Ultrashort-Pulse Burst-Mode Materials Processing and Laser Surgery

Abstract

Laser processing of materials and biological tissues has evolved in stages, ever since the earliest use of the laser for gross deposition of heat and for ablation. For instance, wavelength specificity was an early development that facilitated the treatment of certain biological tissues, while leaving others relatively unaffected. Ultrashort-pulse material ablation escapes the usual paradigm of heat diffusion because of the comparisons of scales: A rarefaction wave can cut through the thin layer of femtosecond-laser-heated material and carry away the absorbed energy before much heat can diffuse into the substrate. Burst-mode femtosecond laser ablation brings yet another paradigm, in which the laser fluence is divided over two disparate timescales: the ultrashort duration of a pulse and the microsecond-scale duration of a burst. This division of timescales opens new avenues for control, because much of the governing physics is about the comparison of timescales—for instance, the timescale of thermalization of heated electrons into the substrate lattice or the timescale of hydrodynamic ablation. Applications to fused silica, to in vitro cell-cultures prepared in hydrogels, and to ex vivo articular cartilage help to show what is different in the science of ultrashort-pulse burst-mode laser processing.

1. Introduction

At the time of its invention, Irnee D’Haenens in Theodore Maiman’s laboratory was credited with describing their first laser to Maiman as “a solution looking for a problem” [1]. Over the years, endless applications have been found, both directly and, perhaps with even greater impact, as an enabling technology.

In laser materials-processing and laser-surgery, this path toward problems solved might be usefully framed in terms of qualitative generations of applications that have re-framed what the laser can do:

First Generation—Power Delivery: cutting without tool bits, offering non-contact, low-contamination; spatially localized delivery of gross heat to workpieces, to cut or weld metals, cut cloth, wood and plastic. From lab to factory before the 1960s ended.

Second Generation—Wavelength-tunable selective absorption: differential control due to intrinsic or extrinsic absorbers; specialized cutting in plastics; surgical cauterization; port-wine-stain birthmark-removal. Roughly from the 1970s onward.

Third Generation—Modes of Fluence Delivery: controlling duration/intensity/pattern of pulses; ultrashort-pulse chirped-pulse amplification (CPA) lasers, low collateral damage surgery and micromachining, custom machining of microfluidics (emerging in the 1990s) and direct-write of internal optical waveguide structures in bulk glasses (emerging in the early 2000s).

At the most basic level, the final outcomes of laser treatment of materials or biological tissues are governed by several key observations:

1. At its simplest, material modification requires deposition of specific energy (energy/unit mass), a per-atom energy characteristic of chemical or material-structure changes, e.g., latent heat of melting, or of vaporization.

2. This deposited specific energy derives from a given absorbed laser fluence (radiant exposure: energy/unit area), together with a characteristic range of heat diffusion into the sample.

3. Therefore the most basic issues around laser materials-processing and laser-ablative surgery are the absorption and subsequent disposition of incident laser energy as heat.

In broad terms, the impact of long- and short-pulse laser materials-processing differ because of characteristic time-scales of materials and of processes, meaning that the two classes bring with them very different relationships to jobs needing to be done. Given that specific energy, and therefore laser fluence, is a driving figure-of-merit, we can use it to compare in generalities:

Long-pulse lasers—For a given delivered fluence, longer-duration pulses mean lower peak intensities. At lower intensities, nanosecond and microsecond-pulse lasers typically exploit linear absorption, either from intrinsic absorption and endogenous chromophores or from Joule heating in the case of conductors. Energy is absorbed over a depth determined by the inverse of the optical absorption coefficient. Dielectrics such as glass depend on nonlinear absorption and therefore high peak intensities in order to surpass the dielectric breakdown threshold; however, after breakdown and plasma creation the absorption becomes linear but largely independent of the original material. The result is that, for nanosecond or longer pulses on dielectrics, this runaway process necessarily means that far more energy than desired may be delivered.

Ultrashort-pulse lasers—For a given delivered fluence, peak intensity goes up as the pulse-duration shortens. Short-enough pulses then assure dielectric breakdown and plasma formation, regardless of whether a material has appreciable linear absorption. Absorption is then plasma-mediated, with the effect of making absorption “universal”: independent of local variations in extrinsic absorption from defects, impurities or dopants, or independent of having distinct endogenous chromophores in different locations, as is the case for a differentiated biological tissue containing a mix of connective tissues, nerve and muscle.

In particular, plasma-mediated absorption, because of the effect of plasma screening, also puts a constraint on the optical absorption depth. This small optical absorption depth, and the limited amount of plasma produced by pulses that are over so quickly, mean that the mediating plasma that absorbs laser energy is thin. These are principal factors in why ultrashort laser-pulse processing leaves so little heat behind in the target.

Ultrashort-pulse lasers, used at intensities near the damage threshold, show much less shot-to-shot variability in outcome than do nanosecond and longer pulses, even in a pure dielectric such as fused silica [2, 3]. This, too, is due to a qualitative change in physics relationships governing ionization [4, 5]. For ultrashort-pulse lasers, shockwaves launched in the material also show a reduced range of shock-damage, a thing particularly important in laser-surgery [6, 7].

Ultrashort-pulse lasers are used to deliver fluence on target at values similar to those used for longer-pulse lasers, but they deliver that fluence over shorter timescales and at higher intensities. Each of these qualitative changes above traces back to a change in physics, obviously, but more particularly these changes trace to ways in which delivery by ultrashort-pulse lasers crosses characteristic timescales and intensities, and thereby qualitatively changes the governing physics-relationships.

2. Physics relationships of single-pulse ultrashort-pulse material processing

In physics, meaning naturally derives from relationship. Every formula relates parameters to an outcome, every plot shows a dependency. Dimensionless numbers mark for us, as ratios, the truly qualitative shifts in relationship that govern major changes in physical interactions. For instance, the Mach number marks the qualitative change that happens between subsonic and supersonic flight—the transition at which the control surfaces at the trailing edge of a wing can no longer affect airflow over the wing, because the pressure change induced by changes in, say, an aileron, cannot travel forward as a sound wave, against the oncoming flow of air which is traveling faster than the speed of sound. The Prandtl number Pr is the ratio between the diffusivity of momentum in a fluid flow to the diffusivity of heat in that fluid—it flags the flow of energy via bulk convection (Pr > 1) as compared to the flow principally via heat diffusion through a fluid.

For laser interactions with materials, Figure 1 helps to give context to our relevant timescales. For instance, the extended plasma plume generated from laser ablation may take hundreds of nanoseconds to a microsecond to dissipate—it makes a few-nanosecond laser pulse look impulsive, like a Dirac delta-function, by comparison. Yet lateral thermal conduction or ambipolar diffusion in the plasma around critical density is so rapid that the rise and fall of a few-nanosecond pulse looks like an adiabatic change by comparison. However, ambipolar diffusion in the plasma, or lateral thermal conduction, seem frozen in time during the interaction of a subpicosecond pulse. Changing from few-nanosecond to subpicosecond laser pulses, the relationship of timescales between laser and material process is inverted—the role of those processes is qualitatively changed, and their significance is fundamentally different: in the case of few-nanosecond pulses, ambipolar diffusion and lateral thermal conduction essentially follow the laser conditions in near steady-state; for subpicosecond laser pulses, they are virtually frozen in time.

Figure 1.

Summary of material and process timescales relevant for laser materials-processing and surgery. For burst-mode ultrashort pulse laser processing, a new timescale is introduced by the time-separation of pulses within a burst. The repetition-rate period is also a timescale, typically long compared to these processes. The significance of the pulse duration or intraburst time delay is context-dependent, emerging from native timescales of the problem [8].

In this general way, ultrashort pulse materials-processing is distinguished by a transition which changes laser-energy deposition from a near-steady state dynamic, with power deposited at a surface and then flowing onward by diffusion, to one in which a small thin volume is suddenly heated, and not long afterwards dispersed. Then whatever little heat has made it into the material, before the mediating plasma disperses, is left to diffuse inward after the fact, and its final impact may be determined long after the laser interaction has ended.

Among modes of fluence-delivery, femtosecond and few-picosecond laser pulses are unique in laser materials-processing and laser surgery for the small amount of collateral damage they typically produce in a target substrate, and the small amount of residual heat they leave behind [2, 3]. How does this categorically different result relate to the inversion of the relationship of timescales?

Fundamentally, free electrons cannot absorb energy from the passage of an infinite-plane oscillating electric field, but of course this changes with collisions. The principal path to plasma formation is avalanche ionization of atoms through collisions of electrons rapidly driven in the intense optical field. Yet collisional ionization by electrons requires that at least some free electrons be available, and original speculation was that in dielectrics like fused silica these were provided by multi-photon ionization [2, 3, 9]. Subsequent wavelength-scaling studies established that initial ionization originates instead from AC tunneling ionization of atoms in strong fields [4, 10]. For materials with intrinsic or extrinsic absorption, initial ionization can begin thermally, following initial linear absorption. This scenario is equally available to nanosecond interactions that create plasma. But there’s a qualitative transition for collisional ionization under intense ultrashort-pulses.

The cross-section for atom ionization by laser-driven electron-impact depends importantly on the electric field strength: assuming constant fluence, the optical field strength going from few-nanosecond- to 100-femtosecond-duration pulses increases by orders of magnitude. Over this range, the cross-section for laser-driven collisions rises by orders and then trends toward saturation at higher field strengths [5, 11], fields routinely accessed by ultrashort-pulse lasers in laser materials-processing, but not typically by nanosecond or longer pulses. The consequence for laser materials-processing is that avalanche ionization is more sensitive to field-strength variations within the range of fields generated in nanosecond pulses than it is within the range of fields of subpicosecond pulses. Consequently, tests of damage threshold for ultrashort pulses are quite repeatable, whereas for longer pulses the range of scatter in laser intensity-values associated with damage is much greater [2, 3].

Once a thin mediating plasma has been established, absorption of laser energy into the plasma becomes quite generic and linear, and is largely determined by electron density and gradients of the electron density profile around the plasma critical-density surface.

2.1 Time scales for depth of heating in plasma-mediated absorption

Under these conditions, one of the relationships governing laser materials-processing is overthrown. During the time (i.e., the pulse duration τ) that laser energy is applied to a material or biological tissue, thermal diffusion produces a characteristic scale-length $L_{th}=\sqrt{D}$, where D is the thermal diffusion constant of the medium. This should not be understood as a range of the heat-affected zone, because it contains no reference to the absolute energy deposited, and, as noted above, a phase transition such as melting requires a specific energy, like the molar latent heat necessary for vaporization and ionization of a solid. Other heat-affected processes may be more complicated, and may depend on more than just the heat delivered or peak temperature achieved: an example would be protein-denaturation, which is governed by both temperature and duration, as expressed through the Arrhenius damage integral. In either case, the extent over which the threshold condition is met for being heat-affected is not the scale length of the distribution of heat. This thermal scale-length is instead a characteristic, much like the skin depth of an optical field penetrating a metal.

Indeed, the laser field has just such an optical skin-depth, δ, for the field (or an absorption scale-length for the intensity), in the thin plasma that has formed (cf. the Bouguer-Lambert law). The comparison of these two scale-lengths—thermal vs. absorption—is the next qualitative change in relationships that arises as the physics of interaction transitions, as progressively brief laser pulses effectively “freeze” important physical processes.

As pointed out by Pronko et al. [12], a wavelength of 800 nm produces an optical absorption scale-length of about 12 nm in metallic silver. The thermal diffusion scale-length L_th above will equal this in the case of a pulse of duration τ = 7 ps. On the timescale of pulses very much shorter than 7 ps, diffusion appears relatively “frozen,” and the heat distribution during the laser pulse is set by the properties of the plasma alone. For substantially longer-duration pulses the heat scale-length during the pulse is governed by diffusion.

At the end of an ultrashort pulse, the tiny optical absorption depth of a dense plasma means a very thin layer of constant thickness has been heated to an ionized state. Therefore the material damage threshold is reached at a reduced laser fluence, which becomes independent of pulse duration.

For pulses tens of picoseconds and longer, a $\sqrt{\tau }$ dependence of damage-threshold fluence on irradiating-pulse duration was well-recognized [13, 14, 15]. For pulses shorter than about 10 ps, early studies from both Livermore and Michigan groups showed a relationship change, for damage in transparent dielectric targets [4, 5, 9]. Researchers initially disagreed about the behavior below this point of transition, but it’s now largely agreed that the damage-threshold fluence does become constant for pulses with τ < 10 ps.

More recently, refinements in modeling the non-thermal transport of electrons generated in intense laser-plasma interaction have added to the understanding of heat deposition in the substrate, including the range and heating of a fraction of electrons that penetrate directly [16, 17].

2.2 Time scales for erosion of thin mediating plasma layer

For femtosecond laser pulses, hydrodynamic expansion is a relatively slow process, and the mediating plasma layer is typically quite thin at the time the pulse ends. The absorbed energy resides as heat in this plasma layer, in close contact with the target substrate, and heat diffusion will carry a small amount of heat inward while the laser pulse is depositing energy into the absorption-depth layer.

A new time scale enters at this point, while the thin heated layer of plasma is still in thermal contact with the substrate. The subsequent erosion of this thin hot plasma layer is by a rarefaction wave—the “negative profile” hydrodynamic wave of loss of density, moving inward through the plasma layer. This rarefaction wave is the same general phenomenon as the process by which an inflated party balloon releases its internal overpressure once the latex rubber has been popped and very rapidly retracts over the whole surface, or by which a collapsed dam creates a traveling depletion wave in the water-level of the reservoir previously contained.

The timescale of erosion of the thin plasma layer is governed by the speed of propagation of a density wave in the plasma, c_s, together with the layer thickness d. After a time $t\cong d/c_s$, the heated plasma has decoupled from the target and been carried away in the expansion—the phenomenon of ablative quenching.

$$c_s=\sqrt{\frac{\overline{Z}{k}_B{T}_e}{M}}$$E1

Here c_s is the ion-acoustic speed; T_e is the isothermal electron temperature. The ion temperature T_i is relatively low, so that T_e ≫ T_i; $\overline{Z}$ is the ion average charge-state; M is the ion mass (the electrons are assumed to be isothermal, typically justified). An ion-acoustic wave is the plasma density wave in which the restoring force is derived from the electron pressure, via the electron temperature, and the inertial term is the ion mass. Effectively, the electrons dress the ion perturbations within a characteristic Debye length, coupling the electron and ion density perturbations together. See also Kerse et al. [18].

Thus, the time of heating is not the duration of the laser, but instead is the lifetime of the plasma layer in thermal contact with the target material. After this point, the heat diffusing inwardly in the target is only what energy had already propagated past the laser-heated plasma and into the substrate during the brief time the mediating plasma was in contact. For a subpicosecond pulse and an absorbed fluence of 40 J/cm², into a laser skin-depth of ~50 nm, a simple estimate of electron temperature gives an ablative-decoupling time of a few picoseconds. For longer-pulse lasers still less than about 100 ps, thicker layers of plasma are heated, and the time to decouple this reservoir of heat from the surface is longer, leading to greater heat-impact in the target. For pulses of roughly 100 fs or less, very little residual heat is left in the material; in biological tissues there may be very little histological impact or inflammatory response, just a few cells away from a laser-cut wound-edge, and thin shock waves will erode as they propagate relatively short distances, due to viscous dissipation.

2.3 Scale lengths for erosion of shock waves

The scaling of ultrashort-pulse lasers leads to another inversion in relationship: for the propagation of laser-created shockwaves. Early in the exponentiation of laser applications, it was identified that strong heating and cavitation from laser interaction could drive shockwaves through water [19]. The nature of such shockwaves is well known: a material surface is driven at a speed greater than the local speed of sound. Pressure increases locally, as the moving surface accrues material faster than it can unload as a pressure wave (acoustic wave). The driving surface ultimately drops to a speed below the speed of sound, and the local region of increased pressure detaches as a propagating feature with a steep front. The steep front propagates at a speed determined from the amplitude of the shock—a speed greater than the speed of sound in the background material.

Originating from a laser focus, the shock wave diverges in 3D, increasing its surface area, and spreading its energy thinner. At some distance depending on the shock strength, the pressure jump degrades until it goes merely sonic.

The transitions at the leading and trailing edges of the shock involve sharp shear stress of the flow, which can result in material or tissue and cell damage. Because of the large shear rates there, the transition is subject to viscous dissipation, with wave kinetic energy converted to local heating, and in the process eroding the shock. Thus the shock weakens and can vanish by viscous effects, in addition to dissipating as the shock diverges and is spread out.

From this arises an additional scaling that ultrashort-pulse lasers can exploit: shockwaves launched in the material from femtosecond pulses are thin, as their driving is brief, and may vanish from viscous dissipation long before their strength is otherwise naturally spread out and reduced. Shocks driven by a fixed fluence of 9 J cm⁻² in corneal tissue show a striking difference depending on mode of fluence-delivery: the range of shocks driven by 150 fs laser pulses is an order of magnitude less than when delivered using 60 ps pulses [6, 7].

2.4 Longer-time diffusion of heat and range of heat-affected zone

The mediating plasma layer decouples rapidly from the substrate, for ultrashort-pulse laser ablation—essentially the absorbed energy is carried away in the ablated material itself, quenching the process. What residual heat has managed to couple to the substrate, in the brief time before quenching, then diffuses normally, but its timescale relation is essentially lost. The residual heat-affected range in this case is determined by the maximum extent of heating in the context of the relevant threshold (e.g., latent heat of melting), as the heating spatially spreads and decays in intensity.

By way of heuristic illustration, consider Figure 2, which supposes heat deposited initially in a Gaussian pattern in one dimension, into a homogeneous material. This profile diffuses as a Gaussian distribution, its width increasing and its amplitude decreasing, preserving the total area under the curve (i.e., without energy loss). At any time, a heat-affected zone can be identified (arrows in Figure 2) as the range over which the local specific heat (cf. temperature profile) exceeds the threshold for a specific effect under consideration, such as melting, or meets the conditions for protein denaturation.¹ In the figures, initially this radius increases, as the heat spreads; but the amplitude also decays, and in the trade-off the boundaries (arrow tips) where the threshold condition is met subsequently shrinks. The ultimate extent is then the maximum extent for which the threshold was met, at any given time.

Figure 2.

A schematic depiction of the diffusion of a generic Gaussian temperature distribution over space, for different times (A–F). Where a specific-energy threshold effect (dashed blue line: e.g., necrosis, latent heat of vaporization), provides the reference, neither the initial full-width at half-max (FWHM) nor the thermal-diffusion length-scale L_th is the figure of merit for the range of heat impact. Instead, the extent of impact grows, then diminishes, and the ultimate heat-affected zone is the maximum value. Video 1 animation of this can be viewed at https://youtu.be/ioogrzE_46I [8].

For single ultrashort pulses, this residual heat is quite small and may not show any heat-affected zone. But for burst-mode delivery of fluence, discussed below, the accumulation of many small residuals can have a useful and controllable impact. The heuristic notion of Figure 2 will be revisited quantitatively and in simulation later in this discussion.

3. Physics relationships of burst-mode ultrashort-pulse material processing

For single ultrashort-pulse laser treatments, at repetition rates much less than about 1 MHz, all plasma and most heat in the substrate will dissipate before the next pulse of a sequence arrives, and the mediating plasma must be re-established by each subsequent pulse. Very little heat is left behind, but it is typically only negligible for repetition-rates less than roughly 100 kHz.

Burst-mode ultrashort-pulses—packets of tens to thousands of pulses delivered at multi-MHz repetition rates—cross time-scales and create new control in two ways: (1) tiny but non-negligible heat left by single ultrashort-pulse lasers will not have dissipated, creating the option for accumulating a desirable amount of residual heat, and (2) ionized atoms comprising the plasma may not have fully recombined, meaning that an opportunity is created for simmering the conditions which control plasma-mediated absorption. We introduced burst-mode ultrashort-pulse laser processing as a new mode of fluence-delivery around 1999, [21, 22, 23, 24] using amplified trains of 1 ps pulses derived from a feedback-controlled Nd:glass oscillator [25].

In Figure 1, red bars illustrate the disparate time scales for pulse duration and for the separation of pulses within a burst—added to this might also be a third bar to indicate the duration of a burst (typically ~100 ns to ~1 μs), and a fourth for the period of the burst-repetition rate. The pulse duration, time-separation between pulses within a burst, total burst-duration, and pause-time between bursts delivered, all have an impact on the amount of heat left within the target, the time-dependent temperature, and the strength of shock waves that may be generated in a biological tissue or material [26, 27, 28, 29].

3.1 Slow heat accumulation

As mentioned above, for nanosecond and longer-duration laser pulses, a heat-affected zone (HAZ) surrounding the focal spot may be large, and significant collateral damage may result. Single ultrashort pulses are known typically to leave behind negligible—but not zero—residual heat. Given that burst-mode ultrashort-pulse laser treatments combine both timescales, do they exhibit long-pulse characteristics like the duration of a burst, or ultrashort-pulse characteristics deriving from the individual pulses that comprise the bursts? The answer is that bursts allow controlled accumulation of small amounts of residual heat typical of ultrashort pulse interaction.

To show this, 100 μm-thick aluminum foils were drilled through by single bursts of 1600 1 ps pulses (12 μs @ 133 MHz), at integrated fluences up to 6 kJ cm⁻², and hole diameters were recorded (Figure 3 [8]). As the burst-fluence increases, the size of the hole cut through increases, but not surprisingly this size is not just the imprint of the focal spot—the hole radius is not simply the radius below the Gaussian focal spot distribution at which the specific energy directly imprinted matches the specific latent heat of vaporization. Ablation was not determined by local heat deposition. Instead, the much larger hole sizes seen can be fitted in Figure 3 by a dependence E₀^1/2.

Figure 3.

Measured dependence of through-hole diameter as a function of average irradiant exposure (fluence), for 100 μm-thick aluminum foils under burst-mode processing. The hole size is shown compared to two simple models: (A) the radius within which the Gaussian focal spot locally “prints” sufficient fluence F so that the specific energy F/l equals the latent heat of vaporization; and (B) the maximum extent (cf.Figure 2) achieved starting from an initial Gaussian temperature-profile derived from the laser-spot profile.

The hole diameters produced in aluminum foils, in the series of Figure 3, can be matched [8] by finding—over a family of equal-area 2D Gaussians, similar to the heuristic of Figure 2—the maximum radius for which the specific energy threshold is met, viz.,

$$r_{\max }=\sqrt{\frac{E_0}{l{Q}_{sp}e}}$$E2

with E₀: absorbed energy shared to the foil (after ablative quenching), l: foil thickness (100 μm in Figure 3), Q_sp: latent heat of vaporization (J cm⁻³) and e is Euler’s number.

Figure 4 illustrates this radius at different times, identifying the maximum above. This shows a model of heat diffusion in aluminum following irradiation by a single 12-μs burst of 1-ps pulses, focused to a spot of 5-μm radius. The simple model is illustrative: it assumes equal-efficiency absorption for all pulses, without hydrodynamics. Two different net-absorbed pulse-energies are compared, corresponding to different pulse-energies or to different absorption efficiencies. The sketched trajectories show the radius r(t) at any time of a disk within which the specific energy exceeds the latent heat of melting for aluminum. The two ultimate melt-diameters of Figure 4 are 15 and 44 μm, to compare to the 30 μm maximum hole-diameter from Figure 3.

Figure 4.

Model of heat diffusion in aluminum for two possible absorbed laser per-pulse energies. A 12-μs train of 1-ps pulses is focused to a focal-spot radius of 5 μm. The trajectory, for each energy, traces the boundary radius of the disk inside of which the temperature exceeds the melting point of aluminum (cf. heuristic Figure 2, in 1D).

3.1.1 Ductile cutting of glass

Brittle materials bring their own challenges for laser materials-processing. For 1 ps single-pulse ablation of fused silica, 200 J cm⁻² was seen to be a limit, corresponding to etch-depths of a few micrometers [8]. Above this single-pulse fluence, the sample typically would shatter in a single shot. Delivering the same fluence, but divided over multiple single pulses at 1 Hz repetition-rate, the weaker shots would cumulatively etch only to about the same ultimate depth before they, too, shattered the glass (Figure 5 (left)). The final effect was that single pulses delivered at the same location could not ultimately etch more deeply than a few micrometers, regardless of delivering a fixed fluence in a single strong pulse, or divided into multiple weaker shots [21].

Figure 5.

Scanning electron-microscope (SEM) micrographs of laser-irradiated fused silica. Left: top view, four individual 1-ps pulses at 1 Hz, λ = 1 μm, 93 J cm⁻² fluence each; Right: oblique view of a ~15-μm deep channel made into BK7 glass by one burst (300 1-ps pulses, λ = 1 μm). The channel has smooth walls and shows no evidence of fractures or cracks.

This contrasts with the effect of a burst of 300 1 ps pulses at an intraburst rate of 133 MHz, which etch to 10–30 μm in one shot. These etch-depths are deeper than those possible by accumulating single shots. Burst-mode irradiation permitted per-shot fluences of 1–60 kJ cm⁻², well beyond the limit at which any number of isolated pulses shattered the fused silica. Figure 5 illustrates the result: an optically smooth bore, and a lip of material apparently raised while the material was ductile [8].

An important theme of burst-mode ultrashort-pulse materials-processing is that while isolated subpicosecond pulses leave negligible heat behind, this small residual heat can be accumulated within a rapid burst. In practice, glass is transformed from a brittle to a ductile state during a burst, and cutting is achieved during that ductile state.

The accumulated heat results in permanent material changes, as well as this glass-transition softening during processing: after hole-drilling in glass, a change in refractive index can be seen in the zone just outside the channel that has been cut (Figure 6).

Figure 6.

Hole from one burst-shot drilled in fused silica; optically smooth sides, showing limb of glass with index-of-refraction changes. 300-pulse burst, τ = 1 ps, λ = 1 μm, intraburst rate of 133 MHz. Dotted line indicates top glass-surface making total internal reflection, for this side-view.

Figure 7 shows the micro-Raman spectrum of untreated fused silica along with the spectrum sampled for the remelted lip around the ablation crater. The features corresponding to three- and four-member breathing modes show that there is a change in the bond-coordination statistics, which may correspond to densification of the glass. The details of the number of pulses in a burst, their energies, and even the pattern—the distribution of their amplitudes within the burst—offer control over the residual heat accumulated and its range.

Figure 7.

Micro-Raman spectra (MRS) of fused silica comparing unmodified glass far from the treatment site to the smooth lip of glass around the ablated hole. Where the glass has been melted and resolidified, there are significant changes in the ring-bond structures.

3.1.2 Control of heat accumulation in hard biological tissues

We can demonstrate control of accumulation of small pulse-to-pulse residual heat by simply changing the duration of a burst. Figure 8 shows burst-mode treatment of ex vivo dentin tissue from rat teeth. Trains of about 650 pulses at 133 MHz show thermal changes that are localized, with a kind of melting of the surface of the dentin. Twice that length, about 1300 pulses, results in gross melting and pooling at the lip of the hole drilled. Three times the original length (2000 pulses) exhibits splashing before re-solidification.

Figure 8.

SEM images of rat dentin tissue irradiated by single bursts of duration 5, 10, and 20 μs (22 kJ cm⁻², 44 kJ cm⁻², 67 kJ cm⁻², respectively). 1 ps pulses at 133 MHz. Magnification scale bars in each image are 5 μm [8, 30].

Micro-Raman spectra (Figure 9) from the inside of laser-cut channels, and from the glassy-looking redeposited material at the hole-lip, show molecular structural changes suggesting that the organic component of dentin ablates away [8, 28].

Figure 9.

Micro-Raman spectra (MRS) of native enamel (bottom trace, red) and of both untreated dentin (middle trace, blue) and 1 ps burst-mode treated dentin (top trace, green), intra-burst rate of 133 MHz. The burst-mode laser-modified dentin is glassy in appearance—MRS shows it has almost completely lost its organic components, the dentin converted to a structure more like enamel [8].

3.1.3 Incubation effects and division of fluence-delivery

The observed differences between modes of delivery, isolated or rapid bursts, raise the question about how one pulse affects the absorption of the next, when the material or plasma has an effective memory with a characteristic timescale. In laser materials-processing of crystalline and amorphous solids, a well-known effect is “incubation” of crystal defects, subtle material modification, or latent damage [16]. For instance, there is evidence in metals that long-lived crystal dislocations can be accumulated in the bulk, following irradiation with many pulses just below the catastrophic damage threshold. These occur over the depth of heat diffusion, accumulating over many shots before gross damage is manifest. In irradiation of dielectrics at intensities below dielectric breakdown, color centers can be developed. Such subtle preconditioning of the material is thought to have an ultimate impact on ablation damage-thresholds. It might well be expected to be a factor that affects pulse-train burst mode treatments.

For burst-mode ultrashort-pulse interactions, mediated by plasma absorption, we investigated incubation-type effects using a principle of “fluence division”—delivering one, constant, net fluence and constant number of pulses, but dividing it over separate bursts that must restart the interaction each time [8].

This constant total fluence (18 kJ cm⁻²) was delivered in four different modes: as a single burst of 12 μs, split into two bursts of 6 μs, three bursts of 4 μs, or four bursts of 3 μs, with a delay of a few seconds between bursts to ensure complete relaxation of the processes involved. Thus, a single pulse-train burst of 1600 pulses was partitioned into N smaller sub-bursts, each with n pulses, keeping $N\times n=1600$. We compared the depth of etching for each of these modes of delivering the same fluence.

Figure 10 shows the results for fused silica; Figure 11 shows the results for human dentin. In either case, breaking up the burst into sub-bursts created progressively shallower net etch-depths: each time the laser-matter interaction was re-started, there was loss of efficiency.

Figure 10.

Fluence-division effect in fused silica: overall fluence, and number of pulses (1600) delivered to each site was kept constant, but delivered in separate bursts: 2 bursts × 800 pulses, 3 × 533, and 4 × 400. “Restarting” the ablation process instead of letting it continue imposes a cost on ablated volume interruption. The “restart cost” is equivalent here to ~155 pulses lost from cutting each time interrupted. Total fluence was fixed at 18 kJ cm⁻² [8].

Figure 11.

Fluence-division effect in dentin at two different per-pulse fluences (cf.Figure 10 for fused silica). In the lower-fluence case, the “restart-cost” is equivalent here to ~280 lost pulses; this reduces to only ~130 pulses lost, in the case of the higher-fluence interaction. Integrated fluences were kept constant: 5.4 kJ cm⁻² (lower fluence, green curve) and 54 kJ cm⁻² (higher fluence, blue curve) [8].

The loss-trend can be explained by the hypothesis that a certain number of pulses at the start of any burst go into conditioning or incubating the material before ablation really begins, and depth of cutting is proportional to the remainder of pulses in each burst.

This can be interpreted as follows: We posit that for any burst with a given per-pulse fluence a number a of pulses are expended at the start before ablation substantially begins. If one burst consisting of A pulses is partitioned into N mini-bursts, then N·a pulses are ultimately lost as “overhead” to seed the ablation process, leaving A − N·a pulses to do the etching. If these remaining pulses then etch with unchanged efficiency, once the material has been preconditioned by the initial a pulses each time, then the etch-depth which results will scale as A − N·a.

For fused silica (Figure 10), the scaling fits the data well on condition that a = 155 pulses go into conditioning at the start of any burst. The more times the initial pulse train is interrupted, the greater the overall “overhead” cost.

For dentin, in Figure 11, there are two cases with different net fluence: low per-pulse fluence at 0.34 J cm⁻², and high fluence an order of magnitude higher at 3.4 J cm⁻². For the lower fluence case, a good linear fit suggests a latency equivalent to the first a = 300 pulses of each mini-burst. For the higher-intensity case, a similar fit suggests a latency of about a = 128 pulses. These results may indicate that under these conditions ablation may not begin immediately, while some transient preconditioning effect is in play, possibly that the density of plasma builds instead of promptly ablating, or perhaps that the material itself changes composition. This is somewhere similar to incubation, but here the process must be reversible, in the sense that re-starting the pulse-train burst means that the process must start all over again.

3.1.4 In vitro: range of cell death

Applied to soft tissues and considering the implications for laser surgery, the issue of residual heat from ultrashort-pulse laser ablation in general, and ultrashort-pulse burst treatment in particular, is less about modification of the material left behind and more about survivability for cells remaining in the tissue around the ablated region. We used a standardized tissue-model with the aim of getting consistent and unambiguous results [31]. Hydrogel cell cultures are common soft-tissue phantoms for laser-irradiation [32, 33] and for studies of cell response to drug and radiation treatments (e.g., photodynamic therapy [34] and interstitial laser photocoagulation [35]).

Our soft-tissue model was a 3D agar-based gel phantom: 1% agar content seeded with live F98 rat glioma cells (1–3 × 10⁶ cells/mL). Staining protocols included Hoechst 33342, propidium iodide (PI), and Annexin-V (see Table 1). After laser-treatment and staining, the samples were 3D-scanned by confocal microscopy, and virtual sections were taken through the ablated regions.

	Live cells	Necrotic	Apoptotic
Hoechst	+	+	+
PI	−	+	−*
Annexin-V	−	+	+

Table 1.

Protocols used for staining cells-in-gels phantoms.

^*

PI can bind to late-apoptotic cells.

Figure 12 shows the distribution of viable (blue) & necrotic (red) cells from our treated phantom, irradiated by a single burst of 133 pulses of 1 ps duration (1 μs @133 MHz), having a peak pulse-intensity of 4.6 × 10¹³ W/cm², a total energy of 1 mJ.

Figure 12.

The 3D distribution of viable (blue) and necrotic (red) cells cultured in hydrogel after irradiation at a peak intensity 4.6 × 10¹³ W/cm² in a 1-μs-duration burst @133 MHz intraburst repetition-rate. Left: 3D confocal-scanning microscope image across the interaction region. Right: the cylindrical projection from 3D of viable and necrotic cells, overlaying the radius-bins used for subsequent analysis. The red solid-line semicircle marks the necrosis range. Video 2 animated 3D rotation can be viewed at https://youtu.be/sA6wmdhtNJg.

Irradiating over a range of pulse peak intensities 1–5 × 10¹³ W/cm², this study showed a necrosis range between 50 and 350 μm that scales as $\sqrt{I}$ where I is the pulse-intensity in the burst (Figure 13). This might be understood, other factors being constant, as the absorbed burst-energy spreading out like the surface of a sphere until the specific energy-density drops below a threshold associated with cell necrosis.

Figure 13.

The cell-necrosis range for the phantom used, as a function of the pulse intensity for a 1-μs-duration pulse-train burst. The fit through the data is a power-law as shown in the figure, where $I_0=1.0\times {10}^{13}W/c{m}^2$, and $C=138\pm 28\mu m$.

The impact above is the result of a single 1 μs burst-shot onto a cultured-cell phantom. In practical use, burst-mode packets are delivered at the interburst repetition rate. Depending on the tissue or material in use, and the system for pointing pulses to different positions across the surgical target, the interburst repetition-rate can also be expected to have an impact on heating.

3.2 Burst-mode ultrafast laser surgery: ex vivo articular cartilage

Diffusion of accumulated heat and damage from shock waves in surgery using burst-mode ultrashort-pulse ablation may depend on the tissue type, and even on new effects in complex differentiated tissues of muscle, bone, connective tissue, and nerves. We examined the impact of burst-mode ultrashort-pulse ablation on porcine and ovine articular cartilage.

The laser for this was a compact Yb:glass fiber, 1030 nm, 300 fs per pulse, 5 ns between pulses (i.e., 200 MHz intraburst rate), 1 ms between bursts (i.e., 1 kHz interburst rate) from FiberLAST Inc./Bilkent University (Turkey). Bursts were 350 ns in duration, comprising about 70 pulses per burst. Average power was up to 240 mW: 3.4 μJ per-pulse energy; 240 μJ per-burst energy.

One question for these studies was about the ultimate depth of cutting, without also changing the laser focus along the axis, deeper into the material—what cutting can be expected under practical conditions? The laser intensity was expected to decrease at the bottom of the channel, for two reasons: loss of propagating laser power to the sidewalls of the channel where plasma would form; and diverging laser spot size, for points past the focal distance.

In previous studies, in which we drilled single channels through metal foils using burst-mode ultrashort-pulse lasers, we characterized a persistent-plasma waveguiding effect. This effect produced channels much longer than a Rayleigh range for the beam [36]. This occurs without translating the laser focus to be deeper into the workpiece, and comes as a result of optically transforming the beam while preserving its global coherence. In order to assess the impact of such guiding in biological tissues, to find the ultimate depth of cutting for laser surgery, and to ascertain what of the effect survives from single channel geometries to extended slices, line-cuts were made in porcine cartilage over multiple passes, without making any changes in focus depth.

Translation speeds 1–10 mm/s were used. Directly after the laser treatment, the cartilage was stained with Calcein AM (live; green fluorescence) and ethidium homodimer (EthD-1) (dead; red fluorescence) to evaluate cell viability² and the stained cartilage pieces were sectioned perpendicular to the line-cuts. The live-dead stain fluorescence was imaged using confocal laser-scanning microscopy (CLSM), in a virtual section plane set about 200 μm deep into the tissue (Figure 14, Top). Thereafter the tissue was fixed in 10% buffered formalin, paraffin-embedded, and sections stained with hematoxylin and eosin (H&E) (Figure 14, Bottom). The cut-depth without refocusing deeper was seen to saturate after about 16 passes, at a depth of about 200 μm.

Figure 14.

Line cuts made by repeated passes without repositioning focus, onto porcine articular cartilage, in order to identify ultimate depth of cutting. Translation speed 2.5 mm/s. (a) Live-dead (green-red, respectively) stain was used to identify the range of cell necrosis in the viable tissue away from the cut surfaces. White bars = 100 μm. (b) White-light microscopy of H&E-stained microtome sections. Black bars = 50 μm.

3.2.1 From line cuts to graft beds

We then prepared small graft-beds, up to 10 mm wide, cut into ovine cartilage using an x-y raster-scan pattern, in this case raising the cartilage toward the lens systematically. A 3-axis high-precision translation stage setup directed the tissue at the laser focus, in lines, in a strictly serial motion, rather than position-dithered. A visible-infrared (IR) spectrograph monitored our depth of cutting through cartilage, employing characteristic spectral lines in the plasma-plume to stop cutting as soon as the ablation touched bone (see Figure 15).

Figure 15.

White light photograph of a simple open-faced section through a small graft bed in ovine articular cartilage (left), showing articular cartilage and underlying bone. Safranin-O stained paraffin section of the graft bed (right). Size-bars 500 μm.

The evolving graft-bed was irrigated with phosphate-buffered saline (PBS) medium at intervals during preparation. The prepared graft beds were cultured after laser-cutting, live-dead stained, and then scanned in three dimensions using laser confocal microscopy.

The left image of Figure 16 is analogous to the left image of Figure 15, but is a composite image: it combines a CLSM image of live-dead stain, and a bright-field white-light microscope image of the same sample. The CLSM scan represents a virtual section made for a plane about 200 μm below the section surface.

Figure 16.

Laser-scanning confocal imaging provides a virtual section across a small graft bed in articular cartilage. Left: live-dead (green-red, respectively) staining helps to identify the range of dead chondrocytes, in the remaining tissue walls. Right: the range of cell-death can be seen to depend on the overall fluence used to prepare the graft-bed. The bed has an asymmetry associated with raster-scanning: tissue was cut in lines corresponding to in and out of the page, with new lines added progressing left to right as shown in left figure, with the starting side sloped and the ending side more upright. For similar final graft-beds, lower-fluence (gentler) cutting reduces the zone of damaged tissue.

A small range of cell death is an essential factor in the success of integration of cartilage tissue-grafts, and below we show the range of dead chondrocytes brought about by integrated laser fluences in the range 1–5 kJ cm⁻². It’s immediately evident how significant an effect it is that most of the heat of burst-mode ultrashort-pulse laser cutting is carried off in the ablated material itself. The range of tissue damage is less than expected from frictional heat in mechanical removals such as drilling and sawing. However, it seems clear as well that the slow serial processing in x-y raster scans likely accumulates more heat than is necessary, burst after burst at 1 kHz [37].

4. Persistence of plasma and burst-mode ultrashort-pulse lasers

As discussed above, for single ultrashort pulses at repetition rates much below 1 MHz, all plasma and most heat in the material dissipates before the next pulse, and the material largely returns to its original state. For multi-MHz intraburst rates, neither plasma nor heat dissipates, meaning that an opportunity is created for keeping alive the transient plasma that governs plasma-mediated absorption. This can be both hindrance and help, depending on details. It’s a “feature,” if one can exploit linear absorption in a residual plasma lying close to the target, meaning that one does not have to re-initiate breakdown. In that case the burst can be shaped, after the first few pulses, to have smaller pulses, less likely to cause strong shocks, optimally tailored to the surgical or processing needs. It’s a “bug,” if substantial plasma plume develops, and interferes with deposition of laser energy onto or close to the ablating target-surface. In practice, the nature of laser-target interaction for any given pulse depends on the history of all previous pulses before it, and possibly in complicated ways.

4.1 Where does the laser energy go?

We studied the development of plasma conditions throughout a burst of pulses by making a complete laser-energy accounting: measuring the transmission, specular reflection, and diffuse backscatter for each of the pulses during a burst-irradiation. Knowing the energies of each incident laser pulse, and the disposition of all light that was not absorbed, let us infer the full dynamics of burst-mode absorption [38].

The measurements amounted to a full laser-calorimetry setup (Figure 17). A reference of incident laser light was measured pulse by pulse using a beam-sampler and a photodiode. Transmitted laser light was collected immediately below the target using an apertured integrating tube coated internally with barium sulfate high-reflectance coating, and fitted with a high-speed photodiode. Diffuse-backscatter light was collected by a similarly coated integrating sphere suspended above the target and fitted around the lens tube holding the 8 mm aspherical target lens, with a 2 mm entrance hole situated about 100 μm above the target, almost in contact with the fused silica targets. A high-speed photodiode collected the light which filled this integrating sphere. Laser light which was specularly back-reflected from the plasma was re-collected by the target lens, naturally collimated backwards along the beam, and a sample was relayed to the input face of a large-core multimode fiber, with fast photodiode at the output end.

Figure 17.

Schematic of the optical layout for time-resolved laser calorimetry, to infer dynamic absorption. Direction of propagation is indicated by red arrows. PBS: polarizing beam splitter, GL: Glan-laser polarizer, λ/2: half-wave plate. All of the energy from light incident on the fused silica target ends up in one of four places: transmitted, specularly reflected, diffusely backscattered, or absorbed by the plasma.

4.2 Measurement of absorption dynamics

With this full accounting for incident laser light, and all laser light not absorbed, the light lost to absorption in the plasma was inferred, pulse-by-pulse for the entire burst. Figure 18 shows the dynamic changes in specular reflection, diffuse backscatter, and transmission, along with the computed history of absorption during burst-irradiation.

Figure 18.

Dynamics of (a) specular reflection, (b) diffuse backscatter, (c) transmissivity, for each pulse within a burst. Knowing each input pulse energy, a full accounting of laser light not recollected gives the time-dependent absorption (d). Laser: λ = 1030 nm, 300 fs pulses @ 200 MHz; 60 pulses/burst [38].

What this shows: specular reflection is high for about 15 pulses of the burst: each pulse sees the plasma it has itself created afresh during 300 fs, added on top of any plasma that still survives 5 ns after the previous pulse (and longer times for effects of earlier pulses). The initial plasmas each pulse creates is expected to be thin, dense, and sharply defined, but as residual ionization or weak plasma accumulates in small remainders following hydrodynamic expansion from pulses 5 ns, 10 ns, 15 ns earlier, it’s expected that the plasma critical-density surface would evolve to be farther out from the substrate surface, thereby reducing specular reflection.

The diffuse backscatter signal is small at all times, indicating an accumulating plume is not very substantial for these conditions and timescales. Given 5 ns each time, to expand, disperse, and recombine before the next pulse arrives, the accumulated plume does not greatly refract or scatter light. Self-transmission of laser pulses is relatively high for the first pulse, and the next pulse or two of a burst, but then shows a sharp drop. This is consistent with the expected formation of a thin plasma overlying the fused silica substrate, with an initially steep density gradient (scale-length less than a laser wavelength) around critical density. In the thin overdense plasma the laser light will be evanescent and not propagate, but will effectively tunnel energy through to the glass, in the manner of frustrated total internal reflection. As the plasma develops over the initial few pulses, its thickness increases and the transmission drops; this is consistent with the fluence-division observations above. Late in the burst, the transmission begins to rise again, which may indicate that the accumulation of plasma has degraded the ability of focused pulses to reach the substrate and form a reflective plasma, or possibly an extended plasma has refracted the incident light enough to cause it to pass outside the nominal focal spot.

By complete accounting of all laser light not absorbed, we find the absorption dynamics from first to last pulse of the burst. We can see the jump in absorption from about 30% for the first pulse, in its context as a single isolated pulse on a dielectric, to more than 40% as the mediating plasma is established, and after that a steady increase in absorption throughout the burst, reaching 70% before declining slightly. This late decline of absorption results from the rise in transmission instead.

4.3 Picosecond probing of plasma persistence

From the time-resolved absorption of each pulse incident on the target, we can infer much about the plasma and plume that gradually builds over the whole time of the burst. A finer-grained understanding of what happens to the plasma created by each pulse, in the 5 ns period between pulses, would lay out the role of the persistence of the plasma from the end of one pulse until it becomes the initial condition for the next pulse.

Figure 19 sets out our schematic for creating a burst-mode ultrashort laser-pulse produced plasma, and then probing that plasma precisely, at times ranging from just before and up to 300 ps after each pulse, for every pulse in the burst. The laser is polarization-divided into pump and probe beams, and the probe is delayed in a timing-slide to arrive at a selected time in the range −30 ps to +5 ns relative to the pump pulses on target. The rapidly dissipating plasma created by each pump-pulse throughout the whole burst is probed this way, so we can examine whether the dynamics of plasma creation and persistence are the same for early pulses, when the fused silica target is bare, as they are for pulses late in the burst, when “fresh” plasma is being added on top of some manner of accumulated background.

Figure 19.

Schematic of the optical setup for pump-probe studies of specular reflectivity and transmissivity for times up to 300 ps following each pulse of a burst of 60 pulses. Polarization is indicated with black arrows for horizontal polarization (parallel to optical table), and black dotted-circles for vertical polarization. Direction of beam travel is indicated by red arrows. PBS: polarizing beam splitter, GL: Glan-laser polarizer, λ/2: half-wave plate.

Pump and probe beams are propagated collinearly to the target, and timed to each other using frequency-domain interferometry. Two aspects of the plasma are probed: specular reflectivity and beam transmissivity. Because the probe is distinguished from the pump by its orthogonal polarization, diffuse backscatter or scattered transmission that do not preserve the laser beam k-vector cannot be directly measured. It was verified that polarization cross-talk signal from the pump line into the probe channel line was less than 5%.

4.3.1 Plasma persistence: specular reflection and transmission

Figure 20 summarizes the specular reflectivity and direct transmissivity of the probe from the plasmas created by the pump pulses, for times from 30 ps before each of the pump pulses arrives until 300 ps after them. This 330 ps time-dependence relaxation is summarized in separate plots for the 3rd, 11th, and 19th pulses in the burst.

Figure 20.

Summarizes the evolution over 300 ps of the probed specular reflectivity and probed direct transmission of the plasmas created by each of the pump pulses. The evolution is similar but not identical, for the 3rd, 11th, and 19th pulses in the burst [38]. (NB: the single data point at −30 ps stands alone, the connecting line does not imply a smooth temporal evolution up to the time of arrival of the pump pulse).

The Fresnel reflectivity of bare fused silica is a few percent for laser pulses, if no plasma is created. For each pulse n = 3, 11, 19 in the burst, there is some specular reflectivity seen for the probe for times before the pump pulse has arrived—of course, these are times about 5 ns after at least one previous pump pulse on target. The reflectivity seen 30 ps before pulse 19 has arrived is half the reflectivity of flat native fused silica, but by the time of the 19th pulse, nearly 100 ns into the burst, a crater at the surface has already been created, and reduced reflectivity is expected.

For the first 50 ps after each pump-pulse of a burst has ended, the probe sees specular reflectivity growing. This reflects that the plasma is an initially very thin layer, much of it at a density above critical density. Within this thin overdense plasma the wave has an evanescent solution. The light tunnels, and recovers a real olution on the other side of the overdense plasma, as discussed above in the context of (self-) transmitted light in the absorption measurements of the pump, above.

As the plasma layer begins to expand over tens of picoseconds, and the gradient scale-length increases while the plasma is still overdense, the reflectivity can rise, and the transmissivity will drop. As expansion continues, past 100 ps, the unloading plasma will eventually go underdense, at which point reflectivity will drop and probe-transmissivity will again increase. Over nanoseconds the plasma dissipates, absorptivity decreases, and eventually reflectivity and transmissivity return to values nearer to native fused silica, albeit with a cratered surface scattering both the reflected and transmitted light, and likely with a little plasma ionization remaining.

The effect is most pronounced for pulses early in the burst, here the 3rd pulse. For pulses late in the train, like the 19th, the plasma that has slowly accumulated during the burst degrades the contrast of reflection and transmission, as does ablative damage to the surface.

5. Conclusions

Intense ultrashort-pulse lasers that employ plasma-mediated absorption minimize residual heat—not because of a diffusion timescale, but through a competition between heat diffusion inward, and the dissipation of hot plasma in which the laser pulse has deposited energy. This “ablative quenching” is distinct from the mechanisms governing heat transfer in nanosecond laser heating.

Burst-mode ultrashort-pulse lasers add additional timescales—the timing between pulses within a burst, and the duration of the entire burst—which depend on new characteristics of the interaction physics, and therefore provide additional measures of control of the heat left behind in the surgical tissue or material being processed. Rapid repetition of pulses, here at 133 MHz or at 200 MHz intraburst rates, leads to the persistence of plasma from one pulse to the next. Keeping the plasma “alive” gives a universal and more predictable and universal linear absorption, without repeating dielectric breakdown, and even without the linear absorption typical of native chromophores, which themselves may vary from location to location in a sample.

This persistence of linear absorption, and not having to re-initiate dielectric breakdown, also means that the opportunity is created to use lower-intensity pulses subsequent to the first few of a burst, which affords the possibility of reducing shockwave damage. Thus the duration of a burst, intra-burst pulse-spacing, and indeed the pattern of intensities of pulses within a burst, all together determine the impact, and support different modes of fluence-delivery customized to particular applications [26, 27, 39].

Acknowledgments

This work was accomplished with funding from the Natural Sciences and Engineering Research Council of Canada, under the Discovery Grants Program (RGPIN-2017-06757), and the Strategic Partnership Grants for Projects (STPGP 494025-16).

Particular thanks for the hands-on contributions of summer-students and co-op students Soho Shim, Lee Sikstrom, Luke Coulter, Amber King, and Sara Early.

The 300 fs burst-mode laser was designed, constructed, and/or improved by Hamit Kalaycioglu, Seydi Yavas, Sohret Görkem Karamuk, variously of the University of Bilkent, and FiberLAST laser company, Türkiye, and currently at Lumos Laser A.Ş., Türkiye. Can Kerse made important contributions in establishing the laser and experimental setup. Professor F. Ömar Ilday from the University of Bilkent, Turkey, and currently at Ruhr Universität Bochum (RUB), Germany, made invaluable and essential contributions to laser design and experimental principles.