Using a high-pressure carbon-dioxide laser amplifier enriched with the oxygen-18 isotope, we produced a 5-ps, 10-µm pulse of the 1 TW peak power without splitting, which otherwise occurs due to spectral modulation by the rotation structure of the CO2 amplification band.
©2011 Optical Society of America
Ultra-fast lasers based on chirped-pulse amplification (CPA) in solid active medium (doped glasses or Ti:Sapphire crystals) can generate few-cycle pulses in excess of 100 TW (1014 W) peak power. The introduction of this research tool opened up new opportunities to study extreme conditions of the laser-matter interaction. Focused to diffraction limits, such lasers generate electromagnetic fields up to 1010 V/m that accelerate electrons to relativistic velocities within a portion of the oscillation cycle. Physics experiments exploring such relativistically strong laser/matter interactions have pushed the frontiers of relativistic plasma physics, nuclear physics, and studies of the fundamental properties of matter in extreme and strongly non-equilibrium states.
All high-intensity CPA laser systems operate at the radiation wavelength close to 1 µm lying in the near-IR spectral region. Meantime, in relativistic laser-matter interactions, the maximum laser energy transferred to a charged particle is determined by the ponderomotive-coupling efficiency, scaling as Iλ 2 with the laser intensity, I, and wavelength, λ. This relationship implies certain advantages of longer wavelengths, such as generating high-energy particles at the reduced intensity or the increase in process-throughput at the same peak power . Slower field oscillation also converts into a higher number of photons per Joule of the laser energy, which can be advantageous for radiation sources based on inverse Compton (Thomson) scattering [2, 3].
Accordingly, the search for practical solutions for generating high-power ultra-short pulses of long-wavelength radiation has become one of the essential problems in extreme-light science. The ability of CO2 lasers to produce high-power radiation in the mid-IR (10 µm) spectral region secures them a niche in photonics science vacated by the otherwise more powerful solid-state CPA lasers.
Achieving ultra-high peak power at and beyond Terawatt level requires concentrating a considerable amount of laser energy (e.g., several Joules) in a short time-domain (e.g., pico- or femto-seconds). Seamless amplification of a laser pulse requires a smooth spectral gain with a bandwidth broader than a Fourier-transform-limited spectrum of the amplified pulse. For molecular-gas lasers, the spectral modulation imposed by periodic rotational lines in the gain spectrum hinders this process. Such regular modulation, applied during amplification to the laser pulse’ spectral envelope, is converted (by inverse Fourier transform) into a train of pulses spaced in time by the inverse interval in the rotational spectrum , where c is measured in cm/s, and in cm−1.
For a 10-µm CO2 laser, the rotational-structure period varies between 1.3 and 1.8 cm−1 for different radiation transitions. The spectrum of a few-picosecond pulse of a CO2 laser can overlap several rotational lines and thus, upon amplification, acquires the corresponding periodic structure. This spectral modulation, inverse-Fourier transformed into the time domain, explains the temporal split of a single pulse in a train of picosecond pulses at the 25 ps period (for the R-branch of a vibrational transition) or the 18 ps period (for the P-branch). This undesirable effect reduces the laser’s achievable peak power.
We can mitigate the problem of splitting the CO2 laser’s pulse by the well-known technique of pressure broadening of individual rotational lines with their merging into a super-continuum. However, this methodology requires raising the gas pressure in the laser amplifier well above 10 bar , which is close to the practical limit for today’s gas-discharge laser technology.
As reported recently , gain saturation in a laser amplifier, combined with Stark broadening in a strong laser field, reduces pulse splitting. However, this highly nonlinear effect might induce timing variations within the laser beams’ cross-section.
An alternative approach to attaining a homogenous molecular spectrum with better overlapping rotational lines rests on the mass difference of various isotopes that cause a slight shift in rotational frequency. A 50% substitution of 16O with 18O entails a fourfold denser concentration of rotational lines in the gain spectrum that was employed previously for facilitating continuous frequency tuning in CO2 lasers [6, 7]. Although well recognized as a possibility for improving bandwidth-limited short-pulse amplification, this approach never was realized practically for this purpose until now in our experiment here, wherein we demonstrated producing a 5-ps, 10-µm pulse at the 1 TW peak power with virtually no temporal splitting using a high-pressure CO2 laser enriched with the isotope 18O.
2. Theoretical considerations
2.1 Approaches to spectrum “smoothing”
The modulation of the gain spectrum can be smeared either by broadening individual rotational lines, thus assuring their better overlap, or by increasing their density. In the first case, we can use collision- (pressure-) and/or field- (power-) broadening effects. Several approaches will increase line density: 1) Using an R-branch of a laser transition having a 1.4 times denser line structure compared to a conventional P-branch. 2) Isotopic enrichment of the CO2 molecules, wherein the superposition of the slightly shifted spectra of different isotopic species (isotopologues) generates a denser effective spectrum. 3) Combining sequential bands of laser transition with regular ones. Below, we briefly overview these approaches.
Pressure broadening. The linewidth (HWHM) of a collisionally broadened line in a mixture of CO2, N2 and He gases is given by
Power broadening. We can approximate the magnitude of line broadening appearing in the intense laser field due to the Autler-Townes effect (or dynamic Stark effect)  by the Rabi frequency:
Using the last formula, and the known value of a laser transition dipole momentum d=0.0275D (the value for the 10P(20) line from HITRAN-2008 database ), we find that the Stark broadening becomes 1.8 cm−1 at a laser intensity ~20 GW/cm2.
Practical realization of this approach was reported by D. Haberberger, S. Tochitsky, and C. Joshi of the UCLA Neptune Laboratory .
R-branch. The R-branches of the CO2 laser transitions have a 1.4 times denser rotational structure than the more often used P-branches ; they offer better overlap between collisionally broadened lines, and, hence, a smoother gain spectrum (Fig. 1 , top). Interestingly, at high-pressure conditions the overlap between rotational lines increases the peak intensity of the R-branch compared to that of the P-branch, which otherwise prevails in conventional atmospheric- and lower-pressure lasers.
Isotopic CO2. By partially substituting the 16O atoms in CO2 gas with another stable 18O isotope, we obtain almost perfectly smooth combined spectrum after superimposing the spectra of three CO2 isotopologues: 16O-12C-16O, 16O-12C-18O and 18O-12C-18O (Fig. 1). These three isotopologues often are denoted as 626, 628 and 828 where 2, 6 and 8 respectively represent 12C, 16O and 18O.
For an equal proportion [16O]:[18O]=1:1, independently of the initial distribution of 16O and 18O between the CO2 molecules, statistical equilibration via intermolecular isotope exchange leads to ::=1:2:1. Note that due to the broken symmetry of the 628 molecule, it has twice as many rotational lines in each vibrational branch, compared to more symmetric 626 and 828 isotopologues. The combination of three CO2 isotopologues, depicted in Fig. 1, results in a smooth spectrum already at 10 bar. The gain of the isotopic mixture at this pressure is 1.4 times lower compared to the regular gas, which is mainly due to the relatively low gain of the 828 CO2 isotopologue. Thus, a longer path through an active medium or a higher CO2 concentration is needed in order to maintain the same net amplification. We used the isotope-based approach in the research discussed here.
Sequence bands. Transitions between high-laying vibrational overtones of the CO2 molecule can contribute considerably to the high-pressure amplifier gain [12, 13]. In this case, the rotational spectra of the fundamental- and sequence-bands overlap providing a denser effective spectrum. Exploiting sequence band for gain spectrum smoothing seems especially promising in the case of the 10R branch where rotational lines belonging to the sequence band 00°2-[1001,02°1]I fall very close to the centers of the gaps between the lines of the regular band 00°1-[1000,02°0]I. Simple calculations using the formula for the ratio of gains of the sequence and the regular band 
Further study is required for estimating the effects of the sequence bands on the picosecond pulse amplification and optimization of amplifier parameters for increasing their contribution into the total gain of a laser amplifier. We consider detailed investigation of this topic for the future research while concentrating our current efforts on investigating the possibilities of the isotopic mixtures.
2.2 Simulations of picosecond pulse amplification
Our approach to finding a practical solution to the pulse-splitting problem in the CO2 laser medium is based on a detailed study of the processes involved in amplifying short pulses. Our use of in-house developed computer code is a part of this study. At the core of the code is the numerical solution of the equations describing the interaction of a short resonant pulse with the gaseous medium of a CO2 amplifier :10] and the 828 constants estimated based on the absorption measurements reported by C. Freed . The code also includes the pumping/relaxation dynamics of the laser’s levels, and the Fourier-integral-based calculations of the pulses' propagation through an arbitrary optical configuration, including multiple passes through the active medium. Sequence bands, however, are not included in the model.
As described in the following experimental part of the paper, we used a two-stage amplification scheme in our laser system. Most of the power gain (about five orders-of- magnitude) is reached over multiple passes in a small-aperture (10 mm) regenerative amplifier. This high amplification rate and relatively low pulse intensity at this stage, insufficient for appearance of the power-broadening effect, explain the major contribution of this amplification stage to the pulse splitting. Thus, the main objective of this study was resolving the pulse-splitting problem at the first amplification stage.
Figure 2 plots the findings from the simulation for a 5-ps pulse amplification in a 10-bar regenerative amplifier with a regular gas mixture and isotope-enriched one. The 106× amplification rate includes 105× net amplification (from 0.1 µJ to 10 mJ), and additional factor of ~10 required for the compensation of optical losses in the amplifier over multiple passes. Undoubtedly, there is an obvious advantage in switching from the P-branch to the R-branch; the number of secondary parasitic pulses falls, and the peak power rises. However, pulse splitting is suppressed completely only in the isotopic mixture where we replaced 50% of the natural 16O oxygen in carbon dioxide with its 18O isotope. Following these results, we tuned the output of our CO2 oscillator to the R-branch and used an isotopic mixture during the initial amplification stage.
The CO2 laser system depicted in Fig. 3 consists of a picosecond pulse generator that produces a linear-polarized 0.1-μJ, 5-ps pulse, and two high-pressure amplifiers that ultimately boost the laser pulses’ energy to the ~5 J level. A 5-ps pulse is sliced by the sequence of optical switchers off the multi-nanosecond, 20 mJ output of a hybrid TEA CO2 laser (WH20, SDI Ltd., Pretoria, RSA) tuned to 10R(14) line (10.2 μm). A 10-ns pulse is cut off the initial 200-ns pulse with a Pockels cell, and then passes a 3-bar UV-preionized electric discharge pre-amplifier. A germanium Brewster plate, used as a semiconductor optical switch , is irradiated by a 14-ps YAG laser pulse that causes the semiconductor slab to function as an electron-hole plasma “mirror”. The ~200 ps duration of a CO2 pulse reflected from this transient “mirror” is defined by recombination and diffusion of the electron-hole plasma. Finally, the 200-ps, 10.2-μm pulse is sent through a Kerr cell  controlled by a co-propagating, 5-ps, frequency-doubled, YAG laser pulse. A polarization filter placed after the Kerr cell selects a 0.1-μJ, 5-ps, 10.2-μm seed pulse that we amplified to 10 mJ in multiple round-trip passes through a regenerative amplifier (HP-5, SDI Ltd., Pretoria, RSA). The amplifier was initially filled with equal amounts of natural and isotopically enriched (95% 18O) CO2 obtained from Cambridge Isotope Laboratories, Inc. We observed complete statistical equilibration (::≈1:2:1) after circulating the laser gases overnight through a catalytic converter (NASA). The isotopic composition was monitored with a gas analyzer (MKS 600A). The amplifier was energized with UV-pre-ionized transverse electric discharge. Lower gain of the isotopic mixture compared to the regular one is compensated by increasing the number of the amplifier passes.
Further amplification to 5 J is attained in 6 passes through a large-aperture (10 cm), x-ray pre-ionized final amplifier (PITER-I, Optoel Ltd, St. Petersburg, Russia). Table 1 summarizes the technical details of these two amplification stages.
3.2 Pulse diagnostics
We used several techniques for measuring a temporal structure of the picosecond 10-µm pulse.
A streak camera (Hamamatsu C1587) is our primary tool for monitoring pulse splitting. The 10-μm pulse is mixed with the 0.9-μm output of a CW diode-laser in an AgGaS2 crystal to shift it from the CO2 wavelength to the sensitivity range of the streak-camera’s photo-cathode. The 2-3 ps resolution of the streak camera limited the accuracy of measuring the duration of individual pulses in the train. The bandwidth of a spectrum measured with a grating spectrometer additionally verified the duration of individual pulses.
As a complementary measure, we implemented an autocorrelator technique and used it occasionally to validate the findings from the measurements with the streak camera and the spectrometer. The 10-μm beam was split into two and recombined in a Michelson interferometer. We intentionally introduced a slight misalignment of the interferometer’s arms to generate an interference pattern on the pyroelectric camera screen. The interference contrast served as a measure of the temporal overlap between pulses in the interferometer’s arms; the maximum modulation corresponds to zero delay, whereas complete separation of the pulses in time results in the disappearance of interference. With this technique, we can study both the duration of individual pulses and the train’s structure, which resulted in the periodic appearance of the interference pattern with gradually reduced modulation at delays in multiples of the 25 ps pulse-splitting period.
3.3 Experimental results
Figure 4 displays the pulse temporal profiles at the output of the regenerative amplifier filled with regular carbon dioxide, and 50% 18O-enriched carbon dioxide.
We used the isotopic mixture only in a regenerative amplifier that affords the greatest amplification; therefore, clamping down on pulse splitting at this stage was most important. The final, large-aperture amplifier that raises the pulse’s energy level to several Joules encompasses larger volume of gas, making it more expensive to operate with an isotopic mixture. However, we did not observe a noticeable increase in secondary pulses after the final amplification in a regular gas; we attribute this to the field-broadening effect in the spectrum at the laser intensity >20 GW/cm2.
We confirmed this assumption by simulating pulse amplification in the final amplifier (Fig. 5 ). Under our experimental conditions (~10 mJ injected pulse energy), the amplification regime becomes essentially non-linear after the first two passes through the final amplifier, at which point the pulse acquires sufficient energy for power-broadening to come into play. In this case, secondary pulses mostly are suppressed; this feature especially is prominent in the center of the beam where the field intensity is highest. In contrast, when we artificially modified the simulation conditions to ensure a linear amplification regime over the entire length of the active medium, intense secondary pulses appeared.
We demonstrated, for the first time, the suppression of the splitting of a picosecond 10-µm pulse upon its amplification in a CO2 laser amplifier. We achieved this result via increasing the density of the rotational lines in the CO2 active medium gain-spectrum by using isotopically enriched gas and employing the R-branch of the laser transition.
Our implementation of this new approach for eliminating the parasitic sub-pulses increased the CO2 laser system’s peak pulse power to the 1 TW level, thereby greatly benefiting the program of using a CO2 laser for strong-field physics experiments.
This work is supported by the US DOE contract DE-AC02-98CH10886 and by the BNL Laboratory Directed R&D (LDRD) grant #07-004. The authors are thankful to Victor Platonenko from Moscow State University for providing original simulation code and supporting further code development, and to Marcus Babzien for help in setting up the pulse diagnostics.
References and links
1. C. A. J. Palmer, N. P. Dover, I. Pogorelsky, M. Babzien, G. I. Dudnikova, M. Ispiriyan, M. N. Polyanskiy, J. Schreiber, P. Shkolnikov, V. Yakimenko, and Z. Najmudin, “Monoenergetic proton beams accelerated by a radiation pressure driven shock,” Phys. Rev. Lett. 106(1), 014801 (2011). [CrossRef] [PubMed]
2. I. V. Pogorelsky, I. Ben-Zvi, T. Hirose, S. Kashiwagi, V. Yakimenko, K. Kusche, P. Siddons, J. Skaritka, T. Kumita, A. Tsunemi, T. Omori, J. Urakawa, M. Washio, K. Yokoya, T. Okugi, Y. Liu, P. He, and D. Cli, “Demonstration of 8×1018 photons/second peaked at 1.8Å in a relativistic Thomson scattering experiment,” Phys. Rev. ST Accel. Beams 3(9), 090702 (2000). [CrossRef]
3. I.V. Pogorelsky, M. Babzien, M.N. Polyanskiy, V. Yakimenko, N.P. Dover, C.A.J. Palmer, Z. Najmudin, P. Shkolnikov, O. Williams, J. Rosenzweig, P. Oliva, M. Carpinelli, B. Golosio, P. Delogu, A. Stefanini, and M. Endrizzi, “Lasers as Particle Accelerators in Medicine: From Laser-driven Protons to Imaging with Thomson Sources,” to be published in conference proceedings CAARI 2010, Fort Worth, Texas, USA, August 8–13, 2010.
4. P. B. Corkum, “Amplification of picosecond 10 µm pulses in multiatmosphere CO2 lasers,” IEEE J. Quantum Electron. 21(3), 216–232 (1985). [CrossRef]
6. A. L. Golger and V. S. Letokhov, “Amplification in a mixture of isotopic CO2 molecules pumped by CO2 laser radiation,” Sov. J. Quant. Electron. 5(7), 811–816 (1975). [CrossRef]
7. R. B. Gibson, A. Javan, and K. Boyer, “Mixed isotope multiatmosphere CO2 laser,” IEEE J. Quantum Electron. 15(11), 1224–1228 (1979). [CrossRef]
8. R. K. Brimacombe and J. Reid, “Accurate measurements of pressure-broadened linewidths in a transversely excited CO2 discharge,” IEEE J. Quantum Electron. 19(11), 1668–1673 (1983). [CrossRef]
9. S. H. Autler and C. H. Townes, “Stark Effect in Rapidly Varying Fields,” Phys. Rev. 100(2), 703–722 (1955). [CrossRef]
10. L. S. Rothman, I. E. Gordon, A. Barbe, D. C. Benner, P. F. Bernath, M. Birk, V. Boudon, L. R. Brown, A. Campargue, and J.-P. Champion, “The HITRAN 2008 molecular spectriscopic database,” J. Quant. Spectrosc. Radiat. Transf. 110(9-10), 533–572 (2009). [CrossRef]
11. W. J. Witteman, The CO2 laser. Berlin Heidelberg New York London Paris Tokyo: Springer-Verlag; 1987.
12. J. Reid and K. J. Siemsen, “Gain of high-pressure CO2 lasers,” IEEE J. Quantum Electron. 14(4), 217–220 (1978). [CrossRef]
13. J. Reid and K. Siemsen, “New CO2 laser bands in the 9–11-μm wavelength region,” Appl. Phys. Lett. 29(4), 250–251 (1976). [CrossRef]
14. V. T. Platonenko and V. D. Taranukhin, “Coherent amplification of light pulses in media with a discrete spectrum,” Sov. J. Quant. Electron. 13(11), 1459–1466 (1983). [CrossRef]
15. C. Freed, “Status of CO2 lasers and their applications in tunable laser spectroscopy,” IEEE J. Quantum Electron. 18(8), 1220–1228 (1982). [CrossRef]
16. A. J. Alcock and P. B. Corkum, “Ultra-fast switching of infrared radiation by laser-produced carriers in semiconductors,” Can. J. Phys. 57, 1280–1290 (1979). [CrossRef]
17. C. V. Filip, R. Narang, S. Ya. Tochitsky, C. E. Clayton, and C. Joshi, “Optical Kerr switching technique for the production of a picosecond, multiwavelength CO2 laser pulse,” Appl. Opt. 41(18), 3743–3747 (2002). [CrossRef] [PubMed]