Abstract:
Cascaded optical harmonic generators and methods for cascaded optical harmonic generation are disclosed. Relative disposition of individual harmonic generators of a cascaded harmonic generator in an optical path of the fundamental optical beam may be reversed. In a third harmonic generator, the fundamental optical beam may enter the third harmonic crystal first, and the second harmonic crystal second. When the fundamental optical beam enters the third harmonic crystal first, the fundamental light may remain non-depleted by second harmonic generation process.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    The present invention claims priority from U.S. Provisional Patent Application No. 62/002,006 filed May 22, 2014, which is incorporated herein by reference. 
     
    
     TECHNICAL FIELD 
       [0002]    The present disclosure relates to light sources, and in particular to devices and methods for cascaded optical harmonic generation. 
       BACKGROUND 
       [0003]    Optical harmonic generation may be used to convert laser light from one wavelength to a shorter wavelength, i.e. a higher frequency. For example, frequency doubling, or second harmonic generation (“SHG”), may be used to obtain visible light from near infrared light. In addition, frequency tripling, also referred to as third harmonic generation (“THG”), may be used to obtain blue, violet, and ultraviolet (UV) light from near infrared light. The frequency doubled and tripled light may then be used for spectroscopy, materials processing, optical pumping, etc. 
         [0004]    The optical frequency of laser light may be tripled using cascaded nonlinear optical crystals. Referring to  FIG. 1 , a prior-art cascaded harmonic tripler  10  is shown as an example. The cascaded harmonic tripler  10  includes sequentially disposed second harmonic  12  and third harmonic  13  crystals, and a dichroic mirror (or filter)  15 . In operation, a fundamental light beam  11  at optical frequency ω impinges on the second harmonic crystal  12 . Since a nonlinear conversion efficiency is less than 100%, only a portion of the fundamental light beam  11  is frequency doubled, so that a second harmonic beam  14  at a second harmonic frequency 2ω exits the second harmonic crystal  12  together with an unconverted portion  11 A of the fundamental optical beam  11 . The second harmonic beam  14  and the unconverted portion  11 A of the fundamental optical beam  11  impinge on the third harmonic crystal  13 , which converts a portion of these beams into a third harmonic beam  19  at a third harmonic frequency 3ω. Thus, three beams exit the third harmonic crystal  13 : an unconverted portion  11 B of the unconverted portion  11 A of the fundamental optical beam  11 , an unconverted portion  14 A of the second harmonic beam  14 , and the third harmonic beam  19 . The dichroic mirror  15  redirects the fundamental  11 B and second harmonic  14 A beam portions, and transmits the third harmonic beam  19  as a desired output. 
         [0005]    One drawback of the prior-art cascaded harmonic tripler  10  is that tight focusing of the fundamental  11 A and second harmonic  14  beams into the third harmonic crystal  13  is typically required to obtain reasonable conversion efficiency. One drawback of tight focusing is that a small spot diameter of the fundamental  11 A and second harmonic  14  beams may compromise beam quality due to a beam walk-off effect. Another drawback is that a UV-induced degradation of the third harmonic crystal  13  output surface may result after tens or hundreds of hours of exposure at UV peak power densities in the 200 MW/cm 2  range and average powers in the Watt range or more. 
       SUMMARY 
       [0006]    In accordance with the disclosure, a relative disposition of individual harmonic crystals of a cascaded harmonic generator in an optical path of the fundamental optical beam may be reversed. For example, in a third harmonic generator, the fundamental optical beam may enter the third harmonic crystal first, and the second harmonic crystal second. When the fundamental optical beam enters the third harmonic crystal first, the fundamental light is not depleted by second harmonic generation process, which may increase the overall conversion efficiency, thereby allowing one to operate the harmonic generator at a larger beam size, thereby improving reliability. 
         [0007]    In accordance with an aspect of the disclosure, there is provided a third harmonic generator comprising: 
         [0008]    a first beam combiner for combining a first fundamental optical beam with a second harmonic optical beam; 
         [0009]    a third harmonic crystal coupled to the first beam combiner, for generating a third harmonic optical beam from the first fundamental optical beam and the second harmonic optical beam, wherein upon generation of the third harmonic optical beam, a residual fundamental optical beam exits the third harmonic crystal; 
         [0010]    a first beam splitter coupled to the third harmonic crystal, for separating the residual fundamental optical beam and the third harmonic optical beam; and 
         [0011]    a second harmonic crystal coupled to the first beam splitter, for generating the second harmonic optical beam from the residual fundamental optical beam, and for coupling the second harmonic optical beam to the first beam combiner. 
         [0012]    In accordance with the disclosure, there is further provided a fourth harmonic generator comprising the above third harmonic generator and 
         [0013]    a second beam combiner for combining a second fundamental optical beam with the third harmonic optical beam generated by the third harmonic crystal; 
         [0014]    a fourth harmonic crystal coupled to the second beam combiner, for generating a fourth harmonic optical beam from the second fundamental optical beam and the third harmonic optical beam, wherein upon generation of the fourth harmonic optical beam, the first fundamental optical beam exits the fourth harmonic crystal; 
         [0015]    a second beam splitter coupled to the fourth harmonic crystal, for separating the first fundamental optical beam and the fourth harmonic optical beam and for coupling the first fundamental optical beam to the first beam combiner of the third harmonic generator. 
         [0016]    In accordance with another aspect of the disclosure, there is further provided a cascaded harmonic generator for cascaded optical harmonic generation from a main optical beam, the cascaded harmonic generator comprising: 
         [0017]    a higher harmonic generator disposed in a path of the main optical beam for generating a higher harmonic optical beam while transmitting a residual lower harmonic optical beam; 
         [0018]    a lower harmonic generator disposed in the path of the main optical beam downstream of the higher harmonic generator, for generating a lower harmonic optical beam while transmitting a residual main optical beam; 
         [0019]    a harmonic separator disposed in the path of the main optical beam between the higher and lower harmonic generators, for splitting the higher harmonic optical beam from the main optical beam propagated through the higher harmonic generator; and 
         [0020]    a harmonic combiner disposed in the path of the residual main optical beam downstream of the lower harmonic generator, for coupling the lower harmonic optical beam generated by the lower harmonic generator to the higher harmonic generator for generating the higher harmonic optical beam. 
         [0021]    In one embodiment, the cascaded harmonic generator further comprises a pulsed light source for providing the main optical beam, wherein the main optical beam is pulsed at a pulse separation of substantially an integer multiple of a light round trip time in an optical loop comprising the lower and higher harmonic generators. 
         [0022]    In accordance with another aspect of the disclosure, there is further provided a method of cascaded optical harmonic generation from a main optical beam, the method comprising: 
         [0023]    propagating a main optical beam in sequence through a higher harmonic generator; and then through a lower harmonic generator, so as to generate a lower harmonic optical beam; 
         [0024]    propagating the lower harmonic optical beam generated by the lower harmonic generator through the higher harmonic generator, such that the lower harmonic optical beam overlaps with the main optical beam in the higher harmonic generator, so as to generate the higher harmonic optical beam. 
         [0025]    In accordance with another aspect of the disclosure, there is further provided a method of cascaded optical harmonic generation from a main optical beam, the method comprising: 
         [0026]    providing a plurality of harmonic generators comprising one each of m th  harmonic generators, wherein m=2, . . . , M, and M≧3; 
         [0027]    propagating the main optical beam through the plurality of harmonic generators in the order of decreasing number m, starting from the M th  harmonic generator and ending with the second harmonic generator; 
         [0028]    propagating each n th  harmonic optical beam, wherein n=2 . . . M−1, through the (n+1) th  harmonic generator, so as to overlap therein with the main optical beam; and 
         [0029]    outputting the M th  harmonic optical beam. 
         [0030]    In one exemplary embodiment, the fundamental or main optical beam is directed so that it does not form a closed optical loop. For example, the fundamental or main optical beam may be directed to an optical beam dump before re-entering the highest-order harmonic generator for the second time. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0031]    Exemplary embodiments will now be described in conjunction with the drawings, in which: 
           [0032]      FIG. 1  illustrates a schematic block diagram of a prior-art cascaded harmonic tripler; 
           [0033]      FIG. 2  illustrates a schematic block diagram of a cascaded third harmonic generator of the present disclosure; 
           [0034]      FIGS. 3A to 3C  illustrate optical paths of a fundamental optical beam ( FIG. 3A ); a second harmonic beam ( FIG. 3B ); and a third harmonic beam ( FIG. 3C ) of the cascaded harmonic generator of  FIG. 2 ; 
           [0035]      FIG. 4  illustrates a schematic block diagram of a cascaded fourth harmonic generator of the present disclosure, incorporating the cascaded third harmonic generator of  FIG. 2 ; 
           [0036]      FIGS. 5A to 5D  illustrate optical paths of a fundamental optical beam ( FIG. 5A ); a second harmonic beam ( FIG. 5B ); a third harmonic beam ( FIG. 5C ); and a fourth harmonic beam ( FIG. 5D ) of the cascaded harmonic generator of  FIG. 4 ; 
           [0037]      FIG. 6  illustrates a schematic block diagram of a cascaded harmonic generator; 
           [0038]      FIG. 7  illustrates a schematic block diagram of the cascaded harmonic generator of  FIG. 6 , including a pulsed source of fundamental light; 
           [0039]      FIG. 8  illustrates a schematic block diagram of an embodiment of a cascaded third harmonic generator using a slanted third harmonic crystal; 
           [0040]      FIG. 9A  illustrates a computed conversion efficiency diagram of the frequency tripler of  FIG. 1 ; 
           [0041]      FIG. 9B  illustrates a computed conversion efficiency diagram of the third harmonic cascaded generator of  FIG. 2 , for comparison with  FIG. 9A ; and 
           [0042]      FIGS. 10 and 11  illustrate flow charts of embodiments of a method of cascaded optical harmonic generation according to the present disclosure. 
       
    
    
     DETAILED DESCRIPTION 
       [0043]    While the present teachings are described in conjunction with various embodiments and examples, it is not intended that the present teachings be limited to such embodiments. On the contrary, the present teachings encompass various alternatives and equivalents, as will be appreciated by those of skill in the art. 
         [0044]    Referring to  FIG. 2 , a third harmonic generator  20  may include: a second harmonic crystal  26  for generating a second harmonic optical beam, a third harmonic crystal  28  for generating a third harmonic optical beam, a first beam combiner  25 , and a first beam splitter  27 . The first beam combiner  25  may include two dichroic mirrors  25 A. The dichroic mirrors  25 A are denoted in  FIG. 2  with “1T2R filter”, which conveniently symbolizes transmitting (“T”) a fundamental (“1”) optical frequency ω, and reflecting (“R”) a doubled (“2”) optical frequency 2ω. The first beam splitter  27  may include upper  27 A and lower  27 B dichroic mirrors. Similarly, the upper dichroic mirror  27 A is denoted with “1R2R3T filter”, which symbolizes reflecting (“R”) the fundamental (“1”) optical frequency ω; reflecting (“R”) the doubled (“2”) optical frequency 2ω; and transmitting (“T”) the tripled (“3”) optical frequency 3ω. The lower dichroic mirror  27 B is denoted with “1R2T filter”, which symbolizes reflecting (“R”) the fundamental (“1”) optical frequency ω, and transmitting (“T”) the doubled (“2”) optical frequency 2ω. The above mirror notation will be followed throughout the rest of the specification and drawings. 
         [0045]    In the first beam combiner  25 , two identical dichroic mirrors  25 A—upper and lower dichroic mirrors  25 A—may be used for combining a first fundamental optical beam  21  at the fundamental optical frequency ω with a second harmonic optical beam  22  at the doubled optical frequency 2ω. The third harmonic crystal  28  may be coupled to the upper dichroic mirror  25 A of the first beam combiner  25  for generating a third harmonic optical beam  23  at the tripled optical frequency 3ω from the first fundamental optical beam  21  at the fundamental optical frequency ω and the second harmonic optical beam  22  at the doubled optical frequency 2ω. Upon generation of the third harmonic optical beam  23  at the tripled optical frequency 3ω, a residual fundamental optical beam  21 A at the fundamental optical frequency ω may exit the third harmonic crystal  28 , and be directed, via the upper filter  27 A of the first beam splitter  27 , to the lower filter  27 B of the first beam splitter  27  and further through the second harmonic crystal  26 , where the residual fundamental optical beam  21 A may be used to generate the second harmonic optical beam  22 . A residual beam  21 B of the residual fundamental optical beam  21 A is directed through the lower dichroic mirror  25 A of the first beam combiner  25 , where it may be absorbed by an optional optical beam dump  29 A (bottom left of  FIG. 2 ). A residual second harmonic beam  22 A from the third harmonic crystal  28  at the doubled optical frequency 2ω may be reflected by the upper dichroic mirror  27 A to propagate through the lower dichroic mirror  27 B to another optional optical beam dump  29 B (bottom right of  FIG. 2 ). The second harmonic optical beam  22 , to the left of the second harmonic crystal  26 , is coupled to the first beam combiner  25  which, as noted at the beginning of this paragraph, may be used for combining the first fundamental optical beam  21  with the second harmonic optical beam  22  for generating the third harmonic optical beam  23 . 
         [0046]    The optical paths of the first fundamental optical beam  21  at the fundamental optical frequency ω, the second harmonic optical beam  22  at the doubled optical frequency 2ω, and the third harmonic optical beam  23  at the tripled optical frequency 3ω may be easier tracked by referring to  FIGS. 3A-3C . In  FIG. 3A , the first fundamental optical beam  21  at the fundamental optical frequency ω propagates in sequence through the third harmonic crystal  28 , then the second harmonic crystal  26  as the residual fundamental optical beam  21 A, and then is directed to the left optical beam dump  29 A as the residual beam  21 B of the residual fundamental optical beam  21 A. In  FIG. 3B , the second harmonic optical beam  22  at the doubled optical frequency 2ω is generated in the second harmonic crystal  26 , propagates through the third harmonic crystal  28 , and is directed to the right optical beam dump  29 B as the residual second harmonic optical beam  22 A. In  FIG. 3C , the third harmonic optical beam  23  is generated in the third harmonic crystal  28 , and is directed to the output of the third harmonic generator  20 . 
         [0047]    Fundamentally, the above-described process may provide a higher efficiency conversion than the prior-art frequency tripler  10  of  FIG. 1 , at least for the following reason. The third harmonic conversion efficiency depends approximately on the product of the input power densities at the fundamental optical frequency ω and at the doubled optical frequency 2ω. In the prior-art frequency tripler  10  of  FIG. 1 , the total power input to the third harmonic crystal  13  is limited to the total power input P to the third harmonic generator, because the second harmonic crystal  12  converts some of the input power P at ω to 2ω, but the total power remains substantially unchanged. Typically, the optimal conversion of ω and 2ω into 3ω may occur when the power at ω is about 0.4 P and that at 2ω is about 0.6 P, and the product is 0.24 P 2 . In the third harmonic generator  20  of  FIG. 2 , the input at the third harmonic crystal  28  consists of 1.0 P at ω and typically about 0.6 P at 2ω, so that the product can be about 0.6 P 2 , which is 2.5 times higher than in the prior-art third harmonic tripler  10 . The total optical power input to the third harmonic crystal  28  is actually greater than P, because much of the power at ω may be used twice: first, in the THG process; and second, in the SHG process. The result is that the power density—and, therefore, the conversion efficiency—may be much higher than in the prior-art third harmonic tripler  10 . 
         [0048]    Referring momentarily back to  FIGS. 3A-3C , the residual fundamental optical beam  21 B may be prevented from re-entering the third harmonic crystal  28 , for example by using the lower dichroic mirror  25 A or by some other suitable filter, to avoid potential optical interference effects. Similarly, the residual second harmonic optical beam  22 A may be prevented from re-entering the second harmonic crystal  26 , for example by using the lower filter  27 B of by some other suitable filter. In other words, the optical paths of the fundamental  21  and second harmonic  22  optical beams may be configured so as not to form a closed loop, i.e. an open loop, at individual optical frequencies, or an optical cavity at an individual optical frequency. Avoiding the closed loop or the optical cavity at individual optical frequencies may facilitate stability of the second and third harmonic generation processes. 
         [0049]    The second  26  and third  28  harmonic crystals may include different materials depending on wavelength, power level, or other parameters. Phase matching for SHG and THG may be of many varieties: Type I or Type II, critical or noncritical, collinear or non-collinear. Quasi-phase matching, e.g. using periodically-poled materials, may also be an option. Various kinds of mirrors or optical filters may be used to separate or combine the beams  21 ,  22 , and  23 : dichroic or trichroic thin-film filters, polarization filters, absorptive filters, prisms, gratings, or other filters or mirrors known to a person skilled in the art. Various orderings and combinations of filters, crystals, mirrors, etc. may be used. Waveplates, non-planar beam paths, or lenses may be included at appropriate locations to provide the desired polarization state or beam size or profile depending on specifics of the conversion configuration. Antireflective coatings or Brewster-angle surfaces may be implemented on the second  26  and third  28  harmonic crystals to reduce power loss due to surface reflections. 
         [0050]    One attractive feature of the third harmonic generator  20  of  FIG. 2  is that, since the first fundamental optical beam  21  at the fundamental optical frequency ω and the second harmonic optical beam  22  at the doubled optical frequency 2ω are launched separately into the third harmonic crystal  28 , the position and angle of the beams  21  and  22  can be optimized for a specific conversion configuration by simple adjustment of the individual dichroic mirrors  25 A. Thus, for example, a birefringent or dispersive walk-off plate may not be needed for walk-off compensation. Similarly, for non-collinear phase matching, no prism or other dispersive element may be needed to create a desired angle between the first fundamental optical beam  21  at the fundamental optical frequency ω and the second harmonic optical beam  22  at the doubled optical frequency 2ω. 
         [0051]    Because of the time required for light to travel around a loop formed by the dichroic mirrors  25 A,  27 A, and  27 B and including the second  26  and third  28  harmonic crystals ( FIG. 2 ), the second harmonic optical beam  22  arrives at the third harmonic crystal  28  delayed with respect to the first fundamental optical beam  21 . Thus, in general, this configuration may be adaptable for operation with input pulses that are longer in duration than the time required for light to travel around the loop. The typical minimum dimension of such a loop, including second  26  and third  28  harmonic crystals, would be several centimeters, for example 3 cm, corresponding to a minimum useful pulse duration on the order of 100 picoseconds. Thus, the reversed-order harmonic conversion technique described above may be well suited for laser systems generating nanosecond or longer pulses, for example Q-switched solid-state lasers, as well as continuous wave (CW) lasers. Smaller loops addressing picosecond pulses, e.g. from mode-locked lasers, may be built using micro-optics of millimeter or smaller size. 
         [0052]    The configuration of the third harmonic generator  20  of  FIG. 2  may also be used with multiple pulses, each of which is shorter than the loop round-trip time, if the loop round-trip trip time is selected to be approximately equal to the pulse separation time, or a multiple of it. In the latter case, the input to the third harmonic crystal  28  includes a new IR pulse and a second harmonic pulse that was generated from an earlier IR pulse. For example, a CW mode-locked laser may continuously deliver pulses of duration about 10 picoseconds or shorter at repetition rates in the range of tens of 1 MHz to 1 GHz. With a 200 MHz mode-locked laser, for example, a reversed-order third harmonic generator, similar to the third harmonic generator  20 , with a loop of round-trip time of 5 nanoseconds, corresponding to 150 cm total optical path length, would allow each pulse to be tripled using SHG light from the preceding pulse. This configuration would provide the same benefits of improved conversion efficiency as in the case of a single longer pulse. Even for a pulse burst consisting only of two pulses, there are benefits, since two input pulses are effectively being combined into one THG pulse, a greater output peak power may be generated for a given peak input power. 
         [0053]    Referring now to  FIG. 4  with further reference to  FIG. 2 , a fourth harmonic generator  40  may include the third harmonic generator  20  of  FIG. 2 . A second beam combiner  45 , including a dichroic mirror  45 A and three turning mirrors  45 B, may be provided for combining a second fundamental optical beam  41  with the third harmonic optical beam  23  generated by the third harmonic crystal  28 . A fourth harmonic crystal  46  (“FHG”, fourth harmonic generation) may be coupled to the second beam combiner  45 , for generating a fourth harmonic optical beam  24  at quadrupled optical frequency 4ω from the second fundamental optical beam  41  and the third harmonic optical beam  23 . Upon generation of the fourth harmonic optical beam  24 , the first fundamental optical beam  21  exits the fourth harmonic crystal  46 , and a residual beam  23 A of the third harmonic optical beam  23  exits the fourth harmonic crystal  46  and may be directed to a top optical beam dump  49  by the upper dichroic mirror  25 A, or another suitable splitter. Essentially, in this embodiment the first fundamental optical beam  21  is a residual fundamental optical beam of the second fundamental optical beam  41 . Just like in the third harmonic generator  20  of  FIG. 2 , the first fundamental optical beam  21  is used in the fourth harmonic generator  40  for generating the third harmonic optical beam  23  and the second harmonic optical beam  22 . A second harmonic splitter (1T3T4R dichroic mirror)  47  may be coupled to the fourth harmonic crystal  46 , for separating the first fundamental optical beam  21  from the fourth harmonic optical beam  24 , and for coupling the first fundamental optical beam  21  to the first beam combiner  25  of the third harmonic generator  20 . 
         [0054]    The optical paths of the first  21  and second  41  fundamental optical beams, the second harmonic optical beam  22 , and the third harmonic optical beam  23  may be easier traced by referring to  FIGS. 5A-5D . In  FIG. 5A , the second fundamental optical beam  41  propagates through the fourth harmonic crystal  46 . The first fundamental optical beam  21 , which is the residual fundamental beam of the second fundamental optical beam  41  as explained above, propagates in sequence through the third harmonic crystal  28 , the second harmonic crystal  26  as the residual fundamental optical beam  21 A, and may be directed to the left optical beam dump  29 A as the residual beam  21 B of the residual fundamental optical beam  21 A. In  FIG. 5B , the second harmonic optical beam  22  is generated in the second harmonic crystal  26 , propagates through the third harmonic crystal  28 , and is directed to the right optical beam dump  29 B as the residual second harmonic optical beam  22 A. In  FIG. 5C , the third harmonic optical beam  23  is generated in the third harmonic crystal  28 , and is directed to the fourth harmonic crystal  46 , and is then directed to the top optical beam dump  49  as the residual third harmonic optical beam  23 A. Finally, in  FIG. 5D , the fourth harmonic beam  24  is generated and is directed to the output of the fourth harmonic generator  40 . 
         [0055]    Similar cascaded configurations incorporating one or more reversed-order stages can be implemented for fifth-harmonic generation and beyond. Turning to  FIG. 6  with further reference to  FIGS. 2 and 4 , a cascaded harmonic generator  60  ( FIG. 6 ) for cascaded optical harmonic generation from a main optical beam  61 , e.g. the first fundamental optical beam  21  ( FIG. 2 ) or the second fundamental optical beam  41  ( FIG. 4 ), may include a “higher harmonic generator”  68  disposed in a path of the main optical beam  61  for generating a “higher harmonic optical beam”  63 . A “lower harmonic generator”  66  may be disposed in the path of the main optical beam  61 , that is, in a path of a residual main optical beam  61 A, downstream of the higher harmonic generator  68 , for generating a “lower harmonic optical beam”  62  from the residual main optical beam  61 A. The “higher” 68  and “lower”  66  harmonic generators may be, for example, the third  28  and second  26  harmonic crystals, respectively, in the third harmonic generator  20  of  FIG. 2 . Another example may include the fourth harmonic crystal  46  of the fourth harmonic generator  40  of  FIG. 4  as the “higher harmonic generator”  68 , and the entire third harmonic generator  20  as the “lower harmonic generator”  66 . 
         [0056]    A harmonic separator  67  may be disposed in the path of the main optical beam  61  between the higher  68  and lower  66  harmonic generators, for splitting the higher harmonic optical beam  63  from the residual main optical beam  61 A propagated through the higher harmonic generator  68 . A harmonic combiner  65  may be disposed in the path of a residual beam  61 B of the residual main optical beam  61 A downstream of the lower harmonic generator  66 , for coupling the lower harmonic optical beam  62  generated by the lower harmonic generator  66 , and the main optical beam  61 , to the higher harmonic generator  68  for generating the higher harmonic optical beam  63 , while optionally disposing of the residual beam  61 B, as shown in  FIG. 6 . Thus, the beam combiners  25 ,  45  and/or the harmonic splitter  47  may be configured so that a path of the main optical beam  61  or the lower harmonic optical beam  62  in the cascaded harmonic generator  60  is absent an optical closed loop, to avoid instability due to positive optical feedback. 
         [0057]    Referring now to  FIG. 7  with further reference to  FIG. 6 , a cascaded harmonic generator  70  includes the cascaded harmonic generator  60  of  FIG. 6  and a pulsed light source  71  for providing the main optical beam  61 . Similarly to the case of the third harmonic generator  20  of  FIG. 2 , the main optical beam  61  of the cascaded harmonic generator  60  may be pulsed at a pulse separation of substantially an integer multiple of a light round trip time in an optical loop  69  including the lower  66  and higher  68  harmonic generators. 
         [0058]    Turning now to  FIG. 8  with further reference to  FIGS. 2 and 6 , a third harmonic generator  80  is a variant of the third harmonic generator  20  of  FIG. 2 , and may be viewed as an example of the cascaded harmonic generator  60  of  FIG. 6 . The third harmonic generator  80  of  FIG. 8  may include a second harmonic crystal  86  as the lower harmonic generator  66 , and a third harmonic crystal  88  as the higher harmonic generator  68 . One distinct feature of the third harmonic generator  80  of  FIG. 8  is that the third harmonic crystal  88  may include input  88 A and output  88 B optical faces slanted relative to the input of the fundamental optical beam  21 , preferably at Brewster angle. Another feature is that a first beam combiner  85  may include upper and lower turning mirrors  85 A, and a first beam splitter  87  may include upper and lower turning mirrors  87 A. The upper and lower turning mirrors  85 A,  87 A do not have to be dichroic mirrors, that is, the upper and lower turning mirrors  85 A,  87 A may be regular mirrors, where beam combining and splitting functions are provided by spatial multiplexing, i.e. one beam is reflected by the mirror whereas a second beam bypasses the mirror spatially. Alternatively, the beam combining and splitting function can be provided by polarization multiplexing, where the beams are of differing polarizations, and the mirror transmits one polarization and reflects the other. 
         [0059]    The third harmonic crystal  88  is preferably oriented such that the first fundamental optical beam  21  and the second harmonic optical beam  22  impinge on the input optical face  88 A of the third harmonic crystal  88  at a non-normal (acute) angle of incidence. Furthermore, the first fundamental optical beam  21  and the second harmonic optical beam  22  may form a nonzero (acute) angle with respect to each other. The first fundamental optical beam  21  may be polarized in the plane of  FIG. 8 . The SHG in the second harmonic crystal  26  may be Type I, generating the second harmonic optical beam  22  at the doubled frequency 2ω polarized perpendicular to  FIG. 8 . The THG in the third harmonic crystal  88  may be Type II, combining the first fundamental optical beam  21  polarized in the plane and the second harmonic optical beam  22  polarized perpendicular to the plane of  FIG. 8 , to generate the third harmonic optical beam  23  at the tripled frequency 3ω polarized in the plane of  FIG. 8 . 
         [0060]    For micrometer wavelength range and a peak input power of greater than about 1 kW, the second harmonic crystal  86  ( FIG. 8 ) may be lithium barium borate (LBO) with preferably non-critical phase matching at about 150° C., and the third harmonic crystal  88  ( FIG. 8 ) may be LBO with critical and either collinear or non-collinear phase matching polarized perpendicular to  FIG. 8 . Because the third harmonic crystal  88  has Brewster angles of incidence and exit, spectral dispersion, that is, wavelength dependence of refractive index, of the third harmonic crystal  88  may provide an angular separation of the optical beams at the input  88 A and output  88 B faces of the third harmonic crystal  88 . 
         [0061]    One benefit of this configuration is that no waveplates or dichroic mirrors may be required to separate residual output beams  21 B and  22 A from third harmonic optical beam  23 , and to rotate polarization. Indeed, the upper turning mirror  85 A of the first beam combiner  85  may couple the second harmonic optical beam  22  and the residual optical beam  21 B to the third harmonic crystal  88 . The upper turning mirror  87 A of the first beam splitter  87 A may split off the residual fundamental optical beam  21 A. When the first fundamental optical beam  21  and the second harmonic optical beam  22  have different angles of incidence on the input face  88 A of the third harmonic crystal  88 , the first fundamental optical beam  21  and the second harmonic optical beam  22  may be substantially collinear within the third harmonic crystal  88 . In the example of Type II LBO THG length in the 1 mm range, the angular separation of the beams  21  and  22  is on the order of 1°-3°, which may suffice for straightforward beam separation using mirror edges or beam blocks. The use of Brewster surfaces may be beneficial, because no anti-reflection (AR) coating may be needed on the output face  88 B of the third harmonic crystal  88 , as both the residual fundamental optical beam  21 A and the third harmonic optical beam  23  are p-polarized for low-loss Brewster transmission. Together with the increased surface area of the faces  88 A,  88 B relative to a normal-incidence face, this significantly improves the UV-damage resistance of the faces  88 A,  88 B. The input face  88 A may preferably be AR-coated for s-polarized second harmonic beam  22  and p-polarized first fundamental optical beam  21 . Another benefit of this configuration is that the residual beam  21 B at the fundamental frequency ω, needs not be immediately dumped, as it will be collinear with the second harmonic beam  22  and, therefore, not collinear with the first fundamental optical beam  21  within the third harmonic crystal  88 , so it will likely not interfere with the THG process and will exit collinearly with the residual second harmonic beam  22 A, whereupon both can be separated from the third harmonic optical beam  23  and ejected in one common optical beam dump, not shown. As in  FIG. 2 , lenses or other optics may be added to generate appropriate beam sizes and spatial profiles at the crystals. 
         [0062]    Referring to  FIGS. 9A and 9B  with further reference to  FIGS. 1 and 2 , calculated optical conversion efficiency of the third harmonic generator  20   FIG. 2  ( FIG. 9B ) is compared to that of the conventional optical frequency tripler  10  of  FIG. 1  ( FIG. 9A ). In both  FIGS. 9A and 9B , the optical conversion efficiency is plotted as a function of input optical power in kW, up to 25 kW input optical power level. 
         [0063]    Referring specifically to  FIG. 9A  with further reference to  FIG. 1 , the optical conversion efficiency is plotted for 70 micrometer second harmonic beam  14  diameter ( 91 ); 200 micrometer second harmonic beam  14  diameter ( 92 ); and 350 micrometer second harmonic beam  14  diameter ( 93 ). The input wavelength is 1064 nm, and the pulse durations are typically tens of nanoseconds. Both SHG  12  and THG  13  crystals are LBO. The second harmonic crystal  12  is 15 mm long, with Type I non-critical phase matching at about 150° C. with a 140 micrometer diameter spot of the fundamental beam  11 . The third harmonic crystal  13  is 20 mm long, and the phase matching is Type II critical, non-collinear phase matching. A highest conversion efficiency  91  corresponds to the spot diameter of the second harmonic beam  14  of 70 micrometer, which may provide the best conversion at 20 kW input power. Middle  92  and bottom  93  conversion efficiencies correspond to the spot diameters of the second harmonic beam  14  of 200 micrometer and 350 micrometer, respectively. These spot diameters result in the efficiencies  92  and  93 , which are traded off for larger spot size and therefore improved beam quality and crystals  12  and  13  lifetime. At 25 kW input power level to the prior-art frequency tripler  10 , the 70 micrometer input spot size results in 63% conversion efficiency  91 ; the 200 micrometer spot size results in 37% conversion efficiency  92 ; and the 350 micrometer spot size results in just below 20% conversion efficiency  93 . 
         [0064]    Turning now specifically to  FIG. 9B  with further reference to  FIG. 2 , a highest optical conversion efficiency  94  corresponds to 200 micrometer beam diameter of the second harmonic beam  22  in the optical harmonic generator  20  of  FIG. 2 . A second highest conversion efficiency  95  corresponds to and 350 micrometer beam diameter of the second harmonic beam  22  in the optical harmonic generator  20  of  FIG. 2 . 
         [0065]    The comparison of  FIGS. 9A and 9B  reveals a much higher conversion efficiency of the optical harmonic generator  20  of  FIG. 2 , as compared with the prior-art optical frequency tripler  10  of  FIG. 1 . For instance, at 25 kW input power level to the third harmonic generator  20  of  FIG. 2 , the 200 micrometer spot size results in 81% conversion efficiency; and the 350 micrometer spot size results in 65% conversion efficiency. Therefore, the third harmonic generator  20  of the present disclosure may provide a higher conversion efficiency at 200 micrometer second harmonic beam  22  diameter than the traditional frequency tripler  10  at 70 micrometer second harmonic beam  14  diameter. 
         [0066]    Referring to  FIG. 10  with further reference to  FIGS. 2 and 6 , a method  100  ( FIG. 10 ) of cascaded optical harmonic generation from the main optical beam  61  ( FIG. 6 ) may include a step  101  of providing the lower optical harmonic generator  66  for generating the lower harmonic optical beam  62 , and the higher optical harmonic generator  68  for generating the higher harmonic optical beam  63 . In a next step  102 , the main optical beam  61  may be propagated in sequence through the higher harmonic generator  68 ; and then through the lower harmonic generator  66 , so as to generate the lower harmonic optical beam  62  by propagating through the lower harmonic generator  66 , such that the lower harmonic optical beam  62  overlaps with the main optical beam  61  in the lower harmonic generator  66 . In a next step  103 , the lower harmonic optical beam  62  generated by the lower harmonic generator  66  is propagated through the higher harmonic generator  68 , such that the lower harmonic optical beam  62  overlaps with the main optical beam  61  in the higher harmonic generator  68 , so as to generate the higher harmonic optical beam  63 . Further, in an optional step  104 , the residual main optical beam  62 A exiting the lower harmonic generator  66 , and/or other residual beams, may be separated from the lower harmonic optical beam and dumped in the optical dumps  29 A,  29 B. 
         [0067]    Similarly to the optical harmonic generator  80  of  FIG. 8 , the lower harmonic optical beam  62  impinging on the higher harmonic generator  68  may form an acute angle with the main optical beam  61  impinging on the higher harmonic generator  68 , for collinear propagation in the higher harmonic generator  68 . Furthermore, the main optical beam may be pulsed at a pulse separation of substantially an integer multiple of the light round trip time in the optical loop  69  comprising the lower  66  and higher  68  harmonic generators. 
         [0068]    The method  100  of  FIG. 10  may be generalized for higher order cascaded higher harmonic generation, for example the fourth harmonic ( FIG. 4 ), fifth harmonic generation, and so on. Turning to  FIG. 11 , a method  110  of cascaded optical harmonic generation from a main optical beam includes a step  111  of providing a plurality of harmonic generators including at least one m th  harmonic generator, where m=2, . . ., M, and M is an integer ≧3. In a next step  112 , the main optical beam may be propagated through the plurality of harmonic generators in the order of decreasing number m, starting from the M th  harmonic generator and ending with the second harmonic generator. By way of illustration, referring momentarily back to  FIG. 5A , the fourth harmonic optical beam  41  is propagated through the fourth harmonic crystal  46 , the third harmonic crystal  28 , and the second harmonic crystal  26 . 
         [0069]    In a next step  113 , each n th  harmonic optical beam may be propagated through the (n+1) th  harmonic generator, so as to overlap therein with the main optical beam, where n=2, . . . , M−1. For example, referring back to  FIGS. 5B and 5C , the second harmonic optical beam  22  is propagated through the third harmonic crystal  28  ( FIG. 5B ), and the third harmonic optical beam  23  is propagated through the fourth harmonic crystal  46  ( FIG. 5C ). Finally, in a step  114 , the M th  harmonic optical beam is outputted. By way of example, referring back to  FIG. 5D , the fourth harmonic beam  24  may be outputted from the fourth harmonic crystal  46 . In one embodiment, the main optical beam is propagated so that an optical path of the main optical beam does not form a closed optical loop, i.e. it is open looped. 
         [0070]    The present disclosure is not to be limited in scope by the specific embodiments described herein. Indeed, other various embodiments and modifications, in addition to those described herein, will be apparent to those of ordinary skill in the art from the foregoing description and accompanying drawings. Thus, such other embodiments and modifications are intended to fall within the scope of the present disclosure. Further, although the present disclosure has been described herein in the context of a particular implementation in a particular environment for a particular purpose, those of ordinary skill in the art will recognize that its usefulness is not limited thereto and that the present disclosure may be beneficially implemented in any number of environments for any number of purposes. Accordingly, the claims set forth below should be construed in view of the full breadth and spirit of the present disclosure as described herein.