180 mW, 1 MHz, 15 fs carrier-envelope phase-stable pulse generation via polarization-optimized down-conversion from gas-filled hollow-core fiber

Carrier-envelope phase stable (CEP) broadband sources¹ in the short-wavelength infrared (SWIR) and mid-infrared (MIR) ranges are crucial for many field-sensitive applications, such as in strong field physics^2–7 or field-resolved metrology.^8–15 CEP stable pulses can be generated by active stabilization of optical oscillators^16–18 or by passive stabilization techniques such as frequency downconversion.^19–21 Since oscillators generate pulses with low peak power, optical parametric amplification has been utilized to enhance the energy of the ultrashort pulses in these spectral regions.^22–26 However, parametric amplifiers require high-energy pump sources, which mostly operate at kilohertz repetition rates. The amplified pulses often exhibit additional phase jitter in their CEP, stemming from the need for interferometric stability between the pump and seed pulses.^27,28 Passive CEP stabilization based on intrapulse difference frequency generation (IPDFG) offers unparalleled stability and minimal CEP fluctuations, making it the preferred method for generating CEP-stable, octave-spanning pulses at megahertz repetition rates.

In IPDFG, down-converted passively CEP-stable pulses are generated through nonlinear frequency mixing of spectral components within a broadband pump pulse in a $χ(2)$ nonlinear crystal. Two types of phase-matching can be used to compensate for the phase velocity mismatch between the interacting beams. In type II phase-matching, the input pump and IPDFG pulses have orthogonal polarizations. On the contrary, in type I phase-matching, the input pump pulses are projected into both orthogonal axes of the nonlinear crystal. This projection compensates for the phase velocity mismatch between the high-frequency and low-frequency components of the pump, as well as the IPDFG pulses. Therefore, enhancing the conversion efficiency in type I phase-matching requires optimizing the projection of the pump's spectral components onto the crystal's orthogonal axes.²⁹ To meet this requirement, the optical axis of the nonlinear crystal can be rotated such that the crystal axes have an angle with respect to the linear polarization of the pump beam in the laboratory frame. In this case, the polarization of the newly generated IPDFG pulses has the same angle relative to the linearly polarized pulse in the laboratory frame, which poses a challenge for polarization-sensitive applications such as electro-optic sampling, spectroscopic ellipsometry, polarization spectroscopy, or optical parametric amplification.^30–36 Broadband half-wave plates provide an alternative for optimizing the spectral distribution of input pump pulses along the crystal axes. However, their performance with ultrashort pulses is restricted by uneven phase retardation over a broad bandwidth and additional material dispersion. These limitations cause temporal broadening of the pump pulses and reduce conversion efficiency.

Gas-filled hollow-core fibers (HCF) are widely utilized to create few-cycle ultrashort pulses at high peak power and megahertz repetition rates with a high polarization purity.^37,38 In capillaries or single-ring hollow-core fibers with an M-fold symmetry, where M indicates the number of tiny capillaries, the intrinsic birefringence is negligible. Therefore, the nonlinear propagation dynamics within the fiber should remain independent of the polarization state of the input pulses.³⁹ In this study, we leverage the inherent symmetry of HCF to address the challenge of optimizing the spectral intensity distribution in type I IPDFG. By employing a half-waveplate to adjust the polarization state of the narrowband input pulses entering a gas-filled HCF, we fine-tune the polarization of the near-single-cycle pulses generated within the HCF. This precise tuning enables more efficient frequency downconversion in subsequent stages. Our findings indicate that the effect of polarization rotation on the nonlinear dynamics within the fiber is minimal and does not alter the temporal duration of the generated near-single-cycle pulse. We demonstrate that enhancing the downconversion efficiency can be achieved by optimizing the polarization rotation of the input pump directed to the fiber. The field-resolved measurement of the IPDFG pulses confirms that this optimization does not affect the electric field of the generated IPDFG pulses.

The schematic of the setup used to generate and characterize IPDFG pulses is shown in Fig. 1. The front end was driven by a 1030 nm Yb:KGW amplifier with an average power of 20 W at 1 MHz repetition rate and a pulse duration of 255 fs. Single-ring HCFs offer low-loss, broadband guidance, and tunable dispersion. Therefore, two stages of gas-filled single-ring HCF were used for temporal compression of the 20 μJ pulses of the frontend. The first fiber stage comprised a 50 cm long HCF with a core diameter of 55 μm, filled with 15 bar of Argon. The dispersion of the gas-filled fiber was adjusted for spectral broadening based on self-phase modulation. A set of tailored dispersive mirrors was used to compensate for the −1800 fs² group-delay dispersion of the spectrally broadened pulses in the fiber. This resulted in the temporal compression of 20 μJ, 1 MHz, 255 fs laser pulses to 18.5 μJ, 25 fs pulses at full width at half maximum (FWHM). Afterward, the compressed pulses were sent to a second gas-filled HCF stage to generate near single-cycle pulses via soliton-effect self-compression. The second fiber stage included a 31 cm HCF, similar to the first stage, filled with 15 bar of helium. A set of tailored chirped mirrors were used to pre-compensate for the accumulated dispersion on the soliton compressed pulses due to propagation in the beam path after the fiber. The second HCF delivered 16.5 μJ, 1 MHz, 4.8 fs octave-spanning pulses. The system had an overall efficiency of 82% and a polarization extinction ratio of 98%. More details of the setup are presented in Ref. 15. 95% of the generated ultra-broadband pulses were used for an efficient and stable downconversion via IPDFG. The remaining 5% was used to characterize the generated IPDFG pulses via electro-optic sampling.

Bismuth borate (BiBO) crystal was chosen for frequency downconversion due to its wide transmission range from 286 to 2500 nm, high damage threshold, and large effective nonlinear coefficient. BiBO exhibits a higher nonlinear coefficient compared to other suitable crystals at this range, such as lithium triborate (LBO), beta barium borate (BBO), and potassium deuterium phosphate (KDP).⁴⁰ Numerical simulations were conducted in a simulation system for optical systems code (SISYFOS)⁴¹ to gain further insight into the phase-matching process. Both types of phase-matching were considered for downconversion of the octave-spanning spectrum in a 0.5 mm-thick BiBO crystal. In type I phase-matching, the polarization of the input pulse has to match the crystal's orthogonal axes. In this paper, we refer to these axes as “o” and “e” to represent ordinary and extraordinary crystal axes, respectively.

We used experimental input as a pump for the following simulation. To do so, the temporal profile of the output pulses from the second HCF stage was characterized by second-harmonic frequency-resolved optical gating (SH-FROG).⁴² The retrieved spectrum and temporal profile of the SH-FROG characterization were used as pump pulses for the IPDFG simulation. For simulating the type I phase-matching, a polarization ratio of 95%–5% (o-e) was assumed. Figures 2(a) and 2(b) compare the spectral bandwidth of the IPDFG pulses vs the phase-matching angle of $θ$ for type I and type II phase-matching. It is seen that the broadest spectral bandwidth is achieved at $θ$ = 11° for type I phase-matching and at $θ$ = 55° for type II phase-matching. The spectra of both phase-matching types at the optimized angles are shown in Fig. 2(c). Both spectra are normalized to the energy of the IPDFG pulses in each case, indicating a broader spectral bandwidth and higher gain in type I phase-matching than type II. Therefore, further investigation was performed on the type I phase-matching.

A one-dimensional simulation was performed to study the efficiency and bandwidth scaling of the IPDFG pulses in type I phase-matching. Figure 3(a) shows the IPDFG spectrum for type I phase matching at $θ$ = 11° vs various crystal thicknesses. The efficiency of the IPDFG process increases with the thickness of the crystal. However, for crystal thicknesses longer than 0.5 mm, the center of mass of the difference frequency spectrum shifts to higher frequencies, and the spectral intensity becomes a U-shape. This can be attributed to the temporal walk-off between the interacting pulses. Figures 3(b) and 3(c) show the group velocity of the pump and IPDFG pulses vs the crystal thickness, respectively. It is seen that complete temporal separation between the IPDFG pulses and o-pump occurs at 0.5 mm crystal thickness due to the different group velocities of the interacting pulses [see Fig. 3(d)].

Moreover, the input pump pulses have a temporal pedestal originating from the residual higher-order phase due to the dispersive mirrors and soliton self-compression in the fiber. On the one hand, the residual higher-order phase of the dispersive mirrors mainly affects the two limits of the input pump spectrum. Therefore, the IPDFG pulses are generated even after the temporal walk-off of the main interacting pulses at 0.5 mm crystal thickness. On the other hand, soliton self-compression causes the center of the pump spectrum to carry higher-order phases. These phases manifest as a temporal pedestal, leading to the generation of low-frequency wings in the IPDFG spectrum. Consequently, for crystal thicknesses greater than 0.5 mm, the spectrum becomes U-shaped.

The energy distribution among the orthogonal components of pump pulses in the crystal is crucial for maximizing the efficiency of difference frequency generation in type I phase-matching. This optimization relies on the principles of energy and momentum conservation. During the downconversion process, the energy of the high-frequency components of the o-pump decreases, as illustrated in Fig. 3(e). Conversely, the low-frequency components of the e-pump are amplified [Fig. 3(f)]. Therefore, a series of simulations have been conducted to investigate the impact of the polarization distribution of pump energy on the efficiency of the IPDFG in a 0.5 mm-thick type I BiBO crystal. The energy of the e-pump pulses was scaled from 0% to 100%, while the total energy of the pump pulses remained constant.

Figure 4(a) shows the generated IPDFG spectra at different pump polarization ratios. An ideal, dispersion-free broadband half-waveplate before the BiBO crystal is assumed in the simulation. The results show that the conversion efficiency peaks at an e-pump ratio of 25%. For extinction ratios higher than 40%, the efficiency and the spectral bandwidth of the IPDFG pulses decrease.

As discussed in the introduction, employing half-waveplates or rotating the crystal axes in the laboratory frame for optimizing IPDFG imposes constraints for polarization-sensitive measurement. Therefore, we took advantage of the fiber symmetry for ideal and dispersion-free tunning of the polarization state of the octave-spanning pump spectrum. A half-waveplate (Altechna 2-APW-L2-018C) was placed at the input of the second gas-filled HCF. The HCF output was focused to a beam size of 44 μm (FWHM) by a 6-inch focal length parabolic mirror, corresponding to 300  $TW/cm2$ peak intensity. A 0.5 mm-thick type I, BiBO crystal cut in the XZ plane and at a phase-matching angle of $θ$ = 11° was used for IPDFG. The crystal was positioned behind the focus to mitigate damage. Afterward, the IPDFG beam was collimated to a $1/e2$ beam diameter of 3.2 mm utilizing a 4-inch focal length parabolic mirror. A custom-designed broadband dichroic beam splitter (UFI BS2214-RC2) separated the pump and IPDFG beam. A custom-built double-angle chirped mirror compressor (UFI IR7202) with four reflections was used to compensate for the accumulated dispersion on the IPDFG pulses due to propagation in the BiBO crystal, refractive optics and air, yielding 15 fs (FWHM) CEP-stable pulses.

To optimize the orthogonal polarization states in the IPDFG process (extinction ratio), the half-waveplate positioned at the input of the second HCF stage was tuned, and the resulting average power was measured. Figure 4(b) shows the measured output power of the IPDFG vs various half-waveplate angles. The observed dip in power at half-waveplate angles between 18° and 30° is due to the presence of polarization-sensitive elements in the optical beam path of the frontend. This includes the chirped mirror compressor, which has a higher reflectivity for o-polarized light, and a pair of wedges, which is placed close to the Brewster angle in the beam path for fine-tuning of the dispersion. By replacing these elements with coated optics for both polarizations, a higher IPDFG efficiency is expected. Neglecting the losses inherent to the diagnostic line, an average output power of 75 mW was measured at a half-waveplate angle of 0°. The maximum output power of 180 mW was detected at a half-waveplate angle of 16°. This corresponds to a value more than double that recorded at 0°.

To verify that polarization tuning of the input pulses does not influence the dynamics of soliton self-compression, we analyzed the temporal profiles of the output pulses from the fiber at the two different half-waveplate angles. The half-waveplate in front of the second HCF stage was adjusted to 0° and 16° to generate two different polarization ratios. It was observed that the output power of the second HCF remained intact at both half-waveplate angles. Further, SH-FROG was employed to characterize the fiber's output pulses. Figures 5(a) and 5(b) show the retrieved temporal profiles and retrieved spectra of the octave-spanning output pulses from the second HCF at two half-waveplate angles of 0° and 16°. The measurements indicate that polarization tuning has a negligible impact on the envelope and spectrum of the fiber's output. This suggests that the soliton dynamic inside the fiber remains unaffected due to the negligible birefringence of the fiber.

Electro-optic sampling with a temporal resolution of 200 as was developed (for more details, see Ref. 15) to characterize the temporal profile of the generated IPDFG pulses. Figure 5(c) shows the field-resolved measurement of the IPDFG pulses at the two half-waveplate angles. It can be seen that while polarization tuning enhanced the amplitude of the IPDFG waveform, the temporal chirp of the generated pulses remains unchanged. Figure 5(d) shows the corresponding IPDFG spectra obtained via Fourier transformation of the time domain measurements.

Over recent decades, the generation of high-energy, high-power pulses has increasingly relied on spectral broadening in fibers or multi-pass compression. IPDFG stands out as a highly promising method for generating octave-spanning pulses in the SWIR and MIR spectral regions, with unparalleled CEP stability from these frontends. Type I phase-matching, in particular, is favored for its superior bandwidth and conversion efficiency, albeit it necessitates an optimized polarization distribution along the crystal axes.

In this work, we conducted a detailed numerical analysis to identify the optimal polarization distribution within type I BiBO crystals to generate octave-spanning, CEP-stable pulses in the SWIR region. Prior approaches primarily utilized broadband waveplates or involved altering the orientation of the crystal axes with respect to the laboratory frame for optimizing the downconversion efficiency. To circumvent the limitations presented by these methods, we have shown that in ultrashort pulse generation from gas-filled HCFs, the efficiency of IPDFG can be maximized by adjusting the polarization ratio of the narrowband pulses before spectral broadening in the fiber. By implementing a narrowband half-waveplate before the soliton compression fiber stage, we tuned the polarization of octave-spanning, near-single-cycle pulses for efficient IPDFG. Our findings indicate that the orientation of polarization relative to the fiber does not impact the soliton dynamics within the fiber. Therefore, the pulse duration and the spectrum of the near single-cycle pulses at the output of the fiber remain intact for different polarization ratios. Electro-optic sampling (EOS) with 200 as temporal resolution was employed to characterize the down-converted IPDFG pulses. Direct electric field sampling of the IPDFG pulses demonstrates that while the polarization rotation of the input pulses to the fiber enhances the IPDFG efficiency, the temporal and spectral profiles of the down-converted pulses remain similar. The highly sensitive electric field detection of the IPDFG pulses at hundreds of attosecond temporal resolutions demonstrates the CEP stability, reproducibility, and robustness of the developed system.

The approach discussed in this work is not only applicable to HCF systems but can be extended to other symmetrical systems like multi-pass geometries or multi-stage spectral broadening.^43–47 These results are particularly vital for broadband downconversion of high-power systems to overtone and fingerprint spectral regions, where the bandwidth and dispersion characteristics of waveplates present challenges, and in experiments demanding pure polarization in the eigenmodes of the laboratory frame.^48,49

We thank Gunnar Arisholm for his support in the numerical analysis presented in this work. This work was supported by research funding from the Max Planck Society.