Abstract:
Provided is a laser system. The laser system includes: a laser device providing a laser pulse; a pulse compressor decreasing a pulse width of the laser pulse; a pulse stretcher disposed between the compressor and the laser device and dispersing the laser pulse; and a filament portion disposed between the pulse stretcher and the pulse compressor, wherein the filament portion transmits the laser pulse to expand a spectrum of the laser pulse by using self focusing and a filament phenomenon of the laser pulse.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This U.S. non-provisional patent application claims priority under 35 U.S.C. §119 of Korean Patent Application Nos. 10-2014-0011009, filed on Jan. 29, 2014, and 10-2014-0039958, filed on Apr. 3, 2014, the entire contents of which are hereby incorporated by reference. 
     BACKGROUND OF THE INVENTION 
     The present invention disclosed herein relates to an optical device, and more particularly, to a laser system that may expand the spectrum of a laser pulse and increase peak intensity thereof. 
     After the invention of the laser in the 1960s, research on industrial applications of the laser actively began in the 1970s. Actually, a laser including a CO 2  laser has been utilized for various fields such as industry, medical treatment, communication, and display since 1980. 
     Also, a solid-state laser has emerged due to the development of a diode laser in 1980&#39;s and as the solid-state laser is applied to a field to which a typical gas-state laser is easily applied, a demand for the laser has gradually increased. Thus, laser application fields are becoming very broad, such as an industry field including laser processing, cutting, welding, drilling, trimming, and etching fields, a medical field including dental treatment, spot, tattoo removal, hair removal, laser-assisted in-situ keratomileusis (LASIK), an academic field studying on the interaction of a laser and a material, national defense and culture fields. 
     The development of an industrial technology needs precision and high productivity in the field in which a laser is used. In response thereto, an ultra-short laser beam is being utilized in various fields, recently. The ultra-short laser beam is generally called a femto second or pico second laser beam. 
     The ultra-short laser beam has a characteristic that optical energy is focused for a very short time, e.g., about 10 −12  s to about 10 −15  s to emit light. Thus, the ultra-short laser beam shows a different characteristic from a typical laser beam. For example, since the ultra-short laser beam is irradiated for a shorter time than a time for which heat is transferred to a medium when the beam is irradiated to the medium, it is possible to avoid thermal effect or thermal deformation that appears in typical laser processing. 
     Since the ultra-short laser beam may process a medium without damage to the surface of the medium, it is being used in fields (semiconductor, electronic chips, and medical treatment) that need precise and micro processing. 
     However, the ultra-short laser alone has a limitation in intensity in order to be industrially used for the increase in yield and the expansion of a processing area. Thus, it works as a constraint on the expansion of application fields. 
     A pico second laser beam has been proposed by A. J. DeMaria, D. A. Stetser, and H. Heynau in 1966. The pico second laser beam may be provided through a pico second Nd:glass laser that uses a dye as saturable absorber. A femto second laser beam has been proposed by C. V. Shank and E. P. Ipen in 1974. The femto second laser beam may be generated by using a dye as a gain material. Then, with the emergence of a diode laser, a femto second solid-state laser that uses a mode locking technology has been introduced by D. E. Spence, et al. in 1991. Also, a high-intensity pico second laser using the mode locking technology or saturable absorber has also developed. Also, the ultra-short laser pulse has combined with a chirped pulse amplification (CPA) technology developed by G. Mourou, et al. in 1985 and thus the amplification of the ultra-short laser pulse has become possible, and at present, a high-intensity ultra-short pulse emitted through a multiple amplification stages is being used in many fields. However, since due to the amplification stage, the size of a laser grows, the cost also increases and a specialist for maintaining the amplification stage is needed, there is a constraint on the expansion of an application in the industrial world. 
     SUMMARY OF THE INVENTION 
     The present invention provides a laser system that may expand the spectrum of a laser pulse. 
     The present invention also provides a laser system that may maximize the peak intensity of a laser pulse. 
     Embodiments of the present invention provide laser systems including: a laser device providing a laser pulse; a pulse compressor decreasing a pulse width of the laser pulse; a pulse stretcher disposed between the compressor and the laser device and dispersing the laser pulse; and a filament portion disposed between the pulse stretcher and the pulse compressor, wherein the filament portion transmits the laser pulse to expand a spectrum of the laser pulse by using self focusing and a filament phenomenon of the laser pulse. 
     In some embodiments, the filament portion may include transparent glass having a lower energy band gap than quartz. The filament portion may have an about 3.3 eV energy band gap. 
     In other embodiments, the laser system may further include: a first lens disposed between the pulse stretcher and the filament portion and focusing the laser pulse on the filament portion; and a second lens disposed between the filament portion and the pulse compressor and providing the laser pulse in parallel to the pulse compressor. 
     In still other embodiments, the pulse stretcher and the pulse compressor may include a chirped pulse stretcher and a chirped pulse compressor, respectively. The chirped pulse stretcher may include: a first chirped mirror reflecting the laser pulse; and a second chirped mirror disposed in parallel to the first chirped mirror, wherein the second chirped mirror reflects the laser pulse reflected from the first chirped mirror to disperse the laser pulse with a negative dispersion. The chirped pulse compressor may include: a third chirped mirror reflecting the laser pulse; and a fourth chirped mirror disposed in parallel to the third chirped mirror, wherein the fourth chirped mirror reflects the laser pulse reflected from the third chirped mirror to decrease the pulse width of the laser pulse. 
     In even other embodiments, the pulse stretcher and the pulse compressor may include a prism stretcher and a prism compressor, respectively. The prism stretcher may include: a first half mirror transmitting the laser pulse; a first prism refracting the laser pulse passing through the first half mirror; a second prism disposed to diagonally face the first prism, wherein the second prism refracts the laser pulse refracted from the first prism to disperse the laser pulse with the negative dispersion; and a first mirror reflecting, the laser pulse provided from the second prism, back to the second prism. The prism compressor may include: a second half mirror transmitting the laser pulse; a third prism refracting the laser pulse passing through the second half mirror; a fourth prism disposed to diagonally face the third prism, wherein the fourth prism refracts the laser pulse refracted from the third prism to decrease a pulse width of the laser pulse; and a second mirror reflecting, the laser pulse refracted from the fourth prism, back to the fourth prism. The laser system may further include: a third mirror between the prism stretcher and the filament portion; a target exposed to a laser pulse provided from the prism compressor; and a fourth mirror between the prism compressor and the target. 
     In yet other embodiments, the pulse stretcher and the pulse compressor may include a grating-based stretcher and a grating-based compressor, respectively. The grating-based stretcher may include: a third half mirror transmitting the laser pulse; a first grating reflecting the laser pulse passing through the third half mirror; a second grating disposed in parallel to the first grating, wherein the second grating reflects the laser pulse reflected from the first grating to disperse the laser pulse with the negative dispersion; and a fifth mirror reflecting, the laser pulse reflected from the second grating, back to the second grating. The grating-based compressor may include: a fourth half mirror transmitting the laser pulse; a third grating reflecting the laser pulse passing through the fourth half mirror; a fourth grating disposed in parallel to the third grating, wherein the fourth grating reflects the laser pulse reflected from the third grating to decrease a pulse width of the laser pulse; and a sixth mirror reflecting, the laser pulse reflected from the fourth grating, back to the fourth grating. The laser system may further include: a seventh mirror between the grating-based stretcher and the filament portion; a target exposed to a laser pulse provided from the grating-based compressor; and an eighth mirror between the grating-based compressor and the target. 
     In further embodiments, the pulse stretcher and the pulse compressor may include a grism stretcher and a grism compressor, respectively. The grism stretcher may include: a fifth half mirror transmitting the laser pulse; a first grism refracting the laser pulse passing through the fifth half mirror; a second grism disposed to diagonally face the first grism, wherein the second grism refracts the laser pulse refracted from the first grism to disperse the laser pulse with the negative dispersion; and a ninth mirror reflecting, the laser pulse refracted from the second grism, back to the second grism. The grism compressor may include: a sixth half mirror transmitting the laser pulse; a third grism refracting the laser pulse passing through the sixth half mirror; a fourth grism disposed to diagonally face the fourth grism, wherein the fourth grism refracts the laser pulse refracted from the third grism to decrease a pulse width of the laser pulse; and a tenth mirror reflecting, the laser pulse refracted from the fourth grism, to the fourth grism. The laser system may further include: an eleventh mirror between the grism stretcher and the filament portion; a target exposed to a laser pulse provided from the grism compressor; and a twelfth mirror between the grism compressor and the target. 
     In other embodiments of the present invention, laser systems include: a laser device providing a laser pulse; a pulse stretcher dispersing the laser pulse with a negative group delay dispersion; and a filament portion transmitting the laser pulse to offset the negative group delay dispersion by positive group delay dispersion to expand a spectrum of the laser pulse by using self focusing and a filament phenomenon of the laser pulse. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The accompanying drawings are included to provide a further understanding of the present invention, and are incorporated in and constitute a part of this specification. The drawings illustrate exemplary embodiments of the present invention and, together with the description, serve to explain principles of the present invention. In the drawings: 
         FIG. 1  represents a laser system according to a first embodiment of the present invention; 
         FIG. 2  represents a laser pulse in a filament portion in  FIG. 1 ; 
         FIG. 3  represents graphs of a source spectrum, a first normal dispersion spectrum, a second normal dispersion spectrum, and an abnormal dispersion spectrum; 
         FIG. 4  represents graphs of the second normal dispersion spectrum and the abnormal dispersion spectrum in  FIG. 3  having a first pulse width and a second pulse width obtained by passing the laser pulses of the spectrums through a pulse compressor; 
         FIG. 5  represents a laser system according to a second embodiment of the present invention; 
         FIG. 6  represents a laser system according to a third embodiment of the present invention; and 
         FIG. 7  represents a laser system according to a fourth embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
     Exemplary embodiments of the present invention are described below in detail with reference to the accompanying drawings. The effects and features of the present invention, and implementation methods thereof will be clarified through following embodiments described to be described in detail with reference to the accompanying drawings. However, the present invention is not limited to embodiments to be described below but may also be implemented in other forms. Rather, these embodiments are provided so that this disclosure can be thorough and complete and fully convey the scope of the present invention to a person skilled in the art, and the present invention is only defined by scopes of claims. The same reference numerals throughout the disclosure refer to the same components. 
     The terms used herein are only for explaining embodiments and not intended to limit the present invention. The terms in a singular form in the disclosure may also include plural forms unless otherwise specified. The terms used herein “comprises” and/or “comprising” do not exclude the presence or addition of one or more additional components, steps, operations and/or elements other than the components, steps, operations and/or elements that are mentioned. Also, a laser pulse and a laser beam that are used herein equally mean light, and a spectrum, pulse width, parallel beam and beam size may be understood as general optical terms related to the wavelength, intensity, and dose of the laser pulse. Since the following description presents an exemplary embodiment, the reference numerals presented according to the order of the description are not limited to the order. 
       FIG. 1  is a schematic view of a laser system according to a first embodiment of the present invention. A laser system may include a laser device  100 , a pulse stretcher  200 , lens  300 , a filament portion  400 , a pulse compressor  500 , and a target  600 . 
     The laser device  100  may generate a laser pulse  700 . The laser device  100  may provide the laser pulse  700  to the pulse stretcher  200 . For example, the laser device  100  may be an oscillator. The laser pulse  700  may be an ultra-short wavelength high-intensity energy beam. The laser pulse may have a pulse width of about several femto seconds to about several hundreds of femto seconds. Also, the laser pulse  700  may be a non-amplification laser beam having a MHz repetition rate and micro joule pulse energy. 
     The pulse stretcher  200  may expand the laser pulse  700  in a time scale direction. In particular, the pulse stretcher  200  may disperse the laser pulse  700  with a negative group delay dispersion. As an example, the pulse stretcher  200  may be a down-chirped pulse stretcher. The pulse stretcher  200  may include a first chirped mirror  210  and a second chirped mirror  220 . The first chirped mirror  210  and the second chirped mirror  220  may face each other and be parallel to each other. The laser pulse  700  may sequentially pass through the first chirped mirror  210  and the second chirped mirror  220 . The first chirped mirror  210  may reflect the laser pulse  700  to the second chirped mirror  220 . The second chirped mirror  220  may reflect the laser pulse  700  back to the first chirped mirror  210 . The second chirped mirror  220  may disperse the laser pulse  700  the negative group delay dispersion. 
     The lens  300  may focus the laser pulse  700  on the filament portion  400 . As an example, the lens  300  may include a first lens  310  and a second lens  320 . The first lens  310  may be disposed between the pulse stretcher  200  and the filament portion  400 . The first lens  310  may focus the laser pulse  700  on the filament portion  400 . The second lens  320  may be disposed between the filament portion  400  and the pulse compressor  500 . The second lens  320  may provide the laser pulse  700  being a parallel beam to the pulse compressor  500 . That is, the second lens  320  may collimate the laser pulse  700 . 
     The filament portion  400  may expand the spectrum of the laser pulse  700 . The laser pulse  700  may pass through the filament portion  400 . The filament portion  400  may be formed of transparent glass. In general, the transparent glass has an energy band gap having various sizes ranging from several eV to several tens of eV. As an example, the filament portion  400  may have an energy band gap lower than quartz. The quartz may have an energy band gap of about 8 eV or higher. For example, the filament portion  400  may include N-SF11 having an energy band gap of about 3.3 eV. 
     The filament portion  400  may induce the filament phenomenon and self-focusing of the laser pulse  700 . The filament phenomenon indicates a phenomenon that involves a self-phase modulation effect and expands the spectrum of the laser pulse  700 . The self focusing is a phenomenon that spontaneously decreases the beam size of the laser pulse  700  in the filament portion  400 . In this case, there is a peak intensity threshold value of the laser pulse  700  self-focused according to the size of the energy band gap of the filament portion  400 . The laser pulse  700  lower than the peak intensity threshold value of the filament portion  400  may not be self-focused in the filament portion  400  and the laser pulse  700  higher than the threshold value may be self-focused. Thus, as the energy band gap of the filament portion  400  decreases, the low peak intensity of the laser pulse  700  is needed. However, when the laser pulse  700  has a MHz repetition rate, the self phase modulation phenomenon may be involved, inducing self focusing by way of exception, even in the case of intensity lower than a peak intensity threshold value. It is possible to restrict the expansion range of the spectrum of the laser pulse  700 . The spectrum of the laser pulse  700  may be expanded to some extent. Most of high-intensity ultra-short laser pulses  700  may be self-focused in the transparent glass having a lower energy band gap than quartz. The filament portion  400  having the energy band gap lower than quartz may minimize a constraint or margin on peak intensity of the laser pulse  700 . The filament portion  400  may widen the options of the laser device  100 . In addition to an expensive high-intensity laser device  100 , it is possible to use an inexpensive low-intensity laser device  100 . 
     On the contrary, the filament portion  400  having a relatively high energy band gap may need the high peak intensity of the laser pulse  700 . That is, the filament portion  400  may self-focus a high peak intensity laser pulse when there is a high peak intensity threshold value. In addition, a wide spectrum of the laser pulse  700  may be obtained. Nevertheless, the filament portion  400  may increase a constrain or margin on the peak intensity of the laser pulse  700 . The filament portion  400  having a high energy band gap may be appropriately used for the high intensity laser device  100 . 
     The filament portion  400  may provide the laser pulse  700  having positive group delay dispersion. The filament portion  400  may offset the negative group delay dispersion of the laser pulse  700  by the positive group delay dispersion. When the laser pulse  700  having the negative group delay dispersion is provided to the filament portion  400 , the dispersion of the laser pulse  700  may be mutually offset and the peak intensity of the laser pulse  700  may be maximized. The reason is because the laser pulse  700  obtains a maximum self phase modulation effect and the spectrum of the laser pulse  700  is further expanded. 
       FIG. 2  shows the laser pulse  700  in the filament portion  400  in  FIG. 1 . The laser pulse  700  may be self-focused in the filament portion  400  to have a filament shape. 
       FIG. 3  shows a source spectrum  102 , a first normal dispersion spectrum  104 , a second normal dispersion spectrum  106 , and an abnormal dispersion spectrum  108 . The source spectrum  102  is a spectrum of the laser pulse  700  provided by the laser device  100 . The first normal dispersion spectrum  104  is a spectrum of the laser pulse  700  passing through the filament portion  400  having a thickness of about 2.7 mm. The second normal dispersion spectrum  106  is a spectrum of the laser pulse  700  passing through the filament portion  400  having a thickness of about 10 mm. The abnormal dispersion spectrum  108  is a spectrum of the laser pulse  700  that the laser pulse  700  having the negative group delay dispersion passes through the filament portion  400  having a thickness of about 10 mm. In this example, the negative group delay dispersion is about −2760 fs 2 . The abnormal dispersion spectrum  108  may have intensity corresponding to a wider wavelength range than the source spectrum  102 , the first normal dispersion spectrum  104 , and the second normal dispersion spectrum  106 . Through the comparison of the first normal dispersion spectrum  104  with the second normal dispersion spectrum  106 , the expansion of a spectrum may be adjusted according to the thickness of the filament portion  400 . 
     Referring back to  FIG. 1 , the laser pulse  700  may be propagated from the filament portion  400  to the pulse compressor  500 . The pulse compressor  500  may temporally compress the laser pulse  700 . That is, the pulse compressor  500  may decrease the width of the laser pulse  700 . The pulse compressor  500  may have a structure similar to that of the pulse stretcher  200 . As an example, the pulse compressor  500  may be a down-chirped pulse compressor. The pulse compressor  500  may be synchronized with the pulse stretcher  200  at the same frequency. The pulse compressor  500  may include a third chirped mirror  510  and a fourth chirped mirror  520 . The third chirped mirror  510  and the fourth chirped mirror  520  may be disposed to face each other and be parallel to each other. The laser pulse  700  may sequentially pass through the third chirped mirror  510  and the fourth chirped mirror  520 . The third chirped mirror  510  may reflect the laser pulse  700  to the fourth chirped mirror  520 . The fourth chirped mirror  520  may reflect the laser pulse  700  to the target  600 . The fourth chirped mirror  520  may decrease the width of the laser pulse  700 . 
     The target  600  may be disposed behind the pulse compressor  500 . The target  600  may include a detector. The detector may detect the peak intensity of the laser pulse  700 . The detector may include a spectrometer or auto-correlator. 
       FIG. 4  shows a first spectrum  112  and a second spectrum  114  that are formed after the laser pulses of the second normal dispersion spectrum  106  and the abnormal dispersion spectrum  108  in  FIG. 3  pass through the pulse compressor  500 . The pulse width of the first spectrum  112  is about 47 femtosecond (fs) and the pulse width of the second spectrum  114  is about 33 femtosecond (fs). As the spectrum of the laser pulse  700  in the filament portion  400  becomes wide, the pulse width of the spectrum of the laser pulse  700  compressed by the pulse compressor  500  may become narrow. In this example, the pulse width may be defined as a time interval at which amplitude becomes half at the rise and fall times of a pulse. When the higher order dispersion of the laser pulse  700  of the abnormal dispersion spectrum  108  is adjusted to zero, the pulse width of the second spectrum  114  may decrease to about 31 femtosecond (fs). The peak intensity of the laser pulse  700  having a narrow pulse width may be stronger than the peak intensity of the laser pulse  700  having a wide pulse width. Thus, the laser system according to the first embodiment of the present invention may maximize the peak intensity of the laser pulse  700 . 
       FIG. 5  shows a laser system according to a second embodiment of the present invention. In  FIG. 5 , a laser device  110 , lens  330 , a filament portion  410 , and a target  610  have the same functions and configurations as those of the laser device  100 , the lens  300 , the filament portion  400 , and the target  600 , respectively. However, a pulse stretcher  230  and a pulse compressor  530  in  FIG. 5  have the same functions as but different configurations from the pulse stretcher  200  and the pulse compressor  500  in  FIG. 1 . 
     The pulse stretcher  230  and the pulse compressor  530  may be a prism stretcher and a prism compressor, respectively. As an example, the pulse stretcher  230  may include a first half mirror  232 , a first prism  234 , a second prism  236 , and a first mirror  238 . The first half mirror  232  may enable a portion of the laser pulse  710  to pass through the first prism  234 , and enable a remaining portion of the laser pulse  710  to be reflected to the third mirror  239 . Also, the first half mirror  232  may reflect, a laser pulse coming back from the first prism  234 , to the third mirror  239 . The first prism  234  and the second prism  236  may be arranged between the first half mirror  232  and the first mirror  238 . The first prism  234  and the second prism  236  may be arranged to diagonally face each other. The first prism  234  and the second prism  236  may refract the laser pulse  710 . The first prism  234  and the second prism  236  may change the propagation path of the laser pulse  710  in opposite directions. For example, when the first prism  234  may propagate a horizontal laser pulse  710  in a downward direction, the second prism  236  may propagate the laser pulse  710  in a horizontal direction. The first prism  236  and the second prism  236  may enable the laser pulse  700  to have negative group delay dispersion. The laser pulse  710  may be reflected from the first mirror  238  to the second prism  236 . The laser pulse  710  may be provided to the third mirror  239  and the first mirror via the second prism  236 , the first prism  234 , and the first half mirror  232 . The third mirror  239  may be disposed between the first half mirror  232  and the first lens  332 . 
     The pulse compressor  530  may include a second half mirror  532 , a third prism  534 , a fourth prism  536 , and a second mirror  538 . The second half mirror  532  may perform transflection on the laser pulse  710  provided from the second lens  334 . The second half mirror  532  may enable a portion of the laser pulse  710  to pass through the third prism  534 . The second half mirror  532  may enable a remaining portion of the laser pulse  710  to be reflected to the fourth mirror  539 . Also, the second half mirror  532  may reflect, the laser pulse  710  coming back from the third prism  534 , to the fourth mirror  539 . The third prism  534  and the fourth prism  536  may be arranged at an interval to diagonally face each other. The third prism  534  and the fourth prism  536  may refract the laser pulse  710  in opposite directions. The third prism  534  may propagate a horizontal laser in a downward direction. The fourth prism  536  may propagate the laser pulse  710  in a horizontal direction. The fourth prism  536  may provide the laser pulse  710  to the second mirror  538 . The third prism  534  and the fourth prism  536  may decrease the pulse width of the laser pulse  700 . The second mirror  538  may reflect the laser pulse  710  to the fourth prism  536 . The laser pulse  710  may be propagated to the fourth prism  536 , the third prism  534 , the second half mirror  532 , the fourth mirror  539 , and the target  610 . The fourth mirror  539  may be disposed between the second half mirror  532  and the target  610 . 
       FIG. 6  shows a laser system according to a third embodiment of the present invention. In  FIG. 6 , a laser  120 , a seventh mirror  249 , lens  340 , a filament portion  420 , an eighth mirror  549 , and a target  620  have the same functions as the laser  110 , the third mirror  239 , the lens  330 , the filament portion  410 , the fourth mirror  539  and the target  610  in  FIG. 5 , respectively. A pulse stretcher  240  and a pulse compressor  540  in  FIG. 6  have the same functions as but different configurations from the pulse stretcher  230  and the pulse compressor  530  in  FIG. 5 . 
     The pulse stretcher  240  and the pulse compressor  540  may be a grating-based stretcher and a grating-based compressor, respectively. As an example, the pulse stretcher  240  may include a third half mirror  242 , a first grating  244 , a second grating  246 , and a fifth mirror  248 . The third half mirror  242  may enable a portion of a laser pulse  720  to pass through the first grating  244 , and enable a remaining portion of the laser pulse  720  to be reflected to the seventh mirror  249 . Also, the third half mirror  242  may reflect, the laser pulse  720  coming back from the first grating  244 , to the seventh mirror  249 . The first grating  244  and the second grating  246  may be arranged to face each other. The first grating  244  and the second grating  246  may disperse the laser pulse  720 . The first grating  244  and the second grating  246  may provide negative group delay dispersion to the laser pulse  720 . The second grating  246  may provide the laser pulse  720  to the fifth mirror  248 . The fifth mirror  248  may reflect the laser pulse  720  back to the second grating  246 . The laser pulse  720  may be propagated to the second grating  246 , the first grating  244 , the third half mirror  242 , and the seventh mirror  249 . 
     The pulse compressor  540  may include a fourth half mirror  542 , a third grating  544 , a fourth grating  546 , and a sixth mirror  548 . The fourth half mirror  542  may perform transflection on the laser pulse  720 . The fourth half mirror  542  may enable a portion of the laser pulse  720  to pass through the third grating  544 . The fourth half mirror  542  may enable a remaining portion of the laser pulse  720  to be reflected to the eighth mirror  549 . The fourth half mirror  542  may reflect, the laser pulse  720  coming back from the third grating  544 , to the eighth mirror  549 . The third grating  544  and the fourth grating  546  may be arranged to face each other. The third grating  544  and the fourth grating  546  may decrease the pulse width of the laser pulse  720 . The fourth prism  546  may provide the laser pulse  720  to the sixth mirror  548 . The sixth mirror  548  may reflect the laser pulse  720  back to the fourth grating  546 . The laser pulse  720  may be propagated to the fourth grating  546 , the third grating  544 , the fourth half mirror  542 , the eighth mirror  549 , and the target  620 . 
       FIG. 7  shows a laser system according to a fourth embodiment of the present invention. In  FIG. 6 , a laser  130 , an eleventh mirror  259 , lens  350 , a filament portion  430 , a twelfth mirror  559 , and a target  630  have the same functions and configurations as the laser  120 , the seventh mirror  249 , the lens  340 , the filament portion  420 , the eighth mirror  549  and the target  620  in  FIG. 5 , respectively. However, a pulse stretcher  250  and a pulse compressor  550  in  FIG. 7  have the same functions as but different configurations from the pulse stretcher  240  and the pulse compressor  540  in  FIG. 6 . 
     The pulse stretcher  250  and the pulse compressor  540  may be a grism stretcher and a grism compressor, respectively. As an example, the pulse stretcher  250  may include a fifth half mirror  252 , a first grism  254 , a second grism  256 , and a ninth mirror  258 . The fifth half mirror  252  may enable a portion of a laser pulse  730  to pass through the first grism  254 , and enable a remaining portion of the laser pulse  730  to be reflected to the eleventh mirror  259 . Also, the fifth half mirror  252  may reflect, the laser pulse  730  coming back from the first grism  254 , to the eleventh mirror  259 . The first grism  254  and the second grism  256  may be arranged to diagonally face each other. The first grism  254  and the second grism  256  may provide negative group delay dispersion to the laser pulse  730 . The second grism  256  may provide the laser pulse  730  to the ninth mirror  258 . The ninth mirror  258  may reflect the laser pulse  730  back to the second grism  256 . The laser pulse  730  may be propagated to the second grism  256 , the first grism  254 , the fifth half mirror  252 , and the eleventh mirror  259 . 
     The pulse compressor  540  may include a sixth half mirror  552 , a third grism  554 , a fourth grism  556 , and a tenth mirror  558 . The sixth half mirror  552  may perform transflection on the laser pulse  730 . The sixth half mirror  552  may enable a portion of the laser pulse  730  to pass through the third grism  554 . The sixth half mirror  552  may enable a remaining portion of the laser pulse  730  to be reflected to the twelfth mirror  559 . The sixth half mirror  552  may reflect, the laser pulse  730  coming back from the third grism  554 , to the twelfth mirror  559 . The third grism  554  and the fourth grism  556  may be arranged to diagonally face each other. The third grism  554  and the fourth grism  556  may decrease the pulse width of the laser pulse  730 . The fourth grism  556  may provide the laser pulse  730  to the tenth mirror  558 . The tenth mirror  558  may reflect the laser pulse  730  back to the fourth grism  556 . The laser pulse  730  may be propagated to the fourth grism  556 , the third grism  554 , the sixth half mirror  552 , the twelfth mirror  559 , and the target  630 . 
     As described above, the laser system according to embodiments of the present invention may include a pulse stretcher, a filament portion, and a pulse compressor. The pulse stretcher may provide a laser pulse having negative group delay dispersion. The laser pulse may be provided to the filament portion. The filament portion may offset the negative group delay dispersion of the laser pulse by positive group delay dispersion thereof. The filament portion may expand the spectrum of the laser pulse. The pulse compressor may maximize the peak intensity of the laser pulse having offset dispersion. 
     While embodiments of the present invention are described with reference to the accompanying drawings, a person skilled in the art may understand that the present invention may be practiced in other particular forms without changing technical spirits or essential characteristics. Therefore, the above-described embodiments and applications should be understood as illustrative and not limitative in every aspect.