**2. Extraction during pumping (EDP) method**

TASE and TPG within the booster amplifier volume. As a result, the suppression of parasitic generation is a very important task that has been solved for the next generation of the ultrahigh power laser systems. The technology allowed to solve this bottleneck problem will be

The making of the output short pulse shorter and keeping the same energy paved another way to the next milestone of the ultra-high peak power. Nevertheless, pulse duration of CPA lasers is strongly limited by gain narrowing of the pulse spectra in the gain medium of the multipass amplifiers (to around 30 fs of 100 TW–1 PW lasers based on Ti:Sa). Different approaches were entertained to overcome this limitation. Among them, there is a gain narrowing control by introduction of the thin film etalon into the front-end regenerative amplifier cavity. Impressive results were reached with this technique (pulse duration—16 fs with spectral width—72 nm) [19], but this method still suffers some restrictions, such as losses of the energy, a finite possibility of the broadening of the spectra due to the fluorescence spectrum limitation of the amplifier crystal, further gain narrowing in the buster and final ampli-

fiers, as well as the limitation of the spectral transmission of the grating compressor.

The application of concept of optical-parametrical chirped pulse amplification (OPCPA) for broadband pulse allowed to reach a pulse duration of around 10 fs [20], but extremely severe requirements on the parameters of the pump laser which discussed above restrict output energy only to a few mJs. This way, an adequate method for shortening high-energy pulses has not yet been found. Two promising methods of the saving and restoring spectral band-

With the light sources of 10–100 PW peak power, the accelerated electron beams can reach the energy up to TeV and ion beams up to GeV, (see **Figure 1**) as well as by using these secondary sources the ultra-bright X and Y-rays can be obtained [21]. These results could be widely applied into many areas of science, industry, medicine, homeland security, and so on. Nevertheless, it will be possible if the ultra-high peak power laser systems also will be able to combine with high repetition rate (hundreds of Hz to kHz) or high average power (kWs). In the petawatt class laser amplifiers, a pump pulse energy exceeds a few hundred J regime, which means significant thermal load in the gain medium even at low repetition rates.

Thin disk laser technology (TDT) is able to eliminate thermal distortions and damages of the laser crystals in the systems with both high peak and average output power [22]. However, conventionally used in TDT, Nd:YAG and Yb:YAG possess the narrow emission spectra and the low emission cross-section that lead to very complicated multipass amplification schemes which is practically acceptable only for low peak power systems with the ps-level pulse duration. The most promising crystal with required characteristics for ultra-high peak power laser is Ti:Sa, especially if one is taking into account its higher emission cross-section and thermal conductivity (compare 10 W/(mK) for YAG to 40 W/(mK) for sapphire at the room temperature and

discussed below in this chapter.

68 High Power Laser Systems

**1.2. Gain narrowing during amplification**

width will be discussed also in this chapter.

**1.3. Requirements for high repetition rate**

As it was mentioned above, the main limitation that arises on the path toward ultra-high output power and intensity of the CPA laser systems is the restriction on the pumping and extraction energy imposed by TASE and TPG within the booster and final large aperture amplifier volume [23].

The reflectivity reduction of the side wall of the gain crystals by grinding, sandblasting and/ or coating with an index-matched absorptive polymer or liquid layer in the laser amplifiers is the conventional procedure used to prevent parasitic generation (TPG) [24]. However, the difficulty to find the exact index matching within existing absorbers still restricts the diameter of the pump area to 6–8 cm, corresponding to an extracted energy to around 30 J from Ti:Sa [16]. The amplifier apertures enlarging, or to further pump fluence increasing has led to severe parasitic generation and has failed to increase extracted energy. The additional restriction on storing and extracting energy by TASE in larger gain apertures was demonstrated [25]. TASE necessarily increases with the aperture size, limiting the maximum stored energy that is why this restriction is even stronger than parasitic lasing because the threshold for the latter can be increased due to development of the new index matching materials for absorbers. The uniform luminescence on the left picture of **Figure 4** should not delude us, if one will find method to reduce reflections down to zero; the losses remain still incredible big for amplifiers with the large aperture.

The method of the calculation of total volume of TASE radiated out from the crystal during its pumping was developed by Chvykov et al. [25]. **Figure 5a** shows the evolution of normalized fluorescence of the crystals vs. pumping time when pumped by 100 ns-pulse for different crystal apertures. Here, Emax is the theoretical maximum of the extracted energy, and Eloss is the lost energy due to TASE. As seen from the plot, ASE grows dramatically after a certain time of pumping, even for 10 cm—crystal and soon becomes equal to the pumping energy. This means that further pumping is useless because all additional energy will be irradiated out of the crystal as ASE. The critical points of anomalous ASE (APs) are moving to the pumping process beginning with the growing crystal diameter. No more than 20–50% of the pump energy can be stored in the crystals with aperture of 15–20 cm as seen in **Figure 5**.

Shortening of the pump pulse duration does not help to reduce the losses, at least until pulse duration becomes shorter than the time-length of the light distribution through the crystal in transverse direction. This is about several 100 ps, and thus such a pump would be useless due to the very low damage threshold. Fluorescence during pumping for different pump pulse

**Figure 5.** Fluorescence evolution of gain volumes vs. pumping time. (a) Normalized ASE to its maximal value for different crystal apertures, D: blue dash-doted curve D = 20 cm (Emax = 824 J, Eloss = 590 J), green dots D = 15 cm (Emax = 460 J, Eloss = 290 J), red dashes D = 10 cm (Emax = 210 J, Eloss = 100 J), and violet solid D = 6 cm (Emax = 74 J, Eloss = 20 J); (b) TASE for different pump pulse durations, τ pump (15 cm crystal diameter): violet solid curve τpump = 10 ns (Eloss = 325 J), red dashes τpump = 30 ns (Eloss = 321 J), green dots τpump = 50 ns (Eloss = 315 J), blue dash-dots τpump = 100 ns (Eloss = 290 J).

durations are shown for 15 cm crystal diameter (**Figure 5b**). As seen, the losses slightly grow due to the higher pump rate that enhances TASE with reduction of the pump pulse duration.

If the total compensation of transverse gain by the index-matched absorber coating is not possible, the reflectivity from the side wall will be enough for parasitic generation-TPG. Therefore, one can establish the TPG threshold as an equality transverse gain of the crystal to absorption coefficient of its side wall. There are two most probable transverse modes which can develop: first one is due to the maximal population inversion which is a generation near two working parallel surfaces [23] and the z-pass between these surfaces due to total internal reflection [26] (**Figure 6a**). The latter mode surpasses the first one in large aperture crystals with a high aspect ratio and respectively low crystal doping because higher gain for second mode. One can define the TPG threshold small signal gain *Gt* through the pump intensity *Fp* as: *Gt* <sup>=</sup> exp( \_

$$\mathcal{G}\_t = \exp\left(-\frac{\mathcal{G}\_{\text{vibr}\_{\text{p}}}}{zh\nu} \mathcal{D}F\_p\right) \tag{1}$$

or index matching of the absorber and crystal thickness. Therefore, enlargement of the crystal aperture requires reducing the pump fluence. Moreover, the pump fluence will be limited for any crystals and absorbers because the complete matching is impossible for both polarizations of the transverse modes. The dependence of the maximal possible pump fluence on the crystal diameter was shown in **Figure 6b**, where the purple rhombus-marked curve is the ideal case of upper bound for 3 cm crystal thickness and reflectivity of σ-polarization under

**Figure 6.** (a) Two transverse optical paths with highest gain for TASE within a crystal; (b) dependence of pump fluence on crystal diameter: solid curves: calculated for TPG (K = 24, light blue squares; K = 32, green triangles; K = 42, blue

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The same dependences can be built for TASE limitation based on the APs (**Figure 5a**, crosses with gray dashed line indicating 0.9 of the maximum volume). TASE curve for crystals with B = 0.01 nearly match the TGP curve with K values of 32 (these values correspond to existing absorbers [16]) and is located below the purple ideal curve as shown in the **Figure 6**. The main conclusion to be drawn from this correspondence is that there remains no motivation to develop better absorber materials, owing to restrictions of TASE. Therefore, the situation for laser amplifiers with large apertures appears bleak, especially with respect to their application as final amplifiers in very high power laser systems. For example, one can conclude from

, when saturated one for Ti:Sa crystal is 0.9 J/cm<sup>2</sup>

the deeply inefficient amplifier operation. Nevertheless, below, we will demonstrate that the parasitic losses due to both TASE and TPG can be significantly reduced using EDP technique. We suggest to change the conventional method of pumping and amplifying the multipass amplifiers to overcome the restrictions discussed above. Conventional method is based on the energy stored in the amplifier media prior to the arrival of the first pass of the input pulse [26]. We are able to forestall TASE and parasitic lasing and increase the extracted energy by continuing to pump after the arrival of the amplified pulse. In this case, the energy extracted during one pass of the amplified pulse through the crystal could be restored by pumping up to AP or TPG threshold before the next pass. An extended pump pulse duration ranging from tens to hundreds of nanoseconds, or several delayed pulses is required for EDP process. One

meaning the extracted

, which indicates

the condition of total index matching for π-polarization.

squares); dot-dashed curves: calculated for TASE (red squares: B = 0.01).

fluence is about 0.7 J/cm<sup>2</sup>

**Figure 6**, that for 20 cm crystal diameter, the maximum Fp is 1.5 J/cm<sup>2</sup>

Introducing *K = D • Fp* as a *K*-parameter, we can find the dependence of pump fluence TPG threshold on the crystal diameter (**Figure 6b**) calculating *K* for different crystal geometry and used absorber.

$$\mathbf{K}\_s = \frac{\mathbf{v}\_r}{\mathbf{V}\_m} \ast \ln \mathbf{G}\_l \ast \frac{z \, F\_s}{\ln \mathbf{B}'} ; \quad \mathbf{K}\_z = \frac{\mathbf{v}\_r}{\mathbf{V}\_m} \ast \ln \mathbf{G}\_l \ast \frac{z \, F\_s}{2n} \tag{2}$$

There (2) are two formula of the *K*-factor calculations for two transverse parasitic modes consequently, the generation near working surfaces (*Ks* ) and the z-pass between them (*Kz* ), where *D* is the pump area diameter, *Gt* is the highest transverse gain that would be compensated by an index-matched absorptive coating, *z* is the crystal thickness, *n* is the index of refraction of the crystal, and the absorption coefficient for the pump frequency—*B*.

A crystal with a given aperture fixes the maximum pump fluence because the product of crystal diameter and the pump fluence is constant for each value of the critical transverse gain New Generation of Ultra-High Peak and Average Power Laser Systems http://dx.doi.org/10.5772/intechopen.70720 71

**Figure 6.** (a) Two transverse optical paths with highest gain for TASE within a crystal; (b) dependence of pump fluence on crystal diameter: solid curves: calculated for TPG (K = 24, light blue squares; K = 32, green triangles; K = 42, blue squares); dot-dashed curves: calculated for TASE (red squares: B = 0.01).

durations are shown for 15 cm crystal diameter (**Figure 5b**). As seen, the losses slightly grow due to the higher pump rate that enhances TASE with reduction of the pump pulse duration. If the total compensation of transverse gain by the index-matched absorber coating is not possible, the reflectivity from the side wall will be enough for parasitic generation-TPG. Therefore, one can establish the TPG threshold as an equality transverse gain of the crystal to absorption coefficient of its side wall. There are two most probable transverse modes which can develop: first one is due to the maximal population inversion which is a generation near two working parallel surfaces [23] and the z-pass between these surfaces due to total internal reflection [26] (**Figure 6a**). The latter mode surpasses the first one in large aperture crystals with a high aspect ratio and respectively low crystal doping because higher gain for second mode. One

τpump = 30 ns (Eloss = 321 J), green dots τpump = 50 ns (Eloss = 315 J), blue dash-dots τpump = 100 ns (Eloss = 290 J).

**Figure 5.** Fluorescence evolution of gain volumes vs. pumping time. (a) Normalized ASE to its maximal value for different crystal apertures, D: blue dash-doted curve D = 20 cm (Emax = 824 J, Eloss = 590 J), green dots D = 15 cm (Emax = 460 J, Eloss = 290 J), red dashes D = 10 cm (Emax = 210 J, Eloss = 100 J), and violet solid D = 6 cm (Emax = 74 J, Eloss = 20 J); (b) TASE for different pump pulse durations, τ pump (15 cm crystal diameter): violet solid curve τpump = 10 ns (Eloss = 325 J), red dashes

> *Ϭ zhν <sup>p</sup>*

threshold on the crystal diameter (**Figure 6b**) calculating *K* for different crystal geometry and

There (2) are two formula of the *K*-factor calculations for two transverse parasitic modes con-

an index-matched absorptive coating, *z* is the crystal thickness, *n* is the index of refraction of

A crystal with a given aperture fixes the maximum pump fluence because the product of crystal diameter and the pump fluence is constant for each value of the critical transverse gain

*lnB*; *Kz* <sup>=</sup> *<sup>ν</sup><sup>p</sup>* \_\_\_

*νem*

*<sup>z</sup> <sup>F</sup>* \_\_\_*<sup>s</sup>*

through the pump intensity *Fp*

*z F* \_\_\_*<sup>s</sup>*

is the highest transverse gain that would be compensated by

) and the z-pass between them (*Kz*

as a *K*-parameter, we can find the dependence of pump fluence TPG

\* *ln Gt* \*

<sup>D</sup> *Fp*) (1)

as:

<sup>2</sup>*<sup>n</sup>* (2)

), where

can define the TPG threshold small signal gain *Gt*

Introducing *K = D • Fp*

*Ks* <sup>=</sup> *<sup>ν</sup><sup>p</sup>* \_\_\_

*D* is the pump area diameter, *Gt*

used absorber.

70 High Power Laser Systems

*Gt* <sup>=</sup> exp( \_

sequently, the generation near working surfaces (*Ks*

*νem*

the crystal, and the absorption coefficient for the pump frequency—*B*.

\* *ln Gt* \*

or index matching of the absorber and crystal thickness. Therefore, enlargement of the crystal aperture requires reducing the pump fluence. Moreover, the pump fluence will be limited for any crystals and absorbers because the complete matching is impossible for both polarizations of the transverse modes. The dependence of the maximal possible pump fluence on the crystal diameter was shown in **Figure 6b**, where the purple rhombus-marked curve is the ideal case of upper bound for 3 cm crystal thickness and reflectivity of σ-polarization under the condition of total index matching for π-polarization.

The same dependences can be built for TASE limitation based on the APs (**Figure 5a**, crosses with gray dashed line indicating 0.9 of the maximum volume). TASE curve for crystals with B = 0.01 nearly match the TGP curve with K values of 32 (these values correspond to existing absorbers [16]) and is located below the purple ideal curve as shown in the **Figure 6**. The main conclusion to be drawn from this correspondence is that there remains no motivation to develop better absorber materials, owing to restrictions of TASE. Therefore, the situation for laser amplifiers with large apertures appears bleak, especially with respect to their application as final amplifiers in very high power laser systems. For example, one can conclude from **Figure 6**, that for 20 cm crystal diameter, the maximum Fp is 1.5 J/cm<sup>2</sup> meaning the extracted fluence is about 0.7 J/cm<sup>2</sup> , when saturated one for Ti:Sa crystal is 0.9 J/cm<sup>2</sup> , which indicates the deeply inefficient amplifier operation. Nevertheless, below, we will demonstrate that the parasitic losses due to both TASE and TPG can be significantly reduced using EDP technique.

We suggest to change the conventional method of pumping and amplifying the multipass amplifiers to overcome the restrictions discussed above. Conventional method is based on the energy stored in the amplifier media prior to the arrival of the first pass of the input pulse [26]. We are able to forestall TASE and parasitic lasing and increase the extracted energy by continuing to pump after the arrival of the amplified pulse. In this case, the energy extracted during one pass of the amplified pulse through the crystal could be restored by pumping up to AP or TPG threshold before the next pass. An extended pump pulse duration ranging from tens to hundreds of nanoseconds, or several delayed pulses is required for EDP process. One can get sufficient time in this case for proper pumping between passes, allowing increased total pump fluence due to the longer pump pulse duration and overcoming problems with temporal jitter. This approach was shown to double the output flux above the parasitic lasing limit in the experiments in University of Michigan [27].

Optimization of EDP method for presently available large aperture Ti:Sa amplifiers was made in Ref. [28] . The description of amplified transmission of pulses through the multipass amplifiers can be done by broadly applying Frantz-Nodvik solution for the 1-D photon transport Eq. [26]. Solution for optimal EDP-amplifiers can be rewritten as a single equation, in contrast to conventional amplifiers, where this equation is applied iteratively with adjustment of small signal gain for each pass, because the restoration of the population inversion by the pump between passes in case of EDP, and hence of the small signal gain, for each pass:

$$F\_{out} = F\_s \ln\left\{ 1 + \left[ \exp\left(\frac{F\_{\bar{n}}}{F\_s}\right) - 1 \right] \exp\left(N \frac{\nu\_m}{\nu\_r} \frac{F\_r}{F\_s}\right) \right\} \tag{3}$$

This absorber is able to accommodate the maximum transverse gain of 4000, which leads to a value of *K* = 32. We can find the output energy of ~800 J from the blue rhombus curve in **Figure 7b**, which corresponds to 50 J input energy. In Ref. [16], the authors demonstrate the final EDP-amplifier 60 J, making 800 J realistic output energy for the next stage of amplification. This output energy can be reasonable for crystals with this diameter due to output

**Figure 7.** (a) Dependence of the output fluence of the 4-pass amplifier on the input fluence for several pump ones; (b) dependence of the output energy on diameter of pumped area for different input energies and K-factor; dashed red

The EDP-technology was successfully spread out in the many world class laboratory for application in the ultra-high power laser systems, demonstrated today's world record near 200 J extracted energy and 5.0 PW output power [30]. Below several examples will be

First time, this method was used in the 4-pass amplifier of the HERCULES-300 TW Laser [31]. Four-pass amplifier crystal was cooled cryogenically to 120 K avoiding wave-front thermodistortion of the output beam. Because the amplifier crystal was located in the vacuum chamber to avoid the surface deposition, cladding of the side surface was impossible. Extracted flux

The authors of [16] have successfully developed a high-energy Ti:Sa laser system that delivers 33 J before compression at 0.1 Hz using LASERIX-4-pass EDP-amplifier. 100 mm diameter Ti:Sa crystal (pumped area-60 mm) was used as the final amplifier which was pumped with 72 J of energy delivered by frequency-doubled high-repetition rate Nd:Glass lasers. The good amplification efficiency of 45% with a homogeneous flat-top spatial amplified intensity profile

The EDP-method has also been applied on several Ti:Sa booster amplifiers of petawatt scale. One of them was 3-pass EDP-amplifier of APRI 1.5 PW CPA-laser (South Korea) [32]. The team of laser developers reported about the generation of 1.5 PW by using two stage final EDP-amplification with the maximum output energy of 60.2 J at a pump energy of 120 J.

due to application of EDP [27].

and the extraction efficiency close to theoretical one 65% which is reachable

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fluence 2 J/cm<sup>2</sup>

exhibited.

for EDP-amplifiers.

curve: damage threshold fluence.

was finally obtained.

was increased from 0.6 to 1.2 J/cm<sup>2</sup>

where *N* is the number of passes, νem is the emission frequency, ν<sup>p</sup> is the pump frequency, *Fout* is the *N*-pass output fluence, *Fs* is the saturation fluence, *Fin* is the incident fluence, and *Fp* is the initial pump fluence (before signal arrives).

Therefore, we simply introduce a factor of N into the small signal gain expression to get the output flux after N-passes of amplification. This could be easily proved by introducing the output flux from any *N*−1 passes as *Fin* for *N*-th pass and following the usual iterative procedure.

Dependences of the output fluence calculations for 4-pass amplification with conventional amplification and EDP for various pump fluence are presented in **Figure 7a**. From this graph, one can get the next conclusions. First—EDP amplifiers can deliver significantly more energy (up to four times for four-pass amplifier) compared to regular ones with the same initial pump fluence. Second—the input fluence that saturates the amplifier is much higher than that for the regular case because the graphs asymptotically approach to the value of four times of the initial pump flux multiplied by coefficient of quantum defect. From comparison of the two green or two blue curves in **Figure 7a**, one can see that the curvature slope becomes twice lower at 50–70 mJ/cm<sup>2</sup> of the input fluence for conventional amplifier and near 200 mJ/cm<sup>2</sup> for EDPamplifier. We have a higher extracted energy with growing input flux and so are able to add more pump fluence between passes. So, the input fluence for amplification with EDP has to be much higher to make them efficient and the process of amplification mimics the case of a high value of F<sup>s</sup> . On the other hand, this says us about a much higher energy capacity of the amplifier.

The optimal diameter for the pump area of the EDP-amplifiers can be demonstrated if into Eq. (3), in place of *Fin* and *Fp* , will be introducing the ratios *Ein/A* and *K/D* (2), respectively, where *Ein* is the total incident energy and *A* is the pump area. The dependences of the output energy on diameter of the pump area, for different *K* values and incident energies, are presented in **Figure 7b**. The output fluence of damage threshold was marked by the red dashed line. Using these graphs, we can calculate the highest output energy for amplification with EDP for a practically available liquid absorber and a crystal with 20–25 cm diameter [29].

can get sufficient time in this case for proper pumping between passes, allowing increased total pump fluence due to the longer pump pulse duration and overcoming problems with temporal jitter. This approach was shown to double the output flux above the parasitic lasing

Optimization of EDP method for presently available large aperture Ti:Sa amplifiers was made in Ref. [28] . The description of amplified transmission of pulses through the multipass amplifiers can be done by broadly applying Frantz-Nodvik solution for the 1-D photon transport Eq. [26]. Solution for optimal EDP-amplifiers can be rewritten as a single equation, in contrast to conventional amplifiers, where this equation is applied iteratively with adjustment of small signal gain for each pass, because the restoration of the population inversion by the pump

> *F* \_\_\_*in*

where *N* is the number of passes, νem is the emission frequency, ν<sup>p</sup> is the pump frequency, *Fout*

Therefore, we simply introduce a factor of N into the small signal gain expression to get the output flux after N-passes of amplification. This could be easily proved by introducing the output flux from any *N*−1 passes as *Fin* for *N*-th pass and following the usual iterative

Dependences of the output fluence calculations for 4-pass amplification with conventional amplification and EDP for various pump fluence are presented in **Figure 7a**. From this graph, one can get the next conclusions. First—EDP amplifiers can deliver significantly more energy (up to four times for four-pass amplifier) compared to regular ones with the same initial pump fluence. Second—the input fluence that saturates the amplifier is much higher than that for the regular case because the graphs asymptotically approach to the value of four times of the initial pump flux multiplied by coefficient of quantum defect. From comparison of the two green or two blue curves in **Figure 7a**, one can see that the curvature slope becomes twice lower

of the input fluence for conventional amplifier and near 200 mJ/cm<sup>2</sup>

. On the other hand, this says us about a much higher energy capacity of the amplifier.

, will be introducing the ratios *Ein/A* and *K/D* (2), respectively,

amplifier. We have a higher extracted energy with growing input flux and so are able to add more pump fluence between passes. So, the input fluence for amplification with EDP has to be much higher to make them efficient and the process of amplification mimics the case of a high

The optimal diameter for the pump area of the EDP-amplifiers can be demonstrated if into

where *Ein* is the total incident energy and *A* is the pump area. The dependences of the output energy on diameter of the pump area, for different *K* values and incident energies, are presented in **Figure 7b**. The output fluence of damage threshold was marked by the red dashed line. Using these graphs, we can calculate the highest output energy for amplification with EDP for a practically available liquid absorber and a crystal with 20–25 cm diameter [29].

*Fs*) <sup>−</sup> <sup>1</sup>] *exp*(*<sup>N</sup> <sup>ν</sup>*

\_\_\_*em νp Fp* \_\_ *Fs*

is the saturation fluence, *Fin* is the incident fluence, and *Fp*

)} (3)

is

for EDP-

between passes in case of EDP, and hence of the small signal gain, for each pass:

limit in the experiments in University of Michigan [27].

*Fout* <sup>=</sup> *Fs ln*{<sup>1</sup> <sup>+</sup> [*exp*(

the initial pump fluence (before signal arrives).

is the *N*-pass output fluence, *Fs*

procedure.

72 High Power Laser Systems

at 50–70 mJ/cm<sup>2</sup>

Eq. (3), in place of *Fin* and *Fp*

value of F<sup>s</sup>

**Figure 7.** (a) Dependence of the output fluence of the 4-pass amplifier on the input fluence for several pump ones; (b) dependence of the output energy on diameter of pumped area for different input energies and K-factor; dashed red curve: damage threshold fluence.

This absorber is able to accommodate the maximum transverse gain of 4000, which leads to a value of *K* = 32. We can find the output energy of ~800 J from the blue rhombus curve in **Figure 7b**, which corresponds to 50 J input energy. In Ref. [16], the authors demonstrate the final EDP-amplifier 60 J, making 800 J realistic output energy for the next stage of amplification. This output energy can be reasonable for crystals with this diameter due to output fluence 2 J/cm<sup>2</sup> and the extraction efficiency close to theoretical one 65% which is reachable for EDP-amplifiers.

The EDP-technology was successfully spread out in the many world class laboratory for application in the ultra-high power laser systems, demonstrated today's world record near 200 J extracted energy and 5.0 PW output power [30]. Below several examples will be exhibited.

First time, this method was used in the 4-pass amplifier of the HERCULES-300 TW Laser [31]. Four-pass amplifier crystal was cooled cryogenically to 120 K avoiding wave-front thermodistortion of the output beam. Because the amplifier crystal was located in the vacuum chamber to avoid the surface deposition, cladding of the side surface was impossible. Extracted flux was increased from 0.6 to 1.2 J/cm<sup>2</sup> due to application of EDP [27].

The authors of [16] have successfully developed a high-energy Ti:Sa laser system that delivers 33 J before compression at 0.1 Hz using LASERIX-4-pass EDP-amplifier. 100 mm diameter Ti:Sa crystal (pumped area-60 mm) was used as the final amplifier which was pumped with 72 J of energy delivered by frequency-doubled high-repetition rate Nd:Glass lasers. The good amplification efficiency of 45% with a homogeneous flat-top spatial amplified intensity profile was finally obtained.

The EDP-method has also been applied on several Ti:Sa booster amplifiers of petawatt scale. One of them was 3-pass EDP-amplifier of APRI 1.5 PW CPA-laser (South Korea) [32]. The team of laser developers reported about the generation of 1.5 PW by using two stage final EDP-amplification with the maximum output energy of 60.2 J at a pump energy of 120 J.

Shanghai Institute of Optics and Fine Mechanics, Chinese 5 PW CPA: laser, 4-pass EDPamplifier [30]. Effective suppression of the parasitic lasing in the final booster amplifier was done using the EDP-technology combined with index-matching cladding technique and the precise control of the time delay between the input seed pulse of 35 J and pump pulses of 312 J. The output energy of 192.3 J from the final amplifier was corresponding to a pump conversion efficiency of 62% to the output laser energy.

The design of the final EDP-amplifiers was recently developed for three pillars of the Extreme Light Infrastructure (ELI) project [33]. ELI is the ambitious pan-European laser research project. The major mission of the ELI facility is to make a wide range of cutting-edge ultrafast light sources available to the international scientific community. The first purpose of the facilities is to design, develop and build ultra-high-power lasers with focusable intensities and average powers reaching far beyond the existing laser systems. The secondary purpose is to contribute to the scientific and technological development toward generating 200 PW pulses, being the ultimate goal of the ELI project. PW-class lasers have been planned to build in the three pillars of ELI. 2 PW peak power, 10 Hz repetition rates and <20 fs pulse duration lasers will be part of the ELI-BEAMLINES and the ELI-ALPS, while the L4 of the ELI-BEAMLINES as well as the ELI-NP lasers aiming at 300 J/10 PW lasers. The roadmap for 200 PW laser facility was paved by the ELI consortium. This will increase the available laser power by at least one order of magnitude in its first three pillars, and on another more order of magnitude in its fourth ultra-high-intensity pillar. The laser power frontier was planned to be pushed into sub-exawatt regime by the establishment of ELI s fourth pillar.

The examples of final EDP-amplifiers design of 10s PW laser system are presented on the **Figures 8** and **9**. As the estimations demonstrate, the EDP-technology is able to significantly increase the output energy and intensity. There are calculated as optimal output parameters: the diameter of the pump area and crystal −19 and 20 cm, the pump energy −960 J, the input and the output energy −60 and 600 J. The losses with the EDP technology can be made under 5% (**Figure 8**).

have reached 30 cm crystal diameter. The estimations demonstrate the 40-cm crystals with 6-cm thickness which is nearly maximum for EDP amplification due to geometric reasons. This amplifier is able to supply ~3 kJ/140 PW with 250 J of seed energy while suffering TASE losses of about 207 J. Two EDPCPA channels will be enough for approaching 200 PW in this case.

**Figure 9.** Final EDP-amplifiers with 3- and 4-passes: (a) EDP amplifier with a 19-cm-diameter pump area can approach 500-J energy with a 60-J input (100 J losses) during 3-pass; (b) 4-pass EDP amplifier with a 19-cm-diameter pump area

**Figure 8.** Dependences of losses for 4 (blue-dashed curve) and 3 cm (pink-solid curve) thickness of the crystal:

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Here, we will concern another way of the peak power increasing, namely pulse shortening. It was discussed above that the gain narrowing and saturation limit the achievable pulse duration to about 30 fs [30, 31]. To achieve the 10–15 fs pulse duration designed for the Apollon system as well as for the 10 PW laser of the ELI [18], further scientific and technological efforts

The idea to use optical rotatory dispersion (ORD) (the angle of polarization rotation dependence on wavelength) spectral filter was suggested for conservation of bandwidth in low gain multipass Ti:Sa amplifiers, typically used for the intermediate and duty end amplifiers of multi-TW-PW class systems [34]. The spectral gain can be effectively re-shaped using difference of

**3. Pulse duration shortening**

(a) conventional amplifier; (b) EDP-amplifier.

**3.1. Preserving and restoring pulse spectral bandwidth**

can approach 600-J energy with a 60-J input, when pumped by 960 kJ (28 J losses).

have to be made to avoid spectral narrowing in the power amplifiers.

The total losses in 4 cm thickness crystal of conventional amplifier is about 70%, and for 3 cm, it is −80% as seen from the **Figure 8a**, and significant gross begins from 30 and 20 ns of the pump, respectively. On the **Figure 8b**, dependences of losses for optimal extraction of the 3-pass and 4-pass EDP amplifier are demonstrated with the crystal thickness of 4 cm.

For 3-pass, the delay between passes 1 and 2 is about 20 ns and 2 and 3–30 ns, whereas the scheme with delays between passes of the 4-pass amplifier (15, 20, 30 ns) is presented also in the **Figure 8**b. Taking in account the compressor transmission efficiency 70% [32], the compressed energy up to 400 J can be expected. Output peak power about 30 PW can be reached in one channel with pulse duration 10–15 fs. This amplifier could serve as a building block for ELI fourth pillar, and seven EDPCPA channels will be enough for approaching 200 PW.

As a final remark of this part, we can emphasize that there is a big gap between the reached now output energy of 200 J and potential possibilities of the EDP amplifiers of 600–800 J extracted energy with today's available Ti:Sa crystals, which should be filled in the closest future. Moreover, manufacturers are working now under the larger aperture Ti:Sa crystal and

**Figure 8.** Dependences of losses for 4 (blue-dashed curve) and 3 cm (pink-solid curve) thickness of the crystal: (a) conventional amplifier; (b) EDP-amplifier.

**Figure 9.** Final EDP-amplifiers with 3- and 4-passes: (a) EDP amplifier with a 19-cm-diameter pump area can approach 500-J energy with a 60-J input (100 J losses) during 3-pass; (b) 4-pass EDP amplifier with a 19-cm-diameter pump area can approach 600-J energy with a 60-J input, when pumped by 960 kJ (28 J losses).

have reached 30 cm crystal diameter. The estimations demonstrate the 40-cm crystals with 6-cm thickness which is nearly maximum for EDP amplification due to geometric reasons. This amplifier is able to supply ~3 kJ/140 PW with 250 J of seed energy while suffering TASE losses of about 207 J. Two EDPCPA channels will be enough for approaching 200 PW in this case.
