Filamentation and Propagation of Ultra-Short, Intense Laser Pulses in Air



A.C. Ting, D.F. Gordon, R.F. Hubbard, J.R. Peñano, and P. Sprangle
Plasma Physics Division

C.K. Manka
RSI, Inc.

Ultra-short (femtosecond), high-power laser pulses can exceed the threshold for nonlinear self-focusing in air. This results in an extended propagation from the dynamical balance between the plasma formation and the nonlinear focusing. Experiments were performed using the chirped-pulse-amplification (CPA) lasers in the Plasma Physics Division to study the physics of extended propagation in air and its effects on atmospheric breakdown, laser-induced electrical discharge, and chemical/biological (chem/bio) agent detection. Self-guiding of the laser beams for extended distances and formation of multiple laser and plasma filaments were observed. Time-resolved images of laser-induced electrical discharges showed the initiation and sustention of the discharges by the plasma filaments. Measured optical spectra of the white light generated in the laser propagation revealed the presence of molecular plasmas that are useful for identifying chem/bio agents. Potential applications include directed energy weapons, remote sensing for both chem/bio defense, and environmental air pollutant monitoring.

INTRODUCTION

Ultra-high-power lasers that can deliver intense radiation have raditionally resided in a few, very large national laboratories. This is because more energy is usually required as the power of the laser increases, and thus the size of the laser correspondingly increases. Therefore, research into the physics associated with intense radiation from these ultra-high-power lasers could only be carried out at these large institutions. In addition, the size and cost of the lasers severely limited the range of potential applications. This has all changed during the last decade when a new way of generating high-power lasers was discovered. This simple but effective "trick" to increase laser power starts with the recognition that power is, by definition, energy per unit time. Instead of increasing the energy carried in a laser pulse for a fixed time duration to obtain higher power, one can produce the same laser power if one decreases the pulse duration while maintaining the same amount of energy in it. By utilizing ultra-short laser pulses with durations as short as a few tens of femtoseconds (thousand-trillionth of a second), laser pulses with power as high as tens of terawatts (trillion watt) can now be obtained by using table-top sized laser systems. Research on these lasers can now be performed in reasonably sized laboratories, and many potential applications are envisioned.

Many interesting phenomena are associated with the interactions of these very intense and short laser pulses with various media. In particular, the propagation of a short intense laser pulse in a gas such as air is very different from that of a long or continuous wave (CW) laser pulse. For example, the high intensity of these pulses can produce nonlinear contributions to the index of refraction of the medium. The intensity of the laser pulse could also become so high that the air molecules would ionize and form a plasma. The inter-play between the laser pulse and the plasma that it creates can be very complicated and can profoundly affect the evolution of the laser pulse as it propagates through the atmosphere. Experiments using ultra-short (~100 fs), high intensity (>1013W/cm2) laser pulses have demonstrated long-distance self-guided atmospheric propagation,1 air breakdown, filamentation, and white light generation. Intense, directed white light pulses have been generated and backscattered from atmospheric aerosols. The generation of pulsed THz radiation in plasma channels formed by femtosecond pulses has also been observed and analyzed. Although many of the observations cannot be completely explained, the experimental, theoretical, and numerical results obtained to date indicate potential applications for both passive and active remote sensing and induced electric discharges, among others. In addition, the individual micropulses in a shipboard free electron laser (FEL) system may exhibit short-pulse propagation characteristics. To achieve these potential applications, it is necessary to have a comprehensive and quantitative understanding of the physical mechanisms that govern the propagation of intense, short laser pulses in air.

The following sections begin with a description of the table-top ultra-high-power lasers in the laboratory. Next, the physics of propagating femtosecond terawatt laser pulses in air is discussed, with experimental demonstration of the novel phenomena of self-guided laser filaments and numerical verification of the experimental results. These filaments and the associated broadband radiation that they generate can be used in the remote sensing of cal/biological agents in defense or anti-terrorism applications or detecting hazardous air pollutants in environmental monitoring and enforcement. The plasma filaments associated with a self-guided femtosecond intense laser pulse can also be used for triggering high-voltage electrical discharges. This phenomenon is next discussed, with emphasis on the discharge initiation mechanism, by studying the time evolution of the discharge. There is considerable interest worldwide in studying this phenomenon so that it can be applied to areas such as lightning arrest around power plants. The concluding section summarizes research efforts at NRL in studying ultra-short intense laser pulse propagation in air.

NRL T3 AND TFL LASERS

The NRL High Field Physics Laboratory was one of the first laboratories to have a table-top terawatt (TW) laser system soon after the invention of the chirped pulse amplification (CPA) method. The T3 laser was installed in 1992 as the first commercial CPA laser ever built. It has been upgraded several times over the years and is still a state-of-the-art CPA laser. It is a solid state laser involving two lasing media, titanium-doped sapphire (Ti:sapphire) and neodymium-doped glass (Nd:glass). The lasing wavelength is in the infrared at 1054 nanometers (nm). Like most lasers, it consists primarily of a laser oscillator that generates the seed laser pulse and then a series of laser amplifiers to boost the energy in the pulse. The difference is that the seed laser pulse has a pulse length of only 100 femtoseconds (fs). As the laser pulse is amplified, the power and intensity of the pulse continuously increases and eventually will reach the breakdown threshold of the laser glass medium. To avoid such disastrous consequences, the CPA technique stretches the laser pulse after the oscillator with a diffraction grating to ~10,000 times and thus reduces the laser intensity and power by the same factor. The stretched pulse can now be safely amplified to the desired high energy per pulse. The stretching process is then reversed by re-compressing the amplified pulse with diffraction gratings in air or vacuum to produce a high-power, ultra-short pulse. One interesting observation is that in the stretched pulse, the frequency content of the pulse is arranged such that the high-frequency (pitch) components are moved to the back of the stretched pulse, reminiscent of the chirped tune of a singing robin, and hence the "chirped" pulse amplification technique.

Figure 1 shows the T3 laser. The final amplifier is in the foreground, and the oscillator and preamplifiers are in the back and to the left. It can generate a laser pulse 400 fs long with 5 Joules (J) of laser energy in it. The peak power of the pulse is therefore >10 TW. It has a repetition rate of one shot every 20 minutes. Most experiments on intense laser interactions require both the high power and high energy in the laser pulse. However, a number of interesting behaviors of an ultra-short laser pulse are primarily the consequence of the high power and intensity of the pulse. Since a shorter pulse with less energy could have the same high power, a smaller laser with less energy per pulse could be adequate for some of the high-intensity laser experiments.

Fig 1

FIGURE 1
The NRL T3 laser is a table-top Ti:sapphire/Nd:glass CPA laser system that produces laser pulses at a wavelength of 1054 nm with 5 J of laser energy in a 400-fs pulse. It is operated at a repetition rate of one shot every 20 minutes. The amplified stretched pulse is compressed with diffraction gratings inside an evacuated chamber (not shown in the picture) to avoid nonlinear propagation effects that would degrade the laser beam quality.

The NRL TFL laser shown in Fig. 2 is a TW laser with a smaller footprint than the T3 laser, and most importantly, it can be rep-rated at 10 times a second (10 Hertz). It is based entirely on Ti:sapphire technology, and it is lasing at the infrared wavelength of 810 nm. The laser pulse width is 50 fs with 50 milli-Joules (mJ) of energy in each pulse. Both lasers are located in our well-equipped laboratory, with extensive optical and electronic diagnostic equipment that can be used to study the effects and mechanisms of these ultra-short intense laser pulses interacting with various media.

Fig 2



FIGURE 2
The NRL TFL laser is a table-top Ti:sapphire CPA laser system that produces laser pulses at a wavelength of 810 nm with 50 mJ of laser energy in a 50-fs pulse. It is operated at a repetition rate of 10 Hz. The amplified stretched pulse is compressed in a portable compressor (not shown in the picture), which allows optimized positioning of the laser for air propagation experiments.

PROPAGATION OF INTENSE SHORT LASER PULSES IN AIR

The propagation of intense, short laser pulses in the atmosphere involves a variety of diverse linear and nonlinear optical processes. The nonlinear processes are the consequences of the high intensity of the laser pulse. Processes affecting the laser spot size include diffraction, nonlinear self-focusing, ionization, and plasma defocusing. In addition, self-phase modulation, stimulated Raman scattering, and plasma formation also contribute to considerable spectral broadening and white light generation by the laser pulse. On the other hand, the ultra-shortness of the laser pulse also needs to be taken into consideration. The physics governing the atmospheric propagation of short intense laser pulses can be very different from that of long laser pulses. For example, the Raman instability associated with the excitation of molecular rotational modes, which can disrupt the long-distance propagation of long, e.g., nanosecond (ns) pulses, may not be as disruptive for laser pulses that are shorter than the characteristic picosecond (ps) period of the rotational mode. The implication of this observation is that the nonlinear refractive index of air could be a function of the laser pulse length. A 100-fs pulse could have an effective nonlinear refractive index several times smaller than that of a picosecond pulse. The inherently large spectral bandwidth of a short pulse also renders it more susceptible to dispersion effects in the atmosphere. Finally, the broad spectrum of the short laser pulse could affect the absorption characteristic of the laser in the atmosphere. In conventional narrow bandwidth, long-pulse lasers that are used in laser radar (LIDAR) applications, the laser line can be positioned between absorption lines to minimize attenuation in the atmosphere. However, the broad spectrum of a short pulse could be overlapping several individual absorption lines, and this could affect the thermal blooming process, which is a sensitive function of the absorption rate. These effects could be important for proposed shipboard FEL systems.

Perhaps the most prominent phenomenon observed when a high-power laser beam propagates in air is the formation of self-guided laser filaments. When no external focusing is provided, the wave nature of the light emitted from a laser will naturally diffract, and the laser beam size will continuously diverge and increase in size. However, the refractive index of air varies with the intensity of the laser in such a way that the higher intensity portion of a laser pulse encounters a higher value of the refractive index. Since the refractive index is a measure of the ratio of the speed of light in vacuum to that in the medium under consideration, a higher index of refraction signifies a slower speed of propagation for that portion of the laser pulse, and the laser pulse will converge (focus) onto this lower velocity portion. This has a very close analog to the propagation of light inside an optical fiber where the core of the fiber has a higher index of refraction. The higher intensity core portion of a laser pulse in air now also encounters a higher index of refraction. Therefore, it will be guided just like the light traveling down an optical fiber.

The condition for which such self-focusing can occur is governed by the initial laser power in the pulse. When the laser power reaches a threshold value, the nonlinear self-focusing effect can overcome the diffractive divergence of the laser beam, and an ideal laser beam will remain at a constant size forever. For air, the conventionally known value for this critical power is about 3 gigawatts (GW). If the laser power is above this critical value, the laser beam will converge instead, and theoretically it will continue to decrease in size until a catastrophic collapse is reached.

Fortunately, at high enough intensities, the air will break down and a plasma is formed. One of the optical properties of plasma is that it has a negative contribution to the index of refraction. Since more plasma is formed where the laser intensity is high, the refractive index is less near the core of the laser beam. This is exactly the opposite of the nonlinear contribution to the refractive index before the ionization occurs. The two opposing effects can, in certain circumstances, balance each other and result in a long-lived, noncollapsing filament. More filaments can be formed if the laser power is many times higher than the critical power for self-focusing. These filaments can propagate extended distances, much longer than would be allowed if diffraction effect alone is considered. An example is shown in Fig. 3, where a 3.56 TW laser pulse from the 1.054-?m wavelength T3 laser was propagated for 10 meters in the laboratory. Many tens of filaments are clearly visible. The initial laser beam size is 4 cm in diameter, and the individual filaments have diameters of about 200 ?m. At this small size, the propagation distance for which the filament diameter will expand by 41.4% due to diffraction (known as the Rayleigh range) is only ~3 cm. The combined effects of nonlinear focusing and plasma formation have kept the filament from diverging for very much longer than was expected. Also, at the small-diameter size of these filaments, the laser intensity are in the range of 1013 to 1014 W/cm2. At such intensities, almost all solid or liquid media will break down and be damaged. The intense field can also generate secondary radiation that can disrupt the operation of many electronic devices. Therefore, these filaments are suitable for applications that involve sensor damage or electronic countermeasure processes.

An interesting observation was that the initial power of the laser pulse was about a thousand times more than the critical self-focusing power. Theory predicts that 1,000 filaments could be formed. The comparatively low number of filaments brought out the question of whether the critical self-focusing power was correctly evaluated in the past. Since the critical power was calculated from the nonlinear refractive index of air, one begins to wonder about the correct value of the index for short, intense laser pulses. A literature search reveals that, indeed, the nonlinear refractive index of air had been measured primarily with optical methods that involved pulses much longer than a picosecond. However, there is strong experimental and theoretical evidence that the standard long pulse value for the nonlinear refractive index for air is not applicable to the self-focusing of femtosecond laser pulses.

Fig 3


FIGURE 3
False-color image of self-guided filaments in a 3.56 TW laser pulse produced by the T3 laser after propagating 10 meters in the laboratory. The beam diameter is 4 cm. The pattern of the filament distribution is correlated with the initially nonuniform transverse beam profile.

An indirect way of obtaining the value of the nonlinear refractive index of air is to compare experimental results of filamentation with numerical results from theoretical models that include all the relevant physics. The NRL air propagation simulation code models atmospheric laser pulse propagation effects with a system of three-dimensional, nonlinear equations. These include diffraction, group velocity, and higher order dispersion, stimulated molecular Raman scattering, photoionization, nonlinear bound electron effects, ionization energy depletion, and propagation in a spatially varying atmosphere.2 A coupled set of equations that was derived for the laser amplitude and electron density is used to analyze a number of physical processes, such as optical/plasma filamenta-tion, pulse compression, nonlinear focusing, and white light generation. An experiment was performed using the T3 laser to generate filaments with a known initial condition that could be simulated with the NRL air propagation code. A circular aperture was imposed on the initial laser beam to create a well-defined "top-hat" transverse profile suitable as an input to the simulation code. As the shaped laser beam propagates through the atmosphere, normal diffraction effects reshape the profile to a donut-looking form. Nonlinear effects enhance the fluctuations in the intensity around this donut shape and filaments are formed. At a distance of 10 m, four distinct filaments are formed, as shown on the left-hand side of Fig. 4. The experimental laser parameters of 400-fs pulse length and 108 GW peak power are imported into the simulation code, and the results are compared to the experiment. The nonlinear refractive index of air is varied in the simulation runs. It was found that in order to match the experimental result for the same number of filaments at the same distance, the simulation had to use a nonlinear refractive index 50% less than the conventional value. The simulation result is shown in on the right-hand side of Fig. 4. This is the first quantitative experimental/numerical verification that the nonlinear refractive index of air has different values when ultra-short intense lasers are involved.

Fig 4
FIGURE 4
The formation of filaments from an apertured 400-fs laser beam with peak power of 108 GW at a distance of 10 meters. The experimental result is shown on the left, with the simulation result on the right. The value of the nonlinear refractive index used in the simulation to obtain the best match with the experiment is found to be 50% of standard value for long pulses.

Another interesting phenomenon arising from the propagation of short intense laser pulses in air is the generation of broadband radiation, often referred to as "white light" or "supercontinuum." This radiation is the result of the nonlinear self-phase modulation and ionization effects that are caused by the rapid variation in the index of refraction from the front to the back of the laser pulse. Nonlinear generation of optical frequencies outside the original laser linewidth can be as broad as 100%. Because the laser wavelength is in the infrared, the broadened spectrum can extend into the ultraviolet (UV) and far infrared. Figure 5 shows a portion of the spectrum of the radiation collected after the laser pulse from the 0.81-?m wave-length TFL laser has propagated for about 7 meters. It shows that radiation was produced in the UV, and many of the spectral features have been identified as those of the neutral or ionic species of the oxygen and nitrogen molecules. These features indicate that the molecules in the air where the laser has traversed can be excited, and it offers the potential application of these ultra-short pulse lasers for identification and detection of chemical and biological molecules from various airborne pollutants or compounds. Substantial spectral broadening is also routinely observed in simulations with the NRL air propagation code.

LASER-INDUCED ELECTRICAL BREAKDOWN

The presence of a plasma column in the filamentation of a femtosecond TW laser pulse in air offers another interesting application for ultra-short intense laser pulses. The plasma column is electrically conducting and can, therefore, support a current between two electrodes that are charged to sufficiently high voltages. Induced high-voltage breakdown has been studied using electron beams or high-power lasers as the trigger mechanism, but the power required is usually quite formidable and the discharge is often erratic. The breakdown is usually caused by an ionization front (streamer) initiated by the laser that progressively links the two electrodes until the circuit is completed for the final discharge. The path of the discharge and the time of discharge after the laser trigger are both quite random. The plasma columns associated with the filaments of a propagating ultra-short pulse could generate a conducting path that will lead to a deterministic discharge time and path for the breakdown. This realization is important to applications such as the arrest of lightning discharges where precise control of the lightning path is required. There are also other applications in which the discharge must be synchronized with other optical and electrical signals so knowledge of the precise discharge time after the laser trigger is crucial.

Fig 5
FIGURE 5
Broadband radiation spectrum in the UV region from a 100-fs, 300 GW laser pulse propa-gating for 7 meters in air. Spectral line structures are identified as electronic transitions of neutral and ionic molecular species in air.

An experiment has been carried out using the 0.81-?m wavelength TFL laser at peak powers of ~100 to 400 GW to initiate electrical breakdown between two electrodes maintaining an average electric field of ~1.5 to 2 MV/m. The discharge was monitored with streak cameras that could record its time evolution beginning with the passage of the laser pulse between the two electrodes. Two classes of discharge were observed that would not be distinguishable if it were not for the streak camera catching the discharges in their actions. They are shown in the two pictures in Fig. 6. The pictures are essentially multiple exposures of a discharge, with each image slightly displaced vertically. Images near the bottom of the pictures happen earlier in time, and they move upward as time progresses. The ground electrode is on the left, and the negatively charged high-voltage electrode (cathode) is on the right side of the picture. The picture on the left in Fig. 6 shows a streamer starting from the bottom left and moving from the ground electrode toward the cathode. Because the images are shifted upward as the streamer moves, it appears to be tracing out a parabolic trajectory but, in reality, it moves directly across the space between the electrodes. From the time scale indicated on the vertical axis of the picture, the speed of the streamer can be estimated to be close to 1% of the speed of light. The effort of this streamer apparently is not enough to cause a breakdown between the electrodes, and one can see that more streamers are involved at later times. Eventually the air between the electrodes breaks down, but at a time much later than could be displayed in this picture.

The picture on the right in Fig. 6 shows a totally different behavior in time. There appears to be no indication of any presence of streamers. Instead, there are illuminated horizontal paths that repeat themselves at time intervals of ~5 ns as can be measured from the vertical scale. This indicates that a complete conducting path has been formed and a current is flowing between the two electrodes. Since the flow of current occurs at the speed of light, the images are essentially horizontal lines in this picture. The multiple lines represent an oscillation in the flow of current between the two electrodes, with a frequency governed by the circuit inductance and capacitance of the experimental setup. The lowest bright line has a gap in the middle, and it is an indication that the conducting path is not complete at the early stage of the discharge. The width of the gap shortens as time progresses. The speed of approach of the two ends of the gap is found to be around 1% of the speed of light. This is consistent with the motion of an ionization front under these experimental conditions, as seen in the left picture in Fig. 6.

Fig 6
FIGURE 6
Streak camera images of laser-induced electrical discharges. The left-hand picture shows streamer initiated discharges with streamer velocity estimated to be ~1% of light speed. The right-hand picture shows a fully guided discharge occurring at ~255 ns after the laser trigger. The multiple discharges are the consequence of resonant electrical circuit oscillations.

The time delay between the laser and the triggering of the discharge for these fully guided discharges is consistently around 200 ns. This delay is much longer than the expected time for the plasma density to decay due to recombination. Simulations with an NRL air chemistry code that follows a large number of molecular, atomic, and ionic species support the following scenario to explain the long delay time. The applied electric field drives current through the laser-produced plasma filament and produces a sufficiently high electron temperature to maintain the plasma electron density. Eventually, the electron density rises rapidly due to collisional (avalanche) ionization. This leads to a rapid, uniform, fully guided breakdown across the gap. The time for breakdown to occur in the simulations varies with filament size and initial electron density and is consistent with the ~200-ns delay observed in the experiment. This observation and its verification with simulation confirm the utility of an ultra-short intense laser to precisely triggered high-voltage electrical discharges.

CONCLUSIONS

Experimental, theoretical, and numerical studies have been performed on the propagation and interactions of ultra-short intense laser pulses in air. Filamentation of the laser pulse and the formation of plasma columns and the generation of broadband radiation in the UV region were observed. Through the benchmark process between experimental and numerical model calculations, we have gained valuable knowledge of the underlying principles such as the measurement of the nonlinear refractive index of air for fs TW laser pulses and the origin of fully guided and well-defined electric discharges triggered by these laser pulses. There are many applications including the detection of airborne pollutants or chemical/biological compounds and laser-triggered lightning arrests. Further understanding can be achieved with experimental and theoretical/numerical studies of fundamental physics such as the onset of various nonlinear processes as a function of the laser characteristics of the intense laser pulses.

ACKNOWLEDGEMENTS

The authors thank Drs. Philip Girardi and Tim Andreadis of the Tactical Electronic Warfare Division, Drs. Andrew Baronavski and Harold Ladouceur of the Chemistry Division, Drs. Steven Slinker, Richard Fernsler, and Mr. Edgar McLean of the Plasma Physics Division, Dr. Christopher Moore of Space Systems Development Department, and Dr. Bahman Hafizi of Icarus, Inc., for useful discussions, and Mr. Eldridge Briscoe from RSI, Inc. for technical support.

[Sponsored by ONR, JTO, NAVSEA, and U.S. Army SBCCOM]

References
1A. Braun, G. Korn, X. Liu, D. Du, J. Squier, and G. Mourou, "Self-channeling of High-peak-power Femtosecond Laser Pulses in Air," Opt. Lett. 20, 73-75 (1995).
2 P. Sprangle, J.R. Peñano, and B. Hafizi, "Propagation of Intense Short Laser Pulses in the Atmosphere," Phys. Rev. E 66, 046418 (2002).