Temporally tailored optical pulse profiles have emerged as critical enablers for enhancing the efficiency of optical communications and laser-matter interactions, establishing optical arbitrary waveform generators (OAWGs) as indispensable tools in fields such as optical communications, laser micromachining, and high-energy-density physics (HEDP). In these domains, precisely shaped pulses with exceptional temporal resolutions and prolonged record lengths are highly sought after for their potential to enable breakthroughs. Contemporary OAWG implementations predominantly utilize electrical arbitrary waveform generators integrated with electro-optical intensity modulators, achieving pulse shaping durations exceeding 100 ns. An emerging semiconductor optical amplifier (SOA)-based intensity modulation architecture [1], designed for high-power laser systems, has demonstrated equivalent long-duration capabilities. However, these approaches are limited by temporal resolution constraints ranging from approximately 100 ps to multiple nanoseconds. The ongoing quest for enhanced resolution OAWGs has driven technological innovations including 4f spectral shapers, acousto-optic programmable dispersive filters (AOPDFs) [2,3], and time domain telescopes [4]. While achieving remarkable temporal resolutions from picosecond to femtosecond regimes, these solutions exhibit inherent limitations in maximum achievable record lengths. Chirped pulse spectral shaping techniques [5,6] can provide shaped pulses with record lengths up to a few nanoseconds while preserving a reasonable resolution on the order of tens of picoseconds. An innovative method known as space-time induced linearly encoded transcription for temporal optimization (STILETTO) [7–9] represents a significant advancement, delivering single-mode outputs with picosecond (∼1ps) resolution and extended record length (>600ps) through adaptive closed-loop optimization. Nevertheless, residual chirp in output pulses continues to impose operational limitations on system flexibility. Additionally, pulse scaling transformations via time imaging [10] demonstrate potential for further enhancing either the temporal resolution or record length of existing methods.

A pulse shaping method capable of simultaneously achieving high resolution, extended record length, and chirp cancellation holds significant promise for future applications. Chirp-free pulse sequences are essential for various applications because they reduce the detrimental dispersion effects on pulses and exhibit higher efficiency in optical amplification and harmonic frequency conversion. By precisely controlling the dispersion within the pulse shaping system, it is feasible to achieve chirp cancellation for pulse sequences, ensuring that each part of the pulse maintains a consistent central wavelength. Pulse train replicators [11,12] provide a simple method for generating chirp-free pulse sequences; however, their inability to regulate temporal spacing, pulse duration, and intensity profile limits their applicability in OAWGs. To achieve high-resolution pulse shaping while ensuring chirp-free output pulses, a novel technique called the spectrally transcribed and chirp-corrected arbitrary temporal optimizer (STACCATO) [13] has been proposed. By utilizing spectral transcription through difference-frequency generation (DFG) via an optical parametric amplifier (OPA), STACCATO has demonstrated chirp-free pulse generation with a resolution of 4 ps and a record length of 330 ps for the first time, with potential for further performance enhancements. This innovative method of spectral transcribed parametric conversion provides an effective solution for high-speed chirp-free pulse shaping. Table 1 systematically compares the temporal resolutions and record lengths of the discussed technologies.Table 1.

Resolution and Record Length of Different Pulse Shaping Methods

The integration of arbitrary waveform generator with advanced optical waveguide platforms has precipitated a transformative evolution in photonic systems engineering, notably revolutionizing the development of ultra-stable laser seeding sources for HEDP applications such as inertial confinement fusion [14]. This synergistic combination has catalyzed substantial progress in both scientific research and industrial instrumentation. Nevertheless, experimental implementations of STACCATO-like pulse shaping technology integrated into optical waveguide architectures have not yet been demonstrated. The fundamental constraint impeding STACCATO-based optical waveguide pulse shaping stems from the substantial spectral detuning (Δλ>500nm) between pump and idler wavelengths inherent to DFG processes using OPA. Although silicon waveguides have demonstrated ultrabroadband parametric conversion capabilities [15–17], conventional waveguide architectures typically exhibit operational bandwidths limited to approximately 100 nm, which poses significant challenges for STACCATO-type pulse shaping implementations. The inherent bandwidth limitations in waveguide-integrated systems significantly hinder the implementation of octave-spanning spectral control mechanisms essential for achieving STACCATO-type pulse shaping.

In this paper, we introduce an innovative chirp-free pulse shaping method utilizing fiber-based four-wave mixing (FWM) spectral transcription, designated as four-wave optical-waveguided chirp-free ultrafast shaping (FOCUS). The spectral transcription process in the FOCUS method is analogous to STACCATO, essentially constituting a frequency-to-time conversion. Comprehensive theoretical investigations of spectral-transcription-based pulse shapers have been conducted, covering chirp cancellation mechanisms and inherent system performance limitations. Experimentally, we demonstrated the generation of chirp-free pulses with a resolution of ∼2ps and a record length of ∼400ps. The adoption of FWM confines the spectral bandwidth introduced into the entire system to within tens of nanometers, well within the operational range of standard optical waveguides. Crucially, the inherent distinct central wavelength separation among signal, pump, and idler spectra in FWM enables high-contrast pulse extraction through spectral filtering. Furthermore, the FOCUS method can achieve arbitrary shaping of pulse sequences, including modulation of the amplitude, interval, pulse duration, and central wavelength of sub-pulses. Notably, in contrast to the FOCUS method, time-to-frequency conversion has been achieved through fiber-optic and on-chip FWM, which has been successfully applied for high-resolution pulse characterization [19–22]. This functional equivalence suggests significant potential for FOCUS implementation in on-chip photonic platforms. Recent demonstrations of FWM in silicon photonic circuits [23] further support the feasibility of direct chip-scale integration of FOCUS technology. Silicon waveguide implementations of chip-scale mode-locked lasers [24] and electro-optically modulated frequency comb synthesizers [25] have demonstrated stable pulse generation, thereby establishing a critical foundation for realizing optical arbitrary waveform generators through fully integrated on-chip pulse sources. Collectively, these advancements indicate that FWM-based parametric conversion and pulse shaping offer substantial potential for miniaturization and functional integration in next-generation OAWG systems.

The schematic diagram and experimental setup of the FOCUS method are illustrated in Figs. 1(a) and 1(c). By employing FWM, the system achieves spectral transcription, meaning that the shaped spectrum’s profile is directly mapped onto the temporal profile of the output pulse. Initially, an ultrashort pulse generated from a mode-locked laser is stretched using a single-mode fiber (SMF) bundle with a group delay dispersion (GDD) of φs. Two chirped replicas are created using a fiber splitter, serving as the signal pulse and pump pulse in the subsequent FWM process. The pump pulse is stretched by an additional SMF to ensure that an accumulated GDD φp equals 2φs. The central portion of the pump spectrum is then filtered out by a band-pass filter, resulting in a relatively flat spectral shape. The signal pulse is shaped into a specific profile according to the expected output temporal profile. A time delay line (TDL) is employed to synchronize the signal and pump pulses. Two fiber amplifiers and three polarization controllers are used to enhance the power of the pulses to meet the demands for the FWM process. The two coupled pulses, Es and Ep, are then input into a highly nonlinear fiber (HNLF), which can be written as [21] {Es(t)=F−1{F[As(t)e−iωst]e−i2φsω2},Ep(t)=F−1{F[Ap(t)e−iωpt]e−i2φpω2},(1)where As(t) and Ap(t) represent the temporal amplitude of signal and pump pulses; ωs and ωp are the central angular frequency of signal and pump pulses. Due to the relatively flat spectral shape and the effect of frequency-to-time mapping, the pump pulse can be simplified into a quadratic temporal phase expressed by Ep(t)=exp(−i2·t22φs)exp(−iωpt).(2)

The FWM output idler pulse is given by Ei(t)=ηEp2(t)Es*(t), where η is the nonlinear coefficient. Substituting Eq. (1) and Eq. (2) into this formula, the Fourier transform of the idler in the FWM output can be written as $$\begin{gathered} F[Ei(t)]=ηF[Ep2(t)]⊗F[Es*(t)] \\ =η2πφse−iπ4eiφs2(ω+2ωp−ωs)2∫As*∼(Ω)e−iφsΩ(ω+2ωp−ωs)dΩ \\ =η2πφse−iπ4eiφs(ω+2ωp−ωs)22As[φs(ω+2ωp−ωs)]. \end{gathered}$$(3)

Thus, by introducing ωi=2ωp−ωs, the output idler spectrum after FWM is given by Si(ω)=2η2πφs|As[φs(ω+ωi)]|2.(4)

Equation (4) indicates that the system exhibits time-to-frequency conversion characteristics, meaning that the initial temporal profile of the signal pulse is mapped to the idler spectrum of the FWM output. The initial pulse of FOCUS is nearly transform-limited, and according to the time-to-frequency conversion relationship, the resulting spectrum is close to monochromatic. At this stage, the impact of chirp on the idler pulse can be considered negligible. It is important to note that at this point, the overall envelope of the output pulse is chirp-free, meaning that each temporal feature has the same central wavelength. By introducing a compressor with a GDD of −φs, the residual dispersion of the idler pulse can be eliminated. After passing through the compressor, the final output temporal profile of the system takes the form of |Ef(t)|2=2πη2φse−iωit|As*∼(tφs)|2.(5)

From Eq. (5), it can be observed that the temporal profile of the final output from the compressor is a scaled version of the shaped signal spectrum, representing the spectral transcription as illustrated in Fig. 1(a). The FOCUS system can be conceptualized as a Fourier transformer realized through a time lens, analogous to its spatial counterpart shown in Fig. 1(b). After passing through the FWM time lens, the chirped pulse becomes chirp-free. The time-to-frequency conversion relationship remains unaffected by the compressor, ensuring that Eq. (4) holds consistently. Due to the relationship described in Eq. (5), arbitrary shaping of the signal spectrum enables the generation of idler pulse sequences with customizable duration, amplitude, and pulse interval, such as STUD pulses [26,27].

The FOCUS system exhibits five principal advantages in photonic signal processing applications. First, the FWM mechanism inherently generates a narrow spectral span, addressing a fundamental constraint of current DFG-based techniques that require octave-spanning spectra. This enables seamless integration with commercially available waveguide devices. Second, in contrast to the DFG scheme limited by more stringent phase-matching conditions, the FWM scheme exhibits superior potential for achieving broader bandwidth across both signal and pump spectra, thereby improving temporal resolution and extending the record length in FOCUS. Third, FOCUS’s waveguide configuration achieves low energy consumption (∼1nJ/pulse), avoiding the high-power-density requirements of bulk-optic DFG systems. Fourth, the distinct central wavelength separation among signal, pump, and idler pulses ensures high-contrast, chirp-free output, allowing complete isolation of the final idler pulse via spectral filtering. Finally, the central wavelength of the output pulse can be precisely adjusted across a range of several nanometers by tuning the time delay line, enhancing the system’s adaptability to various application requirements. Figure 1(d) illustrates the potential on-chip configuration of the FOCUS method. Due to the relatively low pulse energy requirements, additional optical amplification can be avoided in this setup.

The system’s temporal resolution, denoted as Δt, is related to the spectral resolution of the spectral shaper, which can be derived from Eq. (4), expressed as Δt=γ2πcφsλ2Δλ, where λ is the central wavelength of the shaped time slice of the signal pulse, c is the speed of light, Δλ is the spectral shaping resolution, and γ is a coefficient related to the spectral shape. The resolution of the spectral shaper is determined by the combined properties of the grating, imaging system, and the width of the employed mask’s slits. By replacing the mask with a spatial light modulator (SLM), arbitrary spectral shaping capabilities can be realized. After passing through the spectral shaper employing a mask for spectral shaping, the temporal shape of the signal pulse consists of a sequence of sub-pulses. Due to the frequency-to-time mapping induced by the chirp, the duration of each sub-pulse can be derived from the spectral resolution. In practical applications, it is crucial to differentiate between two distinct operational conditions, which hinges on whether the shaped sub-pulses maintain the original chirp rate of the unshaped signal pulse.

On one hand, when the slits on the mask are sufficiently wide, the spectral bandwidth of each sub-pulse exceeds its transform-limited bandwidth, enabling the sub-pulses to retain their chirp rate as slices of the signal profile. Due to the frequency relationship of FWM ωi(t)=2ωp(t)−ωs(t) and the twofold GDD value φp=2φs, the pump and signal wavelengths at each temporal position within the sub-pulse are well compensated, resulting in a nearly chirp-free envelope of the output idler pulse sequence. As a result, the output idler sub-pulses after FWM exhibit a nearly monochromatic spectrum, rendering the influence of chirp on their duration negligible.

On the other hand, when the slits are too narrow to preserve the temporal profile of the sub-pulses as slices of the chirped signal pulse, the chirp rate is modified. In this scenario, the duration of the sub-pulses becomes longer than the product of the original chirp rate and their spectral bandwidth, as the spectral bandwidth carried by each sub-pulse is insufficient to support its original transform-limited pulse duration. Consequently, each signal sub-pulse can be considered as an independent, transform-limited pulse, whose ensemble can be represented by a new signal amplitude As′(t), which can be substituted into Eq. (1). As a result, the relationship established in the previous section remains valid. After the time-to-frequency conversion, the bandwidth of the output idler pulse will be broader than in the previous condition due to the expansion of the signal’s temporal profile, allowing it to support higher resolution. As a result of the variation in chirp rate induced by spectral shaping, each sub-pulse of the idler pulse carries a small amount of chirp before compression, while the overall pulse envelope remains chirp-free, consistent with the first condition. The residual linear chirp of sub-pulses can be fully eliminated by the compressor, which compresses the final output to near-transform-limited duration. Therefore, Eq. (5) indicates that this condition corresponds to a conversion from narrow bandwidth to narrow pulse duration.

It is evident that there exists a threshold in spectral shaping bandwidth between these two conditions, which corresponds to a threshold in the system’s temporal duration of the output sub-pulses. By combining the relationship between angular frequency and time in the chirped pulse with the Fourier transform limit formula, the threshold of temporal duration can be mathematically described as Δtthreshold=PTBφs,(6)where PTB is the time-bandwidth product of the shaped signal sub-pulse. We have analyzed this phenomenon through numerical simulations based on rectangular (rect), hyperbolic secant (sech2), and Gaussian (Gauss) function shaping. As shown in Fig. 2(a), the uncompressed pulse duration exhibits a significant deviation from the compressed condition when Δt is below the threshold. By utilizing a rectangular mask with an expected temporal output duration of 30 ps for the sub-pulses, Fig. 2(c) illustrates both the compressed and uncompressed idler sub-pulses. It should be noted that under the rectangular assumption, full width at 1/e2 is more suitable for evaluating pulse duration. It can be seen that, in both cases, the full width at 1/e2 is nearly identical, indicating that the duration of the idler sub-pulses aligns well with expectations even in the absence of compression. The primary function of the compressor is to modify the shape of the output pulse, ensuring it adheres to the spectral transcription relationship outlined in Eq. (5). As demonstrated in Fig. 2(d), the single-slit shaped spectrum exactly envelops the eight-slit configuration’s spectral profile, reflecting the interference-derived nature of the multi-slit spectral peaks. Figure 2(e) illustrates the output Gaussian and rectangular idler sub-pulses, with threshold-subcritical expected durations of 3 ps (rect) and 2.2 ps (Gauss). It is observed that the uncompressed output idler pulse displays multiple interference peaks, a consequence of the overlap between the broadened idler sub-pulses. The inset’s uncompressed rectangular sub-pulse (40 ps duration) demonstrates that overlap is inevitable in multi-sub-pulse regimes. This overlap distorts the expected temporal shape, emphasizing the necessity of introducing a compressor to compress the idler sub-pulses to their transform-limited duration. Figure 2(f) displays the corresponding spectral profiles, where their envelopes exhibit excellent alignment with the interference-modulated spectra. Figure 2(b) shows the temporal intensity distribution featuring a cat’s face profile, with a 1 ps resolution and a record length exceeding 1.2 ns. This demonstrates the FOCUS method’s capability for arbitrary waveform generation and its potential performance.

In summary, a spectral shaper with a narrow shaping bandwidth can modify the chirp rate of the signal sub-pulses during shaping, thereby limiting the system’s temporal resolution. By incorporating a compressor, the temporal resolution can be restored to the expected value, offering a notable improvement over chirped pulse spectral shaping. It is important to note that the pump bandwidth fundamentally constrains the minimum duration of the output idler sub-pulses. The current analysis operates within the regime constrained by this bandwidth, below the resolution limit imposed by it.

A FOCUS experimental platform was established to evaluate its operational performance, as shown in Fig. 1(c). The initial ultrashort pulse exhibits a spectral bandwidth of 4 nm. After propagation through a 1 km single-mode fiber (SMF-1060-XP) with a second-order dispersion coefficient of 22.94ps2/km, the bandwidth undergoes broadening from 4 to 24 nm through self-phase modulation effects. The spectral shaping apparatus incorporates a 4× beam expander positioned anterior to the diffraction grating, achieving an ∼70pm spectral resolution. Subsequent to temporal synchronization of the signal and pump pulses, a 15 m highly nonlinear fiber is employed to facilitate the FWM nonlinear process, ensuring high energy conversion efficiency. The characteristic output spectrum derived from the FWM interaction is presented in Fig. 3. The pump spectrum, centered at 1053 nm with a 6.3 nm bandwidth (FWHM), corresponds to a 12.6 nm accessible signal bandwidth during FWM interaction and could yield a maximum temporal record length of approximately 500 ps. The experimental results of FWM indicate that the FOCUS method can effectively operate within a spectral bandwidth of ∼30nm, thereby facilitating its integration into commercially available waveguide devices. Moreover, the idler spectrum exhibits a separation of several nanometers from the pump and signal spectra, enabling effective filtering of the idler pulse and achieving high-contrast pulse sequence output with an extinction ratio surpassing 30 dB. Additionally, the delay line implementation enables wavelength tunability, with Fig. 3 demonstrating available wavelength adjustment from 1058.5 to 1062 nm. The wavelength tuning range is constrained by the time adjustment range of the TDL and the pump bandwidth. The system’s total FWM power of ∼100mW (∼1nJ pulse energy) further highlights its advantage of low operating power requirements. The final dispersion compensation system employs a Treacy-compressor configuration incorporating a precision translation stage with 30 mm displacement range for micrometer-level adjustment of grating separation, thereby enabling precise dispersion management.

Two distinct experimental configurations were implemented to systematically evaluate the temporal performance metrics of the FOCUS system, specifically targeting record length and resolution parameters. The primary configuration utilized a spectral shaping mask comprising eight 1.3 mm wide slits with a 2.2 mm interval, resulting in eight discrete spectral peaks characterized by a modulation bandwidth of ∼0.8nm and an interval of ∼1.4nm, as shown in Fig. 4(a). This configuration was designed to produce sub-pulse trains (idler) with a theoretically predicted duration of ∼30ps, an interval of ∼50ps, and a record length of ∼413ps through spectral transcription. After the FWM process, the idler spectral envelope exhibits an FWHM of ∼0.17nm [Fig. 4(c)], where the inset illustrates a single sub-pulse idler spectrum with an FWHM of ∼0.12nm. The interference between sub-pulses generates multiple spectral peaks and modifies the FWHM in the composite spectrum. Temporal characterization using a 45 GHz photodetector and a 30 GHz oscilloscope with 20 ps instrument-limited temporal resolution revealed eight sub-pulses with durations of approximately 27 ps and intervals of approximately 50 ps [Fig. 4(e)], demonstrating a record length of ∼400ps, consistent with theoretical predictions. This represents the maximum record length that the current system is capable of attaining. Due to the high bandwidth requirements at the rising edges of square pulses, the measurement system is unable to fully characterize the temporal waveform profile. However, the measured pulse duration and interval remain reliable. Significantly, adjustments to the polarization controller enabled dynamic amplitude modulation (red curve) via Lyot-filter-like spectral tuning effects [28], despite the use of fixed geometric masks for static spectral shaping.

The second mask features eight slits with a 0.11 mm slit width and a 0.8 mm interval, generating eight discrete spectral peaks characterized by a modulation bandwidth of ∼0.07nm and an interval of ∼0.5nm, as illustrated in Fig. 4(b). This configuration corresponds to the chirp rate modification scenario presented in Section 2. The spectral resolution limit of 0.02 nm in our characterization system precludes accurate determination of peak profiles, while the narrow slit configuration introduces non-negligible diffraction effects, preventing simple rectangular function approximation for spectral shaping. Gaussian fitting of the idler spectrum in Fig. 4(d) demonstrates optimal conformity, with an envelope FWHM of ∼0.9nm, consistent with the 0.83 nm single-sub-pulse spectrum shown in the inset. Under the Gaussian waveform assumption, the theoretically derived pulse duration is 2.2 ps. Autocorrelation measurements shown in Fig. 4(f) reveal a peak FWHM of 2.6 ps. The indeterminacy of temporal pulse profiles introduces ±0.5ps measurement uncertainty in autocorrelation-derived pulse duration calculations due to shape-dependent deconvolution coefficients. Applying the deconvolution factor of 1.41 (Gaussian), the actual pulse duration resolves to less than 2 ps, demonstrating agreement with the theoretically predicted temporal resolution. This represents the highest resolution attained by the current system to date.

The observed multi-pulse dynamics in the second experimental configuration bears phenomenological similarity to mode-locked laser pulse splitting [29]. However, in stark contrast to the inherently unstable and non-deterministic nature of conventional mode-locking bifurcations, the FOCUS method enables precise independent control over the inter-pulse interval, temporal duration, and intensity distribution among sub-pulses.

A novel optical arbitrary waveform generation (OAWG) technique, termed FOCUS, based on four-wave mixing (FWM) spectral transcription has been proposed and experimentally demonstrated. The FOCUS method can generate shaped output pulse sequences with adjustable duration, intensity, interval, and central wavelength. By precisely controlling the system’s dispersion, FOCUS enables generation of chirp-free shaped pulse sequences with promising applications in optical communication, laser micro-processing, and high-energy-density physics. Our comprehensive system analysis encompasses chirp cancellation principles, sub-pulse chirp rate modulation mechanisms under narrow-band spectral shaping, and theoretical limitations dictated by system parameters. Experimental results demonstrate FOCUS’s capability to generate pulse sequences with a record length of ∼400ps and achieve a temporal resolution of 2 ps under current experimental conditions. These findings validate the feasibility of waveguide-based FWM arbitrary waveform generation, revealing significant potential for on-chip pulse generation. The temporal output of our experimental setup can serve as a burst-mode pulse sequence with a repetition rate exceeding 50 GHz within the record length, which has been shown to enhance ablation efficiency in laser processing [30]. Further improvements in repetition rate and record length may be attained through integration of appropriately delayed pulse replicators [11,12] following mode-locked lasers or GHz-modulated phase-modulated frequency combs [18]. Configuration optimization enables substantial enhancements in temporal resolution and record length, with FOCUS maintaining inherent compatibility with on-chip integration architectures.

The system’s temporal resolution is fundamentally governed by three interdependent factors: the spectral shaper’s resolution, the pump pulse’s spectral bandwidth, and the engineered GDD. Section 2.B’s quantitative analysis establishes an inverse proportionality between temporal resolution and system GDD. Meanwhile, reducing GDD could improve temporal resolution at the expense of proportionally reduced achievable record length. As shown in Fig. 5(a) with fixed GDD, the temporal resolution characteristics are bisected by a white dashed boundary, delineating spectral-resolution-dominated (upper) and pump-bandwidth-limited (lower) regimes. The isoresolution contours explicitly demonstrate the dual-regime behavior: bandwidth expansion fails to improve resolution in the spectral-resolution-dominated regime, while resolution scales conventionally with bandwidth in the complementary regime. In the pump-bandwidth-limited regime, only a single sub-pulse could receive full pump spectrum allocation in the FWM process, with subsequent sub-pulses exhibiting progressively degraded temporal resolution. Therefore, it is advisable to operate FOCUS in the spectral-resolution-dominated regime. Quantitative analysis reveals that the current pump configuration could support a temporal resolution of ∼250fs through spectral resolution optimization. A temporal resolution of ∼100fs could be achieved by concurrently enhancing both spectral resolution (∼3pm) and pump bandwidth (30 nm), as illustrated by the orange star-shaped symbol in Fig. 5(a). Currently, the 30 nm pump bandwidth is viable through waveguide-based FWM, while 3 pm spectral resolution is challenging. With a spatial spectral shaper, this would necessitate scaling up both the spot size and the corresponding grating size to the order of tens of centimeters. Another potential solution is to implement optical frequency comb sources [25] with an optimized line-by-line spectral shaping method. For on-chip implementation, according to the prior research of achievable spectral resolution (∼0.15nm) [31], realizing high-resolution and flexible spectral shaping on a chip necessitates further technological advancements. A Lyot filter, with a moderate spectral resolution, may serve as a viable candidate for on-chip spectral shaping but it could not support arbitrary spectral shaping. Furthermore, the attainment of high temporal resolution in FOCUS systems requires the implementation of higher-order dispersion compensation methodologies.

Record length limitations arise from engineered GDD and pump-signal spectral matching conditions. Current implementations achieve ∼400ps record lengths, falling short of the theoretical predictions of ∼500ps due to the utilization of only 5.2 nm operational bandwidth within the available 6.3 nm pump bandwidth. The GDD-mediated trade-off between record length enhancement and temporal resolution degradation necessitates optimal parameter balancing. Under fixed GDD configurations, broader-bandwidth ultrashort-pulse sources combined with optimized spectral allocation could extend the record length. Based on prior research about broad-band parametric wavelength conversion [15], consider the implementation of the on-chip FOCUS method employing 100 nm bandwidth [16] waveguides, where theoretically surpassing 2.3 ns record lengths with 30 nm pump bandwidth operation could be achieved. Figure 5(b) illustrates that the current setup achieves a maximum record length of 500 ps, limited by pump bandwidth, while potential on-chip performance could extend record length to ∼2ns through GDD engineering and pump bandwidth optimization, as denoted by the white dashed line. Additionally, the fixed-size spectral shapers exhibit inherent trade-offs between resolution and record length, where extending the record length without compromising resolution requires larger optical components, complicating system integration.

The stability of the FWM process is a critical factor in determining overall system performance and may be influenced by factors such as noise, temporal jitter, or spectral instability. To improve the stability of FOCUS, a relatively flat portion of the spectrum was selected as the pump pulse, and the FWM process was operated under pump depletion conditions. Spectral amplitude noise can degrade spectral stability, which can be reduced through pump depletion operation. In addition, excessive spectral phase noise may result in incomplete dispersion compensation within the system, potentially limiting the achievable resolution. Moreover, the temporal jitter influences the central wavelength of the output pulse in FOCUS. Given that both the pump pulses and the signal pulses are derived from the same mode-locked pulse sequence, the resulting impact is minimal and considered negligible. Experimental results indicate that these influences currently remain within acceptable bounds.

The transition of FOCUS to on-chip platforms has become increasingly feasible with recent breakthroughs in key enabling components, while achieving high resolution remains a challenge warranting further investigation. Silicon waveguide implementations of chip-scale mode-locked lasers [24] and electro-optically modulated frequency comb synthesizers [25] have demonstrated stable pulse generation. Additionally, experimentally validated on-chip dispersion engineering [32,33] enables the generation of sufficient GDD through meter-scale waveguides, facilitating on-chip replacement of SMFs and compressors. Meanwhile, the dispersion value, accuracy, and flexibility of on-chip GDD control require further improvement to achieve sub-picosecond temporal resolution. Moreover, integrated FWM pulse measurement platforms [19] have demonstrated the substitution of the photonic crystal fiber with on-chip waveguide architectures. The realization of on-chip high-resolution FOCUS continues to face significant technical challenges, including the attainment of fine spectral shaping resolution, precise GDD control, and robust higher-order dispersion management. By leveraging established technical approaches alongside ongoing advancements in spectral resolution and dispersion engineering, the realization of high-resolution on-chip FOCUS-type OAWG systems would represent a pivotal advancement, paving the way for next-generation ultrafast photonic applications.