Surface emitting second harmonic generating device
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation in part of Application Ser. No. 047,969, filed Apr. 15, 1993, now U.S. Pat. No 5,341,390. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates generally to a surface emitting second harmonic generating device, and more particularly to a surface emitting second harmonic generating device which is capable of highly efficient extraction of a second harmonic (especially monochromatic light, such as violet, blue and green), in a direction perpendicular to a substrate. 
     BACKGROUND OF THE INVENTION 
     Lasers and light emitting diodes (LEDs) are used as sources of blue light in various fields of optoelectronics, such as optical measurement, optical transmission and optical displays. Light-emitting devices which use LEDs (particularly those which emit blue light) utilizing GaN semiconductors are known (see, e.g., refer to S. Nakamura, T. Mukai and M. Senoh: Jpn. J. Appl. Phys., Vol. 30 (1991) L1998). However, since the line width of LED light is wide (a single wavelength cannot be created), lasers have in recent years been more widely used than LEDs in the field of optoelectronics. 
     For example, with some ZnCdSSe semiconductor lasers, an acceptable blue light output is obtainable (see, e.g., M. A. Hasse, J. Qiu, J. M. DePuydt and H. Cheng: Appl. Phys. Lett., Vol. 59 (1991) 1272). Nevertheless, under the present circumstances such devices have problems of reliability and usability in obtaining a light output at a room temperature. 
     In addition, light-emitting devices that introduce high-power solid laser light or high-power semiconductor laser light into non-linear optical crystals (e.g., dielectric substances such as LiNbO 3  and KNbO 3 , semiconductors such as GaAs, organic substances, etc.) to generate a second harmonic are known (e.g., refer to A. Yariv, Introduction to Optical Electronics, 4th ed.; Saunders College Publishing, (Holt, Rinehart and Winston, 1991)). As shown in FIG. 6, in this type of device a laser source 23 and non-linear optical crystals 24 are arranged between a pair of optical reflectors 21, 22, and laser light is launched through the non-linear optical crystals 24 to generate a second harmonic, and blue light is extracted from the reflector 22 which has the higher transmission of the second harmonic. However, the larger the size of the device, the greater the cost of its production, and since it is composed of a combination of multiple components, its problems include extremely difficult control and unstable output. 
     Further, devices are known which extract a second harmonic from the end surface of usual edge-emitting GaAs or AlGaAs semiconductor lasers (see, e.g., N. Ogasawara, R. Ito, H. Rokukawa and W. Katsurashima: Jpn. J. Appl. Phys., Vol. 26 (1987) 1386), but the power of the fundamental wave inside these devices is low due to a low end facet reflectivity. Also, the absorption loss is large due to the long cavity, These device have even greater difficulty in achieving a structure for phase matching. These disadvantages make it impossible to generate the second harmonic with high efficiency. 
     Further thought has been directed towards extraction of a second harmonic in the direction perpendicular to the cavity. See, e.g., D. Vakhshoori, R. J. Fisher, M. Hong, D. L. Sivco, G. J. Zydzik, G. N. S. Chu and A. Y. Cho: Appl. Phys. Lett., Vol. 59 (1991)896. However, in a device of the type disclosed in this publication, the output power of the second harmonic is small and the emitted light is distributed over a wide range, therefore condensing of the light is difficult; thus, at present, a practical application for this device has not yet been achieved. 
     SUMMARY OF THE INVENTION 
     To solve the problems identified previously herein, the inventors of the present invention previously proposed, in the U.S. patent Ser. No. 047,969, filed at Apr. 15, 1993, now U.S. Pat. No. 5, 347,390, a surface emitting second harmonic generating device comprising a III-V compound semiconductor as an active layer, which is capable of generating a higher output of a shorter wave length second harmonic in higher efficiency in the neighborhood of a room temperature (-30° to +100° C). This patent application is incorporated herein by reference. Further research efforts of the inventors revealed the following results: 
     (1) Even using a II-VI compound semiconductor crystal in the active layer, a high output second harmonic can be generated in high efficiency in the neighborhood of a room temperature (-30° to +100° C.), moreover a compact, low power consumption and low fabrication cost surface emitting second harmonic generating device is possible; 
     (2) The phase-matching layer need not always be a superlattice structure in that case; 
     (3) The fact (2) is applicable to the surface emitting second harmonic generating device using a III-V compound semiconductor as an active layer, as proposed in the specification; 
     (4) When the phase-matching layer is a superlattice the recent progress of the crystal growth technology for semiconductor crystals have given rise to a technology where the crystal can be grown while changing the crystallographic axes. 
     An object of the present invention is to provide a surface emitting second harmonic generating device having excellent characteristics as described above by using a crystal of either a III-V compound semiconductor or a II-VI compound semiconductor. 
     Another object of the present invention is to provide a surface emitting second harmonic generating device manufactured in lower cost compared to the previously proposed surface emitting second harmonic generating device using a III-V compound semiconductor crystal. 
     Still another object of the present invention is to provide a surface emitting second harmonic generating devices capable of generating second harmonic over a wider wavelength region. 
     Yet another object of the present invention is to provide a surface emitting second harmonic generating devices capable of generating second harmonic at higher efficiency at room temperature. 
     Other aspects and advantages of the present invention will become apparent from the following detailed description, taken in conjunction with the accompanying drawings, illustrating by way of example the principles of the invention. 
    
    
     A BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a drawing showing an example of a second harmonic generating device according to the present invention, providing a cross-sectional view of the entire device. 
     FIG. 2 is a cross-sectional diagram showing each layer of the section α in FIG. 1. 
     FIG. 3 is a cross-sectional diagram showing each layer of another example of a second harmonic generating device according to the present invention. 
     FIGS. 4A and 4B are drawings showing matrices of non-linear coefficients and substrate orientations for the purpose of explanation of the function of the present invention. 
     FIGS. 5A and 5B and 5C are drawings showing matrices of non-linear coefficients and substrate orientations for the purpose of explanation of the function of the present invention. 
     FIG. 6 is a drawing showing an embodiment of a second harmonic generating device according to the prior art. 
     FIG. 7 is a cross-sectional diagram showing an overview of a surface emitting laser. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Much attention has been given recently to vertical cavity surface emitting lasers (e.g., refer to&#34;Surface Emitting Lasers&#34; by Kenichi Iga and Fumio Koyama: Ohmusha, Ltd., 1990). These surface emitting lasers are used as, for example, (1) a light source for writing and reading data in light magnetic disk devices, (2) a light source for medical equipment which utilize photo-luminescence, and (3) a light source in displays which utilize a laser. 
     As shown, for example, in FIG. 7, surface emitting lasers are constructed in such a way as to include a vertical cavity 33 containing an active region 32, which is constructed on a (100) substrate (for example, a crystal base plate whose surface orientation matches the [100] crystallographic axis direction), and reflectors 34, 35 which are formed on both ends of vertical cavity and have a high reflectivity. The reflectors 34, 35 generally am semiconductor multi-layer films or dielectric multi-layer films. At room temperature, such surface emitting lasers exhibit single mode lasing with a single wavelength up to an output power of a several milliwatts. The light intensity inside the cavity is estimated to be over 100 times the output power, or a several hundred milliwatts. 
     The inventors of the present invention noted the following properties of a III-V compound semiconductor vertical cavity surface emitting laser and also a vertical cavity surface emitting laser using II-VI compound semiconductor: 
     (1) the efficiency when converting a fundamental wave to a second harmonic is in proportion to the power of the fundamental wave, and thus if the second harmonic can be generated inside the vertical cavity surface emitting laser, the light intensity of the fundamental wave is extremely favorable to generation of the second harmonic; 
     (2) the vertical cavity surface emitting laser includes a pair of reflectors, one of which may be characterized to transmit the second harmonic; and 
     (3) the crystals comprising it have a large non-linear coefficient. The second harmonic above mentioned can be generated in a near-room temperature. 
     Additionally, further research revealed that a phase-matching layer formed inside the vertical cavity surface emitting laser can contribute to manufacture a second harmonic generating device that is smiler, has lower energy consumption, and has a lower production cost. 
     A surface emitting second harmonic generating device according to the present invention comprises, as a cavity, an active layer of semiconductor crystals of a III-V compound or a II-VI compound; spacer layers constructed on each side of the active layer; and a pair of reflectors constructed one on each spacer layer and positioned on the side opposite from the active layer, where one of the reflectors transmits the second harmonic at a certain rate. The device is characterized in that the &lt;100&gt; direction of the semiconductor crystals within the cavity makes an angle of 5 degrees or more with the direction of the light rays. Preferably, one of the &lt;111&gt;,&lt;211&gt; and &lt;110&gt; directions of the semiconductor crystals within the cavity roughly matches the direction of the light rays. Here,&lt;a b c&gt; (a, b, c are integers) are symbols indicating directions equivalent to [a b c]; for example,&lt;100&gt; signifies the directions shown in Table 1. 
     
                       TABLE 1                                                     
______________________________________                                    
[100]           [010]  [001]                                              
[- 100]         [0- 10]                                                   
                       [00- 1]                                            
______________________________________                                    
 
    
     The principle behind second harmonic generation in the context of the present invention is summarized below. Over-lined numbers are customarily used to indicate crystallographic axes/directions and orientations, but hereinafter a minus symbol is added to the displayed numbers instead. Generally, a non-linear optical crystal is used when generating a second harmonic from a fundamental wave. In accordance with the present invention, crystal such as ones with a zincblende-type crystalline structure may be used as a non-linear crystal. When light is propagated through a zincblende-type crystal, a secondary (for example, twice the fundamental frequency) non-linear polarization P NL  is induced in the crystal, and a second harmonic is generated which has an electrical field in proportion to the size of the polarization P NL . 
     Further, the amount of the generated second harmonic depends on the orientation of the semiconductor crystal of the cavity (including the phase-matching layer). This orientation is usually the same as that of the crystal making up the substrate. And thus, hereinafter, the substrate orientation is treated as the crystal orientation of the cavity for convenience of explanation. 
     A case will now be considered wherein the x-axis of an x-y-z orthogonal coordinate system is set along the direction normal to the substrate surface and a fundamental wave is propagated in the direction of the x-axis. The x, y, and z components of the polarization P NL , for example, P NLx , P NLy , and P NLz , may be represented as shown in Equation 1: ##EQU1## Here, P NLx , P NLy  and P NLz  represent the x, y and z components of the polarization P NL , and the matrix elements d mn  (m=1, 2, 3; n=1, 2, . . . , 6) represent the coefficients relating the non-linear polarization to the electric field of the fundamental wave. The electric field components E x , E y , E z  are the x, y and z components of the light fundamental wave. Also, since the fundamental wave is propagated along the direction of the x-axis, E x  can be set to zero. 
     Matrices which include the symbol dm are often only defined for the case where the x-axis is [100] 
     , the y-axis is [010] and the z-axis is [001]. Here, the definition is generalized in order to use the same symbol for any arbitrary set of orthogonal axes x, y and z. 
     Assume a substrate such as the one shown in FIG. 4 (A), wherein [100] is directed to the x-axis, [010] to the y-axis, and [001] to the z-axis. In this substrate, as shown in FIG. 4 (A), the matrix element d mn  holds non-zero values for d 14  =d 25  =d 36  (in FIG. 4 (A) this is set to 1.000 for convenience of explanation), while the other elements of the matrix are zero. If fundamental light is propagated along the x-axis within the substrate, P NLy  and P NLz  both become zero, and therefore the generated second harmonic is not propagated along the x-axis (the direction perpendicular to the substrate surface). 
     As shown in FIG. 4 (B), when the substrate crystal in FIG. 4 (A) are rotated -45° around the x-axis, that is, when [100] is directed to the x-axis, [011] to the y-axis, and [0-11]to z-axis, the second harmonic is not propagated along the x-axis, as is clear from the matrix elements. 
     For the case that the x-axis is not directed to [100], the change in efficiency of generating the second harmonic will be studied by using a few representative examples, wherein the substrate shown in FIG. 4 (B) is rotated around the z-axis (or [0-11] axis) from the x direction to the y direction. These examples are shown in FIGS. 5 (A)-5(C). The angles of rotation are -5°, about -35.3° and about 54.7°, respectively. In FIG. 5 (B), the x-axis is parallel to [211], the y-axis to [-111] and the z-axis to [0-11], while in FIG. 5 (C) the x-axis is parallel to [111], the y-axis to [-211] and the z-axis to [0-11]. 
     The non-linear coefficient matrix elements corresponding to the coordinate axes are shown respectively in FIGS. 4(A) and 4(B), and in FIGS. 5(A)-5(C). As is clear from these matrix elements, if E x  =0 for the rotation operation from FIG. 4(B) to FIG. 5(C) , then the non-linear polarization P NLy  and P NLz  which contributes to the second harmonic propagated along the x-axis may be expressed as follows: 
     
         P.sub.NLy =d.sub.22 E.sub.y E.sub.y +d.sub.23 E.sub.z E.sub.z 
    
     
         P.sub.NLz =2d.sub.23 E.sub.y E.sub.z 
    
     (Note that d 34  =d 23 ) 
     In simple terms, in this rotation, since -d 22  ≧d 23  &gt;0, the polarization parallel to the y-z plane 
     
         P.sub.NL =(P.sub.NLy.sup.2 +P.sub.NLz.sup.2).sup.1/2 
    
     under the constant fundamental wave 
     
         E=(E.sub.y.sup.2 +E.sub.2.sup.2).sup.1/2 
    
     has its maximum value when the fundamental wave is polarized along the y-axis (that is, E z  =0, E=E y ). 
     On the other hand, if the fundamental wave is polarized along the y-axis, as the angle of rotation is larger, P NL  increases and has a maximum value in the case of FIG. 5(B). When the angle of rotation is further increased, Pm decreases again, but since -d 22  =d 23  in the case of FIG. 5(C), 
     
         P.sub.NL =-d.sub.22 E.sup.2, 
    
     providing a very favorable property such that the efficiency of the second harmonic generation is independent of the polarization of the fundamental wave. 
     The actual calculation is not included here, but if the ratio is taken of the square of P NL  in the case of FIG. 5(A) and the square of P NL  in the case of FIG. 5(C), then 
     
         (0.260/0.816).sup.2 =0.1 
    
     The above equation supports that when the &lt;100 &gt; direction of the substrate (for example, the &lt;100 &gt; direction of the semiconductor crystals within the cavity) makes a 5° angle with respect to direction of the light rays, it is possible to obtain roughly 10% of the second harmonic generation obtained when the &lt;111&gt; direction of the substrate (for example, the &lt;111&gt; direction of the semiconductor crystals within the cavity) matches the direction of the light rays. If such 10% efficiency can be achieved, then an adequate practical use thereof is apparent, and this explains why the &lt;100&gt; direction of the semiconductor crystals within the cavity makes an angle of 5° or more with respect to the direction of the light rays. The particulars of a case where the rotation is in a direction different from the one described above or where the rotation is around the y-axis are not described herein, but basically, in these cases as well, the following statements are true: 
     (1) as the angle between the x-axis and the &lt;100&gt; direction increases, so does P NL;   
     (2) when the x-axis is in the direction &lt;211&gt; (see FIG. 5 (B)) or in the direction &lt;100&gt;, the efficiency is maximized if the polarization of the fundamental wave is appropriate; 
     (3) when the x-axis is in the direction &lt;110&gt;, an efficiency is achievable which is slightly less than that in 
     (2) above, but it does not depend on the polarization of the fundamental wave. 
     Some prior studies disclose the substrate&#39;s &lt;100&gt; direction oriented at an angle of about 4° with respect to the direction of the light rays. However, this is based on the fact that such an angle is favorable to the growth of the crystals, and is not based on the generation of a second harmonic. Therefore, the devices disclosed in these studies are not constructed so that the reflectors transmit the second harmonic. In addition, since technology other than that by the present inventors does not exist for generating the second harmonic using a surface emitting laser, there has been no attempt to take a phase-match for second harmonic generation. 
     As described above, if a second harmonic generating device is constructed such that the &lt;100&gt; direction of the semiconductor crystals within the cavity makes an angle of 5° or more with respect to the direction of the light rays (for example, the bearing of the substrate surface), or such that any one of the &lt;100&gt;, &lt;211&gt; or &lt;100&gt; bearings of the crystals within the cavity roughly matches the direction of the light rays, it is possible to make a highly efficient extraction of the second harmonic. 
     By using a material with a large non-linear coefficient, for example GaAs, ZnSe etc., as a zincblende structure crystal, there is an even higher generation efficiency of the second harmonic. 
     As regards the second harmonic, when a phase-matching layer is not inside the cavity, the second harmonic generation is not very efficient, due to negative phase interference, etc. In order to prevent this, the present invention may provide a phase-matching layer of a compound semiconductor constructed between the reflector which transmits the second harmonic and the spacer layer which is positioned on the reflector side. The term &#34;phase-matching layer&#34; referred in the present invention means a layer provided for optimally generating a second harmonic, and it may be made from either a material having or not having a superlattice structure. An embodiment using a superlattice structured material for the phase-matching layer is described below. Where a superlattice is used as a phase-matching layer, a variety of methods may be utilized to create the phase-matching layer according to the present invention, including a method which modulates the value of the nonlinear coefficient and a method which inverts the sign, etc. 
     When phase matching is done by modulation of the non-linear coefficient, the superlattice structure is alternately laminated with different compositions and/or different group compound semiconductors, for example, a III-V group compound semiconductor (such as AlGaAs, InGaAs, AIGaInP, GainAsP, etc.) and a II-VI group compound semiconductor (such as ZnCdSSe, ZnSSe, ZnCdS, ZnCdSe, ZnMgSS etc.). In this manner, it is possible to reduce the negative phase interference of the second harmonic. 
     In realizing the phase-matching by reversing the minus and plus signs of the non-linear coefficient, a layer of a different semiconductor (e.g., Si) is incorporated during growing a crystal of, for example, GaAs, at a thickness as thin as possible (a thickness corresponding to one to several atomic layers, for example, several angstrom (Å)). 
     If a sufficiently intense optical output can be obtained even when the phase-matching layer is reduced to a thickness thinner than the value at which a negative interference should occur (for example, half of coherent length), the phase-matching layer need not have a superlattice structure. In such cases, optimal generation of second harmonic, inclusive of the laser operation, can be easily achieved by forming the phase matching layer separately from the active layer and the spacer layer. Moreover, a surface emitting second harmonic generating device according to the present invention with lower power consumption can be fabricated at reduced cost because the fabrication process can be made simpler. 
     It is further possible to form the spacer layer at the second harmonic output side, as well as the active layer and both of the spacer layers, using a superlattice of a compound semiconductor constructed as a phase-matching layer. In such a case, if the number of laminations of the superlattice is increased, the efficiency of generation of the second harmonic is improved, but if the number is excessively increased, a stronger electrical resistance results and the generation of the fundamental wave itself is reduced. 
     The following is a more concrete description of the above principle. Along with the fundamental wave (for example, wavelength λ 1 ) inside the cavity, the second harmonic thereof (in this case, blue light of wavelength λ 2  λ 1  /2) is generated. As the fundamental wave is reflected inside the cavity by a reflector with a high reflectivity for the fundamental wave (for example, a reflectivity of 99% or over), the power of the wave becomes higher. On the other hand, the second harmonic is emitted out of the device by the output terminal reflector which transmits the second harmonic (for example, with a transmissivity of 50% or over). 
     The power of the fundamental wave is extremely high in a vertical cavity surface emitting laser. The efficiency of generation of the second harmonic is proportional to the power of the fundamental wave, and thus a high-power second harmonic is generated. 
     Also, when the second harmonic is not phase-matched inside the cavity, the generated light is not efficiently amplified. It is therefore favorable to include a phase-matching layer inside the cavity, or to have the spacer layer and the active layer composed of a superlattice functioning as a phase-matching layer. Thus, a surface emitting device provided in accordance with the present invention generates a second harmonic with high efficiency. 
     Further, a second harmonic generating device according to the present invention may be constructed by using various types of surface emitting lasers, such as: 
     (1) a buried structure surface emitting laser; 
     (2) a mesa-cap structure surface emitting laser; 
     (3) a DBR surface emitting laser; 
     (4) a multi-quantum well surface emitting laser; 
     (5) a single-quantum well surface emitting laser; 
     (6) a multi-quantum-barrier surface emitting laser; 
     (7) a strained surface emitting laser; or 
     (8) combinations of (1)-(7); 
     and by adjusting the substrate orientation, and forming a phase-matching layer, or a spacer layer or active layer, etc., having phase-matching effect. 
     In addition, in a surface emitting second harmonic generating device according to the present invention, III-V compound semiconductors, such as GaAs, AlGaAs, GainAsP, AIGaInP, GaInAs and II-VI compound semiconductors such as ZnSe, ZnMgSSe, CdZnSe, CdZnS, CdSSe, CdZnSSe, etc., may be utilized, depending on the wavelength of the fundamental wave, while GaAs, GaAsP, GaP, ZnSe, etc., may be utilized as the substrate. 
     FIG. 1 is a cross-sectional diagram of an example of a surface emitting second harmonic generating device according to the present invention. The device in this example has a cavity, reflectors, etc., described below, which are constructed on a (111) GaAs substrate 1 (a substrate with a substrate orientation of [111]). A formed electrode 2 is formed on the bottom of the substrate, and a reflector 3 composed of multi-layer film is provided on the upper side of the formed electrode 2. Further, as described above, the orientation of the semiconductor crystals within the cavity is assumed to be identical to the substrate orientation, and thus the orientation of the latter determines that of the former. 
     Formed on the upper side of the reflector 3 are a spacer layer 4, an active layer 5 and a spacer layer 6. Also, an insulation layer 11 is formed between the electrode 2 and the spacer layer 4 (except for the center section). 
     An electrode 7 is formed on the upper surface of the substrate 1, and the substrate is etched to form a second harmonic output port 8 on the side of the electrode 7. 
     In the output port 8, a phase-matching layer 9 is formed on the upper side of the spacer layer 6, and a reflector 10 for output of the second harmonic on the upper surface of the phase-matching layer 9 is paired with the reflector 3. 
     The cavity is composed of the above-mentioned reflectors 3, 10 and the layers formed between them (the layers comprised of the spacer layer 4, the active layer 5, the spacer layer 6 and the phase-matching layer 9). In this example, the phase-matching layer 9 does not lie between the electrodes 2, 7 (in the section through which no current flows), as shown in FIG. 1. Therefore, disadvantages such as a decrease in the power of the fundamental wave due to an increase in electric resistance do not arise. 
     FIG. 2 is an enlarged diagram of the vertical cavity in FIG. 1. In FIG. 2, a dielectric multi-layered film (composed of alternating layers of SiO 2  and TiO 2 ) is used to form the reflector 10 at the output side, by piling up about 10 pairs (or more, depending on the process used) of the alternating layers, whose thicknesses t may be expressed as 
     
         t.sub.d1 =λ.sub.1 /[4n.sub.d1 (λ.sub.1)]; and 
    
     
         t.sub.d2 =λ.sub.1 /[4n.sub.d2 (λ.sub.1)], respectively. 
    
     Here, n(λ) is the refractive index at the wavelength, while the λ 1  is the wavelength of the fundamental wave. The subscript d 1  denotes the film thickness and refractive index for SiO 2 , while the subscript d 2  denotes the film thickness and refractive index for TiO 2 . 
     The phase-matching layer 9 has a superlattice structure and is composed of two AlGaAs or ZnMgSSe layers with different contents of Al, represented by s1 and s2 (FIG. 2 shows the case of ZnMgSSe and composition ratio of S1 and S2 are represented by A and B respectively). Here, the thickness t s1 ,t s2  of each layer s1, s2 are determined using their respective reflective indices n s1  (λ) and n a2  (λ) in the following equation: 
     
         t.sub.s1 =[n.sub.s1 (λ.sub.2)/λ.sub.2 -2n.sub.s1 (λ.sub.1)/λ.sub.1 ].sup.-1 /2 
    
     
         t.sub.s2 =[n.sub.s2 (λ.sub.2)/λ.sub.2 -2n.sub.s2 (λ.sub.1)/λ.sub.1 ].sup.-1 /2               Equation 2 
    
     The total thickness of the phase-matching layer 9 is within a few times of the reciprocal of the average absorption constant in case of highly absorptive phase-matching layers. 
     In the above example, the substrate orientation was [111] (for example, a (111) substrate was employed); however, the present invention is not limited to this, as a second harmonic may be generated, albeit with a difference in efficiency using a substrate, wherein its orientation is greatly different from &lt;100&gt;; this means that the substrate orientation makes an angle of 5° or more with respect to the &lt;100&gt; direction of the substrate crystal. 
     The active layer 5 may by composed of AlGaAs, ZnSe, etc., its composition being determined according to the wavelength of the fundamental wave. In FIG. 2, ZnSe is utilized. In FIG. 2 a spacer layer 4, 6 is ZnMgSSe (composition ratio: C). 
     The composition of the reflectors 3, 10 is not necessarily restricted to dielectric multi-layered films, and may be, for example, of semiconductor multi-layered films, metallic films, or a combination of metallic and dielectric films. 
     The reflector 10 on the output end needs only to have a reflectivity high enough to cause lasing of the fundamental wave, and a transmissivity high enough to extract the generated second harmonic. The reflector 3 on the non-output end need only have a reflectivity high enough to cause lasing of the fundamental wave. A semiconductor multi-layered film reflector (often referred to as DBR) may be used because its electrical resistance is lower than that of the dielectric multi-layered film. 
     In the above example, the superlattice of the phase-matching layer 9 was composed of an AlGaAs or ZnMgSSe compound semiconductor, but it may be composed of any III-V compound semiconductor, such as InGaAs, AlGaInP, GainAsP, GaAsP, AIGaP, etc. It may also be composed of any II-VI group compound semiconductor such as ZnCdSSe, ZnSSe, ZnCdS, ZnCdSe, etc. 
     As described above, when the above mentioned phase-matching layer 9 is formed and a absorption of the phase-matching layer is very low, the width of the phase-matching layer 9 may be increased to a degree which is allowed by the fabrication process and which will support the lasing of the fundamental wave of the surface emitting laser. 
     Besides the above embodiments, any well-known method (see, for example, those shown in the reference by A. Yariv and the reference by D. Vahkshoori referred previously) may be employed to realize phase-matching. For example, the second harmonic may also be effectively generated even where the thickness of layers corresponding to Equation 2 takes the following values: 
     
         t.sub.s1 =λ.sub.2 /[2.sub.ns1 (λ.sub.2)] 
    
     
         t.sub.s2 =λ.sub.2 /[2.sub.ns2 (λ.sub.2) 
    
     This method is well known to realize phase-matching in standing waves. Also, those described before utilize modulation in the value of the non-linear coefficients, but phase-matching is also possible through changing signs of the non-linear coefficients. In addition to the method of modulation of a non-linear coefficient described in the above example in which the non-linear coefficient changes in a rectangular shape and each layer corresponds to half part of phase shift (phase shift between second harmonic propagating and second harmonic being generated), any other ways of modulation may be used - for example, modulation with continuously changing non-linear coefficient or each layer not taking half part of phase shift, combination of the methods for propagating wave and standing wave etc., as long as the negative interference can be effectively prevented. Furthermore, due to the finite thickness of the whole phase-matching layers, the period of modulation of non-linear coefficient has a spectrum with finite line width and accompanies a corresponding tolerance in the layer thickness. 
     It is also possible to introduce a superlattice structure into the spacer layer or the active layer in order to fulfill the phase-matching condition, combining the function of these layers with that of the phase-matching layer. In other words, by utilizing (i) the spacer layer, (ii) the spacer layer and the active layer on the second harmonic output side, and (iii) both the spacer layers and the active layer as the phase-matching layer, it is possible to reduce the thickness of the phase-matching layer or eliminate it. 
     FIG. 3 illustrates an embodiment employing both the spacer layer and the active layer as the phase-matching layer. In this case, the thickness of the layer functioning as the phase-matching layer is adjusted to be a few times as great as the reciprocal of the absorption coefficient. As explained above, introduction of the superlattice being used as the phase-matching layer into the spacer layer or the active layer causes an increase in the electrical resistance of the semiconductor laser, resulting in a trade-off with efficiency of the second harmonic generation. 
     Nevertheless, the following statements are true: 
     (1) a phase-matching layer such as the one shown in FIG. 1 either becomes unnecessary or may be constructed more thinly; 
     (2) absorption loss of the fundamental wave is reduced due to (1); 
     (3) the modes are well unified, also due to (1); and 
     (4) the fabrication process is facilitated, also due to (1). 
     The present invention produces the following effects: 
     (1) A second harmonic may be emitted from a surface emitting device with high efficiency. Additionally, a wavelength from violet to green may be generated. Further, a wavelength from red to ultraviolet may be generated by modifying the materials, the substrate orientation, and composition of the reflectors. 
     (2) A second harmonic generating device having a small size, low energy consumption and low manufacturing cost may be provided by utilizing the inherent advantages of the surface emitting laser. Consequently, since a circular, single mode second harmonic may be generated, it may be efficiently coupled into fibers, etc. In addition, multiple devices can be easily arrayed, and it is possible to emit different monochrome wavelengths from each of the arrayed devices. 
     (3) A second harmonic generating devices utilizing the present invention can generate sufficient output at near-room temperature, thus have wider application area. 
     Although specific embodiments of the invention have been described and illustrated, the invention is not to be limited to the specific forms or arrangements of parts so described and illustrated, and various modifications and changes can be made without departing from the scope and spirit of the invention. Within the scope of the appended claims, therefore, the invention may be practiced otherwise than as specifically described and illustrated.