Spectrum shuttle for producing spatially shapable GHz burst pulses

Abstract. Spatiotemporal shaping of ultrashort pulses is pivotal for various technologies, such as burst laser ablation and ultrafast imaging. However, the difficulty of pulse stretching to subnanosecond intervals and independent control of the spatial profile for each pulse limit their advancement. We present a pulse manipulation technique for producing spectrally separated GHz burst pulses from a single ultrashort pulse, where each pulse is spatially shapable. We demonstrated the production of pulse trains at intervals of 0.1 to 3 ns in the 800- and 400-nm wavelength bands and applied them to ultrafast single-shot transmission spectroscopic imaging (4 Gfps) of laser ablation dynamics with two-color sequentially timed all-optical mapping photography. Furthermore, we demonstrated the production of pulse trains containing a shifted or dual-peak pulse as examples of individual spatial shaping of GHz burst pulses. Our proposed technique brings unprecedented spatiotemporal manipulation of GHz burst pulses, which can be useful for a wide range of laser applications.


Introduction
The production of ultrashort pulse trains is important for various applications, such as laser ablation, [1][2][3][4][5] ultrafast imaging, [6][7][8][9][10] and acoustic wave generation. 11Laser processing methods using pulse trains, such as double-pulse processing 1,4 and burst processing, 2,3,5 have been widely applied to improve processing accuracy and efficiency.][8][9][10] In acoustic wave generation, multicycle acoustic waves can be tuned in the GHz frequency range by changing the time interval of the pulse train absorbed by the transducer. 11One of the typical pulse trains contains pulses of different wavelengths.In this spectrally separated pulse train, the spatiotemporal profiles, such as pulse duration, and wavefront, of each pulse can be individually modulated by pulseshaping techniques using a diffraction grating, lens, and spatial light modulator (SLM). 12,13Such spatiotemporal pulse shaping is crucial for the electron dynamics control in laser ablation, 14,15 fluorescence imaging, 16 and manipulation of terahertz signals, 17 among others.In addition, a spectrally separated pulse train is essential as a probe for sequentially timed all-optical mapping photography (STAMP), 6 which is a single-shot imaging technique that can capture twodimensional burst images of ultrafast events.Therefore, producing spectrally separated ultrashort pulse trains and controlling their individual properties have promising implications in different applications.
Recently, the extension of the time interval of spectrally separated pulse trains to subnanoseconds or longer has attracted considerable attention.In particular, it is expected to pave the way for novel ablation techniques using ablation cooling and provide fundamental understanding on ultrafast phenomena through imaging with nanosecond time windows.One method for producing pulses with nanosecond intervals is a dispersive-fiber-based device, [18][19][20][21] However, optical loss in fibers, which is a fundamental trade-off with pulse stretching, is severe at wavelengths other than the near-infrared communication bands.In addition, it is difficult to produce high-power pulses because of the nonlinear effects and optical damage to the fibers.In contrast, pulse-stretching methods that utilize the delay due to free space are not subject to these restrictions.Free-space angular-chirp-enhanced delay (FACED) 22 can produce pulse trains with sub-nanosecond or longer time intervals, and has been used for ultrafast imaging. 22,23FACED enables the illumination of an area spread out into a line shape with GHz burst pulses without significant optical loss.In contrast, its optical configuration does not allow the illumination of a specific area with all wavelength components of the burst pulses or the coaxialization of them.This is because, within each of the burst pulses produced by FACED, all wavelength components exhibit wavelength-dependent divergence and propagate in different directions.In applications such as laser processing and ultrafast imaging, there are many instances where the illumination of a point or circular area or the illumination from a single direction is necessary.In these cases, the spatial dispersion must be suppressed by sacrificing the bandwidth of each pulse, which inevitably results in optical losses.As methods to overcome this problem, a spectrum circuit 24 and recirculation-filtering method 25 are used for producing pulse trains with nanosecond intervals.
However, the optical configuration, where the pulses circulate among four and three mirrors, respectively, cannot achieve sub-nanosecond time intervals.Meanwhile, a grating-based stretcher with an additional adjustable delay between sub-pulses 26 can produce spatially nondispersive pulse trains with sub-nanosecond intervals.However, the number of mirrors increases with the number of pulses, which inevitably complicates the optical system.Therefore, the facile production of spatially nondispersive and spectrally separated GHz burst pulses remains a challenge.
In addition, independent control of the spatial profiles of the GHz burst pulses has not been achieved with these burst pulse production systems.Individual pulse shaping of GHz burst pulses has the potential for pulse-by-pulse optimization in ablation and probing.Particularly, this would improve the accuracy and efficiency of burst processing techniques.However, the conventional burst pulse production systems require a pulse-shaping system using a diffraction grating, lens, and SLM to achieve individual shaping, which inevitably complicates and enlarges the overall system.A burst pulse production system that can internally modulate the spatial profile of each pulse without adding the entire pulse shaping system provides a possible solution to address this.
In this study, we propose a spectrum shuttle as a method to produce pulse trains with subnanosecond to nanosecond intervals and individually shapable spatial profiles.First, we introduce pulse train production and individual spatial pulse shaping using a spectrum shuttle with an SLM.Subsequently, we demonstrate the production of spectrally separated pulse trains with time intervals of 100 ps to 3 ns.For imaging applications, we incorporate spectrum shuttles into twocolor (TC)-STAMP to achieve ultrafast single-shot transmission spectroscopic imaging of laser ablation.Furthermore, we demonstrate the production of individually phase-modulated pulse trains as an example of spatial shaping.

Principles of spectrum shuttle
Figure 1(a) shows the overall optical configuration of a spectrum shuttle.An ultrashort pulse horizontally dispersed by a dispersion device (e.g., grating pair) is incident on a pair of parallel mirrors (mirrors 1 and 2) from above mirror 1.The incident light travels back and forth between the parallel mirrors, in which a daughter pulse with a specific wavelength component travels across the side of mirror 2 to mirror 3 (or an SLM) at every lap, whereas the pulse with the other wavelength components continuously travels between the parallel mirrors, as shown in Fig. 1(b).
Consequently, the daughter pulses are vertically aligned and incident on mirror 3 (or the SLM).
Here, when an SLM is used, each pulse can be individually spatially modulated.Subsequently, the reflected pulses return along their initial incoming paths and are picked off with a beam splitter (BS) as a spatially nondispersive and spectrally separated pulse train.

Number, time interval, and duration of daughter pulses
In this section, we will discuss the principle of a spectrum shuttle based on ray tracing.A detailed derivation of the equations is provided in the Supplementary Material.As shown in Figs.1(a) and 1(b), we take the -direction as the dispersion direction of the incident light, the -direction as the   travel direction to mirror 3, and the -direction as perpendicular to the -and -directions.As shown in Fig. 1(c), let the distance between the parallel mirrors in the -direction be , and the   rotation angles of the mirrors around the -and -axis are and , respectively.and are the       absolute shifts in the -and -directions in each lap, respectively.Here, the normal vector from   mirror 1 to mirror 2, , is expressed by the following equation using the constant : Accordingly, the following equation is derived to: Therefore, and are expressed as follows, respectively: is equal to the width in the -direction of the daughter pulses extracted to mirror 3, and is    equal to the interval in the -direction of the pulses on mirror 3, which should be longer than the  beam diameter of the incident light, .Using , the number of the daughter pulses, , is expressed    by: where is the dispersion width by the dispersion device.
The time interval between the adjacent daughter pulses in the generated pulse train, , is given  by: where is the temporal delay derived from the parallel mirrors, and is the delay derived  pm  dis from the other elements.In the parallel mirrors, the optical path length difference between the adjacent daughter pulses is represented by twice the length of the red bold line in Fig. 1(c), considering the paths before, and after the reflection on mirror 3. Therefore, is given by:  pm where is the speed of light.Since , has the minimum limit of: When , the incident angle to the mirrors is 45°.In contrast, when , , the approximation is: For example, when and are 5 and 2 mm, respectively, according to is shown in The delay derived from the elements other than parallel mirrors, , and pulse duration of  dis each daughter pulse, , are determined by the pulse duration of the light source and configuration  of the dispersive elements.If a positively chirped pulse is used as a light source optimally compressed with a dispersion device in the spectral shuttle, can be reduced to zero and can  dis  be minimized.In this case, , and the minimized pulse duration is: where and are the center wavelength and bandwidth of each daughter pulse, respectively,  c ∆ and is a constant determined by the spectral waveform of the pulse.Assuming a square spectral  waveform, = 0.892.Although the pulse duration increases with the number of pulses because of  the shortened bandwidth for each pulse, pulse trains with sub-picosecond durations can be generated with optimal compression in the spectrum shuttle.In contrast, if the pulses are not optimally compressed, the temporal delay derived from elements other than parallel mirrors must be considered.In this case, is given by:  dis (11) where is the delay derived from the elements other than parallel mirrors for each wavelength, () ; and and are the center wavelengths of two adjacent daughter pulses.The pulse duration of   c  ′ c each daughter pulse, , is similarly expressed using as follows: When a compressed pulse is used as the light source and a grating pair is used as the dispersion device, the delay other than that of the parallel mirrors is determined by the dispersion in the grating pair.In this case, is given by: () where is the groove spacing of the diffraction gratings, is the incident angle of the grating pair,   and is the distance between the gratings.In addition, the wavelength according to the -   coordinate after diffraction by the second grating (grating 2), , is given by the following () equation when the point of incidence to the first grating (grating 1) is set to :  = 0 () =  { sin  + sin tan -1 ( / + sin  cos  )} .# (14)spectrum shuttle can independently control the number of pulses, , and time interval, , by   adjusting the positions, and angles of mirrors 1 and 2. The control of the pulse interval is independent of the pulse duration, which allows for longer intervals with short pulse duration.

Optical loss
The optical loss is determined by four factors when a grating pair is used as the dispersion device, namely the reflectivity of the mirrors, diffraction efficiency of the gratings, splitting by the BS, and splitting of the pulse at the edge of mirror 2, which occurs only at wavelengths that are incident on the edge.Let at the edge of mirror 2, the wavelength is split at the edge when  =  0 ()  satisfies: where is any integer satisfying , and is the beam diameter of the incident light. 0 ≤  ≤  -2 These wavelengths span two daughter pulses and are partially lost because of the diffuse reflection and diffraction at the edge.This spanning should be noted in some spectroscopic techniques.If a spectral discretization is required, certain wavelengths can be shielded between mirrors 2 and 3, in exchange for additional optical loss.
For wavelengths without optical loss due to splitting at the edge of mirror 2, the optical loss at each wavelength, , can be expressed by: () (16)  where is the reflectivity of mirrors 1 and 2, is the reflectivity of mirror 3 (or the SLM), Γ Γ′ () -th is the pulse number that includes , is the diffraction efficiency of the gratings, and and   g  r are the transmittance and reflectance of the BS, respectively.Here, the optical loss is  e independent of the time interval of a pulse train, and the use of optical elements with high efficiency enables a high throughput.

Spatial shaping
Each daughter pulse can be individually spatially shaped using an SLM in the spectrum shuttle.A pixel resolution of the modulation in the -direction, , is given by: where is the pixel pitch of the SLM.In contrast, a pixel resolution in the -direction, , is given     by: Each wavelength component is subjected to different spatial modulation, unless the entire modulation in the -axis direction is identical.

Production of pulse train
We constructed spectrum shuttles and demonstrated the production of GHz burst pulses.Two wavelength bands at approximately 800 and 400 nm were chosen to represent the flexibility of the light source wavelength.A mode-locked Ti:sapphire laser with chirped pulsed amplifier system (Astrella-USP-1K, Coherent, US) was used to generate a chirped pulse with a positive dispersion of 2 ps/nm, which was split by a BS before compression, and a compressed femtosecond laser pulse (duration of 35 fs).Both pulses have a center wavelength of 803 nm and bandwidth of 35 nm (FWHM) at 100 Hz.A beta barium borate (BBO) crystal (BBO-1001H, EKSMA Optics, LT) was used to double the frequency of the femtosecond laser pulse.The chirped pulse before compression in the 800-nm band and second harmonic in the 400-nm band were used as the incident light to the spectrum shuttles after reducing their beam diameter to ~2 mm.The incident lights were split using a 50:50 BS (BSW11 for 800 nm and BSW20 for 400 nm, Thorlabs, US) and dispersed by a grating pair (PC 1200 25x25x6 NIR / PC 1200 30x64x10 NIR for 800 nm and PC 2400 25x25x6 VIS / PC2400 50x50x6 VIS for 400 nm, Spectrogon, SE).In both bands, and  were adjusted to 20° and 520 mm in the 800-nm band and 20° and 600 mm in the 400-nm band,  respectively.Mirrors 1 and 2 (BBSQ-E03 for 800 nm and BBSQ-E02 for 400 nm, Thorlabs, US) were mounted on a kinematic mount (POLARIS-K1, Thorlabs, US) and goniometer stage for angle adjustment.In addition, mirror 1 was mounted on a single-axis stage for adjustment in the - direction, and mirror 2 was mounted on a dual-axis stage for adjustment in the -and -direction.

𝑥 𝑧
The distance between grating 2 and mirror 3 was set to more than 250 mm to produce pulse trains with intervals of up to 3 ns.To adjust the delay time in the two bands, a single-axis stage in the - direction was attached to mirror 3 in the 400-nm band.For the parallel mirrors, we employed highstability kinematic mounts and lockable stages to minimize optical system instability during experiments.
We first demonstrated the production of five pulses with an interval of 250 ps in the 800-and 400-nm bands.To measure the time-varying signal and spectrum of each daughter pulse, each pulse was extracted by a slit between mirrors 2 and 3.The time-varying signals of the pulse trains were measured using a fiber patch cable (M122L02, Thorlabs, US), a 33-GHz photodiode  Subsequently, the number and time interval of daughter pulses were changed in the 800-nm band to demonstrate the flexibility of the spectrum shuttle.Gsamples/s.In a spectrum shuttle, GHz burst pulses with the desired number and time interval can be generated by adjusting the angles and positions of the parallel mirrors.The production of a large number of pulses with longer intervals requires a high parallelism of the parallel mirrors, in which precision mirrors, and their mounts with a high angular resolution can be effectively applied.

Demonstration of singles-shot spectroscopic imaging
One of the applications of the pulse trains produced by a spectrum shuttle is ultrafast imaging with a time window in the range of sub-nanoseconds to nanoseconds.To demonstrate this application of the pulse trains, we applied them to TC-STAMP 27 and conducted single-shot transmission spectroscopic imaging of the sub-nanosecond dynamics of laser ablation.TC-STAMP is an ultrafast single-shot spectroscopic imaging technique based on the STAMP systems in two wavelength bands, which enables the analysis of wavelength-dependent parameters, such as absorption, scattering, and diffraction.Although the spectral properties of a laser ablation plasma have been acquired with a picosecond time window, the extension of the time window to the nanosecond scale will broaden the scope of analysis of ultrafast phenomena.In TC-STAMP, the stretched fundamental, and second harmonic pulses of the same light source are used as probe pulses.Here, we demonstrated TC-STAMP imaging with a time window extended to 1 ns using spectrum shuttles for the pulse stretching in two bands.A spectrum shuttle is advantageous in STAMP imaging using light sources with narrow bandwidths or low intensities, including second harmonics, because the sacrifice of the bandwidth in pulse stretching needs to be suppressed.respectively, during the laser ablation dynamics.The plasma plume evolved 1 ns after ablation.In addition, shock waves were generated, and evolved in air and glass after 500 ps.The transmittance is affected by various factors, including electron absorption, scattering of heavy particles, and diffraction due to the refractive index distribution of plasmas and shock waves, which have different properties depending on the wavelength.To highlight these spectral characteristics, the transmittance ratio between the two wavelength bands, , is shown in Fig. 4(b).In the  400 / 800 plasma plume, decreased after 750 ps.This is presumably attributed to the dominance  400 / 800 of the wide scattering by the heavy particles in short wavelengths, instead of the high absorption by the dense electrons in long wavelengths.The lower transmittance in the 400-nm band in the glass can be ascribed to the particle scattering.In contrast, the transmittance gradient at the shock wavefront in air is larger in the 800-nm band owing to large diffraction at long wavelengths.Therefore, TC-STAMP imaging with an extended time window was realized using spectrum shuttles, which allow for the detailed analysis of the spectral properties of ultrafast phenomena.

Demonstration of individual pulse shaping
We next demonstrated spatial pulse shaping in the 800-nm spectrum shuttle by replacing mirror 3 with an SLM (SLM-100, Santec, JP).Among the five daughter pulses generated with the interval of 250 ps by the spectrum shuttle, only the third pulse was independently modulated by the SLM, as shown in Fig. 5(a).Two different phase modulations were conducted.The first phase pattern was tilted in the -direction, which tilts the wavefront of the incident beam, thereby shifting the -  axis during propagation and focusing.The second phase pattern includes a step that splits the  incident beam into two equal regions.This modulation can produce dual-peak pulses, which are applied to metal nanowire patterning. 29We detected the beam profiles of the third pulse under three conditions: when the phase pattern is originally flat, has a gradient of 2 /3 rad/mm, and has  a step of , as shown in Fig. 5

Conclusions
In this study, we demonstrated a pulse manipulation technique, referred to as spectrum shuttle, to produce spectrally separated GHz burst pulses from an ultrashort pulse without deteriorating the spectral components.A spectrum shuttle allows the use of pulse trains by adjusting the parallel mirrors with minimum time intervals of ~30 ps.We experimentally obtained pulse trains with time intervals of 0.1-3 ns.Although the average pulse duration was 40 ps in the experiment owing to the temporal dispersion of the grating pair, adding a conventional pulse compressor using a diffraction grating and lens 30 either before or after the spectrum shuttle can bring the pulse duration of the burst pulses closer to the Fourier limit.The applicability of the produced GHz burst pulses was demonstrated by an ultrafast transmission spectroscopic imaging of a laser ablation with a time window of 1 ns.Burst pulses with the time interval of 250 ps in the 800-and 400-nm bands produced by the spectrum pulses were used as probes.The use of the spectrum shuttle in ultrafast imaging enables a multifaceted analysis of ultrafast phenomena.Furthermore, we achieved the production of individually spatially shaped GHz burst pulses using the spectrum shuttle incorporated with an SLM, which allows unprecedented spatiotemporal manipulation of GHz burst pulses.Therefore, the proposed spectrum shuttle has strong potential as a pulse manipulation technique for various applications, such as burst laser ablation and ultrafast imaging.

Caption List
Fig. 1 Schematic of a spectrum shuttle.

Fig. 1
Fig. 1 Schematic of a spectrum shuttle.(a) Top view of the overall optical configuration.(b) Pulse separation by a pair of parallel mirrors (mirrors 1 and 2) indicated by the orange dashed square in (a).(c) A pulse traveling between parallel mirrors indicated in the blue dashed square in (b).BS, beam splitter; SLM, spatial mapping device.

Fig. 2
Fig. 2 Relationships of the basic parameters in a spectrum shuttle.(a) Variations of the temporal delay derived from the parallel mirrors, , with a distance between the parallel mirrors in the -direction, , and (b) rotations angles  pm   of the mirrors around the -and -axis, and , according to , respectively, when the absolute shifts in the -     pm  and -directions in each lap, and , are fixed at 5, and 2 mm, respectively.

(
DP070E1, Tektronix, US) and a 23-GHz oscilloscope (MSO72304DX, Tektronix, US); the results are shown in Figs.3(a) and 3(b).The normalized spectra measured with a spectrometer (EPP2000 HR-NIR3 for 800 nm and HR-X-UV3 for 400 nm, SterllarNet, US) are shown in Figs.3(c) and 3(d).Spectrally separated pulse trains are observed.The average pulse duration calculated from the measured spectra is 43 and 36 ps in the 800-and 400-nm band, respectively.Figures3(e) and 3(f) show the spectra when a portion of the wavelength component in each pulse was shielded by a blocker inserted between mirrors 2 and 3 from the negative direction of the -axis.The pulse  trains were fully spectrally discretized.This discretization is effective in some spectral measurement techniques, including STAMP, where the overlap of the wavelength components between pulses can be a noise source.

Fig. 3
Fig. 3 Production of spectrally separated pulse trains by a spectrum shuttle.(a-d) Time-varying signals and spectra of five pulses with the intervals of 250 ps in the 800-and 400-nm bands.(e, f) Spectra of the pulse trains discretized

Figure 3 (
g) shows the time-varying signals when the number of pulses was increased to 10 and 20 at an interval of 250 ps.Figure3(h)shows the signals when the time interval of 10 daughter pulses was changed to 0.1, 1.0, and 3.0 ns.Note that the pulse distortion and artifacts beside the pulses are due to the electronic measurement using the oscilloscope with an analog bandwidth of 23 GHz and a sample rate of 100

Figure 4 (
Figure 4(a) shows the experimental setup.We used pulse trains with the interval of 250 ps in

Figure 4 (
Figure 4(b) shows the transmittance distributions in the 800-and 400-nm band, and ,  800 400 (b).Under each condition, the third pulse was extracted by the slit  between mirror 2 and the SLM in the spectrum shuttle, and detected by an image sensor (ORCA-Flash4.0V3, Hamamatsu Photonics, JP) installed at a position where the third pulse propagated at approximately 1700 mm from the SLM.

Fig. 5 Figure 5
Fig. 5 Production of individually spatially shaped pulse trains by a spectrum shuttle with an SLM.(a) Experimental setup for modulating the third pulse only.(b) Phase patterns of the third pulse modulated by the SLM.(c) Beam profiles of the pulse propagated at approximately 1700 mm after under three conditions.On the right side, the average intensities of the pulses in the range of 2 mm at each -coordinate are shown.

Fig. 2
Fig. 2 Relationships of the basic parameters in a spectrum shuttle.

Fig. 3
Fig. 3 Production of spectrally separated pulse trains by a spectrum shuttle.

Fig. 4
Fig.4 Single-shot transmission spectroscopic imaging of laser ablation dynamics using pulse trains

Fig. 5
Fig. 5 Production of individually spatially shaped pulse trains by a spectrum shuttle with an SLM.