Abstract:
Saturated tabletop lasers having increased output energy and operating at 5 Hz repetition rate, were demonstrated at wavelengths about 18.9 nm for molybdenum targets, 16.4 nm for ruthenium targets, 14.7 nm for palladium targets, 13.9 nm for silver targets, and 13.2 nm for cadmium targets in transitions of nickel-like ions. The results were obtained using a sequence of two, plasma-generating pre-pulses, each having sub-Joule energy followed after a selected delay period by picosecond laser plasma excitation pulses having with an energy of about 1 J at angles of incidence optimized for maximum energy deposition.

Description:
STATEMENT REGARDING FEDERAL RIGHTS 
   This invention was made with National Science Foundation (NSF) Center for Extreme Ultraviolet Science and Technology under NSF support under NSF Award No. EEC-0310717; NSF Grant No. ECS-9977677. The government has certain rights in the invention. 

   FIELD OF THE INVENTION 
   The present invention relates generally to soft x-ray lasers and, more particularly, to a method and apparatus for increasing the output intensity thereof. 
   BACKGROUND OF THE INVENTION 
   The widespread use of coherent soft x-ray light in numerous areas of science and technology requires the development of small-scale sources. Significant effort has been placed in the development of high repetition rate soft x-ray lasers. Discharge pumped lasers operating at 4-10 Hz repetition rate have produced milliwatts of laser average power at a wavelength of 46.9 nm [See, e.g., B. R. Benware et al., Phys. Rev. Lett. 81, 5804 (1998), and C. D. Macchieto et al., Opt. Lett. 24 1115 (1999)]. More recently, laser-pumped saturated optical field ionization lasers operating in Pd-like Xe at 41.8 nm and in Ni-like Kr at 32.8 nm have been demonstrated at repetition rates of 10 Hz using femtosecond optical laser excitation pulses of 0.33 J and 0.76 J pulses, respectively [See, e.g., S. Sebban et al., Phys. Rev. Lett. 86, 3004 (2001); and S. Sebban et al., Phys. Rev. Lett. 89, 253901 (2002)]. However, these excitation procedures have produced only saturated lasers at wavelengths above 30 nm to date. Many applications required the development of high repetition rate lasers capable of operating at shorter wavelengths. 
   Transient collisional electron excitation of targets using a sequence of two laser pulses impinging on the target at near-normal incidence has produced several saturated lasers in the 12-23 nm range, but required 3-10 J of pump energy, which contributed to limit operating repetition rates to only one shot every several minutes [See, e.g., P. V. Nickles et al., Phys. Rev. Lett. 78, 2748 (1997); and J. Dunn et al., Phys. Rev. Lett. 84, 4834 (2000); and K. A. Janulewicz et al., Phys. Rev. A 68, 051802 (2003).]. Where more than two laser excitation pulses impinging at normal incidence to a suitable target are used, the saturated x-ray laser gain was found to increase in some situations, and decrease in others [See, e.g., R. E. King et al., Phys. Rev. 64, 053810 (2001).]. 
   Several excitation schemes have been investigated to reduce the necessary pumping energy and enable operation at higher repetition rates. For example, excitation of a Mo target with 150 fs, 300 mJ pulses impinging at 60° from normal incidence resulted in the appearance of the 18.9 and 22.6 nm laser lines of Ni-like Mo [See, e.g., R. Tommasini et al., Proc. of SPIE 4505, 85 (2001)], but this procedure did not produce sufficient amplification to have practical interest. 
   Recently, it has been demonstrated that the energy deposition efficiency of a short laser pulse can be significantly increased by directing it at grazing incidence [See, e.g., V. N. Shlyaptsev et al., Proc. of SPIE 5197, 221 (2003); and R. Keenan et al., Proc. of SPIE 5197, 213 (2003)]. In this scheme, a first laser pulse impinges on a target of selected material creating a plasma that is subsequently rapidly heated by a second pulse of picosecond duration to create a population inversion and soft x-ray laser amplification. This inherently traveling wave pumping geometry takes advantage of the refraction of the second pulse in the plasma created by the first pulse to increase its path length through the gain region of the plasma, thereby increasing the fraction of the pump energy absorbed in that region. 
   Accordingly, it is an object of the present invention to provide a method for increasing the output energy of soft x-ray lasers excited by grazing incidence laser pumping. 
   It is another object of the present invention to provide soft x-ray lasers excited by grazing incidence laser pumping having increased output energy and average power. 
   Additional objects, advantages and novel features of the invention will be set forth, in part, in the description that follows, and, in part, will become apparent to those skilled in the art upon examination of the following or may be learned by practice of the invention. The objects and advantages of the invention may be realized and attained by means of the instrumentalities and combinations particularly pointed out in the appended claims. 
   SUMMARY OF THE INVENTION 
   To achieve the foregoing and other objects of the present invention, and in accordance with its purposes, as embodied and broadly described herein, the method for generating soft x-ray laser radiation hereof includes the steps of: directing at least one first laser pulse having a first chosen energy and a first chosen pulse width onto an exposed surface of a target comprising selected atoms at a first angle to the normal to the surface effective for generating an expanding plasma in the vicinity of the surface comprising ions of the selected atoms; directing a second laser pulse having a second chosen energy and a second chosen pulse width onto the surface of the selected target at a second angle to the normal to the surface effective for increasing the degree of ionization of the ions of the expanding plasma, at a first chosen time after the step of directing the at least one first laser pulse onto the target; and directing a plasma excitation pulse having a third chosen energy and a third chosen pulse width into the plasma at a third chosen angle to the normal to the surface of the target effective for producing a population inversion in the ions of the plasma, said third chosen angle being greater than 40°, and at a second chosen time after the step of directing a second laser pulse onto the target, whereby soft x-ray laser radiation is generated. 
   In another aspect of the present invention, and in accordance with its objects and purposes, the apparatus for generating soft x-ray laser radiation includes: a target comprising selected atoms; means for generating at least one first laser pulse having a first chosen energy and a first chosen pulse width; means for directing the at least one first laser pulse onto an exposed surface of the target at a first angle to the normal to the surface of the target such that an expanding plasma comprising ions of the selected atoms is generated in the vicinity of the surface; means for generating a second laser pulse having a second chosen energy and a second chosen pulse width at a first chosen time after the at least one first laser pulse; means for directing the second laser pulse onto the surface of the target at a second angle to the normal to the surface of the target such that the degree of ionization of the ions of the expanding plasma is increased; means for generating a plasma excitation pulse having a third chosen energy, the third chosen angle being greater than 40° to the normal to the surface of the target and a third chosen pulse width at a second chosen time after the second laser pulse; and means for directing the plasma excitation pulse into the expanding plasma at a third chosen angle to the normal to the surface of the target, such that a population inversion in the ions of the plasma is produced, and soft x-ray laser radiation is generated. 
   Benefits and advantages of the present method include the generation of soft x-radiation having increased intensity and improved efficiency at wavelengths below 35 nm at high repetition rates from numerous atomic species. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The accompanying drawings, which are incorporated in and form a part of the specification, illustrate the embodiments of the present invention and, together with the description, serve to explain the principles of the invention. In the drawings: 
       FIG. 1  is a schematic representation of the multi-pulse sequence for excitation of a population inversion in a target plasma suitable for soft x-ray lasing, showing a first (early) pre-pulse for generating a plasma which includes ions of atoms from a chosen target, a second pre-pulse for increasing the degree of ionization of the plasma, and a main pulse for producing a population inversion in the plasma effective for generating laser radiation; time evolves from right to left in the FIGURE. 
       FIG. 2  is a schematic representation of one embodiment of the apparatus for generating soft x-ray laser radiation in accordance with the teachings of the present invention, illustrating, in particular, the two pre-pulses being directed approximately normal to the chosen target, while the main pulse is directed at a chosen grazing incidence angle thereto. 
       FIG. 3  is a graph of the output intensity of the soft x-ray laser of the present invention in arbitrary units for nickel-like silver ions at 13.9 nm as a function of the energy of the first prepulse, the two pre-pulses having a duration of about 120 ps, the second pre-pulse having an energy of approximately 300 mJ, both pre-pulses being directed approximately perpendicular to the target, the delay between the first pre-pulse and the second pre-pulse being approximately 5.6 ns, and the delay between the second pre-pulse and the main plasma excitation pulse having 1 J pulse energy, being approximately 300 ps with the grazing incidence angle being about 70° to the normal line to the target surface. 
       FIG. 4  is a graph of the output intensity of the soft x-ray laser of the present invention in arbitrary units as a function of the ratio of intensities between the first pre-pulse and the second prepulse described in  FIG. 1  hereof for nickel-like silver ions at a wavelength of 13.9 nm, the two pre-pulses having a duration of about 120 ps, the delay between the first pre-pulse and the second prepulse being approximately 5.6 ns, both pre-pulses being directed approximately perpendicular to the target, and the delay between the second pre-pulse and the main plasma excitation pulse having 1 J pulse energy, being about 300 ps with the grazing incidence angle being about 70° to the normal line of the target surface. 
       FIG. 5  is graph of the output intensity of the soft x-ray laser of the present invention in arbitrary units for nickel-like silver ions at 13.9 nm as a function of the energy of the second pre-pulse, the two pre-pulses having a duration of about 120 ps, the first pre-pulse having an energy of approximately 25 mJ, both pre-pulses being directed approximately perpendicular to the target, the delay between the first prepulse and the second pre-pulse being approximately 5.6 ns, and the delay between the second pre-pulse and the main plasma excitation pulse having 1 J pulse energy, being approximately 300 ps with the grazing incidence angle being about 70° with the normal line to the target. 
   

   DETAILED DESCRIPTION 
   Briefly, the present invention includes an apparatus and method for increasing the output intensity of optically pumped, saturated collisional soft x-ray lasers excited by grazing (≧40° to the normal to the surface of the target material employed) incidence laser pumping, where a laser pre-pulse having normal incidence to a target generates a plasma which is subsequently excited by another laser pulse directed therethrough. An earlier pre-pulse directed to the same location on the target as the now second prepulse, has been found to significantly increase the output intensity of the laser for Ni-like metal ions. Although the details of the exact process involved are being investigated, without intending to limit the scope of the present invention, it is believed that since absorption of radiation in a plasma volume is related to the electron density and temperature, and its propagation is determined by the electron density gradients within the plasma, the early pre-pulse assists in creating a pre-plasma with decreased density gradients and simultaneously favorable absorption conditions for the pump beam in which the subsequent excitation by the main pulse gives rise to a more robust and increased gain region in which the soft x-ray radiation will propagate, thereby experiencing an increased integrated gain. The invention has been demonstrated for Ni-like Cd ions lasing at about 13.2 nm, Ni-like Ag ions lasing at about 13.9 nm, Ni-like Pd lasing at about 14.7 nm, Ni-like Ru targets lasing at about 16.4 nm, and Ni-like Mo ions lasing at about 18.9 nm. but it is anticipated by the present inventors that soft x-ray lasers comprising plasmas containing other Ni-like ions, such as Sn and Sb, as examples, and other ions useful for generating soft x-ray laser radiation by collisional electron impact excitation, such as Ne-like ions, as examples, will exhibit similar improvement. 
   Reference will now be made in detail to the present preferred embodiments of the invention examples of which are illustrated in the accompanying drawings. In what follows, identical callouts will be used for similar or identical structure. Turning now to  FIG. 1 , a schematic representation of the pulse sequence for excitation of a population inversion in a target plasma suitable for soft x-ray lasing is shown. First (early) pre-pulse,  10 , and second pre-pulse,  12 , having a chosen spacing in time, Δt 1 , generate a plasma which includes ions of atoms from a chosen target, and main pulse,  14 , delayed from pre-pulse  12 , by Δt 2 , produces a population inversion in the plasma effective for generating laser radiation. Time, t, evolves from right to left in  FIG. 1 . 
   As understood by the present inventors, and not intended to limit the scope of the invention, the early pre-pulse generates a plasma containing ions of the chosen target material prior to the arrival of the pre-pulse that precedes the main excitation pulse. As this plasma expands, the level of ion excitation diminishes. The second pre-pulse increases the ion excitation to the desired Ni-like ionic states, while the main excitation pulse establishes the required population inversion. It should be pointed out at this point that those skilled in the art would understand that a greater number of suitably chosen pulses than 3 would also be useful for generating soft x-ray laser operation. Moreover, the use of a sufficiently prolonged foot on the rising edge of a pre-pulse would also be expected to provide a similar result. 
     FIG. 2  is a schematic representation of one embodiment of the apparatus,  16 , for generating soft x-ray laser radiation in accordance with the teachings of the present invention, illustrating, in particular, pre-pulses  10  and  12  being directed at approximately normal incidence to chosen target,  18 , while main pulse  14  is directed at an angle chosen to optimize the soft x-ray laser output relative to the normal,  20 , thereto. That is, the angle of incidence of the third pulse is selected to optimally couple the pump laser energy into the plasma region having suitable electron density of laser amplification. For example, grazing angles between 67° and 76° relative to the normal to the surface of the target have been successfully used to excite transient collisional lasers in numerous Ni-like ions between molybdenum and tin. It is expected that angles greater than about 40°, and more preferably between about 50° and 80°, will also be useful in accordance with the teachings of the present invention. It should be mentioned that the pre-pulses do not have to be normal to the target to achieve soft x-radiation, and that main or third pulse energies between about 0.1 J and 100 J are expected to be useful in accordance with the teachings of the present invention. 
   Target  18  was a 4 mm long by 2 mm thick slab of metallic silver. As stated, the effect has also been observed for Cd, Ag, Pd, Ru, and Mo targets, and it is anticipated that targets comprising Sn, Sb and other elements would behave similarly. It should be mentioned that a different portion of the target was accessed for each series of three or more plasma generation and excitation pulses. One manner of increasing the available area of the target is to use a cylindrical substrate having a helical groove cut into the outer surface thereof, onto which surface the target material is deposited. The multi-pulse excitation radiation is focused onto the portion of the surface between the grooved portions, and the cylinder rotated slightly with each set of pulses, thereby providing a fresh target surface for each set of pulses. 
   Mode-locked Ti:Sapphire laser oscillator,  22 , and three stages of chirped-pulse pulse amplification,  24 , not shown in  FIG. 2 , provided laser pump laser energy at 800 nm. Excitation pulses having wavelengths between about 0.2 μm and 1.5 μm are expected to be useful in accordance with the teaching of the present invention. Dielectric multilayer-coated beam-splitter,  26 , intercepts the output,  28 , of the third amplifier stage of amplifier  24  and directs about 20% of output laser energy  28  to pre-pulse arm,  30 , (120 ps pulses). It should be mentioned that other splitting ratios and pulse durations would also work; 30% and 600 ps, respectively, as examples. The remainder,  32 , of the third stage output was directed through a lens pair,  33 , comprising an f=2 m and an f=−2 m cylindrical lenses, before being compressed to 8 ps pulses,  34 , using vacuum grating compressor,  36 . Pulse durations between about 0.1 ps and 30 ps are also expected to be useful in accordance with the teachings of the present invention. The repetition rate of soft x-ray laser  16  corresponds to the repetition frequency of 10 Hz for the two commercially available Nd:YAG lasers used to pump amplifiers in amplifier  24 , not shown in  FIG. 2 . It was found that if the repetition rate of the third stage amplifier was reduced to 5 Hz, the pump beam mode quality improved. However, it is expected that in general, pulse repetition rates between 1 Hz and 500 Hz will be useful in accordance with the teachings of the present invention. An electromechanical shutter was placed on the pump beam of the first amplifier, not shown in  FIG. 2 , to allow for single shot data acquisition in some of the measurements. 
   Picosecond pulses  34  are focused into a line focus onto target  18  using collimating lens,  38 , and parabolic mirror,  40  (a spherical mirror could also be used). For the present apparatus, the angle of incidence  20  was between about 67° and 76° with respect to the normal to the surface of target  18 , but other grazing incidence angles will also work depending on the lasing ion chosen, and the wavelength of the light used to pump the soft x-ray laser. For optimized soft x-ray laser output, ions having higher atomic charge require larger angles with respect to the normal to the target. The second beam  30  generated by beam splitter  26  is in turn divided into two beams using the combination of waveplate,  42 , and first cube polarizer,  44 . Beam,  46 , is directed through a first delay line,  48 , formed by translation stage,  49 , onto which mirrors,  50  and  52 , are mounted, forming thereby early pre-pulse,  10 . Beam,  54 , is directed to second, longer delay line,  56 , comprising mirrors,  58  and  60 , mounted on translation stage,  62 , to form main pre-pulse  12 . The relative energy of each of pre-pulses  10  and  12  is selected by rotating waveplate  42 . The two beams are recombined by second cube polarizer,  64 , and the resulting beams are directed along the same path,  66 . Lens pair,  68  and  70 , focuses the overlapping beams into a line on the surface of soft x-ray target  18  which spatially overlaps with the excitation pulse  14  on this surface. 
   In one embodiment of the present apparatus, line foci (30 μm×4.1 mm FWHM) on target  18  were obtained for  120  ps pre-pulses  10  and  12  using a combination of an f=67.5 cm focal length spherical lens,  68 , and an f=200 cm focal length cylindrical lens  70 . For excitation pulse  14 , multilayer-coated f=76.2 cm parabolic mirror  40  was placed at 7° from normal incidence in combination with an f=2 m, f=−2 m cylindrical lens pair,  33 , which added a controllable amount of astigmatism to the excitation pulse. As stated hereinabove, the pre-pulses were directed towards target  18  at near normal incidence and the excitation pulse for creating a transient population inversion following the formation of the plasma was directed at a selected grazing incidence angle  20  to target  18 . This angle was varied between about 64° and 76°, although an approximately 67° grazing incidence angle was found to be optimum for the irradiation of the Ag and Cd targets which generate laser action at about 13.9 nm and about 13.2 nm, respectively. The overlap of the two line foci on target was monitored by imaging the target onto a CCD (not shown in  FIG. 2 ). The on-axis plasma emission was spectrally resolved and recorded using a 1200 l/mm gold-coated variably spaced spherical grating placed at 3° grazing incidence and a back-illuminated 1 in. 2  CCD detector placed 48 cm from the target (not shown in  FIG. 2 ). Soft x-ray laser intensity,  72 , was measured using combinations of Zr filters and meshes of measured transmissivity having attenuation factors up to 1500. The meshes were carefully positioned to avoid the formation of a Moire pattern that would cause a spatial variation of the transmissivity. 
   By selecting the length of delay lines  48  and  56 , the time relationship among pulses  10 ,  12  and  14  is adjusted such that early pre-pulse  10  arrives a few nanosecond prior to second pre-pulse  12  (about 5 ns in the data shown hereinbelow), but delays between about 1 and 10 ns may be successfully employed). The main pre-pulse (pulse  12 ) is adjusted to arrive between about 10 ps and 1000 ps (more preferably, between about 100 ps and 700 ps depending on the x-ray laser media, but the exact optimum delay will also depend on the characteristics of the pulses. 
     FIG. 3  is a graph of the output intensity in arbitrary units of the soft x-ray laser of the present invention for nickel-like silver ions at 13.9 nm as a function of the energy of the first pre-pulse, the two pre-pulses having a duration of about 120 ps, the second pre-pulse having an energy of approximately 300 mJ, both pre-pulses being directed approximately perpendicular to the target, the delay between the first pre-pulse and the second pre-pulse being approximately 5.6 ns, and the delay between the second pre-pulse and the main plasma excitation pulse having 1 J pulse energy, being approximately 300 ps with the grazing incidence angle being about 70° to the normal line to the target surface. It should be noticed that strong soft x-ray laser output is observed with first pre-pulse energies below 10 mJ. 
     FIG. 4  is a graph of the output intensity of the soft x-ray laser of the present invention in arbitrary units as a function of the ratio of intensities between the first pre-pulse and the second pre-pulse described in  FIG. 1  hereof for nickel-like silver ions at 13.9 nm, the two pre-pulses having a duration of about 120 ps, the delay between the first pre-pulse and the second pre-pulse being approximately 5.6 ns, both pre-pulses being directed approximately perpendicular to the target, and the delay between the second pre-pulse and the main plasma excitation pulse having 1 J pulse energy, being about 300 ps with the grazing incidence angle being about 70° to the normal line to the target surface. 
     FIG. 5  is graph of the output intensity of the soft x-ray laser of the present invention in arbitrary units for nickel-like silver ions at 13.9 nm as a function of the energy of the second pre-pulse, the two pre-pulses having a duration of about 120 ps, the first pre-pulse having an energy of approximately 25 mJ, both pre-pulses being directed approximately perpendicular to the target, the delay between the first pre-pulse and the second pre-pulse being approximately 5.6 ns, and the delay between the second pre-pulse and the main plasma excitation pulse having 1 J pulse energy, being approximately 300 ps with the grazing incidence angle being about 70° with normal line to the target surface. 
   The foregoing description of the invention has been presented for purposes of illustration and description and is not intended to be exhaustive or to limit the invention to the precise form disclosed, and obviously many modifications and variations are possible in light of the above teaching. 
   For example, the excitation laser can be other than a Ti:sapphire laser and can lase at other wavelengths; for example, a wavelength of approximately 1 μm or the second or third harmonic of such wavelengths. Shorter wavelengths provide the advantage in the implementation of the apparatus of the present invention of enhancing lasing at shorter x-ray wavelengths. Additionally, the pre-pulses could be generated using more than one laser each of which being synchronized to the laser which generates the main excitation pump pulse. Other apparatus than the delay lines described hereinabove could also be used to impart selected delays in the arrival times of the pulses at the target. 
   The embodiments were chosen and described in order to best explain the principles of the invention and its practical application to thereby enable others skilled in the art to best utilize the invention in various embodiments and with various modifications as are suited to the particular use contemplated. It is intended that the scope of the invention be defined by the claims appended hereto.