**3. High average power wavelength conversion of picosecond solid-state lasers**

The extreme ultraviolet lithography is now in an introductory phase in semiconductor industry. The EUVL has been developed in the field of various component technologies such as Mo/Si high reflectivity mirror at 13.5 nm wavelength, new types of resist of higher sensitivity at this wavelength, and plasma-based 100 W class stable EUV sources. Further increase in average power is expected for large-scale manufacturing to kW level and shorter wavelength to 6.7 nm where a higher reflectivity mirror seems available. The present source architecture is the laser-produced plasma (LPP) and is recently considered in its practical scaling limitation in average power in the range of kW. Free electron laser has been emerging as the new shortwavelength source in the EUV to X-ray region in the past decade. The present generation is based on lower repetition rate operation for scientific applications, but the next generation is aiming at high repetition rate for high average power. Several research papers are discussing on the possibility of high repetition rate FEL by superconducting RF cavity technology for the generation of more than kW average power at 13.5 nm wavelength [28, 29]. The present FEL is operated in the SASE mode, in which the pulses are generated in undulator and composed of many short-pulse length spikes. The typical pulse parameters are 0.1 mJ pulse energy, 100 fs pulse length, and the beam diameter is 1 mm. The beam fluence is higher than the ablation threshold of a resist [30], and the high spatial coherence results in much higher localized peak fluence on the resist. The interaction mechanism is now in a basic study to overcome these effects compared to the present LPP-generated 100 kHz, mJ EUV pulses with no coherence and longer pulse length as 10 ns.

The scaling of the FEL technology to kW average power level requires the photocathode operation in higher repetition rate in industrial environment together with optical technology to optimize the FEL beam for lithography application and scaling to the 6.7 nm wavelength region.

The first consideration is the industrial operation of photocathode at >MHz repetition rate. The bunch charge is typically 1 nC. Metal photocathode is robust, but the quantum efficiency (QE) is lower for higher charge generation. Several semiconductor cathodes were studied for higher efficiency to reduce the requirement for the driver laser average power in the repetition rate mode. The Advanced Photo-Injector (APEX) experiment in Lawrence Berkley National Laboratory is working to realize a high repetition rate at MHz, high-brightness photocathode. The photocathode is a normal conducting, 187 MHz RF cavity in the CW mode, and designed for short bunches as 1–10 ps of 750 keV energy up to 1 nC charges. Several semiconductor cathode materials are tested for better beam emittance for various operational conditions. CsK2Sb is irradiated by SHG of Yb fiber pulses, and Cs2Te is irradiated by 4HG. Both semi‐ conductor cathodes have nearly 1% quantum efficiency. The laser pulse energy is 0.5 μJ with the MHz repetition rate, and the average power is 0.5 W [31]. Cu and Mg photocathodes were studied for use in an RF photocathode. The gun was manufactured by a technique of hot isostatic pressing with diamond polishing and tested under a peak electric field of 57 MV/m. The quantum efficiency of the Cu cathode was 10−4, while Mg cathode achieved a high QE of up to 10−3 under 262 nm laser-light illumination. The QE of the Mg cathode under 349 nm laserlight illumination was measured to be 2.2 × 10−5. The experimental setup and the results of the photocathode QE measurement are shown in **Figure 9** [32].

**3. High average power wavelength conversion of picosecond solid-state**

The extreme ultraviolet lithography is now in an introductory phase in semiconductor industry. The EUVL has been developed in the field of various component technologies such as Mo/Si high reflectivity mirror at 13.5 nm wavelength, new types of resist of higher sensitivity at this wavelength, and plasma-based 100 W class stable EUV sources. Further increase in average power is expected for large-scale manufacturing to kW level and shorter wavelength to 6.7 nm where a higher reflectivity mirror seems available. The present source architecture is the laser-produced plasma (LPP) and is recently considered in its practical scaling limitation in average power in the range of kW. Free electron laser has been emerging as the new shortwavelength source in the EUV to X-ray region in the past decade. The present generation is based on lower repetition rate operation for scientific applications, but the next generation is aiming at high repetition rate for high average power. Several research papers are discussing on the possibility of high repetition rate FEL by superconducting RF cavity technology for the generation of more than kW average power at 13.5 nm wavelength [28, 29]. The present FEL is operated in the SASE mode, in which the pulses are generated in undulator and composed of many short-pulse length spikes. The typical pulse parameters are 0.1 mJ pulse energy, 100 fs pulse length, and the beam diameter is 1 mm. The beam fluence is higher than the ablation threshold of a resist [30], and the high spatial coherence results in much higher localized peak fluence on the resist. The interaction mechanism is now in a basic study to overcome these effects compared to the present LPP-generated 100 kHz, mJ EUV pulses with no coherence

The scaling of the FEL technology to kW average power level requires the photocathode operation in higher repetition rate in industrial environment together with optical technology to optimize the FEL beam for lithography application and scaling to the 6.7 nm wavelength

The first consideration is the industrial operation of photocathode at >MHz repetition rate. The bunch charge is typically 1 nC. Metal photocathode is robust, but the quantum efficiency (QE) is lower for higher charge generation. Several semiconductor cathodes were studied for higher efficiency to reduce the requirement for the driver laser average power in the repetition rate mode. The Advanced Photo-Injector (APEX) experiment in Lawrence Berkley National Laboratory is working to realize a high repetition rate at MHz, high-brightness photocathode. The photocathode is a normal conducting, 187 MHz RF cavity in the CW mode, and designed for short bunches as 1–10 ps of 750 keV energy up to 1 nC charges. Several semiconductor cathode materials are tested for better beam emittance for various operational conditions. CsK2Sb is irradiated by SHG of Yb fiber pulses, and Cs2Te is irradiated by 4HG. Both semi‐ conductor cathodes have nearly 1% quantum efficiency. The laser pulse energy is 0.5 μJ with the MHz repetition rate, and the average power is 0.5 W [31]. Cu and Mg photocathodes were studied for use in an RF photocathode. The gun was manufactured by a technique of hot isostatic pressing with diamond polishing and tested under a peak electric field of 57 MV/m. The quantum efficiency of the Cu cathode was 10−4, while Mg cathode achieved a high QE of

**lasers**

112 High Energy and Short Pulse Lasers

and longer pulse length as 10 ns.

region.

**Figure 9.** Left: Experimental setup of photocathode QE measurement. Right: Electron charge vs. input laser energy (266 nm) from Mg photocathode, • is for before laser cleaning.

It is concluded that 5 μJ, 266 nm, picosecond pulse is enough for Mg photocathode operation and the required average power at the MHz repetition rate is 5 W. Cu photocathode is proven to be robust material and usable by a 50 W 4HG picosecond laser. The progress of the laser technology is now making the metal photocathode again usable for the emerging requirement for long-life industrial application.

The other consideration is the reduction of the temporal microspikes in the SASE FEL pulses. Coherence is characterized in a report on the FLASH operation at 8.0 nm wavelength [33]. The single FEL femtosecond beam is passed through double pinholes for diffraction pattern, and the measured transverse coherence length is 6.2 ± 0.9 μm in the horizontal and 8.7 ± 1.0 μm in the vertical directions. The mutual coherence function K is given as 0.42, and a measurement of K by a laser plasma source is 3.2 × 10−9. It is concluded from these measurements that a beam spatial homogenization is required at EUV wavelength by using total reflection. Temporal coherence was also reported by using a split and delay unit. The coherence time of the pulses produced in the same operation conditions of FLASH was measured to be 1.75 fs. The measured coherence time has a value, which corresponds to about 65.5 ± 0.5 wave cycles (*cτ*/*λ*). It is well known that the SASE FEL pulses are composed of many small spikes and random spectrum due to SASE process. It is reported that the averaged spectrum has a 1.4% bandwidth typically, which is favorable for the Mo/Si EUV multilayer mirror at 13.5 nm (bandwidth 2%). It is necessary to smooth the temporal spikes to avoid random EUV flux change in the resist absorption process. The requirement is similar to most FEL applications, and we must consider efficient seed technology for MHz repetition rate operation.

It is desirable to increase the brightness and pointing/energy stability compared to SASE mode. An efficient seeding method was established by using a UV wavelength laser, in which the seed laser modulates the electron beam into coherent bunching at the harmonics of the seed laser wavelength. The bunching is intensified in another undulator for coherent FEL action, and the method is called as high-gain higher harmonic generation (HGHG). FERMI is the leading institute in this specific technology, and it is reported on the double-stage-seeded FEL with the fresh bunch injection technique [13]. The main limitation for the direct extension of the HGHG to shorter wavelength is the required small electron beam energy spread and higher average power seed laser source. The fresh bunch scheme is the solution for this problem, in which the FEL radiation is initially produced in an earlier stage undulator and used as the seeder for shorter wavelength generation (**Table 1**).


**Table 1.** Comparison of wavelengths for HGHG operation in FERMI FEL-2 and EUV FEL.

The external seed laser was the third harmonic of a Ti:Sapphire laser with a duration of ∼180 fs (FWHM) and up to 20 μJ energy per pulse. Its transverse size in the modulator was made larger than the electron beam size to ensure as uniform as possible electron beam energy modulation. Once the same laser energy is required for MHz EUV FEL, 20 W average power is required for 324 nm with 180 fs at MHz repetition rate. There are two approaches to generate such laser pulses, the first is based on the MHz repetition rate Ti:Sapphire laser with 100 μJ level pulses, and the second one is based on OPCPA.

The short-pulse, short-wavelength laser technology is now advancing to realize the specifica‐ tion described here in a compact box, due to the new suitable laser configuration as thin-disc laser and an efficient wavelength conversion method.

An ultrafast thin-disc multipass laser amplifier demonstrated the advantage recently by delivering 1.4 kW of average output power with 4.7 mJ pulse energy and duration of 8 ps at a repetition rate of 300 kHz [18]. The beam quality factor was better than M2 = 1.4. The experi‐ ments show that the thin-disc multipass amplifier can scale pulse energy and average output power independently for the investigated repetition rates between 300 and 800 kHz. Frequency doubling by means of an LBO crystal generated 820 W SHG average power at the wavelength of 515 nm with 1170 W of incident IR power, which corresponds to a conversion efficiency of 70% and an SHG pulse energy of 2.7 mJ. By sum-frequency generation between the beams at 1030 and 515 nm in a second LBO crystal, an average UV power of 234 W (780 μJ of pulse energy) was generated at the wavelength of 343 nm THG with a conversion efficiency of 32%.

A wavelength conversion experiment was performed in the HiLASE project to evaluate the high average power generation of picosecond harmonics, namely, SHG (515 nm) and FHG (257.5 nm), in LBO and BBO/CLBO crystals, respectively [34]. The pumping of the crystals was performed by the PERLA C Yb:YAG thin-disc laser operating at 100 kHz and 60 W average power with 4 ps pulse duration. The average output power of 6 W DUV was achieved in CLBO at a spectral bandwidth of 0.2 nm and the FHG/fundamental conversion efficiency was 10%. The basic optical configuration is shown in **Figure 10** together with a photo. The input beam (upper left) is reflected by two motorized mirrors controlled by a beam stabilizer ensuring pointing stability better than 20 μrad (RMS). The following half-wave plate and polarizer is used for energy tuning. The beam is frequency doubled in an LBO at 50°C and 10 mm long, cut for the critically phase-matched generation at *θ* = 90° and *ϕ* = 12.8°, and antireflection coated for 1030 and 515 nm. The second harmonic beam passes two dichroic mirrors and is injected into an argon-filled box with a BBO or CLBO crystal. To ensure a stable long-term functioning of the crystals the temperature was kept at 150°C. The experimental results are shown in **Figure 11**. It is visible that the 4HG/SHG conversion in the CLBO crystal has 30% higher efficiency than in the BBO crystal. The next step of the experiment is to increase the pumping power to 500 W to confirm the linearity of the conversion efficiency for 50 W FHG output power.

laser wavelength. The bunching is intensified in another undulator for coherent FEL action, and the method is called as high-gain higher harmonic generation (HGHG). FERMI is the leading institute in this specific technology, and it is reported on the double-stage-seeded FEL with the fresh bunch injection technique [13]. The main limitation for the direct extension of the HGHG to shorter wavelength is the required small electron beam energy spread and higher average power seed laser source. The fresh bunch scheme is the solution for this problem, in which the FEL radiation is initially produced in an earlier stage undulator and used as the

The external seed laser was the third harmonic of a Ti:Sapphire laser with a duration of ∼180 fs (FWHM) and up to 20 μJ energy per pulse. Its transverse size in the modulator was made larger than the electron beam size to ensure as uniform as possible electron beam energy modulation. Once the same laser energy is required for MHz EUV FEL, 20 W average power is required for 324 nm with 180 fs at MHz repetition rate. There are two approaches to generate such laser pulses, the first is based on the MHz repetition rate Ti:Sapphire laser with 100 μJ

The short-pulse, short-wavelength laser technology is now advancing to realize the specifica‐ tion described here in a compact box, due to the new suitable laser configuration as thin-disc

An ultrafast thin-disc multipass laser amplifier demonstrated the advantage recently by delivering 1.4 kW of average output power with 4.7 mJ pulse energy and duration of 8 ps at a repetition rate of 300 kHz [18]. The beam quality factor was better than M2 = 1.4. The experi‐ ments show that the thin-disc multipass amplifier can scale pulse energy and average output power independently for the investigated repetition rates between 300 and 800 kHz. Frequency doubling by means of an LBO crystal generated 820 W SHG average power at the wavelength of 515 nm with 1170 W of incident IR power, which corresponds to a conversion efficiency of 70% and an SHG pulse energy of 2.7 mJ. By sum-frequency generation between the beams at 1030 and 515 nm in a second LBO crystal, an average UV power of 234 W (780 μJ of pulse energy) was generated at the wavelength of 343 nm THG with a conversion efficiency of 32%.

A wavelength conversion experiment was performed in the HiLASE project to evaluate the high average power generation of picosecond harmonics, namely, SHG (515 nm) and FHG (257.5 nm), in LBO and BBO/CLBO crystals, respectively [34]. The pumping of the crystals was performed by the PERLA C Yb:YAG thin-disc laser operating at 100 kHz and 60 W average power with 4 ps pulse duration. The average output power of 6 W DUV was achieved in CLBO

**Fermi FEL-2 EUV FEL**

seeder for shorter wavelength generation (**Table 1**).

114 High Energy and Short Pulse Lasers

level pulses, and the second one is based on OPCPA.

laser and an efficient wavelength conversion method.

Seed wavelength (nm) 260 324 1nd FEL (nm) 32 40.5 2nd FEL (nm) 10.8 13.5

**Table 1.** Comparison of wavelengths for HGHG operation in FERMI FEL-2 and EUV FEL.

**Figure 10.** Optical configuration of the SHG and FHG, and SHG light is introduced into a box filled with argon.

**Figure 11.** Left: Fourth harmonic output power dependence on the second harmonic in BBO (AR coated) and CLBO (uncoated) crystals. Right: Relevant FHG spectra from CLBO.

A small part of the beam is absorbed in the crystal and converted into heat that leads to temperature gradients in the crystal in the high average power wavelength conversion. This causes partial phase mismatch and reduces the conversion efficiency. It is estimated that the fundamental power absorption at the 60 W input is <20 mW in the 10 mm long LBO crystal. The total absorbed power may be higher due to the fact that a green laser beam has higher absorption than the fundamental beam [35]. The absorption in the antireflective coating increases the temperature, which causes the mismatch more than the bulk absorption [36].

A tunable, 112 W optical parametric chirped-pulse amplifier (OPCPA) was demonstrated for FEL seeding in a burst mode with center frequencies ranging from 720 to 900 nm, pulse energies up to 1.12 mJ, and a pulse duration of 30 fs at a repetition rate of 100 kHz [14]. The results demonstrated the feasibility of 112 W femtosecond OPCPA in a burst mode with a duty cycle of 8 × 10−3, where no heating effects were observed. It was indicated from the measurements of absorption coefficients of BBO and LBO and calculations, the feasibility of much higher powers up to 1 kW in continuous mode was expected. Absorption causes a spatially and temporally varying temperature distribution in the sample. This leads to local changes of the refractive index and results in the development of a thermal lens. Especially in anisotropic crystals, this has consequences on increased phase mismatch in optical parametric processes with a conversion efficiency decrease. In the case of anisotropic crystal in electro-optical devices such as Pockels cells, the thermally induced depolarization reduces the contrast ratio. Though the absorption of the anisotropic crystal in these applications is usually very low, the related effects can be significant with input powers at the kilowatt level. In order to estimate the influence of thermal effects and taking it into account in the optical system design, the comprehensive knowledge of material absorption at the operation wavelength is unavoidable. An extended photothermal method was demonstrated for the quantitative determination of laser-induced wavefront deformations, which enables the separation of bulk and surface contributions to absorption in the more complex case of optically anisotropic crystalline media [36]. Experimental setup is shown in **Figure 12**. The wavefront deformations of the test beam (light source) are measured and used for absorption evaluations. The results show that the absorption is highest at the AR-coated KTP surface of input side (**Figure 13**, left), while it is higher at the surface of the output side of noncoated KTP (**Figure 13**, right). This photothermal method is usable in the real OPCPA for a better cooling system installation.

**Figure 12.** Setup of the photothermal method by crossed beam measurement. Wavefront measurement is performed by a Hartmann-Shack sensor.

High-Brightness Solid-State Lasers for Compact Short-Wavelength Sources http://dx.doi.org/10.5772/64147 117

**Figure 13.** Wavefront deformation measurement results for AR-coated (left) and noncoated KTP samples. Blue indi‐ cates the largest wavefront deformation. The heating laser beam comes into the crystal horizontally from the left, while the probe beam passes vertically to the readers.

#### **4. Cryogenic laser technology for high pulse energy picosecond amplifier**

The basic principle of the laser Compton short-wavelength source is similar to an undulator emission, and high-intensity laser field is used as the modulating electromagnetic field. Basic principle of the laser Compton X-ray source is well studied, and a single-shot imaging is critical for many practical applications. The required specification is explained as the laser pulse must exceed some threshold parameters. It is known that the highest peak brightness is obtained in the case of counterpropagating laser pulse and electron beam bunch, in the minimum focusing area before nonlinear threshold. **Figure 14** describes the schematic of the laser Compton interaction between the electron beam and the laser.

**Figure 14.** Schematic of the laser Compton scattering process.

A small part of the beam is absorbed in the crystal and converted into heat that leads to temperature gradients in the crystal in the high average power wavelength conversion. This causes partial phase mismatch and reduces the conversion efficiency. It is estimated that the fundamental power absorption at the 60 W input is <20 mW in the 10 mm long LBO crystal. The total absorbed power may be higher due to the fact that a green laser beam has higher absorption than the fundamental beam [35]. The absorption in the antireflective coating increases the temperature, which causes the mismatch more than the bulk absorption [36].

A tunable, 112 W optical parametric chirped-pulse amplifier (OPCPA) was demonstrated for FEL seeding in a burst mode with center frequencies ranging from 720 to 900 nm, pulse energies up to 1.12 mJ, and a pulse duration of 30 fs at a repetition rate of 100 kHz [14]. The results demonstrated the feasibility of 112 W femtosecond OPCPA in a burst mode with a duty cycle of 8 × 10−3, where no heating effects were observed. It was indicated from the measurements of absorption coefficients of BBO and LBO and calculations, the feasibility of much higher powers up to 1 kW in continuous mode was expected. Absorption causes a spatially and temporally varying temperature distribution in the sample. This leads to local changes of the refractive index and results in the development of a thermal lens. Especially in anisotropic crystals, this has consequences on increased phase mismatch in optical parametric processes with a conversion efficiency decrease. In the case of anisotropic crystal in electro-optical devices such as Pockels cells, the thermally induced depolarization reduces the contrast ratio. Though the absorption of the anisotropic crystal in these applications is usually very low, the related effects can be significant with input powers at the kilowatt level. In order to estimate the influence of thermal effects and taking it into account in the optical system design, the comprehensive knowledge of material absorption at the operation wavelength is unavoidable. An extended photothermal method was demonstrated for the quantitative determination of laser-induced wavefront deformations, which enables the separation of bulk and surface contributions to absorption in the more complex case of optically anisotropic crystalline media [36]. Experimental setup is shown in **Figure 12**. The wavefront deformations of the test beam (light source) are measured and used for absorption evaluations. The results show that the absorption is highest at the AR-coated KTP surface of input side (**Figure 13**, left), while it is higher at the surface of the output side of noncoated KTP (**Figure 13**, right). This photothermal

method is usable in the real OPCPA for a better cooling system installation.

by a Hartmann-Shack sensor.

116 High Energy and Short Pulse Lasers

**Figure 12.** Setup of the photothermal method by crossed beam measurement. Wavefront measurement is performed

The general formula of obtainable X-ray photon flux *N*<sup>0</sup> is calculated in the counter collision by the following expression:

$$\mathrm{N}\_{0} \propto (\sigma\_{\mathrm{c}} \,\mathrm{Ne} \,\mathrm{Np}) / (4\pi \mathrm{r}^{2})$$

where *σ*<sup>c</sup> is the Compton cross section (6.7 × 10−25 cm<sup>2</sup> ), Ne is the total electron number, Np is the total laser photon number, and *r* is the interaction area radius. It is predicted that an increase in Ne and Np, and the reduction in *r* results in the increase in the photon flux *N*0. The practical limitation of these operations are the instrumental condition of electron beam emittance in higher charge, M2 of laser beam at higher pulse energy, and optimization for reduced focusing diameter *r*. It is possible to assume these parameters as 1 nC charge with 3 ps pulse duration to be focused down to 10 μm at 38 MeV voltage. Another limitation is the maximum of singlepulse laser intensity to reach the nonlinear threshold of the higher harmonics generation in the X ray region. The nonlinear Compton threshold is characterized by the laser field strength

#### a0 eE/m LC = w

where parameters *E*, *ω*L, and *C* correspond to the amplitude of the laser electric field, laser frequency, and the speed of light, respectively. The laserfield strength is a function of the laser wavelength. The nonlinear threshold *a*<sup>0</sup> is given around 0.6 which corresponds to 1 J pulse energy in 1 ps pulse duration at 10 μm focusing intensity in the solid-state laser wavelength. The threshold laser energy for a single-shot imaging is similarto this critical laser pulse energy in the expected tight focus condition. The laser technology was not matured to realize such parameters simultaneously in the past, and usual approach was to increase the repetition rate of the event to increase the effective obtainable X-ray photon average flux in the affordable imaging time period such as <millisecond for bioimaging. The first approach is the pulsed laser storage in an optical enhancement cavity for laser Compton X-ray sources [37]. It is descri‐ bed in the experimental report that "the enhancement factor *P* inside the optical cavity was 600 (circulating laser power was 42 kW), in which the Finess was more than 2000, and the laser beam waist of 30 μm (2σ) was stably achieved using a 1 μm wavelength Nd:Vanadium modelocked laser with repetition rate 357 MHz, pulse width 7 ps, and average power 7 W." The second approach is the multipass optical cavity, in which the laser Compton generation focus exists inside the multipass cavity. The minimum focusing diameter is limited due to the requirement of the cavity design. SHG picosecond pulse of 0.2 J pulse energy is circulated 32 times to collide electron bunches [38].

An approach is undertaken by the thin-disc laser technology to generate 1 J, picosecond high beam quality pulses at 100 Hz repetition rate in the Max Born Institute, Berlin, Germany. The development is based on a ring cavity concept combined with chirped pulse amplification (CPA) [39]. The regenerative amplifier produced more than 300 mJ energy when pumped with the maximum available pump power of 1.7 kW. The regenerative amplifier is followed by a large aperture ring amplifier that increases the pulse energy further to 600 mJ. This ring

amplifier consists of a Pockels cell and a set of polarizers for the in- and out-coupling, two amplifier heads and a spatial filter in between. The amplifier heads are equipped with 750 μm thick Yb:YAG (7%) discs of 25 mm diameter. Each disc is pumped by 1 ms long pulses of 4 × 1.5 kW. Booster amplifierfor 1 J pulse is based on the large aperture ring amplifier design withoutinternal Pockels cell. The amplifier discs were pumped by diode modules that deliver 6 kW peak power out of a 2 mm fiber. Each amplifier is equipped with two of these pump modules, which together provide about twice the pump power compared to the large aperture ring amplifier. The booster amplifieris changed from former multipass configuration to a large aperture ring amplifier. The result is a multiple amplifier stage configuration with many thindisc laser modules.

The general formula of obtainable X-ray photon flux *N*<sup>0</sup> is calculated in the counter collision

<sup>2</sup> N ( Ne Np) / (4 r ) <sup>0</sup> ¥

the total laser photon number, and *r* is the interaction area radius. It is predicted that an increase in Ne and Np, and the reduction in *r* results in the increase in the photon flux *N*0. The practical limitation of these operations are the instrumental condition of electron beam emittance in higher charge, M2 of laser beam at higher pulse energy, and optimization for reduced focusing diameter *r*. It is possible to assume these parameters as 1 nC charge with 3 ps pulse duration to be focused down to 10 μm at 38 MeV voltage. Another limitation is the maximum of singlepulse laser intensity to reach the nonlinear threshold of the higher harmonics generation in the X ray region. The nonlinear Compton threshold is characterized by the laser field strength

> a0 eE/m LC = w

where parameters *E*, *ω*L, and *C* correspond to the amplitude of the laser electric field, laser frequency, and the speed of light, respectively. The laserfield strength is a function of the laser wavelength. The nonlinear threshold *a*<sup>0</sup> is given around 0.6 which corresponds to 1 J pulse energy in 1 ps pulse duration at 10 μm focusing intensity in the solid-state laser wavelength. The threshold laser energy for a single-shot imaging is similarto this critical laser pulse energy in the expected tight focus condition. The laser technology was not matured to realize such parameters simultaneously in the past, and usual approach was to increase the repetition rate of the event to increase the effective obtainable X-ray photon average flux in the affordable imaging time period such as <millisecond for bioimaging. The first approach is the pulsed laser storage in an optical enhancement cavity for laser Compton X-ray sources [37]. It is descri‐ bed in the experimental report that "the enhancement factor *P* inside the optical cavity was 600 (circulating laser power was 42 kW), in which the Finess was more than 2000, and the laser beam waist of 30 μm (2σ) was stably achieved using a 1 μm wavelength Nd:Vanadium modelocked laser with repetition rate 357 MHz, pulse width 7 ps, and average power 7 W." The second approach is the multipass optical cavity, in which the laser Compton generation focus exists inside the multipass cavity. The minimum focusing diameter is limited due to the requirement of the cavity design. SHG picosecond pulse of 0.2 J pulse energy is circulated 32

An approach is undertaken by the thin-disc laser technology to generate 1 J, picosecond high beam quality pulses at 100 Hz repetition rate in the Max Born Institute, Berlin, Germany. The development is based on a ring cavity concept combined with chirped pulse amplification (CPA) [39]. The regenerative amplifier produced more than 300 mJ energy when pumped with the maximum available pump power of 1.7 kW. The regenerative amplifier is followed by a large aperture ring amplifier that increases the pulse energy further to 600 mJ. This ring

*c*

 p

), Ne is the total electron number, Np is

s

by the following expression:

118 High Energy and Short Pulse Lasers

where *σ*<sup>c</sup> is the Compton cross section (6.7 × 10−25 cm<sup>2</sup>

times to collide electron bunches [38].

Cryogenic laser technology is suitable for the generation of large-pulse energy in a laser configuration of lower stages. A cryogenic thick-disc Yb:YAG laser was reported as 1 J was generated at 100 Hz repetition rate [3]. The picosecond CPA laser was developed for driving high average power soft X-ray lasers. This is one of the greatest breakthroughs in the history of high-energy solid-state laser, and it is described in the report on the configuration and operation as "Seed pulses of 100 mJ energy were produced by the laser frontend and ampli‐ fied to 1.5 Joules pulse energy by the five-pass power amplifier which consists of two Yb:YAG disks mounted in vacuum on a single cryo-cooling head. The Yb:YAG disks are bonded on all lateral sides with a Cr:YAG cladding to eliminate feedback of spontaneous emission into the active region to prevent amplified spontaneous emission (ASE) losses and transverse parasit‐ ic lasing. Cryogenic cooling of Yb:YAG to liquid nitrogen temperature increases the heat conductivity and reduces the saturation fluence, allowing for efficient high energy pulse generation at high repetition rates. High capacity cooling was accomplished by flowing cryogenic liquid coolant through the laser head. Each disk was pumped with 1.5 ms dura‐ tion, 4 kW pulses from a *λ* = 940 nm laser diode array. At the maximum pump power, 1.5 J laser pulses were obtained. These pulses were compressed by a dielectric grating pair producing 1 J, 5 ps FWHM duration pulses at 100 Hz repetition rate." The repetition rate is recently increased to 500 Hz and the picosecond pulse energy is 1 J, and the resulting aver‐ age power is 500 W. Temporally pulse-shaped laser pulses were focused into a ∼5 mm long, 30 μm FWHM wide line on a solid target using cylindrical optics. The beam quality is indicated by the focusing specification. The resulting plasma was in the Ni-like stage, and strong collisional excitation leads to a large transient population inversion on the 4d1S0 → 4p1P1 transition of Ni-like ions at wavelengths ranging from 10.9 to 18.9 nm.

Cryogenic solid-state laser is preferred for power scalability with better beam quality, especially in higher pulse energy mode, and improvement of efficiency at the cost of longer pulse length [40]. Yb:YAG is the most tested material due to its low quantum defect and still broadband absorption in low temperatures. Various thermal optical properties are reported for base materials as YAG (ceramic and single crystal), GGG, GdVO4, and Y2O3 on the thermal conductivity, thermal expansion, refractive index, absorption cross section, emission cross section, and fluorescence lifetime in the cryogenic condition.

One of the key features of the cryogenic laser is its better beam quality. A quantitative evaluation is important for a practical laser design for dedicated applications and a measure‐

ment was performed on the wavefront distortion caused by the thermal origin in a cryogen‐ ic Yb:YAG crystal in the temperature range 250–130 K in nonlasing condition [41]. The wavefront aberration was evaluated by a wavefront sensor. The measurement results showed a significant reduction of the wavefront aberration in lower temperature. The thermal defocus was concluded as originated to the thermal lensing effect together with electronically induced change of the refractive index by the excitation of ion activators (electronic lensing). The dominant reason of the aberration was found as the thermal lensing in the experimental condition as 6.3 kW/cm2 pumping intensity and pumping repetition rate of 100 Hz. The Strehl ratio was observed to be improved in the lower temperature even the absorbed energy was increased. The experiment showed the advantage of the cryogenic technology in terms of efficiency and beam quality.

**Figure 15.** LEFT: Experimental configuration of the aberration measurement. FLD1, fiber-coupled pump diode at 936.6 nm; FLD2, fiber-coupled probe beam laser diode at 1065 nm; GT, Galilean telescope; W, windows; M, turning mirrors; DM, dichroic mirrors; A1, 2, achromatic doublets with focal lengths of 100 and 250 mm, respectively, L1, 2, lenses with a focal length of 250 mm; ND, neutral density filters; LPF, longpass filter with cutoff wavelength at 1050 nm. Right: Multipass amplification configuration. WS, wavefront sensor; PM, power meter.

The experimental setup used for the measurement of the wavefront aberrations in a cryogen‐ ically cooled Yb:YAG slab is shown in **Figure 15** (left). The right side figure shows the configuration of multipass amplification from the 100 mJ level input. A Yb:YAG crystal is mounted in a copper holderin a closed-loop pulse tube cryostat (Q Drive). The cooling capacity is 12 W at 100 K. The crystal was supplied from Crytur, Czech Republic, and the specifica‐ tion was thickness 2 mm, diameter 10 mm, and doping concentration 3 at%. A fiber-coupled laser diode (DILAS) pumped the crystal from one side. The peak wavelength was 936.9 nm, and the peak intensity was 6.3 kW/cm2 . Two achromatic doublet lens of focal length 100 and 250 mm imaged the 1 mm core of the fiber with NA 0.22 to the Yb:YAG surface. The result‐ ing pump spot size was 2.5 mm (1/e2) in super-Gaussian intensity distribution. **Table 2(a)** summarizes the absorbed energy per pump pulse at each temperature. The absorbed energy increases by about 19 % if the temperature decreases by 120 K from initial 250 K. The absor‐ bed power and thus generated heat is higher with decreasing temperature, and the aberra‐ tions are lower because of higher thermal conductivity, lower d*n*/d*T*, and lower expansion coefficient. Theoretical thermal decay time constants were calculated according to the formula *t*T = *r*<sup>p</sup> 2 /4*κ*, where *r*p is the radius of the pump, and *κ* is the thermal diffusion coefficient, which is defined as *k*/(*ρ*cp) where *k* is the thermal conductivity, *ρ* is the mass density, and cp is the specific heat. The estimated values are shown in **Table 2(b)** for the thermal relaxation time constants for different temperature conditions in 3 at% doped Yb:YAG as an estimation from data for 2 and 4 at% doped crystals. The thermal decay time is around 31 ms at 150 K, which is three times longer than the time interval between pumping at 100 Hz. This value is 93 ms at 250 K.

ment was performed on the wavefront distortion caused by the thermal origin in a cryogen‐ ic Yb:YAG crystal in the temperature range 250–130 K in nonlasing condition [41]. The wavefront aberration was evaluated by a wavefront sensor. The measurement results showed a significant reduction of the wavefront aberration in lower temperature. The thermal defocus was concluded as originated to the thermal lensing effect together with electronically induced change of the refractive index by the excitation of ion activators (electronic lensing). The dominant reason of the aberration was found as the thermal lensing in the experimental condition as 6.3 kW/cm2 pumping intensity and pumping repetition rate of 100 Hz. The Strehl ratio was observed to be improved in the lower temperature even the absorbed energy was increased. The experiment showed the advantage of the cryogenic technology in terms of

**Figure 15.** LEFT: Experimental configuration of the aberration measurement. FLD1, fiber-coupled pump diode at 936.6 nm; FLD2, fiber-coupled probe beam laser diode at 1065 nm; GT, Galilean telescope; W, windows; M, turning mirrors; DM, dichroic mirrors; A1, 2, achromatic doublets with focal lengths of 100 and 250 mm, respectively, L1, 2, lenses with a focal length of 250 mm; ND, neutral density filters; LPF, longpass filter with cutoff wavelength at 1050 nm. Right:

The experimental setup used for the measurement of the wavefront aberrations in a cryogen‐ ically cooled Yb:YAG slab is shown in **Figure 15** (left). The right side figure shows the configuration of multipass amplification from the 100 mJ level input. A Yb:YAG crystal is mounted in a copper holderin a closed-loop pulse tube cryostat (Q Drive). The cooling capacity is 12 W at 100 K. The crystal was supplied from Crytur, Czech Republic, and the specifica‐ tion was thickness 2 mm, diameter 10 mm, and doping concentration 3 at%. A fiber-coupled laser diode (DILAS) pumped the crystal from one side. The peak wavelength was 936.9 nm,

250 mm imaged the 1 mm core of the fiber with NA 0.22 to the Yb:YAG surface. The result‐ ing pump spot size was 2.5 mm (1/e2) in super-Gaussian intensity distribution. **Table 2(a)** summarizes the absorbed energy per pump pulse at each temperature. The absorbed energy increases by about 19 % if the temperature decreases by 120 K from initial 250 K. The absor‐ bed power and thus generated heat is higher with decreasing temperature, and the aberra‐ tions are lower because of higher thermal conductivity, lower d*n*/d*T*, and lower expansion

. Two achromatic doublet lens of focal length 100 and

Multipass amplification configuration. WS, wavefront sensor; PM, power meter.

and the peak intensity was 6.3 kW/cm2

efficiency and beam quality.

120 High Energy and Short Pulse Lasers



**Table 2.** (a) Absorbed energy per pump pulse by the 2 mm thick, 3 at% doped Yb:YAG slab pumped by energy of 310 mJ at a wavelength of 936.6 nm for different temperatures of the cooling finger. (b) Calculated thermal decay time for 3 at% Yb:YAG crystal.

Cryogenic cooling is usually applied in booster amplifiers with more than one pass of the seed beam through the active medium in order to efficiently extract the stored energy. Therefore, it is assumed to evaluate four beam passes, and the measured wavefront with subtracted tilt and defocus was four times multiplied to calculate the real Strehl ratio in multipass amplifi‐ cation. The calculated Strehl ratio was 0.96 at 130 K and decreased to 0.93 at 250 K as shown in **Figure 16**. The practical Strehl ratio to obtain the same pulse energy decreases at higher temperature to obtain the same pulse energy in lower gain. The measurement indicates the linearity of the Strehl ratio to the temperature decrease, and it is expected further increase in the beam quality is possible in lower temperature of about less than 130 K.

In the last part of this chapter, a large aperture cryogenic laser is evaluated. The perform‐ ance of a gas-cooled multislab laser is recently reported from the DiPOLE project within the Central Laser Facility (CLF RAL STFC), UK. The development is aiming at an efficient high pulse energy diode-pumped solid-state laser (DPSSL) architecture based on cryogenic gascooled, multislab ceramic Yb:YAG amplifier technology. A prototype amplifier is delivering up to 10.8 J pulse energy at 1030 nm wavelength with 10 Hz repetition rate. The optical-optical conversion efficiency is 22.5% [42]. The long-term energy stability was observed as 0.85% RMS with 7 J pulse energy for 48 h operation (2 million shots). An extension of the cryogenic technology is now under test in the DiPOLE 100 to confirm the cryogenic concept at 100 J, 10 Hz region (kW average power). The present laser system is built for the HiLASE project and will deliver 100 J temporally shaped ns pulses at 10 Hz with a fully integrated control system. A second system is also under development for the high-energy density (HED) beamline of the European XFEL project.

**Figure 16.** Strehl ratio for the four passes of the probe beam through the Yb:YAG slab and absorbed pump power per single pass as a function of temperature. Lines represent a linear fit with slopes of –6 × 10−4/K and −0.064%/K, respec‐ tively.

The 10 J amplifier architecture is based on the multislab approach. The gain medium is composed of four circular Yb:YAG slabs with two different Yb doping levels as 1.1 and 2.0 at % to confirm a uniform temperature distribution among each slab. The diameter of the circular slab is 45 mm with a 5 mm thickness, and the pump area is square of 23 × 23 mm2 . The pump beam is supplied from 939 nm diodes in stack with a pumping time duration of 700 μs at 10 Hz. The Yb:YAG circular slab is cladded with a 5 mm wide Cr:YAG absorber with 6 cm−1 absorption coefficient. This is effective to prevent amplified spontaneous emission (ASE) and parasitic oscillations. A cryogenic He flow cools the slab and keeps the temperature as 150– 170 K. The pressure of the He flow is 10 bar. **Figure 17** shows the optical arrangement for amplification. A seed beam is injected into the amplifier through a dichroic mirror and then image relayed by a spatial filter (*f* = 1 m) to a back reflector and reflected back to the amplifi‐ er module. One spatial filter locates on each side of the amplifier head. Each pass is com‐ posed by a set of separate mirrors. A deformable mirror is placed in the amplifier after the third pass for the aberration compensation. After seven passes, the beam is extracted from the amplifier with pulse energy increased to 9 J with a size of 21 mm × 21 mm2 .

Numerical modeling of the multislab amplifier is conducted in the HiLASE project to ensure the scaling of the cryogenic technology forfurtherincreased parameterregion in pulse energy, repetition rate, and better beam quality. Comsol Multiphysics software was chosen to model the thermal and stress effects in the amplifiers [43]. The sources of heat were calculated in the ASE code [44]. The axial surfaces of the slabs are assumed to be cooled only by flowing helium gas at 160 K. The slab was assumed to have no thermal contact with its 2 cm thick Invar holder; and all heat is removed by convection through the faces. From the temperature and stress maps of the slab, the optical path difference (OPD) and birefringence depolarization losses were calculated for a single slab according to a prior approach. The gradual decrease of cooling efficiency in the direction of gas flow, caused by He heating, results in the loss of left-right symmetry of the temperature, stress, depolarization, and OPD maps.

**Figure 17.** Schematic of the 10 J cryogenic multislab amplifier. It consists of Yb:YAG ceramic slabs in the laser head, dichroic beam splitters (DBSs), lens arrays (LAs), vacuum spatial filters (VSFs), and homogenized pump diode laser modules (PDs).

It is planned to increase the repetition rate of the 10 J amplifier to 100 Hz by keeping the basic performance. Once the operation is as expected, the cryogenic laser offers a technological stage for a single module to generate picosecond multipulses of a few joules of energies, for a singleshot imaging Compton source.
