Filamentary Mode (F)

In the F mode, filamentary or linear ionization patterns are formed. The plasma density within these filaments is below the critical value. The self-focusing effect is responsible for the most important characteristics of the dose distribution. The diameter of these filamentary ionization traces is the same within 20% (in the order of a few microns). Their length, their number, and their relative position are controllable parameters. The plasma density and the yield of photolytic species is homogeneously distributed along these filaments. The local intensity reached by the laser light during propagation is also practically constant along their length.

The power range of operation of the F mode is above self-focusing (SF) threshold and below OB threshold. Consequently, a necessary condition for it to exist is that the self-focusing threshold must be smaller then the OB threshold.

I personally contributed to the description of the F mode (see my research HERE). It exhibits very important characteristics, which in combination with the other three photoionization modes makes possible the generation of a wide range of dose distributions, expanding the application range of lasers in the domain of material processing. The F mode is the only mode capable of generating linear ionization traces.

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

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

• The theory of non-linear propagation, to account for the spatial redistribution of the laser light, intensity clamping, and the formation of filaments, as well as for frequency conversion processes.

Applications

Until recently, the filamentary mode was viewed more as a nuisance. The self-focusing effect was responsible for a dramatic increase in intensity that caused damage to optical equipment. The interest behind the study of this phenomenon was primarily negative, the goal being to avoid it. In the late 1960's, Alphano and Shapiro [1] discovered the continuum generation phenomena. Later, the strong connection between self-focusing and the continuum generation was firmly established [2-4]. The use of the supercontinuum in time-resolved spectroscopy and imaging become very popular. It was also proposed to use the F mode for wave guide writing, as it is less destructive then the OB mode.

When sub-ps lasers were introduced in opthalmology, some researchers reported patterns of unwanted filamentary damage. The OB mode is used to process/cut the tissue (cornea, lens, retina) with sub-micron precision. The filamentary tissue damage extends in the direction of the laser, and reduce the precision of the surgical tool, inducing unwanted collateral damage. Again it was blamed on the self-focusing. After understanding the mechanisms causing the filamentary damage patterns, and after learning to control them, interesting applications could be proposed for the F mode. The linear photoionization pattern resembles the ionization tracks left behind by heavy charged particles streaming through a material (high LET radiation). In my theses (part1 , part2) I explore new applications of the F mode in radiobiology, and radiochemistry.

Control of important characteristics of the F mode

To design applications of the F mode, one must learn to control the effects on materials of laser pulses in the self-focusing regime. The characteristics that must be controlled are: diameter, length, number, and space distribution of the filaments, as well as the relative yields of photolytic species. Parameters that can be directly controlled, and that are coupled to the characteristics mentioned above are: pulse duration, average intensity, spatial and temporal intensity distribution, wavelength and chirp, and material composition/impurity. The conceptual frame of self-focusing developed by Chin et al. makes it possible to link these parameters to the desired effects.

Range of operation of the F mode

The scope of this section is to depict the domain of laser parameters where the F mode is possible, given a certain type of material.

Relative to the light parameters

The F mode exists within a domain of laser parameters defined by two important events: the first one is the generation of SF process, and the second one is the occurrence of OB. In short, the F mode is possible on a domain of laser parameters for which SF is sustained, and is balanced by photoionization; or for which the equilibrium between the optical Kerr effect and all dissipative mechanisms put together (photoionization, frequency conversion, etc.) is maintained, avoiding OB. The section Self-focusing treats about SF of laser pulses, and it is crucial for the understanding of the F mode, and its range of operation.

Average intensity

Self-focusing (SF) is the fundamental effect behind the F ionization mode. We know that SF has an intensity threshold, which depends on the type of material, wavelength, and pulse duration. The same intensity threshold is also associated with the F mode. The intensity range of the F mode is between the SF and optical breakdown (OB) threshold, where the first must be smaller then the second. This intensity range depends on wavelength, on pulse duration, and on the focusing conditions (NA). For example, in the visible-IR domain, sub-ps time regime, and at small NA, the difference between OB and SF threshold increases as the pulse duration diminishes - SF appears at a lower intensity than OB.

Pulse duration

The F mode is closely associated with SF, but we have to keep in mind that SF is also possible without ionization. In the ns time regime, filaments can be observed for powers just above SF threshold, and below the OB threshold. The equilibrium intensity in the core was estimated to be lower than multiphoton ionization (MPI) threshold. Experimental results also suggest that avalanche ionization (AI) doesn’t have sufficient energy to develop. SF will be counterbalanced mainly by the stimulated Raman and Brillouin emission. Here, Raman and Brillouin conversions dissipate the energy of the laser pulse. It is also important to recognize that these mechanisms have a given dissipative efficiency. By gradually increasing the entry intensity of the ns laser pulse, there is a point where the capacity of energy dissipation by Raman and Brillouin conversions is exceeded. SF becomes stronger at higher intensities, and surpassing the counter effect these dissipative mechanisms, will collapse the beam even farther. Eventually, the AI intensity threshold is reached and OB occurs. OB is observed at intensities lower then the threshold of other nonlinear optical processes. Continuum generation is not observed. If OB occurs on the trajectory of the pulses, the propagation is largely affected, and the light is scattered.

The pulse duration can be used to adjust the width of the intensity domain for witch the F mode and the F-OB mixed mode are possible. The difference between SF intensity threshold and OB intensity threshold increases as the pulse duration diminishes. This is how we can understand this: In the fs time regime the contribution of AI to the plasma formation becomes less important, and SF is equilibrated at higher intensities, as MPI must intensify to keep the plasma density at the equilibrium point. The OB intensity threshold increases with the decrease of the pulse duration, and the range between the SF and OB intensity thresholds increases. The contribution of the AI, can be neglected for impulses <40fs. As the pulse duration is increased, the contribution of AI to the plasma formation becomes progressively more important, having more time to develop. Since AI is a very effective charge generator, the equilibrium plasma density is achieved at lower intensities. With a lower intensity in the core of the SF zones, MPI becomes less important. The OB threshold decreases with the increase of the pulse duration, and the range between the SF and OB intensity thresholds diminishes. At a given pulse duration, SF and OB intensity thresholds become indistinguishable, and filamentary ionization becomes impossible. Therefore, we can talk about a pulse duration threshold for the F regime: the value for witch SF and OB have the same intensity threshold.

Wavelength

The SF power threshold increases with the reduction of the wavelength of the laser pulse. Moreover, for short wavelength (in the UV) the OB intensity threshold becomes smaller then SF threshold, and the F mode becomes impossible.

Polarization

In ordered materials, the non-linear Kerr refraction index and the photoionization processes depend on the polarization of the light. This parameter plays an important role on the equilibrium between the SF effect and the dissipative processes. Therefore, SF intensity threshold is affected, as well as the diameter of the filaments and the maximum intensity level (see intensity clamping).

Material impurities

The effects of impurities go hand in hand with the importance of the AI’s contribution to the total plasma generation. Impurities can be considered as electron donors, and can feed the AI with initial free electrons. If we consider only the AI, the final plasma density depends exponentially on the concentration of impurities. If only MPI is active, the dependency becomes linear. For a time regime where both types of processes are involved, we have an intermediary situation. In conclusion, impurities affect the lower and the upper intensity limits of the F mode, which are the photoionization threshold and the OB threshold respectively. Their effect is modulated by the pulse duration.

Control of the nature of primary species

The nature of photolytic species depends on the composition of the material, its structure, and on the properties of the laser beam. Excited electronic and vibrational state populations can be controlled, and ionization and dissociation channels can be selectively induced, by manipulating the pulse’s intensity, and its spectral temporal distribution. For ordered materials, the polarization state has a selective effect on the ionization and dissociation processes induced. The nature and relative population of the photolytic species, resulting from these fundamental processes, can then be controlled, up to a certain extent, by manipulating the pulse characteristics.

Maximum intensity value reached within the filament (intensity clamping)

The maximum intensity inside the core operates a selection on the ionization/dissociation/excitation channels. Ultimately, this has an effect on the relative yields of photolytic species. The maximum intensity reached during the propagation remains stable along the light filaments. This value is dictated by the SF equilibration conditions. Pulse parameters such as pulse duration and wavelength, and impurities’ concentration and nature, can be instrumental to control the maximum intensity.

Wavelength

The wavelength operates a selection on the ionization/dissaciation/excitation channels, and can also have an effect on the free electron energy spectrum, as well as on the distance between free electrons and their geminate ions. That in turn affects the yields of primary photolytic species.

Furthermore, the SF threshold increases with the reduction of the wavelength. The maximum intensity reached inside the filaments, as well as the ionization density, are wavelength dependent, as the Kerr/ionization equilibrium conditions is shifted.

Pulse duration

This parameter operates a selection on fast occurring processes, and can influence the path of relaxation/dissociation of atoms or molecules. Molecular vibration, rotations, and dissociation occur at longer delays (ps time scale). At a given wavelength, and with a pulse duration comparable to the internal conversion relaxation times, one can control the fate of an excited molecule/ion.

The pulse duration also plays an important role in fixing the relative importance of AI and MPI. The energy spectrum of the free electrons, as well as the average distance between free electrons and their geminate ions, are ultimately connected to this parameter.

Chirp

The temporal spectral distribution can influence several ultra-fast processes. By controlling this aspect of the laser pulse one can in principle influence the outcome of the photolysis. A chirped pulse is normally produced using a pair of gratings or prisms. Chirpping can also normally occur during nonlinear propagation of a laser pulse in a dispersive medium, which could be the sample itself. Most materials are normal dispersing at most interesting wavelengths. In this case, the pulse accumulates a positive chirp (shorter wavelengths towards the end of the pulse). An external chirpping device can be used in front of the sample in order to achieve the desired chirp at the target’s location. We have to consider that this modification of the pulse’s spectrum temporal distribution always comes with a change in the pulse duration.

A. Lindinger demonstrated how the chirp affects ionization and fragmentation of Na₃ clusters [7]. The same principles should apply for other molecular systems.

Temporal intensity distribution

Some ultra-fast processes are very sensitive to the temporal intensity distribution, as well as to the intensity change rate. Understanding temporal pulse breaking and steepening becomes important. By controlling these aspects of the laser pulse one can in principle control these ultra-fast processes. This could have important consequences on the yields of the 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 [7]. The same principles should apply to other molecular systems.

The intensity and the spectrum of each pick within the laser pulse can be controlled, as well as the delay between the picks. A variety of interesting outcomes can be generated by controlling these parameters. For example, the heating of the plasma within the filaments generated by the front pick, or the stimulation of specific relaxation channels. The problem is that the non-linear propagation of a pulse train is not well understood. We have to acknowledge the fact that the pick behind propagate in a medium modified by the pick upfront.

A temporal pulse-break can also occur during nonlinear propagation of a powerful laser pulse in a dielectric medium. This phenomenon was studied by Chin et al, and by Jinendra K. Ranka et al [8].

Steepning

Propagating of a powerful laser pulse in a non-linear medium can induce a temporal intensity redistribution, where the intensity change rate at the front is much higher then at the tail of the pulse. Some ultra-fast processes are sensitive to the rate of change in intensity.

Polarization

The polarization becomes an important parameter for applications involving ordered materials. It has a direct effect on the channels of ionization/excitation/dissociation, and ultimately on the distribution of photolytic species.

In an amorphous material, molecules are arranged in an arbitrary manner, so the polarization doesn’t change the overall distribution of photolytic species. Although, we have to keep in mind that this parameter operates a selection on molecules that are affected. It induces an anisotropy within the affected region: molecules that undergo certain processes under the influence of the laser light tend to be oriented in a given directions.

The polarization becomes more important in ordered materials.

Control of the dose spatial distribution

Filament length, number and their spatial distribution

The initial intensity space distribution has a great influence on the propagation of a high power laser pulse. Zones with intensity higher then SF threshold separate and become more confined, and more intense, as they independently undergo SF. By shaping the spatial distribution of the laser beam, one can control the number of filaments as well as their spatial distribution. Figure 1 is a very good example, where a series of filaments are created in a circular fashion (the filaments are perpendicular to the image and parallel to each other), by passing the laser beam through a small circular aperture before the sample, to generate a ring diffraction pattern.

J. Liu et al. [6] used a narrow slit to generate a series of parallel and coplanar filaments, Figure2. The picture was taken by a CCD camera from a single laser pulse, from a lateral position, by collecting fluorescence coming from the sample (see more on the image).

In the fs time regime, for powers on the range above SF threshold and below OB threshold, by gradually increasing the entry intensity (keeping the pulse duration unchanged), we increase the length of the filaments, as well as their number. This is easily understood by remembering that by increasing the intensity we increase the energy available around the core, and a longer distance is needed to dissipate it in the SF/photoionization equilibrium state (see self-focusing section). Furthermore, for a laser beam with irregular spatial intensity distribution, by increasing the average beam’s intensity we increase the number of peaks above SF threshold, thus creating a larger number of SF areas, or filaments.

Diameter of filaments

The diameter of filaments (the diameter of the core) is a characteristic of the material and is regulated by the conditions of Kerr/photoionization equilibrium. The parameters of the laser pulse that are instrumental in modifying the diameter are the wavelength, and the pulse duration. The degree of impurities can also play a role, either by modifying the refraction index, at higher concentrations, or by seeding the AI, at longer pulse durations.

The diameter of filaments does not seem to be influenced by the increase of the initial intensity. An increase in intensity will rather translate in an increase in the length and number of filaments.

Use of lenses

In the laboratory one often uses lenses in order to induce SF earlier in the propagation. Without it, the SF length could be too long: it can reach several tens of centimeters in condensed materials, and several tens of meters in gases. Moreover, in the fs time regime, where group velocity dispersion is very important given the broad spectrum, the shape of the pulse is modified after on a long propagation distance. For certain applications this effect is undesirable. This is one of the reasons why lenses become necessary in certain cases, hence the importance to understand their effect.

Using a lens to focus the beam, we observe a global convergence of the light, i.e. on a greater scale, and a convergence on a smaller scale due to SF. The latter develops on the irregularities of the radial distribution of the intensity. The larger the focal length, the grated the SF effects, filaments form at a greater distance, and are longer. The continuum generation is also more intense. In the case of tight focusing, the propagation mainly depends on the global convergence induced by the lens, the filaments are shorter, and the continuum less intense.

Because of the global convergence induced by the lens, the light filaments generated will not be parallel. Their directions have a convergence point coinciding with the geometrical focal point of the lens. For appropriate intensity levels, and for a short focal length, the light filaments can meet at the focal point and cause OB, for entry intensities below OB threshold. A superposition of F and OB modes is then induced. By carefully balancing the focal length and the entry intensity, the relative importance of the two modes is controlled. A F-OB mixed mode can be induced in this fashion.

Lenses are also instrumental for controlling the position of the affected area within the sample material.

Other effects

Heat deposition

There is very little heat deposited inside the filaments in the fs time regime.

Non-linear optical processes

In the ns time regime filaments are formed for intensities below OB threshold, and the intensity is clamped below AI and MPI threshold. In this case SF is counterbalanced mainly by stimulated Raman and Brillouin emission. It is also important to recognize that these mechanisms have a limited dissipative efficiency. By gradually increasing the entry intensity of the ns laser pulse the capacity of energy dissipation of Raman and Brillouin conversions can be exceeded. SF becomes stronger at higher intensities, it surpasses the counter-effect of Raman and Brillouin conversions, causing the collapse of the beam even farther. Eventually, AI's intensity threshold is reached, and OB appears suddenly. The filamentary ionization mode is not possible.

As we diminish the pulse duration, the contribution of AI to the plasma density becomes less important. That raises the OB intensity threshold, making it more stable and more predictable. As OB intensity threshold becomes higher in the fs time regime, other optical non-linear effects can be observed, such as: self-phase modulation, multiphoton absorption, and 2-4 photons wave mixing. On the other hand, stimulated Raman emission decreases for powers just above the SF threshold, and becomes important only at very high powers. The Brillouin stimulated emission, disappears. The generation of continuum, which develops inside the core, is observed with an intensity threshold practically equal to that of SF. Being generated in the core, the continuum becomes more intense by increasing the intensity, as the filaments become longer, and as their number increases. Group velocity dispersion also becomes very important in the sub-ps time regime.

During the non-linear propagation of an intense laser pulse there is also an important temporal redistribution of the intensity. Effects like self-steepening [9, 11, 12] and pulse splitting [8, 10] are observed. These effects are very important as they can influence fast occurring processes like molecular dissociation, and affect the nature and the yield of primary photolytic species.

Self-focusing, filamentation, and continuum generation

We spoke about continuum generation in the ps and fs time regime. A. Embroiderer et al. explored the link between continuum generation and SF. Their experimental results show that the power threshold for continuum generation and SF practically coincide. The continuum generation is easily detectable with the naked eye, therefore it presents a practical interest, as it becomes a sign for SF and filamentation. Being generated within filaments, the intensity of the continuum increases with the length and with the number of filaments.

The spectrum of the continuum generation is also related to the maximum intensity reached inside the core; it can extend from the near infrared to the UV. The spatial color distribution of the continuum gives information on the core’s intensity distribution and diameter. The sampling and measurement of the continuum’s spectrum constitutes a convenient way to estimate and monitor these other important parameters.

There is another very important reason to consider continuum generation. Some of the photolytic processes (ionization, excitation) observed can be induced by the UV radiation produced during propagation. When evaluating the long-term effects of sub-ps laser pulses on complex systems one should bear in mind that short wavelength radiation is always produced during the F mode.

References

[1] Observation of self-phase modulation and small-scale filaments in crystals and glasses; R. R. Alfano and S. L. Shapiro; Physical Review Letters, Volume 24, Number 11, 16 March 1970

[2] Superbroadening in H₂O and D₂O by self-focused picosecond pulses from a YAIG:Nd laser; W. Lee Smith, P. Liu, and N. Bloembergen; Physical Review A, Volume 15, Number 6, 2396 June 1977

[3] Ultrafast wihte-light continuum generation end self focusing in transparent condensed media; A. Brodeur and S.L. Chin; 1999 Optical Society of America Vol. 16, no. 4/April 1999/J. Opt. Soc. Am. B 637

[4] Band Gap Dependence of the ultrafast white-light continuum; A. Brodeur and S.L. Chin; Phys rev lett, Vol 80, No 20, 4406, 18 may 1998

[5] Microscopic processes in dielectrics under irradiation by subpicosecond laser pulses; A. Kaiser, B. Rethfeld, M. Vicanek and G. Simon, Physical Review B, 1 May 2000-I, Vol. 61, No. 17

[6] Nonlinear propagation of fs laser pulses in liquids and evolution of supercontinuum generation; Jiansheng Liu, H. Schroeder, S. L. Chin, Ruxin Li, and Zhizhan Xu; Optics Express, Vol. 13, No. 25, 10248, 12 December 2005

[7] Optimal control on multi-photon ionization dynamics of small alkali aggregates; A. Lindinger, A. Bartelt, C. Lupulescu, Vajda, L. Wöste; Proceedings of SPIE Vol. 5258 IV Workshop on Atomic and Molecular Physics

[8] Observation of Pulse Splitting in Nonlinear Dispersive Media; Jinendra K. Ranka, Robert W. Schirmer, Alexander L. Gaeta; Phys. Rev. Lett., Vol 77, No 18, 28 October 1996

[9] Self-transformation of a powerful femtosecond laser pulse into a white-light laser pulse in bulk optical media (or supercontinuum generation); V.P. kandidov, O.G. Kosareva, I.S. Golubtsov, W. Liu, A. Becker, N. Akozbek, C.M. Bowden, S.L. Chin; Appl. Phys. B 77, 149–165 (2003)

[10] Self-Guided Propagation of Ultrashort IR Laser Pulses in Fused Silica; S. Tzortzakis, L. Sudrie, M. Franco, B. Prade, A. Mysyrowicz; A. Couairon, L. Bergé; Phys. Rev. Lett. Vol 87, No 21, 19 November 2001

[11] Catastrophic Collapse of Ultrashort Pulses; Alexander L. Gaeta; Phys. Rev. Lett. Vol 84, No 16, 17 April 2000

[12] Propagation Dynamics of Intense Femtosecond Pulses: Multiple Splittings, Coalescence, and Continuum Generation; Alex A. Zozulya, Scott A. Diddams, Amelia G. Van Engen, Tracy S. Clement; Phys. Rrev. Lett., Vol. 82, No. 7, 15 February 1999