Patent Publication Number: US-2023137277-A1

Title: Optical oscillator, method for designing optical oscillator, and laser device

Description:
TECHNICAL FIELD 
     The present invention relates to an optical oscillator, a method for designing an optical oscillator, and a laser device. 
     BACKGROUND ART 
     In this technical field, technologies described in Non-Patent Literatures 1 to 3 are known. Each of the optical oscillators described in Non-Patent Literatures 1 to 3 is a passive Q-switched microchip laser including a pair of plane mirrors constituting a resonator, a ceramic laser medium disposed between the pair of plane mirrors, and a ceramic Q-switch element. 
     CITATION LIST 
     Patent Literature 
     
         
         [Non-Patent Literature 1] Taira, Takunori, “Micro-domain controlled high power laser materials,” Applied Physics, 2016, Vol. 85, No. 10, p. 863-869 
         [Non-Patent Literature 2] Masaki Tsunekane, et. al., “High Peak Power, Passively Q-switched Microlaser for Ignition of Engines,” IEEE JOURNAL OF QUANTUM ELCTRONICS, February 2010, VOL. 46, NO. 2, p. 277-284 
         [Non-Patent Literature 3] Masaki Tsunekane, et. al., “High Peak Power, Passively Q-switched Yb:YAG/Cr:YAG Micro-Lasers,” IEEE JOURNAL OF QUANTUM ELCTRONICS, May 2013, VOL. 49, NO. 5, p. 454-461 
       
    
     SUMMARY OF INVENTION 
     Technical Problem 
     Laser light may be condensed by a condensing optical system (for example, a lens), and the high energy at a condensing position may be used. At this time, preferably, the energy in an Airy disk (hereinafter, also referred to as “effective energy”) in the laser light at the condensing position is high. The energy of the laser light depends on the energy of excitation light. 
     Therefore, an object of the present invention is to provide a technology capable of realizing high effective energy with respect to the energy of excitation light at a condensing position when laser light is condensed. 
     Solution to Problem 
     An optical oscillator according to one aspect of the present invention includes a first reflection part configured to reflect light of a first wavelength, a laser medium excited by excitation light of a second wavelength different from the first wavelength and configured to emit light of the first wavelength, a second reflection part disposed on a side opposite to the first reflection part with respect to the laser medium and configured to form an unstable resonator together with the first reflection part, the unstable resonator being configured to output annular laser light of the first wavelength, and a saturable absorption part disposed on the side opposite to the first reflection part with respect to the laser medium and of which a transmittance increases with absorption of light of the first wavelength, wherein, when a power of the excitation light of the second wavelength is indicated by P p  (kW), an inner diameter of the annular laser light is indicated by d i  (mm), and an outer diameter is indicated by d o  (mm), and d o /d i  is a magnification m, the magnification m satisfies the following Equation (A): a 0 +a 1  Log(P p )≤m≤b 0 +b 1 P p +b 2 P p   2  . . . (1), provided that,
     a 0 =1.421   a 1 =0.10678   b 0 =2.8698   b 1 =0.79408   b 2 =−0.022536.   

     In such a configuration, since the unstable resonator is provided, pulsed annular laser light is output. When the annular laser light is condensed by the condensing optical system, the energy of an Airy disk (a central part) of the annular laser light at a condensing position is referred to as the effective energy. In the optical oscillator, the magnification m satisfies Equation (A). Therefore, it is possible to realize high effective energy with respect to the energy of the excitation light. 
     A size of the second reflection part may be smaller than that of the first reflection part when seen from the first reflection part. 
     A laser device according to another aspect of the present invention includes the optical oscillator, and an excitation light supply part configured to output the excitation light supplied to the laser medium. In such a configuration, since the unstable resonator is provided, pulsed annular laser light is output. In the optical oscillator, the magnification m satisfies Equation (A). Therefore, it is possible to realize high effective energy with respect to the energy of the excitation light. 
     The laser device may further include a condensing optical system configured to condense the annular laser light output from the unstable resonator. 
     The laser device may further include a non-linear optical system configured to convert the annular laser light output from the unstable resonator. 
     A method for designing an optical oscillator according to yet another aspect of the present invention is a method for designing an optical oscillator which includes a first reflection part configured to reflect light of a first wavelength, a laser medium excited by excitation light of a second wavelength different from the first wavelength and configured to emit light of the first wavelength, a second reflection part disposed on a side opposite to the first reflection part with respect to the laser medium and configured to form an unstable resonator together with the first reflection part, the unstable resonator being configured to output annular laser light of the first wavelength, and a saturable absorption part disposed on the side opposite to the first reflection part with respect to the laser medium and of which a transmittance increases with absorption of light of the first wavelength, wherein, in a case in which the annular laser light output from the unstable resonator is condensed by supplying the excitation light to the laser medium, when a conversion efficiency of an energy in an Airy disk of the annular laser light with respect to an energy of the excitation light is defined as an effective energy conversion efficiency η eff  (%), an inner diameter of the annular laser light is indicated by d i (mm), and an outer diameter is indicated by d o (mm), and d o /d i  is a magnification m, a conversion efficiency distribution that is a distribution of the effective energy conversion efficiency η eff  with respect to the magnification m is obtained, and the magnification m is set so that a standardized effective energy conversion efficiency obtained by standardizing the effective energy conversion efficiency η eff  with a maximum effective energy conversion efficiency in the conversion efficiency distribution is 50% or more. 
     The magnification m set by the above-described designing method can satisfy Equation (A). Therefore, when the annular laser light output from the optical oscillator designed as described above is condensed, it is possible to realize high effective energy with respect to the energy of the excitation light at the condensing position. 
     Another example of the optical oscillator according to the present invention includes a first reflection part configured to reflect light of a first wavelength, a laser medium excited by excitation light of a second wavelength different from the first wavelength and configured to emit light of the first wavelength, a second reflection part disposed on a side opposite to the first reflection part with respect to the laser medium and configured to form an unstable resonator configured to output annular laser light of the first wavelength together with the first reflection part, and a saturable absorption part disposed on the side opposite to the first reflection part with respect to the laser medium and of which a transmittance increases with absorption of light of the first wavelength, wherein, when an inner diameter of the annular laser light is indicated by d i (mm), and an outer diameter is indicated by d o (mm), and d o /d i  is an magnification m, the magnification m is larger than 2 1/2 . 
     In such a configuration, since the unstable resonator is provided, pulsed annular laser light is output. The optical oscillator has a magnification m larger than 2 1/2 . Therefore, it is possible to realize high effective energy with respect to the energy of the excitation light. 
     Another example of the laser device according to the present invention includes the above-described optical oscillator as another example, and an excitation light supply part configured to output the excitation light supplied to the laser medium, wherein, when a power of the excitation light is 1.5 kW or more and 12 kW or less, the magnification m is 1.44 or more and 4.01 or less, when a power of the excitation light is 3 kW or more and 12 kW or less, the magnification m is 1.47 or more and 5.1 or less, or when a power of the excitation light is 6 kW or more and 12 kW or less, the magnification m is 1.50 or more and 6.82 or less. 
     Advantageous Effects of Invention 
     According to the present invention, it is possible to provide a laser device and an optical oscillator capable of realizing high effective energy. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG.  1    is a view showing a schematic configuration of a laser device according to an embodiment. 
         FIG.  2    is a schematic view showing an example of pulsed laser light output from the laser device shown in  FIG.  1   . 
         FIG.  3    is a view showing a measurement result of a beam diameter in a reference experimental example. 
         FIG.  4    is a graph in which a beam radius of a donut beam (pulsed laser light) near a focal point and a radius of an Airy disk of the donut beam are plotted in the reference experimental example. 
         FIG.  5    is an image of a beam pattern at a focal position in the reference experimental example. 
         FIG.  6    is a view showing an intensity distribution in a y-axis direction when a white line shown in  FIG.  5    is taken as a y-axis. 
         FIG.  7    is a schematic view showing a model of an optical oscillator used for a numerical calculation. 
         FIG.  8    is a graph showing magnification dependence of energy conversion efficiency η and an effective energy rate E eff . 
         FIG.  9    is a graph showing the magnification dependence of the effective energy conversion efficiency η eff . 
         FIG.  10    is a graph showing the magnification dependence of standardized effective energy conversion efficiency η eff . 
         FIG.  11    is a schematic view of a first application example of the laser device. 
         FIG.  12    is a schematic view of a second application example of the laser device. 
         FIG.  13    is a schematic view of a third application example of the laser device. 
         FIG.  14    is a schematic view of a fourth application example of the laser device. 
         FIG.  15    is a schematic view of a fifth application example of the laser device. 
         FIG.  16    is a schematic view of a sixth application example of the laser device. 
         FIG.  17    is a schematic view of a seventh application example of the laser device. 
         FIG.  18    is a schematic view showing a first modified example of the optical oscillator. 
         FIG.  19    is a schematic view showing a second modified example of the optical oscillator. 
         FIG.  20    is a schematic view showing a third modified example of the optical oscillator. 
         FIG.  21    is a schematic view showing a fourth modified example of the optical oscillator. 
         FIG.  22    is a drawing for describing a relationship between a radius of curvature and a magnification when a first reflection part and a second reflection part are curved. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings. In the description of the drawings, the same reference numerals are used for the same or equivalent elements, and duplicate description will be omitted. Dimensional ratios in the drawings do not always match those described. 
     As shown in  FIG.  1   , a laser device  1 A according to an embodiment includes an excitation light supply part  2 , an optical oscillator  3 A, and a condensing optical system  4 . The laser device  1 A outputs pulsed laser light L 2  when excitation light L 1  supplied from the excitation light supply part  2  is incident on the optical oscillator  3 A. The laser device  1 A according to the present embodiment is a passive Q-switched laser device. In the laser device  1 A, the pulsed laser light L 2  is further condensed by the condensing optical system  4 . The laser device  1 A is appropriately used for laser ignition, laser-induced breakdown spectroscopy, a variety of laser processing for the purpose of ablation, or surgery using laser light. In the present embodiment, the pulsed laser light L 2  has a first wavelength, and the excitation light L 1  has a second wavelength. 
     The second wavelength is, for example, a wavelength of 808 nm or a wavelength of 885 nm when a laser medium  31  included in the optical oscillator  3 A is Nd:YAG, and a wavelength of 940 nm or a wavelength of 968 nm when the laser medium  31  is Yb:YAG. The first wavelength is, for example, a wavelength of 1064 nm when the laser medium  31  is Nd:YAG, and a wavelength of 1030 nm when the laser medium  31  is Yb:YAG. 
     The excitation light supply part  2  has a configuration capable of supplying the excitation light L 1  to the optical oscillator  3 A. The excitation light supply part  2  includes, for example, an optical fiber  21 , a laser diode (LD)  22 , and an incident optical system  23 . The excitation light supply part  2  may have a bundle of a plurality of optical fibers  21 . 
     The excitation light supply part  2  may have a configuration in which the optical fiber  21  is not provided and the excitation light L 1  is supplied from the LD  22  to the optical oscillator  3 A via the incident optical system  23 . 
     The LD  22  outputs the excitation light L 1 . A power of the excitation light L 1  is, for example, 0.8 kW or more. The LD  22  may be oscillated in a continuous wave or may be oscillated in a quasi-continuous wave. An input end of the optical fiber  21  is coupled to the LD  22 . The optical fiber  21  outputs the excitation light L 1  output from the LD  22  to the incident optical system  23 . The incident optical system  23  condenses the excitation light L 1  output from the optical fiber  21  and causes the excitation light L 1  to be incident on the optical oscillator  3 A. The incident optical system  23  includes, for example, a lens  23   a  and a lens  23   b  as shown in  FIG.  1   . The excitation light L 1  may be incident on the first reflection part  33  as, for example, parallel light or loosely condensed light that is substantially close to the parallel light. 
     The optical oscillator  3 A includes a laser medium  31 , a Q-switch element (a saturable absorption part)  32 , a first reflection part  33 , a support  34 , and a second reflection part  35 . The first reflection part  33 , the second reflection part  35 , the laser medium  31 , and the Q-switch element  32  are disposed in the order of the first reflection part  33 , the laser medium  31 , the Q-switch element  32 , and the second reflection part  35  along a Z axis. The Z-axis corresponds to an optical axis of the optical oscillator  3 A. 
     [Laser Medium] 
     The laser medium  31  forms a population inversion in which amplification exceeds absorption in an excited state, and amplifies light using stimulated emission. The laser medium  31  is also referred to as a gain medium. As the laser medium  31 , various known laser media can be used as long as light having the first wavelength can be emitted by supplying the excitation light L 1  having the second wavelength. 
     Examples of a material of the laser medium  31  include a light gain material formed of an oxide to which rare earth ions that serve as a center of light emission are added, a light gain material formed of an oxide to which transition metal ions that serve as a center of light emission are added, a light gain material formed of an oxide that serves as a color center, and the like. 
     Examples of the rare earth ions include Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, and Yb. Examples of the transition metal ions include Ti, V, Cr, Mn, Fe, Co, Ni, and Cu. Examples of a base material include a garnet-based material such as YAG, YSAG, YGAG, YSGG, GGG, GSGG, and LuAG, a fluoride-based material such as YLF, LiSAF, LiCAF, MgF 2 , and CaF 2 , a vanadate-based material such as YVO 4 , GdVO 4 , and LuVO 4 , an apatite-based material such as FAP, sFAP, VAP, and sVAP, an alumina-based material such as Al 2 O 3  and BeAl 2 O 3 , a dioxide or trioxide-based material such as Y 2 O 3 , Sc 2 O 3  and Lu 2 O 3 , and a tungstate-based material such as KGW and KYW. The base material may be a single crystal or a polycrystalline ceramic material. The base material may be various amorphous glasses. 
     Examples of a shape of the laser medium  31  include a plate shape and a columnar shape. In the embodiment shown in  FIG.  1   , a central axis of the laser medium  31  coincides with the Z axis. The laser medium  31  has a first end surface  31   a  and a second end surface  31   b  (a surface on the side opposite to the first end surface  31   a  in the Z-axis direction). The first end surface  31   a  and the second end surface  31   b  are orthogonal to the Z axis. An example of a length of the laser medium  31  in the Z-axis direction is 0.2 mm to 26 mm. 
     Examples of a shape (a shape in a plan view) of the laser medium  31  seen in the Z-axis direction include a circle, a rectangle, a square, and a polygon. When the shape of the laser medium  31  in a plan view is circular, an example of a diameter thereof is 1.4 mm to 100 mm. When the shape of the laser medium  31  in a plan view is a rectangle or a square, an example of an approximate diagonal length thereof is 1.9 mm to 140 mm. 
     Hereinafter, a shape of an element when seen in the Z-axis direction is also referred to as a “shape in a plan view” as described above. 
     The Q-switch element  32  is a saturable absorber having a characteristic that absorption capacity is saturated when intensity of the light of the first wavelength incident on the Q-switch element  32  increases. A transmittance of the Q-switch element  32  increases with absorption of the light having the second wavelength. The Q-switch element  32  may be disposed coaxially with the laser medium  31 . The Q-switch element  32  may be joined to the second end surface  31   b.    
     When seen in a Z-axis direction, a size of the Q-switch element  32  is, for example, Cr:YAG, and when the laser medium  31  is Nd:YAG, the laser medium  31  is smaller. When the laser medium  31  is Nd:YVO 4  or Yb:YAG, a length of the laser medium  31  in the Z-axis direction is shorter than that of the Q-switch element  32 . Examples of a shape of the Q-switch element  32  include a plate shape and a columnar shape. The Q-switch element  32  has a first end surface  32   a  on the laser medium  31  side, and a second end surface  32   b  (a surface on the side opposite to the first end surface  32   a  in the Z-axis direction). The first end surface  32   a  is orthogonal to the Z axis. An example of a length of the Q-switch element  32  in the Z-axis direction is 0.1 to 10 mm. 
     When both the laser medium  31  and the Q-switch element  32  are made of ceramic, the laser medium  31  and the Q-switch element  32  may be sinter-joined, but more preferably surface-activation-joined. The surface activation joining is a method in which an oxide film or surface deposits on joining surfaces of materials to be joined in a vacuum are removed by ion beam irradiation or neutral atom beam (FAB) irradiation, and the joining surfaces that are flat and on which constituent atoms are exposed are joined to each other. The above-described joining is a direct joining using an intermolecular bond. In the surface activation joining, without limiting the laser medium to ceramics, not only single crystals joining or hybrid joining thereof can be performed, but also joining can be performed after applying an excitation light reflection coating or the like. When the laser medium  31  and the Q-switch element  32  are joined to form a joined body, a length (corresponding to a length in the Z-axis direction) of the laser medium  31  and the Q-switch element  32  in a joining direction of the joined body is smaller than, for example, 10 mm. 
     A coating layer for adjusting reflection characteristics (for example, reflection characteristics of the light having the second wavelength) of the second end surface  31   b  and the first end surface  32   a  may be provided on at least one of the second end surface  31   b  of the laser medium  31  and the first end surface  32   a  of the Q-switch element  32 . When such a coating layer is provided on at least one of the second end surface  31   b  and the first end surface  32   a , for example, the laser medium  31  and the Q-switch element  32  can be joined as described above with the coating layer interposed therebetween. A coating layer that functions as an HR coat for the excitation light L 1  of the second wavelength and functions as an AR coat for the light of the first wavelength may be provided on at least one of the first end surface  32   a  and the second end surface  32   b  of the Q-switch element  32 . However, when a composite resonator is formed, the coating layer may be a coating layer that realizes partial reflection with respect to the light of the first wavelength. Such a coating layer may be a part of the saturable absorption part. That is, the saturable absorption part may have the coating layer in addition to the saturable absorber (the Q-switch element  32  in  FIG.  1   ), and when the coating layer is provided on an end surface of the saturable absorber, an end surface of the coating layer corresponds to the end surface of the saturable absorption part. 
     [First Reflection Part] 
     The first reflection part  33  is provided on the first end surface  31   a  of the laser medium  31 . The first reflection part  33  transmits the excitation light L 1  of the second wavelength while reflecting the light of the first wavelength. A transmittance of the first reflection part  33  with respect to the excitation light L 1  of the second wavelength is 80% or more (preferably 95% or more), and a reflectance of the first reflection part  33  with respect to the light of the first wavelength is 90% or more (preferably 99% or more). The first reflection part  33  is, for example, a dielectric multilayer film. The first reflection part  33  is, for example, a dielectric multilayer film that functions as an AR coat for the excitation light L 1  of the second wavelength and as an HR coat for the light of the first wavelength. When the first reflection part  33  is a dielectric multilayer film, the first reflection part  33  may be formed on the first end surface  31   a  by a thin film forming technique. 
     The first reflection part  33  has a first surface  33   a  and a second surface  33   b . The first surface  33   a  is a surface on which the excitation light L 1  is incident. The second surface  33   b  is a surface on the side opposite to the first surface  33   a  in the Z-axis direction. The first surface  33   a  and the second surface  33   b  are planes orthogonal to the Z axis. Therefore, the first reflection part  33  is a plane mirror having the above-described transmission characteristics and reflection characteristics. However, the first reflection part  33  may be a mirror having a curvature (a curved mirror), for example, a concave mirror. 
     [Support] 
     The support  34  is disposed apart from the Q-switch element  32 . The support  34  supports the second reflection part  35 . The support  34  transmits the light of the first wavelength (the pulsed laser light L 2 ). A transmittance of the support  34  with respect to the light of the first wavelength is 90% or more. Examples of a material for the support  34  include glass. In the present embodiment, a central axis of the support  34  coincides with the Z axis. 
     The first surface  34   a  (the surface on the Q-switch element  32  side) of the support  34  is curved toward the Q-switch element  32  side. A radius of curvature of the first surface  34   a  is, for example, the same as that of the second reflection part  35 . The second surface  34   b  (the surface on the side opposite to the Q-switch element  32 ) of the support  34  is, for example, a flat surface. An example of the support  34  is a plano-convex lens. The AR coat with respect to the light of the first wavelength may be applied to the first surface  34   a . Such an AR coat may also be a part of the support  34 . The second reflection part  35  is provided on the first surface  34   a.    
     [Second Reflection Part] 
     The second reflection part  35  reflects the light of the first wavelength formed on the first surface  34   a . The second reflection part  35  is, for example, a dielectric multilayer film. An optical axis of the second reflection part  35  coincides with the Z axis. A reflectance of the second reflection part  35  with respect to the light of the first wavelength is 80% or more (preferably 99% or more). The second reflection part  35  is, for example, a dielectric multilayer film that functions as an HR coat for the light of the first wavelength. When the second reflection part  35  is a dielectric multilayer film, the second reflection part  35  may be formed on the first surface  34   a  by a thin film forming technique. 
     The optical oscillator  3 A may have a lens  36  as shown in  FIG.  1   . The lens  36  is a lens that parallelizes the pulsed laser light L 2 . 
     [Condensing Optical System] 
     The condensing optical system  4  is an optical system that condenses the pulsed laser light L 2  output from the optical oscillator  3 A. In the embodiment shown in  FIG.  1   , the condensing optical system  4  is a lens. An example of a focal length of the condensing optical system  4  is 5 mm to 500 mm. 
     The laser device  1 A may further include an accommodation part  5 . The accommodation part  5  is, for example, a housing. The accommodation part  5  accommodates the incident optical system  23 , the optical oscillator  3 A, and the condensing optical system  4 . In this case, for example, an output end of the optical fiber  21  is mounted on a first end wall  5   a  of the accommodation part  5  (one of a pair of wall portions orthogonal to the Z axis). An opening  5   c  is formed in a second end wall  5   b  of the accommodation part  5  (the end wall on the side opposite to the first end wall  5   a  along the Z axis). The opening  5   c  is closed by a window member  6 . The window member  6  is a member that is transparent to the pulsed laser light L 2 . 
     The optical oscillator  3 A will be further described. 
     The first reflection part  33  and the second reflection part  35  included in the optical oscillator  3 A form an unstable resonator UR. In the embodiment shown in  FIG.  1   , an optical axis of the unstable resonator UR formed by the first reflection part  33  and the second reflection part  35  coincides with the Z axis. 
     When seen in the Z-axis direction, a size of the second reflection part  35  is smaller than the size of the first reflection part  33 . Further, the second reflection part  35  is curved toward the first reflection part  33  side. The second reflection part  35  is curved in the same manner as the first surface  34   a , for example. Since the second reflection part  35  is curved as described above, the second reflection part  35  diverges the light of the second wavelength. Therefore, the first reflection part  33  and the second reflection part  35  form a magnification optical system. 
     When seen in the Z-axis direction, the second reflection part  35  has a circular or polygonal shape, and an example of a diameter or diagonal length thereof is 1 mm to 20 mm. The diameter or diagonal length of the second reflection part  35  may be 1 mm to 3 mm. An example of a radius of curvature of the second reflection part  35  is 10 mm to 2 m. An example of the radius of curvature of the second reflection part  35  may be 10 mm to 100 mm. 
     An example of a distance (hereinafter, referred to as a “resonator length Lc”) between a portion of the second reflection part  35  closest to the first reflection part  33  (a top portion of the second reflection part  35 ) and the second surface  33   b  of the first reflection part  33  is about 4 mm to 50 mm. The resonator length Lc may be smaller than 15 mm. 
     The first reflection part  33  and the second reflection part  35  form the unstable resonator UR. Therefore, as shown in  FIG.  2   , a donut-shaped (donut mode) pulsed laser light L 2  (annular laser light) is output from the optical oscillator  3 A with the Q-switch element  32 . This point will be specifically described. 
     When the excitation light L 1  from the excitation light supply part  2  is incident on the first surface  33   a  of the first reflection part  33 , the excitation light L 1  passes through the first reflection part  33  and is supplied to the laser medium  31 . Thus, the laser medium  31  is excited and light of the first wavelength is emitted. The light of the first wavelength emitted from the laser medium  31  is reflected by the second reflection part  35  toward the first reflection part  33 . The first reflection part  33  reflects the light of the first wavelength. Thus, the light of the first wavelength passes through the laser medium  31  a plurality of times. The light of the first wavelength is amplified by stimulated emission when the light of the first wavelength passes through the laser medium  31 , and is output as the pulsed laser light L 2  by an action of the Q-switch element  32 . 
     Since the second reflection part  35  is curved toward the first reflection part  33 , the light of the second wavelength reflected by the second reflection part  35  is diverged. Therefore, the pulsed laser light L 2  is output from the outside of the second reflection part  35  when seen in the Z-axis direction. As a result, a shape (an intensity distribution) of the pulsed laser light L 2  is a donut (annular) shape as shown in  FIG.  2   . That is, the laser device  1 A can output a donut-shaped pulsed laser light L 2 . 
     When an inner diameter of the pulsed laser light L 2  is d i , and an outer diameter of the pulsed laser light L 2  is d o , a magnification m is defined as d o /d i . 
     In the laser device  1 A, when the excitation light L 1  is input to the optical oscillator  3 A, the donut-shaped pulsed laser light L 2  is output. The laser device  1 A has the condensing optical system  4 . Therefore, the pulsed laser light L 2  is condensed by the condensing optical system  4 . 
     Here, characteristics of the laser device having the unstable resonator will be described with reference to a reference experimental example. Hereinafter, the donut-shaped pulsed laser light will be referred to as a donut beam in the description of the reference experimental example. 
     In the reference experimental example, the same laser device as the laser device  1 A shown in  FIG.  1    was used except that the accommodation part  5  and the window member  6  were not provided. 
     In the reference experimental example, the excitation light L 1  is incident on the first reflection part  33  by the incident optical system  23  using the LD  22  in which the optical fiber  21  is coupled. The incident optical system  23  was a telescope using the lens  23   a  and the lens  23   b . An excitation method of LD  22 , a wavelength of the excitation light L 1  and an output power were as follows.
         Excitation method: quasi-continuous wave excitation   Wavelength of excitation light L 1 : 808 nm   Output power of excitation light L 1 : 700 W       

     Nd:YAG ceramic (addition amount of Nd 3+ : 1.1 at. %) was used for the laser medium  31 . Cr 4+ :YAG ceramic was used for the Q-switch element  32 . An initial transmittance of the Q-switch element  32  was 30%. The laser medium  31  and the Q-switch element  32  were joined. A length of the joined body of the laser medium  31  and the Q-switch element  32  in the Z-axis direction was 7 mm, and a volume of the joined body was 6×6×7 mm 3 . Both end surfaces of the joined body of the laser medium  31  and the Q-switch element  32  (that is, the first end surface  31   a  of the laser medium  31  and the second end surface  32   b  of the Q-switch element  32 ) were subjected to AR coating for each light having a wavelength of 1064 nm and a wavelength of 808 nm. 
     For the first reflection part  33 , a plane mirror that reflects light having a wavelength of 1064 nm and transmits light having a wavelength of 808 nm was used. For the support  34 , a plano-convex lens of which a radius of curvature of the first surface  34   a  was 52 mm was used. A central portion of the first surface  34   a  of the support  34  was partially coated with a dielectric multilayer film that functions as an HR coat for the light having a wavelength of 1064 nm as the second reflection part  35 . Regions in the first surface  34   a  other than the second reflection part  35  were subjected to the AR-coating. When seen in the Z-axis direction, a shape of the second reflection part  35  was a circle with a diameter of 2 mm. The resonator length Lc was 10 mm. 
     In the above-described configuration, the magnification m in the unstable resonator corresponds to 2 1/2 . 
     A convex lens was used as the lens  36  for parallelizing the donut beam (the pulsed laser light L 2 ). A lens (having a focal length of 300 mm) was used as the condensing optical system  4 . 
     In the reference experimental example, pulse energy and a pulse width of the pulsed laser light L 2  were measured. The pulse energy was measured using a pyroelectric energy sensor (manufactured by Ophir Optronics Solutions Ltd.). The pulse width was measured using a photodetector with a rise time of 30 ps and an oscilloscope of 13 GHz. The pulse energy and the pulse width were measured without using the condensing optical system  4 . The pulse energy obtained by the measurement was 13.2 mJ at a repetition frequency of 10 Hz, and the pulse width was 476 ps in full width at half maximum. 
     In the reference experimental example, beam quality (M 2 ) in the vicinity of the condensing position of the condensing optical system  4  was measured. For the measurement of the beam quality, a beam quality M 2  tool (manufactured by Cinogy technologies GmbH) according to ISO11146 and analysis software (RayCi) were used. 
     The beam quality (M 2 ) was obtained as follows. A beam diameter was measured at a plurality of positions before and after the condensing position in a propagation direction of the donut beam. M 2  was calculated from measurement results thereof. The measurement results of the beam diameter were as shown in  FIG.  3   . A horizontal axis in  FIG.  3    indicates a position (mm) at which the beam diameter is measured, and a vertical axis indicates a donut beam radius.  FIG.  3    shows the radius of the donut beam in an X-axis direction and a Y-axis direction in a three-dimensional coordinate system set with respect to the Z-axis. Each of square marks in  FIG.  3    is the radius of the beam in the X-axis direction, and each of black circle marks is the radius of the beam in the Y-axis direction. The donut beam is theoretically a perfect circle, but actually has a slightly elliptical shape. The X-axis corresponds to a major axis direction of the ellipse, and the Y-axis corresponds to a minor axis direction of the ellipse.  FIG.  3    also shows a beam pattern at each measurement position. As shown in  FIG.  3   , a fur-field pattern at the focal position was an Airy disk and an Airy pattern. 
     The M 2  calculated from  FIG.  3    was 6.8 in the X-axis direction and 5.3 in the Y-axis direction. A numerical value of M 2  in the reference experimental example is a value based on the secondary moment beam diameter. In addition, M 2   PC  based on a beam diameter of 86.5% of optical power was also calculated. The M 2   PC  in each of the X-axis direction and the Y-axis direction was 6.5 and 5.2. Here, an average M 2   ave  of M 2  in the X-axis direction and the Y-axis direction is defined by the following Equation. 
         M   ave   2 =√{square root over ( M   X   2   M   Y   2 )}  [Math. 1]
 
     In this case, the average M 2   ave  of M 2  calculated in the X-axis direction and the Y-axis direction was 6. Similarly, the average M 2   ave  of M 2   PC  calculated in the X-axis direction and the Y-axis direction was 5.8. 
       FIG.  4    is a graph in which the beam radius of the donut beam in the vicinity of the focal point and the radius of the Airy disk of the donut beam are plotted. The beam radius of the donut beam is an average value of the radii in the X-axis direction and the Y-axis direction shown in  FIG.  3   . A curve α 1  in  FIG.  4    shows a fitting curve with respect to the measurement result of the beam radius of the donut beam. A curve α 2  in  FIG.  4    shows a fitting curve with respect to the measurement result of the Airy disk radius. Further, a curve α 3  in  FIG.  4    shows a Gaussian beam radius when a Gaussian beam is condensed by the same lens. 
     From the results shown in  FIG.  4   , the radius of the Airy disk was about 0.2 times the beam radius of the donut beam. Here, a width and beam quality of the Airy disk are indicated by w Airy  and M 2   Airy , and a width and beam quality of the donut beam are indicated by w d  and M 2   d . 
     In this case, the following relationship is established. 
     
       
         
           
             
               
                 
                   
                     
                       w 
                       Airy 
                     
                     
                       w 
                       d 
                     
                   
                   = 
                   
                     
                       M 
                       Airy 
                       2 
                     
                     
                       M 
                       d 
                       2 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Math 
                     . 
                         
                     2 
                   
                   ] 
                 
               
             
           
         
       
     
     As described above, M 2   d  is 6, and w Airy /w d  is about 0.2. Therefore, the beam quality M 2  of the entire donut beam is 6, while the beam quality of about 1.2 can be obtained in the Airy disk. In other words, the Airy disk provides the beam quality close to that of Gaussian mode. 
     Further, when focusing on a region corresponding to the Airy disk of the donut beam in  FIG.  4   , a long Rayleigh length (about four times that of the Gaussian beam in  FIG.  4   ) can be realized. 
       FIG.  5    is an image of the beam pattern at the focal position. It can be understood from  FIG.  5    that the Airy disk and the Airy pattern are formed at the focal position. 
       FIG.  6    is a view showing the intensity distribution in the y-axis direction when the white line shown in  FIG.  5    (the white line that extends in a vertical direction in  FIG.  6   ) is taken as the y-axis. In  FIG.  6   , the intensities (experimental results) of cross sections in the y-axis direction in the central portion of  FIG.  5    are plotted with white circles. A horizontal axis in the drawing indicates a position in the y-axis direction, and a vertical axis indicates standardized strength. The secondary moment beam diameter (2w y ) of the Airy disk and the Airy pattern was 0.29 mm. In  FIG.  6   , a Gaussian distribution having the same beam diameter (0.29 mm) is shown by a solid line, and a Gaussian distribution having a diameter of 0.2w y  is shown by a broken line. A width w y  is a width of a positive (or negative) region with respect to a position 0. A length da shown in  FIG.  6    corresponds to the diameter of the Airy disk. 
     When a plane wave passes through a circular aperture lens, an Airy disk pattern is generated by a diffraction. Therefore, the intensity distribution of the donut beam was fitted by Equation (1) (for example, referring to B. Lu, et al., “The beam quality of annular lasers and related problems,” J. Mod. Opt. 48, 1171 (2001)) showing an intensity distribution at a condensing position (a focal position) of light when the plane wave was condensed by the circular aperture lens. 
     
       
         
           
             
               
                 
                   [ 
                   
                     Math 
                     . 
                         
                     3 
                   
                   ] 
                 
               
               
                  
               
             
             
               
                 
                   
                     I 
                     ⁡ 
                     ( 
                     
                       r 
                       , 
                       f 
                     
                     ) 
                   
                   = 
                   
                     
                       
                         
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                           ⁢ 
                               
                           
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                             ⁡ 
                             ( 
                             
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                               , 
                               f 
                             
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                     2 
                   
                 
               
               
                 
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                   1 
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     m in Equation (1) is b/a. In Equation (1), b which defines m is an outer radius of the circular aperture lens, and a is an inner radius of a circular aperture. f is a focal length of the circular aperture lens. r is a position in a radial direction of the Airy disk at the focal position. I(0, f) is a peak intensity at the focal plane. I(0, f) is indicated by S 2 /(λ 2 f 2 ). S is an aperture area of the circular aperture lens. S is indicated by πa 2 (m 2 −1). J 1  is the first order Bessel function. k (=2π/λ) is a wave number. 
     In a fitting curve shown in  FIG.  6   , m,  2   b  and  f  were as follows.
         m=1.48   2b=7.5 mm   f=315 mm       

     The magnification m of the unstable resonator in the reference experiment is 2 1/2 . Therefore, the fitting results based on Equation (1) allows the intensity distribution of the Airy disk at the focal position of the donut beam (the pulsed laser light L 2 ) to be calculated based on Equation (1) by regarding m in Equation (1) as a magnification of the unstable resonator (in other words, d i =2a and d o =2b). 
     Returning to  FIG.  1   , the laser device  1 A will be further described. 
     In the present embodiment, when a power of the excitation light L 1  (hereinafter, also referred to as “excitation power”) is P p  (kW), the magnification m satisfies the following Equation (2a). In other words, the unstable resonator UR (specifically, the first reflection part  33  and the second reflection part  35 ) is designed so that the magnification m satisfies Equation (2a). 
         a   0   +a   1  Log( P   p )≤ m≤b   0   +b   1   P   p   +b   2   P   p   2   (2a)
         where a 0 , a 1 , b 0 , b 1 , and b 2  in Equation (2a) are as follows.   a 0 =1.421   a 1 =0.10678   b 0 =2.8698   b 1 =0.79408   b 2 =−0.022536       

     The magnification m may satisfy the following Equation (2b). In other words, the unstable resonator UR (specifically, the first reflection part  33  and the second reflection part  35 ) may be designed so that the magnification m satisfies Equation (2b). 
         a   0   +a   1  Log( P   p )≤ m≤b   0   +b   1   P   p   +b   2   P   p   2   (2b)
         where a 0 , a 1 , b 0 , b 1 , and b 2  in Equation (2b) are as follows.   a 0 =1.613   a 1 =0.16827   b 0 =2.6961   b 1 =0.71522   b 2 =−0.023234       

     The magnification m may satisfy the following Equation (2c). In other words, the unstable resonator UR (specifically, the first reflection part  33  and the second reflection part  35 ) may be designed so that the magnification m satisfies Equation (2c). 
         a   0   +a   1  Log( P   p )≤ m≤b   0   +b   1   P   p   +b   2   P   p   2   (2c)
         where a 0 , a 1 , b 0 , and b 1  in Equation (2c) are as follows.   a 0 =1.886   a 1 =0.28888   b 0 =2.6771   b 1 =0.51375   b 2 =−0.021411       

     The magnification m may satisfy the following Equation (2d). In other words, the unstable resonator UR (specifically, the first reflection part  33  and the second reflection part  35 ) may be designed so that the magnification m satisfies Equation (2d). 
         a   0   +a   1  Log( P   p )≤ m≤b   0   +b   1   P   p   +b   2   P   p   2   (2d)
         where a 0 , a 1 , b 0 , and b 1  in Equation (2d) are as follows.   a 0 =1.9308   a 1 =0.37083   b 0 =2.9116   b 1 =2.3422       

     Specifically, the magnification m is larger than 2 1/2 . The magnification m is, for example, 10 or less. The magnification may be 7 or less, 6 or less, 5 or less, or 4 or less. 
     [When the excitation power P p  is 1.5 kW or more and 12 kW or less (or 3 kW or less or 6 kW or less) (particularly when it is 1.5 kW)]
         The magnification m may be 1.44 or more and 4.01 or less.   The magnification m may be 1.64 or more and 3.72 or less.   The magnification m may be 1.93 or more and 3.40 or less.   The magnification m may be 1.99 or more and 3.32 or less.       

     [When the excitation power P p  is 3 kW or more and 12 kW or less (or 6 kW or less) (particularly when it is 3 kW)]
         The magnification m may be 1.47 or more and 5.1 or less.   The magnification m may be 1.69 or more and 4.64 or less.   The magnification m may be 2.02 or more and 4.03 or less.   The magnification m may be 2.10 or more and 4.03 or less.       

     [When the excitation power P p  is 6 kW or more and 12 kW or less (particularly when it is 6 kW)]
         The magnification m may be 1.50 or more and 6.82 or less.   The magnification m may be 1.74 or more and 6.20 or less.   The magnification m may be 2.11 or more and 4.99 or less.   The magnification m may be 2.22 or more and 4.74 or less.       

     [When the excitation power P P  is 12 kW]
         The magnification m may be 1.53 or more and 9.16 or less.   The magnification m may be 1.79 or more and 7.94 or less.   The magnification m may be 2.19 or more and 5.76 or less.   The magnification m may be 2.33 or more and 5.44 or less.       

     In the laser device  1 A, when excitation light L 1  is input to the optical oscillator  3 A, donut-shaped pulsed laser light L 2  is output. The laser device  1 A has the condensing optical system  4 . Therefore, the pulsed laser light L 2  is condensed by the condensing optical system  4 . 
     Energy contained in a center of the pulsed laser light L 2  as the Airy disk at a condensing position (a focal position) of the condensing optical system  4  is referred to as “effective energy”. In the laser device  1 A, the magnification m satisfies Equation (2). Therefore, it is possible to realize high effective energy with respect to the energy of the excitation light L 1 . Therefore, the laser device  1 A and the optical oscillator  3 A are effective in the field of laser application in which laser light is condensed and used. 
     A size of the Airy disk is smaller than a size of the pulsed laser light L 2 . Since high effective energy can be realized in the region of the Airy disk, for example, microfabrication and surgery in a fine region are also possible. At the condensing position, since the energy of the pulsed laser light L 2  is contained more in the Airy disk, and a depth of focus corresponding to the Rayleigh length is also long, a stable breakdown can be expected. 
     Next, the fact that high effective energy can be realized with respect to the energy of the excitation light L 1  will be further described with reference to the numerical calculation results. 
       FIG.  7    is a schematic view showing a model of the optical oscillator used for the numerical calculation. As shown in  FIG.  7   , the optical oscillator as a numerical calculation model includes the first reflection part  33 , the laser medium  31 , the Q-switch element  32 , and the second reflection part  35 . In the numerical calculation, it is assumed that the excitation light L 1  is input to the optical oscillator and the pulsed laser light L 2  having a magnification m (=d o /d i ) is output. 
     A shape and size of the excitation light L 1 , and a diameter and reflectance of the second reflection part  35  were assumed as follows.
         Shape of excitation light L 1  (shape seen in the Z-axis direction): circular   Size (diameter) of the excitation light L 1 : diameter d o  of the pulsed laser light L 2  to be output was used.   Diameter d i  of second reflection part  35 : 1 mm   Reflectance (or coupling efficiency) of second reflection part  35 : 1/m 2          

     Further, an effective mode area (A g ) of the laser medium  31  and an effective mode area (A SA ) of the Q-switch element  32  were set to be the same. 
     In the numerical calculation, when the output pulsed laser light L 2  was condensed by the lens, a ratio of the effective energy E Airy disk  to the energy E pump  of the excitation light L 1  (hereinafter, referred to as “effective energy conversion efficiency η eff ”) was calculated. The effective energy E Airy disk  is energy in the Airy disk at a condensing position of the pulsed laser light L 2 , as described above. 
     The following Equations (3) and (4) were used for the above calculation (refer to, for example, Reference Literatures 1 to 3 below). E pulse  indicated by Equation (4) is the energy of the pulsed laser light L 2 . 
     
       
         
           
             
               
                 
                   [ 
                   
                     Math 
                     . 
                         
                     4 
                   
                   ] 
                 
               
               
                  
               
             
             
               
                 
                   
                     E 
                     Pump 
                   
                   ≅ 
                   
                     
                       P 
                       p 
                     
                     ⁢ 
                     
                       
                         τ 
                         g 
                       
                       [ 
                       
                         ln 
                         ⁡ 
                         ( 
                         
                           
                             
                               W 
                               p 
                             
                             ⁢ 
                             
                               τ 
                               g 
                             
                           
                           
                             
                               
                                 W 
                                 p 
                               
                               ⁢ 
                               
                                 τ 
                                 g 
                               
                             
                             - 
                             
                               n 
                               gi 
                             
                           
                         
                         ) 
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   [ 
                   
                     Math 
                     . 
                         
                     5 
                   
                   ] 
                 
               
               
                  
               
             
             
               
                 
                   
                     E 
                     pulse 
                   
                   ≅ 
                   
                     
                       
                         hvA 
                         g 
                       
                       
                         2 
                         ⁢ 
                         
                           γ 
                           g 
                         
                         ⁢ 
                         
                           σ 
                           g 
                         
                       
                     
                     ⁢ 
                     
                       ln 
                       ⁡ 
                       ( 
                       
                         1 
                         R 
                       
                       ) 
                     
                     ⁢ 
                     
                       ln 
                       ⁡ 
                       ( 
                       
                         
                           n 
                           gi 
                         
                         
                           n 
                           gf 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     where n gi  in Equations (3) and (4) is an initial population inversion density of the laser medium  31  (an initial population inversion density of gain medium) indicated by Equation (5). 
     
       
         
           
             
               
                 
                   [ 
                   
                     Math 
                     . 
                         
                     6 
                   
                   ] 
                 
               
               
                  
               
             
             
               
                 
                   
                     n 
                     gi 
                   
                   ≅ 
                   
                     
                       
                         ln 
                         ⁡ 
                         ( 
                         
                           1 
                           
                             T 
                             0 
                             2 
                           
                         
                         ) 
                       
                       + 
                       
                         ln 
                         ⁡ 
                         ( 
                         
                           1 
                           R 
                         
                         ) 
                       
                       + 
                       L 
                     
                     
                       2 
                       ⁢ 
                       
                         σ 
                         g 
                       
                       ⁢ 
                       
                         l 
                         g 
                       
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
     Each parameter in Equations (3) to (5) is as follows.
         T 0 : Initial transmittance of Q-switch element   R: Reflectance corresponding to diffraction loss of the second reflection part  35     L: Reciprocating loss in unstable resonator UR   σ g (m 2 ): Induced release cross-sectional area   l g (mm): Length of laser medium  31     A g (=π(d o /2) 2 ): Mode area in laser medium  31     γ g : Population inversion reducing factor of laser medium  31     n gf : Final population inversion of laser medium  31     P p : Peak power of excitation light L 1     τ g (ms): Upper level life   W p : Excitation rate       

     Reference Literature 1: N. Pavel, J. Saikawa, S. Kurimura, and T. 
     Taira, “High average power diode end-pumped composite Nd:YAG laser passively Q-switched by Cr4+:YAG saturable absorber,” Jpn. J. Appl. Phys. 40 (Part 1, No. 3A), 1253-1259 (2001). 
     Reference Literature 2: H Sakai, H Kan, T Taira, “1 MW peak power single-mode high-brightness passively Q-switched Nd 3 ”:YAG microchip laser Optics Express; Vol. 16, Issue 24, pp. 19891-19899, (2008). 
     Reference Literature 3: A. Kausas and T. Taira, “Giant-pulse Nd:YVO4 microchip laser with MW-level peak power by emission cross-sectional control,” Opt. Express 24(4), 3137-3149(2016). 
     In the numerical calculation, T 0 , R, L, σ g , l g (mm), γ g , and τ g  were taken as the following values.
         T 0 =0.3   R=0.5   L=0.06   σ g =2.63×10 −23  (m 2 )   l g =4 mm,   γ g =2   τ g =0.23 ms       

     n gf  was sequentially calculated in the numerical calculation process. W p  was determined by the excitation power P p  and an excitation area thereof. 
     Further, the energy E Airy disk  in the Airy disk was calculated based on the intensity distribution calculated based on Equation (1). When Equation (1) is used, m in Equation (1) is taken as the magnification m. Specifically, a in Equation (1) was set to d i /2, and b in Equation (1) was set to d o /2. 
     A ratio of the energy Epi, of the pulsed laser light L 2  to the energy E PUMP  of the excitation light L 1  is referred to as energy conversion efficiency η. 
     A ratio of the effective energy E Airy disk  in the energy E pulse  of the pulsed laser light L 2  is referred to as effective energy rate E eff . 
     A ratio of the energy E pulse  of the pulsed laser light L 2  to the energy E PUMP  of the excitation light L 1  is referred to as effective energy conversion efficiency η eff . 
     The energy conversion efficiency η, the effective energy rate E eff , and the effective energy conversion efficiency eff are expressed by the following Equations, respectively. 
     
       
         
           
             [ 
             
               Math 
               . 
                   
               7 
             
             ] 
           
         
       
       
         
           
             
               
                 
                   η 
                   = 
                   
                     
                       E 
                       pulse 
                     
                     
                       E 
                       pump 
                     
                   
                 
               
               
                 
                   ( 
                   
                     6 
                     ⁢ 
                     a 
                   
                   ) 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     E 
                     eff 
                   
                   = 
                   
                     
                       E 
                       
                         Airy 
                         ⁢ 
                             
                         disk 
                       
                     
                     
                       E 
                       pulse 
                     
                   
                 
               
               
                 
                   ( 
                   
                     6 
                     ⁢ 
                     b 
                   
                   ) 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     η 
                     eff 
                   
                   = 
                   
                     
                       E 
                       
                         Airy 
                         ⁢ 
                             
                         disk 
                       
                     
                     
                       E 
                       pump 
                     
                   
                 
               
               
                 
                   ( 
                   
                     6 
                     ⁢ 
                     c 
                   
                   ) 
                 
               
             
           
         
       
     
     The energy conversion efficiency η, the effective energy rate E eff  and the effective energy conversion efficiency η eff  were calculated for various magnifications m when the excitation power Pp was 1.5 kW, 3 kW, 6 kW and 12 kW. The magnification m was adjusted by fixing d i  (corresponding to the inner diameter of the pulsed laser light L 2 ) and changing d o  (corresponding to the outer diameter of the pulsed laser light L 2 ). The calculation results are as shown in  FIGS.  8  and  9   . 
       FIG.  8    is a graph showing magnification dependence of the energy conversion efficiency η and the effective energy rate E eff . A horizontal axis of  FIG.  8    shows the magnification. In  FIG.  8   , a vertical axis on the right side shows the energy conversion efficiency η, and a vertical axis on the left side shows the energy conversion efficiency η.  FIG.  9    is a graph showing the magnification dependence (conversion efficiency distribution) of the effective energy conversion efficiency η eff . A horizontal axis of  FIG.  9    shows the magnification. A vertical axis of  FIG.  9    shows the effective energy conversion efficiency η eff .  FIG.  9    is the product of the effective energy rate E eff  and the energy conversion efficiency η shown in  FIG.  8   , as can be understood from Equation (6c). 
     Further, standardized effective energy conversion efficiency η n_eff  was calculated by standardizing the magnification dependence of the effective energy conversion efficiency η eff  shown in  FIG.  9    by maximum effective energy conversion efficiency (a maximum value) of the effective energy conversion efficiency η eff . The standardized effective energy conversion efficiency η n_eff  was calculated for the magnification dependence of the effective energy conversion efficiency η eff  of the excitation power P p  of each excitation light L 1 . The results were as shown in  FIG.  10   . A horizontal axis of  FIG.  10    is the magnification m, and a vertical axis is the standardized effective energy conversion efficiency η n_ef . 
     A hatched region in  FIG.  10    indicates a region in which the standardized effective energy conversion efficiency η n_eff  is 50% or more. The relationship between the magnification m with respect to the hatched region and the excitation power P p  is expressed by Equation (2a). 
     Therefore, when the magnification m satisfies Equation (2a), the standardized effective energy conversion efficiency η n_eff  of 50% or more can be obtained. That is, the energy of the excitation light L 1  can be efficiently converted into the effective energy. As a result, high effective energy can be realized. 
     Equation (2b) shows a region in which the standardized effective energy conversion efficiency η n_eff  is 63.21% or more. Therefore, when the magnification m satisfies Equation (2b), the standardized effective energy conversion efficiency η n_eff  of 63.21% or more can be obtained. That is, the energy of the excitation light L 1  can be more efficiently converted into effective energy. As a result, higher effective energy can be realized. 
     Equation (2c) shows a region in which the standardized effective energy conversion efficiency η n_eff  is 86.47% or more. Therefore, when the magnification m satisfies Equation (2c), the standardized effective energy conversion efficiency η n_eff  of 86.47% or more can be obtained. That is, the energy of the excitation light L 1  can be more efficiently converted into effective energy. As a result, higher effective energy can be realized. 
     Equation (2d) shows a region in which the standardized effective energy conversion efficiency η n_eff  is 90% or more. Therefore, when the magnification m satisfies Equation (2d), the standardized effective energy conversion efficiency η n_eff  of 90% or more can be obtained. That is, the energy of the excitation light L 1  can be more efficiently converted into effective energy. As a result, higher effective energy can be realized. 
     The following facts can also be understood from  FIG.  10   . 
     [When the excitation power P p  is 1.5 kW or more and 12 kW or less (or 3 kW or less or 6 kW or less) (particularly when it is 1.5 kW)] 
     When the magnification m is 1.44 or more and 4.01 or less, the standardized effective energy conversion efficiency η n_eff  of 50% or more can be realized. 
     When the magnification m is 1.64 or more and 3.72 or less, the standardized effective energy conversion efficiency η n_eff  of 63.21% or more can be realized. 
     When the magnification m is 1.93 or more and 3.40 or less, the standardized effective energy conversion efficiency η n_eff  of 86.47% or more can be realized. 
     When the magnification m is 1.99 or more and 3.32 or less, the standardized effective energy conversion efficiency η n_eff  of 90% or more can be realized. 
     The following facts can also be understood from  FIG.  10   . 
     [When the excitation power P p  is 3 kW or more and 12 kW or less (or 6 kW or less) (particularly when it is 3 kW)] 
     When the magnification m is 1.47 or more and 5.1 or less, the standardized effective energy conversion efficiency η n_eff  of 50% or more can be realized. 
     When the magnification m is 1.69 or more and 4.64 or less, the standardized effective energy conversion efficiency η n_eff  of 63.21% or more can be realized. 
     When the magnification m is 2.02 or more and 4.03 or less, the standardized effective energy conversion efficiency η n_eff  of 86.47% or more can be realized. 
     When the magnification m is 2.10 or more and 4.03 or less, the standardized effective energy conversion efficiency η n_eff  of 90% or more can be realized. 
     The following facts can also be understood from  FIG.  10   . 
     [When the excitation power P p  is 6 kW or more and 12 kW or less (particularly when it is 6 kW)] 
     When the magnification m is 1.50 or more and 6.82 or less, the standardized effective energy conversion efficiency η n_eff  of 50% or more can be realized. 
     When the magnification m is 1.74 or more and 6.20 or less, the standardized effective energy conversion efficiency η n_eff  of 63.21% or more can be realized. 
     When the magnification m is 2.11 or more and 4.99 or less, the standardized effective energy conversion efficiency η n_eff  of 86.47% or more can be realized. 
     When the magnification m is 2.22 or more and 4.74 or less, the standardized effective energy conversion efficiency η n_eff  of 90% or more can be realized. 
     The following points can also be understood from  FIG.  10   . 
     [When the excitation power P p  is 12 kW] 
     When the magnification m is 1.53 or more and 9.16 or less, the standardized effective energy conversion efficiency η n_eff  of 50% or more can be realized. 
     When the magnification m is 1.79 or more and 7.94 or less, the standardized effective energy conversion efficiency η n_eff  of 63.21% or more can be realized. 
     When the magnification m is 2.19 or more and 5.76 or less, the standardized effective energy conversion efficiency η n_eff  of 86.47% or more can be realized. 
     When the magnification m is 2.33 or more and 5.44 or less, the standardized effective energy conversion efficiency η n_eff  of 90% or more can be realized. 
     When the optical oscillator  3 A included in the laser device  1 A is designed, for example, the following design method is possible. 
     First, the standardized effective energy conversion efficiency η n_eff  is calculated by the same method as the above-described numerical calculation. The magnification m is set so that the standardized effective energy conversion efficiency is 50% or more. The shapes and sizes of the first reflection part and the second reflection part are determined to realize the magnification m set in this way. Thus, it is possible to design the optical oscillator  3 A capable of realizing the laser device  1 A, and as a result, it is possible to design the laser device  1 A capable of realizing the standardized effective energy conversion efficiency η n_eff  of 50% or more. 
     Next, various application examples using the laser device disclosed in the present embodiment will be described. 
       FIG.  11    is a schematic view of a first application example of the laser device.  FIG.  11    shows an example in which the laser device  1 A is used for laser ignition of an internal combustion engine  100  in an automobile, cogeneration, or the like. In this case, the laser device  1 A is mounted in the internal combustion engine so that the condensing position of the pulsed laser light L 2  output from the laser device  1 A is located inside a combustion chamber  101  of the internal combustion engine  100 . Since the laser device  1 A has high effective energy as described above, the laser ignition can be performed efficiently. 
       FIG.  12    is a schematic view of a second application example of the laser device.  FIG.  12    shows an example in which the laser device  1 A is used for laser ignition of a jet engine  200 . In this case, the laser device  1 A is mounted in the jet engine  200  so that the condensing position of the pulsed laser light L 2  output from the laser device  1 A is located inside a combustion chamber  201  of the jet engine  200 . Since the laser device  1 A has high effective energy as described above, the laser ignition can be performed efficiently. 
       FIG.  13    is a schematic view of a third application example of the laser device.  FIG.  13    shows a case in which the laser device  1 A is applied to laser processing such as marking and microfabrication. In the example shown in  FIG.  13   , the laser device  1 A (specifically, the accommodation part  5 ) is mounted in a robot arm  300 . The pulsed laser light L 2  can be applied to a processing position of a target object  301  to be processed by operating the robot arm  300 . Therefore, the above-described laser processing such as marking and microfabrication can be performed. Since the laser device  1 A has high effective energy with respect to the energy of the excitation light L 1 , the laser processing can be performed efficiently. Further, since the effective energy is the energy in the Airy disk, microfabrication is also possible. 
       FIG.  14    is a schematic view of a fourth application example.  FIG.  14    shows a case in which a target object  302  to be processed is subjected to laser processing such as laser peening processing and laser forming processing. The example shown in  FIG.  11    is substantially the same as the third application example shown in  FIG.  13    except that a liquid injection part  303  used for the laser peening process, the laser forming process, and the like is mounted in the accommodation part  5 . In the example shown in  FIG.  14   , the above-described laser peening processing and laser forming processing can be performed by irradiating a processing position with the pulsed laser light L 2  while a liquid  304  (for example, water) is supplied from the liquid injection part  303  to the processing position of the target object  302 . Since the laser device  1 A has high effective energy with respect to the energy of the excitation light L 1 , the laser peening processing, the laser forming processing, and the like can be efficiently performed. Further, since the effective energy is the energy in the Airy disk, microfabrication is also possible. 
       FIG.  15    is a schematic view of a fifth application example. In  FIG.  15   , a laser device  1 B which is a modified example of the laser device is used.  FIG.  15    shows an example of when the laser device  1 B is applied to the laser-induced breakdown spectroscopy (LIBS) of a sample  400 . Light radiated from the laser device  1 B and emitted from the sample  400  is referred to as inspection light L 3 . 
     The laser device  1 B includes an excitation light supply part  2 , an optical oscillator  3 A, and a condensing optical system  4 . Since the excitation light supply part  2 , the optical oscillator  3 A, and the condensing optical system  4  are the same as in the case of the laser device  1 A, the description thereof will be omitted. Also in the fifth application example, the condensing optical system  4  is, for example, a lens. Since the laser device  1 B includes the excitation light supply part  2 , the optical oscillator  3 A, and the condensing optical system  4 , the pulsed laser light L 2  can be output in the same manner as the laser device  1 A. The laser device  1 A is disposed with respect to the sample  400  so that the condensing position of the pulsed laser light L 2  is located in an inspection region of the sample  400 . 
     In order to analyze the light from the sample  400  (hereinafter referred to as “inspection light”) generated by the radiation of the pulsed laser light L 2 , a spectroscope  401  is mounted in the laser device  1 B via an optical fiber  402 . Further, the laser device  1 B includes an optical branching filter  7 , a reflection part  8 , and an accommodation part  5 B. 
     The optical branching filter  7  is disposed between the lens  36  and the condensing optical system  4 . The optical branching filter  7  transmits the pulsed laser light L 2 , while reflecting inspection light L 3  that is from the sample  400  and is condensed by the condensing optical system  4 . The optical branching filter  7  is, for example, a wavelength selection filter. 
     The reflection part  8  reflects the light reflected by the optical branching filter  7  to be incident on one end of the optical fiber  402  mounted in the accommodation part  5 B. 
     The accommodation part  5 B accommodates an incident optical system  23  included in the excitation light supply part  2 , the optical oscillator  3 A, the condensing optical system  4 , the optical branching filter  7 , and the reflection part  8 . An optical fiber  21  is mounted in a first end wall  5   a  of the accommodation part  5 B, and an optical fiber  402  is mounted in a third end wall  5   d . Further, an opening  5   c  for outputting the pulsed laser light L 2  is formed in a second end wall  5   b  of the accommodation part  5 B. The opening  5   c  is closed by the condensing optical system  4 . As a result, the pulsed laser light L 2  can be output from the accommodation part  5 B as in the case of the laser device  1 A. 
     The pulsed laser light L 2  output from the laser device  1 B irradiates the inspection region disposed at the condensing position of the pulsed laser light L 2 . Thus, laser-induced breakdown occurs in the inspection region, resulting in plasma emission. Inspection light L 3  generated by the plasma emission is incident on the condensing optical system  4  again and is reflected toward the reflection part  8  by the optical branching filter  7 . The inspection light L 3  reflected in this way is reflected by the reflection part  8  and is incident on the optical fiber  21 . Since the optical fiber  21  is connected to the spectroscope  401 , the inspection light L 3  can be split by the spectroscope  401 . 
     The laser device  1 B can output the same pulsed laser light L 2  as in the laser device  1 A. The pulsed laser light L 2  at the condensing position has high effective energy with respect to the energy of the excitation light L 1 . Therefore, it is possible to efficiently generate the laser-induced breakdown. 
       FIG.  16    is a schematic view of a sixth application example. In  FIG.  16   , a laser device  1 C which is a modified example of the laser device is used. The configuration of the laser device  1 C is the same as that of the laser device  1 A except that the window member  6  is not provided and the opening  5   c  is closed by the condensing optical system  4 . Therefore, the laser device  1 C outputs the pulsed laser light L 2  which is the same as in the laser device  1 A. 
       FIG.  16    shows an example when the laser device  1 C is applied to photoacoustic imaging. Specifically, the laser device  1 C irradiates an inspection target  500  such as a living tissue. At this time, the laser device  1 C is disposed with respect to the inspection target  500  so that the pulsed laser light L 2  is condensed in an inspection region within the inspection target  500 . 
     When the inspection region is irradiated with the pulsed laser light L 2 , the inspection region thermally expands. Ultrasonic US is generated by the thermal expansion. The ultrasonic US is detected by a detector  501  (for example, a high-sensitivity micro-vibration detector). 
     The pulsed laser light L 2  at the condensing position has high effective energy with respect to the energy of the excitation light L 1 . Therefore, it is possible to efficiently generate the thermal expansion and the associated ultrasonic US. 
       FIG.  17    is a schematic view of a seventh application example. In  FIG.  17   , a laser device  1 D which is a modified example of the laser device  1 A is used. The laser device  1 D is mainly different from the configuration of the laser device  1 A in that a laser operation part  10  is further provided. The laser device  1 D will be described focusing on such a difference.  FIG.  17    shows an example in which the laser device  1 D is applied to surgery of an eye  600  (for example, surgery for glaucoma, cataract, or the like). 
     The laser device  1 D includes an excitation light supply part  2 , an optical oscillator  3 A, a condensing optical system  4 , an accommodation part  5 , and a laser operation part  10 . Since the excitation light supply part  2 , the optical oscillator  3 A, and the condensing optical system  4  are the same as in the case of the laser device  1 A, description thereof will be omitted. 
     The accommodation part  5  accommodates the incident optical system  23  included in the excitation light supply part, and the optical oscillator  3 A. The accommodation part  5  is the same as the accommodation part of the sixth application example except that the condensing optical system  4  is not accommodated. The opening  5   c  of the accommodation part  5  is closed by the lens  36 . 
     The laser operation part  10  includes a light propagation optical system  11 , a scanning part  12 , and a condensing optical system  4 . The light propagation optical system  11  is an optical system that propagates the pulsed laser light L 2  toward an eye  600  to be treated. The light propagation optical system  11  may be configured of, for example, a plurality of lenses, mirrors, and the like. A part of the scanning part  12  and the condensing optical system  4  also functions as a part of the light propagation optical system. The scanning part  12  is a part that scans the pulsed laser light L 2  for treatment and has, for example, a mirror and a driving part that scans the mirror. The condensing optical system  4  condenses the pulsed laser light L 2  as in the case of the laser device  1 A. 
     The laser device  1 D has an optical oscillator  3 A. Therefore, the pulsed laser light L 2  that is the same as in the optical oscillator  3 A included in the laser device  1 A is output. The laser operation part  10  has a condensing optical system  4  and condenses the pulsed laser light L 2 . Therefore, the laser device  1 D has the same actions and effects as in the laser device  1 A. Therefore, the pulsed laser light L 2  at the condensing position has high effective energy with respect to the energy of the excitation light L 1 . Therefore, the eye  600  can be treated efficiently. 
     The various forms described above are examples of the present invention. The present invention is not limited to the various forms exemplified and is intended to include the scope indicated by the claims and all modifications within the meaning and scope equivalent to the claims. 
       FIG.  18    is a schematic view showing a first modified example of the optical oscillator. The first reflection part  33  may be separated from the laser medium  31  as in the optical oscillator  3 B shown in  FIG.  18   . In this case, for example, the first reflection part  33  may be supported by a support  37 A that is transparent to the excitation light L 1 . 
       FIG.  19    is a schematic view showing a second modified example of the optical oscillator. An optical oscillator  3 C shown in  FIG.  19    is different from the optical oscillator  3 A shown in  FIG.  18    in that the first reflection part  33  is curved. In this case, for example, the first reflection part  33  may be supported by a support  37 B which is transparent to the excitation light L 1  and of which a support surface supporting the first reflection part  33  is curved. As long as the donut-shaped pulsed laser light L 2  can be obtained, a curving direction of the first reflection part  33  may be opposite to a direction shown in  FIG.  19   . 
       FIG.  20    is a schematic view showing a third modified example of the optical oscillator. As in the optical oscillator  3 D shown in  FIG.  20   , the second reflection part  35  may be provided on the second end surface  32   b  of the Q-switch element  32 . In this case, the second end surface  32   b  may be curved so that the second reflection part  35  is curved in a desired shape. 
       FIG.  21    is a schematic view showing a fourth modified example of the optical oscillator. An optical oscillator  3 E shown in  FIG.  21    is different from the optical oscillator  3 D shown in  FIG.  20    in that the first reflection part  33  is curved. In this case, the first end surface  31   a  of the laser medium  31  may be curved so that the first reflection part  33  is curved in a desired shape. As long as the donut-shaped pulsed laser light L 2  can be obtained, the curving direction of the first reflection part  33  may be opposite to a direction shown in  FIG.  21   . 
     As shown in  FIG.  22   , when the first reflection part  33  and the second reflection part  35  are curved, the first reflection part  33  and the second reflection part  35  may be reflection parts having R1 and R2 that can be expressed by the following Equations. R1 is a radius of curvature of the first reflection part  33 , and R2 is a radius of curvature of the second reflection part  35 . 
         R 1=−2 Lc /( m− 1)
 
         R 2=2 mLc /( m− 1) 
     In Equations of R1 and R2, m is the magnification m (=d o /d i ) described with reference to  FIG.  2   , and Lc is the resonator length Lc described with reference to  FIG.  1   . 
     The d i  in the magnification m corresponds to a size (a diameter, or the like) of the second reflection part  35 , and the d o  corresponds to a diameter of the output pulsed laser light (the donut beam). Therefore, the laser device can be designed to obtain a donut-shaped pulsed laser light having a desired magnification m using the above-described Equations of R1 and R2. 
     The saturable absorber exemplified as the Q-switch element and the laser medium may be separated from each other. When seen in an optical axis direction of the optical oscillator, a size of the saturable absorber may be larger than that of the second reflection part and smaller than that of the laser medium. 
     The laser device may further include a non-linear optical system (for example, a non-linear optical element) that has birefringent phase matching (BPM) for converting the annular laser light (for example, the donut beam-shaped pulsed laser light L 2  of the above embodiment) output from the unstable resonator or quasi phase matching (QPM), or combines both. In this case, for example, since a conversion from fundamental waves with a wavelength of 1 μm (laser oscillation wavelength depends on an additive element that is the center of light emission) to a short wavelength such as a visible region and an ultraviolet region by harmonics and sum frequencies, and a combination of them including a parametric process and differential frequencies, and a conversion from a mid-infrared region to terahertz waves by a parametric process, and a difference frequency, and a combination of them including harmonics and sum frequencies can be efficiently performed, it is effective for processing and measurement. Further, the nonlinear optical system (for example, a non-linear optical element) is also useful for pulse shaping including pulse compression and expansion using a spectrum chirp. 
     The various embodiments and modified examples described above may be appropriately combined as long as they do not deviate from the gist of the invention. 
     REFERENCE SIGNS LIST 
     
         
           1 A,  1 B,  1 C,  1 D Laser device 
           2  Excitation light supply part 
           3 A,  3 B,  3 C,  3 D,  3 E Optical oscillator 
           4  Condensing optical system 
           31  Laser medium 
           32  Q-switch element 
           33  First reflection part 
           34  Support 
           35  Second reflection part 
           36  Lens 
         L 1  Excitation light 
         L 2  Pulsed laser light (annular laser light) 
         UR Unstable resonator