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Nanosecond laser pulse modulation using seed electrons from cascade ionization induced by inverse-Bremsstrahlung photon absorption

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Abstract

Nanosecond (ns) laser pulses are modulated by seeding electrons on the laser beam path. The seed-electrons are from auxiliary ns-laser-induced breakdown (ALIB), and the ALIB is induced by a focused 1064-nm pulse, which is split after the frequency-doubling that generates the 532-nm pulse; therefore, the 532-nm and 1064-nm pulses are synchronized. The slowly converging (focal length = 500 mm) 532-nm pulse is re-directed to transmit through the region in where the ALIB-generated electrons reside. The seed-electrons from the ALIB then absorb the 532-nm photons via the inverse-Bremsstrahlung photon absorption (IBPA) process. The number density of the seed-electrons on the 532-nm beam path (ne,ALIB) is controlled by varying 1) the 532-nm pulse arrival time at the ALIB region (ΔPAT) after the 1064-nm pulse triggers the ALIB and 2) the location of the 532-nm beam relative to the core of the ALIB; the electron number density in ALIB is highly non-uniform and evolves in time. Electron-seeded laser-induced breakdown (ESLIB) occurs when ne,ALIB is sufficiently high. The 532-nm beam convergence (controlled by the focusing lens) is adjusted so that the breakdown does not occur without the electron seeding. The ESLIB immediately stops the transmission of the trailing edge of the laser pulse acting as a fast shutter, and ne,ALIB above a threshold can cut the pulse leading edge to modulate the 532-nm laser pulse.

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1. Introduction

Tables Icon

Table 1. Nomenclature.

Laser-induced breakdown (LIB) in a gaseous medium is triggered by intensive interactions between the photons of a focused laser pulse and atoms and molecules in the focal volume. The LIB accompanies fast ionization and dissociation of neutral species to generate a plasma of high temperature and pressure [1]. This breakdown plasma emits photons, and their energy spectrum consists of a broadband continuum emission and atomic/molecular emission lines. This plasma emission spectrum contains gas property information at the focus of the laser pulse where the plasma is generated. Local composition of the gas mixture [25] and flow properties [68] at the focus in various reacting/non-reacting flows have been measured analyzing the emission spectrum. Nevertheless, practical use of LIB has been often limited for various reasons, e.g., unwanted ignition when probing flammable mixtures, unstable breakdown at low-density conditions, fast convection of the plasma in high-speed flows, etc. The characteristics of the LIB strongly depend on the temporal-spatial laser pulse profile, and many of the issues limiting the practical use of LIB can be resolved by properly modulating the pulse profile. A convenient and effective way of pulse modulation employing electron seeding from an auxiliary ns-laser-induced breakdown (ALIB) is proposed in this paper.

In the LIB with nanosecond laser pulses (ns-LIB), the inverse-Bremsstrahlung photon absorption (IBPA) process is the predominant photon-matter interaction for the pulse duration (typically FWHM < 10 ns), and the photon energy deposition to the gas medium via the IBPA process is significant [1,2]. During the early stage (e.g., ≤ 50 ns) of the ns-LIB, the broadband continuum emission from the electrons, which are accelerated via the IBPA and produced by the impact (collisional) ionization of the fast-moving electrons, prevails over the atomic/molecular emission lines. On the other hand, non-collisional photoionization, e.g., multiphoton ionization (MPI) and tunnel ionization, becomes dominant as the laser pulse width gets shorter, e.g., ps- or fs-pulses. Without the IBPA, the LIB-induced thermal heating is suppressed and unwanted ignition in flammable mixtures can be avoided. In addition, as the stochastic collisional energy transferring mechanisms of the IBPA-accelerated electrons are de-activated, the broadband continuum emission is suppressed to enhance the signal-to-noise ratio (SNR) of the atomic/molecular emission lines in the plasma emission spectrum [2]. This helps improve the accuracy of the gas property measurements calibrating the distinctive spectral features such as the emission lines and bands. Moreover, the LIB by the shorter pulses can minimize the flow disturbances from the LIB-induced shockwaves and the interference of thermo-chemical photon emission on the plasma emission. Nevertheless, ns-pulses of relatively longer pulse width with increased pulse energy are still needed for intensifying the plasma emission signal under low gas-density conditions. Therefore, a pulse modification technique for adjusting the pulse profile depending on the target gas conditions is essential for extending the application of laser-induced breakdown spectroscopy (LIBS).

To generate short-duration laser pulses from typical ns-pulses of 5–10 ns FWHM, electro-optical shutters and stimulated-Brillouin scattering (SBS) pulse compression technique have been used [9,10]. The electro-optical shutter requires high electric potential applied across the electro-optical material for a substantially short time period, which limits the shutter performance; i.e., the rise-fall time of the electric potential and the response time of the material would limit the minimum shutter opening/closing time. The SBS enables pulse compression using the interaction of a laser pulse with a back-scattered acoustic wave generated by the electrostriction effect in a cell filled with a high-density medium, e.g., water. However, the setup is bulky (e.g., a meter-long water tube), and it is difficult to vary the pulse width. Moreover, the operation of the pulse compressor is limited by nonlinear effects such as optical breakdown (self-focusing), Raman scattering, and diffuse Brillouin scattering. Alternatively, Oh et al. [3] have developed a much simpler and compact optical shutter employing the IBPA-induced plasma of high electron number density that can immediately block the transmission of a laser pulse through the region. The shutter closing time (τIB) could be effectively controlled by varying the gas pressure at the shutter location [3,11].

In this study, a frequency-doubled (532 nm) Nd:YAG ns-laser pulse (main pulse) was chopped by electron-seeded LIB (ESLIB). The ESLIB was triggered by seed-electrons from preceding auxiliary LIB (ALIB) induced by the fundamental (1064 nm) Nd:YAG pulse (auxiliary pulse) that was split after frequency doubling. Since the ESLIB controls the pulse profile, a simplified model of the ESLIB process was proposed, and the dependency of this optical shuttering on the model parameters was experimentally investigated. Seed-electron number density (ne,ALIB), laser pulse energy (Epulse), and the neutral species number density (N) are the main parameters of the model, which determine the temporal-spatial characteristics of the ESLIB. The 532-nm pulse profile and energy could be varied by controlling the ESLIB with the ALIB-seeded electrons, and an injection-seeded Nd:YAG laser with guiding optics was used to verify the pulse chopping capability of this configuration. This proposed pulse modulation technique can conveniently adjust the characteristics of ns-/ps-laser pulses in a broad range as needed, e.g., a ns-laser system can produce high-peak-power and reduced-temporal-width pulses generating minimal heat for non-intrusive measurements or high-precision machining, and relatively long temporal-width pulses modulated to intensify the inverse-Bremsstrahlung process while not much disturbing the flow for non-intrusive LIBS at low-density conditions.

2. Modeling of ESLIB

With typical ns Nd:YAG laser pulses being focused to induce LIB, the multiphoton ionization (MPI) process initiates the photo-ionization of neutral species in the focal volume. The electrons initially produced by the MPI process (ne,i) for a time period (τMPI) quickly absorb photon energy via the IBPA process to trigger much faster impact ionization from collisions of electrons accelerated by IBPA; both the collisional ionization (ionization rate = νcoll · ne, where, νcoll is the collisional ionization frequency) and electron attachment/recombination loss (electron loss rate = νloss · ne, where, νloss is the effective electron loss frequency) are expedited by the increased number of fast-moving electrons. Due to the rapid electron production after the breakdown, IBPA becomes the dominating photon energy absorption process to make the plasma volume optically thick (inhibiting the transmission of laser pulse through the medium); a critical electron number density, ne,c, defines the threshold of this optical breakdown. Considering the MPI, collisional ionization, and electron loss, the net electron production rate is given by [1]:

$$\frac{{d{n_\textrm{e}}}}{{dt}} = {W_\textrm{m}}{I^\textrm{m}}N + ({\nu _{\textrm{coll}}} - {\nu _{\textrm{loss}}}){n_\textrm{e}},$$
where Wm, I, m, and N are the MPI rate coefficient, laser irradiance (W/cm2), the integer part of ɛI/ + 1 (ɛI, h and ν are ionization potential, Planck constant, and the photon frequency, respectively), and initial neutral species number ${W_\textrm{m}}{I^\textrm{m}}N$ density, respectively. The term represents the electron production by MPI which becomes negligible once the fast collisional ionization is activated. Recall that the transition from the MPI to the optical breakdown due to the cascade collisional ionization would take a specific time delay, τIBD. Therefore, three consecutive time durations for the laser radiation period are separately modeled for simplification: Period I for MPI (from 0 to τMPI), Period II for fast IBPA triggering breakdown (from τMPI to τIB, where τIB = τMPI + τIBD), and Period III after the breakdown.

In this study, seed-electrons were supplied by the ALIB prior to the arrival of the 532-nm laser pulse near the location of ALIB. Under the conditions generating the ESLIB, the number density of the MPI-produced electrons (ne,i) is negligible compared to the seed-electron number density (ne,ALIB), and Period I can be ignored (τMPI ∼ 0). Then, integration of Eq. (1) for Periods I and II yields (see Table 1):

$$\int_0^{{\tau _{\textrm{IB}}}} {\left\{ {\frac{{{W_\textrm{m}}{I^\textrm{m}}N}}{{{n_\textrm{e}}}} + ({{\nu_{\textrm{coll}}} - {\nu_{\textrm{loss}}}} )} \right\} \cdot dt = } \ln \left( {\frac{{{n_{\textrm{e,c}}}}}{{{n_{\textrm{e,ALIB}}}}}} \right) \approx \ln \left( {\frac{{{n_{\textrm{e,c}}}}}{{{n_{\textrm{e,i}}} + {n_{\textrm{e,ALIB}}}}}} \right) = \int_{{\tau _{\mathrm{MPI\sim 0}}}}^{{\tau _{\textrm{IB}}}} {{\nu _{\textrm{i,eff}}} \cdot dt} .$$
The integration from 0 to τIB becomes the same as the integration from τMPI to τIB. The effective ionization frequency (νi,eff = νcoll - νloss) in Eq. (2) is a function of I and N. The exponent of I, that is k in ${\nu _{\textrm{i,eff}}} \propto N{I^\textrm{k}}$, was numerically derived by Rosen and Weyl [12] and experimentally confirmed by Oh et al. [11]; its value is between 1 and 2. Since Period I is ignored with the electron-seeding from ALIB, the neutral species number density at t = 0 or τMPI (∼ 0) is N - NALIB, where, NALIB is the number density of neutral species ionized in the plasma generated by ALIB. Ionization during Period II before the succeeding breakdown (ESLIB) would be insignificant in comparison with the fast cascade ionization from ALIB. Therefore, the neutral species number density would be N - NALIB prior to the ESLIB during Periods I and II. The laser pulse irradiance profile, I(t), is Gaussian (see Eq. (3) and Fig. 1 (R2 = 0.984)):
$$I(t) = {I_\textrm{0}} \cdot exp \left( { - 4\ln 2 \cdot {{\left( {\frac{{t - {\tau_\textrm{m}}}}{{{\tau_\textrm{p}}}}} \right)}^2}} \right),$$
where terms I0, τm and τp in the Eq. (3) represent the peak intensity, peak time (see Fig. 1), and FWHM of the laser pulse, respectively. For the time interval, where corresponds to 10 - 90% of the peak intensity, the Gaussian profile is nearly linear (R2 = 0.99). Therefore, the I(t) during the Periods I and II can be modeled as a linear function ($I(t)\sim {E_{\textrm{pulse}}} \cdot {C_{\textrm{fit}}} \cdot t/(A \cdot {\tau _\textrm{p}})$) with a gradient constant (Cfit), a normalization factor (A ∼ 1.06), and the FWHM (τp) ($\int_{ - \infty }^\infty {I(t) \cdot dt = {E_{\textrm{pulse}}},\int_{ - \infty }^\infty {I(t)/{I_\textrm{0}} \cdot dt = {E_{\textrm{pulse}}}/{I_\textrm{0}} = A \cdot {\tau _\textrm{p}}} }$); the breakdown (ESLIB) will occur before reaching the peak intensity while the laser irradiation rises rapidly. This linear fit simplifies the analytical expression of τIB as derived in Eqns. (4) – (6) (see Table 1):
$$\bar{I} = \frac{{\int_0^{{\tau _{\textrm{IB}}}} {I(t)} \cdot dt}}{{{\tau _{\textrm{IB}}}}} = \frac{{{E_{\textrm{pulse}}} \cdot {C_{\textrm{fit}}}}}{{2A \cdot {\tau _\textrm{p}}}} \cdot {\tau _{\textrm{IB}}},$$
$$\int_0^{{\tau _{\textrm{IB}}}} {{\nu _{\textrm{i,eff}}} \cdot dt = \overline {{\nu _{\textrm{i,eff}}}} \cdot {\tau _{\textrm{IB}}} = (N - {N_{\textrm{ALIB}}}){{\bar{I}}^\textrm{k}} \cdot {\tau _{\textrm{IB}}} = \ln \left( {\frac{{{n_{\textrm{e,c}}}}}{{{n_{\textrm{e,ALIB}}}}}} \right)} ,$$
$${\tau _{IB}} \propto \frac{{\ln \left( {\frac{{{n_{\textrm{e,c}}}}}{{{n_{\textrm{e,ALIB}}}}}} \right)}}{{({N - {N_{\textrm{ALIB}}}} ){{\bar{I}}^\textrm{k}}}} \propto {\left( {\frac{{\ln \left( {\frac{{{n_{\textrm{e,c}}}}}{{{n_{\textrm{e,ALIB}}}}}} \right)}}{{N\left( {1 - \frac{{{N_{\textrm{ALIB}}}}}{N}} \right)}}} \right)^{\frac{1}{{\textrm{k} + 1}}}}{({{E_{\textrm{pulse}}}} )^{ - \frac{\textrm{k}}{{\textrm{k} + 1}}}}.$$

 figure: Fig. 1.

Fig. 1. Linear fit of the Gaussian pulse profile for the 10-to-90% of the peak intensity.

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The average pulse intensity before the breakdown ($\bar{I}$) for the duration of 0-to-τIB can be written as in Eq. (4) using the linear fit of I(t), which gives a time-averaged effective ionization frequency, $\overline {{\nu _{\textrm{i,eff}}}} = (N - {N_{\textrm{ALIB}}}){\bar{I}^\textrm{k}}$ as in Eq. (5). The analytical expression of τIB shown in Eq. (6) dictates that ne,ALIB, Epulse, and N determine the τIB. When N is constant, e.g., at an atmospheric condition, and the range of adjustable Epulse is limited, the ne,ALIB can still be employed as the primary control parameter varying the τIB in a broad range without a pressure cell controlling N and a high-power laser system of an extended Epulse range. Recall that the τIB is the plasma shutter closing time, and the temporal intensity profile of the laser pulse transmitted through the region where the ESLIB occurs can be effectively modulated using this shutter.

In this study, the τIB could be varied in a wide range by controlling the ne,ALIB at an atmospheric condition of fixed Epulse and N. In general, as N increases with the ambient gas density or the Epulse increases, τIB will get shorter, terminating 532-nm beam transmission through the ESLIB region earlier, i.e., closing the optical shutter earlier. ne,ALIB will increase as the 532-nm beam path moves closer to the core of ALIB or the 532-nm beam arrives at the ALIB region when the ALIB-induced electron number density is higher. As ne,ALIB increases, τIB will decrease if NNALIB; NALIB naturally increases with ne,ALIB. However, when the ne,ALIB is exceedingly high so that NALIB approaches N, which in turn dramatically reduces (N - NALIB), τIB will start to increase again. Moreover, under the high ne,ALIB conditions, the ALIB-produced seed-electrons can absorb a large portion of the 532-nm pulse energy to essentially block the leading edge of the pulse (Fig. 1). However, the electron number density near the ALIB will decrease rapidly since the supplied 532-nm pulse energy during the leading-edge period is insufficient to maintain such high electron number density. Therefore, the shutter will open eventually to allow the pulse transmission, and the ESLIB will follow later to cut the trailing edge of the 532-nm laser pulse.

3. Experimental setup

A schematic experimental setup modulating ns-laser pulses with electron-seeding is shown in Fig. 2(a). Here, LIB (ESLIB and ALIB) is employed under a standard atmospheric condition of dry air (1 atm, 300 K) using a pulsed Nd:YAG laser (Continuum, PL8000, 532/1064 nm, Q-switched, 10 Hz, injection-seeded). The auxiliary laser pulse (1064 nm, 6.02 ns FWHM, red beam in Fig. 2(a)) from the Nd:YAG laser is focused along –z direction (z is the vertical axis, see Fig. 2(b)) to induce the ALIB using a spherical plano-convex lens (SCL2 in Fig. 2(a), f = 30 mm). The 1064-nm and 532-nm photons are split inside the laser system, and the 1064-nm photons are terminated internally if not used. Therefore, the 1064-nm pulse that is split after the frequency-doubling can be controlled independently from the 532-nm pulse. The position of the ALIB is adjustable in the x-y-z directions with two mirrors (MWS) and the SCL2 mounted on a 3-way (x-y-z) translation stage. Long (Case 1) and short (Case 2) auxiliary laser beam paths are installed for testing two 1064-nm pulse arrival times. The 532-nm laser pulse passes through the ALIB region approximately 2 ns (Case 1) and 7 ns (Case 2) after the auxiliary laser beam arrives at the focus, respectively. The two time-delays, 2-ns and 7-ns, nominally represent the earliest and the latest arrivals of the main pulse, respectively, to keep the high electron number density in the ALIB region for the pulse duration of the main laser pulse. A quarter-wave plate (QWP) converts the polarization of the 1064-nm pulse from circular (by Type II KD*P Crystal) to linear to make both the 532-nm and 1064-nm pulses linearly polarized. A rotational half-wave plate (HWP) before a polarizing beam splitter (PBS) at the entrance of the two 1064-nm beam paths for the Case 1 and 2, and a mirror on a flip mount (Thorlabs, FM90/M, MWF) at the junction of the paths are used to switch the beam path (Fig. 2(a)). The polarization direction and laser pulse energy in both the cases are identical, p-polarized and 100 mJ/pulse, respectively. The auxiliary laser pulse energy is measured by a thermal power meter (TPM3, Ophir), and a photodiode (PD2, Electro-Optics Technology, ET-3500F, rise/fall time < 25 ps) is used to record the temporal pulse profile.

 figure: Fig. 2.

Fig. 2. (a) A schematic of the experimental setup used for modulating ns-laser pulses with electron seeding. M, mirror; HWP, zero-order half-wave plate; QWP, zero-order quarter-wave plate; PBS, polarizing beam splitter; W, fused silica window; NDF, absorptive neutral density filter; PD, photodiode; MWF, mirror with flip mount; MWS, mirror with linear translation stage; SCL, spherical plano-convex lens; ID, iris diaphragm; BT, beam trap. (b) The yz-plane at the intersection on where the ALIB is relocated.

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Another split part (main laser beam) of the fundamental laser pulse is frequency-doubled (532 nm, 5.62 ns FWHM, green beam in Fig. 2(a)) and focused (SCL1, f = 500 mm) along the + x direction (see Fig. 2(b)) for inducing the ESLIB near the ALIB. The seed-electrons produced by the preceding ALIB (using the focused 1064-nm pulse) absorb the 532-nm pulse energy to trigger the ESLIB. The focal length of the FL1 is relatively long so that the optical breakdown does not occur without the electron seeding from ALIB (Fig. 2(b)). The laser pulse transmitted through the ESLIB is then collimated and filtered (neutral density filter, NDF) before reaching a photodiode (PD1, Electro-Optics Technology, ET-4000F, rise/fall time < 30 ps) that records the temporal pulse profile. The initial pulse energy (Epulse) and the transmitted pulse energy (Etrans) are measured at TPM1 and TPM2, respectively, using a thermal power meter (Ophir). An iris diaphragm (ID) blocks residual stray rays from the main laser beam prior to being detected by the photodiodes and the power meter.

The ALIB on the converging 532-nm beam path upstream of the focus is moved to vary the ne,ALIB. Since the ALIB-induced electron number density field is highly non-uniform, the ne,ALIB can be varied by relocating the ALIB while the 532-nm beam path is fixed. The ALIB location on the x-axis that is parallel to the 532-nm beam path is fixed so that the 532-nm beam diameter is maintained nearly constant at the intersection, approximately 60 µm. The ALIB is then moved with a 50-µm step in the y-z directions (Fig. 2(b)).

A portion of the forward scattered 532-nm photons from the ESLIB are captured by a biased photodiode (PD3, Thorlabs, SM05PD2A, rise/fall time = 1 ns, PBM42, bias module) through two spherical plano-convex lenses, SCL3 of f = 100 mm and SCL4 of f = 125 mm, a short-pass filter (SPF, Thorlabs, FESH0900, 900 nm cut-off wavelength), and a bandpass filter (BPF, Thorlabs, FL532-3, 532 nm center-wave-length, 3 nm FWHM) block the 1064-nm photons scattered from the preceding ALIB and the plasma emission (Fig. 3). All the optics are mounted on a coaxial lens tube aligned in the direction approximately 20 ° from the 532-nm beam path. The scattering signal captured on PD3 is recorded by an oscilloscope (Keysight Technologies, InfiniiVision MSOX-3104A, 1 GHz bandwidth) that also records the 1064-nm (PD2) and 532-nm (PD1) pulses; fast pulses of > 900 ps width can be fully resolved with the current setup.

 figure: Fig. 3.

Fig. 3. Forward scattered 532-nm photon collection. SCL, spherical plano-convex lens; SPF, shortpass filter; BPF, bandpass filter; NDF, absorptive neutral density filter; PD, photodiode.

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4. Results and discussion

4.1. Transmitted laser pulse energy without seed-electrons

Figure 4 confirms that in the current setup, breakdown via the main laser pulse (532 nm) does not occur without electron seeding from ALIB. The transmitted pulse energy (Etrans) is a 30 shot-averaged value. Etrans increases linearly with the original pulse energy (Epulse) (R2 = 0.999) when Epulse = 20 - 200 mJ/pulse, and the transmittance (T = Etrans / Epulse) stays unchanged at around 93–96%. This energy loss (4–7%) is primarily from the guide-optics including the iris diaphragm, focusing lenses, and occasional, sporadic breakdowns induced as the pulse energy increases (perhaps triggered by dust particles in the laboratory).

 figure: Fig. 4.

Fig. 4. Transmitted laser pulse energy (Etrans) and transmittance (T) versus Epulse.

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4.2. Breakdown characteristics of ESLIB

The ALIB is induced by the focused (SCL2) auxiliary laser pulse (1064 nm), and the interactions between the main laser beam (532 nm) and the ALIB in their intersection area triggers the ESLIB. The electron number density in the ALIB region is spatially non-uniform and temporally evolving, which increases during the intensive laser radiation period; however, the electron number decays rapidly afterwards. Therefore, the location of the intersection and the delay of the main pulse arrival after the ALIB (ΔPAT) determine the seed electron number density (ne,ALIB) that controls the characteristics of ESLIB.

The shape, size, and electron distribution of the ALIB are determined by the spatial-temporal profile of the 1064-nm pulse, pulse energy, focusing optics (SCL2), and the ambient gas condition (N), which are all fixed in this study. The input laser pulse energy of the main 532-nm pulse (Epulse) and the auxiliary 1064-nm pulse energy are fixed at approximately 100 mJ, which are measured at TPM1 and TPM3, respectively (Fig. 2(a)). Etrans (30 shot-averaged) is measured at TPM2, while the location of the intersection area is moved at 510 points (10 points (0.45 mm) × 51 points (2.5 mm)) on the yz-plane (see Fig. 2(b) and Fig. 5 on top). As shown in Eq. (6), τIB decreases as the ne,ALIB increases when NNALIB to terminate the pulse transmission earlier (earlier induction of ESLIB). Further increases in ne,ALIB will eventually elongate the τIB as predicted by the model; however, the highly populated seed-electrons will absorb significant photon energy to keep the Etrans low. The optical density ($OD ={-} {\log _{10}}({{E_{\textrm{trans}}}/{E_{\textrm{pulse}}}} )$) fields on the y-z plane in Cases 1 (ΔPAT ∼ 2 ns) and 2 (ΔPAT ∼ 7 ns) are plotted in Figs. 5(a) and 5(b), respectively. The red area in the schematic plot on top of Fig. 5 indicates a high electron number density (ne,ALIB) region where the intersecting 532-nm pulse would be mostly absorbed, scattered, and refracted, i.e., optically thick area (OD > 1). On the other hand, as the 532-nm beam moves away from the ALIB (increasing y-position), the beam passes through lower electron number density region near the boundary or outside of the ALIB area. Figure 5 indicates that the radius (y-axis) and the length (z-axis) of the ALIB volume are approximately 250 µm and 2 mm for Case 1, and 350 µm and 2.25 mm for Case 2, respectively, assuming z-axis-symmetry of the plasma volume. This is a typical geometry of the LIB plasma generated in atmospheric dry air: a cylindrically stretched region along the laser beam path. It is clear that the volume of the ALIB expands from Case 1 (2-ns delay) to Case 2 (7-ns delay) in both the y and z directions, presumably due to the absorption of the 1064-nm pulse energy (6-ns FWHM) during the extended delay. The OD field corresponds to the ne,ALIB distribution, and the range of OD at y = 0 in Case 2 is the widest, 0–1.5, which is preferable for controlling the ne,ALIB on the 532-nm beam path. Moreover, relatively uniform ne,ALIB in the intersection area (532-nm beam diameter = 60 µm) is expected near the plasma center (y = 0); therefore, the intersection is moved along the z-axis to modulate the 532-nm laser pulse.

 figure: Fig. 5.

Fig. 5. Optical density fields on the y-z plane in (a) Case 1 (ΔPAT ∼ 2 ns) and (b) Case 2 (ΔPAT ∼ 7 ns): relative standard deviation is estimated at y = 0 using individual pulse signal traces.

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The scattering signal profiles presented in Fig. 6 also delineate the ALIB region; these profiles agree reasonably well with the observation in Fig. 5. Each data point represents an average of 100 single-shot time-integrated measurements, normalized by the peak value of each case. The outlier points at z = 1.25, 1.5 mm in Case 2 were repeatedly observed; this behavior is not reflected in OD or Etrans profiles shown in Fig. 5. Similar spatial discontinuities of the plasma emission in early-stage (< 50 ns) LIB were reported by Chen [13] and Glumac [14], probably from bifurcation of the plasma. Recall that the scattering signal is captured in a narrow solid angle (θscat ∼ 20 °) in this study, and therefore it strongly depends on the irregular plasma surface geometry that evolves in time.

 figure: Fig. 6.

Fig. 6. Peak-normalized and time-integrated scattering signal of 532-nm photons when the 532-nm beam is on the z-axis (y = 0) and the ALIB is moved along the z-axis; Case 1 (blue) and Case 2 (red).

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It was previously reported that Thomson scattering predominates over Rayleigh scattering in the early-stage LIB [15]; therefore, the 532-nm scattering signal would strongly depend on the ne,ALIB. Thomson scattering intensity (Escat) can be expressed as [16,17]:

$${E_{\textrm{scat}}}d\Omega d\omega \propto {E_{\textrm{pulse}}}d\Omega d\omega \cdot {n_e} \cdot L \cdot {|{\hat{s} \times ({\hat{s} \times \hat{e}} )} |^2} \cdot S({{\mathbf k},\omega } ),$$
where, dΩ, , L, $\hat{s}$, $\hat{e}$, and S(k) are the solid angle, frequency range, intersecting length of the laser beam through the plasma, unit vector in the scattering direction, unit vector along the laser electric field, and a spectral density function. The S(k) depends on ω (wave frequency)$,$ k (differential scattering wave vector), scattering parameter, α (∝1/λD, λD = Debye length), and plasma properties including electron/ion temperature [17]. The α in the early-stage (5 - 90 ns) of LIB was derived by Diwakar [18], which indicates collective scattering behaviors (α ≫ 1). Equation (7) predicts that the Escat will monotonically increase with ne under the condition of collective scattering [16] since all other parameters are fixed in current setup. This was confirmed in previous experimental investigations [18]. The electrons causing the Thomson scattering can be from either the ALIB (ne,ALIB) or the ESLIB (ne,ESLIB). The early scattering signal that intensifies with the increasing pulse intensity (leading edge of the 532-nm pulse) would be induced by the seed-electrons from ALIB, while the electron number density (ne,ALIB) decays quickly, and a more intensive photon scattering signal will follow, which is from ESLIB-produced electrons. Two separate scattering peaks from the two different electron sources are clearly resolved in the scattering signal traces at z = 1.95 and 1.45 mm of Case 1 presented in Fig. 7; the two peaks are merged in some cases, depending on the z-position and ΔPAT. Recall that both the OD (Fig. 5(a)) and the scattering signal intensity (Fig. 6) at z = 1.45 mm are higher than the values at z = 1.95 mm. This implies that the seed electron number density is higher at z = 1.45 mm; therefore, the τIB is shorter to terminate the trailing edge earlier as shown in the transmitted pulse profiles. Note that a third-order Savitzky-Golay filter was applied to the temporal profiles in Fig. 7, which are normalized by the peak intensity.

 figure: Fig. 7.

Fig. 7. Transmitted pulse profiles and corresponding 532-nm scattering signal traces, normalized intensity versus time (ns), at z = 1.95 and 1.45 mm in Case 1 (100 single shots are plotted in gray). Black circles indicate the half-maximum, and τp is the FWHM. σpeak is the standard deviation of the temporal peak position.

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4.3. Pulse profile modification using ALIB-seeded and ESLIB-produced electrons

The ESLIB model simplified in Eq. (6) predicts that the τIB will decrease as ne,ALIB increases when NNALIB but rapidly increase again when ne,ALIB is exceedingly high with the result that the leftover neutral species population (N - NALIB) is depleted. The transmitted pulse profiles (532 nm) in Fig. 8 indicate that the τIB decreases, i.e., ESLIB occurs earlier to cut the trailing edge off earlier, as the 532-nm laser beam approaches the core of the ALIB region, increasing the ne,ALIB in the intersection area. Consequently, the FWHM of the transmitted pulse (τp in Fig. 8) decreases as the z-position moves from 2.5 mm to 1.45 mm in Case 1, and from 2.5 mm to 1.65 mm in Case 2, which is here defined as Type I modulation (Fig. 9). Transition to Type II modulation is observed as the z-position further approaches the core of the ALIB region; the OD reached its maximum at approximately z = 1.15 mm in Case 1 and 1.35 mm in Case 2. The pulse profile at z = 1.2 mm in Case 1 well explains the reason of this transition. Since the ne,ALIB at z = 1.2 mm is greater than that at z = 1.45 mm, τIB decreased to trigger the ESLIB earlier. However, the neutral species number density is low in this instance, mostly consumed by the preceding ALIB. Therefore, the additional electron production by the ESLIB is insufficient for terminating the 532-nm pulse tail, leaving behind a strongly modulated laser pulse. As the 532-nm beam further approaches the core, the ne,ALIB becomes so high that most of the pulse energy is quickly absorbed to block the leading edge of the pulse (z = 0.95 mm in Case 1, and z = 1.4 and 1.15 mm in Case 2 (Fig. 8)). Nevertheless, the photon energy supply from the 1064-nm laser pulse stops soon, and the leading edge of the 532-nm pulse is substantially weak to sustain the high electron number density in the intersection area. Therefore, the shutter opens later to allow the pulse transmission, and the ESLIB follows at significantly delayed τIB to cut the trailing edge off. This is defined as the Type II modulation (Fig. 9). As shown in Fig. 8 at z = 0.95 mm in Case 1 and z = 1.4 and 1.15 mm in Case 2, peak of the transmitted pulse, therefore, appears near the original peak in the Type II modulation.

 figure: Fig. 8.

Fig. 8. Transmitted 532-nm pulse profiles, normalized intensity versus time (ns); Case 1 in left column and Case 2 in right column. Black circles indicate the half-maximum, τp is the FWHM, and 100 single shots are plotted in gray. σpeak is the standard deviation of temporal peak position.

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 figure: Fig. 9.

Fig. 9. Temporal profiles of the original main laser pulse (black dashed), Type I-modulated pulse (red solid) and Type II-modulated pulse (blue solid) in (a) Case 1 and (b) Case 2.

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In Case 2 (ΔPAT = 7 ns), the auxiliary pulse does not overlap the main pulse (532 nm, 5.6 ns FWHM) at the intersection, and consequently, ne,ALIB monotonically decays before the interaction period. However, the auxiliary pulse partly overlaps the 532-nm pulse, arriving at the intersection approximately 2 ns later for Case 1. This makes the interaction difficult to control, and multiple short peaks appear; for avoiding the pulse overlap, laser pulses of shorter trailing edge (e.g., Type I modulated pulse) can be used to induce the ALIB. The diatomic species, nitrogen and oxygen in air, are another source of the complex physicochemical interactions, e.g., dissociation of the diatomic species, ionization and recombination of the dissociated atoms, and rotational-vibration internal energy modes. We conjecture that much finer control over the transmitted pulse profile is possible with monatomic noble gas in the breakdown area, which will be tested in future work.

5. Conclusions

A novel ns-laser pulse modulation method seeding electrons on the laser beam path was proposed. The seed-electrons quickly absorb the laser pulse energy to trigger the consecutive optical breakdown (electron-seeded laser-induced breakdown, ESLIB) that terminates the rest of the laser pulse after the ELSIB; that is, the plasma shutter stops laser transmission. The shutter closing time could be controlled by varying the number density of the seed-electrons (ne,ALIB) from a preceding auxiliary laser-induced breakdown (ALIB) generated near the beam path. Location of the ALIB and the time delay of the laser pulse arrival after the ALIB were adjusted to control the ne,ALIB and ultimately to vary the temporal width and energy of the laser pulse passing through the region near ALIB. The ALIB was generated by focusing a 1064-nm Nd:YAG pulse which was split after frequency doubling, and the frequency-doubled 532-nm pulse was redirected to pass through the near-ALIB region to be modulated.

It was found that the shutter closing time gets shorter as the ne,ALIB increases; therefore, the trailing edge of the 532-nm pulse could be cut off at a designated time, which is Type I modulation that can vary the FWHM of the transmitted pulse from 5.6 ns (original FWHM) to 1.5 ns. On the other hand, the photon absorption by the seed-electrons becomes significant to temporarily block the leading edge of the 532-nm pulse when the ne,ALIB exceeds a threshold. Later, the shutter re-opens due to the fast decay of the ne,ALIB, and the ESLIB will follow to terminate the trailing edge, which is Type II modulation that could reduce the FWHM further down to 0.83 ns cutting both the leading and trailing edges. A simplified analytical model of the electron-seeded plasma shutter was built and well predicted the two different pulse modulation types.

This pulse modulation method will potentially extend the application of LIBS via conveniently adjusting the characteristics of the breakdown plasma induced by the modulated pulses; modulated pulses of shorter FWHM can significantly reduce the plasma heat generation, while longer pulses will intensify the plasma emission signal under low gas-density conditions.

Funding

National Research Foundation of Korea (2021R1A4A1032023, 2021R1A2C2012697), Korea Institute of Energy Technology Evaluation and Planning, (20206710100030).

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

References

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Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (9)

Fig. 1.
Fig. 1. Linear fit of the Gaussian pulse profile for the 10-to-90% of the peak intensity.
Fig. 2.
Fig. 2. (a) A schematic of the experimental setup used for modulating ns-laser pulses with electron seeding. M, mirror; HWP, zero-order half-wave plate; QWP, zero-order quarter-wave plate; PBS, polarizing beam splitter; W, fused silica window; NDF, absorptive neutral density filter; PD, photodiode; MWF, mirror with flip mount; MWS, mirror with linear translation stage; SCL, spherical plano-convex lens; ID, iris diaphragm; BT, beam trap. (b) The yz-plane at the intersection on where the ALIB is relocated.
Fig. 3.
Fig. 3. Forward scattered 532-nm photon collection. SCL, spherical plano-convex lens; SPF, shortpass filter; BPF, bandpass filter; NDF, absorptive neutral density filter; PD, photodiode.
Fig. 4.
Fig. 4. Transmitted laser pulse energy (Etrans) and transmittance (T) versus Epulse.
Fig. 5.
Fig. 5. Optical density fields on the y-z plane in (a) Case 1 (ΔPAT ∼ 2 ns) and (b) Case 2 (ΔPAT ∼ 7 ns): relative standard deviation is estimated at y = 0 using individual pulse signal traces.
Fig. 6.
Fig. 6. Peak-normalized and time-integrated scattering signal of 532-nm photons when the 532-nm beam is on the z-axis (y = 0) and the ALIB is moved along the z-axis; Case 1 (blue) and Case 2 (red).
Fig. 7.
Fig. 7. Transmitted pulse profiles and corresponding 532-nm scattering signal traces, normalized intensity versus time (ns), at z = 1.95 and 1.45 mm in Case 1 (100 single shots are plotted in gray). Black circles indicate the half-maximum, and τp is the FWHM. σpeak is the standard deviation of the temporal peak position.
Fig. 8.
Fig. 8. Transmitted 532-nm pulse profiles, normalized intensity versus time (ns); Case 1 in left column and Case 2 in right column. Black circles indicate the half-maximum, τp is the FWHM, and 100 single shots are plotted in gray. σpeak is the standard deviation of temporal peak position.
Fig. 9.
Fig. 9. Temporal profiles of the original main laser pulse (black dashed), Type I-modulated pulse (red solid) and Type II-modulated pulse (blue solid) in (a) Case 1 and (b) Case 2.

Tables (1)

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Table 1. Nomenclature.

Equations (7)

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d n e d t = W m I m N + ( ν coll ν loss ) n e ,
0 τ IB { W m I m N n e + ( ν coll ν loss ) } d t = ln ( n e,c n e,ALIB ) ln ( n e,c n e,i + n e,ALIB ) = τ M P I 0 τ IB ν i,eff d t .
I ( t ) = I 0 e x p ( 4 ln 2 ( t τ m τ p ) 2 ) ,
I ¯ = 0 τ IB I ( t ) d t τ IB = E pulse C fit 2 A τ p τ IB ,
0 τ IB ν i,eff d t = ν i,eff ¯ τ IB = ( N N ALIB ) I ¯ k τ IB = ln ( n e,c n e,ALIB ) ,
τ I B ln ( n e,c n e,ALIB ) ( N N ALIB ) I ¯ k ( ln ( n e,c n e,ALIB ) N ( 1 N ALIB N ) ) 1 k + 1 ( E pulse ) k k + 1 .
E scat d Ω d ω E pulse d Ω d ω n e L | s ^ × ( s ^ × e ^ ) | 2 S ( k , ω ) ,
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