Patent Publication Number: US-11644540-B2

Title: Optical scanning device, photoreceiver device, and photodetection system

Description:
BACKGROUND 
     1. Technical Field 
     The present disclosure relates to an optical scanning device, to a photoreceiver device, and to a photodetection system. 
     2. Description of the Related Art 
     Various devices capable of scanning a space with light have been proposed. 
     International Publication No. WO2013/168266 discloses a structure that can perform optical scanning using a driving unit for rotating a mirror. 
     Japanese Unexamined Patent Application Publication (Translation of PCT Application) No. 2016-508235 discloses an optical phased array including a plurality of nanophotonic antenna elements arranged in two dimensions. Each antenna element is optically coupled to a corresponding variable optical delay line (i.e., a phase shifter). In this optical phased array, a coherent light beam is guided to each antenna element through a corresponding waveguide, and the phase of the light beam is shifted by a corresponding phase shifter. In this manner, an amplitude distribution of a far-field radiation pattern can be changed. 
     Japanese Unexamined Patent Application Publication No. 2013-16591 discloses a light deflection element including: a waveguide including an optical waveguide layer through which light is guided and first distributed Bragg reflectors formed on the upper and lower surfaces of the optical waveguide layer; a light inlet for allowing light to enter the waveguide; and a light outlet formed on a surface of the waveguide to allow the light entering from the light inlet and guided through the waveguide to be emitted. 
     SUMMARY 
     One non-limiting and exemplary embodiment provides a novel optical scanning device having a relatively simple structure capable of optical scanning. 
     In one general aspect, the techniques disclosed here feature an optical scanning device according to one aspect of the present disclosure includes: a first mirror; a second mirror facing the first mirror; an optical waveguide layer that is located between the first mirror and the second mirror and that propagates inputted light as propagating light; a pair of electrodes sandwiching the optical waveguide layer; and a driving circuit that applies a voltage to the pair of electrodes. The first mirror, the second mirror, and the optical waveguide layer have respective structures extending in a same direction. The first mirror allows part of the propagating light propagating through the optical waveguide layer to be emitted as emission light to outside of the optical waveguide layer. The optical waveguide layer contains a liquid crystal material or an electrooptical material. When the voltage is not applied to the pair of electrodes, an alignment direction of the liquid crystal material or a direction of a polarization axis of the electrooptical material is parallel or perpendicular to the direction in which the optical waveguide layer extends. The driving circuit applies the voltage to the pair of electrodes to change a refractive index of the liquid crystal material or the electrooptical material for the propagating light propagating through the optical waveguide layer to thereby change a direction of the emission light emitted from the optical waveguide layer. 
     According to the above aspect of the present disclosure, one-dimensional optical scanning or two-dimensional optical scanning can be achieved using a relatively simple structure. 
     It should be noted that general or specific embodiments of the present disclosure may be implemented as a device, a system, a method, an integrated circuit, a computer program, a storage medium, or any selective combination thereof. 
     Additional benefits and advantages of the disclosed embodiments will become apparent from the specification and drawings. The benefits and/or advantages may be individually obtained by the various embodiments and features of the specification and drawings, which need not all be provided in order to obtain one or more of such benefits and/or advantages. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1    is a perspective view schematically showing the structure of an optical scanning device in an exemplary embodiment of the present disclosure; 
         FIG.  2    is an illustration schematically showing an example of a cross-sectional structure of one waveguide element and an example of light propagating therethrough; 
         FIG.  3    is an illustration schematically showing a computational model used for a simulation; 
         FIG.  4 A  shows the results of computations of the relation between the refractive index of an example of an optical waveguide layer and the emission angle of light therefrom; 
         FIG.  4 B  shows the results of computations of the relation between the refractive index of another example of the optical waveguide layer and the emission angle of light therefrom; 
         FIG.  5    is an illustration schematically showing an example of the optical scanning device; 
         FIG.  6 A  is a cross-sectional view schematically showing an example of a structure in which light is inputted to the waveguide element; 
         FIG.  6 B  is a cross-sectional view schematically showing an example of a structure in which light is inputted to the waveguide element through an optical fiber; 
         FIG.  7    is a graph showing changes in coupling efficiency when the refractive index of a waveguide is changed; 
         FIG.  8    is an illustration schematically showing connections between a plurality of first waveguides and a plurality of second waveguides; 
         FIG.  9    is a cross-sectional view schematically showing a structural example of a waveguide element in which spacers are disposed on both sides of an optical waveguide layer; 
         FIG.  10    is a cross-sectional view schematically showing a structural example of a waveguide array in an optical scanning device; 
         FIG.  11    is an illustration schematically showing propagation of guided light in an optical waveguide layer; 
         FIG.  12    is a cross-sectional view schematically showing part of the structure of an optical scanning device in an exemplary embodiment of the present disclosure; 
         FIG.  13    is a cross-sectional view schematically showing another example of the structure of the optical scanning device; 
         FIG.  14    is a cross-sectional view schematically showing yet another example of the structure of the optical scanning device; 
         FIG.  15    shows an example in which light enters an optical waveguide layer sandwiched between two multilayer reflective films; 
         FIG.  16 A  shows an example in which light is introduced into a first waveguide through a grating; 
         FIG.  16 B  shows an example in which light is inputted from an end surface of the first waveguide; 
         FIG.  16 C  shows an example in which light is inputted from a laser light source to the first waveguide; 
         FIG.  17    shows the d 2  dependence of the coupling efficiency of guided light from a first waveguide to a second waveguide; 
         FIG.  18    shows the d 2  dependence of the coupling efficiency in another example; 
         FIG.  19    is a graph showing the above results classified by whether the coupling efficiency is 0.5 or more or less than 0.5; 
         FIG.  20    is an illustration showing a structure in which the center, with respect to the direction of thickness, of an optical waveguide layer of a first waveguide is offset from the center, with respect to the direction of thickness, of an optical waveguide layer of a second waveguide; 
         FIG.  21    is a graph showing the Δz dependence of the coupling efficiency of light from a first waveguide to a second waveguide; 
         FIG.  22 A  shows the d 2  dependence of the coupling efficiency in still another example; 
         FIG.  22 B  shows the d 2  dependence of the coupling efficiency in yet another example; 
         FIG.  23 A  is an illustration showing a computational model used to compute propagation of light with a different mode order; 
         FIG.  23 B  is an illustration showing the results of computations of propagation of the light with the different mode order; 
         FIG.  24 A  is a cross-sectional view showing an optical scanning device in another embodiment; 
         FIG.  24 B  is a graph showing the results of computations of the gap width dependence of the coupling efficiency; 
         FIG.  25 A  is an illustration showing a cross section of a waveguide array that emits light in a direction perpendicular to the emission surface of the waveguide array; 
         FIG.  25 B  is an illustration showing a cross section of a waveguide array that emits light in a direction different from the direction perpendicular to the emission surface of the waveguide array; 
         FIG.  26    is a perspective view schematically showing a waveguide array in a three-dimensional space; 
         FIG.  27 A  is a schematic diagram showing how diffracted light is emitted from the waveguide array when p is larger than λ; 
         FIG.  27 B  is a schematic diagram showing how diffracted light is emitted from the waveguide array when p is smaller than λ; 
         FIG.  27 C  is a schematic diagram showing how diffracted light is emitted from the waveguide array when p is substantially equal to λ/2; 
         FIG.  28    is a schematic diagram showing an example of a structure in which a phase shifter is connected directly to a waveguide element; 
         FIG.  29    is a schematic diagram showing a waveguide array and a phase shifter array as viewed in a direction normal to a light-emission surface; 
         FIG.  30    is an illustration schematically showing an example of a structure in which waveguides of phase shifters are connected to optical waveguide layers of waveguide elements through additional waveguides; 
         FIG.  31    is an illustration showing a structural example in which a plurality of phase shifters arranged in a cascaded manner are inserted into an optical divider; 
         FIG.  32 A  is a perspective view schematically showing an example of the structure of a first adjusting element; 
         FIG.  32 B  is a perspective view schematically showing another example of the structure of the first adjusting element; 
         FIG.  32 C  is a perspective view schematically showing yet another example of the structure of the first adjusting element; 
         FIG.  33    is an illustration showing an example of a structure in which a waveguide element is combined with an adjusting element including a heater; 
         FIG.  34 A  is an illustration showing a first example of a structure in which a liquid crystal material is used for the optical waveguide layer; 
         FIG.  34 B  is an illustration showing the first example of the structure in which the liquid crystal material is used for the optical waveguide layer; 
         FIG.  35    is a cross sectional view showing an example of an optical scanning device including a light input device; 
         FIG.  36 A  is an illustration showing a second example of the structure in which the liquid crystal material is used for the optical waveguide layer; 
         FIG.  36 B  is an illustration showing the second example of the structure in which the liquid crystal material is used for the optical waveguide layer; 
         FIG.  37 A  is an illustration showing a third example of the structure in which the liquid crystal material is used for the optical waveguide layer; 
         FIG.  37 B  is an illustration showing the third example of the structure in which the liquid crystal material is used for the optical waveguide layer; 
         FIG.  38 A  is an illustration showing a fourth example of the structure in which the liquid crystal material is used for the optical waveguide layer; 
         FIG.  38 B  is an illustration showing the fourth example of the structure in which the liquid crystal material is used for the optical waveguide layer; 
         FIG.  39    is a graph showing the dependence of the emission angle of light on the voltage applied in a structure in which the liquid crystal material is used for the optical waveguide layer; 
         FIG.  40    is a cross-sectional view showing the structure of a waveguide element used in the experiment; 
         FIG.  41    is an illustration showing a first example of a structure in which an electrooptical material is used for the optical waveguide layer; 
         FIG.  42    is an illustration showing the first example of the structure in which the electrooptical material is used for the optical waveguide layer; 
         FIG.  43 A  is an illustration showing an example in which the pair of electrodes are disposed only in the vicinity of the second mirror; 
         FIG.  43 B  is an illustration showing an example in which the pair of electrodes are disposed only in the vicinity of the first mirror; 
         FIG.  44    is an illustration showing an example of a structure in which common wiring lines are led from electrodes of waveguide elements; 
         FIG.  45    is an illustration showing an example of a structure in which the wiring lines and some of the electrodes are shared; 
         FIG.  46    is an illustration showing an example of a structure in which common electrodes are provided for a plurality of waveguide elements; 
         FIG.  47    is an illustration schematically showing an example of a structure in which waveguides are integrated into a small array while a large arrangement area is allocated for a phase shifter array; 
         FIG.  48    is an illustration showing a structural example in which two phase shifter arrays are disposed on respective sides of a waveguide array; 
         FIG.  49 A  shows a structural example of a waveguide array in which an arrangement direction of waveguide elements is not orthogonal to an extending direction of the waveguide elements; 
         FIG.  49 B  shows a structural example of a waveguide array in which waveguide elements are arranged at non-regular intervals; 
         FIG.  50 A  is an illustration schematically showing an optical scanning device in an embodiment; 
         FIG.  50 B  is a cross-sectional view of the optical scanning device shown in  FIG.  50 A ; 
         FIG.  50 C  is another cross-sectional view of the optical scanning device shown in  FIG.  50 A ; 
         FIG.  51 A  is an illustration showing a structural example in which a dielectric layer is disposed between a second mirror and a waveguide; 
         FIG.  51 B  is an illustration showing a structural example in which a second dielectric layer is disposed on the first waveguide; 
         FIG.  52    is an illustration showing a structural example in which the second mirror is not disposed in a region between the first waveguide and the substrate; 
         FIG.  53    is an illustration showing a structural example in which, between the first waveguide and the substrate, the second mirror is thinner; 
         FIG.  54 A  is an illustration showing a structural example in which the thickness of the second mirror varies gradually; 
         FIG.  54 B  is an illustration showing a structural example in which an upper electrode, a first mirror, and a second substrate are disposed so as to extend over a protective layer of the first waveguide and the optical waveguide layer of the second waveguide; 
         FIG.  54 C  is an illustration showing part of a production process in the structural example in  FIG.  54 B ; 
         FIG.  55    is an illustration showing a cross section of a plurality of second waveguides in an optical scanning device having the structure shown in  FIG.  54 B ; 
         FIG.  56    is an illustration showing a structural example in which the first waveguide and the second waveguide are reflective waveguides; 
         FIG.  57    is an illustration showing a structural example in which the upper electrode is disposed on the upper surface of the first mirror and the lower electrode is disposed on the lower surface of the second mirror; 
         FIG.  58    is an illustration showing an example in which the first waveguide is separated into two portions; 
         FIG.  59    is an illustration showing a structural example in which electrodes are disposed between adjacent optical waveguide layers; 
         FIG.  60    is an illustration showing a structural example in which the first mirror is thick and the second mirror is thin; 
         FIG.  61    is a cross-sectional view of an optical scanning device in an embodiment; 
         FIG.  62    is a graph showing the relation between the ratio of light loss and y 1 ; 
         FIG.  63    is a cross-sectional view of an optical scanning device, schematically showing another example of the waveguide array in the present embodiment; 
         FIG.  64 A  is a graph showing the results of computations of an electric field intensity distribution in the structural example in  FIG.  10   ; 
         FIG.  64 B  is a graph showing the results of computations of an electric field intensity distribution in the structural example in  FIG.  63   ; 
         FIG.  65    is a cross-sectional view of an optical scanning device, schematically showing a structural example in an embodiment in which spacers having different refractive indexes are present; 
         FIG.  66    is a cross-sectional view of an optical scanning device, schematically showing a structural example of a waveguide element in a modification of the present embodiment; 
         FIG.  67    is an illustration showing a structural example of an optical scanning device including elements such as an optical divider, a waveguide array, a phase shifter array, and a light source integrated on a circuit substrate; 
         FIG.  68    is a schematic diagram showing how two-dimensional scanning is performed by irradiating a distant object with a light beam such as a laser beam from the optical scanning device; 
         FIG.  69    is a block diagram showing a structural example of a LiDAR system that can generate a range image; 
         FIG.  70    is an illustration showing a schematic structure of a total reflection waveguide; 
         FIG.  71    is a graph showing an electric field intensity distribution in the total reflection waveguide; 
         FIG.  72    is an illustration showing a schematic structure of a slow light waveguide; and 
         FIG.  73    is a graph showing an electric field intensity distribution in the slow light waveguide. 
     
    
    
     DETAILED DESCRIPTION 
     Before embodiments of the present disclosure are described, findings underlying the present disclosure will be described. The present inventors have found that a problem with conventional optical scanning devices is that it is difficult to optically scan a space without increasing the complexity of the structures of the devices. For example, in the technique disclosed in International Publication No. WO2013/168266, the driving unit for rotating the mirror is necessary. Therefore, the device structure is complicated. A problem with this device is that the device is not robust against vibration. 
     In the optical phased array described in Japanese Unexamined Patent Application Publication (Translation of PCT Application) No. 2016-508235, light must be split and introduced into a plurality of row waveguides and a plurality of column waveguides to guide the split light beams to the plurality of antenna elements arranged in two dimensions. Therefore, wiring lines for the waveguides for guiding the light beams are very complicated. Moreover, the range of two-dimensional scanning cannot be increased. To change the amplitude distribution of the emitted light two dimensionally in a far field, the phase shifters must be connected to the plurality of antenna elements arranged in two dimensions, and wiring lines for phase control must be attached to the phase shifters. The phases of the light beams entering the plurality of two-dimensionally arranged antenna elements can thereby be changed by different amounts. Therefore, the structure of the elements is very complicated. 
     In the structure in Japanese Unexamined Patent Application Publication No. 2013-16591, by changing the wavelength of light entering the light deflection element, a large area can be scanned one-dimensionally with the emitted light. However, a mechanism for changing the wavelength of the light entering the light deflection element is necessary. When such a mechanism is installed in the light source such as a laser, a problem arises in that the structure of the light source becomes complicated. 
     The present inventors have focused attention on the problems in the conventional techniques and have conducted studies to solve these problems. The present inventors have found that the above problems can be solved by using a waveguide element including a pair of opposed mirrors and an optical waveguide layer sandwiched between these mirrors. One of the pair of mirrors of the waveguide element has a higher light transmittance than the other and allows part of light propagating through the optical waveguide layer to be emitted to the outside. The direction of the emitted light (or its emission angle) can be changed by adjusting the refractive index of the optical waveguide layer, as described later. More specifically, by changing the refractive index, a component of the wave vector of the emitted light can be changed. The component is along the lengthwise direction of the optical waveguide layer. One-dimensional scanning is thereby achieved. 
     When an array of a plurality of waveguide elements is used, two-dimensional scanning can be achieved. More specifically, light beams with appropriate phase differences are supplied to the plurality of waveguide elements, and the phase differences are controlled to change a direction in which light beams emitted from the plurality of waveguide elements are reinforced. By changing the phase differences, a component of the wave vector of the emitted light is changed. The component is along a direction intersecting the lengthwise direction of the optical waveguide layer. Two-dimensional scanning can thereby be achieved. When two-dimensional scanning is performed, it is unnecessary to change the refractive indexes of the plurality of optical waveguide layers by different amounts. Specifically, two-dimensional scanning can be performed by supplying light beams with appropriate phase differences to the plurality of optical waveguide layers and changing the refractive indexes of the plurality of optical waveguide layers by the same amount in a synchronous manner. As described above, in the above embodiment of the present disclosure, two-dimensional optical scanning can be achieved using the relatively simple structure. 
     The above-described basic principle is applicable not only to the application in which light is emitted but also to an application in which a light signal is received. By changing the refractive index of an optical waveguide layer, a light-receivable direction can be changed one-dimensionally. Moreover, the light-receivable direction can be changed two-dimensionally by changing phase differences between light beams using a plurality of phase shifters connected to a plurality of waveguide elements arranged in one direction. 
     An optical scanning device and a photoreceiver device in embodiments of the present disclosure can be used for, for example, antennas of a LiDAR (Light Detection and Ranging) system. The LiDAR system uses electromagnetic waves (visible light, infrared light, or ultraviolet light) having shorter wavelengths than radio waves such as millimeter waves used in a radar system and can therefore detect a distance distribution of an object with high resolution. Such a LiDAR system is mounted on a mobile unit such as an automobile, a UAV (Unmanned Aerial Vehicle, a so-called drone), or an AGV (Automated Guided Vehicle) and used as one of crash avoidance techniques. 
     In the following description, unnecessarily detailed description may be omitted. For example, detailed description of well-known matters and redundant description of substantially the same structures may be omitted. This is to avoid unnecessary redundancy in the following description and to facilitate understanding by those skilled in the art. The present inventors provide the accompanying drawings and the following description to allow those skilled in the art to fully understand the present disclosure. The accompanying drawings and the following description are not intended to limit the subject matter defined in the claims. In the following description, the same or similar components are denoted by the same reference numerals. 
     In the present disclosure, the “light” means electromagnetic waves including not only visible light (wavelength: about 400 nm to about 700 nm) but also ultraviolet rays (wavelength: about 10 nm to about 400 nm) and infrared rays (wavelength: about 700 nm to about 1 mm). In the present specification, the ultraviolet rays may be referred to as “ultraviolet light,” and the infrared rays may be referred to as “infrared light.” 
     In the present disclosure, the “scanning” with light means that the direction of the light is changed. The “one-dimensional scanning” means that the direction of the light is linearly changed in a direction intersecting the direction of the light. The “two-dimensional scanning” means that the direction of the light is changed two-dimensionally along a plane intersecting the direction of the light. 
     In the present disclosure, some or all of circuits, units, devices, members, and portions or some or all of functional blocks in block diagrams may be implemented as one or a plurality of electronic circuits including semiconductor devices, semiconductor integrated circuits (ICs), or LSIs (large-scale integrated circuits). The LS Is or ICs may be integrated on one chip or may be configured as a combination of a plurality of chips. For example, functional blocks other than memory elements may be integrated on one chip. Although the terms “LSI” and “IC” are used, the term “system LSI,” “very-large-scale integrated circuit (VLSI),” or “ultra-large-scale integrated circuit (VLSI)” may be used depending on the degree of integration. A Field Programmable Gate Array (FPGA) that can be programmed after manufacturing an LSI or a reconfigurable logic device that allows reconfiguration of the connection or setup of circuit cells inside the LSI can be used for the same purpose. 
     The functions or operations of some or all of the circuits, units, devices, members, and portions can be implemented by software processing. In this case, the software is stored in one or a plurality of non-transitory recording mediums such as ROMs, optical discs, and hard disk drives. When the software is executed by a processor, a function specified by the software program is executed by the processor and a peripheral device. A system or a device may include one or a plurality of non-transitory recording mediums storing the software, the processor, and necessary hardware devices such as an interface. 
     In the present specification, the phrase “two directions parallel to each other” means not only that they are strictly parallel to each other but also that the angle between them is 15 degrees or less. In the present specification, the phrase “two directions perpendicular to each other” means not only that they are strictly perpendicular to each other but also that the angle between them is from 75 degrees to 105 degrees inclusive. 
     &lt;Structural Example of Optical Scanning Device&gt; 
     An exemplary structure of an optical scanning device that performs two-dimensional scanning will be described.  FIG.  1    is a perspective view schematically showing the structure of an optical scanning device  100  in an exemplary embodiment of the present disclosure. The optical scanning device  100  includes a waveguide array including a plurality of waveguide elements  10  regularly arranged in a first direction (the Y direction in  FIG.  1   ). Each of the plurality of waveguide elements  10  has a shape elongated in a second direction (the X direction in  FIG.  1   ) that intersects the first direction. Each of the plurality of waveguide elements  10  propagates light in the second direction and allows the light to be emitted in a third direction D 3  that intersects a virtual plane parallel to the first and second directions. In the present embodiment, the first direction (the Y direction) and the second direction (the X direction) are orthogonal to each other but may not be orthogonal to each other. In the present embodiment, the plurality of waveguide elements  10  are arranged in the Y direction at regular intervals but are not necessarily arranged at regular intervals. 
     The orientation of each of the structures shown in the drawings of the present disclosure is set in consideration of the ease of understanding of description, and the orientation of a structure when an embodiment of the present disclosure is actually implemented is not limited thereto. The shape and size of part or all of any of the structures shown in the drawings do not limit the actual shape and size. 
     Each of the plurality of waveguide elements  10  includes a first mirror  30  and a second mirror  40  (hereinafter may be referred to simply as mirrors) that face each other and further includes an optical waveguide layer  20  located between the mirrors  30  and  40 . Each of the mirrors  30  and  40  has a reflecting surface that intersects the third direction D 3  and is located at an interface with the optical waveguide layer  20 . Each of the mirrors  30  and  40  and the optical waveguide layer  20  has a shape elongated in the second direction (the X direction). 
     As described later, the first mirrors  30  of the plurality of waveguide elements  10  may be a plurality of portions of an integrally formed third mirror. The second mirrors  40  of the plurality of waveguide elements  10  may be a plurality of portions of an integrally formed fourth mirror. The optical waveguide layers  20  of the plurality of waveguide elements  10  may be a plurality of portions of an integrally formed optical waveguide layer. A plurality of waveguides can be formed when at least one of the following conditions is met: (1) Each of the first mirrors  30  is formed separately from the other first mirrors  30 . (2) Each of the second mirrors  40  is formed separately from the other second mirrors  40 . (3) Each of the optical waveguide layers  20  is formed separately from the other optical waveguide layers. The phrase “each of the first mirrors is formed separately from the other first mirrors” means not only that physical spaces are provided between the first mirrors but also that a material having a different refractive index is disposed between the first mirrors to separate them from each other. 
     The reflecting surface of each first mirror  30  and the reflecting surface of a corresponding second mirror  40  are approximately parallel to each other and face each other. Among the two mirrors  30  and  40 , at least the first mirror  30  has the capability of allowing part of light propagating in the optical waveguide layer  20  to pass through. In other words, the first mirror  30  has a higher transmittance for the above light than the second mirror  40 . Therefore, part of the light propagating in the optical waveguide layer  20  is emitted to the outside through the first mirror  30 . Each of the above-described mirrors  30  and  40  may be, for example, a multilayer film mirror formed from a multilayer film (may be referred to as a “multilayer reflective film”) made of a dielectric material. 
     By controlling the phases of light beams to be inputted to the waveguide elements  10  and changing the refractive indexes of the optical waveguide layers  20  of the waveguide elements  10  simultaneously in a synchronous manner, two-dimensional optical scanning can be achieved. 
     To implement the above two-dimensional scanning, the present inventors have analyzed the details of the operating principle of the waveguide elements  10 . Based on the results obtained, the inventors have succeeded in implementing two-dimensional optical scanning by driving the plurality of waveguide elements  10  in a synchronous manner. 
     As shown in  FIG.  1   , when light is inputted to each waveguide element  10 , the light is emitted from the emission surface of the waveguide element  10 . The emission surface is located opposite to the reflecting surface of the first mirror  30 . The direction D 3  of the emitted light depends on the refractive index and thickness of the optical waveguide layer and the wavelength of the light. In the present embodiment, the refractive indexes of the optical waveguide layers are controlled in a synchronous manner such that light beams are emitted from the waveguide elements  10  in approximately the same direction. In this manner, the X direction component of the wave vector of the light emitted from the plurality of waveguide elements  10  can be changed. In other words, the direction D 3  of the emitted light can be changed in a direction  101  shown in  FIG.  1   . 
     Since the light beams emitted from the plurality of waveguide elements  10  are directed in the same direction, the emitted light beams interfere with each other. By controlling the phases of the light beams emitted from the waveguide elements  10 , the direction in which the light beams are reinforced by interference can be changed. For example, when a plurality of waveguide elements  10  having the same size are arranged at regular intervals in the Y direction, light beams having different phases shifted by a given amount are inputted to the plurality of waveguide elements  10 . By changing the phase differences, the Y direction component of the wave vector of the emitted light can be changed. In other words, by changing the phase differences between the light beams introduced into the plurality of waveguide elements  10 , the direction D 3  in which the emitted light beams are reinforced by interference can be changed in a direction  102  shown in  FIG.  1   . Two-dimensional optical scanning can thereby be achieved. 
     The operating principle of the optical scanning device  100  will next be described in more detail. 
     &lt;Operating Principle of Waveguide Element&gt; 
       FIG.  2    is an illustration schematically showing an example of a cross-sectional structure of one waveguide element  10  and light propagating therethrough. In  FIG.  2   , a direction perpendicular to the X and Y directions shown in  FIG.  1    is referred to as the Z direction, and a cross section of the waveguide element  10  parallel to the XZ plane is schematically shown. In the waveguide element  10 , a pair of mirrors  30  and  40  are disposed so as to sandwich an optical waveguide layer  20  therebetween. Light  22  introduced from one X direction end of the optical waveguide layer  20  propagates through the optical waveguide layer  20  while repeatedly reflected from the first mirror  30  disposed on the upper surface of the optical waveguide layer  20  (the upper surface in  FIG.  2   ) and the second mirror  40  disposed on the lower surface (the lower surface in  FIG.  2   ). The light transmittance of the first mirror  30  is higher than the light transmittance of the second mirror  40 . Therefore, part of the light can be outputted mainly from the first mirror  30 . 
     In an ordinary waveguide such as an optical fiber, light propagates through the waveguide while undergoing total reflection repeatedly. However, in the waveguide element  10  in the present embodiment, light propagates while repeatedly reflected from the mirrors  30  and  40  disposed on the upper and lower surfaces, respectively, of the optical waveguide layer  20 . Therefore, there is no constraint on the propagation angle of the light (i.e., the incident angle at the interface between the optical waveguide layer  20  and the mirror  30  or  40 ), and light incident on the mirror  30  or  40  at an angle closer to the vertical is allowed to propagate. Specifically, light incident on the interface at an angle smaller than the critical angle of total reflection (i.e., an angle closer to the vertical) can be propagated. Therefore, the group velocity of light in its propagation direction is much lower than the velocity of light in free space. Thus, the waveguide element  10  has such characteristics that the propagation conditions of light are largely changed according to changes in the wavelength of the light, the thickness of the optical waveguide layer  20 , and the refractive index of the optical waveguide layer  20 . 
     The propagation of light through the waveguide element  10  will be described in more detail. Let the refractive index of the optical waveguide layer  20  be n w , and the thickness of the optical waveguide layer  20  be d. The thickness d of the optical waveguide layer  20  is the size of the optical waveguide layer  20  in the direction normal to the reflecting surface of the mirror  30  or  40 . In consideration of light interference conditions, the propagation angle θ w  of light with a wavelength λ satisfies formula (1) below.
 
2 dn   w  cos θ w   =mλ   (1)
 
     Here, m is the mode order. Formula (1) corresponds to a condition for allowing the light to form a standing wave in the thickness direction within the optical waveguide layer  20 . When the wavelength λ g  in the optical waveguide layer  20  is λ/n w , the wavelength λ g ′ in the thickness direction of the optical waveguide layer  20  is considered to be λ/(n w  cos θ w ). When the thickness d of the optical waveguide layer  20  is equal to an integer multiple of one half of the wavelength λ g ′ in the thickness direction of the optical waveguide layer  20 , i.e., λ/(2n w  cos θ w ), a standing wave is formed. Formula (1) is obtained from this condition. m in formula (1) represents the number of loops (anti-nodes) of the standing wave. 
     When the mirrors  30  and  40  are multilayer film mirrors, light penetrates into the mirrors at the time of reflection. Therefore, strictly speaking, a term corresponding to the penetration path length of the light must be added to the left-hand side of formula (1). However, since the influences of the refractive index n w  and thickness d of the optical waveguide layer  20  are much larger than the influence of the light penetrating into the mirrors, the fundamental behavior of the light can be explained by formula (1). 
     The emission angle θ when the light propagating through the optical waveguide layer  20  is emitted to the outside (typically the air) through the first mirror  30  can be denoted by formula (2) below according to the Snell&#39;s law.
 
sin θ= n   w  sin θ w   (2)
 
Formula (2) is obtained from the condition that, on the light emission surface, the wavelength λ/sin θ of the light in a surface direction on the air side is equal to the wavelength λ/(n w  sin θ w ) of the light in the propagation direction on the waveguide element  10  side.
 
     From formulas (1) and (2), the emission angle θ can be denoted by formula (3) below. 
     
       
         
           
             
               
                 
                   
                     sin 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     θ 
                   
                   = 
                   
                     
                       
                         n 
                         w 
                         2 
                       
                       - 
                       
                         
                           ( 
                           
                             
                               m 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               λ 
                             
                             
                               2 
                               ⁢ 
                               d 
                             
                           
                           ) 
                         
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     As can be seen from formula (3), by changing the wavelength λ of the light, the refractive index n w  of the optical waveguide layer  20 , or the thickness d of the optical waveguide layer  20 , the emission direction of the light can be changed. 
     For example, when n w =2, d=387 nm, λ=1,550 nm, and m=1, the emission angle is 0°. When the refractive index n w  is changed from the above state to 2.2, the emission angle is changed to about 66°. When the thickness d is changed to 420 nm while the refractive index is unchanged, the emission angle is changed to about 51°. When the wavelength λ is changed to 1,500 nm while the refractive index and the thickness are unchanged, the emission angle is changed to about 30°. As described above, the emission direction of the light can be largely changed by changing the wavelength λ of the light, the refractive index n w  of the optical waveguide layer  20 , or the thickness d of the optical waveguide layer  20 . 
     To control the emission direction of the light by utilizing the above principle, it is contemplated to provide a wavelength changing mechanism that changes the wavelength of the light propagating through the optical waveguide layer  20 . However, when the wavelength changing mechanism is installed in a light source such as a laser, the structure of the light source becomes complicated. 
     In the optical scanning device  100  in the present embodiment, the emission direction of light is controlled by controlling the refractive index n w  of the optical waveguide layer  20 . In the present embodiment, the wavelength λ of the light is unchanged during operation and held constant. No particular limitation is imposed on the wavelength λ. For example, the wavelength λ may be within the wavelength range of 400 nm to 1,100 nm (the visible to infrared range) in which high detection sensitivity can be obtained by using one of a general photo detector and a general image sensor that detect light through light absorption by silicon (Si). In another example, the wavelength λ may be within the near-infrared range of 1,260 nm to 1,625 nm in which transmission loss in an optical fiber or a Si waveguide is relatively small. However, the above wavelength ranges are merely examples. The wavelength range of the light used is not limited to the visible or infrared wavelength range and may be, for example, an ultraviolet wavelength range. In the present embodiment, the wavelength and the thickness of the optical waveguide layer are not controlled. However, in addition to the control of the refractive index, the wavelength and/or the thickness of the optical waveguide layer may be changed and controlled. 
     The present inventors have examined by optical analysis whether light can be actually emitted in a specific direction as described above. The optical analysis was performed by computation using DiffractMOD available from Cybernet Systems Co., Ltd. This is a simulation based on rigorous coupled-wave analysis (RCWA), and the effects of wave optics can be correctly computed. 
       FIG.  3    is an illustration schematically showing a computational model used for the simulation. In this computational model, a second mirror  40 , an optical waveguide layer  20 , and a first mirror  30  are stacked in this order on a substrate  50 . Each of the first mirror  30  and the second mirror  40  is a multilayer film mirror including a dielectric multilayer film. The second mirror  40  has a structure in which six low-refractive index layers  42  having a lower refractive index and six high-refractive index layers  44  having a higher refractive index (a total of twelve layers) are alternately stacked. The first mirror  30  has a structure in which two low-refractive index layers  42  and two high-refractive index layers  44  (i.e., a total of four layers) are alternately stacked. The optical waveguide layer  20  is disposed between the mirrors  30  and  40 . A medium other than the waveguide element  10  and the substrate  50  is air. 
     The optical response to incident light was examined using the above model while the incident angle of the light was changed. This corresponds to examination of the degree of coupling of the incident light from air into the optical waveguide layer  20 . Under the condition that the incident light is coupled into the optical waveguide layer  20 , the reverse process can occur in which the light propagating through the optical waveguide layer  20  is emitted to the outside. Therefore, the determination of the incident angle when the incident light is coupled into the optical waveguide layer  20  corresponds to the determination of the emission angle when the light propagating through the optical waveguide layer  20  is emitted to the outside. When the incident light is coupled into the optical waveguide layer  20 , light loss occurs in the optical waveguide layer  20  due to absorption and scattering of the light. Specifically, under the condition that a large loss occurs, the incident light is strongly coupled into the optical waveguide layer  20 . When there is no light loss due to absorption, etc., the sum of the light transmittance and reflectance is 1. However, when there is a loss, the sum of the transmittance and reflectance is less than 1. In this computation, to take the influence of light absorption into consideration, an imaginary part was added to the refractive index of the optical waveguide layer  20 , and a value obtained by subtracting the sum of the transmittance and reflectance from 1 was used as the magnitude of the loss. 
     In this simulation, the substrate  50  is Si, the low-refractive index layers  42  are SiO 2  (thickness: 267 nm), and the high-refractive index layers  44  are Si (thickness: 108 nm). The magnitude of loss was computed while the incident angle of light with a wavelength λ=1.55 μm was changed. 
       FIG.  4 A  shows the results of the computations of the relation between the refractive index n w  of the optical waveguide layer  20  and the emission angle θ of light with a mode order of m=1 when the thickness d of the optical waveguide layer  20  is 704 nm. White lines indicate that the loss is large. As shown in  FIG.  4 A , the emission angle θ of the light with a mode order of m=1 is 0° near n w =2.2. One example of a material having a refractive index n w  of around 2.2 is lithium niobate. 
       FIG.  4 B  shows the results of the computations of the relation between the refractive index n w  of the optical waveguide layer  20  and the emission angle θ of light with a mode order of m=1 when the thickness d of the optical waveguide layer  20  is 446 nm. As shown in  FIG.  4 B , the emission angle θ of the light with a mode order of m=1 is 0° near n w =3.45. One example of a material having a refractive index n w  of around 3.45 is silicon (Si). 
     As described above, the waveguide element  10  can be designed such that, when the optical waveguide layer  20  has a specific refractive index n w , the emission angle θ of light with a specific mode order (e.g., m=1) is set to be 0° by adjusting the thickness d of the optical waveguide layer  20 . 
     As can be seen from  FIGS.  4 A and  4 B , the emission angle θ is largely changed according to the change in the refractive index. As described later, the refractive index can be changed by various methods such as carrier injection, an electro-optical effect, and a thermo-optical effect. However, the change in the refractive index by such a method is not so large, i.e., about 0.1. Therefore, it has been considered that such a small change in refractive index does not cause a large change in the emission angle. However, as can be seen from  FIGS.  4 A and  4 B , near the refractive index at which the emission angle θ is 0°, when the refractive index increases by 0.1, the emission angle θ is changed from 0° to about 30°. As described above, in the waveguide element  10  in the present embodiment, even a small change in the refractive index can cause the emission angle to be changed largely. 
     As described above, by changing the refractive index n w  of the optical waveguide layer  20 , the direction of the light emitted from the waveguide element  10  can be changed. To achieve this, the optical scanning device  100  in the present embodiment includes a first adjusting element that changes the refractive index of the optical waveguide layer  20  of each of the waveguide elements  10 . A structural example of the first adjusting elements will be described later. 
     As described above, the use of the waveguide element  10  allows the emission direction of light to be changed largely by changing the refractive index n w  of the optical waveguide layer  20 . In this manner, the emission angle of the light emitted from the mirror  30  can be changed in a direction along the waveguide element  10 . By using at least one waveguide element  10 , the above-described one-dimensional scanning can be achieved. 
       FIG.  5    is an illustration schematically showing an example of the optical scanning device  100  that can implement one-dimensional scanning using a single waveguide element  10 . In this example, a beam spot extending in the Y direction is formed. By changing the refractive index of the optical waveguide layer  20 , the beam spot can be moved in the X direction. One-dimensional scanning can thereby be achieved. Since the beam spot extends in the Y direction, a relatively large area extending two-dimensionally can be scanned by uniaxial scanning. The structure shown in  FIG.  5    may be employed in applications in which two-dimensional scanning is unnecessary. 
     To implement two-dimensional scanning, the waveguide array in which the plurality of waveguide elements  10  are arranged is used, as shown in  FIG.  1   . When the phases of light beams propagating through the plurality of waveguide elements  10  satisfy a specific condition, the light beams are emitted in a specific direction. When the condition for the phases is changed, the emission direction of the light beams is changed also in the arrangement direction of the waveguide array. Specifically, the use of the waveguide array allows two-dimensional scanning to be implemented. An example of a specific structure for implementing the two-dimensional scanning will be described later. 
     As described above, when at least one waveguide element  10  is used, the emission direction of light can be changed by changing the refractive index of the optical waveguide layer  20  of the waveguide element  10 . Unlike a general waveguide that uses total reflection of light (hereinafter may be referred to as a “total reflection waveguide”), the waveguide element  10  in the present embodiment in the present disclosure has the waveguide structure in which the optical waveguide layer is sandwiched between the pair of mirrors (e.g., multilayer reflective films) (this structure may be hereinafter referred to as a “reflective waveguide”). Coupling of light into such a reflective waveguide has not been studied sufficiently. The present inventors have also examined a structure for efficiently introducing light into the optical waveguide layer  20 . 
       FIG.  6 A  is a cross-sectional view schematically showing an example of a structure in which light is indirectly inputted into the optical waveguide layer  20  through air and the mirror  30 . In this example, the propagating light is indirectly introduced from the outside through air and the mirror  30  into the optical waveguide layer  20  of the waveguide element  10 , which is a reflective waveguide. To introduce the light into the optical waveguide layer  20 , the reflection angle θ w  of the guided light inside the optical waveguide layer  20  must satisfy the Snell&#39;s law (n in  sin θ in =n w  sin θ w ). Here, n in  is the refractive index of the external medium, θ in  is the incident angle of the propagating light, and n w  is the refractive index of the optical waveguide layer  20 . By adjusting the incident angle θ in  in consideration of the above condition, the coupling efficiency of the light can be maximized. In this example, the number of films in the multilayer reflective film is smaller in a portion of the first mirror  30  than in the other portion. The light is inputted from this portion, and the coupling efficiency can thereby be increased. However, in the above structure, the incident angle θ in  of the light on the optical waveguide layer  20  must be changed according to the change in the propagation constant of the optical waveguide layer  20  (the change in θ wav ). 
     One method to maintain the state in which the light can be always coupled into the waveguide even when the propagation constant of the optical waveguide layer  20  is changed is to cause a diverging beam to be incident on the portion of the multilayer reflective film that includes a reduced number of films. In one example of such a method, an optical fiber  7  inclined at an angle θ in  with respect to the direction normal to the mirror  30  is used to cause light to enter the waveguide element  10  from the outside indirectly through air and the mirror  30 , as shown in  FIG.  6 B . The coupling efficiency in this case will be examined. For the sake of simplicity, the light is assumed to be a ray of light. The numerical aperture (NA) of an ordinary single mode fiber is about 0.14. This corresponds to an angle of about ±8 degrees. The range of the incident angle of the light coupled into the waveguide is comparable to the divergence angle of the light emitted from the waveguide. The divergence angle θ div  of the emitted light is represented by formula (4) below. 
     
       
         
           
             
               
                 
                   
                     θ 
                     div 
                   
                   ≈ 
                   
                     λ 
                     
                       L 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       cos 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         θ 
                         out 
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     Here, L is a propagation length, λ is the wavelength of the light, and θ out  is the emergent angle of the light. When L is 10 μm or more, θ div  is at most 1 degree or less. Therefore, the coupling efficiency of the light from the optical fiber  7  is 1/16×100≈6.3% or less.  FIG.  7    shows the results of computations of changes in the coupling efficiency when the refractive index n w  of the waveguide was changed to change the emergent angle θ out  of the light while the incident angle θ in  of the light was fixed. The coupling efficiency is the ratio of the energy of the guided light to the energy of the incident light. The results shown in  FIG.  7    were obtained by computing the coupling efficiency using an incident angle θ in  of 30°, a waveguide thickness of 1.125 μm, and a wavelength of 1.55 μm. In the above computations, the refractive index n w  was changed within the range of 1.44 to 1.78 to change the emergent angle θ out  within the range of 10° to 65°. As show in  FIG.  7   , in this structure, the coupling efficiency is at most less than 7%. When the emergent angle θ out  is changed by 20° or more from the emergent angle that gives the maximum coupling efficiency, the coupling efficiency is reduced to one-half or less of the maximum coupling efficiency. 
     As described above, when the propagation constant is changed by changing the refractive index of the waveguide in order to perform optical scanning, the coupling efficiency is further reduced. To maintain the coupling efficiency, it is also necessary to change the incident angle θ in  of the light according to the change in the propagation constant. However, introduction of a mechanism for changing the incident angle θ in  of the light causes the device structure to be complicated. 
     The present inventors have found that the light incident angle can be fixed when a region including a waveguide whose refractive index is maintained constant is provided upstream of a region including a waveguide whose refractive index is to be changed. 
     There are two important factors for coupling of guided light between two different waveguides. One of them is the propagation constant of the propagating light, and the other one is the electric field intensity distribution of each mode. The closer the propagation constant and the electric field intensity distribution in one of the two waveguides are to those in the other, the higher the coupling efficiency. The propagation constant β of light propagating through a waveguide is represented by β=k·sin θ w =(2πn w  sin θ w )/λ, when the light is treated in a geometrical optics manner for simplicity. Here, k is the wave number, θ w  is the angle of the guided light, and n w  is the refractive index of the waveguide layer. In a total reflection-type waveguide (total reflection waveguide), the guided light is confined in the waveguide layer by utilizing total reflection, so that the total reflection condition n w  sin θ w &gt;1 is satisfied. However, in a slow light waveguide, light is confined in the waveguide by using multilayer reflective films present above and below the waveguide, and part of the guided light is emitted through the multilayer reflective films, so that n w  sin θ w &lt;1. The propagation constant in the total reflection waveguide cannot be the same as the propagation constant in the slow light waveguide from which part of the guided light is emitted. The electric field intensity distribution in a total reflection waveguide shown in  FIG.  70    has a peak within the waveguide as shown in  FIG.  71   , and the electric field intensity decreases monotonically outside the waveguide. In a slow light waveguide shown in  FIG.  72   , the electric field intensity distribution is as shown in  FIG.  73   . The electric field intensity distribution has a peak within the waveguide, as in the above case. However, the guided light is reflected in the dielectric multilayer films due to interference. Therefore, as shown in  FIG.  73   , the electric field intensity penetrates deep into the dielectric multilayer films and varies in a vibrating manner. As described above, the propagation constant of the guided light and the electric field intensity distribution in the total reflection waveguide differ largely from those in the slow light waveguide. Therefore, it has not been contemplated to connect a total reflection waveguide directly to a slow light waveguide. The present inventors have found that a total reflection waveguide can be connected directly to an optical waveguide layer having a variable refractive index. 
     The present inventors have also found that, by disposing these two types of waveguides on a common substrate, an optical scanning device can be produced easily. Specifically, the two types of waveguides may be disposed on a single integrally formed substrate. A general waveguide is produced on a substrate using a semiconductor process. The structure of the waveguide is generally formed on the substrate using, for example, a combination of deposition by vacuum evaporation, sputtering, etc. and fine patterning by lithography, etching, etc. Examples of the material of the substrate include Si, SiO 2 , GaAs, and GaN. 
     A reflective waveguide can be produced using a similar semiconductor process. In the reflective waveguide, one of a pair of mirrors sandwiching an optical waveguide layer allows light to pass through, and the light is thereby emitted. In most cases, the mirrors are formed on a glass substrate available at low cost. A substrate made of Si, SiO 2 , GaAs, GaN, etc. may be used instead of the glass substrate. 
     By connecting a reflective waveguide to another waveguide, light can be introduced into the reflective waveguide. 
       FIG.  8    is an illustration schematically showing connections between a plurality of first waveguides  1  produced on a substrate  50 A and a plurality of second waveguides  10  produced on another substrate  50 B. The two substrates  50 A and  50 B are disposed parallel to each other in the XY plane. The plurality of first waveguides  1  and the plurality of second waveguides  10  extend in the X direction and are arranged in the Y direction. The first waveguides  1  are, for example, general waveguides that use total reflection of light. The second waveguides  10  are reflective waveguides. The first waveguides  1  and the second waveguides  10  disposed on the different substrates  50 A and  50 B, respectively, are aligned and connected with each other, and this allows light to be introduced from the first waveguides  1  into the second waveguides  10 . 
     To introduce light from the first waveguides  1  into the second waveguides  10  efficiently, it is desired that the waveguides are aligned with very high precision on the order of 10 nm. Even when the waveguides are aligned with high precision, if the thermal expansion coefficients of the two substrates  50 A and  50 B differ from each other, the alignment may be changed due to a change in temperature. For example, the thermal expansion coefficients of Si, SiO 2 , GaAs, and GaN are about 4, 0.5, 6, and 5 (×10 −6 /K), respectively, and the thermal expansion coefficient of BK7, which is often used for a glass substrate, is 9 (×10 −6 /K). Even when any two of these materials are used for the above substrates, the difference in thermal expansion coefficient is 1×10 −6 /K or more. For example, when the size of the substrates  50 A and  50 B in the arrangement direction of the plurality of first waveguides  1  and the plurality of second waveguides  10  (in the Y direction in  FIG.  8   ) is 1 mm, a temperature change of 1° C. causes the alignment between the two substrates  50 A and  50 B to be changed by 1 nm. A temperature change of several tens of degrees Celsius causes the alignment between the two substrates  50 A and  50 B to be largely changed by several tens to several hundreds of nanometers. Therefore, light cannot be efficiently introduced from the first waveguides  1  into the second waveguides  10 . 
     The present inventors have found that the above problem can be solved by disposing the first waveguides and the second waveguides on the same substrate. When these waveguides are disposed on the common substrate, the first waveguides and the second waveguides can be easily aligned with each other. Moreover, a change in the alignment between the first waveguides and the second waveguides due to thermal expansion can be prevented. Therefore, light can be efficiently introduced from the first waveguides into the second waveguides. 
     An optical scanning device in one embodiment of the present disclosure includes a first waveguide, a second waveguide connected to the first waveguide, and a substrate that supports the first and second waveguides. The second waveguide includes a first mirror having a multilayer reflective film, a second mirror having a multilayer reflective film facing the multilayer reflective film of the first mirror, and an optical waveguide layer that is located between the first mirror and the second mirror and propagates light inputted to the first waveguide and transmitted through the first waveguide. The first mirror has a higher light transmittance than the second mirror and allows part of the light propagating through the optical waveguide layer to be emitted to the outside of the optical waveguide layer. The optical scanning device further includes an adjusting element that changes the refractive index of the optical waveguide layer to thereby change the direction of the emitted light. 
     In the present embodiment, the “second waveguide” corresponds to the “waveguide element” in the preceding embodiment. In some embodiments of the present disclosure, the first waveguide whose refractive index and thickness are maintained constant is disposed upstream of the second waveguide, and light is inputted to the first waveguide. The first waveguide propagates the inputted light, and the light is inputted to the second waveguide from its end surface. An end surface of the first waveguide may be connected directly to the end surface of the second waveguide, or, for example, a gap may be provided between these end surfaces. In the present specification, the phrase “the first waveguide is connected to the second waveguide” means that the first waveguide and the second waveguide are positioned such that light can be transferred between them. The form of “connection between the first waveguide and the second waveguide” includes not only the form in which the first waveguide is connected directly to the second waveguide (i.e., they are in contact with each other) but also the form in which they are disposed through a gap sufficiently shorter than the wavelength of the propagating light. In the present disclosure, the phrase “A is connected directly to B” means that a portion of A and a portion of B are in contact with each other with no gap such that light can be transferred between A and B. 
     In the above structure, since the first waveguide is disposed upstream of the second waveguide (waveguide element), a reduction in coupling efficiency due to scanning (i.e., loss of energy) can be suppressed even when the incident angle of light incident on the first waveguide is held constant. 
     In the above structure, since the first and second waveguides are disposed on the same substrate, the first and second waveguides are easily aligned with each other. Moreover, a change in the alignment between the first and second waveguides due to thermal expansion can be suppressed. Therefore, light can be efficiently introduced from the first waveguide into the second waveguide. 
     A third waveguide may be disposed upstream of the first waveguide. The third waveguide is connected to the first waveguide and allows light transmitted through the third waveguide to be inputted to the first waveguide. In one embodiment, the third waveguide may be a total reflection waveguide, and the second waveguide may be a reflective waveguide. The substrate that supports the first and second waveguides may further support the third waveguide. 
       FIG.  9    is a cross-sectional view of a waveguide element  10  in the YZ plane, schematically showing a structural example in which spacers  73  are disposed on both sides of an optical waveguide layer  20  located between a first mirror  30  and a second mirror  40 . The refractive index n low  of the spacers  73  is lower than the refractive index n w  of the optical waveguide layer (n low &lt;n w ). The spacers  73  may be, for example, air. The spacers  73  may be, for example, TiO 2 , Ta 2 O 5 , SiN, AlN, SiO 2 , etc., so long as the spacers  73  have a lower refractive index than the optical waveguide layer. 
       FIG.  10    is a cross-sectional view of an optical scanning device in the YZ plane, schematically showing a structural example of a waveguide array  10 A in which the waveguide elements  10  in  FIG.  9    are arranged in the Y direction. In the structural example in  FIG.  10   , the width of the first mirrors  30  in the Y direction is the same as the width of the optical waveguide layers  20 . In an array of a plurality of waveguide elements  10  including a plurality of reflective waveguides, leakage of guided light can be prevented when at least one of the width of first mirrors  30  and the width of second mirrors  40  is larger than the width of the optical waveguide layers  20 . However, such an idea has not been employed previously. 
     To improve light scanning performance, it is desirable to reduce the width of each of the waveguide elements  10  of the waveguide array  10 A. However, in this case, the guided light leakage problem becomes more prominent. 
     The reason for the leakage of guided light will be described. 
       FIG.  11    is an illustration schematically showing propagation of guided light in the X direction within an optical waveguide layer  20 . Since n w &gt;n low , the guided light is confined by total reflection in the ±Y directions and propagates in the X direction. However, in practice, evanescent light leaks out from the Y direction edge surfaces of the optical waveguide layer  20 . As shown in  FIG.  2   , the guided light propagates in the X direction at an angle smaller than the total reflection angle θ in  while reflected by the first and second mirrors  30  and  40  in the ±Z directions. In this case, in the regions with no first mirror  30  shown in  FIG.  10   , the evanescent light is not reflected and leaks to the outside. This unintended light loss may cause the amount of light used for optical scanning to be reduced. 
     The present inventors have found that the above problem can be solved by setting at least one of the width of the first mirrors  30  in the arrangement direction of the plurality of waveguide elements  10  and the width of the second mirrors  40  to be larger than the width of the optical waveguide layers  20 . This can reduce the unintended light loss described above. Therefore, a reduction in the amount of light used for optical scanning is prevented. 
     Embodiments of the present disclosure will next be described more specifically.  FIG.  12    is a cross-sectional view schematically showing part of the structure of an optical scanning device in an exemplary embodiment of the present disclosure. The optical scanning device includes a first waveguide  1  and a second waveguide (waveguide element)  10  connected to the first waveguide. The second waveguide  10  includes a first mirror  30  including a multilayer reflective film, a second mirror  40  including a multilayer reflective film facing the multilayer reflective film of the first mirror  30 , and an optical waveguide layer  20  located between the first mirror  30  and the second mirror  40 . The optical waveguide layer  20  propagates light inputted into the first waveguide  1  and transmitted through the first waveguide  1 . The optical waveguide layer  20  propagates the light in the same direction as the guiding direction of the first waveguide  1 . The first mirror  30  has a higher light transmittance than the second mirror  40  and allows part of the light propagating through the optical waveguide layer  20  to be emitted to the outside of the optical waveguide layer  20 . Although not shown in  FIG.  12   , the optical scanning device  100  further includes an adjusting element that changes the refractive index of the optical waveguide layer  20 . The optical waveguide layer  20  contains a material whose refractive index for the light propagating through the optical waveguide layer  20  is changed when, for example, a voltage is applied. The adjusting element changes the refractive index of the optical waveguide layer  20  by applying a voltage to the optical waveguide layer  20  to thereby change the direction of the light emitted from the second waveguide  10 . 
     The first waveguide  1  includes two opposed multilayer reflective films  3  and  4  and an optical waveguide layer  2  sandwiched between the two multilayer reflective films  3  and  4 . To transmit the light guided by the first waveguide  1  with no loss, it is desirable that the multilayer reflective films  3  and  4  in the first waveguide  1  have higher reflectance (i.e., lower transmittance) than the light-emitting-side multilayer reflective film (i.e., the first mirror  30 ) of the second waveguide  10 . Therefore, the thicknesses of the multilayer reflective films  3  and  4  are larger than the thickness of the first mirror  30 . The refractive index of the first waveguide  1 , i.e., the refractive index of the optical waveguide layer  2  of the first waveguide  1 , is unchanged or is changed by an amount different from the amount of change in the refractive index of the optical waveguide layer  20 . The first waveguide  1  is connected directly to the optical waveguide layer  20  of the second waveguide  10 . 
     For example, an end surface of the optical waveguide layer  2  of the first waveguide  1  is connected to an end surface of the optical waveguide layer  20  of the second waveguide  10 . The multilayer reflective film  3  in this example has a portion  3   a  having a smaller thickness (i.e., lower reflectance) than its adjacent portion. Light is inputted from the portion  3   a  (referred to also as a “light inputting portion  3   a ”). By inputting the light from the low-reflectance region, the light can be efficiently introduced into the optical waveguide layer  2 . The optical waveguide layer  2  propagates the light entering the light inputting portion  3   a , and the light is inputted to the end surface of the optical waveguide layer  20  of the second waveguide  10 . In this manner, the light propagates from the optical waveguide layer  2  to the optical waveguide layer  20  and can be emitted through the mirror  30 . 
     In the second waveguide  10 , the reflectance of the multilayer reflective film of the first mirror  30  is lower than the reflectance of the multilayer reflective film of the second mirror  40  because it is necessary to emit light through the first mirror  30 . The first waveguide  1  is designed such that the reflectance of the multilayer reflective films  3  and  4  is comparable to the reflectance of the second mirror  40  in order to prevent light emission. 
     With the above-described structure, the optical scanning device can efficiently emit light from the second waveguide  10 , as described later. 
       FIG.  13    is a cross-sectional view schematically showing another example of the structure of the optical scanning device. In this example, the first waveguide  1  includes no multilayer reflective films  3  and  4 . The first waveguide  1  propagates light by total reflection. The first waveguide  1  has a grating  5  on part of its surface. Light is inputted through the grating  5 . In this example, the portion in which the grating  5  is disposed serves as a light inputting portion. By providing the grating  5 , the light can be easily introduced into the waveguide  1 . When no multilayer reflective films  3  and  4  are provided as in this example, the first waveguide  1  is designed such that the angle θ w1  of the guided light satisfies the total reflection condition. In this case also, the refractive index of the first waveguide  1  is unchanged or is changed by an amount different from the amount of change in the refractive index of the optical waveguide layer  20 . The first waveguide  1  is connected directly to the optical waveguide layer  20  of the second waveguide  10 . The optical waveguide layer  20  propagates the light in the same direction as the guiding direction of the first waveguide  1 . 
       FIG.  14    is a cross-sectional view schematically showing yet another example of the structure of the optical scanning device. The optical scanning device in this example further includes a third waveguide  1 ′ connected to the first waveguide  1 . The first waveguide  1  is a reflective waveguide and includes two opposed multilayer reflective films  3  and  4  and an optical waveguide layer  2  disposed therebetween. The third waveguide  1 ′ is a total reflection waveguide that propagates light by total reflection. The refractive index of the third waveguide  1 ′ is unchanged or is changed by an amount different from the amount of change in the refractive index of the optical waveguide layer  20 . The third waveguide  1 ′ is connected directly to the optical waveguide layer  2  of the first waveguide  1 . The optical waveguide layer  20  propagates light in the same direction as the guiding direction of the third waveguide  1 ′. The third waveguide  1 ′ has a grating  5 ′ on part of its surface, as does the first waveguide  1  in the example in  FIG.  13   . Light from a light source is inputted to the third waveguide  1 ′ through the grating  5 ′. In this example, the portion in which the grating  5 ′ is disposed serves as a light inputting portion. The refractive index of the optical waveguide layer  20  of the second waveguide  10  is modulated by an unillustrated adjusting element (e.g., a modulating element). No modulating function is provided for the first waveguide  1 . To prevent light emission from the first waveguide  1 , the reflectance of the reflecting mirrors (i.e., the multilayer reflective films  3  and  4 ) of the first waveguide  1  is set to be higher than the reflectance of the first mirror  30  of the second waveguide  10 . The reflectance of the first mirror  30  of the second waveguide  10  is set to be lower than the reflectance of the second mirror  40 . With this structure, the light inputted into the third waveguide  1 ′ propagates through the third waveguide  1 ′ and the first waveguide  1  and is inputted into the second waveguide  10 . The inputted light is emitted to the outside through the first mirror  30  while propagating through the optical waveguide layer  20  of the second waveguide  10 . 
       FIGS.  15  and  16 A to  16 C  are illustrations showing examples of a method for inputting light into the first waveguide  1  in a structure configured such that the light is inputted to the first waveguide  1 .  FIG.  15    shows an example in which light enters an optical waveguide layer  2  sandwiched between two multilayer reflective films, as in the example shown in  FIG.  12   . As shown in  FIG.  15   , by causing the light to be incident on a small-thickness portion (i.e., a low-reflectance portion)  3   a  of a multilayer reflective film, the light can be efficiently introduced into the optical waveguide layer  2 .  FIG.  16 A  shows an example in which light is introduced into a first waveguide  1  through a grating  5  formed on a surface of the first waveguide  1 , as in the example shown in  FIG.  13   .  FIG.  16 B  shows an example in which light is inputted from an end surface of a first waveguide  1 .  FIG.  16 C  shows an example in which light is inputted from a laser light source  6  disposed on a surface of a first waveguide  1  through this surface. The structure shown in  FIG.  16 C  is disclosed in, for example, M. Lamponi et al., “Low-Threshold Heterogeneously Integrated InP/SOI Lasers With a Double Adiabatic Taper Coupler,” IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 24, NO. 1, Jan. 1, 2012, pp 76-78. The entire disclosure of this document is incorporated herein. With any of the above structures, light can be efficiently introduced into the waveguide  1 . 
     The light inputting methods shown in  FIGS.  15  to  16 C  are applicable also to the structure using the third waveguide  1 ′ shown in  FIG.  14   . In the example shown in  FIG.  14   , the grating  5 ′ is provided on part of a surface of the third waveguide  1 ′, but the grating  5 ′ may not be provided. For example, the light inputting method shown in  FIG.  16 B or  16 C  may be applied to the third waveguide  1 ′. When the light inputting method shown in  FIG.  16 B  is applied to the third waveguide  1 ′, the third waveguide  1 ′ propagates the light entering from an end surface of the third waveguide  1 ′, and the propagating light is inputted to an end surface of the first waveguide  1 . When the light inputting method shown in  FIG.  16 C  is applied to the third waveguide  1 ′, light is inputted from the laser light source disposed on a surface of the third waveguide  1 ′ through this surface. The third waveguide  1 ′ propagates the inputted light, and this light is inputted to the end surface of the first waveguide  1 . The third waveguide  1 ′ is not necessarily a total reflection waveguide and may be the reflective waveguide shown in  FIG.  15   . 
     As shown in  FIGS.  12  and  13   , the refractive index of the optical waveguide layer  2  of the first waveguide  1  is denoted by n w1 , and the refractive index of the optical waveguide layer  20  of the second waveguide  10  is denoted by n w2 . The emergent angle of light from the second waveguide  10  is denoted by θ. The reflection angle of the guided light in the first waveguide  1  is denoted by θ w1 , and the reflection angle of the guided light in the second waveguide  10  is denoted by θ w2 . As shown in  FIG.  14   , the refractive index of the optical waveguide layer  2 ′ of the third waveguide  1 ′ is denoted by n w3 , and the reflection angle of the guided light in the third waveguide  1 ′ is denoted by θ w3 . In the present embodiment, to allow light to be extracted from the second waveguide  10  to the outside (e.g., an air layer having a refractive index of 1), n w2  sin θ w2 =sin θ&lt;1 holds. 
     &lt;Principle of Coupling of Guided Light&gt; 
     Referring next to  FIGS.  12  and  13   , the principle of coupling of the guided light between waveguides  1  and  10  will be described. For the sake of simplicity, the light propagating through the waveguides  1  and  10  is approximately assumed to be a ray of light. It is assumed that light undergoes total reflection at the interfaces between the optical waveguide layer  20  and the upper and lower multilayer reflective films of the waveguide  10  and at the interfaces between the optical waveguide layer  2  and the upper and lower multilayer reflective films of the waveguide  1  (or the interfaces between the optical waveguide layer  2  and the external medium). The thickness of the optical waveguide layer  2  of the first waveguide  1  is denoted by d 1 , and the thickness of the optical waveguide layer  20  of the second waveguide  10  is denoted by d 2 . Then, conditions that allow propagating light to be present in the waveguides  1  and  10  are represented by the following formulas (5) and (6), respectively.
 
2 d   1   n   w1  cos θ w1   =mλ   (5)
 
2 d   2   n   w2  cos θ w2   =mλ   (6)
 
Here, λ is the wavelength of the light, and m is an integer of 1 or more.
 
     In consideration of the Snell&#39;s law at the interface between the waveguides  1  and  10 , formula (7) holds.
 
 n   w1  sin(90°−θ w1 )= n   w2  sin(90°−θ w2 )  (7)
 
     By modifying formula (7), formula (8) below is obtained.
 
 n   w1  cos θ w1   =n   w2  cos θ w2   (8)
 
     Suppose that formulas (5) and (8) hold. Then formula (6) holds even when n w2  changes, provided that d 1  is equal to d 2 . Specifically, even when the refractive index of the optical waveguide layer  20  is changed, light can propagate from the optical waveguide layer  2  to the optical waveguide layer  20  efficiently. 
     To derive the above formulas, the light is assumed to be a ray of light for simplicity. In practice, since the thicknesses d 1  and d 2  are comparative to the wavelength λ (at most 10 times the wavelength), the guided light has wave characteristics. Therefore, strictly speaking, it is necessary that the effective refractive indexes of the optical waveguide layers  2  and  20 , instead of the refractive indexes of their materials, must be used as the above refractive indexes n w1  and n w2 . Even when the thickness d 1  of the optical waveguide layer  2  is not the same as the thickness d 2  of the optical waveguide layer  20  or, strictly speaking, when formula (8) does not hold, light can be guided from the optical waveguide layer  2  to the optical waveguide layer  20 . This is because the light is transmitted from the optical waveguide layer  2  to the optical waveguide layer  20  in a near field. Specifically, when the electric field distribution in the optical waveguide layer  2  overlaps the electric field distribution in the optical waveguide layer  20 , light is transmitted from the optical waveguide layer  2  to the optical waveguide layer  20 . 
     The above discussion holds also for the guided light between the third waveguide  1 ′ and the first waveguide  1  in the example shown in  FIG.  14   . 
     &lt;Results of Computations&gt; 
     To examine the effects of the present embodiment, the present inventors computed the coupling efficiency of light under various conditions. FIMMWAVE available from Photon Design was used for the computations. 
     First, the coupling efficiency in a structure in which both the waveguides  1  and  10  were sandwiched between multilayer reflective films as shown in  FIG.  12    was computed. In the following computations, the mode order of light propagating from the waveguide  1  to the waveguide  10  is m=2. When the mode order of light in the waveguide  1  is the same as the mode order of light in the waveguide  10 , the light is coupled by the same principle. Therefore, the mode order of the light is not limited to m=2. 
       FIG.  17    shows the d 2  dependence of the coupling efficiency of guided light from the waveguide  1  to the waveguide  10  when n w1  is 1.45, d 1  is 1.27 μm, and the wavelength λ is 1.55 μm. The horizontal axis represents a value obtained by dividing d 2  by a cutoff thickness d cutoff  (=mλ/(2n w2 )) when the guided light is assumed to be a ray of light. The vertical axis represents the coupling efficiency normalized by setting the value of a peak to 1. The computations were performed from a lower limit value at which a cutoff condition indicating that no guided light is allowed to be present is satisfied to an upper limit value at which light is emitted to the outside. The computations were performed when n w2  was 1.3, 1.6, 1.9, 2.2, and 2.5. The center of the first waveguide  1  in its thickness direction matches the center of the second waveguide  10  in its thickness direction. As can be seen from the results in  FIG.  17   , the larger d 2 /d cutoff , the higher the coupling efficiency. As d 2 /d cutoff  decreases, the mode is not allowed to be present, and the coupling efficiency decreases. 
       FIG.  18    shows the results of computations performed using the same method except that n w1  was changed to 3.48 and d 1  was changed to 0.5 μm. In this case also, the mode order of the light propagating from the waveguide  1  to the waveguide  10  was m=2. However, as described above, the mode order of the light is not limited to m=2. As can be seen from  FIG.  18   , the larger d 2 /d cutoff , the higher the coupling efficiency. As d 2 /d cutoff  decreases, the mode is not allowed to be present, and the coupling efficiency decreases. 
     The reason that the mode is present (i.e., the guided light is coupled) even when d 2 /d cutoff  is smaller than 1 in  FIGS.  17  and  18    is that the effective thickness of the optical waveguide layer  2  is larger than d 2  because of penetration of the light when it is reflected from the multilayer reflective films. The upper limit of d 2  is a value at which light is no longer emitted to the outside. This value is determined by assuming that the guided light is a ray of light and undergoes total reflection at the interfaces between each waveguide and the upper and lower multilayer reflective films thereof. Specifically, the upper limit is the value of d 2  when the reflection angle of the guided light is equal to the total reflection angle with respect to the air. In this case, the following formula (9) holds.
 
 n   w2  sin θ w2 =1  (9)
 
     From formulas (6) and (9) and d cutoff =mλ/(2n w2 ), the following formula (10) holds.
 
 d   2   /d   cutoff   =n   w2 /√( n   w2   2 −1)  (10)
 
     Because of the penetration of the guided light when it is reflected from the multilayer reflective films, the effective refractive index for the guided light becomes lower than n w2 . Therefore, the upper limit of d 2  is larger than that in formula (6). 
     Preferably, the coupling efficiency in the structure in the present embodiment is higher than that in the structure shown in  FIG.  6 B . For example, from the results in  FIGS.  17  and  18   , when the following relations:
 
0.95× d   cutoff   &lt;d   2 &lt;1.5× d   cutoff  and
 
(0.95× m λ/(2 n   w2 )&lt; d   2 &lt;1.5× m λ/(2 n   w2 ))
 
hold, the condition that the coupling efficiency is 7% or more, which is higher than the peak value shown in  FIG.  7   , is satisfied.
 
       FIG.  19    is a graph showing the above results classified by whether the coupling efficiency is 0.5 or more or less than 0.5, with the horizontal axis representing d 2 /d cutoff  and the vertical axis representing the refractive index ratio (|n w1 −n w2 |/n w1 ). For example, when the refractive index ratio is less than 0.4 and the following formula holds:
 
0.95× d   cutoff   &lt;d   2 &lt;1.5× d   cutoff ,
 
the condition that the coupling efficiency is 0.5 (50%) or more is satisfied.
 
     In the present embodiment, the refractive index n w1  of the first waveguide  1  is larger than the refractive index n w2  of the second waveguide  10  (n w1 &gt;n w2 ). However, the present disclosure is not limited to this structure, and n w1 ≤n w2  may hold. 
       FIG.  20    is an illustration showing a structure in which the center, with respect to the direction of thickness, of the optical waveguide layer  2  of the first waveguide  1  is offset by Δz from the center, with respect to the direction of thickness, of the optical waveguide layer  20  of the second waveguide  10 . When the center line, with respect to the thickness direction, of the optical waveguide layer  20  of the second waveguide  10  is located on the light emitting side (i.e., the first mirror  30  side) of the center line, with respect to the thickness direction, of the optical waveguide layer  2  of the first waveguide  1  as shown in  FIG.  20   , the sign of Δz is positive. Let Δd be the absolute difference between the thickness d 1  of the optical waveguide layer  2  of the first waveguide  1  and the thickness d 2  of the optical waveguide layer  20  of the second waveguide  10 . When Δz=Δd/2, the Z direction position of a lower portion (i.e., the side opposite to the light emitting side) of the optical waveguide layer  2  of the waveguide  1  matches the Z direction position of a lower portion of the optical waveguide layer  20  of the waveguide  10 . 
       FIG.  21    is a graph showing the Δz dependence of the coupling efficiency of light from the first waveguide  1  to the second waveguide  10 . The results in  FIG.  21    were obtained by computing the coupling efficiency by setting n w1  to 2.2, the wavelength λ to 1.55 μm, n w2  to 2.2, and Δd to 0.12 μm at different values of Δz. The coupling efficiency normalized by a value at Δz=0 is shown in  FIG.  21   . When the center lines of the optical waveguide layers  2  and  20  with respect to their thickness direction are offset in the Z direction, the coupling efficiency is lower than that when Δz is zero (0). However, even when −Δd/2&lt;Δz&lt;Δd/2, the coupling efficiency is 90% or more of that at Δz=0 and can be maintained at a relatively high level. 
     In the example shown in  FIG.  13   , the first waveguide  1  guides light by total reflection. In this structure also, the same basic principle can be used, and the guided light beams propagating through the waveguides  1  and  10  can be coupled to each other. The d 2  dependence of the coupling efficiency of the guided light from the first waveguide  1  to the second waveguide  10  in the structure shown in  FIG.  13    was also determined by computations.  FIG.  22 A  shows the d 2  dependence of the coupling efficiency when n w1  is 2.2, d 1  is 0.7 μm, and the wavelength λ is 1.55 μm.  FIG.  22 B  shows the d 2  dependence of the coupling efficiency when n w1  is 3.48, d 1  is 0.46 μm, and the wavelength λ is 1.55 μm. When, for example, the following formulas are satisfied, the condition that the coupling efficiency is 7% or more is satisfied:
 
0.95× d   cutoff   &lt;d   2 &lt;1.5× d   cutoff ,
 
(i.e., 0.95× m λ/(2 n   w2 )&lt; d   2 &lt;1.5× m λ/(2 n   w2 )).
 
     When the following formulas are satisfied, the condition that the coupling efficiency is 50% or more is satisfied:
 
1.2× d   cutoff   &lt;d   2 &lt;1.5× d   cutoff ,
 
(i.e., 1.2× m λ/(2 n   w2 )&lt; d   2 &lt;1.5× m λ/(2 n   w2 )).
 
     In the structure in  FIG.  13    also, n w1 &gt;n w2  may hold, or n w1 ≤n w2  may hold. 
     As described above, the mode order of light propagating from the waveguide  1  to the waveguide  10  is not limited to m=2. For example, when a model shown in  FIG.  23 A  was used for the computations under the conditions of n w1 =1.883, d 1 =0.3 μm, n w2 =1.6, and d 2 =0.55 μm, light was coupled into the waveguide as shown in  FIG.  23 B . 
     Next, a structure in which a gap is present between the first waveguide  1  and the second waveguide  10  will be studied. 
       FIG.  24 A  is a cross-sectional view showing a modification of the present embodiment. In this example, the optical waveguide layer  20  of the second waveguide  10  is connected to the first waveguide  1  through a gap (e.g., an air gap). Even when the gap is present between the first waveguide  1  and the second waveguide  10  as described above, the light is coupled in the near field of the waveguide mode. Therefore, when the width of the gap (the width in the X direction) is sufficiently smaller than the wavelength λ, the guided light is coupled between the waveguides  1  and  10 . This differs from the coupling of the light propagating in free space to the waveguide mode in  FIG.  6 A or  6 B . 
       FIG.  24 B  is a graph showing the results of computations of the gap width dependence of the coupling efficiency. The coupling efficiency normalized by a value when the gap is 0 μm is shown in  FIG.  24 B . In the computations, n w1  is 3.48, n w2  is 1.5. d 1  is 0.9 μm, and d 2  is 1.1 μm. The refractive index of the gap is 1, and the wavelength λ is 1.55 μm. As can be seen from  FIG.  24 B , the normalized coupling efficiency is 50% or more when the gap is 0.24 μm or less. In consideration of the case where the gap is a medium other than air and the case where the wavelength λ differs from 1.55 μm, when the optical length of the gap (i.e., the product of the refractive index of the gap and the gap width) is equal to or less than λ/6.5, the normalized coupling efficiency is 50% or more. The optical length of the gap does not depend on the parameters of the waveguides  1  and  10 . 
     Also when light is inputted to the first waveguide  1  from the third waveguide  1 ′ as in the example shown in  FIG.  14   , a gap may be present between an end surface of the third waveguide  1 ′ and an end surface of the first waveguide  1 . As described above, the optical length of the gap (the product of the refractive index of the gap and the gap width) is set to be, for example, λ/6.5 or less. 
     Next, a description will be given of a structure for implementing two-dimensional optical scanning using a plurality of pairs of the first and second waveguides  1  and  10  in the present embodiment (these are referred to as “waveguide units” in the present specification). An optical scanning device that can implement two-dimensional scanning includes: a plurality of waveguide units arranged in a first direction; and an adjusting element (e.g., a combination of an actuator and a control circuit) that controls the waveguide units. The adjusting element changes the refractive index of the optical waveguide layer  20  of the second waveguide  10  of each of the waveguide units. In this manner, the direction of light emitted from the second waveguides  10  can be changed. When light beams with appropriately controlled phase differences are inputted to the second waveguides  10  of the plurality of waveguide units, two-dimensional optical scanning can be performed as described with reference to  FIG.  1   . An embodiment for implementing two-dimensional scanning will next be described in more detail. 
     &lt;Operating Principle of Two-Dimensional Scanning&gt; 
     In a waveguide array in which a plurality of waveguide elements (i.e., second waveguides)  10  are arranged in one direction, interference of light beams emitted from the waveguide elements  10  causes the emission direction of the light to change. By controlling the phases of the light beams to be supplied to the waveguide elements  10 , the emission direction of the light can be changed. The principle of this will next be described. 
       FIG.  25 A  is an illustration showing a cross section of the waveguide array that emits light in a direction perpendicular to the emission surface of the waveguide array. In  FIG.  25 A , phase shift amounts of the light beams propagating through the waveguide elements  10  are shown. The phase shift amounts are values with respect to the phase of a light beam propagating through the leftmost waveguide element  10 . The waveguide array in the present embodiment includes the plurality of waveguide elements  10  arranged at regular intervals. In  FIG.  25 A , broken line arcs represent wave fronts of the light beams emitted from the waveguide elements  10 . A straight line represents a wave front formed as a result of interference of the light beams. An arrow represents the direction of the light emitted from the waveguide array (i.e., the direction of the wave vector). In the example in  FIG.  25 A , the phases of the light beams propagating through the optical waveguide layers  20  of the waveguide elements  10  are the same. In this case, the light is emitted in a direction (the Z direction) perpendicular to the arrangement direction (the Y direction) of the waveguide elements  10  and to the extending direction (the X direction) of the optical waveguide layers  20 . 
       FIG.  25 B  is an illustration showing a cross section of the waveguide array that emits light in a direction different from the direction perpendicular to the emission surface of the waveguide array. In the example in  FIG.  25 B , the phases of the light beams propagating through the optical waveguide layers  20  of the plurality of waveguide elements  10  differ from each other in the arrangement direction by a constant amount (Δϕ). In this case, light is emitted in a direction different from the Z direction. By changing Δϕ, the Y direction component of the wave vector of the light can be changed. 
     The direction of the light emitted from the waveguide array to the outside (air in this case) can be quantitatively discussed as follows. 
       FIG.  26    is a perspective view schematically showing the waveguide array in a three-dimensional space. In the three-dimensional space defined by mutually orthogonal X, Y, and Z directions, a boundary surface between the waveguide array and a region to which light is emitted to air is set to be Z=z 0 . The boundary surface contains the emission surfaces of the plurality of waveguide elements  10 . In a region in which Z&lt;z 0  holds, the plurality of waveguide elements  10  are arranged in the Y direction at regular intervals and extend in the X direction. In a region in which Z&gt;z 0  holds, the electric-field vector E(x, y, z) of light emitted to air is represented by formula (11) below.
 
 E ( x,y,z )= E   0  exp[− j ( k   x   x+k   y   y+k   z   z )]  (11)
 
Here, E 0  is the amplitude vector of the electric field. k x , k y , and k z  are the wave numbers in the X, Y, and Z directions, respectively, and j is the imaginary unit. In this case, the direction of the light emitted to air is parallel to a wave vector (k x , k y , k z ) indicated by a thick arrow in  FIG.  26   . The magnitude of the wave vector is represented by formula (12) below.
 
                         k   x   2     +     k   y   2     +     k   z   2         =       2   ⁢   π     λ             (   12   )               
From the boundary condition for the electric field at Z=z0, wave vector components k x  and k y  parallel to the boundary surface agree with the wave numbers of light in the X and Y directions, respectively, in the waveguide array. This corresponds to the condition in which the wavelengths, in the plane directions, of the light on the air side at the boundary surface agree with the wavelengths, in the plane directions, of the light on the waveguide array side, as in the Snell&#39;s law in formula (2).
 
     k x  is equal to the wave number of the light propagating through the optical waveguide layer  20  of a waveguide element  10  extending in the X direction. In the waveguide element  10  shown in  FIG.  2    above, k x  is represented by formula (13) below using formulas (2) and (3). 
     
       
         
           
             
               
                 
                   
                     k 
                     x 
                   
                   = 
                   
                     
                       
                         
                           2 
                           ⁢ 
                           π 
                         
                         λ 
                       
                       ⁢ 
                       
                         n 
                         w 
                       
                       ⁢ 
                       sin 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         θ 
                         w 
                       
                     
                     = 
                     
                       
                         
                           2 
                           ⁢ 
                           π 
                         
                         λ 
                       
                       ⁢ 
                       
                         
                           
                             n 
                             w 
                             2 
                           
                           - 
                           
                             
                               ( 
                               
                                 
                                   m 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   λ 
                                 
                                 
                                   2 
                                   ⁢ 
                                   d 
                                 
                               
                               ) 
                             
                             2 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
     k y  is derived from the phase difference between light beams in two adjacent waveguide elements  10 . The centers of N waveguide elements  10  arranged in the Y direction at regular intervals are denoted by y q  (q=0, 1, 2, . . . , N−1), and the distance (center-to-center distance) between two adjacent waveguide elements  10  is denoted by p. In this case, the electric-field vectors (formula (11)) of light emitted to air at y q  and y q+1  on the boundary surface (Z=z 0 ) satisfy the following formula.
 
 E ( x,y   q+1   ,z   0 )=exp[− jk   y ( y   q+1   −y   q )] E ( x,y   q   ,z   0 )=exp[− jk   y   p ] E ( x,y   q   ,z   0 )  (14)
 
When the phases in any two adjacent waveguide elements are set such that the phase difference is Δϕ==k y p (constant), k y  satisfies the relation of formula (15) below.
 
                     k   y     =     Δϕ   p             (   15   )               
In this case, the phase of light at y q  is represented by ϕ q =ϕ 0 +qΔϕ(ϕ q+1 −ϕ q =Δϕ). Specifically, the phase ϕ q  is constant (Δϕ=0), linearly increases in the Y direction (Δϕ&gt;0), or linearly decreases in the Y direction (Δϕ&lt;0). When the waveguide elements  10  are arranged in the Y direction at non-regular intervals, the phases at y q  and y q+1  may be set such that, for example, the phase difference for a given k y  is Δϕ q =ϕ q+1 −ϕ q =k y (y q+1 −y q ). In this case, the phase of the light at y q  is represented by ϕ q =ϕ 0 +k y (y q −y 0 ). Using k x  and k y  obtained from formulas (14) and (15), respectively, k z  is derived from formula (12). The emission direction of the light (i.e., the direction of the wave vector) can thereby be obtained.
 
     For example, as shown in  FIG.  26   , the angle between the wave vector (k x , k y , k z ) of the emitted light and a vector (0, k y , k z ) obtained by projecting the wave vector onto the YZ plane is denoted by θ. θ is the angle between the wave vector and the YZ plane. θ is represented by formula (16) below using formulas (12) and (13). 
                     sin   ⁢           ⁢   θ     =         k   x           k   x   2     +     k   y   2     +     k   z   2           =         λ     2   ⁢   π       ⁢     k   x       =         n   w   2     -       (       m   ⁢           ⁢   λ       2   ⁢   d       )     2                     (   16   )               
Formula (16) is exactly the same as formula (3) derived when the emitted light is restricted to be parallel to the XZ plane. As can be seen from formula (16), the X component of the wave vector changes depending on the wavelength of the light, the refractive index of the optical waveguide layers  20 , and the thickness of the optical waveguide layers  20 .
 
     Similarly, as shown in  FIG.  26   , the angle between the wave vector (k x , k y , k z ) of the emitted light (zeroth-order light) and a vector (k x , 0, k z ) obtained by projecting the wave vector onto the XZ plane is denoted by α 0 . α 0  is the angle between the wave vector and the XZ plane. α 0  is represented by formula (17) below using formulas (12) and (13). 
                     sin   ⁢           ⁢     α   0       =         k   x           k   x   2     +     k   y   2     +     k   z   2           =         λ     2   ⁢   π       ⁢     k   y       =     Δϕλ     2   ⁢   π   ⁢           ⁢   p                   (   17   )               
As can be seen from formula (17), the Y component of the wave vector of the light changes depending on the phase difference Δϕ of the light.
 
     As described above, θ and α 0  obtained from formulas (16) and (17), respectively, may be used instead of the wave vector (k x , k y , k z ) to identify the emission direction of the light. In this case, the unit vector representing the emission direction of the light can be represented by (sin θ, sin α 0 , (1−sin 2  α 0 −sin 2  θ) 1/2 ). For light emission, all these vector components must be real numbers, and therefore sin 2  α 0 +sin 2  θ≤1 is satisfied. Since sin 2  α 0 ≤1−sin 2  θ=cos 2  θ, the emitted light is changed within an angle range in which −cos θ≤sin α 0 ≤cos θ is satisfied. Since −1≤sin α 0 ≤1, the emitted light is changed within the angle range of −90°≤α 0  90° at θ=0°. However, as θ increases, cos θ decreases, so that the angle range of α 0  is narrowed. When θ=90° (cos θ=0), light is emitted only at α 0 =0°. 
     The two-dimensional optical scanning in the present embodiment can be implemented using at least two waveguide elements  10 . When the number of waveguide elements  10  is small, the divergence angle Δα of α 0  is large. As the number of waveguide elements  10  increases, Δα decreases. This can be explained as follows. For the sake of simplicity, θ is assumed to be 0° in  FIG.  26   . Specifically, the emission direction of the light is parallel to the YZ plane. 
     Assume that light beams having the same emission intensity and the above-described phases ϕ q  are emitted from N waveguide elements  10  (N is an integer of 2 or more). In this case, the absolute value of the total amplitude distribution of the light beams (electric fields) emitted from the N waveguide elements  10  in a far field is proportional to F(u) represented by formula (18) below. 
                     F   ⁡     (   u   )       =            sin   ⁡     (     Nu   /   2     )         sin   ⁡     (     u   /   2     )                      (   18   )               
Here, u is represented by formula (19) below.
 
     
       
         
           
             
               
                 
                   u 
                   = 
                   
                     
                       
                         2 
                         ⁢ 
                         π 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         p 
                       
                       λ 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           sin 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           α 
                         
                         - 
                         
                           sin 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             α 
                             0 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   19 
                   ) 
                 
               
             
           
         
       
     
     Here, α is the angle between the Z axis and a line connecting the origin and an observation point in the YZ plane. α 0  satisfies formula (17). F(u) in formula (18) is N (maximum) when u=0 (α=α 0 ) and is 0 when u=±2π/N. Let the angle satisfying u=−2π/N be α 1 , and the angle satisfying u=2π/N be α 2  (α 1 &lt;α 0 &lt;α 2 ). Then the divergence angle of α 0  is Δα=α 2 −α 1 . A peak within the range of −2π/N&lt;u&lt;2π/N (α 1 &lt;α&lt;α 2 ) is generally referred to as a main lobe. A plurality of small peaks referred to as side lobes are present on both sides of the main lobe. By comparing the width Δu=4π/N of the main lobe and Δu=2πpΔ(sin α)/λ obtained from formula (19), Δ(sin α)=2λ/(Np) is obtained. When Δα is small, Δ(sin α)=sin α 2 −sin α 1 =[(sin α 2 −sin α 1 )/(α 2 −α 1 )] Δα[d(sin α)/dα] α=α0  Δα=cos α 0  Δα. Therefore, the divergence angle is represented by formula (20) below. 
     
       
         
           
             
               
                 
                   Δα 
                   = 
                   
                     
                       2 
                       ⁢ 
                       λ 
                     
                     
                       N 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       p 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       cos 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         α 
                         0 
                       
                     
                   
                 
               
               
                 
                   ( 
                   20 
                   ) 
                 
               
             
           
         
       
     
     Thus, as the number of waveguide elements  10  increases, the divergence angle Δα decreases, and high resolution optical scanning can be performed on a distant target. The same discussion is applicable to the case when θ≠0° in  FIG.  26   . 
     &lt;Diffracted Light Emitted from Waveguide Array&gt; 
     In addition to the zeroth-order light beam, higher-order diffracted light beams may be emitted from the waveguide array. For the sake of simplicity, θ is assumed to be 0° in  FIG.  26   . Specifically, the emission direction of the diffracted light is parallel to the YZ plane. 
       FIG.  27 A  is a schematic diagram showing how diffracted light is emitted from the waveguide array when p is larger than λ. In this case, when there is no phase shift (α 0 =0°), zeroth-order and ±first-order light beams are emitted in directions indicated by solid arrows shown in  FIG.  27 A  (higher-order diffracted light beams may be emitted, but this depends on the magnitude of p). When a phase shift is given to this state (α 0 ≠0°), the emission angles of the zeroth-order and ±first-order light beams rotate in the same rotation direction as shown by broken line arrows in  FIG.  27 A . Higher-order light beams such as the ±first-order light beams can be used for beam scanning. However, to configure a simpler device, only the zeroth-order light beam is used. To avoid a reduction in gain of the zeroth-order light beam, the distance p between two adjacent waveguide elements  10  may be reduced to be less than λ to suppress the emission of higher-order light beams. Even when p&gt;λ, only the zeroth-order light beam can be used by physically blocking the higher-order light beams. 
       FIG.  27 B  is a schematic diagram showing how diffracted light is emitted from the waveguide array when p is smaller than λ. In this case, when there is no phase shift (α 0 =0°), no higher-order light beams are present because the diffraction angles of the higher-order light beams exceed 90 degrees, and only the zeroth-order light beam is emitted forward. However, in the case where p is close to λ, when a phase shift is given (α 0 ≠0°), the emission angles change, and the ±first-order light beams may be emitted.  FIG.  27 C  is a schematic diagram showing how diffracted light is emitted from the waveguide array when p≈λ/2. In this case, even when a phase shift is given (α 0 ≠0°, the ±first-order light beams are not emitted. Even when the ±first-order light beams are emitted, they are emitted at considerably large angles. When p&lt;λ/2, even when a phase shift is given, no higher-order light beams are emitted. However, even when p is further reduced, no particular advantage is expected. Therefore, p may be set to be, for example, λ/2 or more. 
     The relation between the zeroth-order light beam and ±first-order light beams emitted to air in  FIGS.  27 A to  27 C  can be quantitively explained as follows. F(u) in formula (18) is F(u)=F(u+2π) and is a function with a period of 2π. When u=±2mπ, F(u)=N (maximum). In this case, ±m-th order light beams are emitted at emission angles α satisfying u=±2mπ. Peaks around u=±2mπ (m≠0) (peak width: Δu=4π/N) are referred to as grating lobes. 
     Only ±first-order light beams contained in higher-order light are considered (u=±2π). The emission angles α± of the ±first-order light beams satisfy formula (21) below. 
     
       
         
           
             
               
                 
                   
                     sin 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       α 
                       ± 
                     
                   
                   = 
                   
                     
                       sin 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         α 
                         0 
                       
                     
                     ± 
                     
                       λ 
                       p 
                     
                   
                 
               
               
                 
                   ( 
                   21 
                   ) 
                 
               
             
           
         
       
     
     p&lt;λ/(1−sin α 0 ) is obtained from the condition sin α 0 &gt;1 indicating that the +first-order light beam is not emitted. Similarly, p&lt;λ/(1+sin α 0 ) is obtained from the condition sin α 0 &lt;−1 indicating that the −first-order light beam is not emitted. 
     Conditions indicating whether or not the ±first-order light beams are emitted in addition to the zeroth-order light beam at an emission angle α 0  (&gt;0) are classified as follows. When p≥λ/(1−sin α 0 ), both ±first-order light beams are emitted. When λ/(1+sin α 0 )≤p&lt;λ/(1−sin α 0 ), the +first-order light beam is not emitted, but the −first-order light beam is emitted. When p&lt;λ/(1+sin α 0 ), the ±first-order light beams are not emitted. In particular, when p&lt;λ/(1+sin α 0 ) is satisfied, the ±first-order light beams are not emitted even when θ #0° in  FIG.  26   . For example, to achieve scanning over 10° on one side when the ±first-order light beams are not emitted, α 0  is set to 10°, and p is set such that the relation p≤λ/(1+sin 10°)≈0.85λ, is satisfied. For example, by combining this formula and the above-described lower limit of p, λ/2≤p≤λ/(1+sin 10°) is satisfied. 
     However, to satisfy the condition that the ±first-order light beams are not emitted, p must be very small. This makes it difficult to produce the waveguide array. Therefore, it is contemplated that the angle range of 0°&lt;α 0 &lt;α max  is scanned with the zeroth-order light beam irrespective of the presence or absence of the ±first-order light beams. However, it is assumed that the ±first-order light beams are not present in this angle range. To satisfy this condition, the emission angle of the +first-order light beam when α 0 =0° must be α + ≥α max  (i.e., sin α + =(λ/p)≥sin α max ), and the emission angle of the −first-order light beam when α 0 =α max  must be α − ≤0 (i.e., sin α − =sin α max −(λ/p)≤0). These restrictions give p≤λ/sin α max . 
     As can be seen from the above discussion, the maximum value α max  of the emission angle α 0  of the zeroth-order light beam when the ±first-order light beams are not present within the scanning angle range satisfies formula (22) below. 
     
       
         
           
             
               
                 
                   
                     sin 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       α 
                       
                         ma 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         x 
                       
                     
                   
                   = 
                   
                     λ 
                     p 
                   
                 
               
               
                 
                   ( 
                   22 
                   ) 
                 
               
             
           
         
       
     
     For example, to achieve scanning over 10° on one side when the ±first-order light beams are not present within the scanning angle range, α 0  is set to 10°, and p is set such that the relation p≤λ/sin 10°≈5.76λ is satisfied. For example, by combining this formula and the above-described condition for the lower limit of p, p satisfies λ/2≤p≤λ/sin 10°. Since this upper limit of p (p≈5.76λ) is sufficiently larger than the upper limit (p≤0.85λ) when the ±first-order light beams are not emitted, the waveguide array can be produced relatively easily. When the light used is not single-wavelength light, λ is the center wavelength of the light used. 
     As described above, to scan over a wider angle range, it is necessary to reduce the distance p between waveguides. However, to reduce the divergence angle Δα of the emitted light in formula (20) when p is small, it is necessary to increase the number of waveguides in the waveguide array. The number of waveguides in the waveguide array is appropriately determined according to its intended application and the required performance. The number of waveguides in the waveguide array may be, for example, 16 or more and may be 100 or more in some applications. 
     &lt;Phase Control of Light Introduced into Waveguide Array&gt; 
     To control the phase of light emitted from each waveguide element  10 , a phase shifter that changes the phase of the light before introduction into the waveguide element  10  is disposed, for example, upstream of the waveguide element  10 . The optical scanning device  100  in the present embodiment further includes a plurality of phase shifters connected to the respective waveguide elements  10  and a second adjusting element that changes the phases of light beams propagating through of the phase shifters. Each phase shifter includes a waveguide that is connected to the optical waveguide layer  20  of a corresponding one of the plurality of waveguide elements  10  directly or through another waveguide. The second adjusting element changes the phase differences between the light beams propagating from the plurality of phase shifters to the plurality of waveguide elements  10  to thereby change the direction (i.e., the third direction D 3 ) of light emitted from the plurality of waveguide elements  10 . In the following description, the plurality of arranged phase shifters may be referred to as a “phase shifter array,” as in the case of the waveguide array. 
       FIG.  28    is a schematic diagram showing an example of a structure in which a phase shifter  80  is connected directly to a waveguide element  10 . In  FIG.  28   , a portion surrounded by a broken line frame corresponds to the phase shifter  80 . The phase shifter  80  includes a pair of opposed mirrors (a fifth mirror  30   a  and a sixth mirror  40   a  which may be referred to simply as mirrors) and a waveguide  20   a  disposed between the mirrors  30   a  and  40   a . The waveguide  20   a  in this example is formed of the same material as the material of the optical waveguide layer  20  of the waveguide element  10  and is connected directly to the optical waveguide layer  20 . Similarly, the mirror  40   a  is formed of the same material as the material of the mirror  40  of the waveguide element  10  and is connected to the mirror  40 . The mirror  30   a  has a lower transmittance (i.e., a higher reflectance) than the mirror  30  of the waveguide element  10 . The mirror  30   a  is connected to the mirror  30 . The phase shifter  80  is designed such that the transmittance of the mirror  30   a  is as low as that of the mirrors  40  and  40   a  in order not to emit light. Specifically, the light transmittance of the fifth mirror  30   a  and the light transmittance of the sixth mirror  40   a  are lower than the light transmittance of the first mirror  30 . In this example, the phase shifter  80  corresponds to the “first waveguide” described above. The “first waveguide” may serve as the phase shifter as described above. 
       FIG.  29    is a schematic diagram of a waveguide array  10 A and a phase shifter array  80 A as viewed in a direction normal to a light-emission surface (in the Z direction). In the example shown in  FIG.  29   , all the phase shifters  80  have the same propagation characteristics, and all the waveguide elements  10  have the same propagation characteristics. The phase shifters  80  may have the same length or may have different lengths, and the waveguide elements  10  may have the same length or may have different lengths. When the phase shifters  80  have the same length, a driving voltage, for example, is changed to control the phase shift amount of each of the phase shifters  80 . When the phase shifters  80  have lengths that differ in equal steps, the same driving voltage can be used to give phase shifts that differ in equal steps. This optical scanning device  100  further includes an optical divider  90  that divides light and supplies divided light beams to the plurality of phase shifters  80 , a first driving circuit  110  that drives each of the waveguide elements  10 , and a second driving circuit  210  that drives each of the phase shifters  80 . A straight arrow in  FIG.  29    indicates light input. The first driving circuit  110  and the second driving circuit  210  that are disposed separately are controlled independently to implement two-dimensional scanning. In this example, the first driving circuit  110  serves as a component of the first adjusting element, and the second driving circuit  210  serves as a component of the second adjusting element. 
     As described later, the first driving circuit  110  changes (modulates) the refractive index of the optical waveguide layer  20  of each of the waveguide elements  10  to thereby change the angle of light emitted from the optical waveguide layer  20 . As described later, the second driving circuit  210  changes the refractive index of the waveguide  20   a  of each of the phase shifters  80  to thereby change the phase of light propagating inside the waveguide  20   a . The optical divider  90  may be composed of waveguides in which light propagates by total reflection or reflective waveguides similar to the waveguide elements  10 . 
     The phases of light beams divided by the optical divider  90  may be controlled, and then the resulting light beams may be introduced into the phase shifters  80 . To control the phases, for example, a passive phase control structure in which the lengths of waveguides connected to the phase shifters  80  are adjusted to control the phases of the light beams may be used. Alternatively, phase shifters that have the same function as the phase shifters  80  and are controllable using an electric signal may be used. By using any of these methods, the phases of the light beams may be adjusted before they are introduced into the phase shifters  80  such that, for example, light beams having the same phase are supplied to all the phase shifters  80 . By adjusting the phases as described above, the second driving circuit  210  can control each of the phase shifters  80  in a simpler manner. 
       FIG.  30    is an illustration schematically showing an example of a structure in which the waveguides of the phase shifters  80  are connected to the optical waveguide layers  20  of the waveguide elements  10  through additional waveguides  85 . Each of the additional waveguides  85  may be any of the above-described first waveguides  1 . Each additional waveguide  85  may be a combination of the waveguides  1  and  1 ′ shown in  FIG.  14   . Each phase shifter  80  may have the same structure as the phase shifter  80  shown in  FIG.  28    or may have a different structure. In  FIG.  30   , the phase shifters  80  are simply represented by symbols ϕ 0  to ϕ 5  that indicate the phase shift amounts. The same representation may be used in later figures. A waveguide that can propagate light using total reflection may be used for each phase shifter  80 . In this case, the mirrors  30   a  and  40   a  shown in  FIG.  28    are not necessary. 
       FIG.  31    is an illustration showing a structural example in which a plurality of phase shifters  80  arranged in a cascaded manner are inserted into the optical divider  90 . In this example, the plurality of phase shifters  80  are connected to intermediate points of a channel of the optical divider  90 . The phase shifters  80  give the same phase shift amount ϕ to light propagating therethrough. When the phase shift amounts given by the phase shifters  80  are the same, the phase differences between any two adjacent waveguide elements  10  are the same. Therefore, the second adjusting element can transmit a common phase control signal to all the phase shifters  80 . This is advantageous in that the structure is simplified. 
     Waveguides can be used to efficiently propagate light between the optical divider  90 , the phase shifters  80 , the waveguide elements  10 , etc. An optical material having a higher refractive index than its surrounding material and absorbing less light can be used for the waveguides. For example, materials such as Si, GaAs, GaN, SiO 2 , TiO 2 , Ta 2 O 5 , AlN, and SiN can be used. Any of the above-described first waveguides  1  may be used to propagate light from the optical divider  90  to the waveguide elements  10 . To propagate light from the optical divider  90  to the waveguide elements  10 , the waveguides  1  and  1 ′ shown in  FIG.  14    may be used. 
     The phase shifters  80  require a mechanism for changing a light path length in order to give a phase difference to light. In the present embodiment, the refractive index of the waveguide of each phase shifter  80  is modulated to change the light path length. In this manner, the phase difference between light beams to be supplied from two adjacent phase shifters  80  to their respective waveguide elements  10  can be adjusted. More specifically, the refractive index of a phase shift material in the waveguide of each phase shifter  80  is modulated, and the phase shift can thereby be given. A specific example of the structure for refractive index modulation will be described later. 
     &lt;Examples of First Adjusting Element&gt; 
     Next, a description will be given of structural examples of the first adjusting element that adjusts the refractive index of the optical waveguide layer  20  of each waveguide element  10 . 
       FIG.  32 A  is a perspective view schematically showing an example of the structure of the first adjusting element  60  (hereinafter may be referred to simply as an adjusting element). In the example shown in  FIG.  32 A , the adjusting element  60  includes a pair of electrodes  62  and is installed in the waveguide element  10 . The optical waveguide layer  20  is sandwiched between the pair of electrodes  62 . The optical waveguide layer  20  and the pair of electrodes  62  are disposed between a first mirror  30  and a second mirror  40 . The entire side surfaces (the surfaces parallel to the XZ plane) of the optical waveguide layer  20  are in contact with the electrodes  62 . The optical waveguide layer  20  contains a refractive index modulatable material whose refractive index for the light propagating through the optical waveguide layer  20  is changed when a voltage is applied. The adjusting element  60  further includes wiring lines  64  led from the pair of electrodes  62  and a power source  66  connected to the wiring lines  64 . By turning on the power source  66  to apply a voltage to the pair of electrodes  62  through the wiring lines  64 , the refractive index of the optical waveguide layer  20  can be modified. Therefore, the adjusting element  60  may be referred to as a refractive index modulatable element. 
       FIG.  32 B  is a perspective view schematically showing another example of the structure of the first adjusting element  60 . In this example, only parts of the side surfaces of the optical waveguide layer  20  are in contact with the electrodes  62 . The rest of the structure is the same as that shown in  FIG.  32 A . Even with the structure in which the refractive index of part of the optical waveguide layer  20  is changed, the direction of emitted light can be changed. 
       FIG.  32 C  is a perspective view schematically showing yet another example of the structure of the first adjusting element  60 . In this example, the pair of electrodes  62  have a layer shape approximately parallel to the reflecting surfaces of the mirrors  30  and  40 . One of the electrodes  62  is sandwiched between the first mirror  30  and the optical waveguide layer  20 . The other electrode  62  is sandwiched between the second mirror  40  and the optical waveguide layer  20 . When this structure is employed, transparent electrodes may be used as the electrodes  62 . This structure is advantageous in that it can be produced relatively easily. 
     In the examples shown in  FIGS.  32 A to  32 C , the optical waveguide layer  20  of each waveguide element  10  contains a material whose refractive index for the light propagating through the optical waveguide layer  20  is changed when a voltage is applied. The first adjusting element  60  includes the pair of electrodes  62  sandwiching the optical waveguide layer  20  and changes the refractive index of the optical waveguide layer  20  by applying a voltage to the pair of electrodes  62 . The voltage is applied using the first driving circuit  110  (see  FIG.  29   ) described above. 
     Examples of the materials used for the above components will be described. 
     The material used for the mirrors  30 ,  40 ,  30   a , and  40   a  may be, for example, a dielectric multilayer film. A mirror using a multilayer film can be produced by, for example, forming a plurality of films having an optical thickness of ¼ wavelength and having different refractive indexes periodically. Such a multilayer film mirror can have high reflectance. The materials of the films used may be, for example, SiO 2 , TiO 2 , Ta 2 O 5 , Si, and SiN. The mirrors are not limited to multilayer film mirrors and may be formed of a metal such as Ag or Al. 
     Various conductive materials can be used for the electrodes  62  and the wiring lines  64 . For example, conductive materials including metal materials such as Ag, Cu, Au, Al, Pt, Ta, W, Ti, Rh, Ru, Ni, Mo, Cr, and Pd, inorganic compounds such as ITO, tin oxide, zinc oxide, IZO (registered trademark), and SRO, and conductive polymers such as PEDOT and polyaniline can be used. 
     Various light-transmitting materials such as dielectric materials, semiconductors, electrooptical materials, and liquid crystal molecules can be used for the material of the optical waveguide layer  20 . Examples of the dielectric materials include SiO 2 , TiO 2 , Ta 2 O 5 , SiN, and AlN. Examples of the semiconductor materials include Si-based, GaAs-based, and GaN-based materials. Examples of the electrooptical materials include lithium niobate (LiNbO 3 ), barium titanate (BaTiO 3 ), lithium tantalate (LiTaO 3 ), zinc oxide (ZnO), lead lanthanum zirconate titanate (PLZT), and potassium tantalate niobate (KTN). 
     To modulate the refractive index of the optical waveguide layer  20 , for example, methods utilizing a carrier injection effect, an electrooptical effect, a birefringent effect, and a thermooptical effect can be used. Examples of these methods will next be described. 
     The method utilizing the carrier injection effect can be implemented by a structure utilizing a pin junction of semiconductors. In this method, a structure in which a semiconductor with a low dopant concentration is sandwiched between a p-type semiconductor and an n-type semiconductor is used, and the refractive index of the semiconductor is modulated by injecting carriers into the semiconductor. In this structure, the optical waveguide layer  20  of each of the waveguide elements  10  contains a semiconductor material. One of the pair of electrodes  62  may contain a p-type semiconductor, and the other one may contain an n-type semiconductor. In the first adjusting element  60 , a voltage is applied to the pair of electrodes  62  to inject carriers into the semiconductor material, and the refractive index of the optical waveguide layer  20  is thereby changed. Specifically, the optical waveguide layer  20  may be produced using a non-doped or low-dopant concentration semiconductor, and the p-type semiconductor and the n-type semiconductor may be disposed in contact with the optical waveguide layer  20 . A complex structure may be used in which the p-type semiconductor and the n-type semiconductor are disposed in contact with the low-dopant concentration semiconductor and conductive material layers are in contact with the p-type semiconductor and the n-type semiconductor. For example, when carriers of about 10 20  cm −3  are injected into Si, the refractive index of Si is changed by about 0.1 (see, for example, “Free charge carrier induced refractive index modulation of crystalline Silicon,” 7 th  IEEE International Conference on Group IV Photonics, P102-104, 1-3 Sep. 2010). When this method is used, a p-type semiconductor and an n-type semiconductor may be used as the materials of the pair of electrodes  62  in  FIGS.  32 A to  32 C . Alternatively, the pair of electrodes  62  may be formed of a metal, and the optical waveguide layer  20  itself or layers between the optical waveguide layer  20  and the electrodes  62  may contain a p-type or n-type semiconductor. 
     The method utilizing the electrooptical effect can be implemented by applying a voltage to an optical waveguide layer  20  containing an electrooptical material. In particular, when KTN is used as the electrooptical material, the electrooptical effect obtained can be large. The relative dielectric constant of KTN increases significantly at a temperature slightly higher than its tetragonal-to-cubic phase transition temperature, and this effect can be utilized. For example, according to “Low-Driving-Voltage Electro-Optic Modulator With Novel KTa1-xNbxO3 Crystal Waveguides,” Jpn. J. Appl. Phys., Vol. 43, No. 8B (2004), an electrooptical constant of g=4.8×10 −15  m 2 /V 2  is obtained for light with a wavelength of 1.55 μm. For example, when an electric field of 2 kV/mm is applied, the refractive index is changed by about 0.1 (=gn 3 E 3 /2). With the structure utilizing the electrooptical effect, the optical waveguide layer  20  of each of the waveguide elements  10  contains an electrooptical material such as KTN. The first adjusting element  60  changes the refractive index of the electrooptical material by applying a voltage to the pair of electrodes  62 . 
     In the method utilizing the birefringent effect of a liquid crystal, an optical waveguide layer  20  containing the liquid crystal material is driven using the electrodes  62  to change the refractive index anisotropy of the liquid crystal. In this manner, the refractive index for the light propagating through the optical waveguide layer  20  can be modulated. Generally, a liquid crystal has a birefringence of about 0.1 to 0.2, and a change in refractive index comparable to the birefringence can be obtained by changing the alignment direction of the liquid crystal using an electric field. In the structure using the birefringent effect of the liquid crystal, the optical waveguide layer  20  of each of the waveguide elements  10  contains the liquid crystal material. The first adjusting element  60  changes the refractive index anisotropy of the liquid crystal material by applying a voltage to the pair of electrodes  62  to thereby change the refractive index of the optical waveguide layer  20 . 
     The thermooptical effect is a change in the refractive index of a material due to a change in its temperature. When the thermooptical effect is used for driving, an optical waveguide layer  20  containing a thermooptical material may be heated to modulate its refractive index. 
       FIG.  33    is an illustration showing an example of a structure in which a waveguide element  10  is combined with an adjusting element  60  including a heater  68  formed of a material having high electrical resistance. The heater  68  may be disposed near an optical waveguide layer  20 . When a power source  66  is turned on, a voltage is applied to the heater  68  through wiring lines  64  containing a conductive material, and the heater  68  can thereby be heated. The heater  68  may be in contact with the optical waveguide layer  20 . In the present structural example, the optical waveguide layer  20  of each of the waveguide elements  10  contains a thermooptical material whose refractive index is changed with a change in temperature. The heater  68  included in the first adjusting element  60  is disposed in contact with or near the optical waveguide layer  20 . In the first adjusting element  60 , the thermooptical material is heated by the heater  68  to thereby change the refractive index of the optical waveguide layer  20 . 
     The optical waveguide layer  20  itself may be formed of a high-electric resistance material and sandwiched directly between a pair of electrodes  62 , and a voltage may be applied to the pair of electrodes  62  to heat the optical waveguide layer  20 . In this case, the first adjusting element  60  includes the pair of electrodes  62  sandwiching the optical waveguide layer  20 . In the first adjusting element  60 , a voltage is applied to the pair of electrodes  62  to heat the thermooptical material (e.g., a high-electric resistance material) in the optical waveguide layer  20 , and the refractive index of the optical waveguide layer  20  is thereby changed. 
     The high-electric resistance material used for the heater  68  or the optical waveguide layer  20  may be a semiconductor or a high-resistivity metal material. Examples of the semiconductor used include Si, GaAs, and GaN. Examples of the high-resistivity metal material used include iron, nickel, copper, manganese, chromium, aluminum, silver, gold, platinum, and alloys of combinations of these materials. For example, the temperature dependence do/dT of the refractive index of Si for light with a wavelength of 1,500 nm is 1.87×10 −4  (K −1 ) (see “Temperature-dependent refractive index of silicon and germanium,” Proc. SPIE 6273, Optomechanical Technologies for Astronomy, 62732J). Therefore, by changing temperature by 500 degrees, the refractive index can be changed by about 0.1. When the heater  68  is disposed near the optical waveguide layer  20  to heat it locally, a large temperature change of 500 degrees can be achieved at a relatively fast speed. 
     The speed of response to change in refractive index by carrier injection is determined by the life of the carriers. Generally, the life of carriers is of the order of nanoseconds (ns), and the speed of response is about 100 MHz to about 1 GHz. 
     When an electrooptical material is used, an electric field is applied to induce polarization of electrons, and the refractive index is thereby changed. The speed of polarization induction is generally very high. In materials such as LiNbO 3  and LiTaO 3 , the response time is of the order of femtoseconds (fs), and this allows high-speed driving at higher than 1 GHz. 
     When a thermooptical material is used, the speed of response to change in refractive index is determined by the rate of temperature increase or decrease. By heating only a portion in the vicinity of the waveguide, a steep temperature increase is obtained. By turning off the heater after the temperature is locally increased, the heat is dissipated to the surroundings, and the temperature can be steeply reduced. The speed of response can be as high as about 100 KHz. 
     &lt;Specific Examples of Structure Using Liquid Crystal Material&gt; 
     Next, a description will be given of specific examples of a structure in which a liquid crystal material is used for the optical waveguide layer  20 . 
     As described above, in the method utilizing the birefringent effect of a liquid crystal, the optical waveguide layer  20  containing the liquid crystal material is driven using the electrodes  62  to change the refractive index anisotropy of the liquid crystal. In this manner, the refractive index for the light propagating through the optical waveguide layer  20  can be modulated. Generally, a liquid crystal has a birefringence of about 0.1 to 0.2, and a change in refractive index comparable to the birefringence can be obtained by changing the alignment direction of the liquid crystal using an electric field. In the structure using the birefringent effect of the liquid crystal, the optical waveguide layer  20  of each of the waveguide elements  10  contains the liquid crystal material. The driving circuit of the first adjusting element  60  can change the refractive index anisotropy of the liquid crystal material by applying a voltage to the pair of electrodes  62  to thereby change the refractive index of the optical waveguide layer  20 . 
     To increase the change in refractive index upon application of a voltage, it is desirable that the relation between the arrangement of the pair of electrodes  62  and the alignment direction of the liquid crystal material, i.e., the longitudinal direction of the liquid crystal molecules, is appropriate. Moreover, it is desirable that linearly polarized light is used as the light inputted to the optical waveguide layer  20  and that the polarization direction of the linearly polarized light is set to an appropriate direction. 
     The birefringence of a liquid crystal is caused by the difference between the dielectric constant of the liquid crystal molecules in its longitudinal direction and the dielectric constant in its lateral direction. Therefore, by appropriately controlling the alignment direction of the liquid crystal molecules in the optical waveguide layer  20  according to the polarization direction of the inputted light, the refractive index can be more effectively changed. 
       FIG.  34 A  and  FIG.  34 B  show a first example of the structure in which a liquid crystal material  75  is used for the optical waveguide layer  20 .  FIGS.  34 A  and  34 B show the optical waveguide layer  20  sandwiched between a pair of electrodes  62  and a driving circuit  110  for applying a voltage to the pair of electrodes  62 . The driving circuit  110  in this example includes a driving power source  111  and a switching element  112  (hereinafter may be referred to also as a switch  112 ).  FIG.  34 A  shows the state in which the switch  112  is OFF, and  FIG.  34 B  shows the state in which the switch  112  is ON. 
     The pair of electrodes  62  are transparent electrodes. The pair of electrodes  62  are disposed parallel to unillustrated first and second mirrors. Specifically, the pair of electrodes  62  are disposed such that, when a voltage is applied thereto, an electric field is generated in the Z direction, which is a direction normal to the reflecting surfaces of the first and second mirrors. As shown in  FIG.  34 A , the longitudinal direction of the liquid crystal molecules  76  is parallel to the extending direction of the optical waveguide layer  20  (the Y direction) when no voltage is applied to the pair of electrodes  62 . 
     Solid arrows in  FIGS.  34 A and  34 B  indicate the propagating directions of light, and broken arrows indicate the polarization direction. In this example, P-polarized light is inputted to the optical waveguide layer  20 . The P-polarized light is linearly polarized light whose electric field vibrates parallel to an incidence plane of the light. The incidence plane of the light is a plane formed by the directions of the light incident on the reflecting surfaces of the mirrors and the directions of the light reflected from the reflecting surfaces. In the present embodiment, the incidence plane of the light is substantially parallel to the YZ plane. Let the incident angle and the reflecting angle of the light on the reflecting surface of each mirror be θ. Then the direction of vibration of the electric field of the P-polarized light is a direction inclined an angle of θ from the Y direction in the YZ plane. However, in  FIGS.  34 A and  34 B  and subsequent figures, the angle θ is assumed to be sufficiently small, and the broken arrows indicating the polarization direction of the P-polarized light are parallel to the Y direction in order to clearly distinguish the P-polarized light from S-polarized light. 
     The Z direction size (height) of the optical waveguide layer  20  may be set to, for example, a value from 0.1 μm to 10 μm and more preferably to a value from 0.2 μm to 3 μm. The X direction size (width) of the optical waveguide layer  20  may be set to, for example, a value from 1 μm to 100 μm and more preferably to a value from 1 μm to 30 μm. The Y direction size (length) of the optical waveguide layer  20  may be set to, for example, a value from 100 μm to 100 mm and more preferably to a value from 1 mm to 30 mm. 
     The liquid crystal material may be, for example, a nematic liquid crystal. The molecular structure of the nematic liquid crystal is as follows.
 
R1-Ph1-R2-Ph2-R3
 
     Here, R1 and R3 each independently represent one selected from the group consisting of an amino group, a carbonyl group, a carboxyl group, a cyano group, an amine group, a nitro group, a nitrile group, and an alkyl chain. The alkyl chain is, for example, an alkyl group having 3 or more carbon atoms. Ph1 and Ph2 each independently represent an aromatic group such as a phenyl group or a biphenyl group. The aromatic group represented by Ph1 connects R1 to R2. The aromatic group represented by Ph2 connects R2 to R3. R2 represents one selected from the group consisting of a vinyl group, a carbonyl group, a carboxyl group, a diazo group, and an azoxy group. The vinyl, carbonyl, carboxyl, diazo, or azoxy group represented by R2 connects Ph1 to Ph2. 
     The liquid crystal is not limited to the nematic liquid crystal. For example, a smectic liquid crystal may be used. When the liquid crystal is a smectic liquid crystal, the smectic liquid crystal may exhibit, for example, a smectic C (SmC) phase. The liquid crystal exhibiting the smectic C (SmC) phase may be, for example, a ferroelectric liquid crystal exhibiting a chiral smectic (SmC*) phase in which the liquid crystal molecules have a chiral center (an asymmetric carbon atom). 
     The molecular structure of the SmC* phase is represented as follows. 
     
       
         
         
             
             
         
       
     
     R1 and R4 are each independently one selected from the group consisting of an amino group, a carbonyl group, a carboxyl group, a cyano group, an amine group, a nitro group, a nitrile group, and an alkyl chain. The alkyl chain is, for example, an alkyl group having 3 or more carbon atoms. Ph1 and Ph2 are each independently an aromatic group such as a phenyl group or a biphenyl group. The aromatic group represented by Ph1 connects R1 to R2. The aromatic group represented by Ph2 connects R2 to (CH 2 ) n . R2 is one selected from the group consisting of a vinyl group, a carbonyl group, a carboxyl group, a diazo group, and an azoxy group. The vinyl, carbonyl, carboxyl, diazo, or azoxy group represented by R2 connects Ph1 to Ph2. Ch* represents a chiral center. The chiral center is typically carbon (C*). R3 and R5 are each one selected from the group consisting of hydrogen, a methyl group, an amino group, a carbonyl group, a carboxyl group, a cyano group, an amine group, a nitro group, a nitrile group, and an alkyl chain. R3, R4, and R5 are mutually different functional groups. 
     The liquid crystal material may be a mixture of a plurality of liquid crystal molecules with different compositions. For example, a mixture of nematic liquid crystal molecules and smectic liquid crystal molecules may be used as the material of the optical waveguide layers  20 . 
     Generally, before a liquid crystal material is poured into a liquid crystal cell, the temperature of the liquid crystal cell is increased in order to increase the flowability of the liquid crystal material, and then the liquid crystal material is poured into the liquid crystal cell. It is therefore known that the liquid crystal molecules strongly tend to be aligned in a direction of the flow of the liquid crystal molecules during pouring. In the case where the liquid crystal is poured into the optical waveguide layer  20  shown in  FIG.  34 A , when the liquid crystal material is poured from an edge surface of the optical waveguide layer  20  that is parallel to the XZ plane, the liquid crystal molecules  76  are aligned parallel to the longitudinal direction of the optical waveguide layer  20  (the Y direction). 
     As shown in  FIG.  34 A , when the switching element  112  of the driving circuit  110  is OFF, i.e., no driving voltage is applied to the optical waveguide layer  20 , the polarization direction of the propagating light is close to parallel to the longitudinal direction of the liquid crystal molecules. Strictly speaking, the polarization direction and the longitudinal direction of the liquid crystal molecules intersect at angle θ as described above. In this state, the optical waveguide layer  20  has a relatively high refractive index for the propagating light. The refractive index n ∥  of the liquid crystal in this case is about 1.6 to about 1.7 when the liquid crystal is a commonly used liquid crystal material. In this state, the emergent angle of the light emitted from the optical waveguide layer  20  is relatively large. 
     However, as shown in  FIG.  34 B , when the switching element  112  of the driving circuit  110  is turned ON, i.e., the driving voltage is applied to the optical waveguide layer  20 , the liquid crystal molecules  76  are aligned so as to be perpendicular to the transparent electrodes  62 . Therefore, the angle between the polarization direction of the propagating light and the longitudinal direction of the liquid crystal molecules becomes close to 90 degrees. Strictly speaking, the polarization direction and the longitudinal direction of the liquid crystal molecules intersect at an angle of (90°−θ). In this state, the optical waveguide layer  20  has a relatively low refractive index for the propagating light. The refractive index n ⊥  of the liquid crystal in this case is about 1.4 to about 1.5 when the liquid crystal is a commonly used liquid crystal material. In this state, the emergent angle of the light emitted from the optical waveguide layer  20  is relatively small. 
       FIG.  34 B  shows an example in which an alignment film is present between the optical waveguide layer  20  and the lower electrode  62  in the figure. Since the alignment film is present, liquid crystal molecules  76  on the lower side in the figure tend not to be aligned vertically. The alignment film may be disposed on the upper electrode  62  or may not be provided. 
     By using the liquid crystal material for the optical waveguide layer  20  as described above, the refractive index can be changed by about 0.1 to 0.2 by switching the applied voltage between ON and OFF. The emergent angle of the light emitted from the optical waveguide layer  20  can thereby be changed. 
     In this example, the driving circuit  110  includes the driving power source  111  and the switching element  112 , but this structure is not a limitation. For example, the driving circuit  110  may use a voltage control circuit such as a voltage amplifier instead of the switching element  112 . By using this structure, the alignment of the liquid crystal molecules  76  can be changed continuously, so that the emission angle can be controlled freely. 
       FIG.  35    is a cross-sectional view schematically showing a structural example of a light input device  113  for inputting light into the optical waveguide layer  20 . The light input device  113  in this example includes a light source  130  and a waveguide that propagates light emitted from the light source  130  to input the light into the optical waveguide layer  20 . The waveguide in this example is a phase shifter  80  having the structure shown in  FIG.  28   , but a waveguide having a different structure may be used. For example, a total reflection waveguide connected directly to the optical waveguide layer  20  may be used instead of the phase shifter  80  to input the light from the light source  130  into the optical waveguide layer  20 . In this case, the phase shifter  80  may be disposed upstream of the total reflection waveguide. 
     The light source  130  emits linearly polarized light whose electric field vibrates in the YZ plane in  FIG.  35   . The linearly polarized light emitted from the light source  130  enters the optical waveguide layer  20  through the phase shifter  80  and propagates as P-polarized light. As described above, the optical scanning device may include the light input device  113  that inputs the P-polarized light into the optical waveguide layer  20 . The light source  130  may have a structure that emits S-polarized light, as in examples described later. In this case, the S-polarized light, i.e., linearly polarized light whose electric field vibrates in the X direction, can be inputted to the optical waveguide layer  20 . 
       FIGS.  36 A and  36 B  show a second example of the structure in which the liquid crystal material is used for the optical waveguide layer  20 . The second example differs from the first example in that the incident light is S-polarized light and that, when no voltage is applied to the pair of electrodes  62 , the alignment direction of the liquid crystal molecules  76  is a direction (the X direction) perpendicular to both the extending direction of the optical waveguide layer  20  (the Y direction) and the direction normal to the reflecting surfaces of the first and second mirrors (the Z direction). Since the incident light is the S-polarized light, the direction of its electric field is the X direction perpendicular to the incidence plane. 
     The alignment direction of the liquid crystal molecules  76  can be controlled by rubbing the surfaces of the upper and lower electrodes  62  included in the liquid crystal cell before the liquid crystal is inserted. Alternatively, the alignment direction can be controlled by coating the surface of each of the upper and lower electrodes  62  with, for example, a polyimide to form an alignment layer (referred to also as an alignment film). 
     As shown in  FIG.  36 A , when the switching element  112  of the driving circuit  110  is OFF, i.e., no driving voltage is applied to the optical waveguide layer  20 , the polarization direction of the propagating light is substantially parallel to the longitudinal direction of the liquid crystal molecules. In this state, the optical waveguide layer  20  has a relatively high refractive index for the propagating light. The refractive index n ∥  of the liquid crystal in this case is about 1.6 to about 1.7 when the liquid crystal is a commonly used liquid crystal material. In this state, the emergent angle of the light emitted from the optical waveguide layer  20  is relatively large. 
     However, as shown in  FIG.  36 B , when the switching element  112  of the driving circuit  110  is turned ON, i.e., the driving voltage is applied to the optical waveguide layer  20 , the liquid crystal molecules  76  are aligned so as to be perpendicular to the transparent electrodes  62 . Therefore, the angle between the polarization direction of the propagating light and the longitudinal direction of the liquid crystal molecules becomes substantially 90 degrees. In this state, the optical waveguide layer  20  has a relatively low refractive index for the propagating light. The refractive index n ⊥  of the liquid crystal in this case is about 1.4 to about 1.5 when the liquid crystal is a commonly used liquid crystal material. In this state, the emergent angle of the light emitted from the optical waveguide layer  20  is relatively small. 
     In the structure shown in  FIGS.  36 A and  36 B , when no voltage is applied, the polarization direction coincides with the alignment direction of the liquid crystal molecules  76 . When a high voltage is applied, the polarization direction is orthogonal to the alignment direction of the liquid crystal molecules  76 . Therefore, the change in the refractive index can be larger than that in the structure shown in  FIGS.  34 A and  34 B  even when the same voltage is applied. The emission angle of the light can thereby be changed more largely. However, the structure shown in  FIGS.  34 A and  34 B  is advantageous in that it can be produced easily. 
       FIGS.  37 A and  37 B  show a third example of the structure in which the liquid crystal material is used for the optical waveguide layer  20 . The third example differs from the first example in that the incident light is S-polarized light and that the pair of electrodes  62  are disposed parallel to the YZ plane with the optical waveguide layer  20  therebetween. The pair of electrodes  62  in this example are disposed substantially perpendicular to the first mirror  30  and the second mirror  40 . When a voltage is applied, the pair of electrodes  62  generates an electric field in the X direction that is perpendicular to both the extending direction of the optical waveguide layer  20  (the Y direction) and the direction normal to the mirrors (the Z direction). When no voltage is applied to the pair of electrodes, the alignment direction of the liquid crystal material is parallel to the extending direction of the optical waveguide layer  20 , as in the first example. 
     As shown in  FIG.  37 A , when the switching element  112  of the driving circuit  110  is OFF, i.e., no driving voltage is applied to the optical waveguide layer  20 , the polarization direction of the propagating light is substantially perpendicular to the longitudinal direction of the liquid crystal molecules. In this state, the optical waveguide layer  20  has a relatively low refractive index for the propagating light. The refractive index n ⊥  of the liquid crystal in this case is about 1.4 to about 1.5 when the liquid crystal is a commonly used liquid crystal material. In this state, the emergent angle of the light emitted from the optical waveguide layer  20  is relatively small. 
     However, as shown in  FIG.  37 B , when the switching element  112  of the driving circuit  110  is turned ON, i.e., the driving voltage is applied to the optical waveguide layer  20 , the longitudinal direction of the liquid crystal molecules  76  is changed to a direction (the X direction) perpendicular to both the extending direction of the optical waveguide layer  20  (the Y direction) and the direction normal to the mirrors  30  and  40  (the Z direction). Therefore, the polarization direction of the propagating light is substantially parallel to the longitudinal direction of the liquid crystal molecules. In this state, the optical waveguide layer  20  has a relatively high refractive index for the propagating light. The refractive index n ∥  of the liquid crystal in this case is about 1.6 to about 1.7 when the liquid crystal is a commonly used liquid crystal material. In this state, the emergent angle of the light emitted from the optical waveguide layer  20  is relatively large. 
       FIGS.  38 A and  38 B  show a fourth example of the structure in which the liquid crystal material is used for the optical waveguide layer  20 . The fourth example differs from the third example in that the incident light is P-polarized light. 
     As shown in  FIG.  38 A , when the switching element  112  of the driving circuit  110  is OFF, i.e., no driving voltage is applied to the optical waveguide layer  20 , the polarization direction of the propagating light is close to parallel to the longitudinal direction of the liquid crystal molecules. Strictly speaking, the polarization direction and the longitudinal direction of the liquid crystal molecules intersect at angle θ as described above. In this state, the optical waveguide layer  20  has a relatively high refractive index for the propagating light. The refractive index n ∥  of the liquid crystal in this case is about 1.6 to about 1.7 when the liquid crystal is a commonly used liquid crystal material. In this state, the emergent angle of the light emitted from the optical waveguide layer  20  is relatively large. 
     However, as shown in  FIG.  38 B , when the switching element  112  of the driving circuit  110  is turned ON, i.e., the driving voltage is applied to the optical waveguide layer  20 , the liquid crystal molecules  76  are aligned perpendicularly to the transparent electrodes  62 . Therefore, the polarization direction of the propagating light is substantially perpendicular to the longitudinal direction of the liquid crystal molecules. In this state, the optical waveguide layer  20  has a relatively low refractive index for the propagating light. The refractive index n ⊥  of the liquid crystal in this case is about 1.4 to about 1.5 when the liquid crystal is a commonly used liquid crystal material. In this state, the emergent angle of the light emitted from the optical waveguide layer  20  is relatively small. 
     As described above, in the examples in which the liquid crystal material is used for the optical waveguide layer  20 , the direction of the emission light can be controlled by appropriately setting the polarization direction of the light, the alignment direction of the liquid crystal molecules  76 , and the arrangement of the pair of electrodes  62 . Even when the polarization direction of the incident light is P-polarization or S-polarization, the direction of the light beam can be changed by chaining the emission angle according to the driving voltage. 
       FIG.  39    is a graph showing the dependence of the light emission angle on the voltage applied in a structure in which the liquid crystal material is used for the optical waveguide layer  20 . This graph shows the results of an experiment in which the emission angle of light emitted from the optical waveguide layer  20  was measured while the voltage applied was changed in the structure shown in  FIGS.  34 A and  34 B .  FIG.  40    is a cross-sectional view showing the structure of a waveguide element used in the experiment. In this waveguide element, an electrode  62   b , a second mirror  40  that is a multilayer reflective film, an optical waveguide layer  20  that is a liquid crystal layer, a first mirror  30  that is a multilayer reflective film, and a transparent electrode  62   a  are stacked in this order. A SiO 2  layer is formed so as to sandwich the optical waveguide layer  20 . 
     In this experiment, the liquid crystal material used is 5CB (4-cyano-4′-pentylbiphenyl). The alignment direction of the liquid crystal at 0 V is parallel to the extending direction of the optical waveguide layer  20 , i.e., a direction perpendicular to the drawing sheet of  FIG.  40   . The thickness of the optical waveguide layer  20  is 1 μm, and the width of the optical waveguide layer  20  is 20 μm. The light used for the measurement is TM polarized light (P-polarized light) with a wavelength of 1.47 μm. The electrode  62   b  was deposited between the multilayer reflective film of the second mirror  40  and an unillustrated substrate. In this experiment, since the two multilayer reflective films were disposed between the electrodes  62   a  and  62   b , a relatively high voltage was applied. 
     As shown in  FIG.  39   , when the voltage was applied, the emission angle could be changed by about 15°. In this example, the structure shown in  FIGS.  34 A and  34 B  was used. However, the same or higher effect can be obtained using other structures. 
     &lt;Specific Examples Using Electrooptical Material&gt; 
     Next, specific examples of a structure in which an electrooptical material is used for the optical waveguide layer  20  will be described. 
     In an optical scanning device in which the optical waveguide layer  20  contains an electrooptical material, the optical waveguide layer  20  is formed such that the direction of the polarization axis of the electrooptical material coincides with the direction of an electric field generated when a voltage is applied to the pair of electrodes  62 . With this structure, the change in the refractive index of the electrooptical material caused by the application of the voltage to the pair of electrodes  62  can be increased. 
       FIG.  41    shows a first example of the structure in which an electrooptical material  77  is used for the optical waveguide layer  20 . In this example, the pair of electrodes  62  are disposed such that the direction of the electric field generated between the pair of electrodes  62  when a voltage is applied thereto coincides with a direction (the X direction) perpendicular to both the extending direction of the optical waveguide layer  20  (the Y direction) and the direction normal to the mirrors (the Z direction). The direction of the polarization axis of the electrooptical material in this example is the X direction perpendicular to both the extending direction of the optical waveguide layer  20  and the direction normal to the mirrors. The driving circuit  110  applies a voltage to the pair of electrodes  62  to change the refractive index of the electrooptical material for the light propagating through the optical waveguide layer  20 . 
     The direction of the polarization axis of the electrooptical material is a direction in which the change in refractive index when the voltage is applied is maximum. The polarization axis may be referred to also as an optical axis. In FIG.  41 , the direction of the polarization axis is indicated by a solid two-directional arrow. The refractive index ne in a direction along the polarization axis changes according to the voltage applied. 
     The electrooptical material usable in the present embodiment may be, for example, a compound represented by KTa 1-x Nb x O 3  or K 1-y A y Ta 1-x Nb x O 3  (A is an alkali metal and is typically Li or Na). x represents the molar ratio of Nb, and y represents the molar ratio of A. x is a real number larger than 0 and smaller than 1. y is a real number larger than 0 and smaller than 1. 
     The electrooptical material used may be any of the following compounds. 
     KDP (KH 2 PO 4 ) crystals such as KDP, ADP (NH 4 H 2 PO 4 ), KDA (KH 2 AsO 4 ), RDA (RbH 2 PO 4 ), and ADA (NH 4 H 2 AsO 4 ) 
     Cubic crystal materials such as KTN, BaTiO 3 , SrTiO 3 Pb 3 MgNb 2 O 9 , GaAs, CdTe, and InAs 
     Tetragonal crystal materials such as LiNbO 3  and LiTaO 3    
     Zincblende materials such as ZnS, ZnSe, ZnTe, GaAs, and CuCl 
     Tungsten bronze materials such as KLiNbO 3 , SrBaNb 2 O 6 , KSrNbO, BaNaNbO, and Ca 2 Nb 2 O 7    
     As shown in  FIG.  41   , the polarization axis of the electrooptical material is set to a direction perpendicular to the pair of electrodes  62 , and the voltage applied to the pair of electrodes  62  is changed by the driving circuit  110 . In this manner, the refractive index can be changed. In this case, when the incident light is S-polarized light, the polarization plane is parallel to the polarization axis of the electrooptical material. Therefore, the change in refractive index due to the voltage is most effectively reflected on the incident light, and the change in the emission angle of the light can be increased. 
       FIG.  42    shows a second example of the structure in which the electrooptical material  77  is used for the optical waveguide layer  20 . The structure of the second example differs from that in  FIG.  41    in that the pair of electrodes  62  are disposed parallel to unillustrated first and second mirrors. In this example, the direction of the electric field generated between the electrodes  62  during the application of the voltage, i.e., the direction normal to the electrodes  62 , is the Z direction. Therefore, the direction of the polarization axis of the electrooptical material is also set to this direction. In this example, the incident light is P-polarized light, so that the polarization plane is parallel to the polarization axis of the electrooptical material. Therefore, the change in refractive index due to the voltage is reflected on the incident light, and the change in emission angle of the light can be increased. 
     As described above, by using the electrooptical material for the optical waveguide layer  20 , setting the polarization direction of the light and the polarization axis of the electrooptical material to a direction perpendicular to the electrodes  62 , and controlling the driving voltage applied, the emission angle of the light can be changed to control the direction of the light beam. 
       FIGS.  43 A and  43 B  show other examples of the arrangement of the pair of electrodes  62  perpendicular to the mirrors  30  and  40 . In the example in  FIG.  43 A , the pair of electrodes  62  are disposed only in the vicinity of the second mirror  40 . In the example in  FIG.  43 B , the pair of electrodes  62  are disposed only in the vicinity of the first mirror  40 . The pair of electrodes  62  may be disposed on opposite sides of only part of the optical waveguide layer  20 , as in these examples. These electrodes  62  may be disposed on the substrate supporting the second mirror  40  or the substrate supporting the first mirror  30 . The structures in  FIGS.  43 A and  43 B  are applicable when the material of the optical waveguide layer  20  is the liquid crystal material and also when the material is the electrooptical material. 
     As described above, the optical waveguide layer  20  in each of the optical scanning devices shown in  FIGS.  34 A to  43 B  contains the liquid crystal material or the electrooptical material. When no voltage is applied to the pair of electrodes  62 , the alignment direction of the liquid crystal material or the direction of the polarization axis of the electrooptical material is parallel or perpendicular to the extending direction of the optical waveguide layer  20 . The driving circuit  110  applies a voltage to the pair of electrodes  62  to change the refractive index of the liquid crystal material or the electrooptical material for the light propagating through the optical waveguide layer  20 , and the direction of the light emitted from the optical waveguide layer  20  is thereby changed. By appropriately setting the polarization direction of the incident light, the change in the refractive index of the optical waveguide layer  20  can be increased to increase the change in emission angle of the light. 
     The phrase “two directions are “parallel to each other” or “coincide with each other” is intended to encompass not only the case in which they are perfectly parallel to each other but also the case in which the angle therebetween is 15 degrees or less. The phrase “two directions are “perpendicular to each other”” does not mean that the two direction are strictly perpendicular to each other but encompasses the case in which the angle between them is from 75 degrees to 105 degrees inclusive. 
     &lt;Refractive Index Modulation for Phase Shifting&gt; 
     A description will next be given of a structure for adjusting phases in a plurality of phase shifters  80  using the second adjusting element. The phases in the plurality of phase shifters  80  can be adjusted by changing the refractive indexes of waveguides  20   a  of the phase shifters  80 . The refractive indexes can be changed using the same method as any of the above-described methods for adjusting the refractive index of the optical waveguide layer  20  of each of the waveguide elements  10 . For example, any of the structures and methods for refractive index modulation described with reference to  FIGS.  32 A to  33    can be applied without any modification. Specifically, in the descriptions for  FIGS.  32 A to  33   , the waveguide element  10  is replaced with the phase shifter  80 , the first adjusting element  60  is replaced with the second adjusting element, the optical waveguide layer  20  is replaced with the waveguide  20   a , and the first driving circuit  110  is replaced with the second driving circuit  210 . Therefore, the detailed description of the refractive index modulation in the phase shifter  80  will be omitted. 
     The waveguide  20   a  of each of the phase shifters  80  contains a material whose refractive index is changed when a voltage is applied or temperature is changed. The second adjusting element changes the refractive index of the waveguide  20   a  of each of the phase shifters  80  by applying a voltage to the waveguide  20   a  or changing the temperature of the waveguide  20   a . In this manner, the second adjusting element can change the phase differences between light beams propagating from the plurality of phase shifters  80  to the plurality of waveguide elements  10 . 
     Each phase shifter  80  may be configured such that the phase of light can be shifted by at least 2π when the light passes through. When the amount of change in the refractive index per unit length of the waveguide  20   a  of the phase shifter  80  is small, the length of the waveguide  20   a  may be increased. For example, the size of the phase shifter  80  may be several hundreds of micrometers (μm) to several millimeters (mm) or may be lager for some cases. However, the length of each waveguide element  10  may be several tens of micrometers to several tens of millimeters. 
     &lt;Structure for Synchronous Driving&gt; 
     In the present embodiment, the first adjusting element drives the plurality of waveguide elements  10  such that light beams emitted from the waveguide elements  10  are directed in the same direction. To direct the light beams emitted from the plurality of waveguide elements  10  in the same direction, driving units are provided for their respective waveguide elements  10  and driven synchronously. 
       FIG.  44    is an illustration showing an example of a structure in which common wiring lines  64  are led from electrodes  62  of the waveguide elements  10 .  FIG.  45    is an illustration showing an example of a structure in which the wiring lines  64  and some of the electrodes  62  are shared.  FIG.  46    is an illustration showing an example of a structure in which common electrodes  62  are provided for a plurality of waveguide elements  10 . In  FIGS.  44  to  46   , each straight arrow indicates the input of light. With the structures shown in  FIGS.  44  to  46   , the wiring for driving the waveguide array  10 A can be simplified. 
     With the structures in the present embodiment, two-dimensional optical scanning can be performed using a simple device structure. For example, when a waveguide array including N waveguide elements  10  is driven in a synchronous manner using independent driving circuits, N driving circuits are necessary. However, when common electrodes or wiring lines are used in an ingenious manner, only one driving circuit may be used for operation. 
     When the phase shifter array  80 A is disposed upstream of the waveguide array  10 A, additional N driving circuits are necessary to drive the phase shifters  80  independently. However, as shown in the example in  FIG.  31   , by arranging the phase shifters  80  in a cascaded manner, only one driving circuit may be used for driving. Specifically, with the structures in the present disclosure, a two-dimensional optical scanning operation can be implemented by using 2 to 2N driving circuits. The waveguide array  10 A and the phase shifter array  80 A may be operated independently, so that their wiring lines can be easily arranged with no interference. 
     &lt;Production Method&gt; 
     The waveguide array, the phase shifter array  80 A, and the waveguides connecting them can be produced by a process capable of high-precision fine patterning such as a semiconductor process, a 3D printer, self-organization, or nanoimprinting. With such a process, all necessary components can be integrated in a small area. 
     In particular, the use of a semiconductor process is advantageous because very high processing accuracy and high mass productivity can be achieved. When the semiconductor process is used, various materials can be deposited on a substrate using vacuum evaporation, sputtering, CVD, application, etc. Fine patterning can be achieved by photolithography and an etching process. For example, Si, SiO 2 , Al 2 O 3 , AlN, SiC, GaAs, GaN, etc. can be used as the material of the substrate. 
     &lt;Modifications&gt; 
     Modifications of the present embodiment will next be described. 
       FIG.  47    is an illustration schematically showing an example of a structure in which waveguides are integrated into a small array while a large arrangement area is allocated for the phase shifter array  80 A. With this structure, even when the change in the refractive index of the material forming the waveguides of the phase shifters  80  is small, a sufficient phase shift amount can be ensured. When each phase shifter  80  is driven using heat, the influence on its adjacent phase shifters  80  can be reduced because large spacing can be provided between them. 
       FIG.  48    is an illustration showing a structural example in which two phase shifter arrays  80 Aa and  80 Ab are disposed on respective sides of the waveguide array  10 A. In the optical scanning device  100  in this example, two optical dividers  90   a  and  90   b  and the two phase shifter arrays  80 Aa and  80 Ab are disposed on respective sides of the waveguide array  10 A. Dotted straight arrows in  FIG.  48    indicate light beams propagating through the optical dividers  90   a  and  90   b  and the phase shifters  80   a  and  80   b . The phase shifter array  80 Aa and the optical divider  90   a  are connected to one side of the waveguide array  10 A, and the phase shifter array  80 Ab and the optical divider  90   b  are connected to the other side of the waveguide array  10 A. The optical scanning device  100  further includes an optical switch  92  that switches between supply of light to the optical divider  90   a  and supply of light to the optical divider  90   b . The optical switch  92  allows switching between the state in which light is inputted to the waveguide array  10 A from the left side in  FIG.  48    and the state in which light is inputted to the waveguide array  10 A from the right side in  FIG.  48   . 
     The structure in this modification is advantageous in that the range of scanning in the X direction with the light emitted from the waveguide array  10 A can be increased. In a structure in which light is inputted to the waveguide array  10 A from one side, the direction of the light can be changed from the front direction (i.e., the +Z direction) toward one of the +X direction and the −X direction by driving the waveguide elements  10 . In the present modification, when the light is inputted from the left optical divider  90   a  in  FIG.  48   , the direction of the light can be changed from the front direction toward the +X direction. When the light is inputted from the right optical divider  90   b  in  FIG.  48   , the direction of the light can be changed from the front direction toward the −X direction. Specifically, in the structure in  FIG.  48   , the direction of the light can be changed in both the left and right directions in  FIG.  48    as viewed from the front. Therefore, the scanning angle range can be larger than that when the light is inputted from one side. The optical switch  92  is controlled by an electric signal from an unillustrated control circuit (e.g., a microcontroller unit). In this structural example, all the elements can be driven and controlled using electric signals. 
     In all the waveguide arrays in the above description, the arrangement direction of the waveguide elements  10  is orthogonal to the extending direction of the waveguide elements  10 . However, it is unnecessary that these directions be orthogonal to each other. For example, a structure shown in  FIG.  49 A  may be used.  FIG.  49 A  shows a structural example of a waveguide array in which an arrangement direction d 1  of waveguide elements  10  is not orthogonal to an extending direction d 2  of the waveguide elements  10 . In this example, the light-emission surfaces of the waveguide elements  10  may not be in the same plane. Even with this structure, the emission direction d 3  of light can be changed two-dimensionally by appropriately controlling the waveguide elements  10  and the phase shifters. 
       FIG.  49 B  shows a structural example of a waveguide array in which waveguide elements  10  are arranged at non-regular intervals. Even when this structure is employed, two-dimensional scanning can be performed by appropriately setting the phase shift amounts by the phase shifters. Also in the structure in  FIG.  49 B , the arrangement direction d 1  of the waveguide array may not be orthogonal to the extending direction d 2  of the waveguide elements  10 . 
     &lt;Embodiment in which First and Second Waveguides are Disposed on Substrate&gt; 
     Next, an embodiment of an optical scanning device in which first and second waveguides are disposed on a substrate will be described. 
     The optical scanning device in the present embodiment includes: first waveguides; second waveguides connected to the first waveguides; and a substrate that supports the first and second waveguides. More specifically, the optical scanning device includes: a plurality of waveguide units arranged in a first direction; and the substrate that supports the plurality of waveguide units. Each of the plurality of waveguide units includes a first waveguide and a second waveguide. The second waveguide is connected to the first waveguide and propagates light in a second direction intersecting the first direction. The substrate supports the first waveguide and the second waveguide of each of the waveguide units. 
     The second waveguide corresponds to the reflective waveguide in the embodiment described above. Specifically, the second waveguide includes: a first mirror including a multilayer reflective film; a second mirror including a multilayer reflective film facing the multilayer reflective film of the first mirror; and an optical waveguide layer that is located between the first and second mirrors and propagates light inputted to the first waveguide and transmitted therethrough. The first mirror has a higher light transmittance than the second mirror and allows part of the light propagating through the optical waveguide layer to be emitted to the outside of the optical waveguide layer. The optical scanning device further includes an adjusting element that changes the refractive index of the optical waveguide layer of each of the second waveguides to thereby change the direction of light emitted from the each of the second waveguides. 
     In the present embodiment, the first and second waveguides are disposed on one substrate, so that the first waveguides  1  and the second waveguides  10  can be easily aligned with each other. In addition, positional displacement between the first and second waveguides due to thermal expansion is reduced. Therefore, light beams can be efficiently introduced from the first waveguides to the second waveguides. 
     Each optical waveguide layer may contain a material whose refractive index for the light propagating through the optical waveguide layer is changed when a voltage is applied. In this case, the adjusting element changes the refractive index of the optical waveguide layer by applying a voltage to the optical waveguide layer. In this manner, the adjusting element changes the direction of the light emitted from each second waveguide. 
     At least part of each first waveguide may have the function as the phase shifter described above. In this case, a mechanism that modulates the refractive index of the first waveguide is installed in the first waveguide. The optical scanning device may further include a second adjusting element that modulates the refractive index of at least a partial region of each first waveguide. The second adjusting element may be a heater disposed in the vicinity of the first waveguide. The refractive index of at least the partial region of the first waveguide can be changed by heat generated by the heater. In this manner, the phases of light beams inputted from the first waveguides to the second waveguides are adjusted. As described above, various structures can be used to adjust the phases of the light beams inputted from the first waveguides to the second waveguides. Any of these structures may be used. 
     The phase shifters may be disposed outside of the first waveguides. In this case, each first waveguide is disposed between a corresponding external phase shifter and a corresponding waveguide element (second waveguide). No clear boundary may be present between the phase shifter and the first waveguide. For example, the phase shifter and the first waveguide may share components such as a waveguide and the substrate. 
     Each first waveguide may be a general waveguide that utilizes total reflection of light or may be a reflective waveguide. The phase-modulated light beam passes through the first waveguide and is introduced into the corresponding second waveguide. 
     The embodiment of the optical scanning device in which the first and second waveguides are disposed on the substrate will be described in more detail. In the following description, the optical scanning device includes a plurality of waveguide units. The optical scanning device may include only one waveguide unit. Specifically, an optical scanning device including only one pair of first and second waveguides is included in the scope of the present disclosure. 
       FIG.  50 A  is an illustration schematically showing the optical scanning device in the present embodiment. This optical scanning device includes a plurality of waveguide units arranged in the Y direction and a substrate  50  that supports the plurality of waveguide units. Each of the waveguide units includes a first waveguide  1  and a second waveguide  10 . The substrate  50  supports the first waveguide  1  and the second waveguide  10  of each of the waveguide units. 
     The substrate  50  extends along the XY plane. The upper and lower surfaces of the substrate  50  are disposed approximately parallel to the XY plane. The substrate  50  may be formed of a material such as glass Si, SiO 2 , GaAs, or GaN. 
     A first waveguide array  1 A includes a plurality of the first waveguides  1  arranged in the Y direction. Each of the first waveguides  1  has a structure extending in the X direction. A second waveguide array  10 A includes a plurality of the second waveguides  10  arranged in the Y direction. Each of the second waveguides  10  has a structure extending in the X direction. 
       FIG.  50 B  is a cross-sectional view of the optical scanning device in the XZ plane shown by one of broken lines in  FIG.  50 A . First and second waveguides  1  and  10  are disposed on the substrate  50 . A second mirror  40  extends in a region between an optical waveguide layer  20  and the substrate  50  and between the first waveguide  1  and the substrate  50 . The first waveguide  1  is, for example, a general waveguide that uses total reflection of light. One example of the general waveguide is a waveguide formed of a semiconductor such as Si or GaAs. The second waveguide  10  includes the optical waveguide layer  20  and first and second mirrors  30  and  40 . The optical waveguide layer  20  is located between the first mirror  30  and the second mirror  40  facing each other. The optical waveguide layer  20  propagates light inputted to the first waveguide and transmitted therethrough. 
     The optical waveguide layer  20  in the present embodiment contains a material whose refractive index for the light beam propagating through the optical waveguide layer  20  is changed when a voltage is applied. The adjusting element includes a pair of electrodes. The pair of electrodes includes a lower electrode  62   a  and an upper electrode  62   b . The lower electrode  62   a  is disposed between the optical waveguide layer  20  and the second mirror  40 . The upper electrode  62   b  is disposed between the optical waveguide layer  20  and the first mirror  30 . The adjusting element in the present embodiment changes the refractive index of the optical waveguide layer  20  by applying a voltage to the pair of electrodes  62   a  and  62   b . In this manner, the adjusting element changes the direction of the light emitted from each second waveguide  10 . Each of the electrodes  62   a  and  62   b  may be in contact with the optical waveguide layer  20  as shown in  FIG.  50 B  or may not be in contact with the optical waveguide layer  20 . 
     In the structural example in  FIG.  50 B , the second mirror  40  is stacked on the substrate  50  to form a common support, and other structures are disposed on the support. Specifically, a stack including the first waveguides  1 , the first electrode  62   a , the optical waveguide layers  20 , the second electrodes  62   b , and the first mirrors  30  is formed on the integrally formed support. Since the common support is used, the first waveguides  1  and the optical waveguide layers  20  are easily aligned with each other during production. In addition, positional displacement of connection portions between the first waveguides  1  and the optical waveguide layer  20  due to thermal expansion can be reduced. The support is, for example, a support substrate. 
       FIG.  50 C  is a cross-sectional view of the optical scanning device in the YZ plane shown by the other one of the broken lines in  FIG.  50 A . In this example, the second mirror  40  is shared by the plurality of second waveguides  10 . Specifically, the second mirror  40  is not divided, and this non-divided second mirror  40  is used for the plurality of second waveguides  10 . Similarly, the lower electrode  62   a  is shared by the plurality of second waveguides  10 . This allows the production process to be simplified. 
     In the plurality of second waveguides  10 , the optical waveguide layers  20  are separated from each other. The upper electrodes  62   b  are separated from each other, and the first mirrors  30  are separated from each other. In this manner, each optical waveguide layer  20  can propagate light in the X direction. The upper electrodes  62   b  and the first mirrors  30  may be a single non-divided upper electrode  62  and a single non-divided first mirror  30 , respectively. 
     Modifications of the optical scanning device in the present embodiment will be described. In the following modifications, repeated description of the same components will be omitted. 
       FIG.  51 A  is an illustration showing a structural example in which a dielectric layer  51  is disposed between the second mirror  40  and the waveguide  1 . The optical scanning device in this example further includes the dielectric layer  51  extending between the second mirror  40  and the first waveguide  1 . The dielectric layer  51  serves as an adjustment layer for adjusting the height level of the first waveguide  1  relative to the height level of the optical waveguide layer  20 . Hereinafter, the dielectric layer  51  is referred to as the adjustment layer  51 . By adjusting the thickness of the adjustment layer  51  in the Z direction, the coupling efficiency of light from the first waveguide  1  to the optical waveguide layer  20  can be increased. The adjustment layer  51  serves also as a spacer that prevents the guided light in the first waveguide  1  from being absorbed, scattered, and reflected by the second mirror  40 . The first waveguide  1  propagates light by total reflection. Therefore, the adjustment layer  51  is formed of a transparent material having a lower refractive index than the first waveguide  1 . For example, the adjustment layer  51  may be formed of a dielectric material such as SiO 2 . 
     Another dielectric layer serving as a protective layer may be disposed on the first waveguide  1 . 
       FIG.  51 B  is an illustration showing a structural example in which a second dielectric layer  61  is disposed on the first waveguide  1 . As described above, the optical scanning device may further include the second dielectric layer  61  that covers at least part of the first waveguide  1 . The second dielectric layer  61  is in contact with the first waveguide  1  and is formed of a transparent material having a lower refractive index than the first waveguide  1 . The second dielectric layer  61  serves also as the protective layer that prevents particles and dust from adhering to the first waveguide  1 . This can reduce loss of the guided light in the first waveguide  1 . Hereinafter, the second dielectric layer  61  is referred to as the protective layer  61 . 
     The first waveguide  1  shown in  FIG.  51 B  functions as a phase shifter. The optical scanning device further includes a second adjusting element that modulates the refractive index of the first waveguide  1  to thereby change the phase of the light introduced into the optical waveguide layer  20 . When the first waveguide  1  contains a thermooptical material, the second adjusting element includes a heater  68 . The second adjusting element modulates the refractive index of the first waveguide  1  using heat generated by the heater  68 . 
     A wiring material such as a metal contained in the heater  68  can absorb, scatter, or reflect light. The protective layer  61  keeps the heater  68  at a distance from the first waveguide  1  to thereby reduce loss of the guided light in the first waveguide  1 . 
     The protective layer  61  may be formed of the same material as the material (e.g., SiO 2 ) of the adjustment layer  51 . The protective layer  61  may cover not only the first waveguide  1  but also at least part of the second waveguide  10 . In this case, at least part of the first mirror  30  is covered with the protective layer  61 . The protective layer  61  may cover only the second waveguide  10 . When the protective layer  61  is formed of a transparent material, the light emitted from the second waveguide  10  passes through the protective layer  61 . This allows the loss of light to be small. 
       FIG.  52    is an illustration showing a structural example in which the second mirror  40  is not disposed in a region between the first waveguide  1  and the substrate  50 . The adjustment layer  51  in this example extends in the region between the first waveguide  1  and the substrate  50 . The adjustment layer  51  is in contact with the first waveguide  1  and the substrate  50 . Since the second mirror  40  is not present below the first waveguide  1 , the guided light in the first waveguide  1  is not influenced by the second mirror  40 . 
       FIG.  53    is an illustration showing a structural example in which, between the first waveguide  1  and the substrate  50 , the second mirror  40  is thinner than the second mirror  40  in the structural example in  FIG.  51 B . The second mirror  40  may have a portion disposed between the first waveguide  1  and the substrate  50  and having a smaller thickness than a portion disposed between the second waveguide  10  and the substrate  50 , as in this example. The adjustment layer  51  is disposed between the first waveguide  1  and the second mirror  40 . In this structure, the guided light in the first waveguide  1  is less influenced by the second mirror  40 . In the example in  FIG.  53   , a step is formed by the second mirror  40  at the junction between the first waveguide  1  and the optical waveguide layer  20 , but the height of the step is smaller than that in the example in  FIG.  52   . Therefore, the second mirror  40  can be more easily processed. 
     The thickness of the second mirror  40  may vary along the waveguide  1 . Such an example will next be described. 
       FIG.  54 A  is an illustration showing a structural example in which the thickness of the second mirror  40  varies gradually. Between the first waveguide  1  and the substrate  50 , the thickness of the second mirror  40  varies along the first waveguide  1 . 
     In the example in  FIG.  54 A , the second mirror  40  is not present below a left portion of the first waveguide  1 . The left portion of the first waveguide  1  is located lower than the optical waveguide layer  20 . The second mirror  40  is present below a right portion of the first waveguide  1 , i.e., its portion connected to the optical waveguide layer  20 . The right portion of the first waveguide  1  is located at about the same height as the optical waveguide layer  20 . By adjusting the thickness of the protective layer  61 , the upper surface of the protective layer  61  can be made flat. 
     In the structural example in  FIG.  54 A , the heater  68  disposed on the protective layer  61  is sufficiently spaced apart from the first waveguide  1 . Therefore, the guided light in the first waveguide  1  is less influenced by the wiring of the heater  68 . The loss of the guided light in the first waveguide  1  can thereby be reduced. 
       FIG.  54 B  is an illustration showing a structural example in which the upper electrode  62   b , the first mirror  30 , and a second substrate  50 C are disposed so as to extend over the protective layer  61  of the first waveguide  1  and the optical waveguide layer  20  of the second waveguide  10 .  FIG.  54 C  is an illustration showing part of a production process in the structural example in  FIG.  54 B . 
     In the example in  FIG.  54 B , a structural body including the upper electrode  62   b , the first mirror  30 , and the second substrate  50 C (hereinafter referred to as an “upper structural body”) and a structural body lower than the upper electrode  62   b  (hereinafter referred to as a “lower structural body”) are produced separately. 
     To produce the lower structural body, the second mirror  40  having an inclination is first formed on the first substrate  50 . The adjustment layer  51 , a layer of the waveguide  1 , and the protective layer  61  are formed in this order on a portion of the second mirror  40  that includes the inclination. The lower electrode  62   a  and the optical waveguide layer  20  are formed on a flat portion of the second mirror  40 . 
     The upper structural body is produced by stacking the first mirror  30  and the upper electrode  62   b  in this order on the second substrate  50 C. As shown in  FIG.  54 C , the upper structural body is turned upside down and then laminated onto the lower structural body. With the above production method, it is unnecessary to precisely align the first waveguide  1  and the second waveguide  10  with each other. 
     The upper surface of the protective layer  61 , i.e., its surface opposite to the surface in contact with the first waveguide  1 , is lower than the upper surface of the optical waveguide layer  20  of the second waveguide  10 . The upper surface of the heater  68  on the first waveguide  1  is at about the same level as the upper surface of the optical waveguide layer  20  of the second waveguide  10 . In this case, the upper structural body and the lower structural body can be laminated together with no step. The upper structural body may be formed by, for example, vapor deposition or sputtering. 
       FIG.  55    is an illustration showing a YZ-plane cross section of a plurality of second waveguides  10  in an optical scanning device having the structure shown in  FIG.  54 B . In this example, the plurality of second waveguides  10  share the first mirror  30 , the second mirror  40 , and the electrodes  62   a  and  62   b . A plurality of optical waveguide layers  20  are disposed between the common electrodes  62   a  and  62   b . Regions between the plurality of optical waveguide layers  20  serve as spacers  73 . The spacers  73  are, for example, air (or a vacuum) or a transparent material such as SiO 2 , TiO 2 , Ta 2 O 5 , SiN, or AlN. When the spacers  73  are formed of a solid material, the upper structural body can be formed by, for example, vapor deposition or sputtering. Each spacer  73  may be in direct contact with two adjacent optical waveguide layers  20 . 
     It is unnecessary that the first waveguides  1  be general waveguides that use total reflection of light. For example, the first waveguides  1  may be reflective waveguides similar to the second waveguides  10 . 
       FIG.  56    is an illustration showing a structural example in which the first waveguide  1  and the second waveguide  10  are reflective waveguides. The first waveguide  1  is sandwiched between two opposed multilayer reflective films  3  and  40 . The principle of light propagation through the first waveguide  1  is the same as the principle of light propagation through the second waveguide  10 . When the thickness of the multilayer reflective film  3  is sufficiently large, no light is emitted from the first waveguide  1 . 
     In the structural example in  FIG.  56   , the coupling efficiency of light can be increased by optimizing the connection conditions of the two reflective waveguides, as described above with reference to  FIGS.  20 ,  21   , etc. The optimization allows light to be efficiently introduced from the first waveguide  1  to the second waveguide  10 . 
     Next, modifications of the arrangement of the pair of electrodes  62   a  and  62   b  will be described. In the examples in  FIGS.  50 A to  56   , the pair of electrodes  62   a  and  62   b  are in contact with the optical waveguide layer  20  of the second waveguide  10 . In the examples in  FIGS.  50 C and  55   , the plurality of second waveguides  10  shares one or both of the electrodes  62   a  and  62   b . However, the structure of the electrodes  62   a  and  62   b  is not limited to the above structures. 
       FIG.  57    is an illustration showing a structural example in which the upper electrode  62   b  is disposed on the upper surface of the first mirror  30  and the lower electrode  62   a  is disposed on the lower surface of the second mirror  40 . The first mirror  30  is disposed between the upper electrode  62   b  and the optical waveguide layer  20 . The second mirror  40  is disposed between the lower electrode  62   a  and the optical waveguide layer  20 . As shown in this example, the pair of electrodes  62   a  and  62   b  may sandwich the optical waveguide layer  20  indirectly through the first and second mirrors  30  and  40 . 
     In the example in  FIG.  57   , the lower electrode  62   a  extends to the first waveguide  1  side. When a wiring line is led from the lower electrode  62   a , a space below the first waveguide  1  can be used. Therefore, the design flexibility of the wiring line is increased. 
     In this example, the pair of electrodes  62   a  and  62   b  are not in contact with the optical waveguide layer  20 . The guided light in the optical waveguide layer  20  is less influenced by absorption, scattering, and reflection by the pair of electrodes  62   a  and  62   b . Therefore, the loss of the guided light in the optical waveguide layer  20  can be reduced. 
       FIG.  58    is a cross-sectional view showing another modification. In this example, the first waveguide  1  is separated into a first portion  1   a  and a second portion  1   b . The first portion  1   a  is located at a lower position and spaced apart from the second waveguide  10 . The second portion  1   b  is located at a higher position and connected to the optical waveguide layer  20  of the second waveguide  10 . The first portion  1   a  and the second portion  1   b  overlap each other when viewed in the +Z direction. The first portion  1   a  and the second portion  1   b  are approximately parallel to each other and extend in the X direction. In this example, the adjustment layer  51  is also separated into two portions  51   a  and  51   b . The first portion  51   a  of the adjustment layer is disposed between the first portion  1   a  of the first waveguide and the lower electrode  62   a . The second portion  51   b  of the adjustment layer is disposed between the second portion  1   b  of the first waveguide and the second mirror  40 . The protective layer  61  is disposed on the first portion  1   a  and second portion  1   b  of the first waveguide. A part of the first portion  1   a  of the first waveguide faces a part of the second portion  1   b  of the first waveguide through the protective layer  61 . The arrangement of the electrodes  62   a  and  62   b  is the same as the arrangement in  FIG.  57   . 
     In the structure shown in  FIG.  58   , the spacing between the first portion  1   a  and second portion  1   b  of the first waveguide, i.e., their distance in the Z direction, is equal to or less than the wavelength of light in the waveguide. In this case, the light can be propagated from the first portion  1   a  to the second portion  1   b  through evanescent coupling. In this example, unlike the example in  FIG.  54 A , it is unnecessary to change the thickness of the second mirror  40  along the first waveguides  1   a  and  1   b.    
       FIG.  59    is an illustration showing a structural example in which electrodes  62  are disposed between adjacent optical waveguide layers  20 . The adjusting element in this example includes the electrodes  62  and applies positive and negative voltages (denoted by “+” and “−” in the figure) to the electrodes  62  in an alternate manner. In this manner, electric fields in the left-right direction in  FIG.  59    can be generated in the optical waveguide layers  20 . 
     In the example in  FIG.  59   , two electrodes  62  adjacent in the Y direction are in contact with at least part of an optical waveguide layer  20  disposed therebetween. The area of contact between the optical waveguide layer  20  and each electrode  62  is small. Therefore, even when the electrodes  62  are formed of a material that absorbs, scatters, or reflects light, the loss of the guided light in the optical waveguide layer  20  can be reduced. 
     In the structural examples in  FIGS.  50 A to  59   , light used for scanning is emitted through the first mirror  30 . The light used for scanning may be emitted through the second mirror  40 . 
       FIG.  60    is an illustration showing a structural example in which the first mirror  30  is thick and the second mirror  40  is thin. In the example in  FIG.  60   , light passes through the second mirror  40  and is emitted from the substrate  50  side. The substrate  50  in this example is formed of a light-transmitting material. When the light emitted from the substrate  50  is used for scanning, the design flexibility of the optical scanning device increases. 
     &lt;Discussion about Width of Mirrors&gt; 
       FIG.  61    is a cross-sectional view of an optical scanning device in the YZ plane, schematically showing a structural example of a waveguide array  10 A in an embodiment in which a plurality of waveguide elements  10  are arranged in the Y direction. In the structural example in  FIG.  61   , the width of the first mirrors  30  in the Y direction is larger than the width of the optical waveguide layers  20 . The plurality of waveguide elements  10  share one second mirror  40 . In other words, the second mirror  40  in each waveguide element  10  is a part of one integrated mirror. Each first mirror  30  has portions protruding in the Y direction from edge surfaces of a corresponding optical waveguide layer  20 . The Y direction size of the protruding portions is denoted by y 1 . The distance from an edge surface of the optical waveguide layer  20  in the Y direction is denoted by y. y=0 corresponds to the edge surface of the optical waveguide layer  20 . 
     When the guided light propagates through the optical waveguide layer  20  in the X direction, evanescent light leaks from the optical waveguide layer  20  in the Y direction. The intensity I of the evanescent light in the Y direction is represented by the following formula. 
                   I   =       I   0     ⁢     exp   ⁡     (     -     y     y   d         )                 (   23   )               
Here, y d  is the distance in the Y direction between the edge surface of the optical waveguide layer  20  and a position at which the light intensity of evanescent light from the optical waveguide layer  20  is 1/e of the light intensity of the evanescent light from the optical waveguide layer  20  at the edge surface of the optical waveguide layer  20 . y d  satisfies the following formula.
 
                     y   d     =     λ     4   ⁢   π   ⁢           n   w   2     ⁢     sin   2     ⁢     θ     i   ⁢           ⁢   n         -     n   low   2                     (   24   )               
Here, I 0  is the intensity of the evanescent light at y=0. The total reflection angle θ in  is shown in  FIG.  11   . At y=y d , the intensity of the evanescent light is I 0  times 1/e. Here, e is the base of natural logarithm.
 
     For the sake of simplicity, the guided light in the optical waveguide layer  20  is approximated as a ray of light, as shown in  FIG.  11   . As shown in the structural example in  FIG.  61   , when no first mirror  30  is present in a region satisfying y&gt;y 1 , light leakage, or light loss (L loss ), per reflection of the guided light at y=0 is represented by the following formula. 
     
       
         
           
             
               
                 
                   
                     L 
                     loss 
                   
                   = 
                   
                     
                       
                         
                           ∫ 
                           
                             y 
                             1 
                           
                           ∞ 
                         
                         ⁢ 
                         
                           
                             I 
                             0 
                           
                           ⁢ 
                           
                             exp 
                             ⁡ 
                             
                               ( 
                               
                                 - 
                                 
                                   y 
                                   
                                     y 
                                     d 
                                   
                                 
                               
                               ) 
                             
                           
                           ⁢ 
                           dy 
                         
                       
                       
                         
                           ∫ 
                           0 
                           ∞ 
                         
                         ⁢ 
                         
                           
                             I 
                             0 
                           
                           ⁢ 
                           
                             exp 
                             ⁡ 
                             
                               ( 
                               
                                 - 
                                 
                                   y 
                                   
                                     y 
                                     d 
                                   
                                 
                               
                               ) 
                             
                           
                           ⁢ 
                           dy 
                         
                       
                     
                     = 
                     
                       exp 
                       ⁡ 
                       
                         ( 
                         
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                               y 
                               1 
                             
                             
                               y 
                               d 
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   25 
                   ) 
                 
               
             
           
         
       
     
     As shown in formula (4), to set the divergence angle θ div  of light emitted from the waveguide element  10  to 0.1° or less, it is preferable that the propagation length L in the waveguide element  10  in the X direction is 1 mm or more. Let the width of the optical waveguide layer  20  in the Y direction be “a.” Then the number of total reflections in the ±Y directions in  FIG.  11    is 1,000/(a·tan θ in ) or more. When a=1 μm and θ in =45°, the number of total reflections is 1,000 or more. Using formula (25) representing the light loss per reflection, the light loss after reflections is represented by the following formula. 
     
       
         
           
             
               
                 
                   
                     L 
                     loss 
                     
                       ( 
                       β 
                       ) 
                     
                   
                   = 
                   
                     1 
                     - 
                     
                       
                         { 
                         
                           1 
                           - 
                           
                             exp 
                             ⁡ 
                             
                               ( 
                               
                                 - 
                                 
                                   
                                     y 
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                         } 
                       
                       β 
                     
                   
                 
               
               
                 
                   ( 
                   26 
                   ) 
                 
               
             
           
         
       
     
       FIG.  62    is a graph showing the relation between the ratio of light loss (L (β)  loss) and y 1  when β=1,000. The vertical axis represents the ratio of light loss, and the horizontal axis represents y 1 . As shown in  FIG.  62   , to reduce the ratio of light loss to 50% or less, it is necessary that, for example, y 1 ≥7y d  holds. Similarly, to reduce the ratio of light loss to 10% or less, it is necessary that, for example, y 1 ≥9y d  holds. To reduce the ratio of light loss to 1% or less, it is necessary that, for example, y 1 ≥11y d  holds. 
     As shown by formula (25), in principle, the light loss can be reduced by increasing y 1 . However, the light loss does not become zero. 
       FIG.  63    is a cross-sectional view of an optical scanning device in the YZ plane, schematically showing another example of the waveguide array  10 A in the present embodiment in which the plurality of waveguide elements  10  are arranged in the Y direction. In the structural example in  FIG.  63   , the plurality of waveguide elements  10  share the first and second mirrors  30  and  40 . In other words, the first mirror  30  of each waveguide element  10  is a part of one integrated mirror, and the second mirror  40  of each waveguide element  10  is a part of one integrated mirror. In principle, this can minimize the light loss. 
     Next, leakage of evanescent light from each optical waveguide layer  20  was numerically computed for each of the structural examples in  FIGS.  10  and  63   , and the results were compared. 
       FIG.  64 A  is a graph showing the results of computations of an electric field intensity distribution in the structural example in  FIG.  10   .  FIG.  64 B  is a graph showing the results of computations of an electric field intensity distribution in the structural example in  FIG.  63   . FemSim available from Synopsys was used for the numerical computations. In  FIGS.  64 A and  64 B , the width of the optical waveguide layer  20  in the Y direction is 1.5 μm, and the thickness of the optical waveguide layer  20  in the Z direction is 1 μm. The wavelength of the light is 1.55 μm. n w  is 1.68, and n low  is 1.44. This combination of n w  and n low  corresponds to the case in which, for example, a liquid crystal material contained in the optical waveguide layer  20  is enclosed by SiO 2  spacers  73 . 
     As can be seen from  FIG.  64 A , in the structural example in  FIG.  10   , evanescent light leaks from regions in which no first mirror  30  is present. However, as can be seen from  FIG.  64 B , in the structural example in  FIG.  63   , the leakage of evanescent light is negligible. In  FIGS.  64 A and  64 B , when the guided light propagates in the X direction, the intensity of the guided light decreases because of light emission from the first mirror  30  and leakage of evanescent light. The X direction propagation length of the guided light at which the intensity of the guided light is reduced by a factor of e was computed. The propagation length of the light in  FIG.  64 A  was 7.8 μm, and the propagation length in  FIG.  64 B  was 132 μm. 
     In the present embodiment, the spacers  73  may be formed of two or more different mediums. 
       FIG.  65    is a cross-sectional view of an optical scanning device in the YZ plane, schematically showing a structural example in the present embodiment in which the spacers  73  include spacers  73   a  and  73   b  having different refractive indexes. In the structural example in  FIG.  65   , the refractive index n low1  of the spacers  73   a  adjacent to the optical waveguide layers  20  is higher than the refractive index n low2  of the spacers  73   b  not adjacent to the optical waveguide layers  20  (n low1 &gt;n low2 ). For example, when the optical waveguide layers  20  contain a liquid crystal material, SiO 2  may be used for the spacers  73   a  in order to enclose the liquid crystal material. The spacers  73   b  may be air. When the refractive index n low2  of the spacers  73   b  is low, leakage of evanescent light from the optical waveguide layers  20  can be suppressed. 
       FIG.  66    is a cross-sectional view of an optical scanning device in the YZ plane, schematically showing a structural example of a waveguide element  10  in a modification of the present embodiment. In the structural example in  FIG.  66   , the optical waveguide layer  20  has a trapezoidal cross section in the YZ plane. The first mirror  30  is disposed not only on the upper side of the optical waveguide layer  20  but also on its left and right sides. In this manner, light leakage from the left and right sides of the optical waveguide layer  20  can be prevented. 
     Next, the materials of the optical waveguide layers  20  and the spacers  73  will be described. 
     In the structural examples in  FIGS.  61 ,  63 , and  65   , the refractive index n w  of the optical waveguide layers  20  and the refractive index n low  of the spacers  73  satisfy the relation n w &gt;n low . Specifically, the spacers  73  contain a material having a lower refractive index than the material of the optical waveguide layers  20 . For example, when the optical waveguide layers  20  contain an electrooptical material, the spacers  73  may contain a transparent material such as SiO 2 , TiO 2 , Ta 2 O 5 , SiN, AlN, or air. When the optical waveguide layers  20  contain a liquid crystal material, the spacers  73  may contain SiO 2  or air. By sandwiching the optical waveguide layers  20  between a pair of electrodes and applying a voltage to the electrodes, the refractive index of the optical waveguide layers  20  containing an electrooptical material or a liquid crystal material can be changed. In this manner, the emission angle of the light emitted from each first mirror  30  can be changed. The detailed driving method etc. of the optical scanning device when the optical waveguide layers  20  contain a liquid crystal material or an electrooptical material are as described above. 
     The structure in each of the examples in  FIGS.  63  and  65    may be formed by laminating the first mirror  30  and the other components. In this case, the structure can be produced easily. When the spacers  73  are formed of a solid material, the first mirror  30  may be formed by, for example, vapor deposition or sputtering. 
     In the structural examples in  FIGS.  61 ,  63 , and  65   , the structure of each first mirror  30  has been described on the assumption that the plurality of waveguide elements  10  share the second mirror  40 . Of course, the above discussion is applicable to the second mirror  40 . Specifically, when the width of at least one of the first and second mirrors  30  and  40  in the Y direction is larger than the width of the optical waveguide layers  20 , leakage of evanescent light from the optical waveguide layers  20  can be prevented. A reduction in the amount of light used for optical scanning can thereby be prevented. 
     Application Examples 
       FIG.  67    is an illustration showing a structural example of an optical scanning device  100  including elements such as an optical divider  90 , a waveguide array  10 A, a phase shifter array  80 A, and a light source  130  integrated on a circuit substrate (e.g., a chip). The light source  130  may be a light-emitting element such as a semiconductor laser. The light source  130  in this example emits single-wavelength light with a wavelength of λ in free space. The optical divider  90  divides the light from the light source  130  and introduces the resulting light beams into a plurality of waveguides of a plurality of phase shifters. In the structural example in  FIG.  67   , an electrode  62   a  and a plurality of electrodes  62   b  are provided on the chip. A control signal is supplied to the waveguide array  10 A from the electrode  62   a . Control signals are sent from the plurality of electrodes  62   b  to the plurality of phase shifters  80  in the phase shifter array  80 A. The electrodes  62   a  and  62   b  may be connected to an unillustrated control circuit that generates the above-described control signals. The control circuit may be disposed on the chip shown in  FIG.  67    or on another chip in the optical scanning device  100 . 
     By integrating all the components on the chip as shown in  FIG.  67   , optical scanning over a wide area can be implemented using the small device. For example, all the components shown in  FIG.  67    can be integrated on a chip of about 2 mm×about 1 mm. 
       FIG.  68    is a schematic diagram showing how two-dimensional scanning is performed by irradiating a distant object with a light beam such as a laser beam from the optical scanning device  100 . The two-dimensional scanning is performed by moving a beam spot  310  in horizontal and vertical directions. By combining the two-dimensional scanning with a well-known TOF (time of flight) method, a two-dimensional range image can be obtained. In the TOF method, a target object is irradiated with a laser beam, and the reflected light is observed. The time of flight of the light is computed, and the distance is thereby determined. 
       FIG.  69    is a block diagram showing a structural example of a LiDAR system  300  that is an example of a photodetection system capable of generating a range image. The LiDAR system  300  includes the optical scanning device  100 , a photodetector  400 , a signal processing circuit  600 , and a control circuit  500 . The photodetector  400  detects light emitted from the optical scanning device  100  and reflected from the target object. For example, the photodetector  400  may be an image sensor sensitive to the wavelength λ of the light emitted from the optical scanning device  100  or a photodetector including light-receiving elements such as photodiodes. The photodetector  400  outputs an electric signal corresponding to the amount of the light received. The signal processing circuit  600  computes the distance to the target object based on the electric signal outputted from the photodetector  400  and generates distance distribution data. The distance distribution data is data indicating a two-dimensional distance distribution (i.e., a range image). The control circuit  500  is a processor that controls the optical scanning device  100 , the photodetector  400 , and the signal processing circuit  600 . The control circuit  500  controls the timing of irradiation with the light beam from the optical scanning device  100 , the timing of exposure of the photodetector  400 , and the timing of signal reading and instructs the signal processing circuit  600  to generate a range image. 
     In the two-dimensional scanning, a frame rate for acquisition of range images can be selected from 60 fps, 50 fps, 30 fps, 25 fps, 24 fps, etc. often used for general video images. In consideration of application to vehicle-mounted systems, the higher the frame rate, the higher the frequency of range image acquisition, and the higher the accuracy of obstacle detection. For example, when the frame rate is 60 fps and a vehicle is driving at 60 km/h, an image can be acquired every time the vehicle moves about 28 cm. When the frame rate is 120 fps, an image can be acquired every time the vehicle moves about 14 cm. When the frame rate is 180 fps, an image can be acquired every time the vehicle moves about 9.3 cm. 
     The time required to acquire one range image depends on a beam scanning speed. For example, to acquire an image with 100×100 resolvable points at 60 fps, each point must be scanned with the beam in 1.67 μs or less. In this case, the control circuit  500  controls the emission of the light beam from the optical scanning device  100  and signal accumulation and reading by the photodetector  400  at an operating speed of 600 kHz. 
     &lt;Examples of Application to Photoreceiver Device&gt; 
     The optical scanning device of the present disclosure can also be used as a photoreceiver device having approximately the same structure as the optical scanning device. The photoreceiver device includes the same waveguide array  10 A as that in the optical scanning device and a first adjusting element  60  that adjusts a light-receivable direction. The waveguide array  10 A receives light incident in the third direction by the plurality of waveguide elements  10 . More specifically, each of the first mirrors  30  of the waveguide array  10 A allows the light incident in the third direction on a side opposite to a first reflecting surface to pass through toward a corresponding optical waveguide layer  20  in the waveguide array  10 A. Each of the optical waveguide layers  20  of the waveguide array  10 A propagates the received light, i.e., the light transmitted through a corresponding first mirror  30 , in the second direction. The first adjusting element  60  changes the refractive index of the optical waveguide layer  20  of each of the waveguide elements  10 , and the third direction, i.e., the light-receivable direction, can thereby be changed. The photoreceiver device may further include: the same phase shifters as the plurality of phase shifters  80  or  80   a  and  80   b  in the optical scanning device; and a second adjusting element that changes the phase differences between light beams outputted from the plurality of waveguide elements  10  through the plurality of phase shifters  80  or  80   a  and  80   b . In this case, the light-receivable direction can be changed two dimensionally. 
     For example, by replacing the light source  130  in the optical scanning device  100  shown in  FIG.  67    with a receiving circuit, a photoreceiver device can be configured. When light with a wavelength λ enters the waveguide array  10 A, the light is transmitted to the optical divider  90  through the phase shifter array  80 A, combined into one beam, and sent to the receiving circuit. The intensity of the one combined beam represents the sensitivity of the photoreceiver device. The sensitivity of the photoreceiver device can be adjusted by an adjusting element installed in the waveguide array and another adjusting element installed in the phase shifter array  80 A. In the photoreceiver device, the direction of the wave vector shown in, for example,  FIG.  26    (the thick arrow in the figure) is reversed. The incident light has a light component in the extending direction of the waveguide elements  10  (the X direction in the figure) and a light component in the arrangement direction of the waveguide elements  10  (the Y direction in the figure). The sensitivity to the light component in the X direction can be adjusted by the adjusting element installed in the waveguide array  10 A. The sensitivity to the light component in the arrangement direction of the waveguide elements  10  can be adjusted by the adjusting element installed in the phase shifter array  80 A. θ and α 0  (formulas (16) and (17)) can be determined from the phase difference Δφ between the light beams when the sensitivity of the photoreceiver device is maximized and the refractive index n w  and thickness d of the optical waveguide layers  20 . This allows the incident direction of the light to be identified. 
     The above-described embodiments and modifications can be appropriately combined. For example, the first mirrors  30  shown in  FIG.  61    may be used instead of the first mirrors  30  in a different embodiment or a modification. The waveguide elements  10  shown in  FIG.  65    may be used instead of the waveguide elements  10  in a different embodiment or a modification. 
     As described above, the present disclosure encompasses optical scanning devices, photoreceiver devices, and a LiDAR system in the following items. 
     [Item 1] An optical scanning device including: 
     a first mirror including a multilayer reflective film; 
     a second mirror including a multilayer reflective film facing the multilayer reflective film of the first mirror; 
     an optical waveguide layer that is disposed between the first mirror and the second mirror and that propagates inputted light as propagating light; 
     a pair of electrodes sandwiching the optical waveguide layer; and 
     a driving circuit that applies a voltage to the pair of electrodes, 
     wherein the first mirror, the second mirror, and the optical waveguide layer have respective structures extending in a same direction, 
     wherein the first mirror has a higher light transmittance than the second mirror and allows part of the propagating light propagating through the optical waveguide layer to pass through and be emitted to outside of the optical waveguide layer as emission light, 
     wherein the optical waveguide layer contains a liquid crystal material or an electrooptical material, 
     wherein, when the voltage is not applied to the pair of electrodes, an alignment direction of the liquid crystal material or a direction of a polarization axis of the electrooptical material is parallel or perpendicular to the direction in which the optical waveguide layer extends, and 
     wherein the driving circuit applies the voltage to the pair of electrodes to change a refractive index of the liquid crystal material or the electrooptical material for the propagating light propagating through the optical waveguide layer to thereby change a direction of the emission light emitted from the optical waveguide layer. 
     [Item 2] The optical scanning device according to item 1, further including a total reflection waveguide that is connected directly to the optical waveguide layer and that inputs the inputted light into the optical waveguide layer. 
     [Item 3] The optical scanning device according to item 2, 
     wherein the optical waveguide layer contains the liquid crystal material, 
     wherein, when the voltage is not applied to the pair of electrodes, the alignment direction of the liquid crystal material is parallel or perpendicular to the direction in which the optical waveguide layer extends, and 
     wherein the driving circuit applies the voltage to the pair of electrodes to change the alignment direction of the liquid crystal material to thereby change the refractive index of the liquid crystal material. 
     [Item 4] The optical scanning device according to item 3, 
     wherein the pair of electrodes are disposed such that, when the voltage is applied to the pair of electrodes, an electric field is generated in a direction normal to reflecting surfaces of the first and second mirrors, and 
     wherein, when the voltage is not applied to the pair of electrodes, the alignment direction of the liquid crystal material is parallel to the direction in which the optical waveguide layer extends. 
     [Item 5] The optical scanning device according to item 4, further including a light source that emits linearly polarized light, 
     wherein the linearly polarized light emitted from the light source is inputted to the optical waveguide layer as the inputted light with P-polarization. 
     [Item 6] The optical scanning device according to item 3, 
     wherein the pair of electrodes are disposed such that, when the voltage is applied to the pair of electrodes, an electric field is generated in a direction normal to reflecting surfaces of the first and second mirrors, and 
     wherein, when the voltage is not applied to the pair of electrodes, the alignment direction of the liquid crystal material is perpendicular to both the direction in which the optical waveguide layer extends and the direction normal to the reflection surfaces of the first and second mirrors. 
     [Item 7] The optical scanning device according to item 6, further including a light source that emits linearly polarized light, 
     wherein the linearly polarized light emitted from the light source is inputted to the optical waveguide layer as the inputted light with S-polarization. 
     [Item 8] The optical scanning device according to item 3, 
     wherein the pair of electrodes are disposed such that, when the voltage is applied to the pair of electrodes, an electric field is generated in a direction perpendicular to both the direction in which the optical waveguide layer extends and a direction normal to reflecting surfaces of the first and second mirrors, and 
     wherein, when the voltage is not applied to the pair of electrodes, the alignment direction of the liquid crystal material is parallel to the direction in which the optical waveguide layer extends. 
     [Item 9] The optical scanning device according to item 8, further including a light source that emits linearly polarized light, 
     wherein the linearly polarized light emitted from the light source is inputted to the optical waveguide layer as the inputted light with S-polarization. 
     [Item 10] The optical scanning device according to item 8, further including a light source that emits linearly polarized light, 
     wherein the linearly polarized light emitted from the light source is inputted to the optical waveguide layer as the inputted light with P-polarization. 
     [Item 11] The optical scanning device according to any one of items 1 to 10, 
     wherein the liquid crystal material contains nematic liquid crystal molecules, 
     wherein the nematic liquid crystal molecules have a molecular structure represented by
 
R1-Ph1-R2-Ph2-R3,
 
     wherein R1 and R3 are each independently one selected from the group consisting of an amino group, a carbonyl group, a carboxyl group, a cyano group, an amine group, a nitro group, a nitrile group, and an alkyl chain, 
     wherein Ph1 and Ph2 are each independently an aromatic group, and 
     R2 is one selected from the group consisting of a vinyl group, a carbonyl group, a carboxyl group, a diazo group, and an azoxy group. 
     [Item 12] The optical scanning device according to item 11, 
     wherein the liquid crystal material is a mixture of a plurality of types of liquid crystal molecules with different compositions. 
     [Item 13] The optical scanning device according to item 1 or 2, 
     wherein the optical waveguide layer contains the electrooptical material, 
     wherein the direction of the polarization axis of the electrooptical material is parallel or perpendicular to a direction in which the optical waveguide layer extends, 
     wherein the pair of electrodes are disposed such that, when the voltage is applied to the pair of electrodes, the direction of an electric field generated between the pair of electrodes coincides with the direction of the polarization axis, and 
     wherein the driving circuit applies the voltage to the pair of electrodes to thereby change the refractive index of the electrooptical material. 
     [Item 14] The optical scanning device according to item 13, 
     wherein the direction of the polarization axis of the electrooptical material is perpendicular to both the direction in which the optical waveguide layer extends and a direction normal to reflecting surfaces of the first and second mirrors. 
     [Item 15] The optical scanning device according to item 14, further including a light source that emits linearly polarized light, 
     wherein the linearly polarized light emitted from the light source is inputted to the optical waveguide layer as the inputted light with S-polarization. 
     [Item 16] The optical scanning device according to item 13, 
     wherein the direction of the polarization axis of the electrooptical material coincides with a direction normal to reflecting surfaces of the first and second mirrors. 
     [Item 17] The optical scanning device according to item 16, further including a light source that emits linearly polarized light, 
     wherein the linearly polarized light emitted from the light source is inputted to the optical waveguide layer as the inputted light with P-polarization. 
     [Item 18] The optical scanning device according to any one of items 13 to 17, 
     wherein the electrooptical material contains a compound represented by
 
KTa 1-x Nb x O 3  or
 
K 1-y A y Ta 1-x Nb x O 3  (where A is Li or Na),
 
     wherein x is a real number larger than 0 and smaller than 1, and 
     y is a real number larger than 0 and smaller than 1. 
     [Item 19] An optical scanning device including 
     a plurality of waveguide units arranged in a first direction, 
     wherein each of the plurality of waveguide units includes: 
     a first mirror including a multilayer reflective film; 
     a second mirror including a multilayer reflective film facing the multilayer reflective film of the first mirror; 
     an optical waveguide layer that is disposed between the first mirror and the second mirror and that propagates inputted light as propagating light; 
     a pair of electrodes sandwiching the optical waveguide layer; and 
     a driving circuit that applies a voltage to the pair of electrodes, 
     wherein the first mirror, the second mirror, and the optical waveguide layer have respective structures extending in a same direction, 
     wherein the first mirror has a higher light transmittance than the second mirror and allows part of the propagating light propagating through the optical waveguide layer to pass through and be emitted to outside of the optical waveguide layer as emission light, 
     wherein the optical waveguide layer contains a liquid crystal material or an electrooptical material, 
     wherein, when the voltage is not applied to the pair of electrodes, an alignment direction of the liquid crystal material or a direction of a polarization axis of the electrooptical material is parallel or perpendicular to the direction in which the optical waveguide layer extends, and 
     wherein the driving circuit applies the voltage to the pair of electrodes to change the refractive index of the liquid crystal material or the electrooptical material for the propagating light propagating through the optical waveguide layer to thereby change a direction of the emission light emitted from the optical waveguide layer. 
     [Item 20] The optical scanning device according to item 19, 
     wherein each of the plurality of waveguide units further includes a total reflection waveguide that is connected directly to the optical waveguide layer of the waveguide unit and that inputs the inputted light to the optical waveguide layer of the waveguide unit. 
     [Item 21] The optical scanning device according to item 19 or 20, further including: 
     a plurality of phase shifters; and 
     a second driving circuit that drives the plurality of phase shifters, 
     wherein each of the plurality of phase shifters includes a waveguide that is connected to the optical waveguide layer of a corresponding one of the plurality of waveguide units directly or through the total reflection waveguide of the corresponding one of the plurality of waveguide units, 
     wherein the waveguide of each of the phase shifters contains a material whose refractive index is changed when a voltage is applied or temperature is changed, and 
     wherein the second driving circuit changes a refractive index of the waveguide of each of the phase shifters by applying a voltage to the waveguide or changing the temperature of the waveguide to thereby change phase differences between light beams propagating from the plurality of phase shifters to the plurality of waveguide units. 
     [Item 22] A photoreceiver device including: 
     a first mirror including a multilayer reflective film; 
     a second mirror including a multilayer reflective film facing the multilayer reflective film of the first mirror; 
     an optical waveguide layer that is disposed between the first mirror and the second mirror and that propagates inputted light as propagating light; 
     a pair of electrodes sandwiching the optical waveguide layer; and 
     a driving circuit that applies a voltage to the pair of electrodes, 
     wherein the first mirror, the second mirror, and the optical waveguide layer have respective structures extending in a same direction, 
     wherein the first mirror has a higher light transmittance than the second mirror and allows incident light from outside to pass through and be inputted to the optical waveguide layer as the inputted light, 
     wherein the optical waveguide layer contains a liquid crystal material or an electrooptical material, 
     wherein, when the voltage is not applied to the pair of electrodes, an alignment direction of the liquid crystal material or a direction of a polarization axis of the electrooptical material is parallel or perpendicular to the direction in which the optical waveguide layer extends, and 
     wherein the driving circuit applies the voltage to the pair of electrodes to change a refractive index of the optical waveguide layer to thereby change a direction in which the incident light is receivable. 
     [Item 23] A photodetection system including: 
     the optical scanning device according to any one of items 1 to 21; 
     a photodetector that, when the emission light emitted from the optical scanning device is reflected from an object as reflected light, detects the reflected light; and 
     a signal processing circuit that generates distance distribution data based on an output from the photodetector. 
     [Item 24] An optical scanning device including: 
     a first waveguide; and 
     a second waveguide connected to the first waveguide, 
     wherein the second waveguide includes 
     a first mirror including a multilayer reflective film, 
     a second mirror including a multilayer reflective film facing the multilayer reflective film of the first mirror, and 
     an optical waveguide layer that is disposed between the first mirror and the second mirror and that propagates light inputted into the first waveguide and propagated through the first waveguide, 
     wherein the first mirror has a higher light transmittance than the second mirror and emits part of the light propagating through the optical waveguide layer to outside of the optical waveguide layer, and 
     wherein the optical scanning device further includes an adjusting element that changes a refractive index of the optical waveguide layer to thereby change a direction of the light emitted from the second waveguide. 
     [Item 25] The optical scanning device according to item 24, 
     wherein the optical waveguide layer contains a material whose refractive index for the light propagating through the optical waveguide layer is changed when a voltage is applied to the material, and 
     wherein the adjusting element applies a voltage to the optical waveguide layer to change the refractive index of the optical waveguide layer to thereby change the direction of the light emitted from the second waveguide. 
     [Item 26] The optical scanning device according to item 24 or 25, 
     wherein the first waveguide includes two multilayer reflective films facing each other and an optical waveguide layer sandwiched between the two multilayer reflective films. 
     [Item 27] The optical scanning device according to item 26, 
     wherein the light transmittance of the two multilayer reflective films facing each other is lower than the light transmittance of the first mirror. 
     [Item 28] The optical scanning device according to any one of items 24 to 27, 
     wherein |n w1 −n w2 |/n w1 &lt;0.4 holds, 
     where n w1  is a refractive index of the first waveguide, and n w2  is a refractive index of the second waveguide. 
     [Item 29] The optical scanning device according to any one of items 24 to 28, 
     wherein 0.95×mλ/(2n w2 )&lt;d 2 &lt;1.5×mλ/(2n w2 ) holds, 
     where n w2  is the refractive index of the optical waveguide layer of the second waveguide, d 2  is the thickness of the optical waveguide layer of the second waveguide, and λ is the wavelength of the light inputted into the first waveguide. 
     [Item 30] The optical scanning device according to any one of items 24 to 29, 
     wherein the first waveguide propagates the light inputted into the first waveguide by total reflection, and 
     wherein 1.2×mλ/(2n w2 )&lt;d 2 &lt;1.5×mλ/(2n w2 ) holds. 
     [Item 31] The optical scanning device according to any one of items 24 to 30, 
     wherein n w1 &gt;n w2  holds, 
     where n w1  is the refractive index of the first waveguide, and n w2  is the refractive index of the optical waveguide layer of the second waveguide. 
     [Item 32] The optical scanning device according to any one of items 24 to 31, 
     wherein the optical waveguide layer of the second waveguide is connected to the first waveguide through a gap, and 
     wherein the product of the refractive index of the gap and the width of the gap is equal to or less than λ/6.5, where λ is the wavelength of the light inputted into the first waveguide. 
     [Item 33] The optical scanning device according to any one of items 24 to 32, 
     wherein −Δd/2&lt;Δz&lt;Δd/2 holds, 
     where Δz is the offset between the center of the first waveguide in a thickness direction and the center of the second waveguide in the thickness direction, and Δd is the difference between the thickness of the optical waveguide layer of the first waveguide and the thickness of the optical waveguide layer of the second waveguide. 
     [Item 34] The optical scanning device according to any one of items 24 to 33, 
     wherein the first waveguide includes two multilayer reflective films facing each other and an optical waveguide layer sandwiched between the two multilayer reflective films, 
     wherein one of the two multilayer reflective films has a portion with a smaller thickness than adjacent portions thereof, and 
     wherein the optical waveguide layer propagates the light incident on the portion and inputs the light into an end surface of the optical waveguide layer of the second waveguide. 
     [Item 35] The optical scanning device according to any one of items 24 to 33, 
     wherein the first waveguide includes a grating disposed on part of a surface thereof, propagates the light incident on the grating, and inputs the light into an end surface of the optical waveguide of the second waveguide. 
     [Item 36] The optical scanning device according to any one of items 24 to 33, 
     wherein the first waveguide propagates the light incident on an end surface thereof and inputs the light into an end surface of the optical waveguide layer of the second waveguide. 
     [Item 37] The optical scanning device according to any one of items 24 to 33, further including a third waveguide that is connected to the first waveguide, propagates light inputted from the outside, and inputs the light into the first waveguide. 
     [Item 38] The optical scanning device according to item 37, 
     wherein the first waveguide includes two multilayer reflective films facing each other and an optical waveguide layer sandwiched between the two multilayer reflective films, and 
     wherein the third waveguide propagates the light by total reflection and inputs the light into the first waveguide. 
     [Item 39] The optical scanning device according to item 37 or 38, 
     wherein the third waveguide includes a grating on part of a surface thereof, propagates the light incident on the grating, and inputs the light into an end surface of the first waveguide. 
     [Item 40] The optical scanning device according to items 37 or 38, 
     wherein the third waveguide propagates the light inputted from an end surface of the third waveguide and inputs the light into an end surface of the first waveguide. 
     [Item 41] An optical scanning device including a plurality of waveguide units arranged in a first direction, 
     wherein each of the plurality of waveguide units includes: 
     a first waveguide; and 
     a second waveguide connected to the first waveguide and propagates light in a second direction intersecting the first direction, 
     wherein the second waveguide includes 
     a first mirror including a multilayer reflective film, 
     a second mirror including a multilayer reflective film facing the multilayer reflective film of the first mirror, and 
     an optical waveguide layer that is disposed between the first mirror and the second mirror and that propagates light inputted into the first waveguide and propagated through the first waveguide, 
     wherein the first mirror has a higher light transmittance than the second mirror and emits part of the light propagating through optical waveguide layer to outside of the optical waveguide layer, and 
     wherein the optical scanning device further includes a first adjusting element that changes a refractive index of the optical waveguide layer of each of the second waveguides to change a direction of the light emitted from the each of the second waveguides. 
     [Item 42] The optical scanning device according to item 41, further including a second adjusting element that adjusts phase differences between light beams propagating from the first waveguides to the second waveguides in the plurality of waveguide units to thereby change the direction of the light emitted from the second waveguides.
 
[Item 43] The optical scanning device according to item 42, further including a plurality of phase shifters each having a waveguide connected to the first waveguide of a corresponding one of the plurality of waveguide units,
 
     wherein the waveguide of each of the phase shifters contains a material whose refractive index is changed when a voltage is applied or temperature is changed, and 
     wherein the second adjusting element changes the refractive index of the waveguide of each of the phase shifters by applying a voltage to the waveguide or changing temperature of the waveguide to thereby change phase differences between light beams propagating from the plurality of phase shifters to the plurality of waveguide elements. 
     [Item 44] The optical scanning device according to item 42 or 43, 
     wherein the first adjusting element changes an X component of a wavenumber vector of the light emitted from each of the second waveguide, and 
     wherein the second adjusting element changes a Y component of the wavenumber vector, 
     the X component being a component of the wavenumber vector in the second direction, the Y component being a component of the wavenumber vector in the first direction. 
     [Item 45] The optical scanning device according to item 42 or 43, further including 
     a light source that emits light with a wavelength of λ in free space, and 
     an optical divider that divides the light from the light source into light beams and introduces the divided light beams into the waveguides of the plurality of phase shifters. 
     [Item 46] A photoreceiver device including: 
     a first waveguide; and 
     a second waveguide connected to the first waveguide, 
     wherein the second waveguide includes 
     a first mirror including a multilayer reflective film, 
     a second mirror including a multilayer reflective film facing the multilayer reflective film of the first mirror; and 
     an optical waveguide layer that is disposed between the first mirror and the second mirror and that propagates light, 
     wherein the first mirror has a higher light transmittance than the second mirror and introduces part of light incident on the first mirror into the optical waveguide layer, 
     wherein the part of the light introduced from the first mirror into the optical waveguide layer is inputted to the first waveguide, and 
     wherein the photoreceiver device further includes an adjusting element that changes a refractive index of the optical waveguide layer. 
     [Item 47] A LiDAR system including: 
     the optical scanning device according to any one of items 1 to 22; 
     a photodetector that detects light emitted from the optical scanning device and reflected from a target; and 
     a signal processing circuit that generates distance distribution data based on an output from the photodetector. 
     The optical scanning device and the photoreceiver device in the embodiments of the present disclosure can be used for applications such as LiDAR systems installed in vehicles such as automobiles, UAVs, and AGVs.