Optical Breakdown Mode (OB)

The OB mode is observed when a material is subjected to very powerful laser pulses. It manifests a power threshold in the range of MW for the majority of dielectric materials, witch depends on the duration and on the wavelength of the laser pulse. OB is related to the dielectric breakdown phenomenon which was studied and modeled successfully towards the end of the 1950's [1]. One describes the effect as a strong local ionization of the medium, where the plasma reaches densities beyond the critical value (between 10²⁰ and 10²² electrons/cm³). Energy is very efficiently absorbed from the light pulse, and the local plasma temperature increases dramatically. An explosive Coulombian expansion producing cavitation follows, and forms a very powerful and damaging shockwave that develops on ns timescale [3, 29]. If the rate of plasma formation is relatively slow, in the ns time regime (for ns excitation laser pulses), energy is transfered from the plasma to the lattice, and thermal damages can occur. In the fs time regime (for fs excitation laser pulses) the plasma expansion happens on a timescale smaller than the rate of energy transfer to the lattice, and thermal damages are reduced or eliminated. OB is a very "violent" phenomenon and changes drastically the local structure of the medium. To the naked eye, it looks like a spark, and it is even possible to hear a short noise (burst) caused by the explosive plasma expansion.

There are several photoionization processes involved in OB, which depend on the wavelength, local intensity, and pulse duration, as well as on the electronic structure of the material. First, we should mention that OB is only observed at very high intensities. For pulse durations greater then a few tens of fs avalanche ionization (AI) plays a role. The longer the pulse duration, the greater the AI’s contribution. Multi-photon ionization (MPI) processes are important in the fs time regime, and their role increases as the pulse duration decreases. The type of MPI processes involved is also wavelength dependent. Read section Photoionization Processes to understand how MPI and AI contribute together for the plasma formation, and how their relative importance is affected by the physical characteristics of the laser pulse.

The theory needed to understand the most important features of OB are:

• the physics of strong-(laser)field interaction with matter, to account for the plasma formation;

• the physics of strong-(laser)field interaction with plasma, to account for plasma expansion, and for thermal and mechanical effects;

• the geometrical/linear optical theory, to account at the first approximation for the spatial intensity distribution. Nonlinear propagation theory is usually invoked to account for self-focusing that occurs in experiments conducted at low numerical aperture (NA), and to account for detail features of the plasma density spatial distribution.

Applications

The applications of this photoionization mode are diverse. Its destructive power is used for surface processing (ablation), and bulk processing (modifying the local physical properties of the material and creating patterns - optical guides, greetings, micro-channels). The OB effect can be very localized, which translates into a very high precision (sub-micron) processing. In molecular and cellular biology, OB is to disruptive for the delicate organic structures at the sub-cellular level [16]. It is most used in medicine for tissue cutting/processing [17]. The B/OB mode becomes more appropriate at the sub-cellular level, as the plasma density and the local temperature can be better controlled, and the destructive shock wave is eliminated. B/OB can than be safely used for microsurgery (burning holes in the cellular membrane, targeted destruction of intracellular structures [13, 14, 15, 17]), and DNA processing (cutting chromosomes [12], DNA damage).

OB's capacity to vaporize the surface of any kind of material has been also found useful in thin layer deposition.

OB is also used to acquire information about the composition and structure of materials. This information is extracted either by analyzing the spectrum of the plasma emission form the OB zone (this is also called remote sensing), or by collecting and analyzing the ejected photoelectrons, ions, and other molecular fragments, in the case of surface studies in vacuum ( time-of-flight (TOF) spectroscopy). From time integrated spectral features one can infer the composition and the structure of the material. From time resolved spectral studies one can obtain information on relaxation processes, and on the lifetime of excited states. Being very localized, these spectroscopic techniques have a high spatial resolution, and can be used to study the composition and molecular structure of very fine grain material aggregates.

The acoustic emission from the OB zone has also been used in imaging, extracting information about the density distribution within a small body [reference]. A similar technique is used by geophysicists, where a dynamite is placed into the ground, and detonated. The sound waves are captured a certain distance away, and analyzed. The difference between their initial and final form contains information about the variations in material density encountered.

At very high power levels (peta- and exa-Watt) sub-fs coherent X-ray bursts are emitted from the OB zone, and can be collected, and used for spectroscopic or imaging purposes.

Control of important characteristics of OB mode

Range of operation of the OB mode

The scope of this section is to depict the domain of laser parameters where OB is possible, given a certain type of material. The occurrence of the OB effect is determined by the plasma density generated during the interaction of the laser pulse with the material. But this parameter is not easily measured, and other signs of OB occurrence are used during experiments: for instance the appearance of a spark (plasma emission), the detection of a short acoustic burst, or the scattering of a second laser beam passing through the OB region. These signs become detectable only if the plasma density reaches levels beyond the critical value, and hence are closely related to the fundamental causes of OB.

Relative to laser light parameters

The OB mode exists within a domain of laser parameters defined by an important event, which is the accumulation of plasma above the critical value. If this event takes place before the end of the laser pulse, the interactions between the plasma and the laser light becomes dominant, and drives the most important effects. Energy is absorbed from the electro-optical field in a very efficient manner, and if the remaining of the laser pulse contains enough energy, a violent Coulombian expansion will follow, accompanied by bobble and shock wave formation, plasma emission, and increase of local plasma temperature. The magnitude of these effects depends on the quantity of energy stored in the last part of the laser pulse, from the moment where the critical plasma density is achieved, until the end of the pulse. The dynamics of plasma formation, and its spatial density distribution depends on the pulse duration, as we will see shortly. The section MPI and AI in the context of laser pulses treats plasma formation in the context of laser pulses, and it is crucial for the understanding of the OB phenomenon, and its range of operation.

Average intensity

OB exhibits an intensity threshold. Due to the interplay of different photoionization mechanisms, the pulse duration is an important parameter in determining OB's intensity threshold (see the following section). Moreover, at longer pulse durations (in the ns time regime), the threshold is statistically unstable, and very sensitive to impurities (is reduced in the presence of impurities). It becomes much more predictable, and its dependence on impurities vanishes in the fs time regime [32].

As the input intensity is increased above the threshold value, the plasma density increases, but a saturation regime in observed. In the sub-ps time regime the saturation is mainly due to recombination processes [28], whereas in the ns time regime plasma expansion, reflexion (of the incoming light), defocussing (of the incoming light), and energy conversion into heat also become important. For most relevant applications we can consider that OB intensity range has only a lower limit.

Pulse duration

OB is possible at any pulse duration, but this parameter considerably affects OB's intensity threshold. In the ns time regime, there is plenty of time for plasma growth, hence the intensity threshold is lower. The most important mechanism responsible for plasma formation is AI, and the OB intensity threshold value is determined by the requirement that the ionization rate surpasses the recombination rate, and that the critical density is achieved before the end of the laser pulse. In the sub-ps time regime, there is less time for plasma build-up during the laser pulse. In order to achieve the critical density a higher intensity is needed to speed-up the ionization process. The role of AI, which needs time to develop, forcibly diminishes by decreasing the pulse duration, and MPI processes kick in to compensate the loss. In the fs time regime the rate of ionization needed surpasses the recombination rate, and the threshold value is determined by the requirement that the critical density be reached before the end of the laser pulse. The graphic in Figure 1 below is the result of simulations for water, and shows the variation of the intensity threshold with the pulse duration. The authors concluded that only for pulse durations below 40fs can AI be neglected. In this later case the plasma formation dynamics is entirely dominated by MPI processes.

Figure 2 below shows the variation of OB's fluence threshold with the pulse duration from 100fs to 100ns, for SiO₂, at 780nm [24]. See also ref. [25] for a simple phenomenological model that gives adequate predictions from the picosecond to the microsecond time regime.

Furthermore, the OB intensity threshold is not well defined in the ns time regime, because of the important role of the AI process in plasma formation. AI is very sensitive to initial conditions: a small difference in the number of initial free electrons can result in a big difference in terms of plasma density generated by the avalanche process, at the end of the laser pulse. On the contrary, in the fs time regime MPI becomes more important, and it is a very reliable photoionization process (Figure 3). Even if AI still contributes, MPI supplies most of free electrons to the avalanche process, and the OB becomes more predictable, and more tightly correlated to the input intensity. See section below Relative to material impurities for more.

Wavelength

The OB mode is possible at any wavelength. However, a general tendency emerges: OB intensity threshold increases as the wavelength increases. Firstly, the wavelength controls the relative contribution of AI and MPI to the plasma formation. In the visible-IR domain AI becomes more important, for pulse durations where it can develop. MPI processes tend to contribute more to the generation of free electrons as the photons become more energetic - at shorter wavelengths. This parameter also operates a selection on the type of MPI processes involved (see section Multiphoton Ionization (MPI)). In the IR domain tunnel ionization dominates among MPI processes. In the visible-UV domain resonant or non-resonant multi-photon absorption occurs.

To be completed!

Temporal intensity and wavelength distribution

There are very few papers on the effects of the chirp and the temporal intensity distribution (steepening and multi-pick pulse) on the OB threshold.

To be completed!

Polarization

The OB effect can be induced with any polarization. However, in ordered materials this parameter has an effect on OB's intensity threshold. This is because MPI processes are sensitive to the relative orientation between the polarization of light (when linearly polarized), and the orientation of molecular or lattice bounds; and also because AI is polarization dependent in the case of ordered materials, as the (quasi-)free electron mobility is anisotropic. In the case of crystals, the net effect of the polarization is very clear [5-11]: the plasma density at the end of the laser pulse varies with the relative orientation. This also means that for a given input intensity close to OB's threshold, the OB might occur for a given orientation, but not for others (in the case of a linear polarized beam). This is exactly what appears on Figure 4, where the extent of the damage, which depends on the plasma density, varies with the orientation (for a linear polarized laser beam). The damage pattern is closely related to the structure (symmetries) of the crystal, hence it doesn't vary with the orientation.

In the fs time regime, where MPI processes are dominant, the transition from linear to circular polarization can also affect OB threshold, as for circularly polarized light higher-order multiphoton processes are significantly inhibited.

Use of lenses

When we talk about OB intensity threshold, we refer to the local intensity. For a lower input intensity, OB can still be induced if the beam is tightly focused in/on the target. Lenses are used to converge the light in order to achieve high local intensities, but also to avoid self-focusing (or filamentation), in which case we would obtain a F-OB mixed photoionization mode. Figure 5 below shows how the energy threshold of OB and of self-focusing (or filamentation) varies with the focal length. We can talk about a OB focal length threshold on a given intensity domain.

Moreover, the dimension of the focal region, which is also dependent on the optical focusing equipment, affect the threshold in situations where AI dominates. This behavior is related to the number of initial (quasi-)free electrons present within the focal volume, on which AI starts to develop. If the role of MPI is negligible, the number of initial free charges is given by background electrons (from thermo-ionic processes), and also by the number of impurities or defects (in the case of crystals). The smaller the volume the fewer initial free charges, and the higher the OB intensity threshold.

Relative to material impurities

A. Kaiser at al. makes a distinction between intrinsic and extrinsic OB [18]. This distinction is based on the empirical observation that impurities and defects -in the case of crystals- affect OB's intensity threshold: it is higher for a pure material. Intrinsic OB refers to the OB process that takes place in a pure material, or a perfect crystal, whereas extrinsic OB refers to the OB process that occurs in impure materials or crystals with defects.

Furthermore, it is observed that the influence of impurities is modulated by the pulse duration. How can we understand these observations? The ultimate cause is that impurities and defects are good electron donors, they usually have a lower ionization potential, hence they are easily ionized. Their contribution to the OB depends on the relative importance of AI and MPI, which in turn depends on the pulse duration. For longer pulse durations (ns time regime), AI’s contribution to the total plasma formation is greater, and the local impurity concentration is directly related to the initial population of (quasi-)free electrons on which this process develops. Thus the final plasma density depends exponentially on the concentration of impurities. In the fs time regime, where AI's contribution can be neglected, MPI is mainly responsible for the generation of plasma, and the dependency on impurities in this case is linear. Taking into consideration the high plasma density necessary to trigger OB, the contribution of impurities to the total number of free charges becomes relatively low in this case, and their influence on OB's intensity threshold is small. For a time regime where both types of photoionization processes are involved, we have an intermediary situation.

In the ns time regime, where the contribution of AI to the plasma formation is important, empirical observations show that the OB intensity threshold is not well defined (it doesn't have a precise value), and can be defined only statistically. This is understandable if we consider the fact that for every laser pulse, the contribution of impurities to the initial population of (quasi-)free electrons depends on the number of impurities present in the irradiated volume, and on the percentage of impurities that are initially ionized. A very small variation in the initial (quasi-)free electron population makes a big difference in terms of final plasma density reached at the end of the laser pulse. Hence, for high input intensity values, the probability of OB occurrence is 1, but as the intensity approaches the threshold value, the probability becomes smaller and smaller - not every pulse guaranties an OB event. In the fs time regime, where MPI's contribution to the plasma formation is dominant, variations in the number of contributing impurities represents only a very small percentage of the final free electron population. Hence, the total critical plasma density is reached with a much higher accuracy, and the correlation between the input intensity and the occurrence of OB becomes tighter, therefore OB intensity threshold becomes well defined.

Control of the nature of primary photolytic species

The nature of primary photolytic species depends on the nature of the material (its composition and its structure), as well as on the dissociation channels (ionization or molecular dissociation) that are possible during the interaction. In the case of sub-ps pulses the primary events are only fast occurring processes like ionization and excitation of atomic systems. Bound breaks occur after the passage of the laser pulse, as the excited molecules and the plasma relax. It is important to note that in the fs time regime the laser pulse doesn't interfere with slower relaxation processes, it just creates the initial conditions. For ns pulse durations, most relaxation processes can occur during the laser pulse, and we have to take into account the direct influence of the optoelectric field.

Average local intensity

This parameter affects the ionization and excitation channels, and subsequent fast occurring relaxation mechanisms (on a fs-ps time scale); and consequently it affects the nature of primary photolytic species. The local intensity also has an impact on the energy spectrum of free electrons, and on the plasma density, which in turn affects the relative yield of secondary photolytic species created during the physico-chemical stage, where the plasma relaxation occurs (on a ps time scale). Multiple ionization can also be induced at higher intensities either by MPI, or by impact ionization.

The average intensity also affects the local heat deposition, and the magnitude of the shokwave generated by the Coulombian explosion. Important long-range thermomecanical effects are generated on a ns time scale, which can have dramatic consequences on the chemical and structural properties of the material.

Wavelength

The wavelength has a selective effect on ionization, dissociation, and excitation channels, and it directly controls the nature of primary photolytic species. It also affects the free electron energy spectrum, as well as the distance between free electrons and their geminate ions, which in turn affects the yields of secondary photolytic species, and ultimately the long-term photolytic effects.

Chirp

The temporal spectral distribution can influence several ultra-fast processes. By controlling this aspect of the laser pulse we can influence the outcome of the photolysis. A. Lindinger et al. demonstrated how the wavelength time distribution affects ionization and fragmentation of Na₃ clusters [26].

Temporal intensity distribution

Some ultra-fast processes are very sensitive to the temporal intensity distribution, as well as to the intensity change rate. Understanding the effects of a pulse train, and of steepening, becomes important. By controlling these aspects of the laser pulse we can control some ultra-fast processes with important consequences on the yields of primary photolytic species.

Pulse train

By shaping the temporal intensity distribution, molecular fragmentation channels, and other ultra-fast processes can be controlled. Sinusoidal spectral phase modulations create pulse trains of several pulses with controllable pulse separations. A. Lindinger et al. used this technique to demonstrate how the intensity time distribution affects ionization and fragmentation of Na₂ and NaK clusters [26]. The same principles apply to other molecular systems.

A temporal pulse-break can also occur during a nonlinear propagation of a powerful laser pulse in a dielectric medium.

Steepning

The temporal intensity distribution can be dramatically modified during the propagation of a powerful laser pulse in a dielectric medium. Some ultra-fast processes are sensitive to the rate of change in intensity. Using nonlinear propagation models as a guide, one can modify the temporal pulse shape according to specific needs, and use that to control the nature and yields of primary photolytic species.

Polarization

In the case of crystals the net effect is clear, the OB intensity threshold, and the plasma density reached at the end of the laser pulse depend on polarization, see Figure 4 above. This is because MPI processes are sensitive to the relative orientation between the polarization of light, and the molecular or lattice axes. And also because in the case of structured materials the mobility of (quasi-)free electrons is anisotropic, therefore making AI orientation dependent. In conclusion, all other pulse parameters being kept constant, polarization alone can have an impact on plasma density, free electron energy spectrum, and the type of primary photolytic species created. As a consequence, the long-term photolytic effects are also affected.

In an amorphous material, molecules are arranged in an arbitrary fashion, so the polarization doesn’t affect the overall distribution of photolytic species. Although, we have to keep in mind that MPI and SPI depend on molecular orientation. Consequently, in the fs time regime where AI becomes negligible, the polarization operates a selection on the molecules that are ionized, and it induces an anisotropy within the affected region; i.e. affected molecules tend to be oriented in given directions.

In the fs time regime, where MPI processes are dominant, the transition from linear to circular polarization can also affect the plasma density, as for circularly polarized light higher-order multiphoton processes are significantly inhibited.

Control of the dose spatial distribution

Here we have to distinguish between the area directly affected by the laser light, which can be very localized, and the area affected at longer delays, after the passage of the laser pulse (Figure 6), which is more extended. Normally, when we consider the dose distribution we refer to the first case, the area where the energy is deposited initially. However, OB is a special case, exhibiting important long-range thermomechanical effects, which develop on a ns timescale. The area directly affected is actually the area where the intensity reaches values above AI's and/or MPI's threshold, and it is always smaller then the area covered by the entire laser beam. The thermomechanical effects can extend a few tens of microns beyond the limits of the directly affected area. In general, both areas expand with the increase of the input intensity.

The area directly affected by the OB depends greatly on the pulse duration [21]. In the ns time regime it starts at the geometrical focal point (as lenses are often used in applications), and extends towards the laser source within the focal cone. The end result is depicted on the upper part of Figure 7, with varying focal angle. The critical plasma density is first reached close to the geometrical focal point, and the plasma front moves backwards, towards the laser source. The plasma density reaches a higher density a certain distance before the geometrical focal point (Figure 7). This is an experimentally established fact, and it is explained using the "Moving Breakdown Model" [20] as follows: As the critical density is first reached around the geometrical focal point, incoming light is absorbed very efficiently. The length of the laser pulse (which is the pulse duration multiplied by the group velocity) is greater then the focal region. The incoming light is absorbed manly by the outermost plasma layers, the plasma front expands backward, and the deeper layers become shielded [22]. In the fs time regime, the dynamics of the plasma formation appears to be radically different. The pulse length is comparable or even smaller then the focal region. Here we have a forward plasma formation, with a denser region around the geometrical focal point. OB with lower plasma density, lower temperatures, and lower plasma emission, can be achieved in the fs time regime.

The pulse duration also affects the long-range mechanical effects induced by cavitation, and by the acoustic shock wave. It is observed that the extent of the cavitation bubble, and the pressure achieved are greater in the ns time regime then in the sub-ps time regime [29, 31]. In the ns time regime the cavitation tends to take a more spherical shape, as opposed to the sub-ps time regime where its shape becomes more elongated, as seen in Figure 8 below. In crystals, the plasma expansion follows the mechanically weaker plans, forming the patterns seen in Figure 5 above.

In the fs time regime the spatial distribution of the plasma, and the form of the acoustic perturbation are also affected by the input intensity. It tends to be more confined and spherical at intensities just above threshold. For higher intensity levels the affected area presents a more cylindrical symmetry, as we can see in Figure 9 below.

Use of lenses

High numerical aperture (NA) converging optics are used in practice for the OB mode. One of the reason is to avoid self-focusing, in which case we would obtain a F-OB mixed photoionization mode. Figure 5 shows how the energy threshold of OB and of self-focusing (or filamentation) vary with the focal length of the convergent lens.

For material processing techniques that relying on OB, the beam is focused on the target that has to be processed (by evaporation or melting). Using converging optics one can control the local intensity, as well as the dimension, the shape, and the position within the sample of the affected area (see Figure 7).

Material impurities

The effects of impurities becomes significant in the ns time regime, where AI's contribution to plasma formation is more important. Within this time regime, for intensities below the intrinsic OB threshold (for a pure material) pinpoint bulk damage can be observed in crystals [11, 27]. It is believed that these point-damages are OB centers, initiated by nano-particles, or cluster defects. Figure 10 below shows pinpoint bulk damages (with a diameter that rages from a few to a few hundreds of micrometers) in deuterated potassium dihydrogen phosphate (DKDP), along the trajectory of a 351nm, 1-10ns, laser pulse [11]. The fluence was kept practically constant, and the pulse duration was varied: 1, 3 and 10ns (from left to right on the picture). There are two important conditions for these damages to occur: First, the rate of energy absorption by the nano-particle must be greater than the rate of energy diffusion into the surrounding material. This ratio depends on the size of the particle: for larger particles the ratio is greater. Second, the fluence must be high enough for the OB to occur.

We can remark the striking similarity with the dose distribution produced by high LET radiation. This should be a "wow!" for specialists in radiation science, as it suggests that laser pulses can be used to model the effects of radiation. The recipe seems simple: introduce some kind of absorbing nano-particles into your solution, tune your laser to efficiently ionize them, adjust the pulse duration and the intensity to control the plasma density, and the size of the pinpoint damages (equivalent of spurs), and use the same models developed for radiolysis to fit the yields of long term photolytic species (knowing the geometry of the ionization density distribution).

Other effects

OB emission

The affected OB region emits broadband light for pulses in the ns-ps time regime. This gives OB the aspect of a spark, and it constitutes an important visual signal that can be used in practice to detect the occurrence of an OB event, and to approximate its magnitude. Moreover, the emission can also be used as feedback signal, to monitor the local temperature, the plasma density, and the plasma energy. In other kind of applications, the spectrum of the OB emission is analyzed to obtain information about the composition and the structure of the affected material, or it is simply used as a broad band light source for measurements involving linear light-mater interactions.

C.W. Carr et al. [35] arrived at the conclusion that in wide gap solid dielectric materials, in the the ns time regime the emission from a OB region is blackbody in nature. The authors measured the emission spectrum at different delays after irradiation (with 355, 532, and 1064 nm) of CsI, Al₂O₃, CaF₂, DKDP, SiO₂, and LiF, by integrating the measured intensity for 5ns for each delay. The graphic in the following figure shows the experimental data fitted with Planckian curves. Delay of electron recombination, thermal emission by the shock wave, and thermal equilibrium between the plasma and the lattice are invoked to explain the emission's Planckian spectral shape.

Still in the ns time regime, emission from OB in air presents a more structured spectrum. In the Figure 12 below we have different time-resolved spectra, integrated over the whole space covered by the plasma, obtained at different delays after the onset of OB, induced by a 7ns pulse, at 1060nm, in the air. The time resolution for each spectra is 5ns, which means that the emission signal was integrated for 5ns at each delay. The authors mention that the overall shape of the spectra is greatly affected by the instrumental response. But by looking at the dynamical behavior one can notice the appearance of structure bands at longer delays, as the plasma relaxes. On the right, we have the emission relaxation at three different wavelengths. Basically, in this case the plasma emission is made of two important components: continuum radiation, which comes from bremsstrahlung events, and decays very fast after the passage of the ionizing pulse, and recombination emission, which comes from the recombination of free electrons with the ions. Similar conclusions were advanced recently by S. S. Harilal [37] based on similar experiments in Ar. For shorter pulse durations there is no emission in the visible.

Thermal effects

The plasma generated during OB has a density greater then the critical value, and absorbs energy form the pulse very efficiently. In the ns time regime, a big portion of that energy is converted into heat, as the plasma has more time to absorb energy, and to dump it into the lattice through electron-phonon collisions. Important thermal effects are observed in this time regime. On the other hand, in the fs time regime thermal effects are dramatically reduced [30], because the plasma expansion takes place on a timescale smaller than the electron-phonon collisions.

C.W. Carr et al. [35] inferred the temperature produced during OB from measurements of plasma emission, for six wide gap dielectric materials: CsI, sapphire (Al₂O₃), CaF₂, DKDP (KH_xD_(2-x)PO₄), fused silica (SiO₂), and LiF. They used ns pulses, at 355, 532, and 1064 nm, and intensities approximately double the OB threshold for each material, at each wavelength, see Figure 13 below. The graph on the left shows that the temperature variation at the ns scale, and after the passage of the laser pulse, does not depend on the excitation wavelength for a given material. The authors also inferred that in the ns time regime the plasma temperature is in thermal equilibrium with the lattice. The drop in the local temperature is attributed to three important factors: radiation, thermal conductivity, and shock wave; the last two being by far more important then the first.

Mechanical effects

During OB an explosive Coulombian expansion is observed. A damaging shock wave is produced, that travels for tens of microns outward form the OB region, and can have dramatic effects on material structures encountered. In the ns time regime, for wide band gap materials the maximum pressure that develops in front of this expanding wave was estimated by C.W. Carr et al. [35] at 250 kbar.

Acoustic emission

The violent Coulombian explosion also emits a short acoustic signal. This is important as it can be used in practice to detect the occurrence of OB. Recently the acoustic emission has been used for microscopic sonar imaging.

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