A simple, robust and compact pulse compressor for high-repetition rate high-peak power fiber chirped pulse amplification systems is presented. We use noble-gas-filled hollow fibers for spectral broadening of the optical pulses via self-phase modulation. Subsequent compression with chirped mirrors shortens the pulses by more than a factor 10. Pulses shorter than 70 fs with pulse energies of the order of 100μJ have been obtained resulting in a peak power up to 1 GW at 30.3 kHz. Additionally, nonlinear polarization rotation has been used for temporal pulse cleaning during the nonlinear compression at 30.3 kHz and 100 kHz, respectively.
©2009 Optical Society of America
Ultrashort pulse laser technology has undergone a rapid progress over the last decades . Partly, this development has been driven by Ti:Sapphire based technology that routinely enabled the generation of mJ-class pulses with pulse durations shorter than 25 fs . Therefore, these systems have become the work horse of ultrashort laser science. Unfortunately, Ti:Sapphire laser systems are restricted to a few Watts of average power due to thermal effects. This severely affects on the detection of processes initiated by such ultrashort high-peak power pulses which are typically characterized by low conversion efficiencies. An example of such process is high harmonic generation . Applications of high harmonic radiation, such as new lensless imaging schemes, require long integration times  and would greatly benefit from an increase in repetition rate.
Cryogenic cooling of the Ti:Sapphire crystal in the amplifier has helped to increase the repetition rate of these system due to the improved thermal conductivity of the laser crystal at such ultralow temperatures . However, this approach is limited and further scaling can only be addressed by advanced techniques.
In comparison to Ti:Sapphire based laser and amplifier systems, Ytterbium doped fibers offer higher average power management capabilities. Due to the large ratio of surface to active volume, the heat is distributed and thermo-optical problems can be neglected even at high average powers . Fiber lasers with several kW of average output power have been demonstrated in several works over the last years .
The generation of ultrashort pulses in fiber amplifiers is mainly limited by the onset of nonlinear effects that arise due to the small cores and long interaction lengths in optical fibers. The development of state-of-the-art photonic crystal fibers with mode field diameters of 71μm has led to high-average power fiber chirped pulse amplification (FCPA) systems producing 1 mJ of output energy at pulse durations of about 800 fs which results in GW peak power . Despite this progress the Ytterbium gain bandwidth is not wide enough to support pulses of few tens of femtoseconds . Hence, concepts aimed at converting such high repetition rate FCPA systems to pulse durations shorter than 100 fs is an important step to transforming them into a suitable source for high field physics.
An average power scalable concept able to amplify ultrashort pulses is optical parametric amplification (OPA) . Fiber laser pumped optical parametric amplifiers have the potential to extend the generation of ultrashort pulses to high repetition rate. Recently, we have demonstrated several power-scalable approaches of OPA based on fiber amplifiers. We have presented the generation of sub-20 fs pulses with 500 nJ pulse energy at repetition rates as high as 2 MHz . Using degenerated parametric amplifiers we were able to obtain to 2 GW of peak power with pulse durations shorter than 30 fs [12, 13]. However, from a practical point of view, simpler experimental setups are highly desirable.
An experimentally simple approach for pulse shortening uses nonlinear compression. Conventionally, in this technique pulses are coupled into a standard fiber in which they undergo spectral broadening via self-phase modulation (SPM). Subsequent removal of the SPM induced chirp results in a pulse compression. With this approach 27 fs pulses with 57 W of average power at a repetition rate of 78 MHz have been produced . However, this technique does not work for high energies due to fiber damage.
For mJ-class pulse energies and corresponding peak powers well above 1 GW, a compact pulse compressor has been suggested and demonstrated for Ti:Sapphire laser systems. It exploits self-phase-modulation in noble-gas-filled hollow fibers followed by pulse compression with a chirped mirror compressor [15, 16]. However, due to the lack of peak power, this approach has never been considered for fiber laser systems.
In this contribution we report, to the best of our knowledge, the first experimental demonstration of pulse compression in noble gas filled hollow waveguides for high repetition rate FCPA systems. The availability of a high-peak power FCPA system  enabled spectral broadening in a 1 m-long Xenon gas filled hollow fiber. Subsequent compression with a chirped mirror compressor yielded ultrashort pulses with durations shorter than 70 fs and energies of the order of 100μJ.
2. Design of a hollow fiber based nonlinear compression system
As mentioned above nonlinear compression in conventional fibers is a well known scheme to achieve pulse shortening. Using a waveguide for self-phase modulation offers homogeneous spectral broadening over the spatial beam profile due to the guided nature of the radiation, and therefore, avoids spatial chirp. One of the major limitations is, however, set by the small cores, that imply high intensities when the energy is increased and finally lead to fiber damage. On the other hand, Marcatili and Schmeltzer  have shown that hollow fiber waveguides offer modes similar to those of conventional solid-core fibers. Using this type of fibers paves the way for high-energy compression schemes, since much larger cores can be used that, additionally, are not made of glass, but of air or gas instead. Hence, fiber damage is less critical than for solid-core fibers. Furthermore, they offer an additional degree of freedom by allowing to fill the core with gases which improve the nonlinear interaction inside the fiber. Thus, the pulses interact with the gas, preferably a noble gas, thanks to its χ(3) nonlinearity. The use of noble gas filling offers numerous advantages such as the possibility of varing the nonlinear strength by changing the gas pressure or the high threshold intensity for multiphoton ionization processes .
The modes in such a fiber originate from glancing incidence of the light at the inner walls resulting in more critical coupling conditions and higher losses in comparison to guided modes in conventional fibers. The lowest loss mode, EH11, is a so-called hybrid mode and can be expressed in terms of a zero order Bessel function as I(r) = I 0 · J 0 2(2.405·r/a), where I 0 is peak intensity, r the radial coordinate and a the inner radius. This mode is, therefore, similar to the fundamental mode of a step index fiber. For efficient coupling of an incident Gaussian beam to the EH11 mode, the focal spot size needs to be chosen as ω 0 = 0.64a, where ω 0 is the 1/e 2 radius in the focal plane and a the inner radius of the fiber. However, due to glancing incidence, the propagation losses are much higher than in conventional step index fibers. Thus, for the EH11 mode they can be expressed as 
where λ is the wavelength of the incident light, a the inner radius of the fiber and v the ratio of the refractive indices of the core surrounding glass and the core material, respectively. Clearly, the most crucial parameters for light propagation inside such a fiber are the wavelength and the inner radius. Since the operating wavelength is usually given one needs to increase the inner radius as much as possible.
Summarizing, there are three major design parameters to be optimized, i.e. the fiber length, the gas pressure that controls the nonlinear parameter n 2 and the inner radius of the fiber. Optimization has to be carried out regarding spectral broadening. This implies short pulses in combination with the highest possible transmission. From a practical point of view a maximum fiber length of 1 m has to be assumed . This is because on the one hand it is extremely difficult to align longer fibers and, on the other hand, it is not easy to obtain a uniform inner surface along such lengths which in turn will lead to higher propagation loss.
In  a simple analytical result for optimal spectral broadening is presented in terms of a broadening factor defined as ratio of the final bandwidth ∆ω and the initial bandwidth (∆ω)0
where Φnl max is the maximum nonlinear phase shift as defined in . This simple model accounts for losses, but not for dispersion and self-steepening. However, as will be shown in section 3 the second order dispersion in Xenon at a few bar of pressure is of the order of 100fs2 resulting in a dispersion length LD of a few km validating this approach.
Even though, this provides the opportunity to optimize a single hollow fiber compression stage in terms of the spectral broadening one still has to consider the propagation losses of the particular fiber. For our experimental setup we were highly interested in high energy output combined with short pulses. This requires high transmission combined with suitable spectral broadening. Figure 1 shows the broadening factor F calculated with the help of Eq. (2) for a Gaussian input pulse with 0.6 GW of peak power and a fiber length of 1 m. Several pressures have been considered resulting in a variation of the nonlinear index of refraction n 2. Since we require a high nonlinearity to obtain the targeted spectral broadening for our FCPA system, we chose to use Xenon because it has the highest n 2 = 8.1 · 10-23m2/(W·bar)  of all noble gases. The corresponding losses (dashed black line in Fig.1) are also depicted. Clearly, the optimal spectral broadening is connected to high propagation loss well above 10dB/m which is not desirable for the generation of high energy pulses.
Experimentally, a propagation loss smaller than 3 dB is mandatory, since additional losses due to surface roughness or imperfect coupling will increase the value of the overall loss. Figure 1 shows that a fiber radius of 100 μm is a good tradeoff between losses and achievable spectral broadening. It can also be seen that the spectral broadening at this particular fiber radius is enhanced by increasing the pressure of the noble gas. However, due to the onset of self-focusing the pressure can not be increased arbitrarily. There are several estimations of the self-focusing limit for hollow waveguides, e.g. Pcr,wg = λ 0 2/(2n2)  or Pcr ≈ λ 0 2/(2πn0n2) . Based on this equations and the n2 value stated above, the critical power for self-focusing is Pcr = 6.5GW/bar  or Pcr = 1.9GW/bar , respectively. Since there are also uncertainties on value of n2, especially for femtosecond pulses , the critical pressure for our experiments that uses up to 0.6 GW input pulses is about 4 bar.
3. Nonlinear compression of a FCPA system
Nonlinear compression has been used to shorten the pulses of a state-of-the-art FCPA system . This system was operated at 30.3 kHz repetition rate and provided variable pulse energy up to 1 mJ with a pulse duration of about 800 fs. For the experiments described herein we used a maximum pulse energy of 600 μJ resulting in a maximum peak power of 600 MW.
Coupling of the FCPA output to the hollow fiber compression (HFC) stage was achieved by a single lens (see Fig. 2) that was selected to match the right focal spot size for efficient coupling into the EH11 mode. The hollow fiber was placed inside a tube containing anti reflection coated (980 nm -1030 nm) windows with a thickness of 4 mm.
The overall transmission was measured to be 20 %. This value is well below the theoretical transmission of 63 % that can be calculated by using Eq. (1) for a 100 μm inner radius fiber operating at 1030 nm wavelength. Since the modes are of leaky nature, we expect wall roughness to have a strong influence on the propagation losses of the mode. In addition, the output of the FCPA has a M2 < 1.3 which also introduces some extra coupling losses. In order to separately estimate coupling and propagation loss we measured the transmission of a short piece (12 cm) of the same fiber to be 63%. With this two values and using I(z) = cl·I 0·exp(-γ·z), where cl is the coupling loss and γ the propagation loss, the constants can be calculated to be cl = 0.73 and γ = 1.22m -1 (≈ 5.3 dB/m). This confirms that the propagation losses are higher than expected. It has to be noted that all the transmission values have been measured after passing the mode through an appropriate pinhole to reduce the influence of the stray light that might be guided by the wall of fiber.
In spite of this poor transmission we only observed the EH11 mode at the output. The beam quality of the output of the hollow fiber has been measured to be M 2 < 1.1, hence, providing a diffraction limited beam (see Fig. 3) which is essential for applications in high field physics. This proves that only the lowest loss hybrid mode has been excited.
As described in the previous section, in order to carry out the spectral broadening we filled the 100μm radius 1 m-long fiber with Xenon. The pressure of the noble gas was adjusted for optimal spectral broadening for the particular experimental parameters while keeping it under the critical pressure for self-focussing as discussed in section 2.
In a first experiment, 600μJ pulses from the FCPA output at a repetition rate of 30.3 kHz were coupled to the fiber. As mentioned above the transmission was expected to be low. For 18 W of input average power we measured a output power of 3.4 W which equals 112μJ (at 30.3 kHz) in the EH11 mode at a Xenon pressure of 2.95 bar. We could observe significant spectral broadening of the input signal as can be seen in Fig. 4(a). The input spectrum (blue curve in Fig. 4(a)) is broadened to more than 30 nm (10 dB width).
The chirp induced by the self-phase modulation in the hollow fiber is removed by a simple chirped mirror compressor comprised of mirrors with an individual group velocity dispersion of -250fs2. After going through 28 bounces, which results in a total dispersion of -7000fs2, the pulses are compressed to an autocorrelation width of τAC = 100fs (Fig.4 (b)). The Fourier transformation of the corresponding spectrum (Fig.4 (a)) was stretched by third order dispersion (TOD) to match the autocorrelation width. The dashed blue curve in Fig. 4 (b) shows the autocorrelation of the Fourier transformed spectrum with additional TOD. By applying this method, the pulse duration can be calculated to be 68 fs. Additionally, we performed a numerical simulation of the spectral broadening in the Xenon gas filled hollow fiber based on a split-step Fourier method. As input of the simulation we used the real temporal pulse profile of the FCPA output, including its phase that has been retrieved from a FROG measurement. The input pulse energy was set to 440 μJ, thus accounting for the coupling loss. Furthermore, the simulation included propagation losses as well as dispersion. The dispersion values have been calculated taking into account both gas  and waveguide dispersion  giving values of β 2 ≈ 172fs2/m and β 3 ≈ 170fs3/m for Xenon at a pressure of 2.95 bar. The simulation output has been compared with the experimental data and as can be seen in Fig. 4(a), (b) and agree well. However, the spectrum that has been obtained from the simulation shows typical SPM features while the experimental spectrum differs (Fig. 4(a)). Since, the simulations include also dispersion up to the third order and effects such as self-steepening and shock formation  can be excluded the deviation must be caused by other nonlinear effects, such as four wave mixing. Compressing the numerical results only by adding negative group velocity dispersion matches the experimental results well (Fig. 4(b)) and also gives a pulse duration of 68 fs.
The compressor throughput was measured to be 94% resulting in 105 μJ of compressed pulse energy. With this pulse energy we retrieved a peak power of 1.2 GW for the dashed blue curve in Fig. 4 (b). With about 85% of the energy located in the main pulse the resulting experimental peak power was as high as 1 GW meaning a notable increase of the ipeak power with repsect to the 600 MW at the input. These estimations are also validated by the numerical results (dashed red curve in Fig. 4(b)). Furthermore, the spatial characteristics of the beam were measured in terms of the beam quality factor M 2. The output of the chirped mirror compressor provided a beam quality of M 2 < 1.3 (4σ -method).
4. Pulse cleaning for hollow fiber compressors
For the applicability to high field physics at high repetition rates several requirements have to be met. Basically, the interest is focused on high-peak power pulses with diffraction limited beam quality and the best possible temporal pulse quality, i.e. the best suppression of pre- and post pulses. Diffraction limited beam quality with high-peak power has already been demonstrated in the experiment described above, but the autocorrelation traces taken for this direct nonlinear compression (Fig. 4(b)) indicate the existence of small pre- and post pulses.
Pulse cleaning can be achieved by exploiting nonlinear ellipse rotation (NER) as an effect of third order nonlinearity. For an elliptically polarized input the ellipse rotates due to the nonlinearity along the propagation distance . This can be used to eliminate pre- and post pulses, because this rotation depends on the intensity. Therefore, by adjusting the polarization correctly it will be possible to extract only the main peak. This mechanism has been used to improve the pulse contrast of high energy pulses in hollow fibers filled with noble gas . Basically, elliptically polarized light is propagated through a fiber and subsequently the ellipticity is removed and the then linearly polarized light is transmitted through a polarizer. This polarizer dumps the whole transmitted light at low intensities. When the intensity is increased the NER changes the polarization state such that mainly the high intensity part, i.e. the main peak, is transmitted through the polarizer resulting in a linearly polarized output and then send to the pulse compressor.
We used a slightly different approach to clean our pulses. Before we coupled the light to the hollow fiber we placed a half-wave plate (HWP) and a quarter-wave plate (QWP) in the beam path (Fig. 2) to create elliptically polarized light. The polarizer after the fiber was set to the right linear polarization for the autocorrelator. Then experimentally we aligned the HWP and QWP to achieve the best pulse quality.
We performed this experiments for repetition rates of 30.3 kHz and 100 kHz, respectively. Hence, not only have we demonstrated the possibility of pulse cleaning, but also the scalability in terms of repetition rate and, therefore, average power. The best spectral broadening for this experiment was achieved by setting the Xenon pressure to 3.6 bar.
For a repetition rate of 30.3 kHz the FCPA was operated at 500μJ pulse energy. Since we used nonlinear polarization rotation, the losses were higher due to the elimination of undesired pre- and post pulses resulting in 70μJ compressed pulse energy. The spectrum of the output is depicted in Fig. 5 (a) showing a 10 dB bandwidth of about 30 nm. The overall GVD of the chirped mirror compressor was set to -6000fs2 (24 bounces) resulting in compressed pulses with an autocorrelation width of 99 fs (Fig. 5(b)). To estimate the pulse duration, a Fourier transform of the spectrum (Fig. 5(a)) was performed and TOD was added to match the autocorrelation width of 99 fs resulting in a pulse duration of 70 fs. The wings in the autocorrelation trace (Fig. 5(b)) are notedly reduced in comparison to the experiment without nonlinear polarization rotation (Fig. 4(b)). The peak power of the red autocorrelation trace in Fig. 5 (b) was as high as 837 MW. Taking into account the energy contained in the minor wings a peak power of 795 MW can be obtained if 95% of the energy is considered to be located in the main pulse. Hence, the input peak power of about 500 MW has been increased while clean and short pulses have been obtained.
To show the average power scalability of this approach, we repeated the experiment for a repetition rate of 100 kHz. All the experimental parameters were the same as in the 30.3 kHz experiment. We only changed the output parameters of our FCPA system to 420μJ pulse energy, because the system was operated with somewhat different parameters, e.g. B-Integral, resulting in a different temporal pulse shape. In  we discussed the influence of the temporal shape on the achievable spectral broadening and pulse shortening. Compression of the spectrally broadened pulses(Fig. 6(a)) via a chirped mirror compressor with the same GVD of -6000fs2 (24 bounces) resulted in 63μJ pulses with an autocorrelation width of 99 fs. The pulse duration was estimated to be 57 fs (applying the same method as mentioned before). The Fourier transform with additional TOD was in very good agreement with the autocorrelation trace (Fig. 6(b)) indicating a good temporal pulse cleaning via NER. The peak power of this pulse was 780 MW, similar to the results presented above.
In summary, we have presented a simple, compact, average power scalable pulse compression scheme for high peak power FCPA systems providing pulse shortening factor higher than 10. With this experiment ultrashort pulses with durations shorter than 70 fs and energies of the order of 100μJ become available at repetition rates up to 100 kHz. We demonstrated 68 fs pulses with a energy of 105μJ resulting in a peak power as high as 1 GW at a repetition rate of 30.3 kHz. Further scaling in terms of energy and peak power seems possible by improving the transmission of the hollow fiber via better surface quality of the fibers and improved coupling conditions.
Besides pulse shortening, we demonstrated pulse cleaning via nonlinear ellipse rotation as result of the third order nonlinearity in the noble gas. Utilizing this scheme we were able to obtain linearly polarized light with significantly suppressed wings in the autocorrelation at variable repetition rate of 30.3 kHz and 100 kHz, respectively. Similar pulse parameters have been obtained for the temporally cleaned pulses. Peak powers of 795 MW for 30.3 kHz, 70μJ, 70 fs pulses and 780 MW for 100 kHz, 63μJ, 57 fs pulses are demonstrated. Furthermore this compression scheme offers diffraction limited spatial beam quality making it an interesting source for high field experiments. To the best of our knowledge, this is the first experimental realization of nonlinear compression for high repetition rate FCPA systems.
The scheme presented in this paper is a very flexible method for peak power enhancement at variable pulse energies and repetition rates, since various experimental parameters, e.g. gas pressure, fiber length and diameter, can be optimized. By optimizing the configuration and starting with cleaner pulses with higher peak power we expect to extend this scheme to the multigigawatt range and pulse duration shorter than 30 fs.
This work has been partly supported by the German Federal Ministry of Education and Research (BMBF) with project 03ZIK455 ‘onCOOPtics’ and the Gottfried Wilhelm Leibniz-Programm of the Deutsche Forschungsgemeinschaft. S.H. acknowledges the financial support of the Carl Zeiss Stiftung, Germany.
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