Abstract:
Anisotropic crystals such as Nd:YVO 4 , Nd:YLF, and Nd:GdVO 4  have become preferred gain materials for many laser applications. The anisotropic gain medium without ancillary compensation ensures there is no degradation of laser modes when passing through the gain medium. An optical power amplifier that incorporates an anisotropic gain medium achieves power scaling with multiple passes while also maintaining good mode matching between the laser and the pump during each pass. Preferred embodiments implement for multiple passes of a seed laser beam through an anisotropic gain medium with substantially zero angular beam displacement during each pass. The multi-pass system provides an economical, reliable method of achieving high TEM 00  power to meet the demands of micromachining, via drilling, and harmonic conversion applications.

Description:
COPYRIGHT NOTICE  
       [0001]    © 2008 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  
       [0002]    The present disclosure relates to a solid state laser amplifier used in high power applications. 
       BACKGROUND INFORMATION  
       [0003]    Fiber and semiconductor lasers and diode-pumped solid-state (DPSS) pulsed lasers with output power in the range of several Watts to tens of Watts are applied primarily in laser micromachining in the field of electronic device manufacturing. Micromachining applications require a high pulse repetition frequency (PRF), corresponding to laser pulse durations ranging from nanoseconds to picoseconds, and even femtoseconds. Typical laser output wavelengths range from infrared to ultraviolet. The performance of traditional solid-state lasers that rely on a simple master oscillator is falling behind the overall pace of laser system technology development, primarily because of limited pulse repetition rate and power scaling by a single oscillator. 
         [0004]    As is well known to those skilled persons, progress in power scaling of a TEM 00  laser mode has been limited by the formation of aberrated thermal lenses within the active lasing medium. A thermal lens is mainly caused by a temperature gradient in a laser crystal and results in a distortion of the index of refraction of the crystal in response to non-uniform pump power. Peng, Xu, and Asundi, “Power Scaling of Diode-Pumped Nd:YVO 4  Lasers,”  IEEE-Quantum Electronics, Vol.  38, No. 9, 2002, demonstrate that maximum pump power varies inversely with doping concentration, and that the pump power increases to only 40 W for a 0.3% doped vanadate crystal using an 808 nm pump wavelength and a 0.8 mm diameter pump spot size.  FIG. 1  is a graph showing maximum pump power as a function of doping concentration for an 808 nm-pumped laser. In addition to thermal lens formation, the maximum incident pump power is restricted by thermal fracture of the laser crystal. To date, the highest output power achieved for a TEM 00  mode narrow bandwidth and linearly polarized beam generated by an end-pumped vanadate laser is less than 30 W, while a power level of about 100 W is desirable. Currently, nanosecond pulsed fiber lasers are limited to generating peak power exceeding 1 kW with a TEM 00  mode because of stimulated Brillouin scattering (SBS) and damage issues. 
         [0005]    One way to meet the demand for a high power laser source is to use a laser power amplifier. An advantage of laser power amplifiers is that the final power output may be easily scaled to meet a specific requirement for each different application. Laser power amplifiers also may be paired with different seed laser sources to allow flexibility in seed laser design and manufacturing. However, maintaining a high quality beam and stable output in a laser power amplifier remains a technical challenge. 
         [0006]    A typical laser power amplifier uses a single-pass configuration, meaning that the seed laser beam passes once through the gain medium. One example is presented in Maik Frede et al., “Fundamental mode, single-frequency laser amplifier for gravitational wave detectors,”  Optics Express, Vol.  15, No. 2, 2007. A single-pass, four-stage amplifier described in the Maik Frede et al. paper and diagrammed in  FIG. 2 , extracted only 3 W from an amplifier with a 1 W seed laser and 45 W of pump power, which yields an optical-to-optical efficiency of 6.7%. Even state of the art single-pass power amplifiers typically exhibit a low extraction efficiency or a high (40%-60%) optical conversion rate from a diode laser pumping light source. However, a typical diode end-pumped vanadate laser oscillator has 40% -60% optical-to-optical conversion efficiency. 
         [0007]    A method of improving the energy extraction efficiency entails guiding the laser beam back through the gain material multiple times, thereby compounding the gain until the desired power amplification is achieved. A typical multi-pass amplifier produces much more gain than does a single-pass amplifier. Suitable applications for a multi-pass power amplifier include semiconductor device link processing (IR, green and UV tailored pulse), laser micromachining (picosecond pulse amplification), and via drilling (high-power IR, green, and UV laser). U.S. Pat. No. 5,546,222, of Plaessmann et al. describes several embodiments of a multi-pass light amplifier, four of which embodiments are presented in  FIG. 3 . The Plaessmann et al. patent demonstrates, using a Nd:YLF twelve-pass amplifier at 10 kHz, that 2.5 μJ of energy was amplified to 45 μJ with 1.6 W of pump energy focused in the amplifier gain medium. As is typical for traditional multi-pass configurations, a large gain, in this case, twenty-fold, is achieved at the expense of beam quality. 
         [0008]    A number of patents describe multi-pass amplifiers, but all of them share the problem of laser beam displacement within the gain medium, which displacement has two inherent, serious drawbacks. The first is that the pumped region must be sufficiently large to contain all the laser modes in different passes; otherwise, the result is low efficiency mode matching between the laser and the pump. Second, a non-uniform pump distribution in the gain medium, such as the so-called “super Gaussian” mode, causes distortion in laser beam power distribution with each pass, ultimately resulting in degradation of laser beam quality. Therefore, similar to a laser cavity with thermal lensing, compensation optics are needed to optimize laser output with higher beam quality. In addition, these multi-pass amplifiers generally require a fairly complicated optical setup, possibly even specially shaped optical elements. More important, multi-pass laser beams normally share the same two or three optical elements, making it fairly difficult to control the influence of thermal lensing. This especially causes problems in high-power applications because each pass modifies the laser beam parameters. 
         [0009]    U.S. Pat. No. 5,268,787 of McIntyre describes a method and an apparatus for multi-pass laser amplifiers but does not address thermal depolarization issues and unwanted lasing in the amplifier. It also fails to address how the gain material, the key component of a laser power amplifier, affects performance of the laser amplifier when pumped by a high power light source. In the case of YAG solid state lasers, high power pumping induces significant thermal birefringence, causing orthogonal polarization directions to exhibit different gain in such a setup. Thermally induced birefringence in YAG rods under strong optical pumping has been observed, reported, and analyzed in numerous articles. Q. Lu et al., “A novel approach for compensation of birefringence in cylindrical Nd:YAG rods,”  Optical Quantum Electronics, Vol.  28, pp. 57-69, 1996, showed that 25% of optical power was lost through laser beam depolarization caused by thermal birefringence. Q. Lu et al. report that a carefully designed compensation method reduced the power loss to just 5%. Thus, it would seem that controlling and compensating for thermal birefringence in laser amplifiers is necessary and important. 
         [0010]    U.S. Pat. No. 6,384,966 of Dymott addresses this power loss problem by rearranging optical components of a previous laser amplifier design to compensate for thermal birefringence, while passing the laser beam multiple times through the gain medium. For example, in the Dymott patent, a quarter-wave plate is placed between the gain medium and a first reflecting mirror. The Dymott patent specifies that the quarter-wave plate be oriented such that linearly polarized beam emerging from a Faraday rotator pass through the quarter-wave plate without undergoing any phase retardation. However, because of thermally induced birefringence, light passing once through the gain material generally becomes elliptically polarized. Upon two passes through the quarter-wave plate, the rotation direction of the elliptical polarization is reversed, and the thermally induced birefringence in the gain material is compensated. 
         [0011]    The Dymott patent describes use of additional optical components in the design of the optical power amplifier to address other issues. For example, a 450 polarization rotator, or “Faraday rotator,” is needed in this amplifier to separate amplified light from incident seed light. But the Faraday rotators (reference numerals 2, 4, 23, and 73 in FIGS. 1-5 of the Dymott patent) are placed in a region where the laser beam spot size is difficult to control, potentially causing damage in the case of high-average-power and high-peak-power applications. Another example is the placement of a pair of concave and convex mirrors on either side of each laser crystal to construct an unstable cavity to eliminate undesired lasing action. 
         [0012]    In addition, the strong thermal lens in high-power applications acts as a major lens in the amplifier, contributing to instability of the cavity. As is well-known, the degree of thermal lensing varies with PRF, cooling temperature, and pump power. Multi-pass power amplifiers described in the Dymott patent are fabricated from Nd:YAG, an isotropic gain medium that is subject to depolarization effects. The Dymott patent points out that gain materials may include Nd:YAG, Nd:YVO 4 , Nd:YLF, or Ti:sapphire to compensate for thermally induced birefringence, by design. 
       SUMMARY OF THE DISCLOSURE  
       [0013]    The Dymott patent fails to recognize that anisotropic gain materials, including Nd:YVO 4  and Nd:YLF, exhibit an intrinsic benefit in that they themselves are naturally birefringent, so adding a component to compensate for thermal birefringence is unnecessary in preferred embodiments disclosed. For example, if a seed laser beam polarized along the c-axis of a Nd:YVO 4  crystal passes through an Nd:YVO 4  amplifier crystal, the effect of depolarization on the incident linearly polarized light is negligible. Adding an extra component in a high power laser amplifier increases the cost and the risk of optical damage, while it deteriorates the quality of the amplified beam. Moreover, configurations shown in the Dymott patent drawings cannot benefit from anisotropic gain materials such as Nd:YLF because the emission wavelengths are not the same in all directions. Emission along the a-axis is at 1047 nm, whereas emission along the c-axis is at 1053 nm. Double-pass and quadruple-pass amplifiers have, therefore, effective amplification functions equal to those of single-pass and double-pass amplifiers, respectively. 
         [0014]    None of the above-mentioned patents pertaining to laser power amplifiers explores the use of anisotropic laser gain media. In the past few decades, anisotropic crystals such as Nd:YVO 4 , Nd:YLF, and Nd:GdVO 4  have become preferred gain materials for many laser applications because they have high emission cross sections and, therefore, a high rate of stimulated emission. These materials are also capable of generating a linearly polarized beam without introducing separate polarization compensation. In addition, the anisotropic gain medium can be implemented with suitable optics to correct thermal lensing and reduce thermal lens effects, without ancillary compensation, to ensure there is less degradation of laser modes when passing through the gain medium. 
         [0015]    With these advantages, preferred embodiments of an optical power amplifier that incorporates an anisotropic gain medium can achieve power scaling with multiple passes while also maintaining good mode matching between the laser and the pump during each pass. The present disclosure emphasizes efficiency of the amplifier and quality of the amplified beam in properly matching a pumping light mode and a seed laser mode. Preferred embodiments are capable of maintaining a beam with substantially zero displacement, which leads to greater efficiency, and provide an economical, reliable solution that achieves high power TEM 00  output to meet the demands of micromachining, via drilling, and harmonic conversion applications. 
         [0016]    When constructing a laser amplifier including Nd:YVO 4 , or other anisotropic gain material, neither compensating for thermal birefringence nor undesired lasing is a main concern, as indicated by the placement and configuration of optical components in multiple pass amplifiers. Data from amplifier experiments involving anisotropic laser gain media further support this conclusion. Data for Nd:YVO 4  suggest that a strong seed laser beam impinging upon anisotropic Nd:YVO 4  may be amplified along the a-axis, but at a magnitude of about 3-4 times less than that along the c-axis. 
         [0017]    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  
         [0018]      FIG. 1  is a graph comparing calculated and measured values of maximum pump power as a function of doping concentration for a prior art vanadate laser pumped at 808 nm. 
           [0019]      FIG. 2  is a diagram of a prior art four-stage amplifier design described by Frede et al. 
           [0020]      FIG. 3  is a collection of ray diagrams of four embodiments of a prior art multi-pass amplifier design described by Plaessmann et al. 
           [0021]      FIGS. 4A ,  4 B, and  4 C are implementations of, respectively, double-, triple-, and quadruple-pass amplifiers.  FIG. 4A-1  illustrates the law of reflection in relation to a laser beam incident on and reflected by a curved reflective surface. 
           [0022]      FIGS. 5A ,  5 B,  5 C, and  5 D are plots of simulated seed power and output power as a function of time for the c-axis and a-axis of a gain medium of a single-pass amplifier configuration, one double-pass a-c configuration, and one c-a-a-c quadruple-pass configuration, respectively, with seed laser parameters set at 100 kHz PRF, 20 ns pulse width (PW), and 3 W absorbed pump power. 
           [0023]      FIGS. 6A and 6B  are plots of measured seed power and output power levels achieved using an experimental single-pass amplifier with pump power applied. 
           [0024]      FIG. 7  is a plot of simulated output power (increase) as a function of pump power for a single-pass amplifier and a quadruple-pass amplifier with parameters equal to those used in  FIG. 6 . 
           [0025]      FIGS. 8A ,  8 B,  8 C, and  8 D are plots of simulated power output as a function of time after each successive pass of a seed laser beam through a quadruple-pass power amplifier configuration, with seed laser parameters set at 20 W power, a 40 ns pulse width, and 50 W measured total absorbed pump power. 
           [0026]      FIG. 9  is a plot of measured power amplification of a 100 kHz seed laser, as indicated by output power as a function of seed power along the c- and a-axes of a vanadate crystal pumped with 30 W at a wavelength of 808 nm. 
           [0027]      FIG. 10  is a diagram of a preferred embodiment in a-a or c-c double-pass power amplifier configuration. 
           [0028]      FIG. 11  is a diagram of a preferred embodiment in a-a-c-c or c-c-a-a quadruple-pass power amplifier configuration. 
           [0029]      FIG. 12  is a diagram of a preferred embodiment in c-c-c-a or a-a-a-c quadruple-pass power amplifier configuration. 
           [0030]      FIG. 13  is a diagram of a preferred embodiment in c-c-c-c-a-a and a-a-a-a-c-c six-pass power amplifier configuration. 
       
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS  
       [0031]    Materials suitable for general use as anisotropic gain media in multi-pass configurations are solid state media such as, but not limited to, rare-earth ion-doped crystalline solid state material including Nd:YVO 4 , Nd:YLF, Nd:GdVO 4 , Tm:YLF, Tm:YVO 4 , Ho:Tm:YLF, Ho:Tm:YVO 4 , Ho:Tm:GdVO 4 , Yb:YLF, Yb:YVO 4 , Yb:GdVO 4 ; Cr:LiSAF; Cr:LiCAF; Ti:Sapphire; alexandrite; other Nd-doped materials; and other materials comprising YLF, YVO 4 , and GdVO 4  crystal hosts. Certain semiconductors may also be used as gain media, and optical or electrical pumping may also be employed. Each of the materials listed above has the ability to support light beam amplification at one or more wavelengths. Various pump laser wavelengths may be chosen to improve the conversion efficiency of a gain medium, for example, Nd:YVO 4  at pump wavelengths of 808 nm, 819 nm, 880 nm, 888 nm, and 914.5 nm. The laser may be either end pumped or side pumped. A seed laser suitable for solid-state amplifiers, such as a fiber laser, laser diode, solid-state laser, mode lock laser, or single laser mode (SLM) laser can be a source of a multi-pass amplifier. 
         [0032]      FIGS. 4A ,  4 B, and  4 C show embodiments of a multi-pass optical amplifier in, respectively, double-pass, triple-pass, and quadruple-pass configurations. Each of these embodiments allows for multiple passes of a seed laser beam  100  along a common beam path  101  through an anisotropic gain medium  102  with substantially zero angular beam displacement  104  ( FIG. 4A-1 ) from beam path  101  during each pass. In contrast to the prior art configurations that are shown in  FIG. 3  and entail non-specular reflection, in each of the multi-pass configurations of  FIGS. 4A ,  4 B, and  4 C, seed laser beam  100 , when incident on a curvilinear HR mirror  106 , is perpendicular to a concave surface  107  of the mirror. With reference to  FIG. 4A-1 , according to the law of reflection, in general, the angle of incidence  108  of an incident beam  110 , measured with respect to a surface normal  112 , equals the angle of reflection  114  of a reflected beam  116 . The angle between reflected beam  116  and incident beam  110  defines angular beam displacement  104 . For normal incidence, in which angle of incidence  108  is 0°, reflected beam  116  re-traces beam path  101  of incident beam  110 , resulting in substantially zero angular beam displacement  104 , or equivalently resulting in alignment between incident and reflected beams. The alignment of beams  110  and  116  facilitates control of beam propagation in gain medium  102  and ensures a good mode match between the lasing mode and the pump mode. 
         [0033]    The double-, triple-, and quadruple-pass configurations of  FIGS. 4A ,  4 B, and  4 C, respectively, and employing anisotropic gain medium  102  illustrate a substantially zero angular beam displacement  104  of beam path  101  of seed laser beam  100  with respect to an optic axis  118 . That is, seed laser beam  100  travels and retraces its path in opposite directions generally along optic axis  118  and exits the optical amplifier system as an output laser beam  119   a ,  119   b , or  119   c  in a direction perpendicular to optic axis  118 . In each configuration, seed laser beam  100  first passes through a Faraday isolator  120  and is incident on a polarizing beam splitter  122  ( FIGS. 4A and 4C ) or  133  ( FIG. 4B ) that either allows seed laser beam  100  to pass through polarizing beam splitter  122  or  133  or deflects seed laser beam  100  by 90°, according to the polarization direction of the beam and the orientation of the optics within the beam splitter. Various optical components positioned around gain medium  102  direct laser beam  100  through gain medium  102  for the requisite number of consecutive passes before output laser beam  119   a ,  119   b , or  119   c  exits the optical amplifier system. 
         [0034]    A double-pass configuration  124  shown in  FIG. 4A  includes a quarter-wave plate  126  placed between gain medium  102  and curvilinear HR mirror  106 . Seed laser beam  100  emerging from Faraday isolator  120  first passes through polarizing beam splitter  122 , through gain medium  102 , and then through quarter-wave plate  126 . Reflecting from curvilinear HR mirror  106 , now-amplified laser beam  100  passes back through quarter-wave plate  126 . Quarter-wave plate  126  has an optical axis oriented at an angle of 45° relative to the polarization direction of linearly polarized light emerging from gain medium  102 . The purpose of quarter-wave plate  126  is to rotate the polarization direction of the amplified seed laser beam by a total of 90° for the two passes. The rotated linearly polarized light then passes through gain medium  102  a second time and is separated by polarizing beam splitter  122  before exiting the optical system as output laser beam  119   a . Double-pass configuration  124  is not implemented with a Faraday rotator and, therefore, differs from prior art designs that are intended to compensate for thermally induced birefringence. Such compensation is unnecessary in double-pass configuration  124  because it is implemented with anisotropic gain medium  102 . 
         [0035]    A triple-pass configuration  130  shown in  FIG. 4B  includes a half-waveplate  132  as a substitute for quarter-wave plate  126  used in double-pass configuration  124 ; a polarizing beam splitter  133  as a substitute for polarizing beam splitter  122 ; and as added components a second curvilinear HR mirror  134 , a second polarizing beam splitter  136 , and a Faraday rotator  138 . Seed laser beam  100  emerging from Faraday isolator  120  first passes through polarizing beam splitter  133  and gain medium  102 . Laser beam  100  then passes through Faraday rotator  138 , half-wave plate  132 , and second polarizing beam splitter  136 , reflects from curvilinear HR mirror  106 , and passes back through each optical component of the system until laser beam  100  encounters first polarizing beam splitter  133 , which deflects laser beam  100  by 90° so that it reflects off curvilinear HR mirror  134 . Laser beam  100  then returns to first polarizing beam splitter  133 , which reflects laser beam  100  back to gain medium  102  and then passes through Faraday rotator  138  and half-wave plate  132  a third time. Laser beam  100  is then deflected 90° by second polarizing beam splitter  136  and exits as output laser beam  119   b.    
         [0036]    A quadruple-pass configuration  140  shown in  FIG. 4C  includes components of triple-pass configuration  130 , rearranged, with the addition of quarter-wave plate  126 . Seed laser beam  100  emerging from Faraday isolator  120  first passes through polarizing beam splitter  122 , Faraday rotator  138 , and half-wave plate  132 . After propagating through polarizing beam splitter  133 , laser beam  100  travels back and forth between curvilinear HR mirrors  106  and  134  and thereby passes four times through gain medium  102  and quarter-wave plate  126 . After the fourth pass through gain medium  102 , laser beam  100  passes in reverse direction through polarizing beam splitter  133 , through half-wave plate  132  and Faraday rotator  138 , and toward polarizing beam splitter  122 , and exits as output laser beam  119   c.    
         [0037]    A good mode match between seed laser and pump beams beneficially affords the possibility of achieving a high quality beam with highly efficient extraction. In addition, gain medium  102  can be configured in an end-pumping or in a side-pumping architecture. In the case of single laser mode (SLM) operation, curvilinear HR mirrors  106  and  134  can be replaced by phase conjugate cells to eliminate the need for lenses, because phase conjugation eliminates distortions in the amplifier. Furthermore, there is no undesired lasing action in the amplifier disclosed. Instead, curvilinear HR mirrors  106  and  134  are designed to achieve good mode matching and to improve amplified beam quality. 
         [0038]    A preferred embodiment of the multi-pass configuration resembles a diode-pumped vanadate (Nd:YVO 4 ) power amplifier. Although Nd:YVO 4  has anisotropic gain, it can still be used for this multi-pass scheme because Nd:YVO 4  crystals are capable of lasing when the polarization direction of laser beam  100  is aligned with either the a-axis or the c-axis. When the polarization direction of laser beam  100  is aligned with the c-axis, the gain is about three times greater than the gain when the polarization direction of laser beam  100  is aligned with the a-axis. (This is the reason why the prior art primarily uses the c-axis for lasing.) The laser-related parameters of Nd:YVO 4  along the a- and c-axes are as follows, for 1% Nd doping concentration: 
         [0000]    
       
         
               
               
               
             
               
               
               
             
           
               
                   
                   
               
               
                   
                 Emission cross section, ×10 −19  cm 2   
                 Fluorescence lifetime, μs 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                 c-axis 
                 25 
                 90 
               
               
                 a-axis 
                 7 
                 90 
               
               
                   
               
             
          
         
       
     
         [0039]    A numerical model was designed and developed to simulate amplification in a Nd:YVO 4  crystal along its a- and c-axes. Simulation results comparing amplification along the c- and a-axes are shown in  FIGS. 5A and 5B , respectively, for a single-pass amplifier. Both the simulations and an experiment (presented below) include the following common parameter settings: 100 kHz PRF, 20 ns PW, and 3 W absorbed pump power. Peak power levels are in the kW range while average power values are on the order of 1W-10 W.  FIG. 5A  shows a curve  150   c  that represents the time evolution of single-pass c-axis power output and a curve  152  that represents seed laser power over a 50 ns time interval  154 . Comparison of curves  150   c  and  152  reveals a single-pass c-axis peak power output  156  of 1.4 kW corresponding to a peak seed laser power  158  of 1.1 kW. The average power over a full 100 kHz cycle (equal to 10 μs or 10,000 ns) is calculated as 2.86 W and represents the single-pass c-axis energy emitted within the very short 50 ns time interval  154 .  FIG. 5B  shows a curve  150   a  representing the corresponding time evolution of single-pass a-axis power output and curve  152  over the 50 ns time interval  154 . Comparison of curves  150   a  and  150   c  reveals a peak single-pass a-axis power output  162  of 1.3 kW and average single-pass a-axis power output of 2.6 W. Corresponding extraction efficiencies show that amplification in the c-direction exceeds that in the a-direction by about a factor of three. 
         [0040]    The progression from single-pass, to double-pass, and to quadruple-pass power amplifiers entails sequentially higher extraction efficiencies and corresponding c-axis output powers for the same values of pump power and seed power. Extrapolating from the 12.4% single-pass extraction efficiency along the c-axis corresponding to single-pass amplifier results in  FIG. 5A , the simulation predicts an a-c double-pass amplifier  124  to have 15.5% extraction efficiency and 3.0 W average output power ( FIG. 5C ) corresponding to 1.45 kW peak output power  164 , and a c-a-a-c quadruple-pass amplifier  140  to have 23.0% extraction efficiency and 3.2 W average output power corresponding to 1.6 kW peak output power  165  ( FIG. 5D ). 
         [0041]    Simulation results for the single-pass amplifier agree well with experimental results of single-pass amplification along the c-axis shown in  FIG. 6A  and  FIG. 6B .  FIGS. 6A and 6B  display the outcome of a power amplifier experiment conducted using a 2.5 W average power seed laser at 1064 nm pulsed at 100 kHz PRF with a 20 ns PW to calibrate the numerical model. The laser beam spot size was 250 μm, and the pump beam spot size at the beam waist was 280 μm. The 808 nm pump source was a fiber-coupled laser diode with 100 μm diameter and a numerical aperture (NA) of 0.22. The experiment resulted in absorption of 3 W of pump power at 808 nm by a Nd:YVO 4  crystal. Using a single-pass amplifier configuration based on this power amplifier experiment, 2.8 W average output power was produced with the laser polarization direction aligned with the c-axis, and 2.6 W average output power was produced with the laser polarization direction aligned with the a-axis. A 3 W average output power can be expected from a double-pass configuration, based on the disclosed power amplifier model. 
         [0042]    Using a 0.7 W seed laser pulsed at 100 kHz, with a 20 ns PW, a laser beam spot diameter of 350 μm and a pump beam spot diameter of 380 μm, a simulation was run for both a single-pass amplifier and a quadruple-pass amplifier, showing output power and gain as a function of pump power, respectively. Results presented in  FIG. 7  indicate a roughly linear relationship  166  for both configurations, with a much steeper increase  168  with pump power for the case of the quadruple-pass amplifier. 
         [0043]    The multi-pass power amplifier designs implemented in the embodiments of  FIGS. 4A ,  4 B, and  4 C are also suitable for high-power applications on the order of tens of Watts. A seed laser beam  100  with 20 W average power at 100 kHz PRF and a 40 ns PW passes through the gain medium, which absorbs a total of 50 W of pump power at a 808 nm pump wavelength. The laser beam spot size is 550 μm, and the pump beam spot size is 580 μm. Simulation results  170  for the high-power application are given in  FIGS. 8A ,  8 B,  8 C, and  8 D. The extraction efficiency of a single-pass configuration along the c-axis is 22.9%, producing 31.4 W average power output, increasing to 44.4% efficiency using a c-a-a-c quadruple-pass amplifier like configuration  140 , with average output power of 42.2 W. The high-power amplifier of  FIGS. 8A ,  8 B,  8 C, and  8 D produces peak power levels  176   a ,  176   b ,  176   c , and  176   d  that are approximately 2-3 times greater than the seed laser peak power  178  (about 7 kW-10 kW produced from about 4.5 kW). 
         [0044]    Output power as a function of seed power is shown in  FIG. 9 , in which a distinction between a-axis amplification  182  and c-axis amplification  183  is apparent. As seed laser power  152  increases, power output  160  increases dramatically, especially in the case of a quadruple-pass configuration, and especially when seed laser beam  100  is directed along the c-axis of the vanadate crystal. 
         [0045]    When it is necessary to compensate for thermally induced birefringence, such as in prior art systems, a multi-pass amplifier configuration is limited to an even number of passes, in which the polarization states of the light beam traveling back and forth through the gain medium must be orthogonal. Consequently, on the first pass, if the beam is polarized along the c-axis, it must be polarized along the a-axis on the second pass. Only a-c or c-a configurations would be allowed for a double-pass amplifier, and only a-c-c-a or c-a-a-c configurations would be allowed for a quadruple-pass amplifier. However, with an anisotropic medium such as vanadate, ancillary compensation for thermally induced birefringence is not needed, allowing for more freedom in the amplifier design. 
         [0046]      FIGS. 10 ,  11 ,  12 , and  13  are diagrams of alternative embodiments of multi-pass amplifiers shown in  FIGS. 4A ,  4 B, and  4 C and implemented with anisotropic gain media, thus allowing for variation in the order of passes along the c-axis and a-axis. Optical components in these embodiments are arranged so as to take advantage of the properties of the anisotropic gain media. Specifically, in the first couple of passes, the seed laser beam polarization direction is aligned to the crystal axis of the vanadate gain material yielding the greatest emission cross section (c-axis), before it is aligned to the a-axis. Additional double-pass configurations such as a-a or c-c become possible ( FIG. 10 ), as well as quadruple-pass configurations such as a-a-c-c or c-c-a-a ( FIG. 11 ).  FIG. 10  shows a double-pass configuration similar to that shown in  FIG. 4A , except that a Faraday rotator  138  and a half-wave plate  132  within a first dashed line box  184   a  have been added upstream of gain medium  102 , and quarter-wave plate  126  next to curvilinear HR mirror  106  in  FIG. 4A  has been removed. The same two modifications were made to the quadruple-pass configuration shown in  FIG. 4C  to form the configuration in  FIG. 11 . 
         [0047]    The quadruple-pass configuration shown in  FIG. 12  is based on the double-pass configuration in  FIG. 10 , with added optical components shown in a second dashed line box  184   b . A second gain medium  185  is inserted between polarizing beam splitter  122  and a second curvilinear HR mirror  134 , along with a second quarter-wave plate  186 . The beam therefore passes twice through each of gain medium  102  and gain medium  185 , for a total of four passes. 
         [0048]      FIG. 13  represents a configuration for an even more efficient, six-pass amplifier, which is the same as the quadruple-pass configuration of  FIG. 12  that includes second gain medium  185 , except for an additional block of three optical components shown enclosed in a third dashed line box  188 . The additional optical components include a second polarizing beam splitter  122 , a second Faraday rotator  190 , and a second half-wave plate  192  inserted in the beam path just after Faraday isolator  120 , with second quarter-wave plate  186  removed. 
         [0049]    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. The scope of the present invention should, therefore, be determined only by the following claims.