Abstract:
Provided is an optical mode switch that can effect a more compact optical switch. The optical mode switch ( 100 ) is provided with: a single input port ( 1 ); a single output port ( 2 ); two waveguides ( 10 ) provided in parallel between the input port ( 1 ) and the output port ( 2 ); and a refractive index altering means ( 8 ) that alters the refractive index of the waveguides. Any given mode light input to the input port ( 1 ) is output as any given mode light from the output port ( 2 ) in accordance with the refractive index altered by the refractive index altering means ( 8 ).

Description:
RELATED APPLICATIONS 
     This patent application a continuation of International Application No. PCT/JP2013/072848, filed on Aug. 27, 2013, now pending, which claims priority to Japanese Application No. 2012-186852, filed Aug. 27, 2012, the contents and teachings of each of which are hereby incorporated by reference in their entirety. 
    
    
     TECHNICAL FIELD 
     The present invention relates to an optical mode switch that switches arbitrary mode light into arbitrary mode light. 
     BACKGROUND 
     Conventional spatial optical switch is comprised of: an input waveguide that inputs an optical signal; a slab waveguide that distributes the optical signal to an arrayed waveguide; an arrayed waveguide that is equipped with a triangular-shaped electrode for performing current injection or voltage application in order to change refractive index; a slab waveguide that couples outputted light from the arrayed waveguide to an output waveguide; and a plurality of output waveguides that output optical signals (see Patent Literature 1: Japanese Patent Application Laid-Open No. 2002-72157, for example). This conventional spatial optical switch has a plurality of output waveguides arranged in parallel, which spatially distribute an input optical signal of one wavelength by a control signal to be applied to an electrode, and couples a signal of one wavelength to different output waveguides. 
     SUMMARY 
     Technical Problem 
     In the conventional spatial optical switch, each output waveguide of the plurality of output waveguides is optically connected to one optical fiber and, therefore, it is necessary to widen the distance between adjacent output waveguides, depending on the diameter of the optical fiber (the pitch between adjacent optical fibers). As a result, there is a problem that the spatial optical switch cannot be downsized, and the number of output waveguides is limited and large-scale integration cannot be realized. 
     In contrast, on the background of a recent increase in information traffic, mode multiplexing transmission technology has attracted attention as one of future means for enhancing the capacity. Using this mode multiplexing transmission technology, an optical switch, when spatial position information is switched to mode information by mode switch devices connected before and after the optical switch, functions as a switch for switching the mode. Therefore, it is sufficient to arrange single waveguide for the input port as well as output port of the device. 
     Thus, an optical switch that switches arbitrary mode light into arbitrary mode light (optical mode switch) can be expected to be applied to mode multiplexing transmission, as well as applied to a future high-integrated spatial optical switch, such as the reduction of the number of optical components to be coupled with the end of the optical switch (input waveguide, output waveguide), by associating the mode information with the spatial position information. However, the optical mode switch is in a developmental stage and does not exist as a product at present. 
     This invention has been made to solve the above problems and to provide an optical mode switch that can reduce the size of an optical switch. 
     Solution to Problem 
     An optical mode switch according to the present invention includes: a single input port; a single output port; and mode switch means arranged between the input port and the output port, and the mode switch means outputs arbitrary mode light inputted from the input port, from the output port, as arbitrary mode light. 
     Advantageous Effects of Invention 
     In the optical mode switch according to the present invention, the size of the optical switch can be reduced and any mode light can be switched into any mode light. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The foregoing and other objects, features and advantages will be apparent from the following description of particular embodiments of the innovation, as illustrated in the accompanying drawings in which like reference characters refer to the same parts throughout the different views. The drawings are not necessarily to scale, emphasis instead being placed upon illustrating the principles of various embodiments of the innovation. 
         FIG. 1( a )  is a plan view showing an example of a schematic configuration of an optical mode switch according to the first embodiment; 
         FIG. 1( b )  is an illustration for explaining a dimension of a first branch waveguide shown in  FIG. 1( a ) ; 
         FIG. 1( c )  is an illustration for explaining a dimension of a first merge waveguide shown in  FIG. 1( a ) ; 
         FIG. 1( d )  is an illustration for explaining a dimension of a second merge waveguide shown in  FIG. 1( a ) ; 
         FIG. 2( a )  is an enlarged view of a refractive index changing means in the first merge waveguide shown in  FIG. 1( a ) ; 
         FIG. 2( b )  is an enlarged view of a refractive index changing means in the second merge waveguide shown in  FIG. 1( a ) ; 
         FIG. 2( c )  is a cross-sectional view of the refractive index changing means shown in  FIG. 2( a )  and  FIG. 2( b )  taken along the line B-B′; 
         FIG. 2( d )  is a cross-sectional view of the optical mode switch shown in  FIG. 1( a )  taken along the line A-A′; 
         FIG. 3( a )  to  FIG. 3( f )  are sectional views corresponding to  FIG. 2( c )  for explaining a method of fabrication the optical mode switch shown in  FIG. 1 ; 
         FIG. 4( a )  to  FIG. 4( e )  are cross-sectional views for explaining the continuation of the fabrication method of the optical mode switch shown in  FIG. 3( a )  to  FIG. 3( f ) ; 
         FIG. 5( a )  to  FIG. 5( f )  are cross-sectional views for explaining the continuation of the fabrication method of the optical mode switch shown in  FIG. 4( a )  to  FIG. 4( e ) ; 
         FIG. 6( a )  to  FIG. 6( f )  are sectional views corresponding to  FIG. 2( d )  for explaining the method of fabrication the optical mode switch shown in  FIG. 1 ; 
         FIG. 7( a )  to  FIG. 7( e )  are cross-sectional views for explaining the continuation of the fabrication method of the optical mode switch shown in  FIG. 6( a )  to  FIG. 6( f ) ; 
         FIG. 8( a )  to  FIG. 8( f )  are cross-sectional views for explaining the continuation of the fabrication method of the optical mode switch shown in  FIG. 7( a )  to  FIG. 7( e ) ; 
         FIG. 9( a )  to  FIG. 9( d )  are graphs showing the relationship between amount of refractive index change ΔN, ΔN in a refractive index changing region shown in  FIG. 1( a )  and transmittance of zero-order mode light and first-order mode light, in particular,  FIG. 9( a )  being a graph showing the relationship between the amount of refractive index change ΔN and the transmittance when the zero-order mode light is inputted,  FIG. 9( b )  being a graph showing the relationship between the amount of refractive index change ΔN and the transmittance when the zero-order mode light is inputted,  FIG. 9( c )  being a graph showing the relationship between the amount of refractive index change ΔN and the transmittance when the first-order mode light is inputted, and  FIG. 9( d )  being a graph showing the relationship between the amount of refractive index change ΔN and the transmittance when the first-order mode light is inputted; 
         FIG. 10( a )  to  FIG. 10( d )  show an operational simulation of the optical mode switch shown in  FIG. 1( a )  to  FIG. 1( d ) , in particular,  FIG. 10( a )  being an explanatory drawing showing an optical field in which the zero-order mode light is inputted and the amount of refractive index change ΔN is set to −0.017,  FIG. 10( b )  being an explanatory drawing showing an optical field in which the zero-order mode light is inputted and the amount of refractive index change ΔN is set to −0.023,  FIG. 10( c )  being an explanatory drawing showing an optical field in which the first-order mode light is inputted and the amount of refractive index change ΔN is set to −0.017, and  FIG. 10( d )  being an explanatory drawing showing an optical field in which the first-order mode light is inputted and the amount of refractive index change ΔN is set to −0.023; 
         FIG. 11( a )  is a plan view showing an example of a schematic configuration of an optical mode switch according to the second embodiment; 
         FIG. 11( b )  is an illustration for explaining a dimension of a first branch waveguide shown in  FIG. 11( a ) ; 
         FIG. 11( c )  is an enlarged view of a refractive index changing means in a second linear waveguide shown in  FIG. 11( a ) ; 
         FIG. 12( a )  and  FIG. 12( b )  are graphs showing the relationship between amount of refractive index change ΔN in a refractive index changing region shown in  FIG. 11( a )  and output of zero-order mode light and first-order mode light, in particular,  FIG. 12( a )  being a graph showing the relationship between the amount of refractive index change ΔN and the output when the zero-order mode light is inputted, and  FIG. 12( b )  being a graph showing the relationship between the amount of refractive index change ΔN and the output when the first-order mode light is inputted; 
         FIG. 13( a )  to  FIG. 13( d )  show an operational simulation of the optical mode switch shown in  FIG. 11( a )  to  FIG. 11( c ) , in particular,  FIG. 13( a )  being an explanatory drawing showing an optical field in which the zero-order mode light is inputted and the amount of refractive index change ΔN is set to 0,  FIG. 13( b )  being an explanatory drawing showing an optical field in which the zero-order mode light is inputted and the amount of refractive index change ΔN is set to −0.0039,  FIG. 13( c )  being an explanatory drawing showing an optical field in which the first-order mode light is inputted and the amount of refractive index change ΔN is set to 0, and  FIG. 13( d )  being an explanatory drawing showing an optical field in which the first-order mode light is inputted and the amount of refractive index change ΔN is set to −0.0039; 
         FIG. 14( a )  is a plan view showing an example of a schematic configuration of an optical mode switch according to the third embodiment; 
         FIG. 14( b )  is an enlarged view of a refractive index changing means in a third linear waveguide shown in  FIG. 14( a ) ; 
         FIG. 14( c )  is a cross-sectional view of a 2×1 type MMI waveguide shown in  FIG. 14( a )  taken along the line C-C′; 
         FIG. 15( a )  is a plan view showing an example of a schematic configuration of an optical mode switch according to the fourth embodiment; 
         FIG. 15( b )  is an enlarged view of a refractive index changing means in a second linear waveguide shown in  FIG. 15( a ) ; 
         FIG. 15( c )  is a cross-sectional view of a 1×2 type MMI waveguide shown in  FIG. 15( a )  taken along the line D-D′; 
         FIG. 16( a )  is a plan view showing an example of a schematic configuration of an optical mode switch according to the fifth embodiment; 
         FIG. 16( b )  is an illustration for explaining an example of a mode switching of the optical mode switch shown in  FIG. 16( a ) ; 
         FIG. 16( c )  is a plan view showing another example of a schematic configuration of an optical mode switch according to the fifth embodiment; 
         FIG. 17( a )  to  FIG. 17( d )  are explanatory drawings showing a state (optical field) in which light is switched from zero-order mode to another mode according to a beam propagation method simulation in the optical mode switch shown in  FIG. 16( a ) , in particular,  FIG. 17( a )  being an explanatory drawing showing an optical field in which the zero-order mode light is inputted and zero-order mode light is outputted,  FIG. 17( b )  being an explanatory drawing showing an optical field in which the zero-order mode light is inputted and first-order mode light is outputted,  FIG. 17( c )  being an explanatory drawing showing an optical field in which the zero-order mode light is inputted and second-order mode light is outputted, and  FIG. 17( d )  being an explanatory drawing showing an optical field in which the zero-order mode light is inputted and third-order mode light is outputted; 
         FIG. 18( a )  is a plan view showing an example of a schematic configuration of an optical mode switch according to the sixth embodiment; and 
         FIG. 18( b )  is a plan view showing another example of a schematic configuration of an optical mode switch according to the sixth embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     First Embodiment of the Present Invention 
     Optical mode switch  100  includes single input port  1 , single output port  2 , mode switch means  101  (not shown) arranged between input port  1  and output port  2 . 
     Mode switch means  101  include optical branch waveguide  20   a  (not shown) that divides mode light inputted from input port  1 , refractive index changing means  8  that is arranged after optical branch waveguide  20   a  and changes a refractive index of the waveguide, and optical multiplexing waveguide  30   a  (not shown) that is arranged after refractive index changing means  8  and couples the mode light divided by optical branch waveguide  20   a  to output the coupled mode light from output port  2 . 
     In the following description, the case in which optical branch waveguide  20   a  is a Y-shaped waveguide having two waveguides in its posterior part, and optical multiplexing waveguide  30   a  is a Y-shaped waveguide having two waveguides in its anterior part will be described as an example. However, the number of waveguides between optical branch waveguides  20   a  and optical multiplexing waveguide  30   a  is not limited to two. Optical branch waveguide  20   a  may have three or more waveguides in its posterior part, and optical multiplexing waveguide  30   a  may have three or more waveguides in its anterior part. 
     Optical mode switch  100  includes single input port  1 , single output port  2 , two waveguides  10  that are juxtaposed between input port  1  and output port  2 , and refractive index changing means  8  that changes a refractive index of the waveguide by carrier injection by p-intrinsic-n (PIN) diode structure. In optical mode switch  100 , arbitrary mode light is inputted to input port  1  and arbitrary mode light is outputted from output port  2 . 
     In addition, optical mode switch  100  according to this embodiment further includes, as shown in  FIG. 1( a ) , Y-branch waveguide  20  that is arranged between input port  1  and two waveguides  10  and branches mode light incident from input port  1  into two, and merge waveguide  30  that is arranged between output port  2  and two waveguides  10  and couples the mode light divided by Y-branch waveguide  20  to emit the resultant mode light to output port  2  side. 
     In particular, two waveguides  10  according to the present embodiment are tapered linear waveguides (first linear waveguide  11  and second linear waveguide  12 ) with their waveguide widths gradually changed, according to the difference between the waveguide width of Y-branch waveguide  20  and the waveguide width of merge waveguide  30 . Specifically, in first linear waveguide  11 , the length of waveguide along a waveguiding direction of light (hereinafter referred to as “waveguide length”) is 450 μm, the waveguide width at one end to be coupled with Y-branch waveguide  20  is 0.5 μm, the waveguide width at the other end to be coupled with merge waveguide  30  is 0.6 μm. In second linear waveguide  11 , the waveguide length is 450 μm, the waveguide width at one end to be coupled with Y-branch waveguide  20  is 0.7 μm, and the waveguide width at the other end to be coupled with merge waveguide  30  is 0.6 μm. 
     In the planar view shown in  FIG. 1( a ) , Y-branch waveguide  20  according to the present embodiment has a planar shape in which two divided waveguides (first branched waveguide  21  and second branched waveguide  22 ) are asymmetric (asymmetric Y-shaped waveguide). 
     Specifically, the region (hereinafter referred to as “pre-branching waveguide  23 ”) except for the two divided waveguides (first branched waveguide  21  and second branched waveguide  22 ) of Y-branch waveguide  20  is a linear waveguide having the waveguide length of 200 μm and the waveguide width of 1.2 μm. First branched waveguide  21  is a substantially S-shaped curved waveguide in which the waveguide width is 0.5 μm, the difference in the width direction between the center of core at one end to be coupled with pre-branching waveguide  23  and the center of core at the other end to be coupled with first linear waveguide  11  is 1 μm, and the radius of curvature R1 is 5625.25 μm as shown in  FIG. 1( b ) . Second branched waveguide  22  is a linear waveguide in which the waveguide length is 150 μm and the waveguide width is 0.7 μm. 
     In the planar view shown in  FIG. 1( a ) , merge waveguide  30  according to the present embodiment has a planar shape in which two merging waveguides (first merging waveguide  31  and second merging waveguide  32 ) are symmetric (symmetric Y-shaped waveguide). Specifically, the region (hereinafter referred to as “post-merging waveguide  33 ”) except for the two merging waveguides (first merging waveguide  31  and second merging waveguide  32 ) of merge waveguide  30  is a linear waveguide having the waveguide length of 200 μm and the waveguide width of 1.2 μm. 
     First merging waveguide  31  is a curved waveguide that curves inward (center side of merge waveguide  30 ) in which the waveguide width is 0.6 μm, the difference in the width direction between the center of core at one end to be coupled with first linear waveguide  11  and the center of core at the other end to be coupled with post-merging waveguide  33  is 0.5 μm, and the radius of curvature R2 is 90000.25 μm, as shown in  FIG. 1( c ) . Second merging waveguide  32  is a curved waveguide that curves inward (center side of merge waveguide  30 ) in which the waveguide width is 0.6 μm, the difference in the width direction between the center of core at one end to be coupled with second linear waveguide  12  and the center of core at the other end to be coupled with post-merging waveguide  33  is 0.5 μm, and the radius of curvature R3 is 90000.25 μm, as shown in  FIG. 1( d ) . 
     Refractive index changing means  8  according to the present embodiment is arranged in two merging waveguides (first merging waveguide  31  and second merging waveguide  32 ) of merge waveguide  30 . 
     Furthermore, optical mode switch  100  includes: first clad layer  120  (e.g., SiO 2  layer of silicon-on-insulator (SOI) substrate) laminated onto substrate  110  (e.g., Si substrate of SOI substrate); semiconductor layer  130  (e.g., Si layer of SOI substrate) that is laminated onto first clad layer  120  and includes intrinsic (i-type) semiconductor region  131  having a refractive index higher than the refractive index of first clad layer  120 ; and second semiconductor layer  140  (e.g., SiO 2  layer) that is laminated onto semiconductor layer  130  and has a refractive index lower than the refractive index of semiconductor layer  130 , as shown in  FIG. 2( c )  and  FIG. 2( d ) . 
     Refractive index changing means  8  includes: refractive index changing region  3  in which p-type semiconductor region  132  and n-type semiconductor region  133 , which are formed by doping an impurity to intrinsic semiconductor region  131  of semiconductor layer  130 , are juxtaposed in the waveguiding direction along with intrinsic semiconductor region  131  to constitute pin junction; first electrode  4   a  for applying a voltage to p-type semiconductor region  132  of refractive index changing region  3 ; second electrode  4   b  for applying a voltage to n-type semiconductor region  133  of refractive index changing region  3 ; first connection  5   a  that electrically connects p-type semiconductor region  132  and first electrode  4   a ; and second connection  5   b  that electrically connects n-type semiconductor region  133  and second electrode  4   b , as shown in  FIG. 2( a ) ,  FIG. 2( b )  and  FIG. 2( c ) . 
     In refractive index changing region  3 , when a forward voltage is applied to the pin junction through first electrode  4   a  and first connection  5   a  and second electrode  4   b  and second connection  5   b , carriers (electrons and holes) are supplied to intrinsic semiconductor region  131 . By the plasma effect of the carriers, the refractive index of intrinsic semiconductor region  131  will change. 
     Semiconductor layer  130  of refractive index changing region  3  according to the present embodiment is composed of: intrinsic semiconductor region  131  formed of Si as an intrinsic semiconductor; p-type semiconductor region  132  formed by doping boron (B), as an impurity, to Si of the intrinsic semiconductor; and n-type semiconductor region  133  formed by doping phosphorus (P), as an impurity, to Si of the intrinsic semiconductor. 
     Refractive index changing region  3  has a structure in which intrinsic semiconductor region  131  has two grooves (trench  3   a ) extending in the waveguiding direction at respective boundaries with p-type semiconductor region  132  and n-type semiconductor region  133 . In particular, when the width of trench  3   a  (hereinafter referred to as “trench width W t ”) of refractive index changing region  3  is set to the wavelength order or less (hereinafter referred to as “narrowed trench structure”), overetching can be suppressed using the effect (reactive ion etching lag: RIE lag) that the narrower the pattern is, the shallower the etching depth becomes and less the etching depth amount becomes than the surroundings. 
     Moreover, intrinsic semiconductor region  131  of refractive index changing region  3  includes: rib portion  131   a  that becomes a waveguide; and slab portion  131   b  that has a thickness (a thickness of the etched Si layer, hereinafter referred to as “Si layer residual thickness T Si ”) thinner than the thickness (a thickness of the unetched Si layer, hereinafter referred to as “Si layer overall thickness d”) of rib portion  131   a  and that is juxtaposed on both sides of rib portion  131   a  in the waveguiding direction. In addition, rib portion  131   a  according to this embodiment is a part of each of the two waveguides (first merging waveguide  31  and second merging waveguide  32 ) as shown in  FIG. 1A . 
     Further, all of p-type semiconductor region  132  and n-type semiconductor region  133  have a thickness thicker than the thickness (Si layer residual thickness T Si ) of slab portion  131   b  of intrinsic semiconductor region  131 . 
     Next, a method of fabrication optical mode switch  100  will be explained with reference to  FIG. 3( a )  to  FIG. 8( f ) . In addition, sectional views showing the fabrication process of two waveguides  10  (first linear waveguide  11  and second linear waveguide  12 ) and Y-branch waveguide  20  (first branched waveguide  21  and first branched waveguide  21 ) will be omitted because two waveguides  10  (first linear waveguide  11  and second linear waveguide  12 ) and Y-branch waveguide  20  (first branched waveguide  21  and second linear waveguide  12 ) are different from pre-branching waveguide  23  and merge waveguide  30  only in waveguide width but are the same with pre-branching waveguide  23  and merge waveguide  30  in the fabrication process 
     First, the SOI substrate (the Si substrate (substrate  110 ), the SiO2 layer (first clad layer  120 ), and the Si layer (semiconductor layer  130 )) is coated with a photoresist on semiconductor layer  130 . Then, using a photolithography method with a stepper, mask  161  for etching is formed on semiconductor layer  130  ( FIG. 3( a )  and  FIG. 6( a ) ) to fit the planar shape of the waveguiding region (two waveguides  10 , Y-branch waveguide  20 , and merge waveguide  30 ) shown in  FIG. 1( a )  and the region (rib portion  131   a  of intrinsic semiconductor region  131 , p-type semiconductor region  132 , and n-type semiconductor region  133 ) except for slab portion  131   b  of refractive index changing region  3  shown in  FIG. 2( a )  and  FIG. 2( b ) . 
     By using this mask  161 , through dry etching by RIE (reactive ion etching) method, non-waveguiding regions shown in  FIG. 1( a )  and unnecessary portions, which will be slab portion  131   b  shown in  FIG. 2( a )  and  FIG. 2( b ) , of semiconductor layer  130  are removed partially (only portions in which mask  161  is not formed) to form core layers of the waveguiding region and trench  3   a  ( FIG. 3( b )  and  FIG. 6( b ) ). In this case, openings of mask  161  in slab portion  131   b  shown in  FIG. 2( a )  and  FIG. 2( b )  have a size of wavelength order or less and are extremely narrow compared to openings of mask  161  in the non-waveguiding region shown in  FIG. 1( a ) . By RIE lag effect, therefore, semiconductor layer  130  will remain as slab portion  131   b  (that is, overetching will be suppressed), even when dry etching in the non-waveguiding region has ended. Then, mask  161  on semiconductor layer  130  is removed by an organic solvent and an ashing method ( FIG. 3( c )  and  FIG. 6( c ) ). 
     Thus, by using only mask  161 , the thickness of semiconductor layer  130  that will be p-type semiconductor region  132  and n-type semiconductor region  133  will be substantially the same as the thickness (Si layer overall thickness d) of semiconductor layer  130  that will be rib portion  131   a  of intrinsic semiconductor region  131 . 
     In addition, when the thickness of semiconductor layer  130  that will be p-type semiconductor region  132  and n-type semiconductor region  133  is made thinner than the thickness (Si layer overall thickness d) of semiconductor layer  130  that will be rib portion  131   a  of intrinsic semiconductor region  131 , the thickness of semiconductor layer  130  that will be p-type semiconductor region  132  and n-type semiconductor region  133  needs to be controlled such that the thickness (Si layer residual thickness T Si ) of semiconductor layer  130  that will be slab portion  131   b  of intrinsic semiconductor region  131  will be at least 0.01 μm or more. 
     Then, a photoresist is coated onto first clad layer  120  and semiconductor layer  130  that are exposed. Then, using a photolithography method by a stepper, mask  162  for a dopant is formed on exposed first clad layer  120  and semiconductor layer  130  to fit the planar shape of the region except for p-type semiconductor region  132  shown in  FIG. 2( a )  and  FIG. 2( b ) . Then, p-type dopant (for example, boron) ions are implanted into openings of semiconductor layer  130  ( FIG. 3( d )  and  FIG. 6( d ) ). Then, mask  162  on first clad layer  120  and semiconductor layer  130  is removed by an organic solvent and an ashing method ( FIG. 3( e )  and  FIG. 6( e ) ). 
     Then, a photoresist is coated onto first clad layer  120  and semiconductor layer  130  that are exposed. Then, using a photolithography method by a stepper, mask  163  for a dopant is formed on exposed first clad layer  120  and semiconductor layer  130  to fit the planar shape of the region except for n-type semiconductor region  133  shown in  FIG. 2( a )  and  FIG. 2( b ) . Then, n-type dopant (for example, phosphorus) ions are implanted into openings of semiconductor layer  130  ( FIG. 3( f )  and  FIG. 6( f ) ). 
     Then, mask  163  on first clad layer  120  and semiconductor layer  130  is removed by an organic solvent and an ashing method ( FIG. 3( e )  and  FIG. 6( e ) ) and heat treatment to activate the impurity is performed to form p-type semiconductor region  132  and n-type semiconductor region  133  ( FIG. 4( a )  and  FIG. 7( a ) ). In this case, the region except for p-type semiconductor region  132  and n-type semiconductor region  133  of semiconductor layer  130  will be intrinsic semiconductor region  131 , and intrinsic semiconductor region  131  in refractive index changing region  3  will include rib portion  131   a  and slab portion  131   b.    
     Then, a photoresist having the thickness of about 1 μm is coated onto first clad layer  120  and semiconductor layer  130  that are exposed. Then, using a photolithography method by a stepper, mask  164  for etching is formed to fit the planar shape of the region except for p-type semiconductor region  132  and n-type semiconductor region  133  shown in  FIG. 2( a )  and  FIG. 2( b )  ( FIG. 4( b )  and  FIG. 7( b ) ). 
     Then, using an electron beam evaporation method or sputtering, a metal (Ti (titanium)/Al (aluminum)) that becomes part of first connection  5   a  and second connection  5   b  is deposited on p-type semiconductor region  132 , n-type semiconductor region  133 , and mask  164  to form first metal layer  151  ( FIG. 4( c )  and  FIG. 7( c ) ). 
     Then, mask  164  on first clad layer  120  and intrinsic semiconductor region  131  is removed by an organic solvent, and first metal layer  151  in the region except for p-type semiconductor region  132  and n-type semiconductor region  133  is removed (lift-off) to form part of first connection  5   a  and second connection  5   b  each comprising a Ti layer with a thickness of about 50 nm and an Al layer with a thickness of about 100 nm ( FIG. 4( d )  and  FIG. 7( d ) ). 
     Then, using chemical vapor deposition (CVD) method, a SiO 2  film is deposited on first clad layer  120  and semiconductor layer  130  that are exposed, to form second clad layer  140  ( FIG. 4( e )  and  FIG. 7( e ) ). 
     Then, a photoresist is coated onto second clad layer  140 . Then, using a photolithography method by a stepper, to form contact hole  5  as first connection  5   a  and second connection  5   b , mask  165  for etching is formed on second clad layer  140  to fit the planar shape of the region except for such contact hole  5  ( FIG. 5( a )  and  FIG. 8( a ) ). 
     By using this mask  165 , through dry etching by RIE method, portions to be contact hole  5  in second clad layer  140  are partially removed to form contact hole  5  ( FIG. 5( b )  and  FIG. 8( b ) ). Then, mask  165  on second clad layer  140  is removed by an organic solvent and an ashing method ( FIG. 5( c )  and  FIG. 8( c ) ). 
     Then, using an electron beam evaporation method, a metal (Ti/Al) that becomes part of first connection  5   a  and second connection  5   b  as well as first electrode  4   a  and second electrode  4   b  is deposited in contact hole  5  and on second clad layer  140  to form second metal layer  152  ( FIG. 5( d )  and  FIG. 8( d ) ). 
     Then, a photoresist is coated onto second metal layer  152 . Then, using a photolithography method by a stepper, mask  166  for etching is formed on second metal layer  152  to fit the planar shape of first electrode  4   a  and second electrode  4   b  shown in  FIG. 2( a )  and  FIG. 2( b )  ( FIG. 5( e )  and  FIG. 8( e ) ). 
     By using this mask  166 , through dry etching by ion milling method, second metal layer  152  in the region except for first electrode  4   a  and second electrode  4   b  are removed ( FIG. 5( f )  and  FIG. 8( f ) ), and mask  166  on first electrode  4   a  and second electrode  4   b  is removed by an organic solvent and an ashing method to form first electrode  4   a  and second electrode  4   b  ( FIG. 2( c )  and  FIG. 2( d ) ). 
     Finally, an optical mode switch  100  element having the structure shown in  FIG. 1  and  FIG. 2  can be obtained by cleaving substrate  110 , in which a plurality of optical mode switch  100  elements have been formed, along the boundaries between the optical mode switch  100  elements. It should be noted that, by this cleavage, a rear end facet (input port  1 ) and a front end facet (output port  2 ) of the optical mode switch  100  element is formed, respectively. 
     In the fabrication method according to the present embodiment, the RIE method is used as an etching method for the semiconductor layer: an inductively coupled plasma (ICP) method or a wet etching method may also be applicable. Further, in the fabrication method according to the present embodiment, an ion milling method is used as an etching method for the metal layer: a wet etching method may also be applicable. Further, in the fabrication method according to the present embodiment, a stepper is used for a photolithography method: however, it is not necessarily limited to this. For example, an electron beam exposure apparatus may also be applicable. 
     Next, the operation of optical mode switch  100  will be described with reference to  FIG. 1( a ) ,  FIG. 9 , and  FIG. 10 . Mode light incident on input port  1  of optical mode switch  100  enters pre-branching waveguide  23  of Y-branch waveguide  20 . 
     Here, when the structure of a waveguide changes gradually, the power of each mode is saved, which is called adiabatic process. Further, when the adiabatic process is established, it is called satisfying adiabatic condition. Y-branch waveguide  20 , which gradually changes in waveguide structure, satisfies the adiabatic condition and performs mode sorting. 
     That is, when incident from input port  1 , zero-order mode light propagates through a wide waveguide (second branched waveguide  22 ) of Y-branch waveguide  20 . Also, when incident from input port  1 , first-order mode light propagates through a narrow waveguide (first branched waveguide  21 ) of Y-branch waveguide  20  after switched to the zero-order mode light. 
     Note that the mode existing in pre-branching waveguide  23  and the mode existing in first branched waveguide  21  and second branched waveguide  22  are linked one-on-one in order from the mode having a larger propagation constant (proportional to transmission refractive index) and, therefore, it is called mode sorting. 
     When mode light incident on input port  1  of optical mode switch  100  is zero-order mode light, the zero-order mode light proceeds to second branched waveguide  22  side of Y-branch waveguide  20 , propagates through second linear waveguide  12 , and is incident on second merging waveguide  32  of merge waveguide  30 . 
     Also, when mode light incident on input port  1  of optical mode switch  100  is first-order mode light, the first-order mode light proceeds to first branched waveguide  21  side to switch to zero-order mode light, propagates through first linear waveguide  11 , and is incident on first merging waveguide  31  of merge waveguide  30 . 
     In this state, when a voltage is applied to first electrode  4   a  and second electrode  4   b  of optical mode switch  100 , forward bias is applied to the pin junction composed of p-type semiconductor region  132 , intrinsic semiconductor region  131 , and n-type semiconductor region  133 . This will cause carriers to be supplied from p-type semiconductor region  132  and n-type semiconductor region  133  to rib portion  131   a  of intrinsic semiconductor region  131 . The supplied carries accumulate in rib portion  131   a . By the plasma effect of the carriers, it is possible to change the refractive index of rib portion  131   a.    
     Here, in optical mode switch  100  shown in  FIG. 1( a ) , unnecessary mode components will be generated when mode light incident on input port  1  is switched to another mode light by refractive index changing means  8  or subjected to non-conversion. Therefore, it is necessary to suppress the ratio of unnecessary mode component to necessary mode component (inter-mode crosstalk). 
     Therefore, it can be considered to provide refractive index changing region  3  of refractive index changing means  8  with appropriate amount of refractive index change ΔN, ΔN, based on the relationship, shown in  FIG. 9( a )  to  FIG. 9( d ) , between amount of refractive index change ΔN in refractive index changing region  3  of refractive index changing means  8  arranged in first merging waveguide  31  and amount of refractive index change ΔN in refractive index changing region  3  of refractive index changing means  8  arranged in second merging waveguide  32  and transmittance of zero-order mode light or first-order mode light to incident zero-order mode light or first-order mode light. 
     That is, when mode light incident on input port  1  is zero-order mode light, optical mode switch  100  can transmit the zero-order mode light as it is, by setting the amount of refractive index change ΔN in refractive index changing region  3  of refractive index changing means  8  in first merging waveguide  31  to −0.017 and the amount of refractive index change ΔN in refractive index changing region  3  of refractive index changing means  8  in second merging waveguide  32  to 0, as shown in  FIG. 9( a ) , and emit the zero-order mode light from output port  2  via post-merging waveguide  33  of merge waveguide  30 , as shown in  FIG. 10( a ) . In this case, the inter-mode crosstalk, which is the ratio of unnecessary mode component (the zero-order mode light) to necessary mode component (the first-order mode light), is 29.2 dB, as shown in  FIG. 9( a ) . 
     Also, when mode light incident on input port  1  is zero-order mode light, optical mode switch  100  can switch the zero-order mode light into first-order mode light to transmit, by setting the amount of refractive index change ΔN in refractive index changing region  3  of refractive index changing means  8  in second merging waveguide  32  to −0.023 and the amount of refractive index change ΔN in refractive index changing region  3  of refractive index changing means  8  in first merging waveguide  31  to 0, as shown in  FIG. 9( b ) , and emit the first-order mode light from output port  2  via post-merging waveguide  33  of merge waveguide  30 , as shown in  FIG. 10( b ) . In this case, the inter-mode crosstalk, which is the ratio of unnecessary mode component (the zero-order mode light) to necessary mode component (the first-order mode light), is 29.2 dB, as shown in  FIG. 9( b ) . 
     Similarly, when mode light incident on input port  1  is first-order mode light, optical mode switch  100  can transmit the first-order mode light as it is, by setting the amount of refractive index change ΔN in refractive index changing region  3  of refractive index changing means  8  in first merging waveguide  31  to −0.017 and the amount of refractive index change ΔN in refractive index changing region  3  of refractive index changing means  8  in second merging waveguide  32  to 0, as shown in  FIG. 9( c ) , and emit the first-order mode light from output port  2  via post-merging waveguide  33  of merge waveguide  30 , as shown in  FIG. 10( c ) . In this case, the inter-mode crosstalk, which is the ratio of unnecessary mode component (the zero-order mode light) to necessary mode component (the first-order mode light), is 29.4 dB, as shown in  FIG. 9( c ) . 
     Also, when mode light incident on input port  1  is zero-order mode light, optical mode switch  100  can switch the first-order mode light into zero-order mode light to transmit, by setting the amount of refractive index change ΔN in refractive index changing region  3  of refractive index changing means  8  in second merging waveguide  32  to −0.023 and the amount of refractive index change ΔN in refractive index changing region  3  of refractive index changing means  8  in first merging waveguide  31  to 0, as shown in  FIG. 9( d ) , and emit the zero-order mode light from output port  2  via post-merging waveguide  33  of merge waveguide  30 , as shown in  FIG. 10( d ) . In this case, the inter-mode crosstalk, which is the ratio of unnecessary mode component (the first-order mode light) to necessary mode component (the zero-order mode light), is 29.3 dB, as shown in  FIG. 9( d ) . 
     As described above, optical mode switch  100  according to this embodiment can, by providing refractive index changing region  3  of refractive index changing means  8  with appropriate amount of refractive index change, suppress the inter-mode crosstalk, and selectively emit (switch) the zero-order mode light or first-order mode light, and switch any mode light incident on input port  1  to any mode light to emit from output port  2 . 
     Second Embodiment of the Present Invention 
       FIG. 11( a )  is a plan view showing an example of a schematic configuration of an optical mode switch according to the second embodiment,  FIG. 11( b )  is an illustration for explaining a dimension of a first branch waveguide shown in  FIG. 11( a ) , and  FIG. 11( c )  is an enlarged view of a refractive index changing means in a second linear waveguide shown in  FIG. 11( a ) .  FIG. 12( a )  is a graph showing the relationship between the amount of refractive index change ΔN and the transmittance when the zero-order mode light is inputted, and  FIG. 12( b )  is a graph showing the relationship between the amount of refractive index change ΔN and the transmittance when the first-order mode light is inputted.  FIG. 13( a )  is an explanatory drawing showing an optical field in which the zero-order mode light is inputted and the amount of refractive index change ΔN is set to 0,  FIG. 13( b )  is an explanatory drawing showing an optical field in which the zero-order mode light is inputted and the amount of refractive index change ΔN is set to −0.0039,  FIG. 13( c )  is an explanatory drawing showing an optical field in which the first-order mode light is inputted and the amount of refractive index change ΔN is set to 0, and  FIG. 13( d )  is an explanatory drawing showing an optical field in which the first-order mode light is inputted and the amount of refractive index change ΔN is set to −0.0039. In  FIG. 11( a )  to  FIG. 11( c ) , the same reference numerals as in  FIG. 1( a )  to  FIG. 8( f )  show the same or corresponding parts, and description thereof will be omitted. 
     Two waveguide  10  according to the present embodiment are linear waveguides (first linear waveguide  11  and second linear waveguide  12 ) each having a constant waveguide width, since the waveguide width of Y-branch waveguide  20  and the waveguide width of merge waveguide  30  are the same. Specifically, first linear waveguide  11  and second linear waveguide  12  have the waveguide length of 200 μm, the waveguide width of 0.6 μm at one end to be coupled with Y-branch waveguide  20  is 0.5 μm, and the waveguide width of 0.6 μm at the other end to be coupled with merge waveguide  30 . 
     In the planar view shown in  FIG. 11( a ) , Y-branch waveguide  20  according to the present embodiment has a planar shape in which two divided waveguides (first branched waveguide  21  and second branched waveguide  22 ) are symmetric (symmetric Y-shaped waveguide). Specifically, the region (pre-branching waveguide  23 ) except for the two divided waveguides (first branched waveguide  21  and second branched waveguide  22 ) of Y-branch waveguide  20  is a linear waveguide having the waveguide length of 50 μm and the waveguide width of 1.2 μm. 
     First branched waveguide  21  is a substantially S-shaped curved waveguide in which the waveguide width is 0.6 μm, the difference in the width direction between the center of core at one end to be coupled with pre-branching waveguide  23  and the center of core at the other end to be coupled with first linear waveguide  11  is 5 μm, and the radius of curvature R 4  is 1126.25 μm, as shown in  FIG. 11( b ) . Second branched waveguide  22 , which has a planar shape in which first branched waveguide  21  shown in  FIG. 11( b )  is reversed upside down, is a substantially S-shaped curved waveguide in which the waveguide width is 0.6 μm, the difference in the width direction between the center of core at one end to be coupled with pre-branching waveguide  23  and the center of core at the other end to be coupled with second linear waveguide  12  is 5 μm, and the radius of curvature R 4  is 1126.25 μm. 
     In the planar view shown in  FIG. 11( a ) , merge waveguide  30  according to the present embodiment has a planar shape in which two merging waveguides (first merging waveguide  31  and second merging waveguide  32 ) are symmetric (symmetric Y-shaped waveguide). Specifically, the region (post-merging waveguide  33 ) except for the two merging waveguides (first merging waveguide  31  and second merging waveguide  32 ) of merge waveguide  30  is a linear waveguide having the waveguide length of 150 μm and the waveguide width of 1.2 μm. 
     First merging waveguide  31 , which has a planar shape in which first branched waveguide  21  shown in  FIG. 11( b )  is reversed to right and left, is a substantially S-shaped curved waveguide in which the waveguide width is 0.6 μm, the difference in the width direction between the center of core at one end to be coupled with first linear waveguide  11  and the center of core at the other end to be coupled with post-merging waveguide  33  is 5 μm, and the radius of curvature R 4  is 1126.25 μm. Second merging waveguide  32 , which has a planar shape in which first branched waveguide  21  shown in  FIG. 11( b )  is reversed to right and left and upside down, is a substantially S-shaped curved waveguide in which the waveguide width is 0.6 μm, the difference in the width direction between the center of core at one end to be coupled with second linear waveguide  12  and the center of core at the other end to be coupled with post-merging waveguide  33  is 5 μm, and the radius of curvature R 4  is 1126.25 μm. 
     Refractive index changing means  8  according to the present embodiment is arranged in second linear waveguide  12  of two waveguides  10  (first linear waveguide  11  and second linear waveguide  12 ) that are juxtaposed between input port  1  and output port  2 . 
     Next, the operation of optical mode switch  100  will be described with reference to  FIG. 11( a ) ,  FIG. 12 , and  FIG. 13 . Mode light incident on input port  1  of optical mode switch  100  enters pre-branching waveguide  23  of Y-branch waveguide  20 . 
     Then, mode light incident on pre-branching waveguide  23  of Y-branch waveguide  20  is equally divided and branched into two. One equally-divided mode light propagates through first branched waveguide  21  and first linear waveguide  11  and enters first merging waveguide  31  of merge waveguide  30 . Another equally-divided mode light propagates through first branched waveguide  2   l  second branched waveguide  22  and second linear waveguide  12  (refractive index changing region  3  of refractive index changing means  8 ) and enters second merging waveguide  32  of merge waveguide  30 . 
     In this state, when a voltage is applied to first electrode  4   a  and second electrode  4   b  of optical mode switch  100 , forward bias is applied to the pin junction composed of p-type semiconductor region  132 , intrinsic semiconductor region  131 , and n-type semiconductor region  133 . This will cause carriers to be supplied from p-type semiconductor region  132  and n-type semiconductor region  133  to rib portion  131   a  of intrinsic semiconductor region  131 . The supplied carries accumulate in rib portion  131   a . By the plasma effect of the carriers, it is possible to change the phase of the other mode light by π [rad] with respect to the phase of the one mode light. 
     Then, when the phase of the other mode light is different from the phase of the one mode light by π [rad], post-merging waveguide  33  of merge waveguide  30  emits, from output port  2 , mode light that is different from the mode light incident on input port  1 , by superposing the one equally-divided mode light on the other equally-divided mode light. Further, when the phase of the other mode light matches the phase of the one mode light, post-merging waveguide  33  of merge waveguide  30  emits, from output port  2 , mode light that is same as the mode light incident on input port  1 , by superposing the one equally-divided mode light on the other equally-divided mode light. 
     Here, in optical mode switch  100  shown in  FIG. 11( a ) , unnecessary mode components will be generated when mode light incident on input port  1  is switched to another mode light or subjected to non-conversion. Therefore, it is necessary to suppress the ratio of unnecessary mode component to necessary mode component (inter-mode crosstalk). 
     Therefore, it can be considered to provide refractive index changing region  3  of refractive index changing means  8  with appropriate amount of refractive index change ΔN, based on the relationship, shown in  FIG. 12( a )  and  FIG. 12( b ) , between amount of refractive index change ΔN in refractive index changing region  3  of refractive index changing means  8  arranged in second linear waveguide  12  and output of zero-order mode light or first-order mode light to input of zero-order mode light or first-order mode light. In addition,  FIG. 12( a )  and  FIG. 12( b )  show the zero-order mode light by a solid line, the first-order mode light by a broken line, the second-order mode light by a chain line, and the third-order mode light by a two-dot chain line. The second-order mode light and the third-order mode light overlap the horizontal axis where output is zero. 
     That is, when mode light incident on input port  1  is zero-order mode light, optical mode switch  100  can match the phase of the equally-divided mode light propagating through first linear waveguide  11  and the phase of the equally-divided mode light propagating through second linear waveguide  12  and superpose the resultant mode lights, by setting the amount of refractive index change ΔN in refractive index changing region  3  of refractive index changing means  8  to 0, as shown in  FIG. 12( a ) , and thereby emit the zero-order mode light from output port  2  via post-merging waveguide  33  of merge waveguide  30 , as shown in  FIG. 13( a ) . In this case, the inter-mode crosstalk, which is the ratio of unnecessary mode component (the first-order mode light) to necessary mode component (the zero-order mode light), is 129.5 dB, as shown in  FIG. 12( a ) . 
     Also, when mode light incident on input port  1  is zero-order mode light, optical mode switch  100  can make the phase of the equally-divided mode light propagating through second linear waveguide  12  different from the phase of the equally-divided mode light propagating through first linear waveguide  11  by π [rad] and superpose the resultant mode lights, by setting the amount of refractive index change ΔN in refractive index changing region  3  of refractive index changing means  8  to −0.0039, as shown in  FIG. 12( a ) , and thereby emit the first-order mode light from output port  2  via post-merging waveguide  33  of merge waveguide  30 , as shown in  FIG. 13( b ) . In this case, the inter-mode crosstalk, which is the ratio of unnecessary mode component (the zero-order mode light) to necessary mode component (the first-order mode light), is 36.1 dB, as shown in  FIG. 12( a ) . 
     Similarly, when mode light incident on input port  1  is first-order mode light, optical mode switch  100  can match the phase of the equally-divided mode light propagating through first linear waveguide  11  and the phase of the equally-divided mode light propagating through second linear waveguide  12  and superpose the resultant mode lights, by setting the amount of refractive index change ΔN in refractive index changing region  3  of refractive index changing means  8  to 0, as shown in  FIG. 12( b ) , and thereby emit the first-order mode light from output port  2  via post-merging waveguide  33  of merge waveguide  30 , as shown in  FIG. 13( c ) . In this case, the inter-mode crosstalk, which is the ratio of unnecessary mode component (the zero-order mode light) to necessary mode component (the first-order mode light), is 115.2 dB, as shown in  FIG. 12( b ) . 
     Also, when mode light incident on input port  1  is first-order mode light, optical mode switch  100  can make the phase of the equally-divided mode light propagating through second linear waveguide  12  different from the phase of the equally-divided mode light propagating through first linear waveguide  11  by π [rad] and superpose the resultant mode lights, by setting the amount of refractive index change ΔN in refractive index changing region  3  of refractive index changing means  8  to −0.0039, as shown in  FIG. 12( b ) , and thereby emit the zero-order mode light from output port  2  via post-merging waveguide  33  of merge waveguide  30 , as shown in  FIG. 13( d ) . In this case, the inter-mode crosstalk, which is the ratio of unnecessary mode component (the first-order mode light) to necessary mode component (the zero-order mode light), is 36.1 dB, as shown in  FIG. 12( b ) . 
     Incidentally, this second embodiment differs from the first embodiment only in that incident mode light is divided into two by symmetric Y-branch waveguide  20  instead of utilizing mode sorting by asymmetric Y-branch waveguide  20  and that refractive index changing means  8  is arranged in second straight waveguide  12 . The second embodiment can achieve the same action/effect as the first embodiment except for action/effect by symmetric Y-branch waveguide  20  and refractive index changing means  8 . 
     Further, the present embodiment has described that refractive index changing means  8  is arranged in second linear waveguide  12  of two waveguides  10  (first linear waveguide  11  and second linear waveguide  12 ) that are juxtaposed between input port  1  and output port  2 . As long as it is arranged in at least one of two waveguides  10  that are juxtaposed between input port  1  and output port  2 , it may be arranged in first linear waveguide  11  instead of second linear waveguide  12 , or arranged in first linear waveguide  11  and second linear waveguide  12 . 
     Further, when refractive index changing means  8  is arranged in first linear waveguide  11  and second linear waveguide  12 , a voltage will be applied to first electrode  4   a  and second electrode  4   b  in refractive index changing means  8  of any one of first linear waveguide  11  and second linear waveguide  12 , in order to emit, from output port  2 , different mode light with regard to the mode light incident on input port  1 . In order to emit, from output port  2 , the same mode light with regard to the mode light incident on input port  1 , a voltage will be applied to first electrode  4   a  and second electrode  4   b  in refractive index changing means  8  of neither first linear waveguide  11  nor second linear waveguide  12 , or will be applied to first electrode  4   a  and second electrode  4   b  in refractive index changing means  8  of both first linear waveguide  11  and second linear waveguide  12 . 
     Third Embodiment of the Present Invention 
       FIG. 14( a )  is a plan view showing an example of a schematic configuration of an optical mode switch according to the third embodiment,  FIG. 14( b )  is an enlarged view of a refractive index changing means in a third linear waveguide shown in  FIG. 14( a ) , and  FIG. 14( c )  is a cross-sectional view of the optical mode switch shown in  FIG. 14( a )  taken along the line C-C′. In  FIG. 14( a )  to  FIG. 14( c ) , the same reference numerals as in  FIG. 1( a )  to  FIG. 8( f )  and  FIG. 11( a )  to  FIG. 11( c )  show the same or corresponding parts, and description thereof will be omitted. 
     Optical mode switch  100  according to the present embodiment includes: 1×2 type multi-mode interference (MMI) waveguide (hereinafter referred to as “MMI waveguide”)  40  that is arranged between input port  1  and two waveguides  10 ; 2×1 type MMI waveguide  50  that is arranged between output port  2  and two waveguides  10 ; input waveguide  6 , to one end of which 1×2 type MMI waveguide  40  is connected, and another end of which is made an incident surface (input port  1 ); and output waveguide  7 , to one end of which 2×1 type MMI waveguide  50  is connected, and another end of which is made an output surface (output port  2 ). 
     In particular, two waveguides  10  according to the present embodiment is comprised of: third linear waveguide  13  comprising a linear region; and curved waveguide  14  comprising a curved region. The waveguide length of third linear waveguide  13  is made different from the waveguide length of curve-shaped waveguide  14 . Specifically, third linear waveguide  13  has the waveguide length of 165 μm and the waveguide width of 4 μm. Further, curved waveguide  14  has a structure in which substantially S-shaped curvilinear regions each having the waveguide width of 4 μm and the curvature radius of 100 μm are combined in the middle thereof. 
     Further, refractive index changing means  8  according to the present embodiment is arranged in third linear waveguide  13  of two waveguides  10  (third linear waveguide  13  and curved waveguide  14 ) that are juxtaposed between input port  1  and output port  2 . 
     Furthermore, 1×2 type MMI waveguide  40  according to the present embodiment has a substantially rectangular interference region having the waveguide length of 420 μm (≈3Lc/8, Lc: waveguide length of clad) and the waveguide width of 20 μm. Also, 2×1 type MMI waveguide  50  according to the present embodiment has a substantially rectangular interference region having the waveguide length of 415 μm (≈3Lc′/4, Lc′: waveguide length of clad), the waveguide width is 14 μm. 
     In addition, MMI waveguides can be designed using known techniques. For example, 1×2 type MMI waveguide  40  and 2×1 type MMI waveguide  50  can be designed as follows, based on MMI theory. 
     Formula of waveguide length (L π ) of MMI waveguide can be expressed as the following Formula 1. Here, in Formula 1, W e  denotes effective waveguide width, W1 denotes width of MMI region, Nr denotes refractive index of waveguide, Nc denotes refractive index of clad, and λ 0  denotes wavelength of incident light. Furthermore, σ denotes σ=0 in TE mode, and denotes σ=1 in TM mode.
 
 W   e   =W   1 +(λ 0 /π)( Nc/Nr ) 2σ ( Nr   2   −Nc   2 ) −1/2  
 
 L   π =4 NrW   e   2 /3λ 0   Formula 1
 
     Furthermore, MMI waveguide can operate as a 1×N type waveguide when it is expressed by the following Formula 2. Further, MMI waveguide can operate as an M×N type waveguide when it is expressed by the following Formula 3. Here, M and N are positive integers. M on the input side can be 1 and N on the output side can be set to 2 or more. L shown in Formula 2 and Formula 3 denote length of multi-mode interference waveguide.
 
 L =(3/4 N ) L   π ( N  is a positive integer)  Formula 2
 
 L =(3/ N ) L   π ( N  is a positive integer)  Formula 3
 
     In addition, 1×2 type MMI waveguide  40  and 2×1 type MMI waveguide  50  according to the present embodiment have been designed on the assumption that incident light wavelength λ 0  is 1.55 μm, refractive index Nc of clad is 1.5, and refractive index Nr of waveguide is 3.22. 
     Input waveguide  6  according to the present embodiment is a linear waveguide in which the waveguide length is 50 μm and the waveguide width is 4 μm, and is connected substantially to the middle of the side of 1×2 type MMI waveguide  40  input side. Output waveguide  7  according to the present embodiment is a linear waveguide in which the waveguide length is 50 μm and the waveguide width is 8 μm, and is connected substantially to the middle of the side of 2×1 type MMI waveguide  50  output side. 
     The layer structure of input waveguide  6 , output waveguides  7 , 1×2 type MMI waveguide  40 , 2×1 type MMI waveguide  50 , third linear waveguide  13  (except for refractive index changing means  8 ), and curved waveguide  14  according to the present embodiment is the same as the layer structure (see  FIG. 2( d ) ) of waveguide  10 , Y-branch waveguide  20 , and merge waveguide  30  (except for refractive index changing means  8 ) as previously described in the first embodiment, both layer structures being different only in waveguide width (width of intrinsic semiconductor region  131 ). 
     Next, the operation of optical mode switch  100  will be described with reference to  FIG. 14( a ) . Mode light incident on input port  1  of optical mode switch  100  propagates through input waveguide  6  and enters 1×2 type MMI waveguide  40 . 
     Then, mode light incident on 1×2 type MMI waveguide  40  is equally divided into two and branched. One mode light after equal division propagates through third linear waveguide  13  (refractive index changing region  3  of refractive index changing means  8 ) and enters 2×1 type MMI waveguide  50 . Another mode light after equal division propagates through curved waveguide  14  and enters 2×1 type MMI waveguide  50  while out of phase with the one equally-divided mode light by π. 
     In this state, when a voltage is applied to first electrode  4   a  and second electrode  4   b  of optical mode switch  100 , forward bias is applied to the pin junction composed of p-type semiconductor region  132 , intrinsic semiconductor region  131 , and n-type semiconductor region  133 . This will cause carriers to be supplied from p-type semiconductor region  132  and n-type semiconductor region  133  to rib portion  131   a  of intrinsic semiconductor region  131 . The supplied carries accumulate in rib portion  131   a . By the plasma effect of the carriers, it is possible to change the phase of the other mode light by π [rad] with respect to the phase of the one mode light. That is, with respect to the phase difference π between one mode light equally-divided propagating through third linear waveguide  13  and another mode light equally-divided propagating through curved waveguide  14 , which is caused by the structure having different waveguide lengths of two waveguides  10 , optical mode switch  100  can match phases between the one mode light and the other mode light by applying a voltage to first electrode  4   a  and second electrode  4   b.    
     Then, when the phase of the other mode light is different from the phase of the one mode light by π [rad] (when a voltage is not applied to first electrode  4   a  and second electrode  4   b ), 2×1 type MMI waveguide  50  emits, from output port  2 , mode light that is different from the mode light incident on input port  1 , by superposing the one equally-divided mode light on the other equally-divided mode light. Further, when the phase of the other mode light matches the phase of the one mode light (when a voltage is applied to first electrode  4   a  and second electrode  4   b ), 2×1 type MMI waveguide  50  emits, from output port  2 , mode light that is same as the mode light incident on input port  1 , by superposing the one equally-divided mode light on the other equally-divided mode light. 
     Incidentally, this third embodiment differs from the first embodiment and the second embodiment only in that it includes 1×2 type MMI waveguide  40  (input waveguide  6 ) and 2×1 type MMI waveguide  50  (output waveguide  7 ) instead of Y-branch waveguide  20  and merge waveguide  30 . The third embodiment can achieve the same action/effect as the first embodiment and the second embodiment except for action/effect by 1×2 type MMI waveguide  40  and 2×1 type MMI waveguide  50 . 
     Further, the present embodiment has described that refractive index changing means  8  is arranged in third linear waveguide  13  of two waveguides  10  (third linear waveguide  13  and curved waveguide  14 ) that are juxtaposed between input port  1  and output port  2 . As long as it is arranged in at least one of two waveguides  10  that are juxtaposed between input port  1  and output port  2 , it may be arranged in curved waveguide  14  instead of third linear waveguide  13 , or arranged in third linear waveguide  13  and curved waveguide  14 . 
     Further, when refractive index changing means  8  is arranged in third linear waveguide  13  and curved waveguide  14 , a voltage will be applied to first electrode  4   a  and second electrode  4   b  in refractive index changing means  8  of any one of third linear waveguide  13  and curved waveguide  14 , in order to emit, from output port  2 , the same mode light with regard to the mode light incident on input port  1 . In order to emit, from output port  2 , different mode light with regard to the mode light incident on input port  1 , a voltage will be applied to first electrode  4   a  and second electrode  4   b  in refractive index changing means  8  of neither third linear waveguide  13  nor curved waveguide  14 , or will be applied to first electrode  4   a  and second electrode  4   b  in refractive index changing means  8  of both third linear waveguide  13  and curved waveguide  14 . 
     Also, two waveguides  10  according to the present embodiment provide different waveguide lengths for each other, which causes the phase difference π between one mode light equally-divided propagating through third linear waveguide  13  and another mode light equally-divided propagating through curved waveguide  14 . However, without varying the waveguide length of two waveguides  10 , curved waveguide  14  may be a linear waveguide having a waveguide length same as the waveguide length of third linear waveguide  13 , for example. However, since optical mode switch  100  according to the present embodiment emits mode light incident on input port  1 , as different mode light, from output port  2  (that is, switches the incident mode light into the same mode light or different mode light), refractive index changing means  8  needs to be arranged in at least one of two waveguides  10 . 
     Fourth Embodiment of the Present Invention 
       FIG. 15( a )  is a plan view showing an example of a schematic configuration of an optical mode switch according to the fourth embodiment,  FIG. 15( b )  is an enlarged view of a refractive index changing means in a second linear waveguide shown in  FIG. 15( a ) , and  FIG. 15( c )  is a cross-sectional view of a 1×2 type MMI waveguide shown in  FIG. 15( a )  taken along the line D-D′. In  FIG. 15( a )  to  FIG. 15( c ) , the same reference numerals as in  FIG. 1( a )  to  FIG. 14( c )  show the same or corresponding parts, and description thereof will be omitted. 
     Mode switch means of the present embodiment includes two waveguides  10  (first linear waveguide  11  and second linear waveguide  12 ) that are arranged between input port  1  and output port  2 . An optical branch waveguide according to the present embodiment is 1×2 type multi-mode interference waveguide  40  that is arranged between input port  1  and two waveguides  10  (first linear waveguide  11  and second linear waveguide  12 ). An optical multiplexing waveguide according to the present embodiment is merge waveguide  30  that is arranged between output port  2  and two waveguides  10  (first linear waveguide  11  and second linear waveguide  12 ). In addition, refractive index changing means  8  is arranged in two waveguides  10  (first linear waveguide  11  and second linear waveguide  12 ) or a waveguide (first merging waveguide  31  and second merging waveguide  32 ). Refractive index changing means  8  according to the present embodiment is arranged in second linear waveguide  12 . 
     Next, the operation of optical mode switch  100  will be described with reference to  FIG. 15( a ) . Mode light incident on input port  1  of optical mode switch  100  propagates through input waveguide  6  and enters 1×2 type MMI waveguide  40 . 
     Then, mode light incident on 1×2 type MMI waveguide  40  is equally divided into two and branched. One mode light after equal division propagates through first linear waveguide  11  and enters first merging waveguide  31  of merge waveguide  30 . Another mode light after equal division propagates through second linear waveguide  12  (refractive index changing region  3  of refractive index changing means  8 ) and enters second merging waveguide  32  of merge waveguide  30 . 
     In this state, when a voltage is applied to first electrode  4   a  and second electrode  4   b  of optical mode switch  100 , forward bias is applied to the pin junction composed of p-type semiconductor region  132 , intrinsic semiconductor region  131 , and n-type semiconductor region  133 . This will cause carriers to be supplied from p-type semiconductor region  132  and n-type semiconductor region  133  to rib portion  131   a  of intrinsic semiconductor region  131 . The supplied carries accumulate in rib portion  131   a . By the plasma effect of the carriers, it is possible to change the phase of the other mode light by π [rad] with respect to the phase of the one mode light. 
     Then, when the phase of the other mode light is different from the phase of the one mode light by π [rad] (when a voltage is applied to first electrode  4   a  and second electrode  4   b ), post-merging waveguide  33  of merge waveguide  30  emits, from output port  2 , mode light that is different from the mode light incident on input port  1 , by superposing the one mode light after equal division on the other mode light after equal division. Further, when the phase of the other mode light matches the phase of the one mode light (when a voltage is not applied to first electrode  4   a  and second electrode  4   b ), post-merging waveguide  33  of merge waveguide  30  emits, from output port  2 , mode light that is same as the mode light incident on input port  1 , by superposing the one mode light after equal division on the other mode light after equal division. 
     Incidentally, this fourth embodiment differs from the second embodiment only in that it includes input waveguide  6 , which has a waveguide width same as the waveguide width of pre-branching waveguide  23 , and 1×2 type MMI waveguide  40 , instead of Y-branch waveguide  20 . The fourth embodiment can achieve the same action/effect as the second embodiment except for action/effect by 1×2 type MMI waveguide  40 . 
     Further, the present embodiment has described that refractive index changing means  8  is arranged in second linear waveguide  12  of two waveguides  10  (first linear waveguide  11  and second linear waveguide  12 ) that are juxtaposed between input port  1  and output port  2 . As long as it is arranged in at least one of two waveguides  10  that are juxtaposed between input port  1  and output port  2 , it may be arranged in first linear waveguide  11  instead of second linear waveguide  12 , or arranged in first linear waveguide  11  and second linear waveguide  12 . 
     Further, optical mode switch  100  according to the present embodiment may include output waveguide  7 , which has the same waveguide width as pre-branching waveguide  23 , and 2×1 type MMI waveguide  50 , instead of merge waveguide  30 , in optical mode switch  100  according to the second embodiment. Further, optical mode switch  100  according to the present embodiment may include input waveguide  6 , which has the same waveguide width as pre-branching waveguide  23 , and 1×2 type MMI waveguide  40 , instead of Y-branch waveguide  20 , and output waveguide  7 , which has the same waveguide width as post-merging waveguide  33 , and 2×1 type MMI waveguide  50 , instead of merge waveguide  30 , in optical mode switch  100  according to the second embodiment. 
     Fifth Embodiment of the Present Invention 
       FIG. 16( a )  is a plan view showing an example of a schematic configuration of an optical mode switch according to the fifth embodiment,  FIG. 16( b )  is an illustration for explaining an example of a mode switching of the optical mode switch shown in  FIG. 16( a ) , and  FIG. 16( c )  is a plan view showing another example of a schematic configuration of an optical mode switch according to the fifth embodiment.  FIG. 17( a )  to  FIG. 17( d )  are explanatory drawings showing a state (optical field) in which light is switched from zero-order mode to another mode according to a beam propagation method simulation in the optical mode switch shown in  FIG. 16( a ) , in particular,  FIG. 17( a )  is an explanatory drawing showing an optical field in which the zero-order mode light is inputted and zero-order mode light is outputted,  FIG. 17( b )  is an explanatory drawing showing an optical field in which the zero-order mode light is inputted and first-order mode light is outputted,  FIG. 17( c )  is an explanatory drawing showing an optical field in which the zero-order mode light is inputted and second-order mode light is outputted, and  FIG. 17( d )  is an explanatory drawing showing an optical field in which the zero-order mode light is inputted and third-order mode light is outputted. In  FIG. 16( a )  to  FIG. 17( d ) , the same reference numerals as in  FIG. 1( a )  to  FIG. 15( c )  show the same or corresponding parts, and description thereof will be omitted. 
     In the above-mentioned second embodiment, it has described optical mode switch  100  that corresponds to light having two modes (zero-order mode and first-order mode) and switches zero-order mode light or first-order mode light to zero-order mode light or first-order mode light. In contrast, the present embodiment will extend the function of optical mode switch  100 , and describe optical mode switch  100  that corresponds to light having four modes (zero-order mode, first-order mode, second-order mode, and fourth-order mode) and switches zero-order mode light, first-order mode light, second-order mode light, or fourth-order mode light to zero-order mode light, first-order mode light, second-order mode light, or fourth-order mode light. 
     Mode switch means according to the present embodiment includes, as shown in  FIG. 16( a ) : a Y-branch waveguide (hereinafter referred to as “first Y-branch waveguide  61 ”) that divides mode light incident from input port  1  into two; a Y-branch waveguide (hereinafter referred to as “second Y-branch waveguide  62 ”) that divides mode light propagating through one branched waveguide  61   a  of first Y-branch waveguide  61  into two; a Y-branch waveguide (hereinafter referred to as “third Y-branch waveguide  63 ”) that divides mode light propagating through another branched waveguide  61   b  of first Y-branch waveguide  61  into two; and a Y-branch waveguide (hereinafter referred to as “fourth Y-branch waveguide  64 ”) that divides mode light incident from first merge waveguide  71 , which will be described below, into two. 
     Further, mode switch means according to the present embodiment includes: a merge waveguide (hereinafter referred to as “first merge waveguide  71 ”) that couples mode light propagating through one branched waveguide  62   a  of second Y-branch waveguide  62  and mode light propagating through one branched waveguide  63   a  of third Y-branch waveguide  63 ; a merge waveguide (hereinafter referred to as “second merge waveguide  72 ”) that couples mode light propagating through another branched waveguide  62   b  of second Y-branch waveguide  62  and mode light propagating through one branched waveguide  64   a  of fourth Y-branch waveguide  64 ; a merge waveguide (hereinafter referred to as “third merge waveguide  73 ”) that couples mode light propagating through another branched waveguide  63   b  of third Y-branch waveguide  63  and mode light propagating through another branched waveguide  64   b  of fourth Y-branch waveguide  64 ; and a merge waveguide (hereinafter referred to as “fourth merge waveguide  74 ”) that couples mode light incident from second merge waveguide  72  and mode light incident from third merge waveguide  73  to output the coupled mode light from output port  2 . 
     Refractive index changing means  8  according to the present embodiment is arranged in: another branched waveguide  61   b  of first Y-branch waveguide  61 ; waveguide  71   a  between first merge waveguide  71  and fourth Y-branch waveguide  64 ; one branched waveguide  64   a  and another branched waveguide  64   b  of fourth Y-branch waveguide  64 ; another branched waveguide  63   b  of third Y-branch waveguide  63 ; and waveguide  73   a  between third merge waveguide  73  and fourth merge waveguide  74 , as shown in  FIG. 16( a ) . 
     In addition, refractive index changing means  8  of the present embodiment is a phase inversion region (π phase shift region) that inverts (shifts by π “rad”) the phase of mode light by applying a voltage to first electrode  4   a  and second electrode  4   b . In particular, another branched waveguide  61   b  of first Y-branch waveguide  61 , waveguide  71   a  between first merge waveguide  71  and fourth Y-branch waveguide  64 , and waveguide  73   a  between third merge waveguide  73  and fourth merge waveguide  74  are waveguides through which mode light of first-order mode or less (first-order mode light and zero-order mode light) propagates, as described below. Refractive index changing means  8  arranged in waveguide  61   b , waveguide  71   a , and waveguide  73   a  will be a first-order mode phase inversion region. The term first-order mode phase inversion region here means a region that makes a state in which the phase of first-order mode light is inverted while the phase of zero-order mode light remains unchanged without inversion, when the refractive index in this region has been changed by injecting a current therein, by utilizing the fact that the propagation constants are different between zero-order mode light and first-order mode light, in an optical waveguide through which mode light of first-order mode or less penetrates. Further, one branched waveguide  64   a  and another branched waveguide  64   b  of fourth Y-branch waveguide  64 , and another branched waveguide  63   b  of third Y-branch waveguide  63  are waveguides through which zero-order mode light propagates, as described below. Refractive index changing means  8  arranged in waveguide  64   a , waveguide  64   b , and waveguide  63   b  will be a zero-order mode phase inversion region. 
     In addition, the waveguide width after dividing by the Y-branch waveguides according to the present embodiment (first Y-branch waveguide  61 , second Y-branch waveguide  62 , third Y-branch waveguide  63 , and fourth Y-branch waveguide  64 ) is ½ times wider than the waveguide width before dividing. The waveguide width after coupling by the merge waveguides (first merge waveguide  71 , second merge waveguide  72 , third merge waveguide  73 , and fourth merge waveguide  74 ) is two times wider than the waveguide width before coupling. 
     That is, when the waveguide width of input port  1  and output port  2  is denoted by “W”, the waveguide width of one branched waveguide  61   a  and another branched waveguide  61   b  of first Y-branch waveguide  61  is denoted by “W/2”; the waveguide width of one branched waveguide  62   a  and another branched waveguide  62   b  of second Y-branch waveguide  62  is denoted by “W/4”; the waveguide width of one branched waveguide  63   a  and another branched waveguide  63   b  of third Y-branch waveguide  63  is denoted by “W/4”; the waveguide width of waveguide  71   a  between first merge waveguide  71  and fourth Y-branch waveguide  64  is denoted by “W/2”; the waveguide width of one branched waveguide  64   a  and another branched waveguide  64   b  of fourth Y-branch waveguide  64  is denoted by “W/4”; the waveguide  72   a  between second merge waveguide  72  and fourth merge waveguide  74  denoted by “W2”; and the waveguide width of waveguide  73   a  between third merge waveguide  73  and fourth merge waveguide  74  is denoted by “W/2”. 
     Thus, it is desirable to set the waveguide width after dividing by the Y-branch waveguides to be ½ times wider than the waveguide width before dividing, to set the waveguide width after coupling by the merge waveguides to be two times wider than the waveguide width before coupling, and then to make refractive index changing means  8  into symmetrical and simple structures, in order not to cause excessive loss due to the dividing by the Y-branch waveguides and the coupling by the merge waveguides. 
     Next, the operation of optical mode switch  100  will be described with reference to  FIG. 16( a )  to  FIG. 16( c )  and Table 1. In addition, in optical mode switch  100  according to the present embodiment, since four kinds of mode light: zero-order mode light, first-order mode light, second-order mode light, and third-order mode light enter input port  1  as input modes, 24 patterns, which is the factorial of four (4!), can be considered as the order (permutation) of mode light to be outputted from output port  2  as output modes. 
     In Table 1, with respect to refractive index changing means  8  (π phase shift region), “A” denotes refractive index changing means  8  arranged in another branched waveguide  61   b  of first Y-branch waveguide  61 ; “B” denotes refractive index changing means  8  arranged in waveguide  71   a  between first merge waveguide  71  and fourth Y-branch waveguide  64 ; “C” denotes refractive index changing means  8  arranged in waveguide  73   a  between third merge waveguide  73  and fourth merge waveguide  74 ; “D” denotes refractive index changing means  8  arranged in one branched waveguide  64   a  of fourth Y-branch waveguide  64 ; “E” denotes refractive index changing means  8  arranged in another branched waveguide  64   b  of fourth Y-branch waveguide  64 ; and “F” denotes refractive index changing means  8  arranged in another branched waveguide  63   b  of third Y-branch waveguide  63 . 
     Further, in Table 1, the indication “●” in each column of refractive index changing means  8  (π phase shift region) denotes a state in which refractive index changing means  8  is turned on (a voltage is applied to first electrode  4   a  and second electrode  4   b ). The indication “-” in each column of refractive index changing means  8  (π phase shift region) denotes a state in which refractive index changing means  8  is turned off. 
     
       
         
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 Switching 
                 Refractive Index Changing Means 8 (∩ Phase Shift Region) 
                   
                 Input Mode 
               
             
          
           
               
                 Pattern 
                 A 
                 B 
                 C 
                 D 
                 E 
                 F 
                   
                 0 
                 1 
                 2 
                 3 
               
               
                   
               
             
          
           
               
                 1 
                 — 
                 — 
                 — 
                 — 
                 — 
                 — 
                 Output 
                 0 
                 1 
                 2 
                 3 
               
               
                 2 
                 — 
                 — 
                 — 
                 — 
                 ● 
                 ● 
                 Mode 
                 1 
                 0 
                 3 
                 2 
               
               
                 3 
                 — 
                 — 
                 — 
                 ● 
                 — 
                 ● 
                   
                 3 
                 2 
                 1 
                 0 
               
               
                 4 
                 — 
                 — 
                 — 
                 ● 
                 ● 
                 — 
                   
                 2 
                 3 
                 0 
                 1 
               
               
                 5 
                 — 
                 — 
                 ● 
                 — 
                 — 
                 — 
                   
                 0 
                 1 
                 3 
                 2 
               
               
                 6 
                 — 
                 — 
                 ● 
                 — 
                 ● 
                 ● 
                   
                 1 
                 0 
                 2 
                 3 
               
               
                 7 
                 — 
                 — 
                 ● 
                 ● 
                 — 
                 ● 
                   
                 2 
                 3 
                 1 
                 0 
               
               
                 8 
                 — 
                 — 
                 ● 
                 ● 
                 ● 
                 — 
                   
                 3 
                 2 
                 0 
                 1 
               
               
                 9 
                 — 
                 ● 
                 — 
                 — 
                 — 
                 — 
                   
                 0 
                 3 
                 2 
                 1 
               
               
                 10 
                 — 
                 ● 
                 — 
                 — 
                 ● 
                 ● 
                   
                 1 
                 2 
                 3 
                 0 
               
               
                 11 
                 — 
                 ● 
                 — 
                 ● 
                 — 
                 ● 
                   
                 3 
                 0 
                 1 
                 2 
               
               
                 12 
                 — 
                 ● 
                 — 
                 ● 
                 ● 
                 — 
                   
                 2 
                 1 
                 0 
                 3 
               
               
                 13 
                 — 
                 ● 
                 ● 
                 — 
                 — 
                 — 
                   
                 0 
                 2 
                 3 
                 1 
               
               
                 14 
                 — 
                 ● 
                 ● 
                 — 
                 ● 
                 ● 
                   
                 1 
                 3 
                 2 
                 0 
               
               
                 15 
                 — 
                 ● 
                 ● 
                 ● 
                 — 
                 ● 
                   
                 2 
                 0 
                 1 
                 3 
               
               
                 16 
                 — 
                 ● 
                 ● 
                 ● 
                 ● 
                 — 
                   
                 3 
                 1 
                 0 
                 2 
               
               
                 17 
                 ● 
                 ● 
                 — 
                 — 
                 — 
                 — 
                   
                 0 
                 3 
                 1 
                 2 
               
               
                 18 
                 ● 
                 ● 
                 — 
                 — 
                 ● 
                 ● 
                   
                 1 
                 2 
                 0 
                 3 
               
               
                 19 
                 ● 
                 ● 
                 — 
                 ● 
                 — 
                 ● 
                   
                 3 
                 0 
                 2 
                 1 
               
               
                 20 
                 ● 
                 ● 
                 — 
                 ● 
                 ● 
                 — 
                   
                 2 
                 1 
                 3 
                 0 
               
               
                 21 
                 ● 
                 ● 
                 ● 
                 — 
                 — 
                 — 
                   
                 0 
                 2 
                 1 
                 3 
               
               
                 22 
                 ● 
                 ● 
                 ● 
                 — 
                 ● 
                 ● 
                   
                 1 
                 3 
                 0 
                 2 
               
               
                 23 
                 ● 
                 ● 
                 ● 
                 ● 
                 — 
                 ● 
                   
                 2 
                 0 
                 3 
                 1 
               
               
                 24 
                 ● 
                 ● 
                 ● 
                 ● 
                 ● 
                 — 
                   
                 3 
                 1 
                 2 
                 0 
               
               
                   
               
             
          
         
       
     
     In addition, Table 1 shows one example of 24 output modes by selecting on/off of “A” to “F” of refractive index changing means  8  (π phase shift region) as appropriate. However, besides the on/off selection of “A” to “F” of refractive index changing means  8  (π phase shift region) shown in Table 1, additional on/off selection overlapping 24 patterns of output modes may be available. In particular, 64 (=2×2×23×2) switching patterns may be available for the arrangement of refractive index changing means  8  shown in  FIG. 16( a ) . 
     Therefore, in the description of the operation of optical mode switch  100 , the case where refractive index changing means  8  (π phase shift region) arranged in one branched waveguide  64   a  and another branched waveguide  64   b  of fourth Y-branch waveguide  64 , and waveguide  73   a  between third merge waveguide  73  and fourth merge waveguide  74  is turned on (the eighth switching pattern shown in Table 1), as shown in  FIG. 16( b ) , will be described as one example of the switching patterns. However, the same method of thinking holds for the operation of optical mode switch  100  by other switching patterns. 
     Zero-order mode light (by broken line in  FIG. 16( b ) ), first-order mode light (by chain line in  FIG. 16( b ) ), second-order mode light (by dotted line in  FIG. 16( b ) ), and third-order mode light (by solid line in  FIG. 16( b ) ) that are incident on input port  1  of optical mode switch  100  enter first Y-branch waveguide  61 . 
     Then, mode light incident on first Y-branch waveguide  61  (zero-order mode light, first-order mode light, second-order mode light, and third-order mode light) is equally divided into two and branched. One mode light after equal division propagates through one waveguide  61   a  of first Y-branch waveguide  61  and enters second Y-branch waveguide  62 . Another mode light after equal division propagates through another waveguide  61   b  (refractive index changing region  3  of refractive index changing means  8 ) of first Y-branch waveguide  61  and enters third Y-branch waveguide  63 . 
     In this case, the zero-order mode light incident on first Y-branch waveguide  61  propagates through one waveguide  61   a  and another waveguide  61   b  of first Y-branch waveguide  61  as zero-order mode light, respectively. 
     Further, the first-order mode light incident on first Y-branch waveguide  61  propagates through one waveguide  61   a  of first Y-branch waveguide  61  as zero-order mode light, and propagates through another waveguide  61   b  of first Y-branch waveguide  61  as zero-order mode light (hereinafter referred to as “inverted zero-order mode light”) that is out of phase by π ith the zero-order mode light propagating through one waveguide  61   a  of first Y-branch waveguide  61 . 
     Further, the second-order mode light incident on first Y-branch waveguide  61  propagates through one waveguide  61   a  of first Y-branch waveguide  61  as first-order mode light, and propagates through another waveguide  61   b  of first Y-branch waveguide  61  as first-order mode light (hereinafter referred to as “inverted first-order mode light”) that is out of phase by it with the first-order mode light propagating through one waveguide  61   a  of first Y-branch waveguide  61 . 
     Further, the third-order mode light incident on first Y-branch waveguide  61  propagates through one waveguide  61   a  and another waveguide  61   b  of first Y-branch waveguide  61  as first-order mode light, respectively. 
     As seen above, mode light of first-order mode or less will propagate through one waveguide  61   a  and another waveguide  61   b  of first Y-branch waveguide  61 . 
     Then, mode light incident on second Y-branch waveguide  62  (zero-order mode light, zero-order mode light, first-order mode light, and first-order mode light) is equally divided into two and branched. One mode light after equal division propagates through one waveguide  62   a  of second Y-branch waveguide  62  and enters first merge waveguide  71 . Another mode light after equal division propagates through another waveguide  62   b  of second Y-branch waveguide  62  and enters second merge waveguide  72 . 
     In this case, the zero-order mode light incident on second Y-branch waveguide  62  propagates through one waveguide  62   a  and another waveguide  62   b  of second Y-branch waveguide  62  as zero-order mode light, respectively. Further, the first-order mode light incident on second Y-branch waveguide  62  propagates through another waveguide  62   b  of second Y-branch waveguide  62  as zero-order mode light, and propagates through one waveguide  62   a  of second Y-branch waveguide  62  as zero-order mode light (inverted zero-order mode light) that is out of phase by π with the zero-order mode light propagating through another waveguide  62   b  of second Y-branch waveguide  62 . As seen above, zero-order mode light will propagate through one waveguide  62   a  and another waveguide  62   b  of second Y-branch waveguide  62 . 
     Similarly, mode light incident on third Y-branch waveguide  63  (zero-order mode light, inverted zero-order mode light, inverted first-order mode light, and first-order mode light) is equally divided into two and branched. One mode light after equal division propagates through one waveguide  63   a  of third Y-branch waveguide  63  and enters first merge waveguide  71 . Another mode light after equal division propagates through another waveguide  63   b  of third Y-branch waveguide  63  and enters third merge waveguide  73 . In this case, the zero-order mode light incident on third Y-branch waveguide  63  propagates through one waveguide  63   a  and another waveguide  63   b  of third Y-branch waveguide  63  as zero-order mode light, respectively. 
     Further, the inverted zero-order mode light incident on third Y-branch waveguide  63  propagates through one waveguide  63   a  and another waveguide  63   b  of third Y-branch waveguide  63  as inverted zero-order mode light, respectively. Further, the inverted first-order mode light incident on third Y-branch waveguide  63  propagates through another waveguide  63   b  of third Y-branch waveguide  63  as zero-order mode light, and propagates through one waveguide  63   a  of third Y-branch waveguide  63  as zero-order mode light (inverted zero-order mode light) that is out of phase by π with the zero-order mode light propagating through another waveguide  63   b  of third Y-branch waveguide  63 . Further, the first-order mode light incident on third Y-branch waveguide  63  propagates through one waveguide  63   a  of third Y-branch waveguide  63  as zero-order mode light, and propagates through another waveguide  63   b  of third Y-branch waveguide  63  as zero-order mode light (inverted zero-order mode light) that is out of phase by π with the zero-order mode light propagating through one waveguide  63   a  of third Y-branch waveguide  63 . As seen above, zero-order mode light will propagate through one waveguide  63   a  and another waveguide  63   b  of third Y-branch waveguide  63 . 
     Then, mode light (zero-order mode light, zero-order mode light, inverted zero-order mode light, and inverted zero-order mode light), incident on first merge waveguide  71  from one waveguide  62   a  of second Y-branch waveguide  62 , and mode light (zero-order mode light, inverted zero-order mode light, inverted zero-order mode light, and zero-order mode light), incident on first merge waveguide  71  from one waveguide  63   a  of third Y-branch waveguide  63 , are coupled by first merge waveguide  71 , respectively, and then propagates through waveguide  71   a  (refractive index changing region  3  of refractive index changing means  8 ) between first merge waveguide  71  and fourth Y-branch waveguide  64  and enters fourth Y-branch waveguide  64 . In this case, zero-order mode light incident on first merge waveguide  71  from one waveguide  62   a  of second Y-branch waveguide  62  and zero-order mode light incident on first merge waveguide  71  from one waveguide  63   a  of third Y-branch waveguide  63  are coupled by first merge waveguide  71  and enters fourth Y-branch waveguide  64  as zero-order mode light. 
     Further, zero-order mode light incident on first merge waveguide  71  from one waveguide  62   a  of second Y-branch waveguide  62  and inverted zero-order mode light incident on first merge waveguide  71  from one waveguide  63   a  of third Y-branch waveguide  63  are coupled by first merge waveguide  71  and enters fourth Y-branch waveguide  64  as first-order mode light. Further, inverted zero-order mode light incident on first merge waveguide  71  from one waveguide  62   a  of second Y-branch waveguide  62  and inverted zero-order mode light incident on first merge waveguide  71  from one waveguide  63   a  of third Y-branch waveguide  63  are coupled by first merge waveguide  71  and enters fourth Y-branch waveguide  64  as inverted zero-order mode light. Further, inverted zero-order mode light incident on first merge waveguide  71  from one waveguide  62   a  of second Y-branch waveguide  62  and zero-order mode light incident on first merge waveguide  71  from one waveguide  63   a  of third Y-branch waveguide  63  are coupled by first merge waveguide  71  and enters fourth Y-branch waveguide  64  as inverted first-order mode light. As seen above, mode light of first-order mode or less will propagate through waveguide  71   a  between first merge waveguide  71  and fourth Y-branch waveguide  64 . 
     Then, mode light incident on fourth Y-branch waveguide  64  (zero-order mode light, first-order mode light, inverted zero-order mode light, and inverted first-order mode light) is equally divided into two and branched. One mode light after equal division propagates through one waveguide  64   a  (refractive index changing region  3  of refractive index changing means  8 ) of fourth Y-branch waveguide  64  and enters second merge waveguide  72 . Another mode light after equal division propagates through another waveguide  64   b  (refractive index changing region  3  of refractive index changing means  8 ) of fourth Y-branch waveguide  64  and enters third merge waveguide  73 . In this case, the zero-order mode light incident on fourth Y-branch waveguide  64  propagates through one waveguide  64   a  and another waveguide  64   b  of fourth Y-branch waveguide  64  as zero-order mode light, respectively. 
     Further, the first-order mode light incident on fourth Y-branch waveguide  64  propagates through one waveguide  64   a  of fourth Y-branch waveguide  64  as zero-order mode light, and propagates through another waveguide  64   b  of fourth Y-branch waveguide  64  as zero-order mode light (inverted zero-order mode light) that is out of phase by π with the zero-order mode light propagating through one waveguide  64   a  of fourth Y-branch waveguide  64 . Further, the inverted zero-order mode light incident on fourth Y-branch waveguide  64  propagates through one waveguide  64   a  and another waveguide  64   b  of fourth Y-branch waveguide  64  as inverted zero-order mode light, respectively. Further, the inverted first-order mode light incident on fourth Y-branch waveguide  64  propagates through another waveguide  64   b  of fourth Y-branch waveguide  64  as zero-order mode light, and propagates through one waveguide  64   a  of fourth Y-branch waveguide  64  as zero-order mode light (inverted zero-order mode light) that is out of phase by π with the zero-order mode light propagating through another waveguide  64   b  of fourth Y-branch waveguide  64 . As seen above, zero-order mode light will propagate through one waveguide  64   a  and another waveguide  64   b  of fourth Y-branch waveguide  64 . 
     In this state, when a voltage is applied to first electrode  4   a  and second electrode  4   b  in refractive index changing means  8  (π phase shift region D) arranged in one waveguide  64   a  of fourth Y-branch waveguide  64  and refractive index changing means  8  (π phase shift region E) arranged in another waveguide  64   b  of fourth Y-branch waveguide  64 , forward bias is applied to the pin junction composed of p-type semiconductor region  132 , intrinsic semiconductor region  131 , and n-type semiconductor region  133 . This will cause carriers to be supplied from p-type semiconductor region  132  and n-type semiconductor region  133  to rib portion  131   a  of intrinsic semiconductor region  131 . The supplied carries accumulate in rib portion  131   a . By the plasma effect of the carriers, it is possible to change the phase of the mode light propagating through one waveguide  64   a  and another waveguide  64   b  of fourth Y-branch waveguide  64  by π [rad]. That is, the mode light propagating through one waveguide  64   a  of fourth Y-branch waveguide  64  (zero-order mode light, zero-order mode light, inverted zero-order mode light, and inverted zero-order mode light) will enter third merge waveguide  73  as mode light (inverted zero-order mode light, inverted zero-order mode light, zero-order mode light, and zero-order mode light) after zero-order mode light is switched to inverted zero-order mode light and inverted zero-order mode light is switched to zero-order mode light. 
     Further, the mode light propagating through another waveguide  64   b  of fourth Y-branch waveguide  64  (zero-order mode light, inverted zero-order mode light, inverted zero-order mode light, and zero-order mode light) will enter third merge waveguide  73  as mode light (inverted zero-order mode light, zero-order mode light, zero-order mode light, and inverted zero-order mode light) after zero-order mode light is switched to inverted zero-order mode light and inverted zero-order mode light is switched to zero-order mode light. 
     Then, mode light (zero-order mode light, zero-order mode light, zero-order mode light, and zero-order mode light), incident on second merge waveguide  72  from another waveguide  62   b  of second Y-branch waveguide  62 , and mode light (inverted zero-order mode light, inverted zero-order mode light, zero-order mode light, and zero-order mode light), incident on second merge waveguide  72  from one waveguide  64   a  of fourth Y-branch waveguide  64  via refractive index changing means  8  (π phase shift region D), are coupled by second merge waveguide  72 , respectively, and then enter fourth merge waveguide  74 . In this case, zero-order mode light, incident on second merge waveguide  72  from another waveguide  62   b  of second Y-branch waveguide  62 , and inverted zero-order mode light, incident on second merge waveguide  72  from one waveguide  64   a  of fourth Y-branch waveguide  64  via refractive index changing means  8  (π phase shift region D), are coupled by second merge waveguide  72  and enter fourth merge waveguide  74  as first-order mode light. 
     Further, zero-order mode light, incident on second merge waveguide  72  from another waveguide  62   b  of second Y-branch waveguide  62 , and inverted zero-order mode light, incident on second merge waveguide  72  from one waveguide  64   a  of fourth Y-branch waveguide  64  via refractive index changing means  8  (π phase shift region D), are coupled by second merge waveguide  72  and enter fourth merge waveguide  74  as first-order mode light. Further, zero-order mode light, incident on second merge waveguide  72  from another waveguide  62   b  of second Y-branch waveguide  62 , and zero-order mode light, incident on second merge waveguide  72  from one waveguide  64   a  of fourth Y-branch waveguide  64  via refractive index changing means  8  (π phase shift region D), are coupled by second merge waveguide  72  and enter fourth merge waveguide  74  as zero-order mode light. Further, zero-order mode light, incident on second merge waveguide  72  from another waveguide  62   b  of second Y-branch waveguide  62 , and zero-order mode light, incident on second merge waveguide  72  from one waveguide  64   a  of fourth Y-branch waveguide  64  via refractive index changing means  8  (π phase shift region D), are coupled by second merge waveguide  72  and enter fourth merge waveguide  74  as zero-order mode light. As seen above, mode light of first-order mode or less will propagate through waveguide  72   a  between second merge waveguide  72  and fourth merge waveguide  74 . 
     Similarly, mode light (zero-order mode light, inverted zero-order mode light, zero-order mode light, and inverted zero-order mode light), incident on third merge waveguide  73  from another waveguide  63   b  (refractive index changing region  3  of refractive index changing means  8 ) of third Y-branch waveguide  63 , and mode light (inverted zero-order mode light, zero-order mode light, zero-order mode light, and inverted zero-order mode light), incident on third merge waveguide  73  from another waveguide  64   b  of fourth Y-branch waveguide  64  via refractive index changing means  8  (π phase shift region E), are coupled by third merge waveguide  73 , respectively, and then enter fourth merge waveguide  74 . In this case, zero-order mode light, incident on third merge waveguide  73  from another waveguide  63   b  of third Y-branch waveguide  63 , and inverted zero-order mode light, incident on third merge waveguide  73  from another waveguide  64   b  of fourth Y-branch waveguide  64  via refractive index changing means  8  (π phase shift region E), are coupled by third merge waveguide  73  to be inverted first-order mode light. 
     Further, inverted zero-order mode light, incident on third merge waveguide  73  from another waveguide  63   b  of third Y-branch waveguide  63 , and zero-order mode light, incident on third merge waveguide  73  from another waveguide  64   b  of fourth Y-branch waveguide  64  via refractive index changing means  8  (π phase shift region E), are coupled by third merge waveguide  73  to be first-order mode light. Further, zero-order mode light, incident on third merge waveguide  73  from another waveguide  63   b  of third Y-branch waveguide  63 , and zero-order mode light, incident on third merge waveguide  73  from another waveguide  64   b  of fourth Y-branch waveguide  64  via refractive index changing means  8  (π phase shift region E), are coupled by third merge waveguide  73  to be zero-order mode light. Further, inverted zero-order mode light, incident on third merge waveguide  73  from another waveguide  63   b  of third Y-branch waveguide  63 , and inverted zero-order mode light, incident on third merge waveguide  73  from another waveguide  64   b  of fourth Y-branch waveguide  64  via refractive index changing means  8  (π phase shift region E), are coupled by third merge waveguide  73  to be inverted zero-order mode light. As seen above, mode light of first-order mode or less will propagate through waveguide  73   a  between third merge waveguide  73  and fourth merge waveguide  74 . 
     In this state, when a voltage is applied to first electrode  4   a  and second electrode  4   b  in refractive index changing means  8  (π phase shift region C) arranged in waveguide  73   a  between third merge waveguide  73  and fourth merge waveguide  74 , forward bias is applied to the pin junction composed of p-type semiconductor region  132 , intrinsic semiconductor region  131 , and n-type semiconductor region  133 . 
     This will cause carriers to be supplied from p-type semiconductor region  132  and n-type semiconductor region  133  to rib portion  131   a  of intrinsic semiconductor region  131 . The supplied carries accumulate in rib portion  131   a . By the plasma effect of the carriers, it is possible to change the phase of the first-order mode light, of the mode light propagating through waveguide  73   a  between third merge waveguide  73  and fourth merge waveguide  74 , by π [rad], while the phase of zero-order mode light remains unchanged without inversion. 
     That is, the mode light propagating through waveguide  73   a  between third merge waveguide  73  and fourth merge waveguide  74  (inverted first-order mode light, first-order mode light, zero-order mode light, and inverted zero-order mode light) will enter third merge waveguide  73  as mode light (first-order mode light, inverted first-order mode light, zero-order mode light, and inverted zero-order mode light) after zero-order mode light becomes zero-order mode light as it is, inverted zero-order mode light becomes inverted zero-order mode light as it is, first-order mode light is switched to inverted first-order mode light, and inverted first-order mode light is switched to first-order mode light. 
     Then, mode light (first-order mode light, first-order mode light, zero-order mode light, and zero-order mode light), incident on fourth merge waveguide  74  from second merge waveguide  72 , and mode light (first-order mode light, inverted first-order mode light, zero-order mode light, and inverted zero-order mode light), incident on fourth merge waveguide  74  from third merge waveguide  73  via refractive index changing means  8  (π phase shift region C), are coupled by fourth merge waveguide  74 , respectively, and then emitted from output port  2 . In this case, first-order mode light incident on fourth merge waveguide  74  from second merge waveguide  72  and first-order mode light incident on fourth merge waveguide  74  from third merge waveguide  73  via refractive index changing means  8  (π phase shift region D) are coupled by fourth merge waveguide  74  to be emitted from output port  2  as third-order mode light. 
     Further, first-order mode light incident on fourth merge waveguide  74  from second merge waveguide  72  and inverted first-order mode light incident on fourth merge waveguide  74  from third merge waveguide  73  via refractive index changing means  8  (π phase shift region D) are coupled by fourth merge waveguide  74  to be emitted from output port  2  as second-order mode light. Further, zero-order mode light incident on fourth merge waveguide  74  from second merge waveguide  72  and zero-order mode light incident on fourth merge waveguide  74  from third merge waveguide  73  via refractive index changing means  8  (π phase shift region D) are coupled by fourth merge waveguide  74  to be emitted from output port  2  as zero-order mode light. Further, first-order mode light incident on fourth merge waveguide  74  from second merge waveguide  72  and inverted zero-order mode light incident on fourth merge waveguide  74  from third merge waveguide  73  via refractive index changing means  8  (π phase shift region D) are coupled by fourth merge waveguide  74  to be emitted from output port  2  as first-order mode light. 
     As seen above, optical mode switch  100  can switch zero-order mode light incident on input port  1  to third-order mode light and output the resultant mode light from output port  2 , switch first-order mode light incident on input port  1  to second-order mode light and output the resultant mode light from output port  2 , switch second-order mode light incident on input port  1  to zero-order mode light and output the resultant mode light from output port  2 , and switch third-order mode light incident on input port  1  to first-order mode light and output the resultant mode light from output port  2 , in accordance with the eighth switching pattern shown in Table 1. 
     Furthermore, it could be confirmed, by beam propagation method (BPM) simulation, that optical mode switch  100  according to the present embodiment, when inputting zero-order mode light from input port  1 , outputs zero-order mode light from output port  2  as shown in  FIG. 17( a ) , outputs first-order mode light from output port  2  as shown in  FIG. 17( b ) , outputs second-order mode light from output port  2  as shown in  FIG. 17( c ) , and outputs third-order mode light from output port  2  as shown in  FIG. 17( d ) , by selecting six refractive index changing means  8  (it phase shift region A, π phase shift region B, π phase shift region C, π phase shift region D, π phase shift region E, and π phase shift region F) as appropriate. 
     In the optical mode switch, since mode information is used instead of port information that is used in the conventional spatial optical switch, it is necessary to discuss crosstalk between modes instead of crosstalk between ports. 
     Table 2 shows the results of the most suitable refractive index change in refractive index changing means  8  for switching each input mode (zero-order mode light, first-order mode light, second-order mode light, and third-order mode light) to each output mode (zero-order mode light, first-order mode light, second-order mode light, and third-order mode light) and the lowest inter-mode crosstalk at that time. 
     
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                   
                 TABLE 2 
               
               
                   
                   
               
               
                   
                   
                   
                 Refractive 
                   
               
               
                   
                 Input 
                 Output 
                 Index 
               
               
                   
                 Mode 
                 Mode 
                 Variation 
                 Crosstalk [dB] 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 0 
                 0 
                 0 
                 −31.8 
               
               
                   
                   
                 1 
                 −0.0054 
                 −29.7 
               
               
                   
                   
                 2 
                 −0.0054 
                 −24.2 
               
               
                   
                   
                 3 
                 −0.0054 
                 −32.2 
               
               
                   
                 1 
                 0 
                 0 
                 −26.0 
               
               
                   
                   
                 1 
                 −0.0054 
                 −21.1 
               
               
                   
                   
                 2 
                 −0.0054 
                 −27.5 
               
               
                   
                   
                 3 
                 −0.0054 
                 −19.1 
               
               
                   
                 2 
                 0 
                 0 
                 −24.0 
               
               
                   
                   
                 1 
                 −0.0054 
                 −31.7 
               
               
                   
                   
                 2 
                 −0.0054 
                 −32.0 
               
               
                   
                   
                 3 
                 −0.0054 
                 −29.1 
               
               
                   
                 3 
                 0 
                 0 
                 −27.2 
               
               
                   
                   
                 1 
                 −0.0054 
                 −19.0 
               
               
                   
                   
                 2 
                 −0.0054 
                 −26.2 
               
               
                   
                   
                 3 
                 −0.0054 
                 −21.1 
               
               
                   
                   
               
             
          
         
       
     
     As shown in Table 2, the worst inter-mode crosstalk was estimated to be less than −19.0 dB when the third-order mode light, which was the input mode, was switched into the first-order mode light, which was the output mode. 
     As described above, optical mode switch  100  according to the present embodiment achieves the action/effect that it can correspond to light having four modes (zero-order mode, first-order mode, second-order mode, and third-order mode) and switch zero-order mode light, first-order mode light, second-order mode light, or three-order mode light to zero-order mode light, first-order mode light, second-order mode light, or third-order mode light. 
     In addition, optical mode switch  100  according to the present embodiment has the configuration that can create 24 output modes and minimize the number of refractive index changing means  8 . However, refractive index changing means  8  may be arranged in other than another branched waveguide  61   b  of first Y-branch waveguide  61 ; waveguide  71   a  between first merge waveguide  71  and fourth Y-branch waveguide  64 ; one branched waveguide  64   a  and another branched waveguide  64   b  of fourth Y-branch waveguide  64 ; another branched waveguide  63   b  of third Y-branch waveguide  63 ; and waveguide  73   a  between third merge waveguide  73  and fourth merge waveguide  74 . 
     For example, it may be considered that optical mode switch  100  has the configuration in which refractive index changing means  8  is further arranged in one branched waveguide  61   a  of first Y-branch waveguide  61 ; another branched waveguide  62   b  of second Y-branch waveguide  62 ; another branched waveguide  63   b  of third Y-branch waveguide  63 ; and waveguide  72   a  between second merge waveguide  72  and fourth merge waveguide  74 , as shown in  FIG. 16( c ) . By this configuration, optical mode switch  100  can create desired 24 output modes by making refractive index changing means  8  having caused no malfunction function, when a malfunction was caused in any refractive index changing means  8  of a plurality of refractive index changing means  8 . In addition, optical mode switch  100  shown in  FIG. 16( c )  has refractive index changing means  8  arranged in linear waveguides. However, refractive index changing means  8  may be arranged in curved waveguides. 
     Sixth Embodiment of the Present Invention 
       FIG. 18( a )  is a plan view showing an example of a schematic configuration of an optical mode switch according to the sixth embodiment, and  FIG. 18( b )  is a plan view showing another example of a schematic configuration of an optical mode switch according to the sixth embodiment. In  FIG. 18( a )  and  FIG. 18( b ) , the same reference numerals as in  FIG. 1( a )  to  FIG. 17( d )  show the same or corresponding parts, and description thereof will be omitted. 
     In the above-mentioned fifth embodiment, it has described optical mode switch  100  that corresponds to light having four modes (zero-order mode, first-order mode, second-order mode, and third-order mode) and switches zero-order mode light to third-order mode light into zero-order mode light to third-order mode light. In contrast, the present embodiment will further extend the function of optical mode switch  100 , and describe optical mode switch  100  that corresponds to light having eight modes (zero-order mode, first-order mode, second-order mode, fourth-order mode, fifth-order mode, sixth-order mode, and seventh-order mode) and switches zero-order mode light to seventh-order mode light, to zero-order mode light to seventh-order mode light. 
     Mode switch means according to the present embodiment includes, as shown in  FIG. 18( a ) : a Y-branch waveguide (hereinafter referred to as “first Y-branch waveguide  261 ”) that divides mode light incident from input port  1  into two; a Y-branch waveguide (hereinafter referred to as “second Y-branch waveguide  262 ”) that divides mode light propagating through one branched waveguide  261   a  of first Y-branch waveguide  261  into two; a Y-branch waveguide (hereinafter referred to as “third Y-branch waveguide  263 ”) that divides mode light propagating through another branched waveguide  261   b  of first Y-branch waveguide  261  into two; a Y-branch waveguide (hereinafter referred to as “fourth Y-branch waveguide  264 ”) that divides mode light propagating through one branched waveguide  262   a  of second Y-branch waveguide  262  into two; a Y-branch waveguide (hereinafter referred to as “fifth Y-branch waveguide  265 ”) that divides mode light propagating through another branched waveguide  262   b  of second Y-branch waveguide  262  into two; a Y-branch waveguide (hereinafter referred to as “sixth Y-branch waveguide  266 ”) that divides mode light propagating through one branched waveguide  263   a  of third Y-branch waveguide  263  into two; a Y-branch waveguide (hereinafter referred to as “seventh Y-branch waveguide  267 ”) that divides mode light propagating through another branched waveguide  263   b  of third Y-branch waveguide  263  into two; a Y-branch waveguide (hereinafter referred to as “eighth Y-branch waveguide  268 ”) that divides mode light incident from first merge waveguide  271 , which will be described below, into two; a Y-branch waveguide (hereinafter referred to as “ninth Y-branch waveguide  269 ”) that divides mode light incident from second merge waveguide  272 , which will be described below, into two; and a Y-branch waveguide (hereinafter referred to as “tenth Y-branch waveguide  260 ”) that divides mode light incident from third merge waveguide  273 , which will be described below, into two. 
     Further, mode switch means according to the present embodiment includes: a merge waveguide (hereinafter referred to as “first merge waveguide  271 ”) that couples mode light propagating through one branched waveguide  264   a  of fourth Y-branch waveguide  264  and mode light propagating through one branched waveguide  265   a  of fifth Y-branch waveguide  265 ; a merge waveguide (hereinafter referred to as “second merge waveguide  272 ”) that couples mode light propagating through another branched waveguide  265   b  of fifth Y-branch waveguide  265  and mode light propagating through one branched waveguide  266   a  of sixth Y-branch waveguide  266 ; a merge waveguide (hereinafter referred to as “third merge waveguide  273 ”) that couples mode light propagating through another branched waveguide  266   b  of sixth Y-branch waveguide  266  and mode light propagating through one branched waveguide  267   a  of seventh Y-branch waveguide  267 ; a merge waveguide (hereinafter referred to as “fourth merge waveguide  274 ”) that couples mode light propagating through another branched waveguide  264   b  of fourth Y-branch waveguide  264  and mode light propagating through one branched waveguide  268   a  of eighth Y-branch waveguide  268 ; a merge waveguide (hereinafter referred to as “fifth merge waveguide  275 ”) that couples mode light propagating through another branched waveguide  268   b  of eighth Y-branch waveguide  268  and mode light propagating through one branched waveguide  269   a  of ninth Y-branch waveguide  269 ; a merge waveguide (hereinafter referred to as “sixth merge waveguide  276 ”) that couples mode light propagating through another branched waveguide  269   b  of ninth Y-branch waveguide  269  and mode light propagating through one branched waveguide  260   a  of tenth Y-branch waveguide  260 ; a merge waveguide (hereinafter referred to as “seventh merge waveguide  277 ”) that couples mode light propagating through another branched waveguide  267   b  of seventh Y-branch waveguide  267  and mode light propagating through another branched waveguide  260   b  of tenth Y-branch waveguide  260 ; a merge waveguide (hereinafter referred to as “eighth merge waveguide  278 ”) that couples mode light incident from fourth merge waveguide  274  and mode light incident from fifth merge waveguide  275 ; a merge waveguide (hereinafter referred to as “ninth merge waveguide  279 ”) that couples mode light incident from sixth merge waveguide  276  and mode light incident from seventh merge waveguide  277 ; a merge waveguide (hereinafter referred to as “tenth merge waveguide  270 ”) that couples mode light incident from eighth merge waveguide  278  and mode light incident from ninth merge waveguide  279  to output the coupled mode light from output port  2 . 
     Refractive index changing means  8  according to the present embodiment is arranged in: another branched waveguide  262   b  of second Y-branch waveguide  262 ; one branched waveguide  263   a  and another branched waveguide  263   b  of third Y-branch waveguide  263 ; waveguide  271   a  between first merge waveguide  271  and eighth Y-branch waveguide  268 ; waveguide  272   a  between second merge waveguide  272  and ninth Y-branch waveguide  269 ; waveguide  273   a  between third merge waveguide  273  and tenth Y-branch waveguide  260 ; one branched waveguide  268   a  and another branched waveguide  268   b  of eighth Y-branch waveguide  268 ; one branched waveguide  269   a  and another branched waveguide  269   b  of ninth Y-branch waveguide  269 ; one branched waveguide  260   a  and another branched waveguide  260   b  of tenth Y-branch waveguide  260 ; another branched waveguide  267   b  of seventh Y-branch waveguide  267 ; waveguide  275   a  between fifth merge waveguide  275  and eighth merge waveguide  278 ; waveguide  276   a  between sixth merge waveguide  276  and ninth merge waveguide  279 ; and waveguide  277   a  between seventh merge waveguide  277  and ninth merge waveguide  279 , as shown in  FIG. 18( a ) . 
     In particular, in optical mode switch  100  according to the present embodiment, since four kinds of mode light, zero-order mode light to seventh-order mode light, enter input port  1  as input modes, 40320 patterns, which is the factorial of eight ( 8 !), can be considered as the order (permutation) of mode light to be outputted from output port  2  as output modes. In addition, 65536 (=2 3 ×2 3 ×2 7 ×2 3 ) switching patterns may be available for the arrangement of refractive index changing means  8  shown in  FIG. 18( a ) . 
     Incidentally, this sixth embodiment differs from the fifth embodiment only in that it corresponds to eight kinds of mode light of zero-order mode light to seventh-order mode light. The operation of optical mode switch  100  according to the present embodiment can be easily inferred from the operation of optical mode switch  100  according to the fifth embodiment and, therefore, the explanation thereof will be omitted. 
     As described above, optical mode switch  100  according to the present embodiment achieves the action/effect that it can correspond to light having eight modes (zero-order mode, first-order mode, second-order mode, third-order mode, fourth-order mode, fifth-order mode, sixth-order mode, and seventh-order mode) and switch zero-order mode light to seventh-order mode light, to zero-order mode light to seventh-order mode light. 
     In addition, optical mode switch  100  according to the present embodiment has the configuration that can create desired 40320 output modes and minimize the number of refractive index changing means  8 . However, refractive index changing means  8  may be arranged in other than: another branched waveguide  262   b  of second Y-branch waveguide  262 ; one branched waveguide  263   a  and another branched waveguide  263   b  of third Y-branch waveguide  263 ; waveguide  271   a  between first merge waveguide  271  and eighth Y-branch waveguide  268 ; waveguide  272   a  between second merge waveguide  272  and ninth Y-branch waveguide  269 ; waveguide  273   a  between third merge waveguide  273  and tenth Y-branch waveguide  260 ; one branched waveguide  268   a  and another branched waveguide  268   b  of eighth Y-branch waveguide  268 ; one branched waveguide  269   a  and another branched waveguide  269   b  of ninth Y-branch waveguide  269 ; one branched waveguide  260   a  and another branched waveguide  260   b  of tenth Y-branch waveguide  260 ; another branched waveguide  267   b  of seventh Y-branch waveguide  267 ; waveguide  275   a  between fifth merge waveguide  275  and eighth merge waveguide  278 ; waveguide  276   a  between sixth merge waveguide  276  and ninth merge waveguide  279 ; and waveguide  277   a  between seventh merge waveguide  277  and ninth merge waveguide  279 . 
     For example, it may be considered that optical mode switch  100  has the configuration in which refractive index changing means  8  is further arranged in: another branched waveguide  261   b  of first Y-branch waveguide  261 ; and waveguide  279   a  between ninth merge waveguide  279  and tenth merge waveguide  270 , as shown in  FIG. 18( b ) . 
     Further, it may be considered that optical mode switch  100  has the configuration in which refractive index changing means  8  is further arranged in: one branched waveguide  261   a  and another branched waveguide  261   b  of first Y-branch waveguide  261 ; one branched waveguide  262   a  of second Y-branch waveguide  262 ; another branched waveguide  264   b  of fourth Y-branch waveguide  264 ; waveguide  274   a  between fourth merge waveguide  274  and eighth merge waveguide  278 ; waveguide  278   a  between eighth merge waveguide  278  and tenth merge waveguide  270 ; waveguide  279   a  between ninth merge waveguide  279  and tenth merge waveguide  270 . By this configuration, optical mode switch  100  can create desired 40320 output modes by making refractive index changing means  8  having caused no malfunction function, when a malfunction was caused in any refractive index changing means  8  of a plurality of refractive index changing means  8 . 
     Other Embodiment of the Present Invention 
     In the above-mentioned fifth embodiment, it has described optical mode switch  100  that corresponds to light having four modes (zero-order mode, first-order mode, second-order mode, and third-order mode) and switches zero-order mode light to third-order mode light into zero-order mode light to third-order mode light. Also, in the above-mentioned sixth embodiment, it has described optical mode switch  100  that corresponds to light having eight modes (zero-order mode, first-order mode, second-order mode, third-order mode, fourth-order mode, fifth-order mode, sixth-order mode, and seventh-order mode) and switches zero-order mode light to seventh-order mode light into zero-order mode light to seventh-order mode light. In contrast, the present embodiment will generalize the arrangement of waveguides (Y-branch waveguide and merge waveguide) of optical mode switch  100 , and describe optical mode switch  100  that corresponds to light having 2 n  modes, zero-order mode light to 2 n-1 -order mode light (n is an integer of 2 or more). 
     In the following description, explanation will be made by reference to the plan view ( FIG. 18( a ) ) showing the schematic configuration of optical mode switch  100  according to the sixth embodiment, but it is not limited to this optical mode switch  100 . 
     Mode switch means includes input stage region  310  that is connected to input port  1  and in which one or more Y-branch waveguides (first Y-branch waveguide  261 , second Y-branch waveguide  262 , and third Y-branch waveguide  263 ) for dividing mode light into two are arranged. 
     Further, the mode switch means includes output stage region  320  that is connected to output port  2  and in which one or more merge waveguides (tenth merge waveguide  270 , eighth merge waveguide  278 , and ninth merge waveguide  279 ) for coupling two mode light are arranged. 
     Further, the mode switch means includes reference region  300  that is arranged between input stage region  310  and output stage region  320  and in which 2 n  (eight) waveguides for propagating zero-order mode light (another branched waveguide  264   b  of fourth Y-branch waveguide  264 ; one branched waveguide  268   a  and another branched waveguide  268   b  of eighth Y-branch waveguide  268 ; one branched waveguide  269   a  and another branched waveguide  269   b  of ninth Y-branch waveguide  269 ; one branched waveguide  260   a  and another branched waveguide  260   b  of tenth Y-branch waveguide  260 ; and another branched waveguide  267   b  of seventh Y-branch waveguide  267 ) are juxtaposed. 
     Furthermore, the mode switch means includes former stage region  301  that is arranged in a former stage of reference region  300  and in which two waveguides (another branched waveguide  264   b  of fourth Y-branch waveguide  264  and another branched waveguide  267   b  of seventh Y-branch waveguide  267 ), connected to two outermost waveguides in reference region  300  respectively, and 2 n-1 −1 (three) waveguides (waveguide  271   a  between first merge waveguide  271  and eighth Y-branch waveguide  268 ; waveguide  272   a  between second merge waveguide  272  and ninth Y-branch waveguide  269 ; and waveguide  273   a  between three merge waveguide  273  and tenth Y-branch waveguide  260 ), connected to 2 n-1 −1 Y-branch waveguides (eighth Y-branch waveguide  268 ; ninth Y-branch waveguide  269 ; and tenth Y-branch waveguide  260 ) that each divides into two adjacent waveguides except for the two outermost waveguides in reference region  300 , are juxtaposed. 
     Furthermore, the mode switch means includes second former stage region  302  that is arranged in a former stage of former stage region  301  and in which 2 n −1 (four) waveguides (one branched waveguide  262   a  and another branched waveguide  262   b  of second Y-branch waveguide  262 ; and one branched waveguide  263   a  and another branched waveguide  263   b  of third Y-branch waveguide  263 ) are juxtaposed, via 2 n-1 −1 (three) merge waveguides (first merge waveguide  271 ; second merge waveguides  272 ; and third merge waveguide  273 ) to be coupled with 2 n-1 −1 waveguides in former stage region  301 , and  2   111  (four) Y-branch waveguides (fourth Y-branch waveguide  264 ; fifth Y-branch waveguides  265 ; sixth Y-branch waveguide  266 ; and seventh Y-branch waveguide  267 ) that divide into 2 n  (eight) adjacent waveguides among 2 n-1  (six) waveguides (one branched waveguide  264   a  of fourth Y-branch waveguide  264 ; one branched waveguide  265   a  and another branched waveguide  265   b  of fifth Y-branch waveguide  265 ; one branched waveguide  266   a  and another branched waveguide  266   b  of sixth Y-branch waveguide  266 ; one branched waveguide  267   a  of seventh Y-branch waveguide  267 ) before coupling of the 2 n-1 −1 (three) merge waveguides and two waveguides (another branched waveguide  264   b  of fourth Y-branch waveguide  264 ; and another branched waveguide  267   b  of seventh Y-branch waveguide  267 ) to be connected to two outermost waveguides in former stage region  301  respectively. 
     Further, the mode switch means includes latter stage region  303  that is arranged in a latter stage of reference region  300  and in which 2 n-1  (four) waveguides (waveguide  274   a  between fourth merge waveguide  274  and eighth merge waveguide  278 ; waveguide  275   a  between fifth merge waveguide  275  and eighth merge waveguide  278 ; waveguide  276   a  between sixth merge waveguide  276  and ninth merge waveguide  279 ; and waveguide  277   a  between seventh merge waveguide  277  and ninth merge waveguide  279 ) to be connected to 2 n-1  (four) merge waveguides (fourth merge waveguide  274 ; fifth merge waveguide  275 ; sixth merge waveguide  276 ; and seventh merge waveguide  277 ) that couple two adjacent waveguides in reference region  300 , are juxtaposed. 
     Refractive index changing means  8  according to the present embodiment is arranged in: 2 n −1 (seven) waveguides (one branched waveguide  268   a  and another branched waveguide  268   b  of eighth Y-branch waveguide  268 ; one branched waveguide  269   a  and another branched waveguide  269   b  of ninth Y-branch waveguide  269 ; one branched waveguide  260   a  and another branched waveguide  260   b  of tenth Y-branch waveguide  260 ; and another branched waveguide  267   b  of seventh Y-branch waveguide  267 ) except for one outermost waveguide in reference region  300  (another branched waveguide  264   b  of fourth Y-branch waveguide  264 ); 2 n-1 −1 (three) waveguides (waveguide  271   a  between first merge waveguide  271  and eighth Y-branch waveguide  268 ; waveguide  272   a  between second merge waveguide  272  and ninth Y-branch waveguide  269 ; and waveguide  273   a  between three merge waveguide  273  and tenth Y-branch waveguide  260 ) except for two outermost waveguides in former stage region  301  (another branched waveguide  264   b  of fourth Y-branch waveguide  264 ; and another branched waveguide  267   b  of seventh Y-branch waveguide  267 ); 2 n-1 −1 (three) waveguides (another branched waveguide  262   b  of second Y-branch waveguide  262 ; and one branched waveguide  263   a  and another branched waveguide  263   b  of third Y-branch waveguide  263 ) except for one outermost waveguide in second former stage region  302  (one branched waveguide  262   a  of second Y-branch waveguide  262 ), which does not make one outermost waveguide excluded in reference region  300  (another branched waveguide  264   b  of fourth Y-branch waveguide  264 ) a route; 2 n-1 −1 (three) waveguides (waveguide  275   a  between fifth merge waveguide  275  and eighth merge waveguide  278 ; waveguide  276   a  between sixth merge waveguide  276  and ninth merge waveguide  279 ; and waveguide  277   a  between seventh merge waveguide  277  and ninth merge waveguide  279 ) except for one outermost waveguide in latter stage region  303  (waveguide  274   a  between fourth merge waveguide  274  and eighth merge waveguide  278 ), which does not make one outermost waveguide excluded in reference region  300  (another branched waveguide  264   b  of fourth Y-branch waveguide  264 ) a route. 
     In particular, in optical mode switch  100  according to the present embodiment, since 2 n  kinds of mode light, zero-order mode light to 2 n −1-order mode light, enter input port  1  as input modes, 2 n ! patterns, which is the factorial of 2 n , can be considered as the order (permutation) of mode light to be outputted from output port  2  as output modes. 
     Incidentally, this embodiment differs from the fifth embodiment and the sixth embodiment only in that it generalized the arrangement of waveguides (Y-branch waveguide and merge waveguide) of optical mode switch  100 . The operation of optical mode switch  100  according to the present embodiment can be easily inferred from the operation of optical mode switch  100  according to the fifth embodiment and, therefore, the explanation thereof will be omitted. 
     In addition, optical mode switch  100  according to the present embodiment has the configuration that can create desired 2 n ! (the factorial of 2 n ) output modes and minimize the number of refractive index changing means  8 . However, refractive index changing means  8  may be arranged in other waveguides. 
     For example, by arranging refractive index changing means  8  in all linear waveguides, optical mode switch  100  can create desired 2n! (the factorial of 2n) output modes by making refractive index changing means  8  having caused no malfunction function, when a malfunction was caused in any refractive index changing means  8  of a plurality of refractive index changing means  8 . 
     REFERENCE SIGNS LIST 
     
         
         
           
               1  Input port 
               2  Output port 
               3  Refractive index changing region 
               3   a  Trench 
               4   a  First electrode 
               4   b  Second electrode 
               5  Contact hole 
               5   a  First connection 
               5   b  Second connection 
               6  Input waveguide 
               7  Output waveguide 
               8  Refractive index changing means 
               10  Waveguide 
               11  First linear waveguide 
               12  Second linear waveguide 
               13  Third linear waveguide 
               14  Curved waveguide 
               20  Y-branch waveguide 
               21  First branched waveguide 
               22  Second branched waveguide 
               23  Pre-branching waveguide 
               30  Merge Waveguide 
               31  First merging waveguide 
               32  Second merging waveguide 
               33  Post-merging waveguide 
               40  1×2 type MMI waveguide 
               50  2×1 type MMI waveguide 
               61  First Y-branch waveguide 
               61   a  One waveguide 
               61   b  Another waveguide 
               62  Second Y-branch waveguide 
               62   a  One waveguide 
               62   b  Another waveguide 
               63  Third Y-branch waveguide 
               63   a  One waveguide 
               63   b  Another waveguide 
               64  Fourth Y-branch waveguide 
               64   a  One waveguide 
               64   b  Another waveguide 
               71  First merge waveguide 
               71   a  Waveguide 
               72  Second merge waveguide 
               72   a  Waveguide 
               73  Third merge waveguide 
               73   a  Waveguide 
               74  Fourth merge waveguide 
               100  Optical mode switch 
               110  Substrate 
               120  First clad layer 
               130  Semiconductor layer 
               131  Intrinsic semiconductor region 
               131   a  Rib portion 
               131   b  Slab portion 
               132  P-type semiconductor region 
               133  N-type semiconductor region 
               140  Second clad layer 
               151  First metal layer 
               152  Second metal layer 
               161 ,  162 ,  163 ,  164 ,  165 ,  166  Mask 
               260  Tenth Y-branch waveguide 
               260   a  One waveguide 
               260   b  Another waveguide 
               261  First Y-branch waveguide 
               261   a  One waveguide 
               261   b  Another waveguide 
               262  Second Y-branch waveguide 
               262   a  One waveguide 
               262   b  Another waveguide 
               263  Third Y-branch waveguide 
               263   a  One waveguide 
               263   b  Another waveguide 
               264  Fourth Y-branch waveguide 
               264   a  One waveguide 
               264   b  Another waveguide 
               265  Fifth Y-branch waveguide 
               265   a  One waveguide 
               265   b  Another waveguide 
               266  Sixth Y-branch waveguide 
               266   a  One waveguide 
               266   b  Another waveguide 
               267  Seventh Y-branch waveguide 
               267   a  One waveguide 
               267   b  Another waveguide 
               268  Eighth Y-branch waveguide 
               268   a  One waveguide 
               268   b  Another waveguide 
               269  Ninth Y-branch waveguide 
               269   a  One waveguide 
               269   b  Another waveguide 
               270  Tenth Y-branch waveguide 
               271  First merge waveguide 
               271   a  Waveguide 
               272  Second merge waveguide 
               272   a  Waveguide 
               273  Third merge waveguide 
               273   a  Waveguide 
               274  Fourth merge waveguide 
               274   a  Waveguide 
               275  Fifth merge waveguide 
               275   a  Waveguide 
               276  Sixth merge waveguide 
               276   a  Waveguide 
               277  Seventh merge waveguide 
               277   a  Waveguide 
               278  Eighth merge waveguide 
               278   a  Waveguide 
               279  Ninth merge waveguide 
               279   a  Waveguide 
               300  Reference region 
               301  Former stage region 
               302  Second former stage region 
               303  Latter stage region 
               310  Input stage region 
               320  Output stage region