Abstract:
A semiconductor laser resonator configured to generate a laser beam includes a gain medium layer including a semiconductor material and comprising: a central portion; and protrusions periodically arranged around the central portion, one of the protrusions being configured to confine the laser beam as a standing wave in the one protrusion.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application claims the benefit of Korean Patent Application No. 10-2014-0111044, filed on Aug. 25, 2014, and Korean Patent Application No. 10-2015-0048324, filed on Apr. 6, 2015, in the Korean Intellectual Property Office, the disclosures of which are incorporated herein in their entirety by reference. 
       BACKGROUND 
       [0002]    1. Field 
         [0003]    The exemplary embodiments consistent with the present disclosure relate to a semiconductor laser resonator, and more particularly, to a semiconductor laser resonator capable of selecting or separating a resonant mode from other resonant modes, and a semiconductor laser device including the semiconductor laser resonator. 
         [0004]    2. Description of the Related Art 
         [0005]    A semiconductor laser resonator is the core component for obtaining an optical gain in a semiconductor laser device. In general, a gain medium of the semiconductor laser resonator has a circular disk shape or a rectangular shape, and a metal or a dielectric material surrounds the gain medium. However, the number of resonant modes generated by such a semiconductor laser resonator is high and the resonant modes are complicated. 
       SUMMARY 
       [0006]    Provided are semiconductor laser resonators capable of selecting or separating a resonant mode from other resonant modes, and semiconductor laser devices including the semiconductor laser resonators. 
         [0007]    Additional aspects will be set forth in part in the description which follows and, in part, will be apparent from the description, or may be learned by practice of the presented exemplary embodiments. 
         [0008]    According to an aspect of an example embodiment, a semiconductor laser resonator configured to generate a laser beam includes: a gain medium layer formed of a semiconductor material and including: a central portion; and protrusions periodically arranged around the central portion, wherein one of the protrusions is configured to confine the laser beam as a standing wave in the one protrusion. 
         [0009]    The semiconductor laser resonator may further include a metal layer provided outside the gain medium layer, the metal layer being configured to confine a laser beam generated by the gain medium layer. 
         [0010]    The semiconductor laser resonator may further include a buffer layer provided between the gain medium layer and the metal layer, the buffer layer being configured to buffer an optical loss of the laser beam generated by the gain medium layer. 
         [0011]    The semiconductor laser resonator may further include a dielectric layer provided outside the gain medium layer, the dielectric layer being configured to confine the laser beam generated by the gain medium layer, and having a refractive index different from a refractive index of the gain medium layer. 
         [0012]    The central portion may be configured to further confine the laser beam therein. 
         [0013]    The protrusions may have a same shape as each other. 
         [0014]    The protrusions may include a first protrusions each respectively having a first shape and f second protrusions each respectively having a second shape different from the first shape. 
         [0015]    The first and second protrusions may be alternately arranged around the central portion. 
         [0016]    The central portion may have a circular or quadrangular plane shape. 
         [0017]    The semiconductor laser resonator may further include a through hole formed in the central portion. 
         [0018]    The semiconductor laser resonator may further include recessed portions formed between the protrusions at regular intervals from each other. 
         [0019]    The recessed portions may be formed only at a part of the gain medium layer along a thickness direction of the gain medium layer. 
         [0020]    A number of the protrusions may be from 2 to 10, and an angle between two sides of one of the protrusions, the two sides extending from a center of the gain medium layer to an outer circumference of the gain medium layer, may be from 5° to 175°. 
         [0021]    A thickness of the gain medium layer may be less than or equal to 500 nm, an outer radius of the gain medium layer extending from the center of the gain medium layer to the outer circumference of the gain medium layer may be from 100 nm to 5,000 nm, an inner radius of the gain medium layer extending from the center of the gain medium layer to an inner side of the recessed portions may be from 100 nm to 4,000 nm, and a ratio of the inner radius to the outer radius may be from 0.02 to 1. 
         [0022]    The gain medium layer may include an active layer. 
         [0023]    The active layer may include at least one of a III-V group semiconductor material, a II-VI group semiconductor material, and quantum dots. 
         [0024]    The gain medium layer may further include: a first clad layer provided on a first surface of the active layer; and a second clad layer provided on a second surface of the active layer. 
         [0025]    The semiconductor laser resonator may further include: a first contact layer provided on a first surface of the gain medium layer; and a second contact layer provided on a second surface of the gain medium layer. 
         [0026]    The first contact layer and the second contact layer may have a shape corresponding to a shape of the gain medium layer. 
         [0027]    According to another aspect of another exemplary embodiment, a semiconductor laser device includes: a substrate; and a semiconductor laser resonator provided on the substrate and configured to generate a laser beam by absorbing energy, the semiconductor laser resonator includes a gain medium layer including a semiconductor material and further including: a central portion; and protrusions periodically arranged around the central portion, wherein one of the protrusions is configured to confine a standing wave in the one protrusion. 
         [0028]    The semiconductor laser device may further include a metal layer provided outside the gain medium layer, the metal layer being configured to confine the laser beam generated by the gain medium layer. 
         [0029]    The semiconductor laser device may further include a buffer layer provided between the gain medium layer and the metal layer, the buffer layer being configured to buffer an optical loss of the laser beam generated by the gain medium layer. 
         [0030]    The semiconductor laser device may further include a dielectric layer provided outside the gain medium layer, the dielectric layer being configured to confine the laser beam generated by the gain medium layer, and having a refractive index different from the gain medium layer. 
         [0031]    The central portion may have a circular or quadrangular plane shape. 
         [0032]    The semiconductor laser device may further include a through hole in the central portion. 
         [0033]    The semiconductor laser device may further include recessed portions formed between the protrusions at regular intervals from each other. 
         [0034]    The recessed portions may be formed only at a part of the gain medium layer along a thickness direction of the gain medium layer. 
         [0035]    The semiconductor laser device may further include: a first contact layer provided on a first surface of the gain medium layer; and a second contact layer provided on a second surface of the gain medium layer. 
         [0036]    The semiconductor laser device may further include electrodes electrically connected to the first contact layer and the second contact layer. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0037]    The patent or application file contains at least one drawing executed in color. Copies of this patent or patent application publication with color drawings(s) will be provided by the Office upon request and payment of the necessary fee. 
           [0038]    These and/or other aspects will become apparent and more readily appreciated from the following description of the exemplary embodiments, taken in conjunction with the accompanying drawings in which: 
           [0039]      FIG. 1  is a perspective view of a semiconductor laser device according to an exemplary embodiment; 
           [0040]      FIG. 2  is a partially cutaway perspective view of the semiconductor laser device of  FIG. 1 ; 
           [0041]      FIG. 3  is a cross-sectional view of the semiconductor laser device of  FIG. 1 ; 
           [0042]      FIGS. 4A and 4B  are respectively a perspective view and a plan view of a gain medium layer of a semiconductor device, according to an exemplary embodiment; 
           [0043]      FIG. 5  is a cross-sectional view of a semiconductor laser device according to another exemplary embodiment; 
           [0044]      FIG. 6  is a plan view and a perspective view of a general cylindrical gain medium layer; 
           [0045]      FIG. 7  illustrates a spectrum of a laser beam generated by the gain medium layer of  FIG. 6 ; 
           [0046]      FIGS. 8A ,  8 B,  8 C,  8 D,  8 E,  8 F and  8 G illustrate intensity distributions of an electric field of the laser beam generated by the gain medium layer of  FIG. 6 ; 
           [0047]      FIG. 9  illustrates a spectrum of a laser beam generated by the gain medium layer of  FIGS. 4A and 4B ; 
           [0048]      FIGS. 10A ,  10 B,  10 C and  10 D illustrate intensity distributions of an electric field of the laser beam generated by the gain medium layer of  FIGS. 4A and 4B ; 
           [0049]      FIG. 11  is a diagram for describing a relationship between wavelengths and a ratio of an inner radius to an outer radius of the gain medium layer of  FIGS. 4A and 4B ; 
           [0050]      FIGS. 12A and 12B  are respectively a perspective view and a plan view of a gain medium layer according to another exemplary embodiment; 
           [0051]      FIG. 13  illustrates a spectrum of a laser beam generated by the gain medium layer of  FIGS. 12A and 12B ; 
           [0052]      FIGS. 14A and 14B  illustrate intensity distributions of an electric field of the laser beam generated by the gain medium layer of  FIGS. 12A and 12B ; 
           [0053]      FIG. 15  is a diagram for describing a relationship between wavelengths and a ratio of an outer radius to an inner radius of the gain medium layer of  FIGS. 12A and 12B ; 
           [0054]      FIG. 16A  is a view of the gain medium layer of  FIGS. 12A and 12B , wherein silver (Ag) surrounds the gain medium layer and silicon oxide (SiO 2 ) covers an upper portion of the gain medium layer; 
           [0055]      FIGS. 16B ,  16 C,  16 D and  16 E illustrate intensity distributions of an electric field of a TE 21  mode laser beam generated by the gain medium layer of  FIG. 16A ; 
           [0056]      FIG. 16F  illustrates a spectrum of the TE 21  mode laser beam generated by the gain medium layer of  FIG. 16A ; 
           [0057]      FIG. 17  is a perspective view of a gain medium layer according to another exemplary embodiment; 
           [0058]      FIG. 18  is a perspective view of a gain medium layer according to another exemplary embodiment; 
           [0059]      FIG. 19  is a perspective view of a gain medium layer according to another exemplary embodiment; 
           [0060]      FIGS. 20A ,  20 B,  20 C and  20 D are perspective views of gain medium layers according to other exemplary embodiments; 
           [0061]      FIGS. 21A and 21B  are respectively a perspective view and a plan view of a gain medium layer according to another exemplary embodiment; 
           [0062]      FIG. 21C  illustrates intensity distributions of an electric field of a laser beam generated by the gain medium layer of  FIGS. 21A and 21B ; 
           [0063]      FIGS. 22A ,  22 B,  22 C and  22 D illustrate gain medium layers according to other exemplary embodiments; 
           [0064]      FIGS. 23A ,  23 B,  23 C,  23 D,  23 E and  23 F illustrate gain medium layers according to other exemplary embodiments; 
           [0065]      FIGS. 24A and 24B  illustrate gain medium layers according to other exemplary embodiments; 
           [0066]      FIGS. 25A and 25B  illustrate gain medium layers according to other exemplary embodiments; and 
           [0067]      FIG. 26  illustrates intensity distributions of an electric field of a laser beam generated by the gain medium layer of  FIG. 25A . 
       
    
    
     DETAILED DESCRIPTION 
       [0068]    Reference will now be made in detail to exemplary embodiments, examples of which are illustrated in the accompanying drawings, wherein like reference numerals refer to like elements throughout and thicknesses or sizes of elements may be exaggerated for clarity. When a certain material layer is disposed on a substrate or a layer, the certain material layer may be directly disposed on the substrate or the layer, or an intervening layer may be disposed therebetween. Also, since a material forming each layer is only an example, another material may be used to form the each layer. As used herein, the term “and/or” includes any and all combinations of one or more of the associated listed items. Expressions such as “at least one of,” when preceding a list of elements, modify the entire list of elements and do not modify the individual elements of the list. 
         [0069]      FIG. 1  is a perspective view of a semiconductor laser device  100  according to an exemplary embodiment.  FIG. 2  is a partial cutaway perspective view of the semiconductor laser device  100  of  FIG. 1 , and  FIG. 3  is a cross-sectional view of the semiconductor laser device  100  of  FIG. 1 . 
         [0070]    Referring to  FIGS. 1 through 3 , the semiconductor laser device  100  includes a substrate  110  and a semiconductor laser resonator that is provided on the substrate  110  and generates a laser beam by absorbing external energy. The substrate  110  may be a semiconductor substrate, but is not limited thereto, and may be formed of any material, such as glass. In detail, the substrate  110  may be an indium phosphide (InP) substrate, but is not limited thereto. The semiconductor laser resonator may include a gain medium layer  120  that generates a laser beam by absorbing energy via optical pumping or electric pumping. 
         [0071]    The gain medium layer  120  may include an active layer  123  that includes a semiconductor material. The active layer  123  may include, for example, a III-V group semiconductor material or a II-VI group semiconductor material. Alternatively, the active layer  123  may include quantum dots. In detail, the active layer  123  may include a multi-quantum wall including indium gallium arsenide (InGaAs), aluminum gallium arsenide (AlGaAs), indium gallium arsenide phosphide (InGaAsP), or aluminum gallium indium phosphide (AlGaInP), but is not limited thereto. The gain medium layer  120  may further include first and second clad layers  121  and  122  respectively provided on upper and lower portions of the active layer  123 . 
         [0072]    The first clad layer  121  is provided on a first surface of the active layer  123  (a top surface of the active layer  123  in  FIG. 3 ), and may include an n- or p-type semiconductor material. In detail, the first clad layer  121  may include an n-type InP or a p-type InP, but is not limited thereto. The second clad layer  122  may be provided on a second surface of the active layer  123  (a bottom surface of the active layer  123  in  FIG. 3 ). If the first clad layer  121  includes an n-type semiconductor material, the second clad layer  122  may include a p-type semiconductor material. Alternatively, if the first clad layer  121  includes a p-type semiconductor material, the second clad layer  122  may include an n-type semiconductor material. In detail, the second clad layer  122  may include a p-type InP or an n-type InP, but is not limited thereto. 
         [0073]    A first contact layer  131  may be provided on a top surface of the first clad layer  121 . The first contact layer  131  may have a shape corresponding to the gain medium layer  120 . However, the shape of the first contact layer  131  is not limited thereto, and may vary. A shape of the gain medium layer  120  will be described in detail later. If the first clad layer  121  includes an n-type semiconductor material, the first contact layer  131  may include an n-type semiconductor material, and if the first clad layer  121  includes a p-type semiconductor material, the first contact layer  131  may include a p-type semiconductor material. In detail, the first contact layer  131  may include an n-type InGaAs or a p-type InGaAs, but is not limited thereto. An electrode (not shown) electrically connected to the first contact layer  131  may be further provided. 
         [0074]    A second contact layer  132  may be provided on a bottom surface of the second clad layer  122 . The second contact layer  132  may be provided on a top surface of the substrate  110 . If the second clad layer  122  includes a p-type semiconductor material, the second contact layer  132  may include a p-type semiconductor material, and if the second clad layer  122  includes an n-type semiconductor material, the second contact layer  132  may include an n-type semiconductor material. In detail, the second contact layer  132  may include a p-type InGaAs or an n-type InGaAs, but is not limited thereto. An electrode  160  that is electrically connected to the second contact layer  132  may be further provided on the substrate  110 . If the second contact layer  132  includes a p-type semiconductor material, the electrode  160  may be a p-type electrode, and if the second contact layer  132  includes an n-type semiconductor material, the electrode  160  may be an n-type electrode. 
         [0075]    A metal layer  150  may be further provided to cover the gain medium layer  120  and the first contact layer  131 . The metal layer  150  is provided outside the gain medium layer  120  to confine, in the gain medium layer  120 , a laser beam generated by the gain medium layer  120 . The metal layer  150  may include silver (Ag), gold (Au), copper (Cu), or aluminum (Al), but is not limited thereto and may include any metal material. 
         [0076]    A buffer layer  142  may be further provided between the metal layer  150  and the gain medium layer  120 . The buffer layer  142  may be provided between the metal layer  150  and a side surface of the gain medium layer  120 . The buffer layer  142  may buffer an optical loss that may occur when the laser beam generated by the gain medium layer  120  contacts the metal layer  150 . The buffer layer  142  may include a material having a refractive index different from the gain medium layer  120 . In detail, the buffer layer  142  may include a material having a refractive index smaller than the gain medium layer  120 . For example, the buffer layer  142  may include silicon oxide or silicon nitride, but is not limited thereto. The buffer layer  142  may extend from the side surface of the gain medium layer  120  to cover the second contact layer  132 . 
         [0077]      FIGS. 4A and 4B  are respectively a perspective view and a plan view of the gain medium layer, according to an exemplary embodiment. 
         [0078]    Referring to  FIGS. 4A and 4B , the gain medium layer  120  includes a central portion  120   a  and a plurality of protrusions  120   b  in an outer region of the central portion  120   a . The protrusions  120   b  may be arranged periodically around the outer region of the central portion  120   a , and a plurality of recessed portions  120   c  may be formed between the protrusions  120   b  at regular intervals from each other. In  FIGS. 4A and 4B , the four protrusions  120   b  having the same shape are provided in the outer region of the central portion  120   a.    
         [0079]    The central portion  120   a  of the gain medium layer  120  may have, for example, a circular plane shape. In  FIG. 4A , t denotes a thickness of the gain medium layer  120 . The gain medium layer  120  may have a thickness t in a micro-size or a nano-size, but is not limited thereto. For example, the gain medium layer  120  may have a thickness lower than or equal to about 500 nm. 
         [0080]    In  FIG. 4B , r 1  denotes an outer radius of the gain medium layer  120 , and r 2  denotes an inner radius of the gain medium layer  120 . The gain medium layer  120  may have an outer diameter in a micro-size or a nano-size. The outer diameter of the gain medium layer  120  may be lower than or equal to about 10 μm, but is not limited thereto. For example, the outer radius r 1  of the gain medium layer may be from about 100 nm to about 5,000 nm, and the inner radius r 2  of the gain medium layer  120  may be from about 100 nm to about 4,000 nm. Here, a ratio of the inner radius r 2  to the outer radius r 1 , e.g., r 2 /r 1 , may be from about 0.02 to about 1. Also, θ 1  and θ 2  respectively denote an angle of the protrusion  120   b  and an angle of the recessed portion  120   c . Here, the angle θ 1  of the protrusion  120   b  may be from about 5° to about 175°. Since the protrusion  120   b  and the recessed portion  120   c  exist as a pair, the angle θ 2  of the recessed portion  120   c  may be from about 175° to about 5° considering at least two pairs of the protrusion  120   b  and the recessed portion  120   c  may be provided. The gain medium layer  120  having such a minute size may be formed via a patterning process, such as photolithography, e-beam lithography, plasmonic lithography, or a focused ion beam (FIB) technique. 
         [0081]    As described hereinabove, the central portion  120   a  of the gain medium layer  120  has a circular plane shape, but as will be described below, the central portion  120   a  may have another plane shape. For example, the central portion  120   a  of the gain medium layer  120  may have a quadrangular plane shape, such as a rectangular or a square plane shape. Also, as described hereinabove, the four protrusions  120   b  having the same shape are provided in the outer region of the central portion  120   a  of the gain medium layer  120 , but the number of the protrusions  120   b  may vary. For example, the number of the protrusions  120   b  may be from 2 to 10. Also, hereinabove, the protrusions  120   b  have the same shape, but may alternatively have different shapes. 
         [0082]    In the gain medium layer  120  having such a structure, the protrusions  120   b  are arranged in the periodic structure along the outer region of the central portion  120   a , and thus, a laser beam generated by the gain medium layer  120  may be confined as standing waves in at least one of the protrusions  120   b . Confining the laser beam as standing waves in the protrusions  120   b  refers to a feature by which intensity of the laser beam may change according to time but the laser beam is confined at certain positions in the protrusions  120   b . The intensity of the laser beam confined in the protrusions  120   b  may decrease towards a surface of the protrusions  120   b . The laser beam generated by the gain medium layer  120  may be confined not only in the protrusions  120   b  but also in the central portion  120   a.    
         [0083]    As such, since the laser beam generated by the gain medium layer  120  is confined as standing waves in at least one of the protrusions  120   b , a resonant mode of a desired wavelength may be easily selected as will be described later. Also, resonant modes that are not desired may be removed or a resonant mode that is desired may be effectively separated from other resonant modes. Accordingly, a Q-factor of the semiconductor laser resonator may be improved. A resonant mode may be selected and/or separated based on at least one of the number, shape, and size of the protrusions  120   b  and an interval between the protrusions  120   b . Also, by providing the metal layer  150  outside the gain medium layer  120 , the laser beam generated by the gain medium layer  120  may be efficiently confined. 
         [0084]      FIG. 5  is a cross-sectional view of the semiconductor laser device according to another exemplary embodiment. 
         [0085]    Referring to  FIG. 5 , a dielectric layer  170  is provided to cover the gain medium layer  120 . The dielectric layer  170  may be provided on a side surface of the gain medium layer  120 . Such a dielectric layer  170  confines the laser beam generated by the gain medium layer  120 . Accordingly, the dielectric layer  170  may include a material having a refractive index different from the gain medium layer  120 . In detail, the dielectric layer  170  may include material having a refractive index smaller than the gain medium layer  120 . The dielectric layer  170  may include, for example, silicon oxide or silicon nitride, but is not limited thereto. 
         [0086]      FIG. 6  is a plan view and a perspective view of a general cylindrical gain medium layer.  FIG. 7  illustrates a spectrum of a laser beam generated by the general cylindrical gain medium layer of  FIG. 6 . In detail,  FIG. 7  illustrates fast Fourier transform (FFT) magnitude of an electric field according to a wavelength of the laser beam. Also,  FIGS. 8A through 8G  illustrate intensity distributions of an electric field of the laser beam generated by the general cylindrical gain medium layer of  FIG. 6 . In detail,  FIGS. 8A through 8G  respectively illustrate intensity distributions of an electric field according to wavelengths of the laser beam. In  FIGS. 8A through 8G , a red region indicates a region where intensity of an electric field is strong, and a blue region indicates a region where intensity of an electric field is weak.  FIGS. 7 and 8A  through  8 G illustrate results obtained via simulation when the general cylindrical gain medium layer  20  of  FIG. 6  is formed of InGaAs having a refractive index n of 3.55, has a radius r 0  and a thickness t respectively of 400 nm and 200 nm, and is surrounded by Ag, and an electric dipole is set in a z-axis direction. 
         [0087]    Referring to  FIGS. 7 and 8A  through  8 G, a TM 21 -like resonant mode of 2.077 μm wavelength, a TM 02 -like resonant mode of 1.941 μm wavelength, a TM 41 -like resonant mode of 1.439 μm wavelength, a TM 22 -like resonant mode of 1.311 μm wavelength, a TM 03 -like resonant mode of 1.280 μm wavelength, a hybrid resonant mode of 1.142 μm wavelength, and a hybrid resonant mode of 1.054 μm wavelength are generated in the general cylindrical gain medium layer  20  of  FIG. 6 . According to an exemplary embodiment, a TM mn  resonant mode denotes a transverse magnetic resonant mode representing an electromagnetic field in a resonator when a magnetic field is generated perpendicular to a proceeding direction of electromagnetic waves. In a resonator including the gain medium layer  20  of  FIG. 6 , a proceeding direction of an electromagnetic field is assumed to be a z-axis for convenience. Thus, in a TM resonant mode, a magnetic field is generated on an x-y plane that is perpendicular to the z-axis, and an electric field is generated on the z-axis. m and n are each an integer and respectively indicate a mode number of an azimuthal direction and a mode number of a radial direction. For example, TM 21  resonant mode is a TM resonant mode wherein a mode number of an azimuthal direction is 2 and a mode number of a radial direction is 1, and TM 22  resonant mode is a TM resonant mode wherein a mode number of an azimuthal direction is 2 and a mode number of a radial direction is 2. As such, since many resonant modes are generated in the general cylindrical gain medium layer  20  of  FIG. 6 , it is difficult to easily select a resonant mode of a desired wavelength from among the many resonant modes. 
         [0088]      FIG. 9  illustrates a spectrum of the laser beam generated by the gain medium layer of 120  FIGS. 4A and 4B . In detail,  FIG. 9  illustrates an FFT magnitude of an electric field according to wavelengths of the laser beam. Also,  FIGS. 10A through 10D  illustrate intensity distributions of an electric field of the laser beam generated by the gain medium layer  120  of  FIGS. 4A and 4B . In detail,  FIGS. 10A through 10D  respectively illustrate intensity distributions of an electric field according to wavelengths of the laser beam. In  FIGS. 10A through 10D , a red region indicates a region where intensity of an electric field is strong, and a blue region indicates a region where intensity of an electric field is weak.  FIGS. 9 and 10A  through  10 D illustrate results obtained via simulation when the gain medium layer  120  of  FIGS. 4A and 4B  having the four protrusions  120   b  is formed of InGaAs having a refractive index n of 3.55, has an outer radius r 1 , an inner radius r 2 , a thickness t, an angle θ 1  of the protrusion  120   b , and an angle θ 2  of the recessed portion  120   c  respectively of 400 nm, 300 nm (r 2 /r 1 =0.75), 200 nm, 84°, and 6°, and is surrounded by Ag, and an electric dipole is set in a z-axis direction. 
         [0089]    Referring to  FIGS. 9 and 10A  through  10 D, a TM 21 -like resonant mode of 2.077 μm wavelength, a hybrid resonant mode of 1.870 μm wavelength, a TM 22 -like resonant mode of 1.311 μm wavelength, and a hybrid resonant mode of 1.227 μm wavelength are generated in the gain medium layer  120  of  FIGS. 4A and 4B . The laser beam generated by the gain medium layer  120  may be confined as standing waves in the protrusions  120   b . Also, the laser beam may not only be confined in the protrusions  120   b  but also be confined in the central portion  120   a  according to a resonant mode. Also, as shown in  FIGS. 10A through 10D , the intensity of the laser beam confined in the protrusions  120   b  decreases towards the surface of the protrusions  120   b.    
         [0090]    As described above,  FIG. 7  illustrates a spectrum of the laser beam generated by the general cylindrical gain medium layer  20  of  FIG. 6  and  FIG. 9  illustrates a spectrum of the laser beam generated by the gain medium layer  120  of  FIGS. 4A and 4B . 
         [0091]    Referring to  FIGS. 7 and 9 , the resonant mode of 1.439 μm wavelength, the resonant mode of 1.142 μm wavelength, and the resonant mode of 1.054 μm wavelength from among the resonant modes generated in the general cylindrical medium layer  20  of  FIG. 6  are not generated in the gain medium layer  120  of  FIGS. 4A and 4B . Accordingly, only a desired resonant mode may be easily selected by removing undesired resonant modes in the gain medium layer  120  of  FIGS. 4A and 4B . Also, the resonant mode of 2.077 μm wavelength generated in the gain medium layer  120  of  FIGS. 4A and 4B  has a larger FFT magnitude of an electric field compared to the resonant mode of 2.077 μm wavelength generated in the general cylindrical gain medium layer  20  of  FIG. 6 . Accordingly, a resonant mode of a desired wavelength may be further strengthened in the gain medium layer  120  of  FIGS. 4A and 4B . 
         [0092]      FIG. 11  is a diagram for describing a relationship between wavelengths and a ratio of the inner radius r 2  to the outer radius r 1  of the gain medium layer  120  of  FIGS. 4A and 4B .  FIG. 11  illustrates results obtained via simulation when the gain medium layer  120  is formed of InGaAs having the refractive index n of 3.55, has the outer radius r 1 , the thickness t, the angle θ 1  of the protrusion  120   b , and the angle θ 2  of the recessed portion  120   c  respectively of 400 nm, 200 nm, 84°, and 6°, and is surrounded by Ag. 
         [0093]    In  FIG. 11 , the outer radius r 1  of the gain medium layer  120  has the same uniform value as the radius r 0  of the gain medium layer  20  of  FIG. 6 , whereas a value of the inner radius r 2  of the gain medium layer  120  is gradually decreased. Referring to  FIG. 11 , when the ratio of the inner radius r 2  to the outer radius r 1  is 1, the gain medium layer  120  is the same as the general cylindrical gain medium layer  20  of  FIG. 6 , and the spectrum of the laser beam and the intensity distributions of the electric field are shown in  FIGS. 7 and 8A  through  8 G. Also, the spectrum of the laser beam and the intensity distributions of the electric field when r 2 /r 1  is 0.75 are shown in  FIGS. 9 and 10A  through  10 D. 
         [0094]    When r 2 /r 1  is equal to or higher than 0.75, the resonant mode of 1.439 μm wavelength generated in the general cylindrical gain medium layer  20  of  FIG. 7  is gradually weakened as the inner radius r 2  of the gain medium layer  120  is decreased, whereas the resonant mode of 1.870 μm wavelength generated in the gain medium layer  120  of  FIG. 9  is gradually strengthened as the inner radius r 2  of the gain medium layer  120  is decreased. Alternatively, when r 2 /r 1  is lower than or equal to 0.75, the resonant mode of 1.439 μm wavelength generated in the general cylindrical gain medium layer  20  of  FIG. 7  disappears and then appears as the inner radius r 2  of the gain medium layer  120  is decreased, whereas the resonant mode of 1.870 urn wavelength generated in the gain medium layer  120  of  FIG. 9  is gradually strengthened as the inner radius r 2  of the gain medium layer  120  is decreased. Meanwhile, the resonant mode of 2.077 μm wavelength exists regardless of a value of r 2 /r 1  because the resonant mode of 2.077 μm wavelength is formed symmetric in 90° such as not to be affected by the inner radius r 2  of  FIGS. 4A and 4B . 
         [0095]    As such, by adjusting the ratio of the inner radius r 2  to the outer radius r 1  of the gain medium layer  120 , a resonant mode of an undesired wavelength may be removed or a resonant mode of a desired wavelength may be generated. 
         [0096]      FIGS. 12A and 12B  are respectively a perspective view and a plan view of a gain medium layer according to another exemplary embodiment. 
         [0097]    Referring to  FIGS. 12A and 12B , the gain medium layer  220  includes a central portion  220   a  and a plurality of protrusions  220   b  which are protrudably provided in an outer region of the central portion  220   a . The protrusions  220   b  may be arranged in a periodic structure along the outer region of the central portion  220   a , and a plurality of recessed portions  220   c  may be formed between the plurality of protrusions  220   b  at regular intervals. In  FIGS. 12A and 12B , the four protrusions  220   b  having the same shape are provided in the outer region of the central portion  220   a . The central portion  220   a  of the gain medium layer  220  may have a circular plane shape. In  FIG. 12A , t denotes a thickness of the gain medium layer  220 , and in  FIG. 12B , r 1  denotes an outer radius of the gain medium layer  220  and r 2  denotes a radius of the central portion  220   a , e.g., an inner radius of the gain medium layer  220 . Also, θ 1  and θ 2  respectively denote angles of the protrusion  220   b  and the recessed portion  220   c . The gain medium layer  220  of  FIGS. 12A and 12B  may have the outer radius r 1  and the angle θ 2  of the recessed portion  220   c  larger than the gain medium layer  120  of  FIGS. 4A and 4B . 
         [0098]    According to the gain medium layer  220 , since the protrusions  220   b  are arranged in the periodic structure along the outer region of the central portion  220   a , a laser beam generated by the gain medium layer  220  may be confined as standing waves in at least one of the protrusions  220   b . An intensity of the laser beam confined in the protrusions  220   b  may decrease towards a surface of the protrusions  220   b . Meanwhile, the laser beam generated by the gain medium layer  220  may be confined not only in the protrusions  220   b  but also in the central portion  220   a.    
         [0099]      FIG. 13  illustrates a spectrum of the laser beam generated by the gain medium layer  220  of  FIGS. 12A and 12B . In detail,  FIG. 13  illustrates an FFT magnitude of an electric field according to wavelengths of the laser beam. Also,  FIGS. 14A and 14B  illustrate intensity distributions of an electric field of the laser beam generated by the gain medium layer  220  of  FIGS. 12A and 12B . In detail,  FIGS. 14A and 14B  respectively illustrate intensity distributions of an electric field according to wavelengths of the laser beam. In  FIGS. 14A and 14B , a red region indicates a region where intensity of an electric field is high and a blue region indicates a region where intensity of an electric field is low.  FIGS. 13 ,  14 A and  14 B illustrate results obtained via simulation when the gain medium layer  220  of  FIGS. 12A and 12B  having the four protrusions  220   b  is formed of InGaAs having a refractive index n of 3.55, has an outer radius r 1 , an inner radius r 2 , a thickness t, an angle θ 1  of the protrusion  220   b , and an angle θ 2  of the recessed portion  220   c  respectively of 450 nm, 400 nm (r 2 /r 1 =0.89), 200 nm, 60°, and 30°, and is surrounded by Ag, and an electric dipole is set in a z-axis direction. 
         [0100]    Referring to  FIGS. 13 ,  14 A, and  14 B, a TM 21 -like resonant mode of 2.328 μm wavelength and a TM 22 -like resonant mode of 1.470 μm wavelength are generated in the gain medium layer  220  of  FIGS. 12A and 12B . Here, the laser beam generated by the gain medium layer  220  may be confined as standing waves in the protrusions  220   b . The intensity of the laser beam confined in the protrusions  220   b  may decrease towards the surface of the protrusions  220   b.    
         [0101]    As described above,  FIG. 7  illustrates the spectrum of the laser beam generated by the general cylindrical gain medium layer  20  of  FIG. 6  and  FIG. 13  illustrates the spectrum of the laser beam generated by the gain medium layer  220  of  FIGS. 12A and 12B . 
         [0102]    Referring to  FIGS. 7 and 13 , the resonant mode of 1.439 μm wavelength, the resonant mode of 1.280 μm wavelength, the resonant mode of 1.142 μm wavelength, and the resonant mode of 1.054 μm wavelength from among the resonant modes generated in the general cylindrical medium layer  20  of  FIG. 6  are not generated in the gain medium layer  220  of  FIGS. 12A and 12B . Accordingly, only a desired resonant mode may be easily selected by removing undesired resonant modes in the gain medium layer  220  of  FIGS. 12A and 12B . Also, the TM 21 -like resonant mode of 2.077 μm wavelength and the TM 22 -like resonant mode of 1.311 μm wavelength generated in the general cylindrical gain medium layer  20  of  FIG. 6  are respectively changed to the TM 21 -like resonant mode of 2.328 μm wavelength and the TM 22 -like resonant mode of 1.470 μm wavelength in the gain medium layer  220  of  FIGS. 12A and 12B . As such, a wavelength of a certain resonant mode increases in the gain medium layer  220  of  FIGS. 12A and 12B  compared to the general cylindrical gain medium layer  20  of  FIG. 6 , because a size of the gain medium layer  220  of  FIGS. 12A and 12B  is larger than that of the general cylindrical gain medium layer  20  of  FIG. 6 . Also, as shown in  FIGS. 7 and 13 , an interval between the TM 21 -like resonant mode of 2.328 μm wavelength and the TM 22 -like resonant mode of 1.470 μm wavelength generated in the gain medium layer  220  of  FIGS. 12A and 12B  is greater than an interval between the TM 21 -like resonant mode of 2.077 μm wavelength and the TM 22 -like resonant mode of 1.311 μm wavelength generated in the general cylindrical gain medium layer  20  of  FIG. 6 . Accordingly, resonant modes may be easily separated or selected in the gain medium layer  220  of  FIGS. 12A and 12B  compared to the general cylindrical gain medium layer  20  of  FIG. 6 . 
         [0103]      FIG. 15  is a diagram for describing a relationship between wavelengths and a ratio of the outer radius r 1  to the inner radius r 2  of the gain medium layer  220  of  FIGS. 12A and 12B .  FIG. 15  illustrates results obtained via simulation when the gain medium layer  220  is formed of InGaAs having the refractive index n of 3.55, has the inner radius r 2 , the thickness t, the angle θ 1  of the protrusion  220   b , and the angle θ 2  of the recessed portion  220   c  respectively of 400 nm, 200 nm, 60°, and 30°, and is surrounded by Ag. 
         [0104]    In  FIG. 15 , the inner radius r 2  of the gain medium layer  220  has the same uniform value as the radius r 0  of the cylindrical gain medium layer  20  of  FIG. 6 , whereas the radius r 1  of the gain medium layer  220  is gradually increased. Referring to  FIG. 15 , when r 1 /r 2  is 1, the gain medium layer  220  is the same as the general cylindrical gain medium layer  20  of  FIG. 6 , and the spectrum of the laser beam and the intensity distributions of the electric field are shown in  FIGS. 7 and 8A  through  8 G. Also, the spectrum of the laser beam and the intensity distributions of the electric field when r 1 /r 2  is 1.125 are shown in  FIGS. 13 ,  14 A, and  14 B. 
         [0105]    When r 1 /r 2  is lower than or equal to 1.125, the resonant mode of 1.459 μm generated in the cylindrical gain medium layer  20  of  FIG. 7  is gradually weakened as the outer radius r 1  is increased. Also, when r 1 /r 2  becomes 1.125 as the outer radius r 1  increases, the TM 21 -like resonant mode of 2.077 μm wavelength and the TM 22 -like resonant mode of 1.311 μm wavelength generated in the general cylindrical gain medium layer  20  of  FIG. 6  move to the TM 21 -like resonant mode of 2.328 μm wavelength and the TM 22 -like resonant mode of 1.470 μm wavelength. Also, when r 1 /r 2  is higher than or equal to 1.125, the resonant mode of 1.439 μm wavelength generated in the general cylindrical gain medium layer  20  of  FIG. 6  disappears as the outer radius r 1  increases. As such, by adjusting the ratio of the outer radius r 1  to the inner radius r 2  of the gain medium layer  220 , a resonant mode of an undesired wavelength may be removed or a resonant mode of a desired wavelength may be generated. 
         [0106]      FIG. 16A  is a view of the gain medium layer  220  of  FIGS. 12A and 12B , wherein Ag surrounds the gain medium layer  220  and silicon oxide (SiO 2 ) covers an upper portion of the gain medium layer  220 . Since each portion of the gain medium layer  220  of  FIG. 16A  is described in detail above with reference to the gain medium layer  220  of  FIGS. 12A and 12B , details thereof are not provided again. Also,  FIGS. 16B through 16E  illustrate intensity distributions of an electric field of a TE 21  mode laser beam generated by the gain medium layer  220  of  FIG. 16A . Here, TE mn  mode denotes a transverse electric mode representing an electromagnetic field in a resonator when an electric field is generated perpendicular to a proceeding direction of electromagnetic waves. In a resonator including the gain medium layer  220  of  FIG. 16A , electromagnetic waves are confined in the resonator but since some of the electromagnetic waves are coupled to an upper SiO2 layer and are discharged, a proceeding direction of an electromagnetic field may be assumed to be a z-axis. Accordingly, at this time, an electric field is generated on an x-y plane perpendicular to the z-axis in a TE resonant mode. According to an exemplary embodiment, m and n are each an integer and respectively denote a mode number of an azimuthal direction and a mode number of a radial direction. In detail,  FIGS. 16B ,  16 C, and  16 D illustrate intensity distributions of an electric field on an x-y plane, in an x-axis direction, and in a y-axis direction of the TE 21  mode laser beam generated by the gain medium layer  220  of  FIG. 16A , and  FIG. 16E  illustrates intensity distributions of an electric field viewed from an z-x cross section. In  FIGS. 16B through 16E , a red region denotes a region where intensity of an electric field is strong and a blue region denotes a region where intensity of an electric field is weak. Also,  FIG. 16F  illustrates a spectrum of the TE 21  mode laser beam generated by the gain medium layer  220  of  FIG. 16A .  FIGS. 16B through 16F  illustrate results obtained via simulation when the gain medium layer  220  of  FIGS. 12A and 12B  having the four protrusions  220   b  is formed of InP and has the outer radius r 1 , the inner radius r 2 , the thickness t, the angle θ 1  of the protrusion  220   b , and the angle θ 2  of the recessed portion  220   c  respectively of 400 nm, 250 nm, 235 nm, 60°, and 30°, lower and upper portions of the gain medium layer  220  are respectively covered by Ag and SiO 2 , and an electric dipole is set in a y-axis direction. Referring to  FIGS. 16B through 16F , only one TE 21  like resonant mode of about 2.410 μm wavelength is generated. Accordingly, the laser beam generated by the gain medium layer  220  may be designed to have a desired wavelength and a desired resonant mode. 
         [0107]      FIG. 17  is a perspective view of a gain medium layer according to another exemplary embodiment. 
         [0108]    Referring to  FIG. 17 , the gain medium layer  320  includes a central portion  320   a  and a plurality of protrusions  320   b  around the central portion  320   a . The protrusions  320   b  may be arranged in a periodic structure around the central portion  320   a , and a plurality of recessed portions  320   c  may be formed between the protrusions  320   b  at regular intervals from each other. The central portion  320   a  may have, for example, a circular plane shape, but is not limited thereto. In  FIG. 17 , four protrusions  320   b  are provided around the central portion  320   a . The recessed portions  320   c  between the protrusions  320   b  may have a uniform width along a radius direction of the gain medium layer  320 . 
         [0109]      FIG. 18  is a perspective view of a gain medium layer  420  according to another exemplary embodiment. 
         [0110]    Referring to  FIG. 18 , six protrusions  420   b  having the same shape are provided around the central portion  420   a  in a periodic structure, wherein a plurality of recessed portions  420   c  are formed between the protrusions  420   b  at regular intervals from each other. The number of protrusions  420   b  arranged around the central portion  420   a  may vary. For example, an even number of protrusions  420   b  may be provided around the central portion  420   a . In this case, when the result of dividing the number of protrusions  420   b  by  2  is an even number, even resonant modes (for example, TM 21 , TE 21 , or TM 41 ) may be generated, and when the result of dividing the number of protrusions  420   b  by  2  is an odd number, odd resonant modes (for example, TM 31  or TE 31 ) may be generated. 
         [0111]      FIG. 19  is a perspective view of a gain medium layer according to another exemplary embodiment. 
         [0112]    Referring to  FIG. 19 , at least one first protrusion  521   b  and at least one second protrusion  522   b  are arranged around a central portion  520   a  of the gain medium layer  520  in a periodic structure. In  FIG. 19 , three first protrusions  521   b  and three second protrusions  522   b  are arranged around the central portion  520   a . Here, the first protrusion  521   b  and the second protrusion  522   b  may have different shapes, and may be alternately arranged around the central portion  520   a . The shapes, sizes, or numbers of the first and second protrusions  521   b  and  522   b  may vary. When the protrusions  520   b  include the first and second protrusions  521   b  and  522   b  having different shapes as such, resonant modes may be effectively separated. 
         [0113]      FIGS. 20A through 20D  are perspective views of gain medium layers through according to other exemplary embodiments. 
         [0114]    Referring to  FIGS. 20A and 20B , pluralities of protrusions  620   b  and  720   b  are periodically arranged around central portions  620   a  and  720   a  of the gain medium layers  620  and  720 , respectively, wherein through holes  625  and  725  are formed in the central portions  620   a  and  720   a  of the gain medium layers  620  and  720 , respectively. In  FIGS. 20A and 20B , the through holes  625  and  725  have a circular shape, but alternatively, the through holes  625  and  725  may have any shape, such as a quadrangular shape. Also, the sizes or numbers of the through holes  625  and  725  may vary. Referring to  FIG. 20C , six protrusions  820   b  having the same shape are arranged around a central portion  820   a  of the gain medium layer  820 , wherein a through hole  825  is formed in the central portion  820   a  of the gain medium layer  820 . Referring to  FIG. 20D , six protrusions  920   b  are arranged around a central portion  920   a  of the gain medium layer  920 , wherein a through hole  925  is formed in the central portion  920   a  of the gain medium layer  920 . The protrusions  920   b  include three first protrusions  921   b  and three second protrusions  922   b , wherein the first and second protrusions  921   b  and  922   b  have different shapes and are alternately arranged. Also, the shapes, sizes, or numbers of the first and second protrusions  921   b  and  922   b  may vary. As shown in  FIGS. 20A through 20D , by forming the through holes  625  through  925  in the central portions  620   a  through  920   a  of the gain medium layers  620  through  920 , a desired resonant wavelength may be easily selected. 
         [0115]      FIGS. 21A and 21B  are respectively a perspective view and a plan view of a gain medium layer according to another exemplary embodiment. Referring to  FIGS. 21A and 21B , ten protrusions  1420   b  are periodically arranged around a central portion  1420   a  of the gain medium layer  1420 , wherein a through hole  1425  is formed in the central portion  1420   a  of the gain medium layer  1420 . 
         [0116]      FIG. 21C  illustrates intensity distributions of an electric field of a laser beam generated by the gain medium layer  1420  of  FIGS. 21A and 21B . In  FIG. 21C , a red region denotes a region where intensity of an electric field is strong and a blue region denotes a region where intensity of an electric field is weak.  FIG. 21C  illustrates results obtained via simulation when the gain medium layer  1420  of  FIGS. 21A and 21B  having the ten protrusions  1420   b  is formed of InGaAs having a refractive index n of 3.55, has an outer radius r 1 , an inner radius r 2 , a radius r 3  of the through hole  1425 , a thickness t, an angle θ 1  of the protrusion  1420   b , and an angle θ 2  of a recessed portion  1420   c  respectively of 800 nm, 400 nm, 200 nm, 1100 nm, 18°, and 18°, and is surrounded by Ag, and an electric dipole is set in a z-axis direction. Referring to  FIG. 21C , a laser beam having a TM 10,5  resonant mode of 0.65 μm wavelength and generated by the gain medium layer  1420  is confined as standing waves in the protrusions  1420   b . The laser beam may also be confined in the central portion  1420   a  of the gain medium layer  1420 . 
         [0117]      FIGS. 22A through 22D  illustrate gain medium layers according to other exemplary embodiments. 
         [0118]    Referring to  FIGS. 22A and 22B , the gain medium layers  1020  and  1120  include central portions  1020   a  and  1120   a  having quadrangular plane shapes, and pluralities of protrusions  1020   b  and  1120   b  that are periodically arranged around the central portions  1020   a  and  1120   a . The protrusions  1020   b  and  1120   b  may have, for example, square or rectangular plane shapes, or may have any other plane shape. Referring to  FIGS. 22C and 22D , pluralities of protrusions  1220   b  and  1320   b  are periodically arranged around central portions  1220   a  and  1320   a  of the gain medium layers  1220  and  1320 , respectively, wherein through holes  1225  and  1325  are formed in the central portions  1220   a  and  1320   a  of the gain medium layers  1220  and  1320 , respectively. The through holes  1225  and  1325  may have circular shapes, or any other shapes, such as quadrangular shapes. Also, the sizes or numbers of the through holes  1225  and  1325  may vary. 
         [0119]      FIGS. 23A through 23F  illustrate gain medium layers according to other exemplary embodiments. 
         [0120]    Referring to  FIGS. 23A through 23C , four protrusions  1520   b  through  1720   b  are provided around central portions  1520   a  through  1720   a  of the gain medium layers  1520  through  1720 , and recessed portions between the protrusions  1520   b  through  1720   b  are formed in diagonal directions of the gain medium layers  1520  through  1720 . In  FIG. 23B , a circular through hole  1620  is formed in the central portion  1620   a , and in  FIG. 23C , a square through hole  1725  is formed in the central portion  1720   a.    
         [0121]    Referring to  FIGS. 23D through 23F , central portions  1820   a ,  1920   a , and  2220   a  of the gain medium layers  1820 ,  1920 , and  2220  have rectangular plane shapes, and the six protrusions are periodically arranged around the central portions  1820   a ,  1920   a , and  2220   a . Here, the six protrusions include four first protrusions  1821   b ,  1921   b , and  2221   b , and two second protrusions  1822   b ,  1922   b , and  2222   b . In  FIG. 23E , a circular through hole  1925  is formed in the central portion  1920   a , and in  FIG. 23F , a square through hole  2225  is formed in the central portion  2220   a.    
         [0122]      FIGS. 24A and 24B  illustrate gain medium layers  2320  and  2420  according to other exemplary embodiments. 
         [0123]    Referring to  FIGS. 24A and 24B , pluralities of protrusions  2320   b  and  2420   b  are periodically arranged around central portions  2320   a  and  2420   a  of the gain medium layers  2320  and  2420 , respectively, wherein recessed portions  2320   c  and  2420   c  are formed between the pluralities of protrusions  2320   b  and  2420   b  at regular intervals, respectively. Here, the recessed portions  2320   c  and  2420   c  are formed only at parts of the gain medium layers  2320  and  2420  along a thickness direction, e.g., in a z-axis direction. In other words, the recessed portions  2320   c  and  2420   c  may be formed by depths d from top surfaces of the gain medium layers  2320  and  2420 . For example, the depths d of the recessed portions  2320   c  and  2420   c  may be halves of thicknesses t of the gain medium layers  2320  and  2420 . Alternatively, the depths d of the recessed portions  2320   c  and  2420   c  may vary. Meanwhile, bottoms of the recessed portions  2320   c  and  2420   c  may protrude to surfaces of the protrusions  2320   b  and  2420   b.    
         [0124]    Even when the recessed portions  2320   c  and  2420   c  between the protrusions  2320   b  and  2420   b  of the gain medium layers  2320  and  2420  are formed only at the parts of the gain medium layers  2320  and  2420  in the thickness direction as such, laser beams generated by the gain medium layers  2320  and  2420  may be confined as standing waves in at least one of the protrusions  2320   b  and  2420   b . Also, the gain medium layers  2320  and  2420  may be manufactured via simple processes since the recessed portions  2320   c  and  2420   c  are formed by removing top surfaces of the gain medium layers  2320  and  2420  by a certain depth via etching. 
         [0125]      FIGS. 25A and 25B  illustrate gain medium layers  2520  and  2620  according to other exemplary embodiments. In the gain medium layers  2520  and  2620  of  FIGS. 25A and 25B , two protrusions  2520   b  and  2620   b  are arranged around central portions  2520   a  and  2620   a , respectively, wherein two recessed portions  2520   c  and  2620   c  are formed between the protrusions  2520   b  and  2620   b , respectively. Meanwhile, in the gain medium layer  2620  of  FIG. 25B , the recessed portions  2620   c  are formed only at a part of the gain medium layer  2620  in a thickness direction, e.g., in a z-axis direction.  FIG. 26  illustrates intensity distributions of an electric field of a laser beam generated by the gain medium layer  2520  of  FIG. 25A . 
         [0126]    According to the above exemplary embodiments, by arranging protrusions in a periodic structure around a central portion of a gain medium layer, a laser beam generated by the gain medium layer may be confined as standing waves in at least one of the protrusions. As such, undesired resonant modes may be removed or a desired resonant mode may be effectively separated from other resonant modes. Thus, a Q-factor of a laser resonator may be improved, and the laser resonator may operate in a desired resonant mode of a desired wavelength. In addition, intensity of the desired resonant mode may be selectively reinforced. Since only the desired resonant mode is easily selected as such, a low threshold current may be realized. A resonant mode may be selected and/or separated based on a number, shape, or size of the protrusions that are periodically arranged around the central portion, based on an interval between the protrusions, or based on a size, shape, or number of through holes formed in the central portion. Also, by providing a metal layer outside the gain medium layer or a dielectric layer having a refractive index different from the gain medium layer, the laser beam generated by the gain medium layer may be efficiently confined. 
         [0127]    As such, a semiconductor laser resonator capable of easily controlling a resonant mode may be applied to various fields. For example, an optical source may be realized as a nano-laser resonator so as to manufacture a super-speed, low-power, and miniaturized on-chip photonic integrated circuit (IC). When the nano-laser resonator is used as an optical signal transmitting unit, data may be transmitted at a high speed, and an optical through-silicon via (TSV) capable of transmitting a signal at a high speed and preventing heat emission may be realized. In addition, the nano-laser resonator may be applied as a highly precise and high-speed optical clock source that is compatible with a complementary metal-oxide semiconductor (CMOS). 
         [0128]    While one or more exemplary embodiments have been described with reference to the figures, it will be understood by those of ordinary skill in the art that various changes in form and details may be made therein without departing from the spirit and scope as defined by the following claims.