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Abstract
A simple and compact spectral-broadening system is presented that is based on a single-stage statically pressurized Ar filled hollow core fiber. By optimizing the inner diameter of the hollow core fiber, a bandwidth of 300 nm is obtained. This is the broadest bandwidth known to date with millijoule level energy near the 1-μm wavelength by a single stage gas filled hollow core fiber.
© 2017 Optical Society of America
1. Introduction
Laser pulses with a high repetition rate and high peak power are of great interest for both academic and applied research, such as the generation of X-rays, laser wake field acceleration, and proton beam acceleration. Recently, by taking advantage of the high performance of a Yb:YAG laser at low temperature [1–3] and the low thermal loading and ultra-broadband gain bandwidth during optical parametric chirped pulse amplification (OPCPA), Kawanaka et al. developed a design concept for a 1 PW/10 fs p-DKDP (partially deuterated potassium dihydrogen phosphate) crystal based OPCPA system centered at 1 μm with 100 Hz repetition pumped by a frequency doubled cryogenically cooled Yb:YAG laser [4].
However, to date the pulse duration from a mode-locked oscillator is >20 fs (typically ~200 fs) near 1 μm wavelength [5–7]. To obtain the target of 1 PW/10 fs, we require an ultra-broadband front end near the 1 μm wavelength, for which a spectral broadening system is necessary. Nonlinear propagation through a gas filled hollow core fiber (HCF) is currently the most popular method for achieving efficient spectral broadening because of the high energy, large broadening factor, and high beam quality that it affords [8–15]. In this technique, laser pulses are spectrally broadened primarily by self-phase modulation (SPM) in the gas within the HCF, the use of which dramatically increases the interaction length while maintaining a diffraction-limited beam profile.
Some pioneering work has already been done on spectral broadening in a gas filled HCF near the 1 μm wavelength. By using a single-stage statically pressurized HCF, Andriukaitis et al. demonstrated spectral broadening with a bandwidth of approximately 200 nm in 3 mJ/200 fs laser pulses sent through an HCF with an inner diameter of 300 μm [12]. Similarly, Hädrich et al. achieved a spectral bandwidth of approximately 120 nm in 1.1 mJ/340 fs laser pulses sent through an HCF with an inner diameter of 250 μm [13]. However, those bandwidths are not enough for a 10 fs laser system. To increase the spectral broadening, Ahmad et al. [14] used a two stage HCF system and obtained a bandwidth of approximately 500 nm with 1.5 mJ/25 fs input pulses. Similarly, Rothhardt et al. [15] used a two stages pressure gradient HCF system to obtain a bandwidth of approximately 400 nm in 1 mJ/210 fs input pulses, which is an extremely broad bandwidth. However, using a two stages HCF or a pressure gradient HCF system inevitably complicates the setup and introduces the risk of instability. From a practical point of view, a simpler experimental setup is highly desirable.
In this paper, we present a single stage statically pressurized gas filled HCF system. By optimizing the HCF inner diameter, 300 nm bandwidth 0.5 mJ pulses are obtained from 0.94 mJ/220 fs input pulses. To the best of our knowledge, this is the broadest bandwidth ever obtained at millijoule level near the 1 μm wavelength with this type of HCF system. The calculated Fourier transform limited (FTL) pulse duration is as short as 8.8 fs. These ultra-broadband, high energy pulses are ideal for use as front end light for OPCPA systems with high repetition rate and high peak power.
2. Design of an HCF system
The important parameters of an HCF system are its transmission and its broadening factor. The transmission is the ratio of the output energy to the input energy. The broadening factor is the ratio of the output root-mean-square (RMS) bandwidth Δνout to the input RMS bandwidth Δνin. We want to obtain ultra-broadband pulses with high transmission. To achieve this aim, we follow the procedure of Vozzi et al. [10] for designing an HCF system, and, in particular, we use the procedure to determine the length, inner diameter, and gas pressure of the HCF.
The propagation of pulses in an HCF is described by the nonlinear Schrödinger equation (NLSE) [10, 16]:
In Eq. (1), U is the normalized amplitude U = A/P0½, where A is the field amplitude and P0 is the pulse peak power. The term T is the retarded frame T = t − z/vg, where vg is the group velocity of the pulse. The term α is the power attenuation, and β2 and β3 are the second and third dispersion coefficients, respectively. The term γ is the nonlinearity parameter, and ω0 is the pulse-center angular frequency. The left hand side of Eq. (1) determines the linear effects, including attenuation (second term) and dispersion (third and fourth terms). The right hand side of Eq. (1) determines the nonlinear effects, namely SPM (first term) and self-steepening (second term).The power attenuation α that appears in Eq. (1) can be expressed as
where λ0 is the pulse-center wavelength, D is the HCF inner diameter, and κ is the ratio of the refractive indices of the external (fused silica) and internal (gas) media; a typical value is κ = 1.4532.The nonlinearity parameter γ that appears in Eq. (1) can be expressed as γ = n2ω0/(cAeff), where n2 = κ2p is the nonlinear refractive index and κ2 is a constant that depends on the type of gas used; κ2 = 9.8 × 10−24 m2/(W•bar) for Ar [9]. The term p is the gas pressure in the HCF, Aeff ≈0.48π(D/2)2 is the effective mode area of the HCF, and c is the speed of light in a vacuum.
Next, we introduce analytical formulas for the transmission and the broadening factor. By neglecting dispersion and nonlinear effects, we obtain the transmission as e−αL, where L is the length of the HCF. In addition, there is typically a power loss when a pulse passes from free space into the waveguide. Taking the coupling efficiency ηc of that process into account, the total transmission can be expressed as
In Fig. 1, we show the transmission as a function of HCF inner diameter (blue dashed line). In the calculation, we assumed that the input beam was a Gaussian beam, and that the ratio of the input-beam diameter to the HCF inner diameter was 0.65, which gives the maximum coupling efficiency of ηc = 98%. From Fig. 1, we see that the power attenuation is very sensitive to the HCF inner diameter, and that a larger diameter results in a higher transmission. To obtain a transmission in excess of 50%, the HCF inner diameter should be larger than 175 μm.
Fig. 1 Spectral broadening factor (red solid line) and transmission (blue dashed line) with respect to HCF inner diameter for a fiber length of 1 m.
Neglecting the effects of dispersion and self-steepening, we obtain the following formula for the broadening factor (further details of the derivation process can be found in [16]):
where φmax = γP0Leff is the maximum nonlinear phase shift, and γ and P0 are the nonlinear parameter and pulse peak power, respectively, as before. The term Leff is the HCF effective length, where Leff = [1−exp(−αL)]/α. To restrain the higher order modes in the HCF, the maximum imposed gas pressure is limited by the critical power for self-focusing. It is worth noting that there are different definitions of critical power; we use the definition of Pcr = λ02/(2πn2) [9], where the notation has the same meaning as before. With this limit on the gas pressure, the maximum broadening factor is given byFrom Eq. (5), we see that there are two ways to increase the maximum broadening factor: either use a longer HCF or reduce its inner diameter. However, the former is difficult to achieve while retaining a uniform inner surface and a constant diameter. For this practical reason, we assume here a fixed HCF length of 1 m.
Next, we determine the optimum HCF inner diameter. For a center wavelength of 1.04 μm and a fiber length of 1 m, we show in Fig. 1 the broadening factor (red solid line) as a function of HCF inner diameter. As with the transmission, the broadening factor is also sensitive to HCF inner diameter. The broadening factor achieves a maximum value of 69 for an HCF inner diameter of 125 μm. For HCF inner diameters greater than 125 μm, the effective area Aeff dominates the broadening factor, causing the latter to decrease. For HCF inner diameters less than 125 μm, the effective length Leff dominates the broadening factor, again causing the latter to decrease. However, at the maximum broadening factor, the transmission is only 15%. Taking both the broadening factor and transmission into account, we arrive at a compromise diameter of 190 μm that gives a broadening factor of 51.8 and a transmission of 56.8%. In addition, the analysis of the spectral broadening factor is based on FTL pump pulse. If there is residual spectral phase in the pump pulse, the pulse duration will be larger than FTL duration. And the practical spectral broadening factor should be calibrated by the ratio of the experimental obtained and calculated FTL pump pulse duration. Also the introduced dispersion by SPM effect through gas filled HCF should be calibrated by the similar way. However, we believe there is no impact on the choosing of optimum HCF inner diameter.
3. Experimental setup
In Fig. 2, we show the experimental setup schematically. ~50 fs pulses centered at 1.04 μm from Yb:fiber oscillator are stretched by a Martinez type stretcher. After the stretcher, the pulses are amplified by a diode pumped regenerative amplifier (RA) at room temperature. The gain medium is a 3 at. % doped Yb:CaF2 crystal with size 6 × 6 × 5 mm3. The cavity consists of 1000 mm radius and 500 mm radius concave mirrors. The cavity length is 136.5 cm with roundtrip time 9.1 ns. The cavity mode diameter (full width at 1/e2 maximum, FW1/e2) on Yb:CaF2 crystal is calculated as ~0.5 mm. After the RA, 1.8 mJ pulse energy is obtained. Finally, the pulses go through a Treacy type compressor and compressed to 220 fs with 0.94 mJ energy.
A plano-concave lens (f = 500 mm) directs the laser output through the input window of a gas cell and into the HCF (Nakahara Opto-Electronics Laboratories, Inc.). Both the input and output windows are made of thin fused silica with an anti-reflection (AR) coating tuned to 1 μm. The HCF is 1 m long with an inner diameter of 190 μm. The choice of Ar as the filler gas is due to its relatively high ionization intensity and large nonlinear refractive index. After the HCF, we use a gold-coated concave mirror (f = 304.8 mm) to re-collimate the pulses. The AR coated windows are 1 mm in thickness. The generated nonlinear phase shift though double windows is <1. In experiment, the windows can support at least 10 bar pressure. The pump beam radius on fiber input end was 68 μm, which is close to the theoretical calculated optimum radius. The distance between the input window and the fiber input end was 250 mm. The distance between the output window and the fiber output end was 150 mm. The maximum pulse intensity on the window is ~125 GW/cm2, well below the damage intensity.
4. Results and discussion
In Fig. 3, we show the measured pump pulse spectrum [Fig. 3(a)], autocorrelation trace [Fig. 3(a) inserted figure], beam quality [Fig. 3(b)] and focus spot beam shape [Fig. 3(b) inserted figure]. The center wavelength is 1.04 μm with 13 nm (full width at half maximum, FWHM) bandwidth. The measured deconvolution pulse duration through autocorrelator is 220 fs (FWHM). The measured M2 are 1.3 and 1.2 in horizontal and vertical direction, respectively. The inserted figure in Fig. 3(b) is the focus spot beam shape, which is slightly elliptical.
Fig. 3 Yb:CaF2 based RA output (a) spectrum and autocorrelation trace. (b) beam quality and focus spot beam shape.
In the experiment, we keep the input energy at 0.94 mJ and increase the Ar pressure gradually. In Fig. 4(a), we show the output spectra (the gray areas) measured using a spectrometer (NIR Quest, Ocean Optics). We observe that the spectra broaden rapidly with increasing pressure because of the SPM effect. Meanwhile, the broadened spectra are asymmetric: the red-shifted peaks are more intense than the blue-shifted peaks, and the spectral broadening is more pronounced on the blue side than it is on the red side. Both these asymmetry features are due to the self-steepening effect. For pressures greater than 3 bar, the broadened spectra are beyond the measurement range of the spectrometer and there is supercontinuum generation; hence, we stopped measuring spectra at 3 bar.
Fig. 4 (a) Experimental spectra of output pulses from HCF with 0.94-mJ input energy at different Ar pressures (grey areas). The red solid lines are numerical solutions of the nonlinear Schrödinger equation. The blue dashed lines are visual guides. (b) Experimental output energy and efficiency with 0.94-mJ input energy at different Ar pressures.
Also shown in Fig. 4(a) are numerical solutions of the NLSE [Eq. (1)] (solid red lines). The experimental data agree well with the numerical data, thus demonstrating the high performance of our setup. In Fig. 4(b), we show the output energy and transmission for different pressures. The maximum measured transmission is 53.2%, which is close to the theoretical limit of 56.8%. This difference between experiment and theory is possibly because the input beam is not perfectly Gaussian in shape, thereby reducing the coupling efficiency at the input end. When the pressure reaches 4.5 bar, the calculated critical power of the Ar gas drops to 4 GW, which is comparable with the input pulse peak power of 4.3 GW. Thereafter, the transmission decreases rapidly. Considering the various features of the spectra and the transmission, we deem 3 bar to be the proper pressure.
In Fig. 5(a), we show a detailed spectrum (red solid line) for an input energy of 0.94 mJ at an Ar pressure of 3 bar. The measurement limitations of the spectrometer mean that the spectrum is clipped at shorter wavelengths. By fitting a fourth order super-Gaussian function (blue dashed line) to this spectrum, we determine the bandwidth as 300 nm in relation to the full width at half maximum (FWHM) of the spectrum. To the best of our knowledge, this is the broadest bandwidth ever obtained by a single stage gas filled HCF with millijoule level input energy near the 1 μm wavelength. In Fig. 4(b), we show the calculated shape of the FTL pulse, the duration of which is as short as 8.8 fs (FWHM).
Fig. 5 (a) Experimental spectrum of output pulse from HCF with 0.94 mJ input energy at 3 bar Ar pressure (red solid line). The blue dashed line shows the curve fitted by a 4th super Gaussian function. (b) Calculated FTL pulse shape.
In Fig. 6(a), we show the Yb:CaF2 based RA (black dot) and Ar filled HCF (red dot) output energy stability in 30 minutes. The energy fluctuations are 1.0% and 1.6% (root mean square, RMS) for RA and HCF, respectively. The increasing of the energy fluctuation for HCF is possibly due to the vibration of optical table and air flow, which decrease the coupling efficiency at the fiber input end. In Fig. 6(b), we show the HCF output spectral stability at Ar 3 bar pressure. Since the spectral broadening is sensitive to the pump energy, the spectral shape also fluctuates with the time.
Fig. 6 (a) Energy stability of Yb:CaF2 based RA (black dot) and Ar filled HCF (red dot). (b) Spectral stability under Ar 3 bar pressure.
In Fig. 7, we show the measured beam quality for 0.94 mJ input energy at 3 bar Ar pressure. The fact that the near field is effectively circular shows that only the fundamental mode has been excited. The calculated values of M2 are 1.2 and 1.1 in the x and y directions, respectively. This high beam quality will be important in future applications.
Fig. 7 Measured beam quality from HCF after re-collimation with a concave mirror. The inset shows the near and far fields. The calculated values of M2 are 1.2 and 1.1 in the x and y directions, respectively.
Dispersion compensation is necessary to demonstrate the compressibility of the spectrally broadened pulses. Because the minimum bandwidth of current commercially available chirped mirrors is only approximately 200 nm at 1 μm, we used a Dazzler pulse shaper (Fastlite Inc.) to compensate for dispersion of the spectrally broadened pulses. To avoid damaging the Dazzler, we use a neutral-density filter after the HCF to decrease the pulse energy. In Fig. 8, we show measurements taken at an Ar pressure of 3 bar using a Wizzler pulse measurer (Fastlite Inc.). In Fig. 8(a), we show the reconstructed spectrum (red solid line) and phase (blue dashed line). The spectrum is narrower than the one shown in Fig. 8(a) because the Dazzler transmission range is limited to 900–1200 nm. In Fig. 8(b), we show the measured pulse shape (red solid line) and the calculated FTL pulse shape (blue dashed line). The measured pulse duration of 12.1 fs (FWHM) is slightly larger than the FTL duration of 11.4 fs (FWHM). This compressed near FTL duration demonstrates that the output pulses could be compressed further to sub-10-fs once with an ultra-broadband dispersion compensation setup.
Fig. 8 Pulse dispersion compensated by Dazzler and measured by Wizzler: (a) reconstructed spectral intensity (red solid line) and phase (blue dashed line); (b) measured temporal intensity (red solid line) and calculated FTL pulse shape (blue dashed line).
5. Conclusion
We theoretically designed and experimentally achieved a single stage statically pressurized Ar filled HCF system that was capable of a 300 nm bandwidth high-quality beam of 0.5 mJ pulses. The calculated FTL pulse duration was as short as 8.8 fs. Dazzler was used to demonstrate pulse compressibility, and 12.1 fs pulses were obtained. Such ultra-broadband, high energy pulses represent the ideal front-end light source for a laser system with high repetition rate and high peak power.
Funding
Japan Society for the Promotion of Science (JSPS) KAKENHI Grants JP26287145, JP15K04696; Photon Frontier Network of the Ministry of Education, Culture, Sports, Science and Technology (MEXT).
Acknowledgment
The authors thank Dr. Ding Wang, Dr. Liwei Song, and Dr. Zhiyuan Huang for useful discussions.
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