Laser filament-induced aerosol generation in the atmosphere

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Thesis

Reference

Laser filament-induced aerosol generation in the atmosphere

HENIN, Stefano

Abstract

We investigate the production of aerosols induced by the propagation of TW-class laser filaments through the real atmosphere. We demonstrate that filaments generate new, stable, particles in ambient air, in conditions typical of the lower troposphere. We examine the dependence of this effect on atmospheric parameters and characterize the chemical species produced, identifying several chemical pathways leading to particle formation. By investigating this phenomenon in a cloud simulation chamber, we show that filaments can assist not only the growth of existing particles, but also the direct gas-to-particle conversion. We check that the laser-generated aerosols are potentially capable to serve as cloud condensation nuclei.

Furthermore, we prove that filaments can modify the optical properties of cirrus clouds, by increasing the density of pre-existing ice crystals. These remarkable findings suggest new all-optical methods for cloud seeding and climate engineering, provided that the laser effect is extended to a macroscopic volume. We demonstrate that increasing the laser power is an effective strategy to approach this [...]

HENIN, Stefano. Laser filament-induced aerosol generation in the atmosphere. Thèse de doctorat : Univ. Genève, 2013, no. Sc. 4522

URN : urn:nbn:ch:unige-275202

DOI : 10.13097/archive-ouverte/unige:27520

Available at:

http://archive-ouverte.unige.ch/unige:27520

Disclaimer: layout of this document may differ from the published version.

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UNIVERSITÉ DE GENÈVE FACULTÉ DES SCIENCES

Groupe de Physique Appliquée Professeur J.-P. WOLF

Laser Filament-induced Aerosol Generation

in the Atmosphere

THÈSE

présentée à la Faculté des Sciences de l’Université de Genève pour obtenir le grade de Docteur ès Sciences, mention Physique

par

Stefano HENIN

de Pavia (Italie)

Thèse No 4522

GENÈVE

Atelier de reproduction ReproMail 2013

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Acknowledgements

First of all, I sincerely express my gratitude to my advisor, Prof. Jean Pierre Wolf, who gave me the possibility to join his group and to take part to many interna- tional collaborations. His support and confidence did strongly motivate me and have been fundamental to attain this successful result.

A special thanks to my supervisor, Dr Jerome Kasparian, who has been my guide throughout all my work, as well as the manuscript reviewer. His precious help, spanning from theory to very applied, practical hints and his unlimited optimism pushed me and all the filamentation team towards great achievements.

I’m honoured that Prof. L.Woeste, Prof. T.Leisner, Prof D.Faccio and Prof. J.P.

Reed accepted to take part to my examination board and appreciated my work.

I would like to thank all my previous and actual colleagues: Jerome, Ariana, De- nis, Luigi, Michel, Pierre, Thibaud, Svetlana, Julien, Nicolas, Mary, Sylvain, An- drii, Andrey, Julio, François and the undergrads. I’m grateful for what I learned from all of you and I really enjoyed the friendly, genuine atmosphere of the GAP Biophotonics group.

A special mention to the Teramobile team, in particular to Estelle, who introduced me to the operation of the laser and to all its optics, and Massimo, who allowed me to evolve to a laser expert 2.0! This brings me to thank all the people that joined the many experimental campaigns with our portable laser, by daytime and nighttime, with sun, fog, cold and warm weather. So, thanks a lot to Yannick, Philip, Kamil, Massimo again, and the teams of Berlin, Rossendorf, Dusseldorf, Karlsuhe, Frascati, and Quebec plus INRS. You are too many to be cited one by one!

Going back to Geneva, I’m grateful to the secretaries, Isabel, Laurence and Nathalie, for assisting me while facing this intricate, obscure world called ’administration and bureaucracy’!

Thanks to the neighbours of GAP Optics and to Giorgio and Marco, and to Carmine for the coffee!

Thanks to all the new friends that I have known during my staying in Geneva:

those who welcomed me when I had just arrived - the (large) family - and those that I met later on. I’m really grateful to everyone for your friendship, which helped me to feel a little more ’at home’.

Finally, I thank Valentina, for her courage, smile and love, that gave a deeper sense to my life during these years. For all the adventures that we lived together, and for those that are waiting for us.

I would like to dedicate this work to my family, for their help and support to my education.

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Summary

This work is part of a new line of research, pioneered by the GAP Biophoton- ics group in a joint collaboration with the partners of the Teramobile consortium, aimed at characterizing the production of aerosols induced by the propagation of laser filaments through the real atmosphere.

We demonstrate that light filaments, produced by TW-class lasers, generate new, stable, particles in ambient air, in conditions typical of the lower troposphere.

We investigate the dependence of this effect on temperature and relative humidities (RH), reporting of particle generation at RH as low as 70%. We characterized the chemical species produced within the filaments, identifying nitric acid as the stabilizing factor which prevents aerosols from evaporation. A semi-quantitative model based on the atmospheric thermodynamic equilibrium of solution droplets, in presence of relevant amount of HNO₃, supports this interpretation.

By investigating this phenomenon in a cloud simulation chamber, we show that filaments can assist not only the growth of existing particles, but also the gas-to-particle conversion in a background-free atmosphere. By varying the composition of air mixture, we identified new chemical pathways that lead to particle formation, involving sulfuric and organic acids. We check that the laser-generated aerosols are potentially capable to serve as cloud condensation nuclei, if the air mass subsequently cools down, eventually evolving into a precipitation event.

Furthermore, we prove that laser filaments can significantly modify the optical properties of cirrus clouds, by increasing the density of pre-existing ice crystals.

These remarkable findings suggest new all-optical methods for cloud seeding and climate engineering, provided that the laser effect is extended to a macroscopic volume. By characterizing the aerosol and ozone generation upon irradiation with a 100 TW-class laser, we demonstrate that increasing the laser power is an effective strategy to approach this issue.

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Résumé

Ce travail s’inscrit dans un domaine de recherche émergent, ouvert par le groupe GAP Biophotonics en collaboration avec les partenaires du consortium Teramo- bile, qui vise a caractériser la production d’ aerosols, induite par la propagation de filaments laser à travers l’atmosphère.

Nous avons démontré que les filament lumineux, issus des laser TW, génèrent des nouvelles particules, stables, dans l’air ambiante, dans des conditions typiques de la basse troposphère. En exploitant la dépendance de cet effet par rapport à la température et l’humidité relative, nous avons pu observer la génération de particules pour une humidité aussi basse que 70%. Nous avons ensuite caractérisé les espèces chimiques produites par les filaments, et identifié l’acide nitrique comme étant le facteur stabilisant qui empêche l’évaporation des aerosols. Un modèle semi-quantitatif, basé sur l’équilibre thermodynamique entre l’atmosphère et les gouttes d’une solution, sous l’effet d’une haute concentration de HNO₃, étaye cette hypothèse.

Par le biais de l’étude de ce phénomène dans une chambre à nuages, nous avons montré que les filaments peuvent aussi encourager la conversion directe gaz- particule, dans une atmosphère initialement libre de particule. En faisant varier la composition de l’air dans la chambre, nous avons identifié de nouvelles réac- tions chimiques qui peuvent conduire à la formation des particules, qui impliquent les acides sulfurique et organiques. Nous avons démontré que les aerosols générés par le laser constituent des noyaux de condensation potentiels, si la masse d’air se refroidit, ce qui peut éventuellement mener au développement de précipitations.

De plus, nous avons prouvé que les filaments peuvent modifier de manière signi- ficative les propriétés optiques des cirrus, en multipliant la densité de cristaux de glace.

En raison de ces résultats remarquables, des nouvelles méthodes optiques pour l’ensemencement des nouages et l’ingénierie climatique sont envisageables, à condition que l’effet du laser soit déployé sur un volume macroscopique. Nous nous sommes donc intéressés à la génération d’aerosols et d’ozone par un laser à 100 TW, et avons montré que l’augmentation de la puissance du laser constitue une stratégie efficace pour aborder cette question.

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Introduction

The first demonstration of a functioning LASER (Light Amplification by Stimu- lated Emission of Radiation) device, by T.Maiman [30], which dates back to 1960, marked a spectacular breakthrough in the history of both scientific and technolog- ical progress of humankind.

Such diffraction-limited, coherent light source suggested new promising perspectives in basic research, as a powerful tool for photochemistry, microscopy [31]

and spectroscopy [32], as well as in several applied fields such as optical commu- nications, precision contact-less measurements and machining [33, 34], bloodless surgery, biological tissues treatment [35], and many others.

Atmospheric research is one of the domains that strongly benefit the most from the laser technology, and is nowadays hard to conceive without the essential contribution of laser-based remote sensing techniques. For instance, LIDAR (Light Detection And Ranging) offers a broad range of measurements allowing to remotely profile temperature and wind velocity, measure the concentration of water vapor and trace gases, detect bio-aerosol and pollutants [36].

In the context of LIDAR and other applications involving long-range propagation, the laser is operated at low intensities¹, so that neither the propagation medium nor the target molecules and aerosol are modified by the interaction with the beam.

Therefore, the laser light is employed uniquely as a probe, i.e. a passive tool.

However, these applications don’t take advantage of all the spectacular properties of the most powerful lasers, that yield even more striking potentialities. Indeed, such lasers can operate in a more active way also in the free atmosphere, by initiating chemical processes upon photo-excitation of reactive molecules.

Thanks to the uninterrupted progress of laser technology, remotely irradiating an air volume with high optical intensity is nowadays practically achievable. After the invention of the Chirped Pulse Amplification technique in the late 1980s [37], femtosecond TeraWatt(TW)-class lasers, typically operating at the wavelength of 800 nm, have become commercially available. At such high input power, the frontier of nonlinear optics is broken in air at atmospheric pressure, and a spectacular light propagation regime is established, consisting in narrow light structures called

1typically in the order of MW/cm²for a frequency-doubled YAG laser used in LIDAR setups

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of light beams [1, 3, 38].

This impressive phenomenon provides the way to irradiate the desired air volume with optical intensities as high as 10¹⁴ W/cm². The laser can thus significantly enhance the probability associated to multi-photon processes such as dissocia- tion and ionization, hence the efficiency of photochemical reactions involving air molecules and trace gases. These processes would otherwise be naturally initiated only by the UV component of solar radiation, whose maximum irradiance amounts to 1 W m⁻²nm⁻¹and is thus many orders of magnitudes lower compared to laser filaments. This modulation of the thermodynamic equilibrium between air constituents might be expected to trigger atmospheric processes such as particle formation and growth.

This idea is further supported by previous studies on the photo-nucleation in several gas mixtures, a research field initiated by Wilson [39, 40] at the end of 19^th century, for which he was awarded the Nobel Prize in 1911. He first showed that new condensed particles appear in a cloud chamber filled with air saturated with water vapor, after illumination by different types of energetic radiations. Many researchers pursued on this line of research, focusing their studies on the effects of UV light of suitable wavelengths, and confirmed his results, suggesting that, under adequate conditions, water vapor can condense on photo-chemical prod- ucts. After Wilson, such phenomenon has been observed both in saturated [14]

and sub-saturated conditions [41], but never in the free atmosphere.

The active, essential role of electromagnetic radiation in assisting condensation of new liquid droplets in Wilson-type experiments inspired the innovative idea of using high-power infrared filaments to induce condensation in the real atmosphere. Owing to the different wavelength with respect to UV photo-nucleation, this method relies on different photo-chemical processes, involving multi-photon absorption and thus requiring very high optical intensities, routinely attained within light filaments.

The GAP Biophotonics group, together with our partners (FU Berlin and LASIM Lyon) of the Teramobile consortium [42], pioneered this research field of filament- assisted particle formation in air. This thesis work focuses on the experimental investigation of such spectacular effect, conducted in the free atmosphere under different temperatures and relative humidities, as well as in a cloud chamber for different air chemical compositions and in simulated cirrus clouds.

For those readers who are not familiar with optics, in particular the filamentation regime, and atmospheric physics, Chapters 1 and 2 review the fundamental aspects of these respective domains that are useful to our context.

Encouraged by previous observations of the phenomenon [43] reported by our group, based on cloud chamber experiments, we performed field measurements that demonstrated, for the first time, the filaments-induced droplets generation in

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the real atmosphere. These experiments, based on remote pump-probe LIDAR andin situdetection, are described in Chapter 3, followed by complementary lab- oratory measurements aimed at quantifying the amount of trace gases produced by the laser. In order to explain the observed stability of laser-generated particles, a semi-quantitative model based on the photo-generated nitric acid is suggested.

In order to unravel the complex physico-chemical scenario underlying this striking laser effect, we conducted two experimental campaigns in a aerosol and cloud simulation chamber, that will be described in Chapter 4. By performing a para- metric study of air constituents, under low-tropospheric conditions, we identified several mechanisms that contribute to the particle formation, in addition to the nitric acid pathway. Furthermore, we investigated the effect of ice multiplication upon laser illumination of ice clouds, at temperatures as low as−50^◦C.

The laser-induced modification of the thermodynamic equilibrium between air and atmospheric particles suggests amazing prospects on the triggering of pre- cipitations and the modulation of cloud radiative balance. Therefore, in view of potential large-scale applications of the laser-induced particle production, we ex- perimentally characterized the particle yield under a jump of more than two orders of magnitude of laser irradiation, suggesting that increasing the laser power might be an efficient strategy to upscale the laser effect to a macroscopic volume. The outcome of this study will be described in Chapter 5.

Finally, in the light of the promising perspectives on large-scale droplets generation, the implications of this outstanding phenomenon to local weather modulation are briefly discussed at the end of this work.

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Chapter 1 Laser filamentation in the atmosphere

This thesis work focuses on the new particle formation and growth in the atmosphere, artificially induced by femtosecond laser pulses which propagates freely in the air. Such striking effect owes its feasibility to the capability of ultrashort laser pulses to propagate with negligible losses in the air, over long distances, spontaneously forming narrow, intense light filaments. In this Chapter I first dis- cuss the basic properties of this propagation regime, providing a brief description of the typical phenomena that are always present in a filamenting beam in gaseous media as well as of the underlying physics. It is beyond the scope of this work to give a comprehensive view of the filamentation regime; several authors published detailed reviews on this subject, that can be found in Ref. [1, 3, 38].

Additionally, the long-range propagation of filaments in view of its atmospheric applications will be discussed, especially in the case of TW-class laser beams, which have been used throughout all the experimental measurements.

Typically, the earth’s atmosphere is rich in pre-existing aerosols, dust and eventually cloud droplets; this is a fundamental issue in the context of atmospheric propagation of light beams, which can be strongly affected by the interaction with atmospheric particles. Moreover, light scattering from suspended particles is a widely used all-optical technique, both remote and in situ, for the detection and sizing of particles in the air. Thus, the main aspects of the interaction between laser light and small aerosols, as well as cloud droplets, are briefly reviewed in the last section of the present chapter.

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1.1 Self-guided propagation of ultrashort pulses in gaseous media

Since the early development of nonlinear optics, it was known that intense nanosec- ond laser pulses undergo self-structuring and self spectral broadening, generating filaments of light that routinely damaged transparent media and represented a limiting factor in the design of high-power lasers.

With the development of the Chirped-Pulse Amplification technique (CPA) [37], it became possible to amplify mode-locked ultrashort femtosecond pulses, thus breaking the frontier of the GW and TW pulse peak power. In this regime, an in- triguing phenomenon was reported by Braun et al. [44]; they observed that launching in the air an infrared pulse with femtosecond duration and GW power, resulted in the spontaneous onset of self-guided, narrow light structures.

While the beam shrinks into these self-localized channels, the electric field progressively increases and, interacting nonlinearly with the air, initiates a variety of phenomena that always accompany and also influence the pulse propagation, by preventing beam collapse. The complex scenario resulting from the simultaneous occurrence of the self-guided propagation and the associated phenomena, corresponds to what is commonly referred to asfilamentation.

A qualitative picture of this propagation regime will be first given in Sec. 1.1.1, and the underlying physics is illustrated more in detail in Sec. 1.1.2.

1.1.1 The filamentation regime: general aspects

The filamentation of ultrashort laser pulses in air is an example of a self-established propagation regime that overcomes the natural limitation of diffraction without the help of any external guiding or focusing mechanism. Although this topic is subject of an intense research activity since the last two decades, a universally accepted definition of a filament is yet to be found. Some aspects concerning its deep physical origins, moreover, are still controversial. Considering the context of atmospheric filamentation that this thesis work belongs to, thinking of a filament as a narrow, intense light structure that spontaneously arises at a remote location and keeps its self-confined structure over an extended length, best high- lights its attractive properties in view of laser-based weather modulation. Indeed, filamentation provides a way to convey considerable amounts of energy at a desired location, and is therefore capable of initiating several light-air interaction processes within a more extended volume as compared to a classically focused beam. It will be shown throughout this work that the physico-chemical processes triggered by the laser yield outstanding phenomena such as new particle formation

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1.1 Self-guided propagation of ultrashort pulses in gaseous media

Figure 1.1: (a) Top view of a single filament. (b) Impact of a filamenting beam on a photosensitive paper: the most intense hot spots in the profile indicate an active filament, while the less intense points correpond to a forming or vanishing filament.

or ice crystals multiplication.

Fig. 1.1 displays different views of filaments generated during the propagation of high-power laser beams in air. Many of the most relevant properties of filamentation can be inferred by looking at these pictures.

First of all, this propagation regime strongly affects the spatial beam profile. If the input pulse energy slightly exceeds the filamentation threshold, a single hot spot is formed in the transverse profile, that identifies a single filament. As the energy increases, a complex, unpredictable constellation of such intense spots appears, arranged across the whole beam profile, that leave small burns when impacting on a photo-sensitive paper and can thus be detected (Fig. 1.1b). Each of these focal spots corresponds to a filament: in this case, one speaks of multiple filamentation, a topic that will be discussed in Sec. 1.1.3.

These focal spots regularly damage optical elements by surface ablation, proving that they bear a considerable optical intensity. This is further supported by the observation of a narrow light channel of constant brightness, which stems from the fluorescence of nitrogen molecules, weakly ionized by the propagating pulse (Fig. 1.1a). At the wavelength at play, ionization is only possible via a multi-photon process, proving that extremely high intensities are attained within filaments¹. The electrons ejected from the atoms of the medium form a plasma column², whose length can vary from few centimeters to several tens of meters,

1Kasparian et al. [45] estimated analytically the intensity in a filament core reaches up to∼ 5×10¹³W/cm²

2Often, in the literature, the filament is defined as the plasma channel left behind by the pulse.

This is somehow misleading, since the plasma is actually a product of the self-guided propagation.

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and is considered representative of the effective length of the self-guided filament [9, 47, 48].

The most striking feature of filaments is that their formation is absolutely spontaneous, above a well-defined laser beam power. Filamentation features a sharp power threshold, revealing that its intrinsic nature is nonlinear. Indeed, as will be discussed in Sec. 1.1.2, the physical cause of such beam self-shrinking, that leads to the hot spots pattern displayed in Fig. 1.1b, is the well-known self-focusing of light beams [49].

In the presence of a focusing mechanism alone the beam would be expected to collapse at the nonlinear focus; instead, this collapse is arrested and the narrow light channel is formed, featuring a constant diameter of approximately 100µm.

Therefore, a counteracting de-focusing mechanism must also be active. The dynamical balance between these two effects is at the root of the self-confined propagation of filaments, and will be detailed in Sec. 1.1.2.

In spite of the extremely high fluence, the energy borne by a filament is quite low, i.e. only few percent of the whole beam energy. Most of the photons, indeed, propagate in the wide low-intensity background which surrounds the filaments, therefore calledphoton bath, that is essential to the filamentation process, since it serves as an energy reservoir that continuously feeds filaments and ensures their survival over long distances. The importance of the photon bath is highlighted by two very simple, symmetric experiments respectively conducted by Courvoisier et al. [50] and by Liu et al. [51]. Their findings can be summarized as follows:

while blocking the propagation of the filament core by an obstacle of approximately 100µm diameter, did not prevent the re-formation of a filament immedi- ately downstream, if the propagation of the beam portion surrounding a filament is somewhat impeded, the filamentation is interrupted.

Furthermore, we demonstrated that, as the laser power further increases up to the hundreds of TW, the role of the photon bath in the filamentation and in the associated nonlinear phenomena becomes even more pronounced. This topic will be widely discussed in Sec. 5.2 and 5.3.

The filamentation scenario also features important properties inherent to the temporal domain. Filaments, indeed, are always accompanied by a complex broad spectral emission in the forward direction, an example of which is displayed in Fig. 1.2. It consists of an on-axis, white spot surrounded by a distribution of coloured rings. Recalling that the initial spectrum is centered around 800 nm, this conical emission illustrates that new frequencies are generated within the filament during its propagation, covering the whole visible range and extending to the near- UV. This appearance of new frequencies to the spectrum of a filamenting beam is

Furthermore, recent works predicted the possibility of a virtually plasma-free filamentation in gases [46].

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Figure 1.2: White-light generation from multiple filaments, reflected by a white screen placed on the beam path. Emission from single filaments is visible outside the blurred region: note the central spot surrounded by conical emission rings.

referred to as supercontinuum or white-light generation. Owing to this striking phenomenon, the filaments behave like a broadband coherent light source, thus being an attractive tool for remote spectroscopy of air substances [7] and multi- parameter characterization of cloud properties [52]. The underlying physics of the supercontinuum generation is illustrated in the next section.

1.1.2 The filamentation regime: underlying physics

In this section, the universal physical processes that underlie the most relevant features of the filamentation regime are discussed in detail, i.e. the self-focusing, the de-focusing by free-electrons plasma and the self-phase modulation. All these phenomena are governed by the third-order nonlinearity of the macroscopic polarization induced by the propagating electric field.

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Optical Kerr-effect

In linear optics, when light propagates through an isotropic polarizable medium, the instantaneous macroscopic polarizationPis directly proportional to the electric field:

P=ε0χ⁽¹⁾E (1.1)

whereχ⁽¹⁾is the first order susceptibility. The resulting linear refractive index of the medium is:

n₀= q

1+χ⁽¹⁾ (1.2)

In presence of high optical fields, Eq.(1.1) does not hold anymore; indeed, the displacement of bound electrons in the atoms of the medium becomes so large that the resulting dipole moment, hence the macroscopic polarization, cannot be considered a linear function of the applied field. This is the optical Kerr effect, and mathematically corresponds to the series development of Eq.(1.1):

P=ε₀(χ⁽¹⁾E+χ⁽²⁾EE+χ⁽³⁾EEE+...) (1.3) All the even orders susceptibilities χ⁽²ⁿ⁾ vanish in centrosymmetric materials, such as gaseous media, thus Eq.(1.3) can be rewritten as follows:

P=ε₀(χ⁽¹⁾E+χ⁽³⁾EEE) (1.4) where the series has been truncated to the third order. The refractive index thus reads:

n= q

1+χ⁽¹⁾+χ⁽³⁾EE 'n₀+n₂I (1.5) where the productEE is identified withI=|E|². Therefore, the effect of a strong optical field is to locally modulate the refractive index by superimposing, to the constant linear termn₀, an intensity-dependent termn₂I, whose weight is determined by thenonlinear refractive index:

n₂= 3χ⁽³⁾

4ε₀cn₀ (1.6)

For a 100 fs pulse centered at 800 nm, the air exhibits a nonlinear indexn₂=3.6× 10⁻¹⁹cm²/W. If one first neglects higher orders of the instantaneous polarization, the intensity-dependent refractive index change induced by the field is:

∆n'n₂I (1.7)

∆n has a positive sign, as χ⁽³⁾ is generally positive in usual media. It follows that the light experiences a reduction of its phase velocity due to the self-induced

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modulation of the refractive index, increasing with the intensity.

Considering a typical transverse Gaussian intensity profile for a laser beam, ∆n will also feature a bell-shaped intensity profile, reaching its maximum at the center of the beam and rapidly decaying towards the edges. Therefore, the resulting wavefront will be curved analogously to the propagation through a focusing lens, and the beam will progressively shrink. This effect is often referred to as Kerr- lens. It is responsible for the self-focusing of intense light beams and is essential to the filamentation regime.

The third order term of the polarization is obviously always present, but, at low intensities, the linear regime the diffraction, leading to a transverse spread of the beam during its propagation, is the dominating effect. Conversely, as the intensity increases, self-focusing efficiently counteracts diffraction and, finally, overcomes it. The balance between these two opposite effects is used to define the critical powerfor self-focusing:

P_cr = 3.72λ₀²

8πn₀n₂ (1.8)

which defines the unstable equilibrium point that separate the linear diffractive regime from the catastrophic collapse of the beam. At 800 nm, a laser beam undergoes self-focusing in the air if its input power exceeds the threshold of ∼ 4 GW.

Marburger [53] proposed a semi-empirical formula for the distancez_cat which an initially collimated gaussian beam of waistw₀and wavenumberk₀=2π/λ₀will collapse if its power is larger thanP_cr:

z_c= 0.184w²₀k₀

p((P/P_cr)^1/2−0.853)²−0.0219 (1.9) This expression provides a good estimation of the onset of filamentation for a Gaussian beam in the single filament regime, although it breaks down when the input power is so higher than the critical threshold that the beam undergoes multiple filamentation.

In order to achieve the self-guided propagation of a collimated beam, which defines the filamentation regime, a dynamical balance between a focusing and a defocusing effect must be established, in order to prevent the collapse of the beam at the nonlinear focus.

Multi-photon ionization and plasma defocusing

Due to the availability of high-power lasers emitting in this spectral region, the filamentation regime is generally investigated in the near-infrared, at 800 nm. At this wavelength, the ionization potential of major air constituents (oxygen and

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Figure 1.3: Schematic of Kerr self-focusing (a) and Plasma defocusing (b).

Adapted from [1].

nitrogen) largely exceeds the energy borne by a single photon. Indeed, the simultaneous absorption of 8 photons is required for the ionization of oxygen, which features the lowest ionization barrier. This process is highly improbable at low intensities, that is, before self-focusing, thus the beam propagates lossless conveying the whole beam power towards the onset of filamentation.

However, when the beam collapse approaches, the optical intensity enormously increases and so does the probability associated to the multi-photon absorption, which scales as∼I^K withK =8 for air (oxygen) at 800 nm. At the optical intensities typically featured by the filament core, i.e. 50 TW/cm², Multi-photon ionization (MPI) dominates over the tunnel ionization, which becomes relevant above 10¹⁴ W/cm², according to the Keldysh theory [54].

As a consequence of the MPI, the bound electrons are extracted from their orbitals and a plasma channel is generated, with a typical density of 10¹⁵−10¹⁷cm⁻³. The contribution of the plasma electrons to the refractive index is negative, according to the law:

∆n_plasma= ρ

2ρ_c (1.10)

whereρis the generated plasma density andρ_c=ε₀m_eω₀²/e²is the critical plasma density above which the plasma becomes opaque (me andeare the electron mass and charge,ω₀the pulse frequency, andρ_c∼1.7×10²¹ cm⁻³at 800 nm).

Therefore, the negative index variation induced by the free electrons provides a mechanisms which counteracts the third-order Kerr-focusing, as it is depicted in Fig. 1.3. Indeed, the refractive index spatial profiles induces an opposite curva- ture of the wavefront, resulting in a negative lens that defocuses the beam. Clas- sically, filamentation is said to stem from the dynamical balance between these

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Figure 1.4: Variation of the nonlinear refractive index of the major air constituents at room temperature and 1 atm, induced by a laser pulse, as a function of the optical intensity. Reprint from [2].

two effects: Kerr-focusing and plasma-defocusing. This interplay leads to several beam refocusing cycles that maintains the filament size approximately constant over several Rayleigh distances; the filament has a diameter of 100−200µm and keeps an almost fixed energy (few mJ) and intensity (50 TW/cm² [45]), a phenomenon known asintensity clamping.

The plasma channel is widely used as a diagnostic tool to measure the length and the strength of a filament, through the detection of the charge release [9], the acoustic shock-wave [48], or the backscattered nitrogen fluorescence [47].

Kerr-Driven Laser Filamentation

The classical picture of filamentation attributed to the plasma-induced negative index change the role of de-focusing mechanism, as it has been discussed in the previous paragraph. However, recent measurements of high-order nonlinear refractive indexes of common air constituents [2] suggested that they may themselves yield a defocusing contribution. This topic is nowadays still deeply de- bated [55, 56].

By measuring the transient birefringence of the main air components induced by an intense optical field, Loriot et al. [2] were able to identify the additional contribution to the molecular alignment yielded by the Kerr effect, and thus retrieve the nonlinear refractive index denoted by n_Kerr. Their results, displayed in Fig. 1.4,

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Figure 1.5: Schematic of purely Kerr-driven filamentation. As the beam shrinks, due to Kerr focusing, higher orders nonlinear terms become also important, leading to a dynamical balance between the contributions from positive (n₂, n₆, ...) and negative(n4, n₈, ...) Kerr terms. Dashed lines indicate the beam collapse in the absence of any defocusing mechanism.

evidenced that for N₂ and O₂n_Kerr first linearly increases, then saturates, and finally drops dramatically with the intensity, reversing its sign. This trend cannot obviously be described by Eq.(1.5), thus revealing that higher orders of the instantaneous polarization of Eq.(1.3), up to the ninth, must be included. A polynomial fit of the detected intensity-dependence allowed to infer the values of nonlinear refractive coefficients up to n₈, showing a sign alternation between consecutive terms. Obviously, a positive non-linear coefficient yields a focusing contribution, as already discussed forn₂-driven Kerr self-focusing, while negative coefficients yield the opposite contribution.

In a theoretical work conducted at GAP Biophotonics, Bejot et al. [55] imple- mented the High-Order Kerr terms (HOKE)n₄,n₆,n₈in the Non-Linear Schrödinger Equation (NLSE) for the propagation of ultrashort pulses. Based also on pump- probe experimental measurements, they concluded that the HOKE negative terms yield a considerable de-focusing effect that balances the tendency of the beam to collapse; therefore, for sub-ps pulses, the plasma appears to have a minor role in driving the filamentation [46]. The mechanism of purely Kerr-driven filamentation [46] is schematically depicted in Fig. 1.5.

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Figure 1.6: Frequency shift of the edges of an optical waveform, induced by self- phase modulation, according to Eq.(1.12). Dashed lines represent the Gaussian envelope.

Self-phase modulation

As depicted above, the Kerr nonlinear index, modulated by the spatial intensity gradient of the pulse, leads to self-focusing of the laser beam. Analogously, a temporal effect is induced by the Kerr nonlinear term, owing to the fact that the pulse intensity profile also varies in time. Like in the spatial coordinates, the typical temporal profile of a laser pulse features a Gaussian-like intensity envelope.

Therefore, the central slice will ’see’ a higher refractive index and will be delayed with respect to its wings. This results in a spectral broadening of the pulse. This phenomenon is calledself-phase modulation, and was discovered already in the early days of nonlinear optics [57]. It owes this definition by the fact that the intensity dependent nonlinear refractive index modulates the phase of the waveform according to:

φ(z,t) =φ0+ω c

Z _z

0

∆n_nldz (1.11)

where φ₀ is the initial phase of the electric field, ω is the carrier frequency and

∆n_nl =n₂Iis the nonlinear refractive index change, which depends upon the optical intensityI. Thus, the phase variation experienced by the pulse over a lengthz is∆φ =n₂ωIz/c, and the instantaneous frequency is modulated accordingly:

∆ω(t) =−∂ φ(t)

dt =−n₂ω∂I

∂t z

c (1.12)

Eq.(1.12) describes the self-phase modulation induced by the Kerr nonlinearity;

it depends upon the time derivative of the intensity profile in such a way that the rising edge of the electromagnetic wave generates redder frequencies, while the

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Figure 1.7: Spectrum of the continuum generated by TW filaments in the air. Ab- sorption bands of typical atmospheric constituents are indicated. Reprint from [3].

trailing edge adds up bluer frequencies to the initial spectrum. The resulting optical waveform is displayed in Fig. 1.6. SPM therefore yields a broadening of the initial spectrum of the laser pulse, a phenomenon commonly known as White- light generation (WL) or supercontinuum generation, as discussed in Sec. 1.1.1.

This emitted light preserves the coherence of the driving electromagnetic field;

therefore, different spectral components of the continuum emission maintain a constant phase relationship between each other. More strikingly, the coherence persists also between the WL resulting by two separated filaments of the same beam.

Fig. 1.7 displays the typical WL spectrum emitted by filaments generated by a TW laser beam propagating in the air. The continuum spans from 230 nm to more than 4µm, covering the absorption bands of many typical atmospheric trace gases such as VOCs (Volatile Organic Compounds), NOx, CO₂, H₂O, etc.

1.1.3 Multiple filamentation

It has been stated in Sec. 1.1.2 that the self-focusing of laser pulses prevails over diffraction above a critical optical power, which defines the threshold for filamentation. As a consequence, in air at 800 nm, a single filament is formed as soon as

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the input power exceeds approximately 4 GW.

However, since the early discovery of self-focusing [49], multiple hot-spots at the nonlinear focus were routinely observed, although this transverse spatial break-up into several focal spots may appear counter-intuitive. Indeed, a simple Gaussian radial profile is expected to originate a single focal spot.

In 1973, Campillo et al. [58] demonstrated that such distribution of hot-spots evolved from zones of well-defined dimensions, each conveying a certain number of critical powers and generating one focal spot. While in Campillo’s experiment a circular aperture induced a periodic hot-spots pattern, the complex beam break-up observed in high-power laser beams result from modulation instability of the spatial beam profile seeded by local inhomogeneities that may stem from imperfect amplification, dust, refractive index non-uniformity, etc. The self-focusing cells predicted by Campillo bear a fixed amount of power, depending on their shape;

for square cell this amount is minimum, and was estimated to 6.7 P_cr, where P_cr is the critical power for self-focusing.

Therefore, a beam energy increase corresponding to 6.7 critical powers will not increase the energy conveyed by the single filament, but will rather add one more hot spot to the transverse profile, yielding a linear dependence between the number of such hot spots and the beam power.

From this random distribution of self-focused spots, a multi-filamentary patterns originates, due to the dynamical balance with de-focusing effects (cf Sec. 1.1.2).

Fig. 1.8 displays a typical spatial pattern resulting from the free propagation in air of a TW-class lasers. The filament arrangement is intrinsically unstable, and thus virtually impossible to be reproduced on a shot-to-shot basis. This scenario is referred to as multiple filamentation, and has been well characterized close to the filamentation threshold [5, 59, 60], for TW-class lasers [61] as well as in the case of multi-TW, multi-Joule experiments [62]. These experimental observations reported a slightly different scaling of the filament number with power, corresponding to∼5Pcr per filament, which is now agreed to be the ’classical’ rate. It will be shown in Sec. 5.2 that increasing the input power to the 100 TW-level results in the saturation of the filament density [25], due to the competition between neighbouring filaments that strictly require a minimum surface for their respective self-focusing cells.

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Figure 1.8: Hot-spots distribution detected on a photo-sensitive paper after∼10 m of propagation in air of a 2 TW laser pulse.

1.2 Long-distance propagation of high-power fila- ments in the air

The filamentation regime issued from the propagation of high-power ultrashort laser pulses in the air is very attractive for atmospheric applications, since it allows to convey high optical intensities at long distances. Furthermore, a precise control of the onset of the filaments can be achieved through quite simple strategies that will be discussed throughout this section. It is thus possible to generate a filament at the desired location, even at distances from the laser source in the order of hundreds of meters, or kilometers.

During such long-range propagation, air turbulence must be considered as a potential source of increased losses and beam instability. It will be shown, in the last paragraph of this section, that filamentation exhibits remarkable robustness against typical atmospheric perturbations of the refractive index. For the propagation losses due to scattering from aerosols and interaction with cloud droplets, the reader should refer to Sec 1.3.

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1.2 Long-distance propagation of high-power filaments in the air

1.2.1 Controlling the onset of filamentation

Beam expansion and focusing

It can be inferred from Eq.(1.9) that increasing the beam size (w₀) pushes the nonlinear focus, and thus the onset of filamentation, further away from the laser source. Indeed, expanding the beam before sending it into the atmosphere was one of the strategies employed during the field campaigns described in this work.

Typically, the beam was expanded to∼10 cm of diameter.

However, adapting the beam size to any desired location for the nonlinear focus is not possible, as it would entail re-scaling and realigning the concerned optical elements. For instance, to generate filaments at a distance of∼1 km and∼100 m from the laser source, the beam should have a diameter of, respectively,∼25 cm and∼8 cm.

The Teramobile laser, which was used throughout all the field campaigns presented in this work, made use of a more flexible approach, consisting of a sending telescope as the final stage before launching the beam outdoor. This optical setup allowed both for expanding the beam and for focusing it, by adjusting the distance between the two mirrors of the telescope.

When an additional focusing is applied to the beam, besides the self-induced Kerr effect, the collapse distance of a Gaussian beam is modified according to this simple formula derived by Marburger [53]:

1 z_c^f

= 1 z_c+1

f (1.13)

where z_c^f is the new self-focusing distance and f is the focal length of the additional optics. Fibich et al. [63] showed that longer filaments are generated if filamentation is delayed by making slightly diverging the beam.

By modifying the beam initial focusing, filaments can be moved upstream or downstream with respect to the spontaneous self-focus. The configuration with a sending telescope offers a much broader range of spanned locations, that can be selected by means of a trivial adjustment of the optical setup.

Pre-chirping

Besides modifying the beam size and the focus geometry, filamentation can be controlled also acting on the pulse duration of the optical waveform. Owing to the frequency dispersion of the linear refractive index, the spectral components of a broadband pulse travel at different speeds; more precisely, in the air the red component propagates faster than the blue one. This is known asGroup-velocity dispersion (GVD) and leads to the temporal broadening of an initially Fourier- limited Gaussian pulse.

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Figure 1.9: Pulse temporal broadening as a function of the propagation distance.

The ratio between the actual pulse duration and the initial one is plotted vs the number of dispersion lengths. The chirp parameterCcan be either zero (unchirped beam), positive or negative. For a negative chirp, the pulse duration reaches a minimum at a pre-determined position. Reprint from [4].

Figure 1.10: Principle of GVD pre-compensation. Left: an initially Fourier- Limited pulse is broadened by GVD in the air, which induces a positive chirp.

Right: an initially negatively-chirped pulse is shortened by GVD in the air, recov- ering its minimal pulse duration. Reprint from [3].

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1.2 Long-distance propagation of high-power filaments in the air

By pre-imposing a negative linear chirp to the pulse, i.e. delaying the red part of the spectrum with respect to the blue one, the dispersive propagation in the air will shorten progressively the pulse, which will recover its nominal Fourier- limited pulse duration at the selected location. Conversely, a positively chirped pulse would indefinitely broaden. This is displayed in Fig. 1.9. The increasing intensity accompanying the pulse temporal compression will initiate the non-linear effects leading to the onset of filamentation.

Thanks to the architecture of the Chirped-Pulse Amplified lasers, pre-chirping the pulse is straightforward. Decreasing the distance between the diffraction grat- ings of the compressor is equivalent to propagate the pulse through a dispersive medium which exhibits an opposite dispersion with respect to the air; the pulse broadening due to GVD in the air can thus be easily pre-compensated (see Fig. 1.10).

1.2.2 Turbulence

One of the key advantages of filaments in the context of atmospheric applications is their pronounced resistance to adverse conditions, particularly to air turbulence, that induces refracting index gradients.

Atmospheric turbulence is usually modelled by the Kolmogorov theory [64], which defines the refractive index structure parameter C_n² to quantify the turbulence strength. Typical values for the atmospheric turbulence span from 10⁻¹⁵ to 10⁻¹³ m^−2/3 [64]. In their review on the physics of atmospheric filamentation, Kas- parian and Wolf [3] report about several experimental works showing that "..filaments can propagate through localized, strongly turbulent regions, up to five orders of magnitude above typical atmospheric conditions". Filaments that survived the turbulence show similar spectra to those which propagated through an unper- turbed atmosphere, and preserve the shot-to-shot correlations between their spectra. They are thus almost unaffected by the perturbation they have encountered.

The survival of such filaments is governed by the quantityC²_n×L, L being the length of the turbulence region; Fig. 1.11 shows the transition between a weak turbulence regime where most of the filaments resist, and a strong turbulence regime where most of them are destroyed.

Upscaling the transition threshold of the C_n²×L factor would provide a rough estimation of the maximum length of the turbulence region allowing filaments to be preserved, which is found to be∼4 km. Although questionable, this extrapo- lation suggests that refractive index gradients are not the limiting factors for the atmospheric propagation of filaments.

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Figure 1.11: Percentage of filaments that resist to air turbulence, as a function of the parameterC²_n×L. Squares refer to localized turbulences, while triangles refer to extended turbulences. The solid line is intended to guide the eye. Reprint from [5].

1.3 Interaction between laser light and atmospheric particles

The interaction of a beam of light with atmospheric constituents, including suspended particulate, is a key aspect in the context of laser-based atmospheric applications. Laser beams, indeed, are potentially expected to propagate over long distances before reaching the air portion where filamentation is desired to occur.

It comes without saying that potential propagation losses between the source and the active filamentation zone are a serious issue that may dramatically reduce the competitiveness of laser-based techniques.

The transmission of light through a gaseous medium is characterized by two main phenomena: absorption and scattering. When light impinges on particles³, the electromagnetic energy conveyed by photons induces oscillatory dipoles in the particle itself; the excited internal charges may subsequently convert part of the

3Here, the termparticleis intended in its broadest meaning, and thus includes molecules as well as aerosols and cloud droplets. A distinction based on the size range of such particles will be introduced later in the text.

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1.3 Interaction between laser light and atmospheric particles

excitation energy into heat, thus absorbing the incident light, or alternatively re- irradiate energy, i.e. scattering the incident light. These two phenomena can strongly influence the ability of ultrashort laser pulses to generate filaments at a remote location.

Besides being a source of losses, light scattering is also a powerful tool for optical detection of aerosols and remote sensing, owing to its intrinsic size-dependent nature. The backward scattering from suspended aerosols, for instance, is the fundamental of the LIDAR technique that we adopted in the first field campaign on laser-induced water condensation [17]. Else, the most compact and best performer detection devices for aerosol counting and sizing rely on the scattering properties of the aerosols themselves.

The main aspects of laser-particle interaction are therefore briefly illustrated in this section. For a comprehensive view on the absorption and scattering theory, the reader may refer to Seinfeld and Pandis [6] and Bohren and Huffmann [8].

1.3.1 Absorption and scattering by atmospheric particles

Atmospheric absorption

Typical air molecules, such as ozone, oxygen, carbon dioxide and water vapor, as well as some substances contained in the aerosols, do absorb light. One of the most obvious example of absorption by the atmosphere is the efficient filtering of the UV solar shortwave radiation by ozone and oxygen. The earth’s atmosphere, indeed, is opaque to wavelength shorter than 290 nm. Moreover, it features several broad absorption regions above 1 µm, mainly due to water vapor and CO₂. Conversely, the visible and near-IR portion of the electromagnetic spectrum co- incides with a net transmittance window. Fig. 1.12a displays the atmospheric absorption spectrum from the near UV to the mid-IR, evidencing an almost-total transmission between ∼300 nm and ∼700 nm, above which some absorption lines appear; as the wavelength exceeds 1µm, absorption by H₂O and CO₂dominates. The spectrum of the filamenting laser beam used in the experiments that will be presented in this work is typically centered aroundλ0=800 nm and ex- tends over ∼30 nm FWHM. In the vicinity of λ₀, approximately at ∼815 nm, only few absorption lines may perturb the propagation of the red wing of the laser spectrum (Fig. 1.12b). Therefore, our laser beam is almost unaffected by absorption losses during its propagation in air.

It is important to note, however, that this scenario holds as far as low optical intensities are concerned, like in the case of solar radiation or weak probe laser beams for optical detection. The reported spectra, indeed, refer to thelinearabsorption, that involves single-photon excited molecular transitions. Even a TW laser beam, such as the Teramobile used in our experiments, if expressly expanded before be-

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Figure 1.12: Absorption of the atmosphere: (a) in the visible and near- to mid- IR (Reprint from [6]), (b) around the central wavelength of the Teramobile laser, measured by White-light LIDAR (Reprint from [7]).

ing launched in the atmosphere, conveys low power densities.

The situation dramatically changes when extremely high intensities are at play, such as when the same TW beam undergoes filamentation, where nonlinear multi- photon processes excite multi-photon transitions. Therefore, as long as the filamentation is most active, the beam experiences absorption losses in the air. For instance, water droplets may explode due to strong multi-photon ionization and absorption, a situation discussed in Sec. 1.3.2.

Scattering theory

Here the propagation of high power laser beams from the source towards the nonlinear focus is considered; along this path, as discussed above, the air is almost

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transparent to light of the wavelength used in our experiments. This is important in the context of the theoretical framework of light absorption and scattering, which relies on the fundamental assumption that the scatterer, or absorber, body is embedded in a non-absorbing medium. Considering our laser source before filamentation is established, in terms of optical density and wavelength, the air fulfills this requirement.

Suppose that a particle in a non-absorbing medium is placed in the path of an electromagnetic radiation. The absorbed and scattered optical power,W_absorW_sc, respectively, are proportional to the incoming power density. One can thus write:

W_abs=σ_absI_in W_sc=σ_scI_in (1.14) whereσ_abs andσsc are theabsorptionandscattering cross sections, respectively, and have the unity of an area. The combined effect of absorption and scattering is referred to asextinction, and its corresponding cross section is defined as:

σext =σ_abs+σsc (1.15)

Denoting byAthe cross-sectional area of the particle, the dimensionlessscatter- ing andabsorption efficiency can be defined as Q_abs,sc =σ_abs,sc/A, yielding the extinction efficiency:

Q_ext =Q_abs+Q_sc (1.16)

Although there exist inelastic or quasi-elastic scattering phenomena that don’t conserve the photon energy, i.e. the scattered light features a different wavelength with respect to the incident one, the focus here is on the elastic scattering from spherical particles. The key parameters that govern this light-particle interaction regime are the wavelength λ, the complex refractive index n=η+iκ, and the size of the particleD_p, often expressed as a dimensionless parameter:

α =πD_p

λ (1.17)

The absorption and elastic scattering from a spherical particle is a classical problem in physics, which has been analytically solved in the theoretical framework that is commonly referred to asMie theory[8].

According to the size of the scatterer body, three distinct regimes for light scattering can be identified:

• D_p λ Rayleigh regime: particle small compared with the wavelength

• D_p'λ Mie regime: particle size comparable to the wavelength

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• D_pλ Diffraction regime: particle large compared with the wavelength

These different scattering regimes will be briefly described in the following para- graphs. For the specific cases of Rayleigh and Diffraction domains, it is possible to derive approximate forms of the equations of Mie theory.

Mie regime

The largest mode of atmospheric aerosols consists of particles the lie in the same size range as the wavelength of the laser pulses used in our investigations, i.e.

800 nm. In this size range, solving the problem of light scattering from arbitrary shaped particles becomes a very complicated task. However, for the particular case of spherical particles, Mie theory allows to explicitly calculate the scattering and extinction efficiencies. It can be shown that they read as follows [8]:

Q_sc(m,α) = 2 α²

∞

∑

k=1

(2k+1)

|a_k|²+|b_k|²

(1.18) Q_ext(m,α) = 2

α²

∞

∑

k=1

(2k+1)ℜ[a_k+b_k] (1.19) where

a_k=α ψ_k⁰(mα)ψ_k(α)−mα ψ_k⁰(α)ψ_k(mα) α ψ_k⁰(mα)ζ_k(α)−mα ζ_k⁰(α)ψ_k(mα) b_k=mα ψ_k⁰(mα)ψ_k(α)−α ψ_k⁰(α)ψ_k(mα)

mα ψ_k⁰(mα)ζ_k(α)−α ζ_k⁰(α)ψ_k(mα) with y= _nⁿ

0α, n₀ being the refractive index of the environment. The functions ψ_k(z)andζ_k(z)are the Riccati-Bessel functions.

Eq. (1.18) and (1.19) are the main formula of the Mie theory. There are several re- liable published codes that can be used to compute coefficients of these equations and the scattered electromagnetic field, such as the BHMIE code for homoge- neous spherical scatterers by Bohren and Huffmann [8].

Rayleigh scattering

The Rayleigh scattering regime applies in presence of particles that are much smaller than the incident wavelength. With respect to the central wavelength of our laser beam, any particle with diameter lower than ∼80 nm can be roughly

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Figure 1.13: Angular pattern of the light scattered from a spherical particle small compared with the wavelength. Light with different polarizations, with respect to the scattering plane, impinges on the particle from the left. Reprint from [8].

considered small enough. Therefore, ultrafine aerosols and air molecules lie in the Rayleigh scattering domain.

The patterns of scattered light is approximately independent on the molecule or aerosol shape, and can therefore be connected to the Mie scattering in the limit of very small spherical particles. It features a symmetry in the forward and backward direction, as displayed in Fig. 1.13.

It is possible to express the scattering efficiency as follows:

Q_sc= 1

λ⁴·8(πD_p)⁴ 3

m²−1 m²+2

2

(1.20) According to Eq.(1.20), molecules and small aerosols scatter light with an efficiency scaling as Q_sc ∼λ⁻⁴, resulting in a more prominent effect on shorter wavelengths than for longer ones. Similarly, also absorption is weaker when ap-

Laser filament-induced aerosol generation in the atmosphere

Thesis

Reference

Laser filament-induced aerosol generation in the atmosphere

Laser Filament-induced Aerosol Generation

in the Atmosphere

THÈSE

Stefano HENIN

Acknowledgements

Contents

Summary

Résumé

Introduction

Chapter 1

Laser filamentation in the atmosphere

1.1 Self-guided propagation of ultrashort pulses in gaseous media

1.1.1 The filamentation regime: general aspects

1.1.2 The filamentation regime: underlying physics

1.1.3 Multiple filamentation

1.2 Long-distance propagation of high-power fila- ments in the air

1.2.1 Controlling the onset of filamentation

1.2.2 Turbulence

1.3 Interaction between laser light and atmospheric particles

1.3.1 Absorption and scattering by atmospheric particles

∑

∑