Abstract:
High-power, diode-pumped solid state (DPSS) pulsed lasers are preferred for applications such as micromachining, via drilling of integrated circuits, and ultraviolet (UV) conversion. Nd:YVO 4  (vanadate) lasers are good candidates for high power applications because they feature a high energy absorption coefficient over a wide bandwidth of pumping wavelengths. However, vanadate has poor thermo-mechanical properties, in that the material is stiff and fractures easily when thermally stressed. By optimizing laser parameters and selecting pumping wavelengths and doping a concentration of the gain medium to control the absorption coefficient less than 2 cm −1  such as the pumping wavelength between about 910 nm and about 920 nm, a doped vanadate laser may be enhanced to produce as much as 100 W of output power without fracturing the crystal material, while delivering a 40% reduction in thermal lensing.

Description:
RELATED APPLICATION 
     This is a continuation of U.S. patent application Ser. No. 12/058,564, filed Mar. 28, 2008. 
    
    
     COPYRIGHT NOTICE 
     © 2010 Electro Scientific Industries, Inc. A portion of the disclosure of this patent document contains material that is subject to copyright protection. The copyright owner has no objection to the facsimile reproduction by anyone of the patent document or the patent disclosure, as it appears in the Patent and Trademark Office patent file or records, but otherwise reserves all copyright rights whatsoever. 37 CFR §1.71(d). 
     TECHNICAL FIELD 
     This disclosure pertains to solid state laser devices used in high power applications. 
     BACKGROUND INFORMATION 
     A laser amplifies light by concentrating an external source of energy into light waves of a particular wavelength and direction so that resulting light waves are spatially and temporally aligned, or in phase. A laser medium may be a gas, a liquid, or a solid state material such as a crystal. A crystal laser medium may be doped with atoms of another material to alter the properties of the laser medium. 
     As is well known to those skilled in the art, basic operating principles of a laser are understood to be as follows: when a laser medium is energized, electrons within atoms comprising the laser medium are temporarily elevated to a higher atomic energy level, a process called pumping absorption. When high-energy electrons return to a lower energy state, the atom emits light at a wavelength determined by the separation between the two energy levels. This process is called stimulated or spontaneous emission, and visible light emitted during the emission process is referred to as fluorescence. To achieve amplification at a particular wavelength, the number of stimulated emission events must exceed the number of stimulated absorption events, a condition called a population inversion that requires maintaining more electrons at the upper energy level than at the lower level. This population inversion is achieved by “pumping” the laser with an external source of energy, such as an electric current or another laser beam. By containing a lasing medium in a box, or cavity, with light-reflective interior surfaces, light waves produced by stimulated emission resonate within the cavity and reinforce one another to form a coherent, collimated beam. A portion of the coherent laser beam thus produced is permitted to escape through one end of the cavity. A pulsed laser beam may be generated by periodically interrupting a continuous beam. Typical pulse repetition frequencies exceed 100,000 pulses per second, or 100 kHz. 
     Laser pumping efficiency is expressed by a “quantum defect” level, defined as the percentage of pumping energy lost. Excess energy resides in the laser medium as heat. The quantum defect percent is given by
 
 q =(1−ω s /ω p )·100,
 
in which ω s  is a frequency associated with the laser energy transition and ω p  is the pumping light frequency. Thus, a low quantum defect is desirable. In the case of a lasing material pumped by an intense light source, excited state absorption (ESA) reduces pumping efficiency. A factor γ=[1+(δv/Δv) 2 ] −1  is used to measure overlap between emission and absorption lines, in which δv is the frequency difference between the emitting transition and the absorbing transition, and Δv is the full line-width at half intensity of the pumping diode spectrum. A small value of γ corresponds to a low probability of an ESA transition and a high efficiency pumping scheme with respect to ESA.
 
     High-power, diode-pumped solid state (DPSS) pulsed lasers, with power levels on the order of tens of Watts, are preferred for applications such as micromachining, via drilling of integrated circuits, and ultraviolet (UV) conversion. Neodymium:Yttrium Vanadate (Nd:YVO 4 ) and Neodymium:Gadolinium Vanadate Nd:GdVO 4  lasers, made with Nd 3+ -doped Vanadium Oxide (VO 4 ) crystals are good candidates for high power applications because they feature a high energy absorption coefficient over a wide bandwidth of pumping wavelengths. However, vanadate has poor thermo-mechanical properties, compared with other crystal candidates (e.g., Neodymium:Yttrium Aluminum Garnet, or Nd:YAG) in that the material is stiff and fractures easily when thermally stressed. Vanadate fractures under 53 MPa of pressure, while Nd:YAG crystals used in conventional lasers can withstand pressures as high as 138 MPa. Thus, Nd:YAG allows for a correspondingly larger maximum pump power than does vanadate. 
     In general, power absorbed by a lasing medium decreases exponentially from the point of entry, according to P=P o (1−e −αL ), where P o  is applied pump power, α is the absorption coefficient, and L is the length of the crystal rod. If pump power is absorbed preferentially along one axis of a crystal lattice, the absorption coefficient in the direction of that axis is larger. The high power pumping produces a high temperature gradient and associated tensile stress, which may cause asymmetric “thermal lensing” effects or crystal fracture, especially serious for asymmetric absorptions. A symmetric absorption coefficient indicates that pump energy is absorbed equally in all directions, which can expend the heat along the gain medium and in turn reduce excessive thermal stress in the crystal. The inherent structure of the Nd:YVO 4  crystal unit cell, having a dimension along the optic axis c=6.2 Å that differs from equivalent dimensions perpendicular to the optic axis, a=b=7.1 Å, results in asymmetric absorption. 
     Thermal lensing relates to a generally undesirable phenomenon in high power solid state lasers in which heat from excess energy absorption raises the material temperature and distorts the index of refraction of the laser crystal. This distortion results in an effective “lens,” in which the focal length varies inversely with absorbed pump power. Excessive thermal lensing is detrimental to solid state laser performance because of beam distortion and reduced laser conversion efficiency. Proper control of thermal lensing in the lasing material (e.g., by lowering the quantum defect level) is therefore a critical factor in high power laser engineering. 
     Complications such as thermal lensing have thus far limited the power output of vanadate DPSS lasers in TEM 00  mode to less than 30 W. Limitations caused by thermal lensing and thermal fracture are described in Peng, Xiaoyuan; Xu, Lei; and Asundi, Anand; Power Scaling of Diode-Pumped Nd:YVO 4  Lasers,  IEEE Journal of Quantum Electronics , Vol. 38, No. 9, 1291-99, September 2002. 
     Factors influencing inhomogeneous absorption, thermal lensing, and fluorescence lifetimes include doping concentration and physical dimensions of the laser crystal, as well as pumping wavelength and polarization. A typical pumping wavelength used with vanadate crystals is 808 nm, and typical doping concentrations are 0.2% at.-0.5% at, while values below 0.1% at. are difficult to achieve with the degree of control afforded by current manufacturing processes. Typical crystal rod lengths range from 7 mm-15 mm. 
     Vanadate crystal is an anisotropic material, in which the pump energy absorption, and therefore the laser gain, is polarization-dependent, absorbing some polarized waves more readily than others. A change in the polarization state of the pump laser beam, in response to temperature fluctuations (thermal effects), or random shifts in the polarization direction, may therefore contribute further to inhomogeneous absorption. It may be advantageous to force the pump laser beam to be either polarized in a certain direction or de-polarized to control this effect. 
     A 40% reduction in thermal lensing effects is reported by Dudley et al., ( CLEO  2002  Proceedings ) by pumping at 880 nm directly into the upper energy level of the laser transition, rather than at the traditional 808 nm wavelength. This reduction in thermal lensing effects is thought to result from a decrease in the quantum defect level from 24% to 17%, rather than from improved absorption symmetry, because the directional components of the absorption coefficient still differ by a factor of three. However, the absorption bandwidth that a pump delivers at 880 nm is only 2.5 nm compared to commercial products that offer a 4 nm bandwidth. 
     McDonagh et al.,  Optics Letters , Vol. 31, No. 22, Nov. 15, 2006 published results for a high-power Nd:YVO 4  laser with 0.5% at. Nd 3+  doping, pumped at 888 nm. With reference to  FIG. 1 , lasing wavelengths for Nd:YVO 4  normally include 914.5 nm, 1064 nm, and 1342 nm. As published by A. Schlatter, et al.,  Optics Letters , Vol. 30, No. 1, Jan. 1, 2005, when operating Nd:YVO 4  for emission at 914.5 nm, a neodymium ion behaves as a quasi-three-level system. The low laser energy level Z5 is only 433 cm −1  above the ground state, a condition that results in a high lower-state population of 5% at room temperature. Therefore, Schlatter concludes that there is difficulty in achieving Nd:YVO 4  lasing at 914.5 nm because a very bright pumping light source is needed to overcome the high threshold caused by a high population in the state of 433 cm −1 . 
       FIGS. 2 ,  3 ,  4 , and  5  illustrate certain limitations of vanadate crystals. A primary limitation is maximum pump power, which is the amount of pump energy that may be delivered to a crystal before it fractures.  FIG. 2  is a plot comparing calculated maximum pump power levels  100  and measured maximum pump power levels  102  for a doped vanadate crystal, 3 mm×3 mm×5 mm, with a pump beam radius of 0.4 mm. Dependence of fracture-limited pump power on crystal properties is well established. In this case, crystal dimensions, pump beam radius, pump wavelength, and laser-active ion doping concentration determine the power operating range of the laser device.  FIG. 2  compares calculated results with three experimental data points  104 , indicating the pump power at which vanadate crystals actually fractured for various doping concentrations. The calculation used to predict the curve shown in  FIG. 2  is a three-dimensional finite element model that simulates thermal effects of pumping a doped crystal by solving Fourier&#39;s heat conduction equation.  FIG. 2  shows that low doping concentrations are desirable to prevent fracture, with 0.3% at. doping concentration  106  being optimal, allowing a maximum pump power of 37 W.  FIG. 3  shows that, for an applied pump power of 30 W, just under the maximum from  FIG. 2 , the predicted output power  108  achieved by pumping a vanadate laser with a 0.5% doping concentration is optimized at 9 W. Results in  FIGS. 2 and 3  were obtained using a diode laser pump at the conventional pumping wavelength of 808 nm. 
       FIGS. 4 and 5  show spatial distributions of pump power along the length of a 15 mm vanadate crystal rod that serves as a lasing gain medium. Solid curve  110  and dotted curve  112  trace, at various points along the length of the rod (a-cut), respectively, average power absorbed for polarization in the a-axis direction and average power absorbed for polarization in the c-axis of the crystal rod. An ideal crystal rod exhibits symmetric power absorption, in which both the solid and dotted curves are flat lines that coincide along the full length of the rod. The vanadate crystal rod has asymmetric power absorption with, on average, more power absorbed for polarization in the c-axis direction. Furthermore, when pump power is applied to the ends of a lasing gain medium, more power is absorbed close to the ends, while less power reaches the center, a condition referred to as “end-bulging”  120 . This applies to both c- and a-axes; however, more extreme end-bulging  122  occurs in the c-direction. A reduction in end-bulging  124  and a reduction in asymmetry  126  both occur when the doping level increases from 0.3% at. ( FIG. 5 ) to 0.5% at. ( FIG. 4 ). The integrated temperature gradient on the cross section of the lasing crystal is greater in the c-axis direction than in the a-axis direction. 
     SUMMARY OF THE DISCLOSURE 
     By optimizing operating parameters, an ion-doped vanadate laser may be enhanced to produce 100 W or more of output power in TEM 00  mode at, for example, 1064 nm, without crystal fracture, while reducing thermal lensing by 40%. It has been determined that the degree of energy absorption along orthogonal crystal lattice axes, described by a- and c-absorption coefficients, may be made symmetric by setting the pump wavelength to 914.5 nm, and that this symmetry is maintained over a range of doping concentrations. A 40% reduction in thermal lensing previously discovered at 880 nm and 888 nm persists at 914.5 nm, while the quantum defect level is reduced at 914.5 nm. The following table compares quantum defect levels for 1064 nm Neodymium lasers at different pumping wavelengths: 
                                                               Pump Wavelength   Quantum Defect                                        808   nm   0.2406           880   nm   0.1729           888   nm   0.1654           914.5   nm   0.1400                        
Furthermore, values of γ for pumping at 914.5 nm and 888 nm wavelengths are much smaller compared with the traditional 808 nm pumping. Thus, conversion efficiency is improved due to a high quantum efficiency and a reduced ESA transition probability. The following table lists calculated values of γ for a line-width of 3 nm based on spectroscopic data from “Laser Crystals” by Alexander A. Kaminskii.
 
     
       
         
               
               
               
               
             
               
               
               
               
               
             
           
               
                   
                   
               
               
                   
                 Pump Wavelength 
                 ESA Transition 
                 γ 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 808 
                 nm 
                   4 F 3/2  →  2 D 5/2   
                 0.1715 
               
               
                   
                 880 
                 nm 
                   4 F 3/2  →  2 P 1/2   
                 0.0153 
               
               
                   
                 888 
                 nm 
                   4 F 3/2  →  2 P 1/2   
                 0.0084 
               
               
                   
                 914.5 
                 nm 
                   4 F 3/2  →  2 D 3/2   
                 0.0098 
               
               
                   
                   
               
             
          
         
       
     
     Simultaneously, higher pump power and less thermal lensing may be achieved, enabling a pulse repetition frequency (PRF) up to as high as 1 MHz, while preserving a pumping bandwidth of 4 nm. Boosting the vanadate crystal doping concentration from below 0.5% at, to 2.0% at. and using a longer crystal rod improves pump power absorption and gain. Pump power at the pump wavelengths of 914.5 nm and 888 nm is generally absorbed more evenly along the length of a long (e.g., 60 mm) crystal rod with a low absorption coefficient than pump power at the pump wavelengths of 808 nm and 880 nm in shorter crystal rods with a high absorption coefficient. The fluorescence lifetime of vanadate pumped at 808 nm also decreases linearly with increased doping concentration, achieving 50 μs-100 μs at a 1.0% at.-2.0% at. doping level. 
     Additional aspects and advantages will be apparent from the following detailed description of preferred embodiments, which proceeds with reference to the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a theoretical energy diagram of a prior art Nd:YVO 4  crystal laser. 
         FIG. 2  is a graph of the dependence of maximum pump power on doping concentration for a prior art laser pumped at 808 nm. 
         FIG. 3  is a graph of output power as a function of doping concentration for a prior art laser pumped at 808 nm, indicating an optimal value is achieved at 0.5% at. doping concentration. 
         FIG. 4  is a graph of power absorption in a prior art 15 mm vanadate laser crystal, along two orthogonal crystal lattice axes, a and c, with 0.5% at. doping concentration. 
         FIG. 5  is a graph of power absorption in a prior art 15 mm vanadate laser crystal, along two orthogonal crystal lattice axes, a and c, with 0.3% at. doping concentration. 
         FIG. 6  is a graph of the absorption spectrum of an Nd:YVO 4  crystal with 0.3% at. doping concentration measured with a Perkin Elmer Lambda 900 spectrometer. 
         FIG. 7  is a graph of the absorption spectrum of an alternative Nd:GdVO 4  crystal with 0.3% at. doping concentration measured with a Perkin Elmer Lambda 900 spectrometer. 
         FIG. 8  is a graph of the effective absorption coefficient for an Nd:YVO 4  crystal with a 1% at. doping concentration, along two orthogonal crystal lattice axes, a and c, as a function of pump wavelength, derived from measured data. 
         FIG. 9  is a graph of the effective absorption coefficient for an alternative preferred Nd:GdVO 4  crystal with a 0.3% at. doping concentration, along two orthogonal crystal lattice axes, a and c, as a function of pump wavelength, derived from measured data. 
         FIG. 10  is a version of the graph of  FIG. 8 , showing with an expanded scale effective absorption coefficients for wavelengths ranging between 885 nm and 920 nm. 
         FIG. 11  is a version of the graph of  FIG. 9 , showing with an expanded scale effective absorption coefficients for wavelengths ranging between 885 nm and 920 nm. 
         FIG. 12  is an expanded version of the graph of  FIG. 8 , showing with a compressed scale effective absorption coefficients for pump wavelengths ranging between 800 nm and 920 nm. 
         FIG. 13  is a plot showing the linear relationship of the absorption coefficient of a 914.5 nm-pumped Nd:YVO 4  crystal as a function of doping density. 
         FIG. 14  is a plot comparing theoretical and measured temperature dependences of 914.5 nm light absorption in a Nd:YVO 4  crystal with a 1% at. doping concentration. 
         FIG. 15  is a block diagram of a Nd:YVO 4  laser power amplifier pumped at 914.5 nm. 
         FIG. 16  is a schematic drawing of a preferred 60 mm long vanadate crystal rod designed to exhibit total internal reflection. 
         FIG. 17  is a plot showing the change in the pump beam radius as the beam propagates along the length of the crystal rod of  FIG. 16 . The minimum radius at the −7 mm crystal rod position corresponds to a neck in the beam shown in  FIG. 16 . 
         FIG. 18  is a plot showing, for seed polarization along c- and a-crystal lattice axes, power gain as a function of seed power, for a Nd:YVO 4  crystal pumped by a 914.5 nm, 3 W diode. 
         FIG. 19  is a plot showing, for seed polarization along c- and a-crystal lattice axes, power gain as a function of seed power, for a Nd:YVO 4  crystal pumped by a 914.5 nm, 2.5 W diode. 
         FIG. 20  is a graph showing an inverse linear dependence of fluorescence lifetime on doping concentration at 808 nm pumping. 
         FIGS. 21A and 21B  are oscilloscope traces of a laser pulse displayed as a function of time, respectively, before and after amplification using 914.5 nm pumping. 
         FIG. 22  is a graph of a theoretical temporal pulse before and after amplification, for comparison with experimental results shown in  FIGS. 21A and 21B . 
         FIG. 23  is a family of curves showing theoretical power increase of the power amplifier of  FIG. 15  as a function of pump power for four different pumping wavelengths. 
     
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
       FIGS. 6-12  demonstrate relevant aspects of pumping vanadate crystals at various wavelengths. A significant difference between the two absorption curves in each drawing indicates asymmetric absorption, i.e., more energy is absorbed for pumping light polarized in the c-axis direction than in the a-axis direction. The broad pumping wavelength spectrum (800 nm-920 nm) shown in  FIG. 12  indicates that absorption symmetry improves dramatically above about 880 nm (i.e., at 888 nm and 914.5 nm). At the 888 nm and 914.5 nm wavelengths, spectral profiles  219   a  and  219   c  and spectral profiles  220   a  and  220   c  for the respective orthogonal a- and c-crystal lattice axes nearly coincide, although the total absorption is less than 5%. 
     Absorption spectra for two embodiments, Nd:YVO 4  and Nd:GdVO 4  crystals, pumped at 914.5 nm, represent results of two different measurement methods. With reference to  FIGS. 6 and 7 , the first method is a direct measurement of absorption spectra. The data in  FIG. 6  represent a 0.3% at.-doped Nd:YVO 4  crystal, and the data in  FIG. 7  represent a 0.3% at.-doped Nd:GdVO 4  crystal, each measured with a Perkin Elmer Lambda 900 spectrometer, over the wavelength range 870 nm-930 nm. With particular reference to  FIG. 7 , a disparity  206  in absorption between the c-axis and a-axis curves decreases with increasing wavelength so that at 914.5 nm, the two curves are coincident, indicating that absorption at 914.5 nm is axially symmetric. This axial absorption symmetry represents a significant advantage of pumping at 914.5 nm. 
     The second method of determining absorption spectra entails changing the laser diode temperature, which shifts the emission wavelength. Once the emission wavelength is known, output and input power levels may be measured to determine the effective absorption coefficient, which is shown in  FIGS. 8-12 . Effective absorption spectra obtained using this method show that Nd:GdVO 4  and Nd:YVO 4  exhibit corresponding strong spectral profile peaks  208   a ,  208   c  and  218   a ,  218   c  at 880 nm; relatively weak spectral profile peaks  209   a ,  209   c  and  219   a ,  219   c  at 888 nm; and relatively weak spectral profile peaks  210   a ,  210   c  and  220   a ,  220   c  at 914.5 nm. Absorption coefficients in the range 0-2 cm −1  as shown in the scaled plots in  FIGS. 10 and 11  show magnified versions of prominent local spectral profile peaks  209   a ,  209   c  and  219   a ,  219   c  at 888 nm and  210   a ,  210   c  and  220   a ,  220   c  at 914.5 nm for Nd:GdVO 4  and Nd:YVO 4  having doping concentrations of 0.3% at. and 1% at., respectively. 
       FIG. 12  shows a more complete spectrum of effective absorption coefficients covering the entire range of pumping wavelengths of interest, 800 nm to 920 nm. The strongest peaks of spectral profiles  214   a  and  214   c  occur in vanadate at 808 nm, but the absorption is highly asymmetric, as indicated by the disparity  216  between absorption coefficients  214   a  and  214   c , and thus requires a fairly low doping concentration for high-power applications. The same prescription exists at a pump wavelength of 880 nm. On the other hand, absorption coefficients  218   a ,  220   a  and  218   c ,  220   c  along the respective a- and c-crystal lattice axes are fairly well-matched at 888 nm and at 914.5 nm, although the maximum value of the absorption coefficient at 914.5 nm is only about one-half the maximum value at 888 nm. Symmetry at the highest pumping wavelengths allows neodymium ion-doped vanadate crystals to have a higher doping concentration.  FIG. 13  shows a straight line  223  approximation representing measured absorption coefficients at 914.5 nm as a function of doping concentrations, which doping concentrations range from 0.8% at. to 2.0% at. with a maximum coefficient  226 , 1.0 cm −1 , occurring at a 2.0% at. doping concentration. 
     Because of a low quantum defect level at 914.5 nm, thermal effects are minimized with 914.5 nm pumping. As a result, less heat is generated in the laser crystal, reducing thermal lensing and tensile stress. In addition, because power absorption is isotropic, and because the relatively low absorption of the 914.5 nm photon allows pumping light to travel farther in the laser crystal, energy is distributed more evenly along the entire laser rod, which in turn results in less temperature gradient that causes thermal stress, as is the case for vanadate crystals pumped at lower wavelengths. Thus, the vanadate crystal tolerates heating much better when pumped at 914.5 nm. As a result, a vanadate crystal can handle more pumping power, up to 100 W, which is almost impossible to achieve for 808 nm and 880 nm pumping, as indicated in  FIG. 2  for 808 nm. 
     One reason why vanadate absorbs energy easily at 880 nm and 888 nm is that there exist in states Z1 and Z2  230  than in state Z5 more atoms that are available to absorb pumping energy and jump to higher excited energy states  4 F 3/2 , as diagrammed in  FIG. 1 . Atomic populations at equilibrium at room temperature for the ground state (Z1), the second lowest-state (Z2, 108 cm −1 ), and highest lower state (Z5, 433 cm −1 ) are 40%, 24%, and 5%, respectively. In general, population at an energy state varies with temperature according to Boltzmann&#39;s principle: when a collection of atoms is at thermal equilibrium, T, the ratio of atomic populations (N1 and N2) at any two energy levels E1 and E2 is given by 
                   N   ⁢           ⁢   2       N   ⁢           ⁢   1       =     exp   ⁡     (     -         E   ⁢           ⁢   2     -     E   ⁢           ⁢   1       kT       )         ,         
where k is Boltzmann&#39;s constant. As temperature increases from room temperature (24° C.) to 100° C., the exponential decrease in the number of atoms in excited states becomes less pronounced, so more atoms remain in higher energy states. For instance, the atomic population at energy level Z5 increases from 5% to 6.7%, and the absorption coefficient increases commensurately. Theoretical calculations agree well with the experimental results, as shown in  FIG. 14 . The measured decrease  232  in light transmission at higher temperatures, 50° C. to 170° C., indicates more light is absorbed by the crystal as it rises in temperature. Thus, a vanadate crystal pumped at 914.5 nm actually benefits from the temperature rise because the overall pump power absorption increases.
 
     In the case of an end-pumping configuration, pump energy is concentrated in the central region of the lasing medium to overlap with laser modes. End pumping energy is highly divergent, so a pumping laser beam spot and the cross-sectional area of the lasing medium are preferably closely matched to efficiently produce a waveguide effect along the length of the lasing medium. The waveguide effect enhances beam quality and efficiency because higher order modes outside the waveguide have no gain. Referring again to the energy level diagram of  FIG. 1 , after stimulated emission  234  occurs from upper energy level R1 to lower energy level Y1, atoms in state Y1 decay rapidly to the nearest lower level, Z5, via multi-phonon relaxation. During laser actions, the atomic population at level Z5 thus dramatically increases above its thermal equilibrium value, which again results in increased absorption at 914.5 nm. 
       FIG. 15  shows a Nd:YVO 4  power amplifier  236  optically pumped at 914.5 nm to produce a high-power, high efficiency lasing device at 1064 nm. Power amplifier  236  includes a seed laser  237  emitting a beam  238  of 1064 nm energy that propagates through a Nd:YVO 4  crystal  240 . Nd:YVO 4  crystal  240  is an a-cut, 20 mm long, 3 mm diameter octagonal rod of vanadate crystal, with 2.0% at. doping. The laser mode size is about 600 μm in diameter. A fiber-coupled diode array  241  emits 914.5 nm light that propagates through a focusing lens  242  and a dichroic mirror  243  to optically pump Nd:YVO 4  crystal  240 . Fiber-coupled diode array  241  may be, for example, an array of fiber-coupled single emitters available from JDS Uniphase of Milpitas, Calif., with full-width, half-maximum (FWHM) bandwidth of 4 nm at 5 W. The fiber core diameter of the JDS Uniphase laser is 100 μm, and the numerical aperture is 0.22. 
     With reference to  FIG. 16 , because the absorption coefficient at 914.5 nm is fairly low, a vanadate bulk material crystal or rod  244  of a typical single-piece length (40 mm-60 mm) is preferred or multiple segments of vanadate crystals to form a long gain medium (40 mm-100 mm). Moreover, the overlap between the pump mode and the laser mode in the center of vanadate crystal rod  244  is threatened by the large divergence angle of the fiber-coupled laser diode output emission.  FIG. 16  shows a long vanadate crystal rod structure  244  with total internal reflection (TIR) designed to reduce the loss of the pump power, while the diameter of the circular rod can be matched to the laser mode size (1 mm-3 mm). Currently, such a crystal rod structure, 3 mm diameter×60 mm long, with optical polishing on the end surfaces and barrel, is available from Raicol Crystal, Inc. of Yehud, Israel. Pumping at 914.5 nm with a 2 mm diameter pump beam spot size can provide pump power of as much as a few hundred watts. 
       FIG. 17  shows a curve  245  representing the radius of the pump beam as a function of distance along the pump beam axis and indicates a minimum 500 μm pump beam spot diameter  246  for the embodiment described. 
     The cross section of vanadate crystals can be round, square, or polygonal such as tetragonal, hexagonal, or octagonal. Nd:YVO 4  crystal  240  in the form of a rod with an octagonal cross section has the following advantages: 
     (a) Reduced parasitic oscillations, (known to be problematic in circular cylindrical rods) 
     (b) More TIR (total internal reflection) surfaces 
     (c) Easy determination of the laser polarization axis 
     (d) A symmetric mode structure, improving final laser beam quality. 
     Power amplifier  236  may be configured to facilitate independent power amplification along the a- and c-axes of the vanadate crystal lattice.  FIGS. 18 and 19  show power increase as a function of seed laser beam power and pump power, respectively. When vanadate crystal  240  is pumped by a 914.5 nm diode, the seed laser beam power becomes amplified.  FIG. 18  shows an experimentally determined  310  mW power increase  247  with 3 W pump power and a 2.5 W seed laser beam at 914.5 nm pump wavelength.  FIG. 23  shows a corresponding computer model-predicted power increase curve  248  for a 914.5 nm pump wavelength. Datum point  247   a  on curve  248  corresponds to datum point  247  of  FIG. 18  and represents a computer-model predicted 360 mW power increase with 3 W pump power and a 2.5 W seed laser beam.  FIG. 23  also shows power increase curves  249 ,  250 , and  252  of somewhat smaller magnitude predicted for lower pump wavelengths. Power amplifier  236  is capable of achieving a power increase on the order of 10 W during high power operation because a Nd:YVO 4  crystal  240  can be constructed to withstand 100 W pump power and the power increase is a linear function of pump power. 
     Additionally, JDS Uniphase laser diodes operating at 914.5 nm made with InPGaAs are readily available because of their applications in fiber optic communication technology. These devices feature greater than 70% electrical-to-optical efficiency, while typical commercial efficiency for 800 nm-series diodes is less than 50%. Coherent, Inc. of Santa Clara, Calif. is another source of high power fiber-coupled diodes up to 50 W at 914.5 nm, in which the core fiber diameter is 800 μm and the numerical aperture is less than 0.14. 
       FIG. 20  shows an inverse linear relationship  256  between fluorescence lifetime and doping concentration. A short fluorescence lifetime achieves short pulse durations corresponding to a high pulse repetition frequency. Independent of pumping wavelength, fluorescence lifetime drops to 50 μs when a 2.0% at. doping concentration is achieved, as indicated by datum point  258 . 
     Experimental and theoretical 1064 nm temporal pulses propagating from dichroic mirror  243  as laser output of power amplifier  236  of  FIG. 15  are shown in  FIGS. 21A and 21B  and  FIG. 22 , respectively. A short pulse  262  shown in  FIG. 21A  and a short pulse  264  shown in  FIG. 21B  represent power levels measured, respectively, before and after power amplifier  236 . With reference to  FIG. 22 , curves  266  and  267  represent theoretical temporal pulses, respectively, before and after power amplifier  236  and indicate a total duration  268  of about 20 ns, with most of the power concentrated within a very short time interval of 10 ns. During this time, the peak laser output power is amplified from about 6 kW to about 7.5 kW, representing about a 25% power enhancement. Experimental results set forth in  FIGS. 21A and 21B , using different parameters from the theoretical model, show temporal pulses of about the same width  270  as that predicted by the theoretical model of  FIG. 22 , with a power increase, in this case, of 12.5%. 
       FIG. 23  presents a set of curves  272  representing results of a computer model of power amplifier  236  and gives power increase as a function of pump power at 808 nm, 880 nm, 888 nm, and 914.5 nm pump wavelengths, Specifically, curves  248 ,  249 ,  250 , and  252  represent, respectively, 914.5 nm, 880 nm, 880 nm, and 808 nm pump power. Computer model curves  272  show that power increases at pumping wavelengths 914.5 nm, 888 nm, and 880 nm are much higher than the power increase at 808 nm, and that power increases obtained by pumping at 888 nm and 880 nm are similar to each other. However, the maximum power increase occurs at 914.5 nm. 
     Benefits of disclosed parameter adjustments and associated performance improvements are summarized in the table below. 
     
       
         
               
               
               
               
               
             
           
               
                   
               
               
                   
                 CONVENTIONAL 
                   
                 MCDONAGH 
                 PREFERRED 
               
               
                 PARAMETER 
                 ND:YVO 4  LASER 
                 DUDLEY ET AL. 
                 ET AL 
                 EMBODIMENT 
               
               
                   
               
             
             
               
                 Pumping 
                 808 
                 880 
                 888 
                 914.5 
               
               
                 wavelength, nm 
               
               
                 Doping 
                 0.25 
                 0.5 
                 0.5 
                 2.0 
               
               
                 concentration, % 
               
               
                 at. 
               
               
                 Pump power limit, 
                 60 
                 80 
                 150 
                 ≧200 
               
               
                 W 
               
               
                 Crystal rod length, 
                 8-15 
                 &gt;25 
                 ≧30 
                 ≧40 
               
               
                 mm 
               
               
                 RESULT 
               
               
                 Power out, W 
                 &lt;30 
                 30-40 
                 60 
                 ≧60 
               
               
                 Absorption 
                 4 
                 2.5 
                 3.5 
                 3.5 
               
               
                 bandwidth, nm 
               
               
                 Absorption 
                 6/2 
                 6.4/1.3 
                 1.2/1.1 
                 0.5/0.48 
               
               
                 coefficients c/a 
               
               
                 Quantum defect 
                 24 
                 17.3 
                 16.5% 
                 14 
               
               
                 level, % 
               
               
                 (wavelength- 
               
               
                 dependent) 
               
               
                   
               
             
          
         
       
     
     It will be obvious to those having skill in the art that many changes may be made to the details of the above-described embodiments without departing from the underlying principles of the invention. For example, the vanadate crystal may have laser-active ion doping established by neodymium ion doping in a lutetium host, neodymium ion doping in a yttrium host, or neodymium ion doping in a gadolinium and yttrium mixed host. The scope of the present invention should, therefore, be determined only by the following claims.