototransistor; or the like can be used as the detector in the case of using infrared radiation to measure a gas. A quantum ultraviolet sensor, such as a diode or a phototransistor, or the like can be used as the detector in the case of using ultraviolet rays to measure a gas. 
     [Optical Densitometer According to Embodiment of the Present Disclosure] 
     An optical densitometer according to an embodiment of the present disclosure is described with reference to  FIG. 1 . 
     An optical densitometer  14  according to this embodiment is installed and used in an exterior space  16  containing a gas whose density or the like is to be detected. The optical densitometer  14  of the present embodiment includes an optical waveguide  15  of an embodiment, described below, a light source  17  capable of introducing light into a core layer  12 , and a photodetector  18  capable of receiving the light that has propagated through the core layer  12 . Further, the optical densitometer  14  includes a first diffraction grating portion  11  that receives light from the light source  17  and guides the light to a light propagation portion  10 , and further includes a second diffraction grating portion  13  that receives light from the light propagation portion  10  and guides the light to the photodetector  18 . 
     The light source  17  in the optical densitometer  14  of the present embodiment emits infrared radiation with a wavelength of 2 μm or greater and smaller than 12 μm toward the core layer  12 . As a result of using this infrared radiation, an evanescent wave EW extending from the core layer  12  is absorbed by a substance of interest that is present in the exterior space  16 , such as CO 2 , CO, NO, N 2 O, SO 2 , CH 4 , H 2 O, C 2 H 6 O, or another gas. The density of the substance of interest can thus be detected. 
     Note that the optical densitometer  14  of the present embodiment is obtained by first manufacturing the below-described optical waveguide  15  according to an embodiment of the present disclosure. Subsequently, the light source  17  is installed to be capable of introducing infrared radiation IR into one diffraction grating portion  11  (grating coupler) of the optical waveguide  15 , and the photodetector  18  is disposed to be capable of receiving the infrared radiation IR emitted from the other diffraction grating portion  13  (grating coupler) of the optical waveguide  15 , as illustrated in  FIG. 1 . 
     [Optical Waveguide According to Embodiments of the Present Disclosure] 
     First Embodiment 
     An optical waveguide according to a first embodiment of the present disclosure is described with reference to  FIGS. 1 through 3 . 
       FIG. 1  illustrates the schematic configuration of the optical densitometer  14  according to the first embodiment and a second embodiment, described later, and is also a conceptual drawing of the ATR technique using an optical waveguide  15  according to the first or second embodiment. 
     The optical waveguide  15  includes a substrate  19 , a core layer  12  through which the infrared radiation IR (an example of light) can propagate, and a support layer  20  configured to connect at least a portion of the substrate  19  with at least a portion of the core layer  12  and support the core layer  12  with respect to the substrate  19 . The core layer  12  and the substrate  19  are, for example, formed from silicon (Si), and the support layer  20  is, for example, formed from silicon dioxide (SiO 2 ). The substrate  19  and the support layer  20  are, for example, plate-shaped. The support  20  may support the entire core layer  12 , as illustrated in  FIG. 1 , or may support at least a portion of the core layer  12 . For example, the support  20  can be configured to support the entire diffraction grating portions  11  and  13  and a portion of the light propagation portion  10  discontinuously in the extending direction. In the resulting optical waveguide  15 , the light propagation portion  10  is connected to the support layer  20  discontinuously in the extending direction, and a gap without a certain layer, such as a cladding layer, is present between the light propagation portion  10  and the substrate  19 , except in the regions where the support  20  is provided. 
     The core layer  12  includes a first diffraction grating portion (grating coupler as one example)  11  formed at one end in the extending direction and a second diffraction grating portion (grating coupler as an example)  13  formed at the other end, as illustrated in a schematic diagram illustrating the schematic configuration of the optical waveguide  15  in  FIG. 2 . The core layer  12  includes the light propagation portion  10  between the first diffraction grating portion  11  and the second diffraction grating portion  13  disposed at the respective ends in the extending direction. The film thickness of the light propagation portion  10  in the optical waveguide  15  according to the first embodiment is uniform. The width of the light propagation portion  10  in the optical waveguide  15  according to the first embodiment is also uniform. The width direction is the direction orthogonal to the extending direction and the thickness direction. The thickness direction is the direction parallel to the stacking direction in which the substrate  19 , support layer  20 , and the core layer  12  are stacked. 
     The first diffraction grating portion  11  is disposed in the emission direction of the light source  17 . In the first embodiment, the optical waveguide  15  is arranged so that the stacking direction thereof is parallel to the vertical direction, and the principal surface of the substrate  19  is in a direction orthogonal to vertical direction and is in the vertically downward from the light source  17 . The principal surface of the substrate  19  is a surface orthogonal to the thickness direction of the substrate  19  and refers, in the first embodiment, to the surface with the largest area among the six surfaces forming the substrate  19 . In other words, the emission direction of the light source  17  is the vertically downward direction from the light source  17  when the optical waveguide  15  is installed in this manner. This first diffraction grating portion  11  is configured to introduce the infrared radiation IR emitted from the light source  17  to the core layer  12 . Accordingly, the light that is to propagate through the core layer  12  is entered from the thickness direction of the first diffraction grating portion  11 . The second diffraction grating portion  13  is disposed in the direction facing the photodetector  18 . The direction facing the photodetector  18  is the vertically downward direction from the photodetector  18  when the optical waveguide  15  is installed in the above-described manner. This second diffraction grating portion  13  is configured to extract the infrared radiation IR propagating through the core layer  12  and emit the infrared radiation IR towards the photodetector  18 . Accordingly, the light that has propagated through the core layer  12  is output in the thickness direction of the second diffraction grating portion  13 . 
     In this way, the first diffraction grating portion  11  is provided at one end of the core layer  12  disposed on the light source  17  side (light introduction side), and the second diffraction grating portion  13  is provided at the other end of the core layer  12  disposed on the photodetector  18  side (light emission side). The light propagation portion  10  extends from the center of the core layer  12  toward the two ends in the extending direction, and the infrared radiation IR introduced from the first diffraction grating portion  11  propagates through the light propagation portion  10  and is emitted from the second diffraction grating portion  13 . An evanescent wave EW extending from the core layer  12  is primarily absorbed by the substance of interest present in the exterior space  16  around or near the light propagation portion  10 . 
     The optical waveguide  15  according to the first embodiment is now described in greater detail. 
     As illustrated in  FIG. 1 , a sensor employing the ATR technique can improve the sensitivity of the sensor by expanding the region of interaction between an evanescent wave EW extending from the core layer  12  and a substance of interest (i.e. by expanding the exposed portion of the core layer  12 ). Furthermore, in a sensor employing the ATR technique, the light introduced into the core layer needs to extend from a light propagation portion  10  as an evanescent wave and be absorbed by the external substance of interest, as described above. A long propagation distance of light through the light propagation portion  10  (propagation channel  101 ) is therefore required. The diffraction grating portions for inputs or outputs of light are also required to be structured so as to suit the sizes and shapes of the light source and the photodetector in view of efficient light inputs to the optical waveguide or efficient light outputs from the optical waveguide. In such a sensor, therefore, the required functions of the diffraction grating portions and the light propagation portion  10 , which are all core layers, differ from each other, and it is desirable to form them in the sizes, shapes, and materials to suit the respective functions. 
     To meet the needs, in the optical waveguide  15  according to the first embodiment, as illustrated in  FIG. 3 , the first diffraction grating portion  11  includes a diffraction grating region  111  and an extension region  111   a  connected to the diffraction grating region  111 . The diffraction grating region  111  and the extension region  111   a  are all formed from a material different from the material of the light propagation portion  10 , and are all spatially separated from the light propagation portion  10 . A first optical coupling region  111   b  included in the extension region  111   a  and a second optical coupling region  101   b  included in the light propagation portion  10  are optically coupled with respect to light propagating through the core layer  12 . In an example, the optical coupling surface between the first optical coupling region  111   b  and the second optical coupling region  101   a  is not orthogonal to the principal surface of the substrate  19 . For example, the optical coupling surface may be parallel to the principal surface of the substrate  19 . Although not illustrated, the second diffraction grating portion  13  similarly includes a diffraction grating region  131  and an extension region  131   a  connected to the diffraction grating region  131 . The diffraction grating region  131  and the extension region  131   a  are all spatially separated from the light propagation portion  10 . A first optical coupling region  131   b  included in the extension region  131   a  and a second optical coupling region  101   a  included in the light propagation portion  10  are optically coupled with respect to light propagating through the core layer  12 . 
     Accordingly, in the optical waveguide  15  according to the first embodiment, the diffraction grating regions  111 ,  131  and the extension regions  111   a ,  131   a  connected to the diffraction grating regions  111 ,  131  are all formed from a material different from the material of the light propagation portion  10 , and are all spatially separated from the light propagation portion  10 . Thus, the first diffraction grating portion  11 , the second diffraction grating portion  13 , and the light propagation portion  10  as the core layer  12  can be formed so as to have sizes and shapes, and be formed from materials suited to their respective functions. In this structure, the first optical coupling regions  111   b ,  131   b  included in the extension regions  111   a ,  131   a  and the second optical coupling regions  101   a  included in the light propagation portion  10  are optically coupled with respect to light propagating through the core layer  12 . This ensures that light from the light source received by the first diffraction grating portion  11  is guided from the first diffraction grating portion  11  to the light propagation portion  10 , and light which has propagated through the light propagation portion  10  is guided from the light propagation portion  10  to the second diffraction grating portion  13 . 
     Here, in the optical waveguide  15  according to the first embodiment, the couplings of the first optical coupling regions  111   b ,  131   b  included in the extension regions  111   a ,  131   a  and the second optical coupling region  101   a  included in the light propagation portion  10  are not particularly limited as long as they are optically coupled with respect to the light propagating through the core layer  12  (specifically, the first optical coupling regions  111   b ,  131   b  and the second optical coupling regions  101   a ). Nevertheless, as illustrated in  FIG. 3 , the first optical coupling regions  111   b ,  131   b  and the second optical coupling regions  101   a  are preferably disposed in the direction orthogonal to the extending direction of the light propagation portion  10 , which makes the extension regions  111   a ,  131   a  and the light propagation portions  10  function as directional couplers. By making them function as directional couplers, efficient optical couplings therebetween are established. 
     Specifically in the optical waveguide  15  according to the first embodiment, as illustrated in  FIG. 2 , each of the first diffraction grating portion  11  and the second diffraction grating portion  13  includes one diffraction grating region  111 ,  131 , and the light propagation portion  10  including one propagation channel  101  extends between the first diffraction grating portion  11  and the second diffraction grating portion  13 . The first diffraction grating portion  11  and the second diffraction grating portion  13  include respective extension regions  111   a ,  131   a , as illustrated in  FIG. 3  (illustration of the second diffraction grating portion  13  is omitted), and each of the extension regions  111   a ,  131   a  is made of the same material as one of the materials forming the diffraction grating regions  111 ,  131 . In addition, the diffraction grating regions  111 ,  131  and the extension regions  111   a ,  131   a  are all made from a material different from the material of the propagation channel  101  of the light propagation portion  10 , and are all separated from the propagation channel  101  of the light propagation portion  10 . Further, the extension regions  111   a ,  131   a  include the first optical coupling regions  111   b ,  131   b , respectively. The propagation channel  101  has second optical coupling regions  101   a  in the vicinity of the respective ends of the propagation channel  101 . The first optical coupling regions  111   b ,  131   b  and the corresponding second optical coupling regions  101   a  are optically coupled with respect to light propagating via the first optical coupling regions  111   b ,  131   b  and the second optical coupling regions  101   a.    
     Further, in the optical waveguide  15  according to the first embodiment, specifically as illustrated in  FIG. 3B , each extension region  111   a ,  131   a  and the light propagation portion  10  are disposed so as to be separated from each other in the direction orthogonal to the extending direction of the light propagation portion  10  and at positions different from each other in the thickness direction (in the illustrated example, the light propagation portion  10  is positioned on the substrate side in the thickness direction relative to the extension region  111   a ). In other words, the extension region  111   a ,  131   a  and the light propagation portion  10  overlap each other in the extending direction of the light propagation portion  10 , and are disposed in the different layers. By disposing the extension region  111   a ,  131   a  and the light propagation portion  10  at positions different from each other in the thickness direction so as to be separated from each other in the direction orthogonal to the extending direction of the light propagation portion  10 , portions which have different functions and form the core layer  12  are disposed in the different layers. In addition, the first diffraction grating portion  11 , the second diffraction grating portion  13 , and the light propagation portion  10  can be efficiently processed so as to suit to the respective functions. 
     In the optical waveguide  15  according to the first embodiment, the extension region  111   a  of the first diffraction grating portion  11  and the extension region  131   a  of the second diffraction grating portion  13 , and the light propagation portion  10  may have any positional relationships as long as the first optical coupling regions  111   b ,  131   b  included in the extension regions  111   a ,  131   a  and the corresponding second optical coupling regions  101   a  included in the light propagation portion  10  are optically coupled. Unlike  FIG. 3 , the extension regions  111   a ,  131   a  and the light propagation portion  10  can be provided at the same position in the thickness direction in the optical waveguide  15  so as to be separated from each other in the planar direction. 
     Although the extension regions  111   a ,  131   a  and the light propagation portion  10  extend so as to be separated from each other in the example depicted in  FIG. 3 , the extension regions  111   a ,  131   a  and the light propagation portion  10 , more specifically, the first optical coupling regions  111   b ,  131   b  and the second optical coupling regions  101   a , may be in contact with each other. 
     In the optical waveguide  15  according to the first embodiment, the shapes of the extension regions  111   a ,  131   a  are not particularly limited. For example, as illustrated in  FIG. 3A , one end of the extension region  111   a  of the first diffraction grating portion  11  is continuously connected to the diffraction grating region  111  without being interrupted, and the other end (end portion) is terminated without being connected to another core layer  12  (illustration of the second diffraction grating portion  13  is omitted). Further, as illustrated in the cross-sectional view (in the illustrated example, the cross-sectional view in the thickness direction as illustrated in  FIG. 3B ) including the first optical coupling regions  111   b ,  131   b  of the extension regions  111   a ,  131   a  and the second optical coupling regions  101   a  of the propagation channel  101 , the extension regions  111   a ,  131   a  have first distance modification regions  111   c ,  131   c  which are curved toward the propagation channel  101  so that the first optical coupling regions  111   b ,  131   b  included in the extension regions  111   a ,  131   a  and the corresponding second optical coupling regions  101   a  of the propagation channel  101 , which are portions to be optically coupled, approach each other. In the first distance modification regions  111   c ,  131   c  (i.e., curved portions), the distance from the propagation channel  101  gradually changes from a distance at which the extension region  111   a  and the propagation channel  101  are less likely to be optically coupled (a distance greater than the distance given by Equation (2) or a distance greater than 0.7 μm), to a distance at which an optical coupling is established (a distance equal to or smaller than the distance given of Equation (1) or a distance of 0.7 μm or smaller). Here, n gap  is the refractive index of the material present in the portion sandwiched between the propagation channel  101  and the first distance modification region  111   c ,  131   c . The first distance modification regions  111   c ,  131   c  are continuous with the first optical coupling regions  111   b ,  131   b , respectively. For preventing loss of light, the maximum angle relative to the principal surface of the substrate  19  of the curved portions is preferably 45° or less and more preferably 30° or less. If the angle is too small, on the other hand, a great distance is required for making the first optical coupling region  111   b ,  131   b  and the second optical coupling region  101   a  approach each other. Thus, the maximum angle of the curved portions is preferably 10° or more and more preferably 15° or more relative to the principal surface of the substrate  19 . 
     Further, the propagation channel  101  and the extension region  111   a ,  131   a  have portions which extend parallel to each other in plan view. In other words, the extension region  111   a ,  131   a  has a first distance modification region  111   c ,  131   c  that is curved so that the distance between the extension region  111   a ,  131   a  and the propagation channel  101  gradually decreases to a distance at which the extension region  111   a ,  131   a  and the propagation channel  101  are optically coupled, from one end of the extension region  111   a ,  131   a  (connecting portion with the diffraction grating region  111 ,  131 ) toward the other end (end portion). The extension region  111   a ,  131   a  then includes a portion in which the extension region  111   a ,  131   a  (first optical coupling region  111   b ,  131   b ) extends spaced apart from the propagation channel  101  (second optical coupling region  101   a ) at a constant distance, in the first optical coupling region  111   b ,  131   b . The extension region  111   a ,  131   a  further includes a second distance modification region  111   d ,  131   d  which is curved so that the distance between the extension region  111   a ,  131   a  and the propagation channel  101  gradually increases, and finally terminates at the other end (end portion). 
     In the above example, the propagation channel  101  has the end portion, and the second optical coupling region  101   a  is disposed so as to be separated from the end portion of the propagation channel  101  (light propagation portion  10 ). The second optical coupling region  101   a , however, may be disposed at the end portion of the propagation channel  101  (light propagation portion  10 ). The second optical coupling region  101   a , however, is preferably disposed so as to be separated from the end portion of the propagation channel  101 , rather than being disposed at the end portion of the propagation channel  101 . By disposing the second optical coupling region  101   a  so as to be separated from the end portion of the propagation channel  101 , as illustrated in  FIG. 3B , the respective distances between the end portion of the propagation channel  101  and the first diffraction grating portion  11  or the second diffraction grating portion  13  can be set to a distance at which they are less likely to be optically coupled (a distance greater than the distance given by Equation (2) or a distance greater than 0.7 μm). Here, n gap  represents the refractive index of the material present in the portion sandwiched between the end portion of the propagation channel  101  and the first diffraction grating portion or the second diffraction grating portion. 
     In other words, in the above example, the propagation channel  101  is separated from the first diffraction grating portion  11  or the second diffraction grating portion  13  in the thickness direction at a distance at which an optically coupling is less likely to be established (at a distance greater than the distance given by Expression (2) or a distance greater than 0.7 μm), except in the second optical coupling regions. Here, n gap  is the refractive index of a material present in the portion sandwiched between the portion other than the second optical coupling regions of the propagation channel  101  and the first diffraction grating portion  11  or the second diffraction grating portion  13 . 
     Further, in the first embodiment, the first optical coupling regions  111   b ,  131   b  can be disposed at any positions in the extension regions  111   a ,  131   a . The first optical coupling regions  111   b ,  131   b  may be positioned at the respective end portions of the extension regions  111   a ,  131   a . As illustrated in  FIG. 3B  and described above, the first optical coupling region  111   b ,  131   b , however, is preferably located in the middle of the extension region  111   a ,  131   a  (between the first distance modification region  111   c ,  131   c  where the distance between the extension region  111   a  and the propagation channel  101  gradually decreases and the second distance modification region  111   d ,  131   d  where the distance gradually increases). In other words, the first optical coupling region  111   b ,  113   b  is preferably located between one end of the extension region  111   a ,  131   a  connected to the diffraction grating region  111 ,  131  and the other terminating end (end portion), so as to be separated from the ends. Because the first optical coupling region  111   b ,  131   b  is provided in the middle of the extension region  111   a ,  131   a , as illustrated in  FIG. 3B , the distance between the end portion of the extension region  111   a  and the propagation channel can be set to a distance at which they are less likely be optically coupled (a distance greater than the distance given by Equation (2) or a distance greater than 0.7 μm). Here, n gap  is the refractive index of a material present in the portion sandwiched between the end portion of the extension region  111   a  and the propagation channel  101 . Further, because the first optical coupling region  111   b ,  131   b  is provided in the middle of the extension region  111   a ,  131   a , the end portion of the extension region  111   a ,  131   a  can be etched without damaging the propagation channel  101 , thereby enabling an improvement in the propagation efficiency of light through the propagation channel  101 . 
     In the first embodiment, the shapes of the extension regions  111   a ,  131   a  are not limited as long as they include at least the first optical coupling regions  111   b ,  131   b.    
     In the first embodiment, the extension regions  111   a ,  131   a  and the light propagation portion  10  are separated from each other in the thickness direction, and a layer different from the extension regions  111   a ,  131   a  and the light propagation portion  10  is present between the extension regions  111   a ,  131   a  and the light propagation portion  10 . A material (including the air) with a refractive index relatively lower than that of the core layer  12  (including the extension regions  111   a ,  131   a  and the light propagation portion  10 ) may be interposed between the extension regions  111   a ,  131   a  and the light propagation portion  10 , and in the illustrated example, a silicon oxide film (SiO 2 ) is present between the first diffracting grating portion  11  and the light propagation portion  10 . 
     In the first embodiment, the distance between the first optical coupling region  111   b ,  131   b  and the second optical coupling region  101   a  is preferably equal to or smaller than the distance given by above Expression (1) or equal to or less than 0.7 μm. Here, Xo represents the average wavelength, in vacuum, of light propagating through the core layer, n coup  is the refractive index of the material forming the first optical coupling region  111   b ,  131   b  or the second optical coupling region  101   a , and n mid  is the refractive index of the material present in the portion sandwiched between the first optical coupling region  111   b ,  131   b  and the second optical coupling region  101   a . Because the distance between the first optical coupling region  111   b ,  131   b  and the second optical coupling region  101   a  is set within the above-mentioned range, the first optical coupling region  111   b ,  131   b  and the second optical coupling region  101   a  can be optically coupled efficiently at the short distance (length in extending direction). 
     Further, the length of the optical coupling between the first optical coupling region  111   b ,  131   b  and the second optical coupling region  101   a  in the extending direction is preferably 20 μm or smaller and more preferably 10 μm or smaller. When the length is within one of the above-described ranges, the first optical coupling region  111   b ,  131   b  and the second optical coupling region  101   a  can be optically coupled in a space-saving manner. The length of the optical coupling between the first optical coupling region  111   b ,  131   b  and the second optical coupling region  101   a  in the extending direction refers to the length of the portion in which the distance between the extension region  111   a ,  131   a  and the propagation channel  101  is equal to or smaller than the distance given by above Expression (1) or equal to or less than 0.7 μm, i.e., the length of the portion defined as the first optical coupling region  111   b ,  131   b  and the second optical coupling region  101   a.    
     The diffraction grating portions  11 ,  13  including the extension regions  111   a ,  131   a  and the light propagation portion  10  can be formed from any material in the first embodiment. In the illustrated example, the diffraction grating portions  11 ,  13  and the light propagation portion  10  are formed from different materials. The functions required for the diffraction grating portions  11 ,  13  differ from those of the light propagation portion  10 . When they are formed from different materials, materials that are suited to the functions required for the respective components can be selected and the optical waveguide can be manufactured more suitably. 
     In the illustrated example, the material of the diffraction grating portions  11 ,  13  is polycrystalline silicon and the material of the light propagation portion  10  is monocrystalline silicon. Alternatively, an amorphous silicon material may be used as the material for forming the diffraction grating portions  11 ,  13  or the light propagation portion  10 . 
     Further, in the first embodiment, the equivalent refractive index of the first optical coupling regions  111   b ,  131   b  is preferably from 0.7 times to 1.3 times, more preferably from 0.8 times to 1.2 times, and more preferably from 0.9 times to 1.1 times of the equivalent refractive index of the second optical coupling regions  101   a , with respect to light propagating through the first optical coupling regions  111   b ,  131   b  and the second optical coupling regions  101   a . As the equivalent refractive index of the first optical coupling regions  111   b ,  131   b  becomes closer to that of the second optical coupling regions  101   a  with respect to light propagating through the first optical coupling regions  111   b ,  131   b  and the second optical coupling regions  101   a , the efficiency of an optical coupling therebetween is increased. 
     Further, in the first embodiment, the refractive index of the material forming the first optical coupling regions  111   b ,  131   b  is preferably from 0.9 times to 1.1 times and more preferably from 0.95 times to 1.05 times of the refractive index of the material forming the second optical coupling regions  101   a . As the refractive index of the material forming the first optical coupling regions  111   b ,  131   b  becomes closer to that of the material forming the second optical coupling regions  101   a , the equivalent refractive index of the first optical coupling regions  111   b ,  131   b  is more likely to match that of the second optical coupling regions  101   a  with respect to light propagating through the first optical coupling regions  111   b ,  131   b  and the second optical coupling regions  101   a . This improves the efficiency of the optical coupling. 
     Further, in the first embodiment, the film thicknesses of the extension regions  111   a ,  131   a  and the film thickness of the propagation channel  101  may be set to any values. Nevertheless, as illustrated in  FIG. 3B , the film thicknesses of the first optical coupling regions  111   b ,  131   b  are preferably from 0.7 times to 1.3 times, more preferably from 0.8 times to 1.2 times, and more preferably from 0.9 times to 1.1 times of the film thicknesses of the second optical coupling regions  101   a . More specifically, the film thicknesses of the extension regions  111   a ,  131   a  including the first optical coupling regions  111   b ,  131   b  are preferably from 0.7 times to 1.3 times, more preferably from 0.8 times to 1.2 times, and more preferably from 0.9 times to 1.1 times of the film thickness of the propagation channel  101  including the second optical coupling regions  101   a . As the film thicknesses of the first optical coupling regions  111   b ,  131   b  become closer to those of the second optical coupling regions  101   a , the equivalent refractive index of the first optical coupling regions  111   b ,  131   b  is more likely to match that of the second optical coupling regions  101   a  with respect to light propagating through the first optical coupling regions  111   b ,  131   b  and the second optical coupling regions  101   a . This improves the efficiency of the optical coupling. 
     In the first embodiment, the film thicknesses of the first optical coupling regions  111   b ,  131   b  and the film thicknesses of the second optical coupling regions  101   a  refer to the respective film thicknesses in the portions where the respective distances between the first optical coupling regions  111   b ,  131   b  and the second optical coupling regions  101   a  become the smallest in the case where the film thicknesses of the first optical coupling regions  111   b ,  131   b  vary in the first optical coupling regions  111   b ,  131   b  or the film thicknesses of the second optical coupling regions  101   a  vary in the second optical coupling regions  101   a.    
     The film thicknesses of the first optical coupling regions  111   b ,  131   b  and the second optical coupling regions  101   a  are preferably from 0.2 μm to 1.0 μm in view of manufacturing and the optical properties. 
     Further, in the first embodiment, the widths of the extension regions  111   a ,  131   a  and the propagation channel  101  may be set to any values. Nevertheless, as illustrated in  FIG. 3A , the widths of the first optical coupling regions  111   b ,  131   b  are preferably from 0.7 times to 1.3 times, more preferably from 0.8 times to 1.2 times, and even more preferably 0.9 to 1.1 times of the widths of the second optical coupling regions  101   a . As the widths of the first optical coupling regions  111   b ,  131   b  become closer to those of the second optical coupling regions  101   a , the equivalent refractive index of the first optical coupling regions  111   b ,  131   b  is more likely to match that of the second optical coupling regions  101   a  with respect to light propagating through the first optical coupling regions  111   b ,  131   b  and the second optical coupling regions  101   a . This improves the efficiency of the optical coupling. 
     In the first embodiment, the widths of the first optical coupling regions  111   b ,  131   b  and the widths of the second optical coupling regions  101   a  refer to the respective widths in the portions where the respective distances between the first optical coupling regions  111   b ,  131   b  and the second optical coupling regions  101   a  become the smallest in the case where the widths of the first optical coupling regions  111   b ,  131   b  vary in the first optical coupling regions  111   b ,  131   b  or the widths of the second optical coupling regions  101   a  vary in the second optical coupling regions  101   a.    
     In the first embodiment, the diffraction grating region  111  of the first diffraction grating portion  11  and the diffraction grating region  131  of the second diffraction grating portion  13  are both fan-shaped in the example depicted in  FIGS. 2 and 3 . In the first embodiment, however, the diffraction grating regions  111 ,  131  may have any shapes in plan view. 
     &lt;Method of Manufacturing Optical Waveguide in First Embodiment&gt; 
     Next, a method of manufacturing the optical waveguide  15  according to the first embodiment is described with reference to  FIGS. 4 through 11 .  FIGS. 4 through 11  are cross-sectional views illustrating an example method of manufacturing the section illustrated in  FIG. 3B . 
     In  FIGS. 4 through 11 , one diffraction grating region  111  in the first diffraction grating portion  11  is simplified and illustrated schematically to facilitate the explanation of the method of manufacturing the optical waveguide  15 .  FIGS. 4 through 11  are cross-sectional views, taken at a position corresponding to the A-A line in  FIG. 3A , illustrating the process of manufacturing the optical waveguide  15 . 
     First, as illustrated in  FIG. 4 , a SiO 2  film is formed on either or both of a support substrate  19   a , which is formed from silicon and ultimately serves the substrate  19 , and an active substrate  12   a , which is formed from silicon and from which the core layer  12  is to be formed. The support substrate  19   a  and the active substrate  12   a  are then brought into contact with each other, with the SiO 2  film interposed therebetween, and bonded by thermal process. The active substrate  12   a  is then ground, polished, or the like to a predetermined thickness to adjust the film thickness of the active substrate  12   a . Consequently, an SOI substrate  15   a  is formed to have a “silicon-insulating layer-silicon” structure that includes the support substrate  19   a , a BOX layer  20   a  formed on the support substrate  19   a , and the active substrate  12   a  formed on the BOX layer  20   a.    
     Next, the SOI substrate  15   a  is subjected to lithography and etching to etch the active substrate  12   a  to form the light propagation portion  10 . The optical waveguide main portion is thus formed to include the support substrate  19   a , the BOX layer  20   a  formed on the support substrate  19   a , and the light propagation portion  10  formed on the BOX layer  20   a , as illustrated in  FIG. 5 . 
     Next, as illustrated in  FIG. 6 , a separation film  15   c  for separating the subsequently formed extension region  111   a  of the first diffraction grating portion  11  and light propagation portion  10  is formed by depositing a SiO 2  film using tetraethyl orthosilicate (TEOS) as a raw material, for example. After this separation film  15   c  is formed on the BOX layer  20   a  and the light propagation portion  10 , the surface is polished by chemical mechanical polishing (CMP) or the like to yield the structure illustrated in  FIG. 6 . The light propagation portion  10  can be separated from the first diffraction grating portion  11  in the thickness direction by the separation film  15   c.    
     Next, as illustrated in  FIG. 7 , a photoresist is patterned on the separation film  15   c  and used as a mask layer M 1  to partially etch the separation film  15   c . In this step, buffered hydrofluoric acid (BHF) or the like is used for wet etching to form an inclination as gentle as possible. During the wet etching, a gentler inclination can be formed by adjusting the adhesion at the interface between the separation film  15   c  and the mask layer M 1 . In this way, a hole is defined in the separation film  15   c  for optically coupling the subsequently formed extension region  111   a  of the first diffraction grating portion  11  and the vicinity of the end of the light propagation portion  10  (propagation channel  101 ), as illustrated in  FIG. 7 . 
     The mask layer M 1  is then removed by etching, and as illustrated in  FIG. 8 , a SiO 2  film with a thickness of approximately 30 nm, for example, is formed on the exposed surface of the portion of the light propagation portion  10 . This film is formed by any technique, such as oxidation or chemical vapor deposition (CVD). Furthermore, this film is not necessarily a SiO 2  film and may be a SiN film or the like. 
     Next, as illustrated in  FIG. 9 , a three-layered structure of a polysilicon film (upper layer)  21   a /SiO 2  film  21   b /polysilicon film (lower layer)  21   c  is formed on the entire surface. The two polysilicon films  21   a ,  21   c  are, for example, formed by CVD. The SiO 2  film  21   b  that is the middle layer is formed by oxidation, CVD, or the like. The film thickness of the polysilicon film  21   c  that is the lower layer is preferably substantially equivalent to the film thickness of the light propagation portion  10  (propagation channel  101 ). In this case, the first diffraction grating portion  11  formed from the polysilicon film  21   c  and the light propagation portion  10  can be optically coupled to each other in a highly efficient matter. For example, the polysilicon film  21   c  that is the lower layer and the propagation channel  101  both preferably have a thickness of 0.6 μm. 
     Next, as illustrated in  FIG. 10 , lithography and etching are used to etch the polysilicon film  21   a  that is the upper layer to form an uneven pattern for forming the first diffraction grating portion  11 . In this step, the SiO 2  film  21   b  formed between the two polysilicon films  21   a ,  21   c  functions as a stopper film during the etching. In addition to enabling highly accurate formation of the uneven pattern, it can protect the polysilicon film  21   c  that is the lower layer from being excessively etched. After the uneven pattern is formed, only the exposed portions of the SiO 2  film  21   b  used as the stopper layer are removed by dry etching or wet etching. 
     Next, as illustrated in  FIG. 11 , lithography and etching are used to etch the polysilicon film  21   c  that is the lower layer, thereby forming the profile of the first diffraction grating portion  11 . Subsequently, while illustration is omitted, lithography and etching are used to remove a portion of the separation film  15   c  to expose the surface of a portion of the light propagation portion  10  which will serve for gas sensing. This yields an optical waveguide main portion  15   b  with a structure corresponding to the optical waveguide  15  of the first embodiment. 
     Next, the support substrate  19   a  is cut in a predetermined region to separate the optical waveguide main portion  15   b . The optical waveguide  15  according to the first embodiment is thereby completed. 
     Although the above description has focused on the first diffraction grating portion  11  as the diffraction grating portion, the second diffraction grating portion  13  can be formed in the similar manner. 
     Second Embodiment 
     An optical waveguide according to a second embodiment of the present disclosure is described with reference to  FIGS. 1 through 3 , similarly to the first embodiment. Elements that are not described below are similar to the corresponding elements in the first embodiment, and a description of the elements common to the first embodiment is omitted. 
     A sensor employing the ATR technique can improve the sensitivity of the sensor by expanding the region of interaction between an evanescent wave EW extending from a core layer and a substance of interest (i.e. by expanding the exposed portion of the core layer). In addition, in the sensor employing the ATR technique, it is also desirable to cause more evanescent waves that have been introduced to the core layer to extend, for the purpose of improving the sensitivity of a sensor. In the case where a substrate of an optical waveguide, however, is in immediate proximity to the light propagation portion, an evanescent wave extending from the light propagation portion may reach the substrate, and a part of light propagating through the light propagation portion may leak to the substrate. In order to suppress leakage of evanescent waves to the substrate to thereby improve the propagation efficiency, it is thus important to control the distance L 2  between the light propagation portion and the substrate to a certain value. 
     In addition, in the diffraction grating region for extracting light from the core layer or for introducing light into the core layer, the extraction efficiency and the introducing efficiency (i.e., diffraction efficiency) deviate due to interference of light, as illustrated in  FIG. 15 . A description will be made with reference to an example where light is extracted from the core layer. As illustrated in  FIG. 15A , when light propagating through the core layer is diffracted toward the external side D 1  (the surface side in the thickness direction), diffracted light has light component La that is bent from a diffraction grating region  331  (corresponding to the diffraction grating region  131  of the second diffraction grating portion  13  of the present application) to the external side D 1 , as well as light component Lb that is bent toward the substrate side D 2  in the thickness direction of the optical waveguide. The light component Lb bent by the diffraction grating region formed on the surface of a core layer  32  toward the substrate side D 2  in the thickness direction passes through the core layer  32  and the support layer  40 , and reaches the boundary with (surface of) the substrate  39 . The light may be reflected at the boundary back to the diffraction grating region  331 . As a result, the light component Lb reflected back to the diffraction grating region  331  may interfere with the light component La extracted from the diffraction grating region  331  to the outside without being reflected, in the diffraction grating region  331 . The light component Lb takes a round trip through the core layer  32  and the support layer  40  and the phase of light component Lb delays behind the light component La. When the delayed phase is an integral multiple of 2π, constructive interference between the light component La and the light component Lb is maximized. Here, the effective film thickness t gr  of the core layer  32  is assumed to be a sum of the film thickness of the core layer  32  in recessed portions of the diffraction grating region  331 , and a half the film thickness difference of the core layer  32  between recessed portions and protruding portions of the diffraction grating region  331 . The phase delay due to one round trip of the core layer  32  is expressed by the following Expression (8), and the phase delay due to one round trip of the support layer  40  having a film thickness L 1  is expressed by the following Expression (9): 
     
       
         
           
             
               
                 
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     where n gr  and n L1  represent the respective refractive indices of materials forming the core layer  32  and the support layer  40 , and λ 0  represents the wavelength, in vacuum, of light propagating through the core layer  32 . Further, when the light is reflected at the boundary between the support layer  40  and the substrate  39 , the phase further shifts by  7 C if the refractive index of the support layer  40  is smaller than the refractive index of the substrate  39 . In view of these, the light component La interferes constructively with the light component Lb when the condition of the following Expression (10) is met: 
     
       
         
           
             
               
                 
                   
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     where m is a natural number. Thus, in order to efficiently extract light from the diffraction grating region  331  to the external side D 1 , it is important to control the phase difference between the reflected light component Lb and the non-reflected light component La, in other words, to control the distance L 1  between the diffraction grating region  331  and the substrate  39  to a certain value, as in controlling the distance L 2  between the light propagation portion and the substrate. 
     The above-mentioned principle is similarly applicable for introducing light from a light source into the core layer. Although a detailed description is omitted, in the diffraction grating region for introducing light into the core layer, as illustrated in  FIG. 15B , when light enters a diffraction grating region  311  from the external side D 1  and is introduced into the core layer, the introduced light has light component Lc introduced into the core layer from the diffraction grating region  311  (corresponding to the diffraction grating region  111  of the first diffraction grating portion  11  of the present application), as well as light component Ld passing through the diffraction grating region  311  and travels toward the substrate side D 2  in the thickness direction. The light component Ld traveling toward the substrate side D 2  in the thickness direction passes through the core layer  32  and the support layer  40 . The light then reaches the boundary with (surface of) the substrate  39 , and may be reflected at the boundary back to the diffraction grating region  311 . As a result, the light component Ld reflected back to the diffraction grating region  311  may interfere with the light component Lc directly introduced into the core layer from the external side D 1 , in the diffraction grating region  311 . The phenomenon similar to the light extraction occurs. Thus, in order to efficiently introduce light into the core layer from the diffraction grating region  311 , it is important to control the phase difference between the reflected light component Ld and the non-reflected light component Lc, i.e., to control the distance L 1  between the diffraction grating region  331  and the substrate  39  to a certain value, as in controlling the distance L 2  between the light propagation portion and the substrate. 
     Accordingly, in such a sensor, it is required to optimize the distances L 1  and L 2  in the optical waveguide by taking into consideration the diffraction efficiency of the diffraction grating region for extracting light from the core layer or introducing light into the core layer, and the propagation efficiency of the light propagation portion. 
     In a conventional optical waveguide, however, because a light propagation portion and a diffraction grating region are formed on a flat support layer on an SOI substrate or the like, the distance between the light propagation portion and the substrate equals the distance between the diffraction grating region and the substrate. It is thus difficult to design the optical waveguide so as to improve both the diffraction efficiency of the diffraction grating region and the propagation efficiency of the light propagation portion. 
     To meet the needs, in an optical waveguide  15  of the second embodiment, as illustrated in  FIG. 3 , a substrate  19  and a core layer  12  are separated from each other, and the distance L 1  between diffraction grating region  111  or  131  of the first diffraction grating portion  11  or the second diffraction grating portion  13  and the substrate  19  differs from the distance L 2  between the light propagation portion  10  and the substrate  19  (illustration of the diffraction grating region  131  of the second diffraction grating portion  13  is omitted). This enables the distance L 1  between the diffraction grating regions  111  or  131  of the first diffraction grating portion  11  or the second diffraction grating portion  13  and the substrate  19  and the distance L 2  between the light propagation portion  10  and the substrate  19  to be controlled independently from each other. This makes it possible to improve both the diffraction efficiencies of the first diffraction grating portion  11  and the second diffraction grating portion  13  and the propagation efficiency of the light propagation portion  10 . 
     Here, in the optical waveguide  15  of the second embodiment, the method to separate the substrate  19  and the core layer  12  from each other to control the distance L 1  and the distance L 2  so as to differ from each other is not particularly limited. In the illustrated embodiment, as described above, the substrate  19  and the core layer  12  are separated by providing the support layer  20  between the substrate  19  and the core layer  12 . Further, as illustrated in  FIG. 3 , the distance L 1  and the distance L 2  are controlled so as to differ from each other by disposing the first diffraction grating portion  11  or the second diffraction grating portion  13  and the light propagation portion  10  in the different layers. More specifically, the first diffraction grating portion  11  or the second diffraction grating portion  13  and the light propagation portion  10  are spatially separated in the thickness direction so that the first diffraction grating portion  11  or the second diffraction grating portion  13  and the light propagation portion  10  are disposed in the different layers (in this case, the first diffraction grating portion  11  or the second diffraction grating portion  13  and the light propagation portion  10  may be formed from the same or different materials). Controls of the distance L 1  and the distance L 2  become easier when the first diffraction grating portion  11  or the second diffraction grating portion  13  and the light propagation portion  10  are formed from different materials. Note that the first diffraction grating portion  11  or the second diffraction grating portion  13  and the light propagation portion  10  may not be necessarily separated (in other words, the first diffraction grating portion  11  or the second diffraction grating portion  13  and the light propagation portion  10  may be in at least partial contact with each other). 
     In the second embodiment, the material forming a separation portion between the substrate and the diffraction grating region preferably has a refractive index smaller than the refractive index of the substrate, and the distance L 1  between the diffraction grating region  111  or  131  of the first diffraction grating portion  11  or the second diffraction grating portion  13  and the substrate  19  satisfies preferably the following Expression (11), more preferably the following Expression (12), and even more preferably the following Expression (13): 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             
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     where λ 0  represents the average wavelength, in vacuum, of light propagating through the core layer  12 , n L1  represents the refractive index of the material present between the substrate  19  and the diffraction grating region  111  or  131  of the first diffraction grating portion  11  or the second diffraction grating portion  13 , t g r represents the effective film thickness of the diffraction grating region  111  or  131  of the first diffraction grating portion  11  or the second diffraction grating portion  13 , n gr  represents the refractive index of the material forming the diffraction grating region  111  or  131  of the first diffraction grating portion  11  or the second diffraction grating portion  13 , and m is a natural number. In the case where a plurality of materials are present between the substrate  19  and the diffraction grating region  111  or  131  of the first diffraction grating portion  11  or the second diffraction grating portion  13 , the effective value calculated as {Σ(n L1i   2 ×A L1i )} 1/2  is used as n L1 , where n L1i  represents the refractive index of each material present between the substrate  19  and the diffraction grating region  111  or  131  of the first diffraction grating portion  11  or the second diffraction grating portion  13 , and A L1i  represents the occupation ratio of the each material between the diffraction grating region  111  or  131  of the first diffraction grating portion  11  or the second diffraction grating portion  13  and the substrate  19  (the occupation ratio in the thickness direction in the second embodiment). The effective film thickness of the diffraction grating region  111  or  131  in the first diffraction grating portion  11  or the second diffraction grating portion  13  is defined as a sum of the film thickness of the core layer  12  in recessed portions of the diffraction grating region  111  or  131 , and a half the film thickness difference of the core layer  12  between recessed portions and protruding portions of the diffraction grating region  111  or  131 . Further, in the case in which a plurality of materials are present for forming the diffraction grating region  111  or  131  of the first diffraction grating portion  11  or the second diffraction grating portion  13 , the effective value calculated as {Σ(n gri   2 ×A gri )} 1/2  is used as n gr , where n gri  represents the refractive index of each material forming the core region  12  in recessed portions of the diffraction grating region  111  or  131 , and A gri  represents the occupation ratio of the each material in the recessed portions of the diffraction grating region  111  or  131 , in the core layer  12  in the recessed portions of the diffraction grating region  111  or  131 . When the distance L 1  satisfies one of the above expressions, the diffraction efficiency of light at the first diffraction grating portion  11  or the second diffraction grating portion  13  is maintained to a high level. 
     In the second embodiment, the distance L 1  can be controlled so as to satisfy one of the above expressions by adjusting the thickness of the support layer  20 , and the thickness of an intermediate layer  22  between the diffraction grating region  111  or  131  of the first diffraction grating portion  11  or the second diffraction grating portion  13  and the light propagation portion  10 . Note that the intermediate layer  22  may be a layer made from a material (including the air) having a relatively lower refractive index than that of the core layer  12 , and is a silicone oxide (SiO 2 ) film in the illustrated example. When the intermediate layer  22  and the support layer  20  are formed as silicon oxide films, the refractive index of the material between the diffraction grating region  111  or  131  of the first grating portion  11  or the second grating portion  13  and the substrate  19  is estimated to be about 1.4. Further, the average wavelength λ 0 , in vacuum, of light propagating through the core layer  12  is about 4.3 μm, for example. 
     Further, in the second embodiment, the distance L 2  at which the light propagation portion  10  and the substrate  19  are separated from each other is equal to or greater than the distance given by the following Expression (14): 
     
       
         
           
             
               
                 
                   
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     where λ 0  represents the average wavelength, in vacuum, of light propagating through the core layer  12 , n pro  represents the refractive index of the material forming the light propagation portion  10 , and n L2  represents the refractive index of the material present in the portion sandwiched between the light propagation portion  10  and the substrate  19 . In the case where a plurality of materials are present in the portion sandwiched between the light propagation portion  10  and the substrate  19 , the largest refractive index among the refractive indices of the plurality of materials is used as n L2 . By setting the distance L 2  to the predetermined distance, leakage of an evanescent wave EW extending from the light propagation portion  10  to the substrate  19  is suppressed to a sufficiently low level, thereby further improving the propagation efficiency of the light propagation portion  10 . 
     In the second embodiment, the distance L 2  can be controlled to the aforementioned predetermined distance by using an SOI substrate having a support layer  20  of which thickness is controlled. 
     In the second embodiment, the distance L 1  and the distance L 2  can have any relationship. For example, in an optical densitometer for detecting CO 2 , which is a gas typically present in the environment, infrared radiation with a wavelength of about 4.3 μm (wavelength in vacuum) is typically used as the light to propagate through the core layer  12 . When the separation portion between the diffraction grating region  111  or  131  of the first diffraction grating portion  11  or the second diffraction grating portion  13  and the substrate  19  is formed as a silicon oxide film and the diffraction grating region  111  or  131  is formed from silicon with an effective film thickness of about 0.9 μm, the parameters giving the distance L 1  are: λ 0 =4.3 μm, n L1 =1.4, n gr =3.4, and t gr =about 0.9 μm. The distance L 1  is preferably from 4.1 μm to 5.3 μm, more preferably from 4.3 μm to 5.1 μm, and even more preferably from 4.5 μm to 4.9 μm, for example. Under these conditions, the distance L 2  is about 2.5 μm, for example. In the case where a portion serving as the distance L 2  is formed by using a buried oxide film (BOX) layer on a bonded-type SOI substrate, the process throughput decreases, resulting in a cost increase, as the BOX layer becomes thicker. It is thus desirable to optimize the distance L 1  while maintaining the distance L 2  to a value of about 2.5 μm in view of both the optical performances and the cost. 
     Further, in the optical waveguide  15  of the second embodiment, the entire diffraction grating portions  11  and  13 , including the extension regions  111   a ,  131   a , are separated from the light propagation portion  10  in the thickness direction, and the distance L 1  between the diffraction grating region  111 ,  131  and the substrate  19  differs from the distance L 2  between the light propagation portion  10  and the substrate  19  by a difference equal to or greater than the film thickness of the light propagation portion  10  throughout the diffraction grating regions  111 ,  131 . 
     &lt;Method of Manufacturing Optical Waveguide in Second Embodiment&gt; 
     The method of manufacturing the optical waveguide  15  according to the second embodiment is the same as the manufacturing method described in the first embodiment, and a detailed description thereof is omitted. 
     Third Embodiment 
     Next, an optical waveguide according to a third embodiment of the present disclosure is now described with reference to  FIGS. 12 and 13 . Elements that are the same as those of the first embodiment are denoted by the same reference signs, and a description thereof is omitted. 
     In the third embodiment, as illustrated in  FIG. 12 , a first diffraction grating portion  11  has a plurality of diffraction grating regions  111 . At least two diffraction grating regions  111  among the plurality of the diffraction grating regions  111  in the first diffraction grating portion  11  receive light emitted from the same light-emitting surface of a light source  17 . Specifically, the range R 1  in  FIG. 12  is a range, in plan view, yielded by projecting the range considered to be the same light-emitting surface within the light-emitting surface of the light source  17  onto the diffraction grating portion  11  in a direction orthogonal to the light-emitting surface. At least two diffraction grating regions  111  are present within this range R 1 . 
     There has been a problem in that light cannot be introduced into an optical waveguide (core layer  12 ) from a light-emitting element with high efficiency when light is received from the light-emitting element on one large diffraction grating region. In contrast, as illustrated in  FIG. 12 , in the configuration where light emitted from the same light-emitting surface of the light source  17  is received on at least two first diffraction grating regions  111  among the plurality of diffraction grating regions  111 , the diffraction grating regions  111  can be made relatively smaller. A reduced efficiency due to a large diffraction grating region can be suppressed. Light from the light-emitting element can therefore be introduced into the optical waveguide with high efficiency. 
     Note that the range considered to be the same light-emitting surface is not necessarily limited to one light-emitting surface. In the case of a plurality of light-emitting surfaces, the total range of the plurality of light-emitting surfaces is considered one light-emitting surface when the light outputted from each light-emitting surface is synchronously controlled by a common drive system. 
     All of the diffraction grating regions  111  of the first diffraction grating portion  11  are located within the range R 1  in the example in  FIG. 12 , but a diffraction grating region  111  may be located outside of the range R 1 . Even if a diffraction grating region  111  is located outside of the range R 1 , or if a part of the diffraction grating region  111  is outside the range R 1 , light can be introduced into the core layer  12  by the diffraction grating region  111  located outside, or the part located outside, since light spreads from the light-emitting surface of the light source  17 . 
     In the third embodiment, as illustrated in  FIG. 13 , each diffraction grating region  111  of the first diffraction grating portion  11  has an extension region  111   a , and each diffraction grating region  111  and the extension region  111   a  connected to the diffraction grating region  111  are all made from materials different from each propagating path  101 . Each extension region  111   a  and the corresponding propagation channel  101  are separated from each other in the thickness direction. As a result, as illustrated, on the surface side in the thickness direction of one diffraction grating region  111  relative to one propagation channel  101  optically coupled to an extension region  111   a  connected to the one diffraction grating region  111 , another diffraction grating region  111  can be formed so as to be separated from the one propagation channel  101 . By forming the another diffraction grating region  111  on the surface side in the thickness direction relative to the one propagation channel  101 , diffraction grating regions  111  can be disposed more densely in the first diffraction grating portion  11 , which enables light from the light-emitting element to be introduced into the optical waveguide with high efficiency. 
     In the example in  FIG. 12 , all of the propagation channels  101  of the light propagation portion  10  are present on the substrate side in the thickness direction relative to the diffraction grating regions  111  of the first diffraction grating portion  11 , and the second optical coupling regions  101   a  of all of the propagation channels  101  are optically coupled to the corresponding first optical coupling regions  111   b  of extension regions  111   a  connecting to the diffraction grating regions  111 . Similarly to the first diffraction grating portion  11 , in the diffraction grating region  131  of the second diffraction grating portion  13 , all of the propagation channels  101  are optically coupled to the corresponding diffraction grating regions  131  via the first optical coupling regions  131   b  and the second optical coupling regions  101   a.    
     In the third embodiment, although the diffraction grating portion includes the plurality of diffraction grating regions, a part of the diffraction grating regions may be connected to the corresponding extension regions so that the first optical coupling regions of the extension regions and the second optical coupling regions  101   a  of the propagation channels  101  are optically coupled to each other, and the remaining diffraction grating region may be directly connected to the propagation channels  101  bypassing the first optical coupling regions and the second optical coupling regions  101   a  of the propagation channels  101 . 
     In the optical waveguide  15  of the third embodiment, the light propagation portion  10  of the optical waveguide  15  has a plurality of propagation channels  101  that each receive the light received by one diffraction grating region  111 , propagate the light, and guide the light to one diffraction grating  131 , as illustrated in  FIG. 12 . This enables the diffraction grating regions  111  in the first diffraction grating portion  11  and the diffraction grating regions  131  in the second diffraction grating portion  13  to be disposed more densely, which achieves more efficient utilization of light from the light-emitting element. 
     In the illustrated example, all of the plurality of propagation channels  101  are arranged in parallel between the diffraction grating regions  111  and the diffraction grating regions  131 . The plurality of propagation channels  101 , however, are not necessarily arranged in parallel in the third embodiment, and the propagation channels  101  may take any forms. For example, propagation channels  101  may be merged or may be branched between the diffraction grating regions  111  and the diffraction grating regions  131 . 
     In the third embodiment, the diffraction grating regions  111  in the first diffraction grating portion  11  are all in the same size and shape, but the diffraction grating regions  111  may have different sizes and shapes as the first diffraction grating portion  11 . The optical waveguide  15  can be provided with multifunctionality by forming diffraction grating regions with different sizes and shapes. An example of multifunctionality is to vary the period of unevenness forming each diffraction grating region  111  to enable selection of many wavelengths. 
     The at least two diffraction grating regions  111  among the plurality of diffraction grating regions  111  in the third embodiment are preferably located in a 5×5 mm 2  range, more preferably a 1×1 mm 2  range, and even more preferably a 500×500 μm 2  range. This enables the light-emitting element and the optical waveguide  15  to be coupled highly efficiently. 
     Further, in the third embodiment, the ratio of the area of diffraction grating regions  111  is preferably 30% or more and more preferably 60% or more in the 5×5 mm 2  range or the 1×1 mm 2  range or the 500×500 μm 2  range. This enables the light-emitting element and the optical waveguide  15  to be coupled highly efficiently. 
     In the third embodiment, the second diffraction grating portion  13  may have any structure. Specifically, the structure of the second diffraction grating portion  13  in the illustrated example is the same as the structure of the first diffraction grating portion  11  but may instead be different. A range R 2  in  FIG. 12  is a range, in plan view of the substrate  19  of the optical waveguide  15  (when looking towards the substrate  19 ), yielded by projecting the range of the detector onto the second diffraction grating portion  13  in a direction orthogonal to the detection surface of the detector arranged. The size and arrangement of the diffraction grating regions  131  in the second diffraction grating portion  13  may be changed in any way depending on the detector, for example. 
     &lt;Method of Manufacturing Optical Waveguide in Third Embodiment&gt; 
     The method of manufacturing the optical waveguide  15  according to the third embodiment is the same as the manufacturing method described in the first embodiment except for change of the pattern used in lithography, and a detailed description thereof is omitted. 
     INDUSTRIAL APPLICABILITY 
     The present disclosure can provide an optical densitometer and an optical waveguide provided with a diffraction grating portion and a light propagation portion both exhibiting high performances as a core layer more easily.