Scaling high-energy pulsed solid-state lasers to high average power

Abstract

Techniques are provided for scaling the average power of high-energy solid-state lasers to high values of average output power while maintaining high efficiency. An exemplary technique combines a gas-cooled-slab amplifier architecture with a pattern of amplifier pumping and extraction in which pumping is continuous and in which only a small fraction of the energy stored in the amplifier is extracted on any one pulse. Efficient operation is achieved by propagating many pulses through the amplifier during each period equal to the fluorescence decay time of the gain medium, so that the preponderance of the energy cycled through the upper laser level decays through extraction by the amplified pulses rather than through fluorescence decay.

Claims

1. A method, comprising: providing a gas cooled solid-state laser gain medium; continuously optically pumping said gain medium for a period of time to produce excited state ions; and producing amplified pulses by directing a plurality of pulses to be amplified through said gain medium; wherein said laser gain medium has a fluorescence decay time; and wherein the plurality of pulses to be amplified are directed through said laser gain medium in less time than the fluorescence decay time of said laser gain medium.

2. The method of claim 1, wherein said gain medium comprises at least one slab.

3. The method of claim 1, wherein said gain medium has fluorescence lifetime that is sufficiently long that at least 10% of the stored energy that remains in the gain medium after any one amplified pulse of the amplified pulses carries over to the next amplified pulse of the amplified pulses.

4. The method of claim 1, further comprising: a plurality of optics positioned to receive said plurality of pulses to be amplified; wherein said gain medium has a saturation fluence that is high enough to make it impossible to achieve at least a 20% extraction efficiency without operating at a fluence above the lowest damage threshold of said plurality of optics when only one pulse is propagated through the plurality of optics during the fluorescence decay time of the laser gain medium.

5. The method of claim 1, wherein the operating fluence of said gain medium is lower than its damage fluence, even when its saturation fluence is greater than the damage fluence.

6. The method of claim 1, further comprising a plurality of optics positioned to receive said plurality of pulses to be amplified, wherein said gain medium comprises a gain spectra that is sufficiently broad such that said amplified pulses can be optically compressed to sub-ps duration and wherein said gain medium comprises a saturation fluence that is high enough to make it impossible to achieve at least a 20% extraction efficiency without operating at a fluence above the lowest damage threshold of said plurality of optics, when only one pulse is propagated through the plurality of optics during the fluorescence decay time of the laser gain medium.

7. The method of claim 1, wherein the step of continuously optically pumping said gain medium is carried out with at least one laser diode.

8. The method of claim 1, wherein the extraction efficiency for any one amplified pulse of the amplified pulses is no more than a few percent and the stored energy extracted by the amplified pulses is greater than the energy lost due to fluorescence decay.

9. The method of claim 1, wherein said gain medium comprises a plurality of gas-cooled slabs.

10. The method of claim 1, wherein said gain medium comprises at least one rare-earth dopant.

11. The method of claim 1, wherein said gain medium comprises slabs of at least one anisotropic gain material mounted so that two or more optical axes of said slabs interact with the amplified pulses to increase the gain bandwidth and wherein the order in which said slabs are mounted is selected to minimize the required doping of said gain medium and/or to minimize the pump power required in the step of continuously optically pumping said gain medium.

12. An apparatus, comprising: a gas cooled solid-state laser gain medium; means for continuously optically pumping said gain medium for a period of time to produce excited state ions; and means for producing amplified pulses by directing a plurality of pulses to be amplified through said gain medium; wherein the laser gain medium has a fluorescence decay time; and wherein the apparatus is configured to direct the plurality of pulses to be amplified through said laser gain medium in less time than the fluorescence decay time of the laser gain medium.

13. The apparatus of claim 12, wherein said gain medium comprises at least one slab.

14. The apparatus of claim 12, wherein said gain medium has a fluorescence lifetime that is sufficiently long that at least 10% of the stored energy that remains in the gain medium after any one amplified pulse of the amplified pulses carries over to the next amplified pulse of the amplified pulses.

15. The apparatus of claim 12, further comprising: a plurality of optics positioned to receive said plurality of pulses to be amplified; wherein said gain medium has a saturation fluence that is high enough to make it impossible to achieve at least a 20% extraction efficiency without operating at a fluence above the lowest damage threshold of said plurality of optics when only one pulse is propagated through the plurality of optics during the fluorescence decay time of the laser gain medium.

16. The apparatus of claim 12, wherein the operating fluence of said gain medium is lower than its damage fluence, even when its saturation fluence is greater than the damage fluence.

17. The apparatus of claim 12, further comprising a plurality of optics positioned to receive said plurality of pulses to be amplified, wherein said gain medium comprises a gain spectra that is sufficiently broad such that said amplified pulses comprise sub-ps pulses and wherein said gain medium comprises a saturation fluence that is high enough to make it impossible to achieve at least a 20% extraction efficiency without operating at a fluence above the lowest damage threshold of said plurality of optics, when only one pulse is propagated through the plurality of optics during the fluorescence decay time of the laser gain medium.

18. The apparatus of claim 12, wherein the step of continuously optically pumping said gain medium is carried out with at least one laser diode.

19. The apparatus of claim 12, wherein the extraction efficiency for any one amplified pulse of the amplified pulses is no more than a few percent and the stored energy extracted by the amplified pulses is greater than the energy lost due to fluorescence decay.

20. The apparatus of claim 12, wherein said gain medium comprises a plurality of gas-cooled slabs.

21. The apparatus of claim 12, wherein said gain medium comprises at least one rare-earth dopant.

22. The apparatus of claim 12, wherein said gain medium comprises slabs of at least one anisotropic gain material mounted so that two or more optical axes of said slabs interact with the amplified pulses to increase the gain bandwidth and wherein the order in which said slabs are mounted is selected to minimize the required doping of said gain medium and/or to minimize the pump power required in when said gain medium is continuously optically pumped.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The accompanying drawings, which are incorporated into and form a part of the disclosure, illustrate embodiments of the invention and, together with the description, serve to explain the principles of the invention.

(2) FIG. 1A shows stored energy vs. time for the multi-pulse extraction (MPE) mode of operation.

(3) FIG. 1B shows stored energy vs. time for the single-pulse extraction (SPE) mode of operation.

(4) FIG. 2 shows the η.sub.decayη.sub.ext product plotted vs. PRF.Math.f.sub.ext.Math.τ.sub.storage.

(5) FIG. 3A shows values of f.sub.ext required at specified repetition rates to achieve η.sub.decayη.sub.ext=0.98 when MPE is used in various laser gain materials.

(6) FIG. 3B shows values of f.sub.ext required at specified repetition rates to achieve η.sub.decayη.sub.ext=0.98 when MPE is used in various laser gain materials.

(7) FIG. 4 shows extraction fraction vs. maximum normalized output fluence G.sub.out for a multi-passed amplifier, assuming a single-pass transmittance T=0.90.

(8) FIG. 5 shows f.sub.extη.sub.trans plotted vs. G.sub.out.

(9) FIG. 6 shows extraction fraction times transport efficiency f.sub.extη.sub.trans vs. maximum normalized output fluence G.sub.out for multi-passed amplifiers with single-pass transmission values of 0.85, 0.90, 0.95 and 1.0.

(10) FIG. 7 shows saturation fluence vs. storage lifetime for a variety of different gain media.

(11) FIG. 8 illustrates a gas cooled optical amplifier.

(12) FIG. 9 shows the implementation of two gas-cooled amplifiers in a system.

(13) FIG. 10A illustrates combining anisotropic material and an end-pumped multi-slab amplifier to achieve significant improvement to both the gain spectrum and pump absorption by rotating a fraction of the slabs with respect to the laser polarization axis.

(14) FIG. 10B shows the net gain spectrum of Tm:YLF with 30% of the population in the .sup.3F.sub.4 state for both σ and π polarizations.

(15) FIG. 10C shows the absorption spectra of Tm:YLF for both σ and π polarizations.

(16) FIG. 11A illustrates a pumping scheme in which Tm:YLF is pumped at 793 nm.

(17) FIG. 11B providers a configuration where the pump light comprises two wavelengths.

(18) FIG. 11C shows a variation in which a cassette of slabs are pumped on each end with different polarizations.

DETAILED DESCRIPTION OF THE INVENTION

(19) The present invention provides a method of multi-pulse extraction (MPE) for scaling up the average power of high-energy solid-state lasers while maintaining high efficiency. MPE can be applied when the pulse repetition rate, PRF, is approximately equal to or greater than the inverse of the storage lifetime, τ.sub.storage, i.e., when PRF*τ.sub.storage≥1. With MPE, pumping is continuous and only a small fraction of the energy stored in the amplifier is extracted by any one seed pulse. MPE stands in contrast with single-pulse extraction (SPE), in which a pump pulse of finite duration precedes each extracting pulse, FIG. 1 illustrates key differences between these two modes of operation.

(20) FIG. 1A shows stored energy vs. time for the multi-pulse extraction (MPE) mode of operation. FIG. 1B shows stored energy vs. time for the single-pulse extraction (SPE) mode of operation. Time is normalized with respect to the radiative lifetime of the gain medium so that results are valid for gain media having different radiative lifetimes. In the MPE example in FIG. 1A, the gain medium is pumped continuously at a constant rate starting at time zero. Extracting pulses, which extract about 10% of the stored energy each, are passed through the gain medium at a rate of four such pulses per radiative lifetime. As can be seen, stored energy falls sharply upon the passage of each amplified seed pulse, with energy reduction occurring on a time scale that is short compared with the one radiative lifetime. After 2-3 radiative lifetimes, stored energy settles into a regular repeating pattern. An important characteristic of MPE that contributes to high efficiency is that stored energy that is not extracted on one pulse carries over to help amplify subsequent pulses. Another important characteristic of MPE is that for quasi-three-level lasers, the initial pump energy required to pump the gain medium to transparency is expended once, during the initial settling period, after which only a small fraction of the pump power is expended to maintain transparency. In the SPE example of FIG. 1B, the gain medium is pumped for a duration of ˜83% of one radiative lifetime. At the end of this pump pulse, ˜67% of the stored energy is extracted by a pulse that passes perhaps several tis through the gain medium. After the extracting pulse, the remaining stored energy decays away and does not contribute to the amplification of any subsequent pulses. Additionally, for quasi-three-level lasers, the pump energy required to pump the gain medium to transparency is expended on every pulse.

(21) The long-term efficiency in the steady-state regime for the MPE mode, after the initial transient or settling-in period, can be calculated using the formula

(22) $\begin{array}{cc}{\eta }_{\mathrm{decay}}{\eta }_{\mathrm{ext}}=\frac{R_{\mathrm{ext}}}{R_{\mathrm{ext}}+R_{\mathrm{decay}}}=\frac{\mathrm{PRF}.Math.f_{\mathrm{ext}}.Math.{\tau }_{\mathrm{storage}}.Math.\left[1-e^{-1/\left(\mathrm{PRF}.Math.{\tau }_{\mathrm{storage}}\right)}\right]}{\left[1-\left(1-f_{\mathrm{ext}}\right).Math.e^{-1/\left(\mathrm{PRF}.Math.{\tau }_{\mathrm{storage}}\right)}\right]}& \left(1\right)\end{array}$
where η.sub.decay is the time-averaged fraction of the excited-state population that does not undergo decay between shots; η.sub.ext is the time-averaged fraction of the excited-state population that is extracted; R.sub.ext is the extraction rate, which is given by the product of the pulse repetition frequency PRF and the fraction of stored energy extracted on each shot f.sub.ext; and the decay rate R.sub.decay the inverse of the instantaneous storage lifetime τ.sub.storage. Since all excited-state ions that are not extracted are lost to decay, it makes little sense to consider either one separately. Rather, we consider the product of the two together. FIG. 2 shows the η.sub.decayη.sub.ext product plotted versus the product PRF.Math.f.sub.ext.Math.τ.sub.storage. As expected, efficiency approaches zero in the limit of low PRF.Math.f.sub.ext.Math.τ.sub.storage, since nearly all ions are lost to decay. Efficiency rises as PRF.Math.f.sub.ext.Math.τ.sub.storage product is increased. As the PRF.Math.f.sub.ext.Math.τ.sub.storage product is increased further, the η.sub.decayη.sub.ext efficiency product approaches unity. This plot is general and applies to all amplifiers operating in the multi-pulse extraction mode.

(23) An illustrative simplification can be made by deriving the product η.sub.decayη.sub.ext by calculating the ratio of the time-averaged extraction rate divided by the time-averaged total decay rate. This yields the much simpler expression;

(24) $\begin{array}{cc}{\eta }_{\mathrm{decay}}{\eta }_{\mathrm{ext}}\simeq \frac{\mathrm{PRF}.Math.f_{\mathrm{ext}}.Math.{\tau }_{\mathrm{storage}}}{1+\mathrm{PRF}.Math.f_{\mathrm{ext}}.Math.{\tau }_{\mathrm{storage}}},& \left(2\right)\end{array}$
This simpler form accurately describes the efficiency product for small values of the extraction fraction, f.sub.ext≤0.2 and slightly underestimates the efficiency product for larger values of f.sub.ext. An important use of equation (2) is to determine the PRF.Math.f.sub.ext.Math.τ.sub.storage product needed to achieve a specified or required value of the η.sub.decayη.sub.ext efficiency:

(25) $\begin{array}{cc}\mathrm{PRF}.Math.f_{\mathrm{ext}}.Math.{\tau }_{\mathrm{storage}}\simeq \frac{1}{\frac{1}{{\eta }_{\mathrm{decay}}{\eta }_{\mathrm{ext}}}1}& \left(3\right)\end{array}$
Once a gain medium has been chosen, the storage lifetime τ.sub.storage, can be calculated using the usual methods, which take into account the radiative decay rate, 1/τ.sub.rad, the amplified spontaneous emission decay rate, the concentration quenching rate, upconversion rates and other potentially significant important decay mechanisms. For efficient, well-designed systems, it is often the case that τ.sub.storage˜τ.sub.rad, i.e., these other possible decay mechanisms are small enough that they can be ignored. For a specified PRF, the value of f.sub.ext needed to achieve the required efficiency can be determined uniquely. Specifically, with straightforward rearrangement of the equation above, we obtain:

(26) $\begin{array}{cc}{f}_{\mathrm{ext}}\simeq \frac{1}{\left(\frac{1}{{\eta }_{\mathrm{decay}}{\eta }_{\mathrm{ext}}}1\right).Math.\mathrm{PRF}.Math.{\tau }_{\mathrm{storage}}}& \left(4\right)\end{array}$

(27) FIG. 3A shows values of f.sub.ext required to achieve specified values of f.sub.ext for η.sub.decayη.sub.ext=0.95 when MPE is used. FIG. 3B shows values of f.sub.ext; required to achieve specified values of f.sub.ext for η.sub.decayη.sub.ext=0.98 when MPE is used. These two values of η.sub.decayη.sub.ext are provided as examples, although any value η.sub.decayη.sub.ext could have been used. The calculated values of f.sub.ext are plotted for four different gain media (solid curves), which have been chosen since they have significantly different storage lifetimes. FIGS. 3A and 3B also show values of f.sub.ext required to achieve η.sub.ext=0.95 and η.sub.ext=0.98, respectively, when SPE is used (dashed curves). For these SPE cases, the required values of f.sub.ext are trivially equal to since energy is extracted on a single pulse. Nonetheless, by comparing the dashed curves (single-pulse extraction) with the solid curves (multi-pulse extraction), we can readily see another significant advantages of multi-pulse extraction relative to single-pulse extraction: high values of extraction efficiency (η.sub.decayη.sub.ext for MPE and η.sub.ext for SPE) can be achieved at values of f.sub.ext that are lower, and in some cases orders of magnitude lower, for MPE than for SPE. Being able to operating lasers at low f.sub.ext has significantly advantages, such as simplified design and/or reduced operating fluency, which reduces optical damage risk. These issues are discussed below. Not that for these cases, we have used the simplification τ.sub.storage=τ.sub.rad. Thus, values of f.sub.ext needed to achieve a specified efficiency are lower for MPE than they are for SPE.

(28) Analysis of Performance and Design Tradeoffs

(29) Now we turn our attention to calculating η.sub.ext and f.sub.ext using the Frantz-Nodvik (FN) formalism for analyzing saturated gain. A commonly used equation;
G.sub.out=ln[1+e.sup.G.sup.s(e.sup.G.sup.in−1)]  (4)
uses fluence terms that have been normalized with respect to the saturation fluence φ.sub.sat of the gain medium, which renders the equation useful for gain media with different values of saturation fluence. Specifically, the normalized fluence terms are: G.sub.s=φ.sub.stored/φ.sub.sat, G.sub.in=φ.sub.in/φ.sub.sat, where φ.sub.stored, φ.sub.in, and φ.sub.out are the fluence stored in the amplifier, the input fluence, and the output fluence, respectively. Since normalized fluence is used, rather than energy, the results are useful for laser beams of various transverse dimensions and pulse energies, as scaling the transverse dimensions of the laser beam is a method for scaling the energy of the laser. Specifically, the extractable stored energy in the laser beam is given by E.sub.stored=A.sub.beam*ϕ.sub.stored, the injected pulse energy is given by E.sub.in=A.sub.beam*ϕ.sub.in and the output pulse energy is given by E.sub.out=A.sub.beam*ϕ.sub.out, where A.sub.beam is the cross-sectional area of the laser beam. In this simplified example, the area A.sub.beam is constant as the beam propagates from the injection plane, through the amplifier and on to the output plane, although different amplifier arrangements can be used in which the beam area changes.

(30) Applying energy conservation gives the change in stored fluence due to amplification of the pulse:
ΔG=G.sub.s,initial−G.sub.s,final=G.sub.out−G.sub.in  (5)
where G.sub.s,initial and G.sub.s,final are the normalized stored fluence before and after passage of the pulse, respectively. These equations can be applied repeatedly, once for each pass, to calculate output fluence, gain, and extracted energy for multiple passes of the pulse through an amplifier. Passive losses can be accounted for by reducing the fluence between passes. At the end of these calculations, the extraction fraction is given by:

(31) $\begin{array}{cc}{f}_{\mathrm{ext}}=\frac{G_{s,\mathrm{initial}}-G_{s,\mathrm{final}}}{G_{s,\mathrm{initial}}}& \left(6\right)\end{array}$
where G.sub.s,initial and G.sub.s,final now represent the normalized stored fluence before and after the beam passes, respectively.

(32) FIG. 4 shows extraction fraction f.sub.ext plotted versus the output fluence G.sub.out for a multi-pass amplifier. For all curves, single-pass transmission and normalized injected fluence are 0.90 and 0.001, respectively. Curves are plotted for each of seven different values of normalized stored fluence, G.sub.s, which range from 0.05 to 3.22; these values of stored fluence correspond to single-pass gain values ranging from 1.65 to 25.0. In generating the curve for each value of G.sub.s, the number of passes taken by the laser pulse through the amplifier was varied, from 2 up to 20. For each curve, G.sub.out initially increases due to greater amplification as more passes are taken and f.sub.ext rises monotonically with G.sub.out. Eventually, f.sub.ext approaches unity and G.sub.out attains a maximum value due to gain saturation. At this point G.sub.out, is a large fraction of G.sub.s. (Ignore the portions of the curves that show extraction efficiency decreasing with G.sub.out as these are artifacts of the curve-plotting routine provided in Microsoft Excel.) FIG. 4 also shows curves indicating the number of passes required to produce the specified value of G.sub.out, which have been overlaid on the curves corresponding to the different values of G.sub.s. The number of passes required to attain high extraction efficiency decreases monotonically with G.sub.s. For example, for G.sub.s=3.22 (corresponding to single-pass small-signal gain of 25), only 4 passes are required to attain near-unity η.sub.ext. For G.sub.s=0.5 (corresponding to single-pass small-signal gain of 1.65), ˜30 passes are required.

(33) FIG. 4 is somewhat incomplete in that the ordinate does not include the effect of transport losses, which also need to be accounted for in laser design. Transport losses occur when optics absorb, scatter, reflect, or transmit light in ways that reduce energy in the laser beam. The total energy lost to transport is the sum of all the energy losses occurring each time the pulse interacts with a lossy optic. Transport efficiency for a multi-passed amplifier is given by:

(34) $\begin{array}{cc}{\eta }_{\mathrm{trans}}=1-\frac{E_{\mathrm{lost}}}{E_{in}+E_{\mathrm{ext}}}& \left(7\right)\end{array}$
where E.sub.lost is the total energy lost in transport, E.sub.in is the infected energy, and E.sub.ext is the energy extracted from the amplifier. FIG. 5 shows f.sub.extη.sub.trans plotted vs. G.sub.out. As in FIG. 4, results are given for different values of G.sub.s, and the number of passes is scanned from 2 to 20. Curves showing the number of passes needed to achieve G.sub.out are overlaid.

(35) For each value of G.sub.s, f.sub.extη.sub.trans and G.sub.out initially increase with the number of passes. However, after a certain number of passes have been taken, f.sub.extη.sub.trans achieves a peak value and then falls sharply. After f.sub.extη.sub.trans has peaked, values of G.sub.out are clamped and do not rise further. This behavior is due to transport losses, which rise sharply after a large fraction of the stored energy has been extracted. For those cases gain is reduced and transport losses become relatively more important. The number of passes needed to achieve the maximum value of f.sub.extη.sub.trans decreases as G.sub.s increases.

(36) FIG. 5 shows the product of extraction fraction and transport efficiency vs. maximum normalized output fluence for a multi-passed amplifier, assuming a single-pass transmittance T=0.90. (Ignore the portions of the curves that show extraction efficiency decreasing with G.sub.out as these are artifacts of the curve-plotting routine provided in Microsoft Excel.)

(37) By connecting the maximum values for the curves in FIG. 5, an envelope is formed that gives the maximum value of f.sub.extη.sub.trans vs. G.sub.out. FIG. 6 shows four such envelopes, which were calculated for single-pass transmittance values of 0.85, 0.90, 0.95, and 1.00. Superimposed are curves showing the number of passes needed to achieve G.sub.out. Somewhat remarkably, the modeling shows a one-to-one correspondence between the number of passes required to achieve a particular value of G.sub.out and the normalized stored fluence G.sub.s, with the number of passes decreasing as G.sub.s, increases. Accordingly, superimposed curves are labeled both with the number of passes needed and the value of G.sub.s. Additional modeling, not shown here, indicates that the f.sub.extη.sub.trans vs. G.sub.out curves for different values of T are nearly unchanged as G.sub.in is varied through reasonable values, although the number of passes required to achieve a particular value of G.sub.out falls as G.sub.in is increased.

(38) FIG. 6 shows extraction fraction times transport efficiency f.sub.extη.sub.trans vs. maximum normalized output fluence G.sub.out for multi-passed amplifiers with single-pass transmission values of 0.85, 0.90, 0.95 and 1.0. The seed fluence is held constant at G.sub.in=0.001. FIG. 6 illustrates several important principles of laser design as well as several important considerations when evaluating gain media for use in laser designs. For realistic systems, in which the single-pass transmission is T<1, the product f.sub.extη.sub.trans increases monotonically with G.sub.out.Math.f.sub.extη.sub.trans becomes unity only in the idealized lossless case (T=1), where it remains unity regardless of G.sub.s. As T decreases, the f.sub.extη.sub.trans vs. G.sub.out curses shift downward. Additionally, the maximum value of G.sub.out that is attained for any given value of G.sub.s decreases. G.sub.out is always less than or equal to G.sub.s, with the equality obtained only when T=1. Sensitivity to passive losses increases, i.e., f.sub.extη.sub.trans falls, as single-pass gain decreases. Multi-pass amplifiers operating at G.sub.out>2.2 achieve high values of f.sub.extη.sub.trans extraction fraction in ≤4 passes, provided that G.sub.in>0.001 and T≥0.85. There can be significant advantages to operating a beamline with four or fewer passes.

(39) Gain Media Choices for MPE and SPE

(40) The gain-medium parameters of φ.sub.sat and τ.sub.storage are key factors in determining extraction traction and extraction efficiency in MPE. FIG. 7 shows saturation fluence vs. storage lifetime for a variety of different gain media. FIG. 7 is a plot of two intrinsic material parameters for common Nd-, Yb-, and Tm-doped gain media: φ.sub.sat and τ.sub.storage. Gain media near the bottom left of this plot tend to be efficient in SPE white those at the top right tend to be quite efficient in MPE.

(41) The plot shows a correlation between the two, as there is a tendency for gain media with long storage lifetime to have high saturation fluence. Gain media with low values of φ.sub.sat and τ.sub.storage, in the lower left-hand corner of the plot, usually work well and have high efficiency, in SPE mode. They tend not to be candidates for MPE because their storage lifetimes tend to be short compared with the time between pulses for many application needs. However, gain media with high values of φ.sub.sat and τ.sub.storage, in the upper right-hand corner of the plot, tend not to work well in the SPE mode because damage fluences tend to be lower than the fluences needed for efficient extraction. However, they work well in the MPE mode because of their long lifetimes.

(42) Exemplary Design Steps

(43) This section outlines a series of steps that one might take to determine ranges of design parameters that use MPE, that operate at fluences below damage threshold and that meet efficiency requirements. After identifying these ranges, more detailed analysis and other considerations need to be applied to down-select and optimize designs. However, these steps are useful for quickly eliminating designs that do not meet requirements, for identifying the most attractive designs and for estimating design performance. These steps are:

(44) 1) Identify the key, top-level performance requirements of the system being designed. These include output pulse energy (E.sub.out), pulse repetition rate (PRF) pulse shape, pulse duration (τ.sub.pulse), and various efficiency terms which can include extraction efficiency (η.sub.ext), decay efficiency (η.sub.decay) and transport efficiency (η.sub.trans).

(45) 2) Choose a candidate gain medium. Gain media that are good candidates for MPE designs must have values for the radiative lifetime, τ.sub.rad that are comparable to or greater than the inverse of the PRF. Presumably, the designer has access to published results for various gain media that include τ.sub.rad, optimum laser wavelengths (λ.sub.laser), optimum pump wavelengths (λ.sub.laser), radiative lifetime (τ.sub.rad), saturation fluence (ϕ.sub.sat) and other properties.

(46) 3) Estimate the maximum safe operating fluence (ϕ.sub.damage) above which the laser pulse is apt to cause damage to an optical component, ϕ.sub.damage depends on the laser wavelength, the pulse duration and the quality of optics provided by optical vendors.

(47) 4) Estimate the minimum cross-sectional area of the laser beam needed to safely produce the required pulse energy. This minimum area, A.sub.beam,min, is given by

(48) $\begin{array}{cc}{A}_{\mathrm{beam},min}=\frac{E_{\mathrm{out}}}{{\phi }_{\mathrm{damage}}}& \left(8\right)\end{array}$

(49) 5) Determine whether the optical components that are available from vendors, including the amplifier gain elements (slabs, disks, or rods), are available in sizes that are large enough to transmit single laser beams of the required minimum size. Optics should be large enough to accommodate not only the beam but also to accommodate beam alignment errors, mounting allowances and other necessary allowances and tolerances.

(50) 6) If the gain media or other optics are not available in large-enough sizes to provide the required output pulse energy in a single beamline, decide whether: 1) to use more than one beamline to produce the required energy, or 2) to return to step 2) above and choose a different gain medium for which larger components might be available. This choice will depend on the application, whether the output pulse needs to be produced in one coherent beamline, space requirements, costs and other issues.

(51) 7) For each candidate gain medium, determine the saturation fluence (ϕ.sub.sat). If saturation fluence is not given explicitly, it can be calculated using standard formulas provided that the stimulated emission cross section and the absorption cross section are known at the laser wavelength.

(52) 8) Use results from steps 3) and 7) to calculate the maximum normalized output fluence, G.sub.out,max, that corresponds to the optical damage limit:

(53) $\begin{array}{cc}{G}_{\mathrm{out},\mathrm{ma}x}=\frac{{\phi }_{\mathrm{damage}}}{{\phi }_{\mathrm{sat}}}& \left(9\right)\end{array}$

(54) 9) Using the required efficiencies and equation (3) above, determine the minimum value of extraction fraction, f.sub.ext,min, that corresponds to the efficiency requirements.

(55) 10) Use the results front steps 8) and 9) above, along with a graph like the one in FIG. 5, to determine the range of designs that meet efficiency requirements while operating at a fluence below the optical damage limit. These are the designs which lie above the horizontal line given by
f.sub.ext≥f.sub.ext,min  (10)
and which also lie to the left of the vertical line given by
G.sub.out≤G.sub.ext,max  (11)

(56) Use of FIG. 5 is appropriate for designs for which the single-pass transmission T=0.9, and for which the injected fluence is G.sub.in=0.001. However, should T and G.sub.in have different values, FIG. 5 should be replaced with a similar graph that has been constructed using the appropriate values of T and Gin.

(57) FIG. 8 illustrates a gas cooled optical amplifier. A plurality of slab gain media 100 are located between optical windows 102 and 104. There are openings between each of the active medium so that He gas cooling 106 can flow between the slabs. In this embodiment the amplifier is optically pumped with pump light 108 and 110.

(58) FIG. 9 shows the implementation of two gas-cooled amplifiers in a system. In this system, CW diode lasers 120 and 122 optically pump gas-cooled amplifier 126. CW diode lasers 128 and 130 optically pump gas-cooled amplifier 132. A high contrast short pulse front end laser 136 provides pulses to be amplified. According to the present invention, a plurality of these pulses is provided within the fluorescence lifetime of the laser amplifiers. The series of pulses are located in beam 138 which is injected into the system at or near the focal plane of telescope 140. The beam is reflected from polarizer 142 and then from dichroic mirror 144 to pass a first time through amplifier 126. Dichroic mirrors in this system transmit diode pump light but reflect laser light. The beam is then reflected by dichroic mirror 146 and mirror 148 to pass through spatial filter 150 and then be reflected by mirror 152 and dichroic mirror 154 to make a first pass through amplifier 132 before being reflected by dichroic mirror 156 to pass through relay optics 158, a quarter wave plate 160 and then to be reflected by mirror 162 which reflects the beam back through amplifiers 132 and 126. Then, when the beam is incident on polarizer 142 for a second time, the beam is transmitted, passes through a relay telescope 143, and is incident on an adaptive-optic mirror 145, which reflects the beam back through amplifiers 126 and 132 two more times. When the beam is incident on polarizer 142 for a third time, the beam is reflected through telescope 140, passes through a high average power compressor 164. The beam is then reflected by mirror 166 and focused by concave mirror 168 onto target 170. The beam makes four amplification passes in this system.

(59) The gain bandwidth of an amplifier making use of any anisotropic gain material for which the absorption/gain spectra are different along the various optical axes can be increased by utilizing the gain along multiple crystal axes. This may be accomplished by polarization multiplexing the beam on multiple passes through the gain material, polarization encoding the spectrum of the beam, or simply mounting several crystals at different orientations while extracting with one polarization state. In combining these multi-axis schemes with the diode-pumped gas-cooled-slab architecture (illustrated in FIG. 8 and FIG. 9), the order in which the slabs are placed in the amplifier head can help balance the distribution of deposited pump power among the slain, with benefits of efficiency and material characteristics.

(60) The implementation of FIG. 10A places slabs 201-207 on optical axis 210. Here the center slabs 203-205 are rotated 90 degrees with respect to the outer slabs and the end-pumped laser polarizations 212 and extracting laser polarizations 214 are shown using arrows. The benefit of this technique is illustrated for the specific case of Tm:YLF gain material in FIG. 10B, which shows the net gain spectrum of Tm:YLF for both σ and π axes with 30% of the population in the .sup.3F.sub.4 state. The total gain achieved using both gain material axes yields a combined gain spectrum that is significantly broader than what could be achieved with one gain material orientation alone. FIG. 10C shows the absorption spectra of Tm:YLF for both polarizations. The orientation of the slabs in the cassette takes advantage of the lower absorption along the σ axis in the outer slabs and higher absorption along the π axis in the inner slabs to help balance the deposition of pump power. The need for this technique arises from the fact that in the end-pumped cassette architecture, pump light must travel through one gain element to reach another. Thus, the deposition of pump power in the inner slabs depends on the absorption in the outer slabs. Several examples of implementations of this method are illustrated in FIGS. 11A-C using examples relevant for Tm:YLF to illustrate the benefits. Based on the teachings of this disclosure, those skilled in the art will understand that other materials are usable. This method is applicable to any anisotropic laser gain medium.

(61) FIG. 11A, which is identical to FIG. 10A, illustrates a pumping scheme in which Tm:YLF is pumped at 793 nm. At this wavelength pump light is more strongly absorbed on the π-axis than on its σ-axis. With the slabs in the orientation illustrated, the lower pump light received by the innermost slabs is compensated orienting them so that they absorb pump light more strongly.

(62) FIG. 11B, which is identical in configuration to FIGS. 10A and 11A, except that the pump light 212 comprises two wavelengths. In the Tm:YLF case, the cassette could be pumped at both λ.sub.1=780 and λ.sub.2=793 nm. With the orientation illustrated, the 793 nm light would be efficiently absorbed in the outermost slabs while the 780 nm light would pass through the outer slabs and pump the inner slabs.

(63) FIG. 11C shows a variation in which a cassette of slabs 221-228, located on optical axis 220, are pumped on each by with a different polarization 230 and 232 to obtain extraction polarization 234.

(64) Based on this disclosure, the above techniques could use all three axes of a biaxial material. Different axes of distinct gain materials can also be used. Further, any combination of the aforementioned techniques may be used together.

(65) The most efficient choice of pump polarization, pump center wavelength(s), how many slabs to rotate, and the orientations of the slabs depend on many factors. These include the polarization extraction scheme (linear, polarization multiplexed, or polarization-encoded), the pump bandwidth, the shapes of the absorption/emission spectra, and the efficiencies of the anti-reflection coatings, among other factors. The efficiency as a function of these parameters cannot be expressed in a simple, closed form expression. Instead, the designer must create designs with various combinations of parameters to determine the optimal design point.

(66) The primary benefit of the crystal rotating technique is that it allows the laser designer to minimize crystal doping. For all gain materials, reducing doping tends to improve material properties, such as thermal conductivity and (generally undesirable) non-radiative quenching. In the case of quasi-3-level gain materials, minimizing the required doping also minimizes the pump power, as less pump light is needed to pump the system to transparency. In the special case of materials where cross-relaxation is part of the pumping process (Tm-doped materials are an example), this method can lower the doping in the center slabs, while keeping the doping high enough in the outermost slabs for efficient cross-relaxation.

(67) Concepts

(68) This writing also presents at least the following concepts:

(69) 1. A method, comprising:

(70) providing a gas cooled solid-state laser gain medium;

(71) continuously optically pumping said gain medium for a period of time to produce excited state ions; and

(72) producing amplified pulses by directing a plurality of pulses to be amplified through said gain medium within the fluorescence decay time of said laser gain medium.

(73) 2. The method of concepts 1 and 3-11, wherein said gain medium comprises at least one slab.

(74) 3. The method of concepts 1, 2 and 4-11, wherein said gain medium comprises a fluorescence lifetime that is sufficiently long that at least 10% of the stored energy that remains in the gain medium after any one pulse carries over to the next pulse of said plurality of pulses.

(75) 4. The method of concepts 1-3 and 5-11, wherein said gain medium comprises a saturation fluence that is high enough to make it impossible to achieve at least a 20% extraction efficiency without operating at a fluence above the lowest damage threshold of said plurality of optics when only one pulse is propagated through the amplifiers during the fluorescence decay time of the laser gain medium.

(76) 5. The method of concepts 1-4 and 6-11, wherein the operating fluence of said gain medium is lower than the damage fluence, even when the saturation fluence is greater than the damage fluence.

(77) 6. The method of concepts 1-5 and 7-11, further comprising a plurality of optics positioned to received said amplified pulses, wherein said gain medium comprises a gain spectra that is sufficiently broad such that said amplified pulses can be optically compressed to sub-ps duration and wherein said gain medium comprises a saturation fluence that is high enough to make it impossible to achieve at least a 20% extraction efficiency without operating at a fluence above the lowest damage threshold of said plurality of optics, when only one pulse is propagated through the amplifiers during the fluorescence decay time of the laser gain medium.

(78) 7. The method of concepts 1-6 and 8-11, wherein the step of continuously optically pumping said gain medium is carried out with at least one laser diode.

(79) 8. The method of concepts 1-7, 9 and 11, wherein the extraction efficiency for any one pulse is no more than a few percent and the stored energy extracted by the train of pulses is greater than the energy that is lost to fluorescence decay.

(80) 9. The method of concepts 1-8 and 11, wherein said gain medium comprises a plurality of gas-cooled slabs.

(81) 10. The method of concepts 1-9 and 11, wherein said gain medium comprises at least one rare-earth dopant.

(82) 11. The method of concepts 1-10, wherein said gain medium comprises slabs of at least one anisotropic gain material mounted so that two or more optical axes of said slabs interact with the amplified pulses to increase the gain bandwidth and wherein the order in which said slabs are rotated is selected to minimize the required doping of said gain medium and/or to minimize the pump power required in the step of continuously optically pumping said gain medium.

(83) 12. An apparatus, comprising:

(84) a gas cooled solid-state laser gain medium;

(85) means for continuously optically pumping said gain medium for a period of time to produce excited state ions; and

(86) means for producing amplified pulses by directing a plurality of pulses to be amplified through said gain medium within the fluorescence decay time of said laser gain medium.

(87) 13. The apparatus of concepts 12 and 14-22, wherein said gain medium comprises at least one slab.

(88) 14. The apparatus of concepts 12, 13 and 15-22, wherein said gain medium comprises a fluorescence lifetime that is sufficiently long that at least 10% of the stored energy that remains in the gain medium after any one pulse carries over to the next pulse of said plurality of pulses.

(89) 15. The apparatus of concepts 12-14 and 16-22, wherein said gain medium comprises a saturation fluence that is high enough to make it impossible to achieve at least a 20% extraction efficiency without operating at a fluence above the lowest damage threshold of said plurality of optics when only one pulse is propagated through the amplifiers during the fluorescence decay time of the laser gain medium.

(90) 16. The apparatus of concepts 12-15 and 17-22, wherein the operating fluence of said gain medium is lower than the damage fluence, even when the saturation fluence is greater than the damage fluence.

(91) 17. The apparatus of concepts 12-16 and 18-22, further comprising a plurality of optics positioned to received said amplified pulses, wherein said gain medium comprises a gain spectra that is sufficiently broad such that said amplified pulses comprise sub-ps pulses and wherein said gain medium comprises a saturation fluence that is high enough to make it impossible to achieve at least a 20% extraction efficiency without operating at a fluence above the lowest damage threshold of said plurality of optics, when only one pulse is propagated through the amplifiers during the fluorescence decay time of the laser gain medium.

(92) 18. The apparatus of concepts 12-17 and 19-22, wherein the step of continuously optically pumping said gain medium is carried out with at least one laser diode.

(93) 19. The apparatus of concepts 12-18, 20-22, wherein the extraction efficiency for any one pulse is no more than a few percent and the stored energy extracted by the train of pulses is greater than the energy that is lost to fluorescence decay.

(94) 20. The apparatus of concepts 12-19, 21 and 22, wherein said gain medium comprises a plurality of gas-cooled slabs.

(95) 21. The apparatus of concepts 12-20 and 22, wherein said gain medium comprises at least one rare-earth dopant.

(96) 22. The apparatus of concepts 12-21, wherein said gain medium comprises slabs of at least one anisotropic gain material mounted so that two or more optical axes of said slabs interact with the amplified pulses to increase the gain bandwidth and wherein the order in which said slabs are rotated is selected to minimize the required doping of said gain medium and/or to minimize the pump power required in when said gain medium is continuously optically pumped.

(97) 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. Many modifications and variations are possible in fight of the above teaching. The embodiments disclosed were meant only to explain the principles of the invention and its practical application to thereby enable others skilled in the art to best use the invention in various embodiments and with various modifications suited to the particular use contemplated. The scope of the invention is to be defined by the following claims.