Picosecond pulse amplification in isotopic CO_2 active medium

Picosecond pulse amplification in isotopic CO2

active medium

Mikhail N. Polyanskiy,* Igor V. Pogorelsky, and Vitaly Yakimenko

Brookhaven National Laboratory, Bldg. 820M, Upton, NY 11973, USA

*[email protected]

Abstract: 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

OCIS codes: (140.3470) Lasers, carbon dioxide; (140.3280) Laser amplifiers.

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).

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). 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). 5. D. Haberberger, S. Tochitsky, and C. Joshi, “Fifteen terawatt picosecond CO2 laser system,” Opt. Express

18(17), 17865–17875 (2010).

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).

7. R. B. Gibson, A. Javan, and K. Boyer, “Mixed isotope multiatmosphere CO2 laser,” IEEE J. Quantum Electron.

15(11), 1224–1228 (1979). 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).

9. S. H. Autler, and C. H. Townes, “Stark Effect in Rapidly Varying Fields,” Phys. Rev. 100(2), 703–722 (1955). 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).

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).

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). 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).

15. C. Freed, “Status of CO2 lasers and their applications in tunable laser spectroscopy,” IEEE J. Quantum Electron. 18(8), 1220–1228 (1982).

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). 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).

1. Introduction

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)

#142609 - $15.00 USD Received 14 Feb 2011; revised 7 Mar 2011; accepted 8 Mar 2011; published 6 Apr 2011(C) 2011 OSA 11 April 2011 / Vol. 19, No. 8 / OPTICS EXPRESS 7717

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 Iλ2 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

[1]. 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 1( )t c , where

c is measured in cm/s, and in cm1

.

For a 10-µm CO2 laser, the rotational-structure period varies between 1.3 and 1.8 cm1

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 [4], which is close to the practical limit for today’s gas-discharge

laser technology.

As reported recently [5], 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 16

O with 18

O 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 18

O.

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

2 20.1149 0.0794 0.0598pressure CO N HeP P P [8]

where is measured in cm1

, and P in bar. In the case of the typical 0.5:0.5:9 gas mixture,

used in our 10-bar CO2 amplifier, pressure = 0.63 cm1

i.e., insufficient to effectively fill the

1.3-1.8 cm1

gaps between the rotational lines. The 15-20 bar pressure required for better

suppressing modulation is impractical due to difficulties in arranging the uniform electric-

discharge pumping of the large volume of active gas required for building a terawatt-class

CO2 laser amplifier.

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) [9] by the

Rabi frequency:

-1

-1 [C m] [V m ][s ] ,

[J s]

d EΩ =

h

where d is the transition dipole momentum, E - the laser field and h - the Plank's constant.

Using the following relation between laser field and intensity I

-2

-1

-1 -1

0

2 [W m ][V m ] ,

[F m ] [m s ]

IE =

ε c

where ε0 is the vacuum permittivity, and c is the speed of light and changing the units of d and

I to Debye and W/cm2, respectively, we obtain for field-broadened linewidth (HWHM):

-1

-1 4 -2

-1

[s ][cm ] 4.609 10 [D] [W cm ].

[cm s ]power

Ω= = d I

c

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 [10]), we find that

the Stark broadening becomes 1.8 cm1

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 [5].

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 [11]; 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.

Fig. 1. Simulated gain spectra at10 bar for three CO2 isotopologues with different combinations

of oxygen-16 and oxygen-18 atoms: 16O-12C-16O (626), 16O-12C-18O (628) and 18O-12C-18O

(828) and a combined spectrum of their mixture in the statistically equilibrium proportion 1:2:1 (MIX). The arrow shows the 10R branch used in our laser.

Isotopic CO2. By partially substituting the 16

O atoms in CO2 gas with another stable 18

O

isotope, we obtain almost perfectly smooth combined spectrum after superimposing the

spectra of three CO2 isotopologues: 16

O-12

C-16

O, 16

O-12

C-18

O and 18

O-12

C-18

O (Fig. 1). These

three isotopologues often are denoted as 626, 628 and 828 where 2, 6 and 8 respectively

represent 12

C, 16

O and 18

O.

For an equal proportion [16

O]:[18

O]=1:1, independently of the initial distribution of 16

O

and 18

O between the CO2 molecules, statistical equilibration via intermolecular isotope

exchange leads to [626]:[628]:[828]=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 [13]

3 3/ 2exp( / ),seq regG G h kT

where T3 and ν3 are the vibrational temperature and frequency of the asymmetric stretch mode

of the CO2 molecule and h and k are Plank’s and Boltzmann’s constants, show that sequence

band’s gain reaches 50% of the regular band’s gain at T3 = 2500 K, which is close to the

conditions of our high-pressure CO2 amplifiers.

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 [14]:

0

2 2 2

0

0 2 0

*

2,

( ) 1,

2

Im( ),

j

j

j j j j

j j

j j j

R

iEP

z cn

P i i dP n E

t T

EP n Nn

t T

where E and ω0 are, respectively, the slowly varying amplitude and central frequency of the

laser’s field; Pj, dj, nj and Ωj are the polarization, dipole momentum, inversion and frequency

of the j-th ro-vibrational transition; TR and T2 are the rotational- and polarization-relaxation

times; ρj is the Boltzmann factor of the distribution between the rotational sublevels; N=Σjnj is

the vibrational inversion; n is the linear refractive index; and, t is the time in a coordinate

system traveling together with the pulse. We used spectroscopic constants of 626 and 628

CO2 isotiopologues from the HITRAN-2008 database [10] and the 828 constants estimated

based on the absorption measurements reported by C. Freed [15]. 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 16

O oxygen in carbon dioxide with its 18

O 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.

Fig. 2. 5-ps (FWHM) pulse splitting upon 106× amplification in a 10 bar CO2 laser amplifier.

a) normalized gain profile and pulse spectra; b) pulse temporal structure (power vs. time).

3. Experiment

3.1 Laser

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

[16], 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 [17] 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% 18

O) CO2 obtained from Cambridge Isotope Laboratories, Inc. We observed complete

statistical equilibration ([626]:[628]:[828]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.


Fig. 3. Layout and pulse dynamics in the CO2 laser system. PS: polarizing splitter.

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.

Table 1. Laser amplifier’s parameters

Regenerative amplifier Final amplifier

Working pressure 10 bar 8 bar

Gas mixture: [CO2]:[N2]:[He] 0.5: 0.5: 9 0.6: 0.4: 9

Active volume 1×1×80 cm3 8×10×100 cm3

Small-signal gain 1-2%/cm 1.5-2%/cm

Number of passes 16-24 6

Net amplification 105 103

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% 18

O-enriched carbon dioxide.

Fig. 4. 5-ps (FWHM) pulse amplification in a natural- (top) and isotopically enriched- (bottom)

CO2 laser gas mixture. Inserts in the time structure graphs show raw streak-camera images. The

simulation curves are identical to those in the Fig. 2 (106× net amplification).

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.


Fig. 5. Simulation results for a 5-ps (FWHM) pulse amplification in the final amplifier.

4. Conclusions

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.

Acknowledgements

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.


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Picosecond pulse amplification in isotopic CO_2 active medium