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Highly-tunable, visible ultrashort pulses generation by soliton-plasma interactions in gas-filled single-ring photonic crystal fibers

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Abstract

Ultrashort laser pulses, featuring remarkable spectral tunability, are highly demanded for nonlinear light-matter interactions in a variety of molecules. Here, we report on the generation of soliton-plasma-driven ultrashort pulses with both bandwidth- and wavelength-tunability in the visible spectral region. Using He-filled single-ring photonic crystal fiber (SR-PCF), we demonstrate in the experiments that the spectral bandwidths of blueshifting solitons can be manipulated by adjusting the input pulse energy, gas pressure and core diameter of the SR-PCF, while the central wavelengths of these solitons can be continuously tuned over 200 nm. We found that in a large-core SR-PCF (24.6-µm core diameter), the bandwidths of blueshifting solitons can be effectively broaden to near 100 nm, pointing out the possibility of generating few-cycle, wavelength-tunable visible pulses using this set-up. In addition, we observed in the experiments that in a small-core SR-PCF (with a core diameter of 17 µm), the blueshifting solitons show little residual light near the pump wavelength, resulting in a high-efficiency frequency up-conversion process. These experimental results, confirmed by numerical simulations, pave the way to a new generation of compact, ultrashort light sources with excellent tunability at visible wavelengths, which may have many applications in the fields of time-resolved spectroscopy and ultrafast nonlinear optics.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Ultrashort laser pulses offer ideal tools for investigating basic physical and chemical properties in the ultrafast dynamic processes based on time-resolved spectroscopy (also called ultrafast spectroscopy) [1,2]. Ultrashort pump and probe pulses in a variety of spectral regions, including ultraviolet (UV) [3], visible and infrared wavelengths [4], are highly demanded in different time-resolved spectroscopy experiments. For example, ultrashort pulses in the visible region permit time-resolved capture of the excitionic relaxation and vibrational dynamics of molecules, since many molecules have absorption bands within this spectral range [5]. However, the central wavelength of the ultrashort laser pulses generated from the widely-used mode-locked Ti:Sapphire lasers is limited at around 800 nm.

For extending the spectral range of ultrashort pulses, some methods based on nonlinear frequency conversion, including optical parametric amplification (OPA) [6] and Raman-induced self-frequency redshift [79], have been successfully used for generating wavelength-tunable ultrashort pulses in the near-infrared (NIR) and mid-infrared (MIR) regions. These frequency down-conversion processes, making use of OPA and Raman effects, lead to the shift of the laser optical spectrum to longer wavelengths, limiting the applications of such schemes mostly at NIR and MIR wavelengths. The simplest method for high-efficiency frequency up-conversion of laser pulses is based on the harmonic generation. In the experiments, while second-harmonic and third-harmonic generation processes have been used for producing visible and UV pulses [10,11], high-order harmonic generation was able to push pulse wavelengths into the extreme-UV (10–100 nm) or even soft X-ray (0.01–10 nm) regions [12,13]. In practice the ultrashort pulses generated using these systems don’t, however, feature central-wavelength and spectral-bandwidth tunability, and the frequency-conversion efficiency generally decreases rapidly as the harmonic order increases.

Gas-filled hollow-core photonic crystal fibers (HC-PCFs) [1420] make it possible to generate continuously-wavelength-tunable ultrashort pulses at wavelengths shorter than those of the seed pulses [2123]. For example, nonlinear pulse propagation over a short length gas-filled HC-PCF in the presence of well-engineered higher-order dispersion can result in the phase-matched dispersive wave (DW) emission whose wavelength can be tuned across a wide range from near-UV (300–400 nm) to deep-UV (200–300 nm) or even to vacuum-UV (100–200 nm) region [2429]. In another scheme, soliton-plasma interactions can lead to ionization-induced spectral blueshift of the seed pulses whose central wavelength can be adjusted in the visible (400–760 nm) spectral range [30].

Recently, we demonstrated theoretically and experimentally, that in a short length of gas-filled single-ring photonic crystal fiber (SR-PCF), the central wavelengths of soliton-plasma-driven blueshifting solitons can be continuously tuned over hundreds of nanometers in the visible spectral region through adjusting the pulse energy launched into the fiber, while maintaining a high energy-conversion efficiency [31,32]. However, the simultaneous tuning of both the spectral bandwidths and central wavelengths of blueshifting solitons have not been investigated so far in gas-filled HC-PCFs. Here, we investigate comprehensively the soliton blue-shifted effect driven by soliton-plasma interactions in the gas-filled SR-PCF. The experimental results supported by numerical simulations show that both the central wavelengths and spectral bandwidths of the blueshifting solitons can be manipulated through adjusting the input pulse energy, gas pressure and the core diameter of the SR-PCF. In particular, we report that the use of a large-core SR-PCF allows broadening of the wavelength-tunable visible ultrashort pulses to near 100-nm bandwidths, pointing out the possibility of generation of few-cycle visible pulses. Moreover, we found that in a small-core SR-PCF, within a certain parameter range the blueshifting solitons show surprisingly little residual light at the pump wavelength, leading to a high-efficiency frequency up-conversion. The results presented here provide a deeper insight into the soliton-plasma-driven nonlinear process in gas-filled HC-PCFs, and the highly-tunable, ultrashort light source in the visible region may have many applications in time-resolved spectroscopy for measuring excitionic relaxation and vibrational dynamics of molecules.

2. Experimental set-up

The experimental set-up, including the pulse-compression stage and soliton stage, is shown in Fig. 1(a). In the pulse-compression stage, the ∼0.3-mJ and ∼45-fs pulses from the Ti:Sapphire laser system were first coupled into the 1-m-long hollow-core fiber (HCF) by using a concave mirror with a focal length of 1 m. The spectrum of the pulses was broadened in the HCF filled with ∼0.2-bar Ar gas and with a core diameter of 250 µm via self-phase modulation (SPM) effect. The HCF was in a gas cell, and the input and output ends of the gas cell were both sealed with 0.5-mm-thick uncoated fused silica (FS) windows, which can support a few bar gas pressure. In addition, these two windows were both fixed at the Brewster angle of ∼56° to decrease the light reflection. The pulse transmission out of HCF was measured to be ∼63% (corresponding to ∼190 µJ). A pair of negatively chirped mirrors (LAYERTEC GmbH) introduced a group delay dispersion (GDD) of -40 fs2 per bounce were used to compensate the positive chirp of the output pulses.

 figure: Fig. 1.

Fig. 1. (a) Experimental set-up includes the two stages: (I) Pulse-compression stage and (II) Soliton stage. FSW, fused silica window; HWP, half-wave plate; WGP, wire grid polarizer; MFW, magnesium fluoride (MgF2) window. (b) Scanning electron micrograph of the SR-PCF with 24.6-µm core diameter and 215-nm wall thickness. (c) Measured (red solid line) and simulated (green solid line) fiber losses of the fundamental mode HE11 of the SR-PCF, calculated by the Bouncing-ray model. (d) Simulated dispersion of the SR-PCF filled with 12-bar He gas using the empirical formulae (dark-orange solid line) and the MS capillary model (dark-purple solid line). In both (c) and (d), the light gray bars indicate the resonant spectral regions of the SR-PCF. (e)–(g) Same as in (b)–(d) except for the core diameter of 17 µm and wall thickness of 132 nm. In addition, the simulated dispersion in (g) is calculated at the 13.1-bar He gas.

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In the soliton stage, two pairs of negatively chirped mirrors (Thorlabs) with -54 fs2 GDD per bounce were used to pre-compensate the dispersion induced by the optics before the SR-PCF. The pulse energy launched into the SR-PCF was controlled by a coated half-wave plate and a wire grid polarizer (Thorlabs), which achieves the energy-tunable range of about 0.1∼18 µJ. The pulses, measured to be ∼16 fs [full width at half maximum (FWHM)] through a home-built second-harmonic-generation frequency-resolved optical gating (SHG-FROG), were coupled into the He-filled SR-PCF using coated plano-convex lens with focal lengths of 10 cm and 7.5 cm for different core diameters. The input and output ends of the gas cell were sealed with a 1.5-mm-thick coated FS and a 1.5-mm-thick uncoated magnesium fluoride (MgF2) windows, respectively. The pulses out of the SR-PCF were collimated by the second plano-convex lens and launched into an integrating sphere connected with a spectrometer (Ocean Optics HR2000+).

In the experiments, we measured the input pulse energy before the plano-convex lens as the initial pulse energy launched into the SR-PCF, since both the lens and window before the gas cell have high-transmission coatings. At a certain input pulse energy (≤1 µJ, in order to decrease the plasma-induced energy loss), we measured the in-coupling efficiency of the system, which is defined as the ratio of the pulse energy out of the SR-PCF to the input pulse energy. Here we consider the energy loss due to the reflection of the uncoated MgF2 window at the output port of gas cell. At input pulse energy of 1 µJ, the coupling efficiency was measured to be ∼72% (56%) after propagating a 17-cm-long SR-PCF with a core diameter of 24.6 µm (17 µm). We believe that these relatively-low coupling efficiencies are mainly due to the mismatch between the focused beam profile and the confined mode profile in the SR-PCF at the input port of the fiber. In addition, at high pulse-energy levels gas-ionization effect at the entrance of the fiber can also degrade the coupling efficiency. In practice, we observed lower coupling efficiencies at higher input pulse energies, which we think is induced by the stronger gas-ionization effect at the fiber input port.

In the experiments, we employed two types of SR-PCF. One is six thin-walled capillaries arranged around a hollow core, its scanning electron micrograph (SEM) is shown in Fig. 1(b). This SR-PCF has a core diameter of 24.6 µm and a wall thickness of 215 nm. Figure 1(c) shows the measured (red solid line) and simulated (green solid line) fiber losses calculated by the recently-developed Bouncing-ray (BR) model [33]. The BR model can describe the confinement loss and the UV material absorption in the silica. In addition, an overall adjusted factor used in the BR model is employed to match the finite-element method (FEM) data. The light gray bars represent the first and second resonant spectral regions due to the resonance between the core modes and cladding modes. The SR-PCF presents a low fiber loss of ∼0.1 dB/m in the wavelengths ranging from ∼500 nm to 1000 nm. In Fig. 1(d) we plot the simulated dispersion of the SR-PCF filled with 12-bar He gas, calculated using the empirical formulae (dark-orange solid line) [34] and Marcatili-Schmeltzer (MS) capillary model (dark-purple solid line) [35]. It should be noted that the empirical formulae have been proven to be valid and reliable for calculating the dispersion curve of SR-PCF in both the anti-resonant and resonant regions. While providing acceptable accuracy of dispersion values, the empirical formulae used in our simulations have much better time-consuming performance than the FEM.

The second type of SR-PCF consisting of seven thin-walled capillaries around a hollow core has a 17-µm core diameter and a 132-nm wall thickness [36]. Figures 1(e)–1(g) show its SEM, fiber loss and dispersion at 13.1-bar He gas, respectively. Note that the SR-PCF provides broad transmission bands with fiber loss less than 1 dB/m in the wavelength range from ∼350 nm to ∼850 nm. In addition, there are some fast oscillations between ∼850 and 1000 nm. It should be noted that these fast oscillations are not genuine attenuation features but simply from cutback measurements. The attenuation was calculated by comparing two transmission spectra in cutback measurements, in which only noise (no useful signal) was detected in the long fiber length near the band edge (∼850–1000 nm). The details of the fiber-loss characterization refer to this work [36]. Moreover, when empirical formulae were used in the simulations, the effect that the effective radius of optical mode varies with wavelength has been considered [34,37]. Therefore, the simulated results of empirical formulae are much more precise than the results of the simple MS capillary model, especially at longer wavelengths. This is the reason that a large deviation between these simulation curves is observed in Fig. 1(g).

3. Bandwidth- and wavelength-tunable blueshifting solitons

The underlying mechanism of the blueshifting soliton in a gas-filled SR-PCF can be understood as a result of soliton-plasma interactions [2123,30]. First of all, the combined effects of SPM and waveguide-induced anomalous dispersion lead to soliton self-compression process, resulting in few-cycle or even shorter pulse and thereby rapidly increasing the pulse peak intensity. The gas ionization due to the ultrahigh light intensity then leads to the fast accumulation of plasma which imparts a strong phase modulation on the pulse, driving a spectral blueshift of the pulse.

Figures 2(a) and 2(b) show the normalized spectral intensities out of the SR-PCF as a function of input pulse energy at different gas pressures of 12 bar and 14 bar, respectively. The SR-PCF used in Figs. 2(a) and 2(b) was filled with He gas, and it has a core diameter of 24.6 µm and a fiber length of 17 cm. The red solid lines represent the filtered spectra through the 40-nm FWHM bandpass filters (Thorlabs) centered at different central wavelengths including 650 nm (red letters A and C) and 600 nm (red letters B and D), and the corresponding filtered pulses show good near-field beam profiles out of the SR-PCF, as shown in the second column. In Fig. 2(a), the spectral blueshift is enhanced as input pulse energy increases. Especially for the input pulse energies of 6.6 µJ and 7.1 µJ, when the blueshifting solitons are close enough to the first resonant spectral region of SR-PCF (marked as light gray bars), we can observe the emission of narrow-band spectral peak near the 470 nm, which results from the phase-matched nonlinear processes, including four-wave mixing and DW generation [38].

 figure: Fig. 2.

Fig. 2. The normalized spectral intensities (on the linear scale) after propagating a 17-cm-long SR-PCF (24.6-µm core diameter) filled with 12-bar He (a) and 14-bar He (b) at different input energies. In both (a) and (b), the light gray bars point out the first resonant spectral region of the SR-PCF. (c) Same as in (a) and (b), but for 17-µm core diameter and 13.1-bar He gas in the experiment. A–G denote the near-field output beam profiles after 17-cm-long He-filled SR-PCF using the 40-nm FWHM bandpass filters centered at different central wavelengths 700 nm (E), 650 nm (A, C, F), and 600 nm (B, D, G). The filtered normalized spectra in (a)–(c) are both marked as red solid lines.

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Figure 3(a) plots the measured spectral widths at FWHM (blue circle line) and the central wavelengths (red square line) of the blueshifting solitons, respectively. The spectral widths begin to increase with input pulse energy and then decrease at pulse energy of 6.6 µJ, but the spectral widths both lie in the range between 80 and 100 nm. While the central wavelengths of the blueshifting solitons move quickly to the short-wavelength region when gradually increasing input pulse energy, and the maximum wavelength shift is over 200 nm. When the fiber was filled with 14-bar He gas, the normalized spectral intensities in Fig. 2(b) are similar to that in Fig. 2(a). However, there are two differences between Figs. 2(a) and 2(b) based on the evolutions of the blueshifting solitons. First, tuning the central wavelengths of the blueshifting solitons to the same position, the required input pulse energy in Fig. 2(b) is lower due to a higher gas pressure. For example, with the same central wavelength of the blueshifting soliton at ∼580 nm, the required input pulse energy 6.4 µJ in Fig. 2(b) is lower than 6.6 µJ in Fig. 2(a). Second, the spectral widths of the blueshifting solitons in Fig. 2(b) are mostly larger than that in Fig. 2(a), varying at ∼100 nm. These two differences result from the different gas pressures of 12 bar and 14 bar [corresponding to the zero dispersion wavelengths (ZDWs) of 289 nm and 298 nm], leading to various propagation dynamics.

 figure: Fig. 3.

Fig. 3. (a)–(c) Measured spectral widths (FWHM) (blue and green circle lines) and central wavelengths (red and dark-orange square lines) of the blueshifting solitons in Figs. 2(a)–2(c) as a function of input pulse energy. The corresponding soliton order is shown on the upper axis, and the ZDWs in Figs. 2(a)–2(c) are 289 nm, 298 nm, and 251 nm, respectively.

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In the experiments, we employed the second type of SR-PCF with core diameter of 17 µm at 13.1-bar He gas. Figure 2(c) shows the normalized spectral evolutions after propagating a 17-cm-long SR-PCF at different input pulse energies in the range of 3.6 µJ to 7.7 µJ. The filtered spectra and their beam profiles are marked as red solid lines and letters using different 40-nm FWHM bandpass filters centered at 700 nm (E), 650 nm (F) and 600 nm (G), respectively. Note that the blueshifting solitons generated in the 17-µm core SR-PCF show little residual light near the pump wavelength of 800 nm, resulting in a high-efficiency frequency-conversion process. This can be understood as a result of adiabatic soliton compression, we will explain it in the section of discussion. In addition, the core-cladding resonance has little effect on the pulse propagation, since the resonant wavelength of SR-PCF is far away from the visible spectral region due to the small wall thickness of 132 nm [see Figs. 1(f) and 1(g)]. As a result, the central wavelengths (dark-orange square line) of the blueshifting solitons can be continuously tuned over hundreds of nanometers, as shown in Fig. 3(c). These spectral widths are much smaller than that in Figs. 3(a) and 3(b) due to various propagation dynamics. The blueshifting solitons are generated due to plasma-induced phase modulation, and their frequency shifts can be expressed as $\Delta \omega (z,t)\sim {\partial _t}\rho (z,t)$ [30], where $\rho$ is the plasma density at time of t and propagation position of z. Both the plasma density in the fiber and soliton self-compressed pulse duration are dependent on the soliton dynamics, which are quite sensitive to two parameters: the ZDW and the soliton order. In general, the ZDW is dependent on the core diameter of the fiber, gas type and gas pressure, while the soliton order on the pulse energy and gas pressure. Here, the results shown in Figs. 3(a) and 3(b) were generated in different gas-filled SR-PCFs with different ZDWs of 289 nm and 298 nm respectively, while the ZDW is 251 nm for the case shown in Fig. 3(c). We think that these large ZDW differences are mostly probably the reasons that result in the large differences of spectral widths for different cases.

4. Numerical simulations

In order to investigate the pulse propagation along the fiber and understand the experimental results well, we numerically simulated the pulse propagation based on a single-mode unidirectional field equation [39]. The full-field equation can be expressed as [31,40]:

$${\partial _z}\tilde{E}(z,\omega ) = i[{\beta (\omega ) - {\omega \mathord{\left/ {\vphantom {\omega {{v_p}}}} \right.} {{v_p}}}} ]\tilde{E}(z,\omega ) - {{\alpha (\omega )\tilde{E}(z,\omega )} \mathord{\left/ {\vphantom {{\alpha (\omega )\tilde{E}(z,\omega )} 2}} \right.} 2} + {{i{\omega ^2}{{\tilde{P}}_{NL}}(z,\omega )} \mathord{\left/ {\vphantom {{i{\omega^2}{{\tilde{P}}_{NL}}(z,\omega )} {2{c^2}{\varepsilon_0}\beta (\omega )}}} \right.} {2{c^2}{\varepsilon _0}\beta (\omega )}},$$
where $\tilde{E}(z,\omega )$ is the carrier-resolved full field in the spectral domain, $\omega$ is the angular frequency in rad.s−1, and ${v_p}$ is the group velocity at the pump frequency. $\beta (\omega )$ is the propagation constant, which is calculated by the MS capillary model or the empirical formulae when the core-cladding resonance effect is considered. The fiber loss $\alpha (\omega )$ is simulated by the BR model, c is the speed of light in vacuum, ${\varepsilon _0}$ is the vacuum permittivity, and ${\tilde{P}_{NL}}(z,\omega )$ describes the nonlinear response. The nonlinear effect can be expressed as a combination of Kerr and plasma effects of noble gas. In the time domain, it is given by:
$${P_{NL}}(z,t) = {\varepsilon _0}{\chi ^{(3)}}E{(z,t)^3} + \int_{ - \infty }^t {\frac{{\partial \rho (z,t^{\prime})}}{{\partial t^{\prime}}}} \frac{{{U_i}}}{{E(z,t^{\prime})}}dt^{\prime} + \frac{{{e^2}}}{{{m_e}}}\int {\int_{ - \infty }^t {\rho (z,t^{\prime})E(z,t^{\prime})dt^{\prime}dt^{\prime}} } ,$$
where ${\chi ^{(3)}}$ is the third-order nonlinear susceptibility, $E(z,t)$ is the electric field in the time domain, ${U_i}$ is the ionization potential of the gas, e is the electronic charge, and ${m_e}$ is the mass of an electron. The first term in the right-hand side of Eq. (2) describes the Kerr effect, the rest two terms indicate the loss of pulse energy due to the ionization process and the variation of the refractive index created by the free electrons, respectively. The plasma density variation can be expressed as [41]:
$${\partial _t}\rho = W(I)({\rho _{nt}} - \rho ) + {{\sigma \rho I} \mathord{\left/ {\vphantom {{\sigma \rho I} {{U_i}}}} \right.} {{U_i}}} - f(\rho ),$$
where I is the intensity of laser pulses, W is the optical-field-induced ionization rate, ${\rho _{nt}}$ is the neutral gas density, and $\sigma$ is the cross section describing the process of the collisional ionization. The function $f(\rho )$ is used to describe the process of electron recombination, and it can be neglected in the simulations as the recombination time of ionized noble gas is much longer than the femtosecond pulse. The Perelomov-Popov-Terent’ev model [42], modified with the Ammosov-Delone-Krainov coefficients [43], was used to calculate the ionization rate. It should be noted that the maximum peak power of the self-compressed pulses is calculated to be ∼2.6 GW, which is much smaller than the minimum critical power of self-focusing effect (∼31.9 GW, calculated using ${{{P_{cr}} = \lambda _0^2} \mathord{\left/ {\vphantom {{{P_{cr}} = \lambda_0^2} {2\pi {n_0}{n_2}}}} \right.} {2\pi {n_0}{n_2}}}$ [44], where ${\lambda _0}$ is the central wavelength of pump pulses, ${n_0}$ and ${n_2}$ are the linear and nonlinear refractive index, respectively). In addition, in the simulations the maximum ionization fraction is only ∼0.04% due to the high ionization potential (∼24.59 eV) of the He gas. Therefore, neither the self-focusing nor plasma-induced defocusing effect is included in this propagation model. In the simulations, we used 800-nm and 20-fs Gaussian-shape pulses as the input. The 20-fs pulse duration was used to match the duration of pulses launched into SR-PCF in the experiments, which is slightly broadened from 16 fs by some optics before the SR-PCF, for example the plano-convex lens and FS window.

To investigate the influence of the core diameter, gas pressure and input pulse energy on the bandwidths of the blueshifting solitons, we plot the simulated spectral evolutions out of a 17-cm-long SR-PCF filled with He gas, as shown in Figs. 4(a)–4(d). In the simulations, the fiber loss was calculated by BR model and the dispersion was simulated by MS capillary model [Fig. 4(a)] or the empirical formulae [Figs. 4(b)–4(d)]. Figures 4(a) and 4(b) show the spectral evolutions as a function of the core diameter of SR-PCF at gas pressure of 8 bar. In our simulations, we adjusted the input pulse energy at different fiber core diameters to ensure that the central wavelengths of the blueshifting solitons [marked as (i)] were always at ∼600 nm. By doing this, we can easily study the influence of fiber core diameter on pulse spectral width when the value of the spectral blueshift was maintained at 200 nm (800 nm - 600 nm). Note that the spectral evolutions in Fig. 4(a) are very similar to that in Fig. 4(b) as the resonant spectral region is far away from the pump wavelength. The difference between Fig. 4(a) and Fig. 4(b) is the emission of narrow-band spectral peak near 300 nm [marked as (ii)] due to the wall thickness set at 138 nm. Figures 4(c) and 4(d) show the spectral evolutions versus gas pressure and input pulse energy, respectively. The SR-PCFs used in Figs. 4(c) and 4(d) have the same core diameter of 20 µm but different input pulse energy and gas pressure. In Fig. 4(c), the input pulse energy was set at 5 µJ, while in Fig. 4(d) the gas pressure of 8 bar was used. Note that their spectral evolutions show the similar behaviors, which can be explained by the fact that increasing the pulse energy is equivalent to increasing the gas pressure to some extent. The white circle lines in Figs. 4(a)–4(d) show the maximum plasma density ${\rho _{\max }}$ within the fiber as the function of input energy or gas pressure. It should be noted that the magnitude of the plasma density generally determines the degree of spectral blueshift [see Figs. 4(c) and 4(d)], but the soliton self-compressed pulse duration is also an important influence. In addition, we also plot the normalized spectral intensities (on the linear scale) as the function of fiber-core diameter, gas pressure and input pulse energy, corresponding to Figs. 4(b)–4(d), respectively, as shown in Fig. 5.

 figure: Fig. 4.

Fig. 4. Simulated spectral evolutions after a 17-cm-long SR-PCF filled with He gas, calculated using the MS capillary model (a) and the empirical formulae [(b), (c) and (d)]. In simulations the fiber loss is calculated by the BR model, and the wall thickness is set at 138 nm when the core-cladding resonance is considered. (i) and (ii) indicate the blueshifting soliton and the emission of narrow-band spectral peak, respectively. (a) and (b) The spectral evolutions as a function of the core diameter of the SR-PCF filled with 8-bar He, and the peaks of the blueshifting solitons are both centered at 600 nm through adjusting input pulse energy. (c) The spectral evolutions with respect to gas pressure in the SR-PCF with 20-µm core diameter at the input energy of 5 µJ. (d) The spectral evolutions versus input pulse energy using the 20-µm core diameter and 8-bar He gas. The white circle lines in (a)–(d) indicate the maximum plasma density as the function of input energy or gas pressure.

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 figure: Fig. 5.

Fig. 5. The normalized spectral intensities (on the linear scale) obtained from Figs. 4(b)–4(d) as the function of core diameter (a), gas pressure (b) and input pulse energy (c).

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The spectral widths (FWHM) of the blueshifting solitons in Figs. 6(a)–6(c) are calculated from Figs. 4(b)–4(d). We can see that the variations of core diameter of SR-PCF, gas pressure and input pulse energy can effectively tune the spectral widths of the blueshifting solitons. In particular, the use of a large-core SR-PCF (corresponding to a large ZDW) can significantly increase the bandwidths of the blueshifting solitons compared to the use of high gas pressure and input energy. For example, in Fig. 6(a), the blueshifting soliton shows a ∼200-nm bandwidth when the 36-µm core diameter (corresponding to the ZDW of 312 nm) was used in the simulation, while in Fig. 6(b) the maximum bandwidth is ∼121 nm at the gas pressure of 8.6 bar, and in Fig. 6(c) the maximum bandwidth is ∼115 nm at the input pulse energy of 5.4 µJ. These numerical results are in good agreement with the experimental results shown in Figs. 2 and 3, and demonstrate that both the central wavelengths and spectral bandwidths of the blueshifting solitons can be manipulated through adjusting the core diameter of the SR-PCF, gas pressure and input pulse energy.

 figure: Fig. 6.

Fig. 6. The spectral widths (FWHM) (left axis) calculated from Figs. 4(b)–4(d) as the function of core diameter (a), gas pressure (b), and input energy (c), respectively. The corresponding soliton order and ZDWs are shown on the right or upper axis of Fig. 6.

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5. Discussions

As discussed above, when a large-core SR-PCF (24.6-µm core diameter) was used in the experiments, the bandwidths of the blueshifting solitons can be efficiently enhanced at higher gas pressure. As shown in Fig. 3(b), for input pulse energies of 5.9 µJ and 6.2 µJ, the blueshifting solitons centered at ∼600 nm show bandwidths as broad as ∼100 nm, which can support in theory sub-6-fs Fourier-transform-limited (FTL) pulse durations. Moreover, the simulation results show that the bandwidths of the blueshifting solitons can be further increased through increasing the core diameter of the SR-PCF. As shown in Fig. 6(a), when the core diameter of the SR-PCF is increased to 36 µm, the blueshifting solitons have broader spectral widths of ∼200 nm at the central wavelength of ∼600 nm, corresponding to sub-3-fs pulse durations.

Thanks to the large tuning ranges of both the central wavelength and spectral bandwidth of the output pulses, highly-tunable light sources at visible wavelengths can be easily generated through the cooperation of this system with a few optical filters with properly-designed spectral performances. The filtered light beams can promise good beam profiles, which has been experimentally confirmed [see the middle panel (marked using letters A-G) in Fig. 2]. Here, we would like to mention that when the resonant wavelengths of the SR-PCF lie close to the pump wavelength, the core-cladding resonance may have a strong effect on the blueshifting solitons, which could strongly influence the spectral performance of this system. However, in practice the wall thickness of the SR-PCF can be adjusted so as to shift its resonance frequency far away from the pump wavelength, minimizing the resonance-related energy coupling. It should be noted that it is difficult to fabricate SR-PCF with a large core diameter while maintaining relatively-thin walls. We think some methods such as wall etching with HF acid could be used in the future to reduce the wall thickness of the large-core SR-PCF without increasing the difficulty in fiber fabrication.

Furthermore, when a small-core SR-PCF (17-µm core diameter) was used in the experiments, as shown in Fig. 2(c) we observed that within a certain parameter range the blueshifting solitons show little residual light at the pump wavelength, leading to a high frequency-conversion efficiency. This phenomenon could be explained using the theory of adiabatic soliton compression (the soliton order is usually maintained close to 1 during the pulse propagation), even though the pulse energy cannot be conserved due to ionization-induced optical loss [23,45]. We think that the increasing central frequencies of the solitons over propagation result in the fact that the blueshifting solitons experience a decreasing group velocity dispersion and simultaneously an increasing nonlinear coefficient as their frequencies increase, which counterbalances the ionization-induced optical loss, leading to almost unchanged soliton order of ∼1. The detailed dynamics during such adiabatic soliton compression process need further investigation.

6. Conclusions

In conclusion, we experimentally and theoretically demonstrate the soliton-plasma-driven bandwidth- and wavelength-tunable visible ultrashort pulses generated in a short length of He-filled SR-PCF. We found that the bandwidths of the wavelength-tunable blueshifting solitons can be manipulated through adjusting the input pulse energy, gas pressure and core diameter of the SR-PCF. In particular, in a large-core SR-PCF (24.6-µm core diameter) the bandwidths of the blueshifting solitons can be effectively enhanced to near 100-nm bandwidths. While in a small-core SR-PCF (17-µm core diameter), we observed that the blueshifting solitons show little residual light near the pump wavelength, leading to a high-efficiency frequency up-conversion process, which could be understood as adiabatic soliton compression. The experimental results demonstrated here pave the way to develop highly-tunable broadband ultrashort laser sources in the visible region, which are very useful in studies of molecular dynamics based on pump-probe measurements.

Funding

Program of Shanghai Academic Research Leader (18XD1404200); International S&T Cooperation Program of China (2016YFE0119300); Strategic Priority Research Program of the Chinese Academy of Sciences (CAS) (XDB16030100); Major Project Science and Technology Commission of Shanghai Municipal (STCSM) (2017SHZDZX02).

Acknowledgments

We would like to thank Dr. Meng Pang for his helpful discussions and suggestions, which are really helpful for us to improve the quality of our manuscript.

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Figures (6)

Fig. 1.
Fig. 1. (a) Experimental set-up includes the two stages: (I) Pulse-compression stage and (II) Soliton stage. FSW, fused silica window; HWP, half-wave plate; WGP, wire grid polarizer; MFW, magnesium fluoride (MgF2) window. (b) Scanning electron micrograph of the SR-PCF with 24.6-µm core diameter and 215-nm wall thickness. (c) Measured (red solid line) and simulated (green solid line) fiber losses of the fundamental mode HE11 of the SR-PCF, calculated by the Bouncing-ray model. (d) Simulated dispersion of the SR-PCF filled with 12-bar He gas using the empirical formulae (dark-orange solid line) and the MS capillary model (dark-purple solid line). In both (c) and (d), the light gray bars indicate the resonant spectral regions of the SR-PCF. (e)–(g) Same as in (b)–(d) except for the core diameter of 17 µm and wall thickness of 132 nm. In addition, the simulated dispersion in (g) is calculated at the 13.1-bar He gas.
Fig. 2.
Fig. 2. The normalized spectral intensities (on the linear scale) after propagating a 17-cm-long SR-PCF (24.6-µm core diameter) filled with 12-bar He (a) and 14-bar He (b) at different input energies. In both (a) and (b), the light gray bars point out the first resonant spectral region of the SR-PCF. (c) Same as in (a) and (b), but for 17-µm core diameter and 13.1-bar He gas in the experiment. A–G denote the near-field output beam profiles after 17-cm-long He-filled SR-PCF using the 40-nm FWHM bandpass filters centered at different central wavelengths 700 nm (E), 650 nm (A, C, F), and 600 nm (B, D, G). The filtered normalized spectra in (a)–(c) are both marked as red solid lines.
Fig. 3.
Fig. 3. (a)–(c) Measured spectral widths (FWHM) (blue and green circle lines) and central wavelengths (red and dark-orange square lines) of the blueshifting solitons in Figs. 2(a)–2(c) as a function of input pulse energy. The corresponding soliton order is shown on the upper axis, and the ZDWs in Figs. 2(a)–2(c) are 289 nm, 298 nm, and 251 nm, respectively.
Fig. 4.
Fig. 4. Simulated spectral evolutions after a 17-cm-long SR-PCF filled with He gas, calculated using the MS capillary model (a) and the empirical formulae [(b), (c) and (d)]. In simulations the fiber loss is calculated by the BR model, and the wall thickness is set at 138 nm when the core-cladding resonance is considered. (i) and (ii) indicate the blueshifting soliton and the emission of narrow-band spectral peak, respectively. (a) and (b) The spectral evolutions as a function of the core diameter of the SR-PCF filled with 8-bar He, and the peaks of the blueshifting solitons are both centered at 600 nm through adjusting input pulse energy. (c) The spectral evolutions with respect to gas pressure in the SR-PCF with 20-µm core diameter at the input energy of 5 µJ. (d) The spectral evolutions versus input pulse energy using the 20-µm core diameter and 8-bar He gas. The white circle lines in (a)–(d) indicate the maximum plasma density as the function of input energy or gas pressure.
Fig. 5.
Fig. 5. The normalized spectral intensities (on the linear scale) obtained from Figs. 4(b)–4(d) as the function of core diameter (a), gas pressure (b) and input pulse energy (c).
Fig. 6.
Fig. 6. The spectral widths (FWHM) (left axis) calculated from Figs. 4(b)–4(d) as the function of core diameter (a), gas pressure (b), and input energy (c), respectively. The corresponding soliton order and ZDWs are shown on the right or upper axis of Fig. 6.

Equations (3)

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z E ~ ( z , ω ) = i [ β ( ω ) ω / ω v p v p ] E ~ ( z , ω ) α ( ω ) E ~ ( z , ω ) / α ( ω ) E ~ ( z , ω ) 2 2 + i ω 2 P ~ N L ( z , ω ) / i ω 2 P ~ N L ( z , ω ) 2 c 2 ε 0 β ( ω ) 2 c 2 ε 0 β ( ω ) ,
P N L ( z , t ) = ε 0 χ ( 3 ) E ( z , t ) 3 + t ρ ( z , t ) t U i E ( z , t ) d t + e 2 m e t ρ ( z , t ) E ( z , t ) d t d t ,
t ρ = W ( I ) ( ρ n t ρ ) + σ ρ I / σ ρ I U i U i f ( ρ ) ,
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