Application of femtosecond filamentation in gaseous media

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Application of femtosecond filamentation in gaseous

media

Thèse

Sima Hosseini

Doctorat en physique

Philosophiæ doctor (Ph. D.)

Québec, Canada

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Résumé

Cette thèse décrit plusieurs résultats expérimentaux impliquant le phénomène de la la-mentation laser qui se produit lorsque des impulsions laser ultrabrèves se progagent dans l'air avec une intensité de l'ordre de ∼ 1013 _W/cm2_{. Un laser titane-saphir est utilisé pour} gé-nérer des impulsions femtosecondes dans l'infrarouge (800 nm). En raison de ses propriétés particulières, cette forme de propagation est étudiée pour de nombreuses applications. Nous nous concentrons dans cette thèse sur la télédétection et l'identication de polluants atmo-sphériques. Notre objectif est d'améliorer les résultats et de résoudre certains problèmes dans la détection de polluants, en particulier de ceux qui ont le même spectre de uorescence induit par lamentation. Tous les résultats présentés ici ont été obtenus en laboratoire.

La télédétection de polluants dans l'atmosphère implique la propagation de laments à haute altitude où la pression atmosphérique est basse. Il est donc important de bien com-prendre le phénomène de la lamentation dans ces conditions. Nous avons expérimentalement et numériquement étudié l'eet d'une basse pression sur un lament unique dans l'air. Les expériences furent réalisées en variant la pression à l'intérieur d'une cellule entre 0,3 et 1 fois la pression atmosphérique normale (1 atm ≈ 1.01 × 105 _Pa).

Une approche pour détecter à distance la présence de polluants atmosphériques est de capter la uorescence émise par les fragments moléculaires créés lors du passage de l'impulsion laser. Ce signal est toutefois lourdement atténué avant d'atteindre le détecteur en raison de la grande distance de propagation dans ces applications et il est important de trouver des moyens pour augmenter le signal de uorescence. Nous avons donc étudié la possibilité d'utiliser le lament lui-même comme milieu de gain dans la direction de propagation pour amplier les émissions des impuretés de l'air. Il avait déjà été démontré qu'un lament peut amplier le signal rétrodiusé dans l'air pur alors nous avons débuté nos expériences dans l'air pour ensuite étudier des mélanges air-hydrocarbones ( 2% de CH4, C2H2 et C2H4 dans l'air). Nous avons détecté la uorescence émise par l'azote neutre à ∼ 337 nm dans l'air pur et par les fragments CH à ∼ 431 nm dans des mélanges air-hydrocarbones. Dans les deux cas, le signal de uorescence émis dans la direction opposée à celle du laser a augmenté de manière non-linéaire en fonction de la longueur du lament, tandis que celui émis sur les côtés montrait une tendance linéaire.

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Le dernier chapitre de cette thèse traite d'une nouvelle approche pour identier les molé-cules basée sur leur alignement. Nous montrons en eet que des polluants dans l'air peuvent être détectés et identiés en mesurant les constantes de rotation de diférentes molécules. Il est important de noter que cette technique permet de distinguer des polluants dont les fragments émettent le même spectre de uorescence (les mêmes raies atomiques et bandes moléculaires). Les résultats présentés dans cette thèse ont été obtenus par des études de type pompe-sonde utilisant le signal diusé de l'impulsion de sonde, contrairement à d'autres expériences qui détectent la lumière transmise. Le fait d'observer le signal diusé plutôt que celui transmis rend cette technique pertinente pour des applications de télédétection. Même si les molécules dans un gaz sont orientées de façon aléatoire, une impulsion ultrabrève et intense peut forcer les molécules à s'aligner non seulement pendant le passage de l'impulsion mais aussi après. Plus spéciquement, un paquet d'onde rotationnel peut être créé par une impulsion femto-seconde, ce qui génère un alignement moléculaire en l'absence de champ après le passage de l'impulsion qui peut se reformer à intervalles réguliers. En plus de permettre la détermination des constantes de rotation et l'identication des molécules, cette technique donne également accès à des informations sur la dissipation dans le milieu en étudiant l'évolution du paquet d'onde sur une longue période (plusieurs retours périodiques de l'alignement moléculaire) après le passage de l'impulsion.

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Abstract

This thesis presents experimental results obtained during lamentation of ultrashort and intense laser pulses, with an intensity of ∼ 1013 _W/cm2 _{in air. A femtosecond Ti:Sapphire} laser was used to generate pulses in the infrared at 800 nm. Because of some unique features of the laments, this particular form of propagation has been considered for many applications. In this work, we focus our attention on remote sensing and the detection and identication of atmospheric pollutants. The goal is to improve the results and resolve some problems in the detection of air pollutants, especially those with the same lament-induced uorescence spectrum. The presented experiments were performed inside a laboratory.

The remote sensing of pollutants in the atmosphere mainly relies on the propagation of laments at high altitude where the pressure is low. For this application, it is therefore important to have a good understanding of lamentation in these real conditions. We exper-imentally and numerically studied the eect of lowering the pressure on a single lament in air. The experiment was done by varying air pressure inside a cell between 0.3 and 1 standard atmospheric pressure (1 atm ≈ 1.01 × 105 _Pa).

One way to remotely detect atmospheric pollutants is to record the returning uorescence signal from the molecular fragments that are created during lamentation. Because the prop-agation distance is large in these spectroscopic experiments, the signal is heavily attenuated before reaching the detector and it is important to look for a solution to enhance the uo-rescence signal. We therefore investigated the possibility of using the lament itself as a gain medium along the propagation direction to amplify the emission of some impurities in air. It is known that the femtosecond laser lament can amplify backward-directed signal in pure air, so we started our experiments in air, and then extended them to airhydrocarbons mix-tures ( 2% of CH4, C2H2 and C2H4 in air). The uorescence emission from neutral nitrogen at∼ 337 nm in pure air and from CH fragments at ∼ 431 nm in air-hydrocarbons mixtures was detected. In both cases, the uorescence signal emitted in the direction opposed to the laser propagation increased nonlinearly with the lament length, unlike the emission directed on the sides which showed a linear trend.

The last chapter of the thesis introduces a new way to identify molecules that relies on their alignment. Indeed by measuring the rotational constants of dierent molecules using

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eld-free molecular alignment, we show that pollutants can be detected and identied in air. It is important to mention that this approach can distinguish pollutants for which the excited fragments have the same uorescence spectra (same atomic lines and molecular bands). The results reported in this thesis were obtained by a pump-probe experiment where the scattered signal of the probe pulse was detected, as opposed to other experiments which collected the transmitted light. Observing the scattered signal instead of the transmitted one makes this technique appropriate for remote sensing applications. Even though molecules are randomly oriented in the gas phase, it is shown that ultrafast intense laser pulses can force molecules to align both in the presence of the laser eld as well as after the passage of the pulse. More specically, a rotational wavepacket can be created by an ultrashort laser pulse, leading to a eld-free alignment of the molecules after the laser pulse has passed which can revive at regular intervals. Therefore, in addition to nding rotational constants and identifying molecules, it is possible to extract information about the dissipative medium by studying the changes in the wavepacket a long time (several periodic revivals of molecular alignment) after the passage of the pulse.

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List of Figures

0.1 Principle of lamentation, (a) Self-focusing of the laser beam due to Kerr ef-fect. The refractive index of the medium is intensity dependent and acts as a converging lens. I is the incident intensity. (b) Defocusing of the beam due to ionization of the medium and plasma generation at the nonlinear focus, ωp is

the plasma frequency and ω is the laser angular frequency. . . 4

0.2 A typical picture of a lament in air. Filament establishes itself through a

balance of Kerr self-focusing an defocusing process caused by produced plasma 6

0.3 (a) Spontaneous emission of a photon with energy hν. (b) Stimulated emission

of a photon with energy hν. . . 9

0.4 Sketch of an anisotropic particle in an electric eld E. . . 11

1.1 Principle of the chirped pulse amplication (CPA) technique. The pulse from

the oscillator will be stretched, amplied and compressed (schematic drawing). 19

1.2 The schematic description of 1-kHz laser system using CPA technique. The abbreviations used in this gure are as follows: PC: Pockels cell, P: polarizer,

Ti:sa: Ti:sapphire crystal, λ/2: half-wave plate, λ/4: quarter-wave plate.. . . . 21

1.3 Schematic diagram of the 10 Hz, two-pass amplier. . . 22

1.4 Schematic representation of the experiment used to measure the diameter and length of the lament at dierent pressures. The uorescence coming from

lament is imaged by a A CCD camera equipped with a imaging system . . . . 23

1.5 Beam pattern measured with a CCD camera just before the focusing lens. . . . 24

1.6 (a) Typical CCD image of the lament in air and (b) the integrated intensity prole of the lament along y direction. The input energy is 4 mJ and the air pressure inside the chamber is 0.71 × 105 _{Pa. The image was accumulated over}

40 laser shots.. . . 25

1.7 Filament generated in the wake of the ultrashort pulses for 4 pressures (0.41, 0.61, 0.81 and 1.01 × 105 Pa). The input energy for all pressures is constant as

4 mJ. Onset of lament changes for dierent pressures. . . 25

1.8 Length of plasma channel generated in air cell as a function of pressure with

the incident pulse energy of 4 mJ for all pressures. . . 26

1.9 Diameter of lament versus the pressure with an incident pulse energy of 4 mJ

for all pressures. . . 27

1.10 Diameter of lament versus the pressure at x ratio Pin/Pcr = 5(red circles)

and Pin/Pcr = 3(dark blue triangles) for all pressures. . . 28

1.11 Length of lament versus the pressure at xed ratio Pin/Pcr = 5(red circles)

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1.12 a) Simulated lament diameter for xed initial pulse energy and four dierent pressures: 0.30, 0.51, 0.81 and 1.01 ×105_{Pa. b) Full width half maximum beam}

diameter obtained from the simulated uence distribution at each propagation position z. Vertical lines show that the length of plasma channel decreases at

lower pressures. The initial pulse energy is the same for all pressures . . . 32

1.13 a) Simulated lament diameter at the xed ratio Pin/Pcr = 3 for dierent

pressures, 0.30, 0.51, 0.81 and 1.01 ×105_{Pa. b) Full width half maximum beam}

diameter obtained from the simulated uence distribution at each propagation position z. Vertical lines show that the length of plasma channel decreases at

lower pressures. The ratio Pin/Pcr = 3 is the same for all pressures . . . 33

2.1 Experimental setup used to record the image of the lament and the uorescence signal from the side. A telescope was used to increase the beam diameter. The laser pulses were focused inside the chamber with a 100 cm lens. The

uorescence signal was directed to the spectrometer by an imaging system. . . 37

2.2 Experimental setup for recording the emission signal in backward direction. The laser pulses were focused inside the chamber with a 100 cm lens. A telescope was used to increase the beam diameter. Imaging ber adaptor (IFA) connected the ber bundle to the spectrometer. The interference lter transmitted 431

nm (2.5 nm spectral bandwidth). . . 37

2.3 ICCD images of the air uorescence left behind the laser pulses for a) 2 mJ , b) 3 mJ and c) 4 mJ input energy. Each picture was accumulated for 15 laser

shots. . . 39

2.4 Typical uorescence spectrum obtained from laser lament in air. The C3_Π u−

B3Πg transition of neutral nitrogen molecule at ∼ 337 nm is shown. . . 39

2.5 Fluorescence signal of N2C3Πu− B3Πg transition at dierent time delays from

air in atmospheric pressure. Gate width for each gate delay time is xed to 2 ns. 40

2.6 The integrated emission signal from excited neutral N2versus length of lament

for a) back and b) side directions. . . 41

2.7 The uorescence emission spectrum from the laser-induced lament in ambient air (blue) and contaminated with 2% ethylene (red). The A2_{∆ − X}2_{Π(0, 0)}

transition of CH fragments can be seen at ∼431 nm. . . 42

2.8 The spectrum of the light emission from the laser-induced lament in 2% CH4

mixed with air (dark blue curve), the spectrum of the white light continuum in air (black curve), and the dierence spectrum (pink curve) obtained by sub-tracting the white light continuum from the emission spectrum. Integrated values of the CH band between 429 nm to 431 nm (pink curve) are used as the

backward signal. . . 43

2.9 Fluorescence signal distribution of laser laments for air-methene(CH4)

mix-ture. The input pulses energies are 2, 3, 4, and 5 mJ respectively for (a) to (d).

Each picture was accumulated for 25 laser shots. . . 44

2.10 The integrated emission signal of CH band emitted from air contaminated with 2% C2H2 (a and b, back and side respectively), 2% C2H4 (c and d, back and

side respectively) and 2% CH4 (e and f, back and side respectively) versus

length of lament . . . 45

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3.2 The spectrum of the scattering signal of the probe beam, before arrival of pump pulse to the chamber lled with O2 at 0.53 × 105P a. Spectrum was averaged

over 1500 shots . . . 53

3.3 The spectral-temporal map of the scattered probe pulse as a function of the delay time between the pump and probe pulses in O2 at 0.53 × 105 Pa. The

experiment was done over 1500 laser shots for each delay time. . . 54

3.4 Integrated scattering signal of the probe beam recorded in O2 at 0.53 × 105 Pa

versus delay time between pump and probe up to the sixth revival. . . 55

3.5 Integrated scattering signal of probe recorded in O2 at 0.53 × 105 Pa versus

delay time between pump and probe. First full revival time is depicted. . . 56

3.6 Integrated scattering signal of probe recorded in N2 at 1 atm versus delay time

between pump and probe. The measurements show the occurrence of rotational

alignment a) for eight full revival time b) rst rotational period.. . . 58

3.7 The averaged alignment hcos2_θi_{(black curve) and its components hcos}2_θi p(red

dashed curve and circles) and hcos2_θi

c (dotted curve, blue) versus time,

mea-sured in units of the rotational period. . . 59

3.8 Measured molecular alignment signals of air (black), oxygen (blue), nitrogen (red) 60

3.9 Filament induced uorescence spectra of C2H2(blue), C2H4 (red) and their

mixture (black)) . . . 61

3.10 Integrated scattering signal of the probe beam recorded in acetylene C2H2 at

0.4 × 105 Pa versus delay time between pump and probe up to the fth full

revival. . . 62

3.11 Integrated scattering signal of the probe beam recorded in ethylene, C2H4 at

0.6×105Pa versus delay time between pump and probe. J and C type transients

are indicated. . . 63

3.12 Field-free alignment of linear molecule C2H2 (blue), asymmetric top molecule

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to my spouse and best friend Ali to my beloved mother and to the loving memory of my late father

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Acknowledgments

I would like to express my sincere and deep gratitude to my advisor Prof. Simon Rainville for his professional guidance and constant support. Without his patience, encouragement, understanding and trust this thesis would not have been possible. For everything you have done for me, Prof. Simon Rainville, I am most grateful.

I would also extend my deep respect to my co-supervisor Prof. Bernd Witzel for his invaluable and constructive comments and discussions.

I would like to thank the other members of my thesis committee, Prof. Michel Piché, Prof. Tsuneyuki Ozaki and Prof. Claudine Allen for their advice, ideas, interest and valuable comments.

I would also wish to thank Dr. Olga Kosareva of Lomonosov Moscow State University in Russia for her important collaboration in one of the studies. In addition, I would also like to express my appreciation to Prof. T. Seideman of Northwestern University for her valuable discussions.

My sincere thanks also go to my senior Dr. J. F. Daigle for his constructive guidance, comments and suggestions. I also express my gratitude to Dr. Shigeki Owada of the University of Tokyo for his eective collaboration in one of the experiments.

I must also acknowledge Mr. Mario Martin for his technical support in the Lab. His kind assistance helped me a lot in performing the experiments. Thanks also go out to all the stas in the physics department and the Center for Optics, Photonics and laser.

A thank goes to Dr. S.L. Chin, the former leader of ultra-short intense laser laboratory at Laval University. While working with him I have learned that "being a good person does not depend on your status, race, colour, religion or culture. It depends on how you treat others." I feel a deep sense of gratitude for my beloved husband, best friend and my senior, Dr. Ali Azarm, who has been an endless source of love, support and encouragement during the challenges and frustrations in studies and life. Moreover his scientic assistance and discussions are always incredibly constructive. I am truly thankful for having you in my life.

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Not least of all, I owe so much to my mother, who formed part of my vision and taught me good things that really matter in life. Her undying love and support has always been my strength. Words can not express how grateful I am to her.

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Introduction

With the invention of the laser by T. H. Maiman in 1960 [1] the eld of optics soon entered the new era of nonlinear optics in 1961 by the discovery of second-harmonic generation [2]. By nonlinear optics we mean a regime in which induced polarization depends nonlinearly upon the electric eld of the input light. In other words, in this regime the response of a material system to an applied optical eld depends nonlinearly upon the strength of the optical eld. This nonlinearity is observed at very high light intensities. Typically such intense light can be produced by lasers, which is why the propagation of laser radiation can exhibit nonlinear features and give rise to lots of new phenomena, eects and applications, that are not normally observed in the propagation of light from conventional sources [3,4].

The development of laser technologies that increased the energy and peak power of laser pulses poses new challenges. Indeed, the propagation of ultrashort (femtosecond), high-intensity (as high as ∼ 1013_W/cm2_{) laser pulses in transparent media such as air, exhibits} nonlinear behavior and leads to lamentation [5, 6,7, 8,9]. In fact, lamentation denotes a part of propagation of ultrashort laser pulses where a low density plasma is left in the wake of the pulse in a dynamic structure while keeping a narrow beam size without the help of any external guiding mechanism. A more strict denition will be given in a later section.

When a high power laser pulse propagates through a transparent medium it undergoes change in its own temporal and spatial characteristics. This eect is known as nonlinear self action [3]. These phenomena such as self focusing [10], self phase modulation [11,12], etc. have been studied since the 1960's, however the investigations were started initially in condensed media. Then by generating powerful ultrashort, high intensity laser pulses via the chirped pulse amplication (CPA) technique [13, 14] introduced in 1985, those nonlinear processes could be observed even in slightly nonlinear media including the atmosphere. The nonlinear propagation of ultrashort ultra-intense laser pulses in such media then sets this eld of research as one of the new frontiers of nonlinear optics.

The advent of high-power, ultrashort lasers has opened avenues of novel applications in femtosecond laser science and lamentation, like for example lightning control [15, 16], THz generation [17,18], high harmonic generation [19], remote sensing of pollutants [20, 21,

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identication of pollutants in air, based on laser-techniques has been a subject of intense studies [23]. The adverse eects of air pollution on human health and environmental issues such as global warming, clearly show the necessity of such studies to monitor, identify and control atmospheric pollution.

Several laser-based methods such as Dierential Absorption Lidar 1 _{(DIAL) [}₂₄_{] and} nanosecond Laser-Induced Breakdown Spectroscopy (ns-LIBS), have been proposed to fulll the requested task [25,26]. Although these techniques have been applied to the analysis of a number of materials, there are some disadvantages. For example, in the dierential absorption Lidar technique two laser pulses at slightly dierent wavelengths are used to monitor trace gases, one where the target gas is known to absorb (λon) and one where it does not (λof f). The dierence measured in the decay between the two backscattered signals is used to monitor the concentration of the target species. The drawback of this technique is that it is limited to detect and measure one type of molecule at the time, because the wavelength of the laser source is tuned to a line that the species under investigation absorbs. Since laser sources are wavelength limited in this kind of measurements multiple or wide spectral range tunable laser sources are needed for probing air and detecting distinct molecules simultaneously. Moreover, to probe air, it is required to detect some unknown species and in the DIAL technique we can not choose the suitable wavelengths for them.

On the other hand, nanosecond laser-induced breakdown spectroscopy is a type of spec-troscopy that involves focusing an intense laser pulse laser on the sample to generate a plasma and then analyze the plasma spectrum. Although ns-LIBS has several attractive features in-cluding stando detection capability and simultaneous analysis of multiple components present in a target [27, 28], some challenges still remain. For example, the plasma formed with long duration (nanosecond) laser pulses is very highly ionized which results in continuum emission from plasma that appears in the spectrum. This continuum leads to a low signal-to-noise ratio. Another disadvantage of ns-LIBS processes is the diculty in tightly focusing the laser beam at long distance. Indeed, the diameter of focus linearly increases with focusing distance as a consequence of diraction [4]. Moreover, in linear propagation the laser intensity always decreases over long distances while propagating away from the source because of diraction.

However, recent advances in high-power femtosecond laser pulses and lamentation do contribute to the the evolution of atmospheric remote sensing. Unlike in DIAL it is possible to simultaneously detect multiple atmospheric components with a single laser wavelength. Indeed, the intensity inside the lament core is high enough for ionization and fragmentation of the components of the target and also to excite ions or molecular fragments into excited states through simultaneous absorption of multiple photons to emit uorescence. Moreover continuum emission from the femtosecond pulse-induced plasma is much weaker than that induced by nanosecond laser pulses which results in a good signal to noise ratio in the spectrum

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even without gated detectors [21, 29, 30]. Another advantage of femtosecond laser pulses is the capability of these pulses to deliver high intensities beyond the limitation of diraction on a target at long distance due to nonlinear behavior of short laser pulses during atmospheric propagation. Indeed, horizontal lamentation has been observed over distance larger than 2 kilometer [31] and over more than 20 km vertically in the atmosphere [32]. Consequently, from the application point of view, the propagation of high power ultrashort laser pulses provide a unique feature for performing atmospheric remote sensing [33,34,35,36]. Indeed, observation of uorescence signal from the molecules through lamentation in air is a useful technique in long distance propagation to identify various atmospheric species and contaminants. [21, 34,

37].

Even though the lament-induced uorescence spectroscopy technique is a powerful method to monitor atmosphere, there are still some challenging problems to be solved to improve the produced uorescence signal and achieve more reliable results. For instance, one problem is that some molecules like hydrocarbons dissociate into the same fragments through their in-teraction with a strong eld inside the lament. Then their obtained uorescence spectra are very similar and it is dicult to distinguish dierent hydrocarbons. Therefore solving this problem is a key point for identication of these molecules through lamentation. In addition for atmospheric monitoring over long range in air, it is particularly important to nd a way to amplify backscattered uorescence generated from femtosecond laser-induced lament to increase the sensitivity of experiments.

In this thesis we focus our attention on some lab-scale experimental studies which can provide more precise results in remote detection or target identication in air with femtosec-ond laser pulses. We will show the amplication of backward uorescence signal of hydro-carbons molecules in air, along the lament axis because of amplied spontaneous emission (ASE). Therefore, for long-distance monitoring of the atmosphere the signal is expected to be stronger in the backward direction. Moreover we did an investigation of eld-free molecular alignment inside lament and propose to use the experimental results for molecular identi-cation especially of molecules with the same lament induced uorescence spectrum. Also we investigated the eect of pressure on lament as one real atmospheric condition relevant for remote sensing. In this rst chapter, we give a brief explanation of these phenomena and we concisely describe the physical mechanisms that govern nonlinear propagation of ultrashort pulses and lamentation. A brief outline of the thesis will be given at the end of this chapter.

Nonlinear propagation of ultrashort femtosecond pulses

The propagation of powerful ultrashort pulses in air involves dierent nonlinear processes such as nonlinear self-focusing, multiphoton/tunnel ionization, and plasma defocusing which play an important role in the propagation of laser beams and in the formation of the laments.

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In the following, we briey mention the processes leading to single lamentation. Note that specic reviews about nonlinear propagation of ultraintense laser pulses [5,6,7,8,9,38] give a detailed description of these processes.

Self-focusing

In nonlinear propagation of an ultrashort pulse in air, the primary process responsible for changes in characteristics of this pulse is self-focusing [6,39]. Actually, at high intensities the refractive index of air, n, depends on intensity of the incident beam according to:

n = n0+ n2I (1)

This change in refractive index is called the Kerr eect [3, 10] which induces a change of the medium refractive index. Here, n0 is the linear index of refraction in air. n2 is the nonlinear index of refraction or Kerr coecient which is related to third order susceptibility χ(3) by n2 = 3χ(3)/2n200c, where 0 is permitivity of free space [3]. Often n2 is measured in units of cm2_{/W. Since n}

2 in air is positive, the refractive index increases in the presence of intense radiation. When the intensity in a cross-section of the laser beam is not uniform and it is highest at the center of the beam, the refractive index in the center of the beam is larger than on the edge (Figure 0.1(a)). Under this condition, the refractive index prole behaves like a focusing lens.

Figure 0.1: Principle of lamentation, (a) Self-focusing of the laser beam due to Kerr eect. The refractive index of the medium is intensity dependent and acts as a converging lens. I is the incident intensity. (b) Defocusing of the beam due to ionization of the medium and plasma generation at the nonlinear focus, ωp is the plasma frequency and ω is the laser angular frequency. [5]

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Therefore the spatial intensity prole of the laser light gives rise the medium to act as a focusing lens, causing the beam to come to a focus, i.e. the beam is self-focused. It should be noted that this self-focusing eect is always resisted by diraction (spreading of the Gaussian beam size during its propagation in a medium). In fact this spreading of the beam is balanced by self-focussing when the power of Gaussian beam is exactly equal to the so-called critical power

Pcr =

3.77λ2

8πn0n2 (2)

where λ is the laser pulse's central wavelength in vacuum. This condition in which the beam of light propagates with a constant diameter is known as trapping of the beam. The self-focusing can overcome diraction and leads to collapse only if the beam power exceeds this critical power, Pcr.

Therefore an intense laser beam in a nonlinear medium experiences self-focusing due to Kerr eect which can lead to collapse of the beam by itself (Figure 0.1(a)). The phenomenon of self-focusing was discovered in the mid sixties [40] after the invention of the laser.

Ionization and plasma generation

The collapse of a high-power laser beam yields decreasing beam diameter and increasing pulse intensity. This high local intensity results in multiphoton ionization of air molecules. Indeed, when reaching an intensity over 1013_W/cm2_{the ionization comes into play [}₆_,₄₁_{]. The} number of photons needed for multiphoton ionization are 11 and 8 respectively for nitrogen with ionization potential, Ip = 15.58 eV [42] and oxygen with Ip = 12.063 eV [42] at a wavelength of 800 nm (1.55 eV). The ionization process can involve tunneling as well, owing to high intensity. Indeed, free electrons can be generated by both processes in the presence of intense laser eld [5,43,44]. The Keldysh parameter, γ, was introduced to dene the limit between these two ionisation regimes [45].

γ = ωp2meIp

eE (3)

where e is the electron charge, me is the mass of the electron, ω is the angular frequency of the laser radiation, Ipis the ionization potential and E is the electric eld strength. The value of the Keldysh parameter identies the multiphoton (γK 1) and the tunneling (γK 1) regimes.

The ionization of molecules results in the creation of free electrons, thus the generation of a plasma. This plasma causes a reduction of the refractive index of the medium according to n ∼= 1 − ∆np = 1 − ω2/2ω2 [46,47], where ωp = [e2ne/0me]1/2 is the plasma frequency, ne is

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the density of free electrons and ω is the laser angular frequency (meand e denote the electron mass and charge, respectively). The electron density induces a negative variation of refractive index, which acts as diverging lens that causes laser beam defocusing (gure 0.1(b)).

Consequently, plasma formation results in defocusing of the laser beam because of the negative refractive index induced by electron generation through ionization.

Filamentation and intensity clamping

The combined eects of nonlinear self-focusing, ionization and plasma defocusing play an important role in the propagation of ultrashort laser pulses. Indeed these eects individually prevent long-distance propagation of intense laser pulses in air. However as a consequence of the dynamic balance between Kerr self-focusing and defocusing eects, a self-guiding structure of the beam is created which is called lamentation [5,6].

The lamentation process starts where the initial self-focusing causes the short pulse reaches high enough intensities to ionize the air molecules and generate a column of plasma along the beam axis. The intensity then decreases due to defocusing eect of the plasma and plasma generation stops, so that the Kerr eect dominates again. The repetition of self-focusing and deself-focusing sustains a specic structure in the shape of a lament (Figure 0.2). Since laser energy is lost to ionization whenever refocusing and plasma generation occur, the number of recurrences will be limited. Indeed when the amount of energy lost to ionization causes the pulse power to become below critical power, the refocusing is no longer possible and ultimately the lament terminates. The rst report of the experimental observation of femtosecond laments in air was in 1995 [47], and that started extensive studies on femtosecond lamentation.

Figure 0.2: A typical picture of a lament in air. Filament establishes itself through a balance of Kerr self-focusing an defocusing process caused by produced plasma

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the laser pulse. Actually, the balance between self-focusing and the defocussing eect of the self-generated plasma keeps the intensity almost constant during the laser lamentation by femtosecond laser in air. This is known as intensity clamping and results into the stabilization of the intensity inside the lament. The clamped intensity in air, for 800 nm laser pulses, is of the order of 4 × 1013_W/cm2 _[₄₈_].

Consequently, we can not further increase the intensity inside the lament by increasing the energy of the pulse. Indeed, at high powers(P Pcr), the beam breaks up into several laments without notably inuencing their individual intensity, which is of the order of 4×1013 W/cm2_.

Filament onset (nonlinear focusing distance)

As mentioned above, if a femtosecond laser pulse with a power higher than Pcr propagates in air, it will undergo a self-focusing collapse. The propagation distance until collapse, Zf, at which the lament is generated is given by [39]

Zf =

0.367ka2₀ p

[(Pin/Pcr)1/2− 0.852]2− 0.0219

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where k stands for the pulse central wavenumber, a0 is the the beam radius at 1/e level of intensity and Pin is the input power of the pulse. It is worth mentioning that Eq. (4) is valid for Gaussian beam with powers that are moderately above Pcr [49].

The above equation gives the position of nonlinear focus (Zf) for a collimated beam. How-ever an external lens is used in many practical cases. In the situation where an initial collimated Gaussian beam enters the sample following a lens of focal length f the collapse distance Z0

f for a self-focusing Gaussian beam is determined by

1 Z_f0 = 1 Zf +1 f (5)

where f denotes the focal length of the lens.

As it is clear in this equation, the position of the collapse relocates along the propagation axis, but only within a distance limited by the focal length f of the lens. This position of nonlinear focus point, Z0

f, can be revised by employing Marburger's formula, (Eq.(4)) for collimated Gaussian beams) as

Z_f0 = 0.367ka 2 0 p [(Pin/Pcr)1/2− 0.852]2− 0.0219 + 0.367ka20/f (6)

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Consequently, a pulsed beam with the same parameters, focused by a lens of focal length f, will collapse at smaller propagation distances.

Pressure's eect on lamentation

It is worth mentioning that in propagation of high power laser pulses, the nonlinear eect depends not only on the intensity but also the gas pressure. Pressure variations induce pro-portional changes in the density of air molecules and then its nonlinear refractive index n2. Note that in the case where a medium is so dilute that its linear dielectric constant is nearly equal to unity, we can ignore local-eld corrections [3]. For air pressures used in this thesis (0.3 ≤ p ≤ 1 atm), this approximation implies that the nonlinear refractive index is linearly proportional to pressure, n2 ∼ p [50,51, 52]. Therefore, n2 for dierent pressures, p, can be calculated as follows

n2 = natm2 p

patm (7)

where natm

2 denotes the value of the nonlinear refractive index of air at atmospheric pressure, i.e., when p = patm.

The propagation of high power laser pulses is governed by Kerr eect in the region of self-focusing, which means that the pressure dependent nonlinear refractive index n2 of the air governs this propagation. On the other hand from Eqs.(2) and (7) it can be shown that the critical power, Pcr, varies linearly with the inverse pressure [52] as

Pcr ∝ _n1₂ ∝ 1_p

Because of this dependency of critical power to the pressure, the location of lamentation onset (Zf), is aected by pressure (see Eq.(4)). Therefore the inuence of pressure variations on nonlinear propagation of ultrashort laser pulses in air, especially in the vertical direction, is inevitable. The critical power for self-focusing increases as the pressure decreases. Then at constant power, Pin, the ratio Pin/Pcr decreases. Then the start of lament happens farther from the laser with collimated beams. These eects of pressure variation will be discussed in more details in the next chapter.

Amplied spontaneous emission (ASE)- mirrorless laser

As it is known, in a laser medium, atoms jump from ground state |gi to excited state |ei as a result of pumping process. Such atoms undergo a transition to a state with a lower energy (lower state) by releasing the energy in the form of a photon, which is emitted in a random direction. The process which occurs spontaneously is called spontaneous emission. The energy of the photon is then given by hν = Ee− Eg, where h is Planck's constant, Ei

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is energy of ith level (see Fig. 0.3a). Note that in this situation, another possibility for the atom to decay is non-radiative decay in which the energy dierence Ee− Eg is delivered in some form of energy other than radiation.

On the other hand, it is possible that an incoming photon of energy hν causes the excited atome to decay and undergo the transition |ei → |gi and emit another photon. This process in which the emission is induced, or stimulated, by an incident photon is called stimulated emission. In this case, the emitted photon goes into the same direction as the incoming photon with same energy, so incoming radiation is amplied (see Fig.0.3b). Indeed, this is the physical basis of light amplication in laser ampliers and lasers oscillators.

Figure 0.3: (a) Spontaneous emission of a photon with energy hν. (b) Stimulated emission of a photon with energy hν.

Now we consider a gain medium. In such medium the spontaneous radiation emitted by the excited molecules/atoms of the medium itself, can be amplied as follows. The absorption of the pump energy causes a fraction of the molecules/atoms to move to the upper level to produce a population inversion. However after a while, they spontaneously decay back to the lower level, without any external inuence as explained above. This causes a spontaneous emission in a random direction ( Figure 0.3(a)). A fraction of these photons at one end of the medium, can be directed along the amplier (gain medium) axis or very close to this axis, so they are amplied when passing through the gain medium before escaping from this medium. In fact, each one of these spontaneous emission photons can stimulate the emission of more photons and cause an amplied emission at the other end of the gain medium. This radiation, which appears regardless of whether there is any input radiation, is called amplied spontaneous emission (ASE). In particular, because the gain medium is long and thin the ASE is highly directional like a laser beam. Indeed, with spontaneous emission, the emission of radiation occurs in all directions, while some directions are heavily favored because of higher gain. So such a system in which emission is amplied in a single pass, is often referred to as mirrorless laser [4,53,54].

In laser ampliers the ASE is considered a source of noise which is added to the optically amplied signal. In recent years, this phenomenon has attracted much attention in laser science [55, 56, 57, 58]. The generation of an amplied radiation from such cavity-less laser

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sources in air, holds great potential for remote sensing applications. In the case of femtosecond laser pulses, this approach relies on the remote generation of a weakly ionized plasma channel through lamentation of an ultra intense femtosecond laser pulse. As we will see in this thesis, the uorescence signal of fragments inside the lament, created in air mixed with impurities, is amplied through ASE as it propagates along the lament. Therefore ASE can be used as a technique to enhance the intensity of the return signal which is very useful in remote sensing and stando spectroscopy for the detection of trace impurities in the atmosphere.

Laser induced eld-free molecular alignment

After the work of Friedrich and Herschbach [59] and Seideman [60] in the nineties, molec-ular alignment induced by a strong non-resonant laser pulses has been the topic of many experimental and theoretical activities and this eld has developed rapidly. These studies have shown that molecules can be aligned by strong laser pulses.

Two mechanisms have been demonstrated for non-resonant laser induced alignment: the adiabatic and nonadiabatic processes [61]. Indeed, it was realized that the pulse duration of the laser eld applied to induce alignment plays a signicant role in the alignment dynamics. The adiabatic alignment means that a laser pulse of duration τ which is long compared to the rotational period of the molecule, τrot, allows to align the molecule [62,63]. In this case the molecule is aligned during the interaction with the laser pulse by a slowly increasing electric eld (long laser pulse). As the laser is turned o, this molecular alignment disappears and the molecule goes back to its initial condition i.e, the alignment exists only when the laser is on. So in this regime, the alignment is lost once the laser pulse is turned o. On the other hand, in the nonadiabatic regime (or short pulse induced alignment), the molecule experiences a rotational kick in the direction of the the polarization of the laser, making the molecules rotate. Using an ultrashort pulse, τ < τrot, a rotational wave packet is produced which yields dynamic alignments occurring periodically at well-dened time delays, in time after the initial interaction [61,64,65]. So, unlike the case of adiabatic alignment, there is alignment after the pulse turn-o. Subsequently, the time-evolution of alignment and series of periodic recurrences (eld-free alignment), which are referd to as rotational revivals, can be observed and measured by a delayed probe pulse.

The experiments presented in this thesis are based on using femtosecond laser pulses to study the nonadiabatic molecular alignment regime. Therefore here we present a brief overview of the mechanism of this laser induced molecular alignment regime.

Interaction potential energy

Let us rst consider the interaction between a molecule and an electric eld E. Any molecule with anisotropic polarizability, α, placed in an electric eld will experience a torque

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that tends to align it along the polarization direction of the eld. In general, the applied eld E induces a dipole moment p = αE, which is not parallel to the eld E due to the anisotropic molecular polarizability. Thus a torque τ = p × E is delivered to the molecule.

The interaction between induced dipole moment and electric eld, gives rise to a potential energy, U, for the molecule. This potential energy term arises as follows [3]. Consider a linear molecule having one dominant axis of polarizability, generally the long axis (αk> α⊥), which placed in an electric eld, as shown in Figure 0.4. αk and α⊥ are the components of the polarizability parallel and perpendicular to the molecular axes, respectively.

Figure 0.4: Sketch of an anisotropic particle in an electric eld E.

The usual description of the energy of a molecule in interaction with an electric eld is

U = −p · E. (8)

Then a small change in applied eld dE for a linear molecule, brings about a change in the potential energy as

dU = −p · dE = −pkdEk− p⊥dE⊥ (9)

where, E and p have been decomposed into their components parallel (k) and perpendicular (⊥) to the molecular axis. Now the components of the induced dipole moment; p⊥ = α⊥E⊥ and pk = αkEk can be substituted into Eq. (9) to obtain dU

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dU = −αkEkdEk− α⊥E⊥dE⊥ (10) which can be integrated to give

U = −1 2(αkE

2

k + α⊥E⊥2) (11)

By rewriting the components of electric eld, using the angle θ which is the angle between the molecular axis and the electric eld E, this relation can be written as

U (θ) = −1 2(αkE

2_cos2_{θ + α}

⊥E2sin2θ) (12) Rearranging the equation using cos2_{θ + sin}2_{θ = 1}_{, we arrive at the expression}

U (θ) = −1 2E 2 _{∆α cos}2_{θ + α} ⊥ (13) where ∆α = αk− α⊥.

When the molecule is placed in a linearly polarized laser eld, the electric eld E in Eq.(13) can be replaced by the time-dependent laser electric eld, ε(t) cos ωt, where ε(t) is the envelope of the electric eld of the linearly polarized laser pulse and ω is the angular frequency of the eld. We assume that the central frequency of the pulse is far detuned from any molecular transition. This means that the molecule interacts with a laser eld which is far o-resonant with its rotational frequencies (as it is typical in experiments of molecular alignment with strong elds). Therefore, because the rotational time scale is much longer than the optical period, the interaction can be averaged over one optical cycle which turns the factor cos2_(ωt) into 1/2.

Consequently, in case of a linear molecule interacting with a linearly polarized nonresonant laser eld, the potential energy of the pulse interaction with the induced molecular polarization is given by

U (θ) = −1 4ε

2_{(t)(∆α cos}2_{θ + α}

⊥) (14)

This result shows that, as a consequence of anisotropic polarizability (αk 6= α⊥), the potential energy of molecule in laser eld depends on the angle between electric eld and molecular axis. It is obvious from Eq.(14) that this laser induced potential energy is at its minimum when the molecular axis is aligned along the polarization direction of the laser eld (θ = 0 or π).

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Rotational Hamiltonian

The rotational behavior of a molecule exposed to a short laser pulse, during and following the interaction is evaluated by solving the time-dependent Schrödinger equation

i¯h∂

∂t|ψ(t)i = H|ψ(t)i (15)

where H is the total Hamiltonian for a linear molecule subjected to a nonresonant linearly polarized laser eld which becomes

H = H0+ Hint (16)

where H0 is the eld-free molecular Hamiltonian which represents the energy of the free molecule, and Hint describes the interaction with the laser eld.

Within the rigid-rotor approximation H0 reduces to the rotational Hamiltonian [66,67]

H0= 1 2 J2 a IA +J 2 b IB +J 2 c IC (17)

In this equation the operators Ji with i = a, b, c represent the components of the total angular momentum of the molecule and IA, IBand ICare the corresponding principal moments of inertia around the principal axes a, b and c in molecule-xed coordinate system. The rotational Hamiltonian is commonly expressed in terms of the rotational constants. We dene these constants as A = h/8π2_cI

A, etc. in units of inverse length, where c is the speed of light and h is Planck's constant [68]. Therefore the rotational Hamiltonian is expressed as

H0 = 2πc ¯ h AJ 2 a+ 2πc ¯ h BJ 2 b + 2πc ¯ h CJ 2 c (18)

In case of a linear molecule, if we dene the molecular axis as the a axis, then IA= 0and IB = IC [66, 67, 69]. In this case, rotational constant A is not dened, and the two other rotational constants are equal, i.e. B = C. So in the limit of linear rigid rotors Eq.(18) reduces to H0 = (2πc/¯h)BJ2, with J2 = J_b2+ Jc2.

Therefore, the complete Hamiltonian of a linear molecule subject to an intense linearly polarized laser eld, in the rigid rotor approximation, takes the form [59,65,70]

H = (2πc/¯h) BJ2− 1 4ε 2_{(t) ∆α cos}2_{θ + α} ⊥ (19)

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Rotational wavepacket

In the quantum mechanical description, the interaction of a short laser pulse (short com-pared to the rotational period of the molecule) with the molecule creates a rotational wave packet. This wave packet is a coherent superposition of eld free rotational states [61]. Indeed for linear molecules which are approximated as rigid rotors these states, |JMi, are described by the quantum number of total angular momentum J and the projection M [66]. Then the solutions of Eq.(15) emerges from expanding the wavepacket in a series of, |JMi [69]. In nona-diabatic regime, after the interaction with the laser pulse the molecules rotate free of external elds, so the wave packet will evolvs in time. The time evolution of the wave packet produced by the aligning pulse is found by considering the time evolution of each of the components in the wave packet

|ψ(t)i =X J

CJ Me−iEJt/¯h|J M i (20)

EJ is the rotational energy eigenvalue which in the limit of linear rigid rotor become EJ = hcBJ (J + 1) where B is the rotational constant [66]. The coherent superposition of rotational states can revive some time after the initial impulse. In fact, right after the cut o, the molecules are still aligned but immediately the dierent components of the wavepacket will start to come in and out of phase with each other. Therefore the rotational wave packet will de-phase and re-phase creating a time-dependent alignment long after the pulse has been switched o, leading to recurrences in the alignment degree at well-dened time delays. These recurrence of the alignment degree are termed rotational revivals.

To calculate the response of the molecular gas in interaction with laser pulses, the induced wave packet must be calculated. However, to this end, it is necessary to solve the time depen-dent Schrödinger equation (Eq.(15)) by substituting Eq.(19) and Eq.(20) into it. Solving this equation is not a trivial problem and demands a numerical approach. Once the Schrödinger equation is solved, the expansion coecients CJ M are found and the form of wave packet is determined; all observables of interest can be computed as a function of time.

In the context of time dependent molecular alignment, the observable that has been most commonly used to study the time evolution of alignment is the expectation value of cos2_θ [61,69]. For eld free case, the time dependent measure of alignment is given by

hcos2θi = hψ(t)|cos2θ|ψ(t)i (21)

The measure of alignment shows a value of hcos2_{θi = 1/3} _{before the application of the} aligning pulse [3]. If hcos2_{θi = 1} _{the molecular axes is parallel to the direction of the laser} polarization. With molecular axes perpendicular to the laser polarization direction hcos2_θi

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would have the value of 0 which represents maximum antialignment. In fact, a value less than 1/3 is indicative of a concentration of probability distribution for the axis of the molecules around a plane perpendicular to the polarization direction of the laser beam.

At last, it is important noting that the time-dependent alignment of the molecules creates a time-dependent refractive index which can be probed by a weak laser pulse (probe). This pulse interacts with the molecules subsequently to their exposure to a strong aligning pulse (pump). In fact, this time-dependent refractive index causes a modulation of the spectrum of the probe pulse. The refractive index which is produced along the polarization axis of the pump pulse (lamenting pulse) is given by [3,71]

n2(t) = 1 + Nα⊥+ ∆αhcos2θi(t)

(22) where N is the number density of molecules and ∆α = αk− α⊥.

The isotropic refractive index before the pump arrives is named n0. As it was mentionned above, in this situation hcos2_{θi = 1/3}_{which is the average alignment of a randomly oriented} molecule. The index of refraction is then n2

0 = 1 + N (αk/3 + 2α⊥/3). Consequently, the deviation of the refractive index from the isotropic one ∆n(t) ≡ n−n0, owing to the alignment experienced by a parallel polarized probe pulse is

∆n(t) = N 2n0 ∆α hcos2θi(t) −1 3 (23)

This equation implies that a probe pulse injected collinearly to the wake of the pump pulse at special time delays, will experience a spectral modulation. Indeed the medium loses its optical isotropy after rotational excitation and undergoes temporal modulation of the refractive index. It is worth mentioning that when the probe pulse is perpendicularly polarized to the pump pulse hcos2_θi(t) _{is replaced with [1/2(1 − hcos}2_θi(t))] _[₃_, ₇₂_,₇₃_{]. In this case also the} probe pulse is modulated in suitable time delays(gure 3.3).

In our experiments the pump pulse (femtosecond laser pulse) undergoing lamentation in a molecular gas induces impulsive rotational excitation of the medium. Then the change produced in the gas optical properties can aect the delayed probe pulse propagating in the wake of the pump one at periodic delays, which is the signature of a temporal refractive index modulation occurring in the lament wake.

The outline of this thesis

As mentioned earlier, the unique properties of lamentation which comes with femtosecond (fs) laser pulses have a lot of potential applications and open up new possibilities for using

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fem-tosecond laser technologies in atmosphere and other applications. One of the most important characteristics of femtosecond laser pulses is the possibility of having high density laments at long distance and high altitude which is obtained during the propagation of high-power femtosecond laser pulses in air.

Even though the fundamentals of lamentation and some of its applications are well investigated and several review papers and books have already been published, the application of femtosecond pulses still need to more study to improve the results. In this thesis, we therefore performed some lab scale investigation about lamentation and its applications, which can be useful in remote detection and identication of pollutant in air. The rest of thesis is organized as follows:

Chapter two (The eect of the pressure on the femtosecond lamentation in air) presents experimental and theoretical studies of lamentation at low pressures (less than 1 atm) which corresponds to conditions at high altitude. We simulated vertical propagation and lamentation in the atmosphere for up to 10 km by changing the pressure in a gas cell, in the laboratory. Then we measured the size (length and diameter) of lament at dierent pressures below 1 atm. In particular, the laments onset and size are key parameters for spectroscopic measurements of atmospheric compounds and for depositing the desired intensities on remote targets.

In this chapter we also talk about the laser system used in the present experimental work. The setup has three simultaneous ∼ 45 fs outputs. One operates at 1 kHz with maximum output energy of ∼ 2 mJ, two others at 10 Hz with a maximum output power of 0.2 TW and 2 TW.

Chapter three (Backward amplied spontaneous emission induced by femtosec-ond lament in gas medium) describes our investigation of lament-induced amplied spontaneous emission, ASE, in air and airhydrocarbons (2% ) gas mixture; CH4, C2H2, and C2H4. This was done by detecting the uorescence emitted from neutral N2 in air and CH fragments in gas mixtures prepared in the lament generated by intense ultrashort Ti:sapphire laser pulses. In this experiment we compared the uorescence signal recorded from the side of the lament with the backward direction of the laser propagation. The dierence in the results showed that the lament can act as a gain medium in which the spontaneous emission from N2 and CH was amplied (ASE). This process realized by a small amount of hydrocar-bon molecular species in air can be applied to remote sensing of pollutants in air to receive a stronger signal from them.

Chapter four (Ultrafast laser spectroscopy based on eld-free rotational molecular alignment) shows the eect of laser induced molecular alignment on delay probe pulse. Using the changes in the probe pulse spectrum in the wake of the lament by eld free molecular alignment, we can nd the rotational period of the molecule. This rotational period can be

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used to identify dierent molecules, specially molecules with the same lament induced u-orescence spectrum, so it can have important applications in atmospheric monitoring. Also nonediabatic alignment in dissipative media can be a potential source of information consid-ering the interaction of the molecule with its environment.

In the pump-probe experiments presented in this chapter, we detected the scattering signal of the probe pulse after its interaction with a medium which was exposed to the lamenting (pump) pulse. We observed the periodic spectral modulation of the probe pulse related to the rotational response of the gas, after the interaction with the pump pulse in the wake of the lament. The experiment was started with nitrogen, oxygen and air, and then extended to ethylene, acetylene and mixtures of these gases.

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Chapter 1

The eect of pressure on the

femtosecond lamentation in air

In view of the atmospheric applications of lamentation like remote sensing, it is important to study the lament in air under atmospheric conditions. In these outdoor applications, the pressure of air at high altitude where lamentation process happens, is lower than at atmospheric pressure. Thus it is necessary to study lamentation at low pressures and nd its characteristics as a function of pressure.

Although the Kerr eect is reduced at high altitude (because of dependency of critical power (Pcr(p)) to pressure), it does not prevent lamentation from being initiated and propagating in air at low pressures. This possibility of lament formation in air at pressures as low as 0.20 × 105 Pa (0.2 atm) which corresponds to altitudes up to ∼11 km has been demonstrated by other groups [50, 74]. To quantify long-range vertical propagation in the atmosphere we need to estimate the length and the transverse size of the lament and the location where the lament is initiated.

In this chapter we present the laboratory studies of the eect of pressure on the size and onset of the lament. For this purpose, we considered two distinct initial conditions to model the variation of the lament geometry in air as a function of pressure. First, while the input pulse energy had been kept constant, images of laments for dierent pressures from 0.30×105 up to 1.01×105_{Pa, were recorded. Next, with the constant ratio between input power of laser} pulses, Pin, and critical power constant, i.e., Pin/Pcr(p) =constant, as a new initial condition, we got the data for dierent pressures of air in the gas cell.

An article based on my work on this topic was published in Laser Physics Letters in 2012 [75]. I was the rst author on this paper because I was responsible for the data acquisition and analysis, and for writing the manuscript. Note that the data and gures presented in this chapter are not exactly the same as in the paper. Indeed, the results presented here were

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obtained with dierent experimental initial conditions, such as input energies.

1.1 Experiment

Performing the experiments presented in this thesis entails having a strong eld laser system and a suitable experimental setup. It is obvious that dierent experiments need their own setup, considering the result we want to achieve. Therefore for each experiment I will explain its setup separately in each chapter.

On the other hand, the laser system which produced ultrashort intense laser pulses was the same for all experiments. Hence in this section, rst I give a brief introduction about this system here and then explain the setup which is used to measure the lament size for dierent pressures.

1.1.1 Laser system

Since 1985, the development of the chirped pulse amplication (CPA) technique [13, 14] permitted to produce ultrashort intense laser pulses. This is a technique that allows the amplication of ultrashort laser pulses to high energy levels, while avoiding nonlinear eects and optical damages that could occur in the amplication process. The key to CPA is to avoid amplifying the short pulses directly in the laser amplier.

In a CPA laser, the ultrashort pulse generated at low pulse energy in an oscillator is temporally stretched using an optical stretcher. The stretcher generates a time delay between the dierent wavelengths of the initial short pulse. By lengthening the pulse in time, the intensity is kept below the level of nonlinear eects. The energy of the pulse is then increased in one or more stages of laser amplication. Finally a compressor is used to bring the pulse back to its ultrashort duration [76] (Figure1.1).

Figure 1.1: Principle of the chirped pulse amplication (CPA) technique. The pulse from the oscillator will be stretched, amplied and compressed (schematic drawing).

Oscillator

The oscillator, which produces ultrashort pulses, is a mode-locked laser with a Ti:sapphire crystal as a gain medium. Titanium-doped sapphire is a laser material with properties that

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make it as a excellent solid-state source of ultrashort pulses near-infrared region. For instance, Ti:sapphire encompasses a large gain bandwidth and very high thermal conductivity [76,77]. The wide gain prole of the Ti:sapphire enables the laser to deliver tunable output over a broad range of near IR wavelengths and generate ultrashort pulses. Ti:sapphire also allows the laser to operate with high power and high repetition rate because of its thermal characteristics. In fact, very high cw optical pumping powers are achievable in this material [78].

The gain medium of the oscillator is pumped by a cw diode-pumped frequency-doubled neodymium yttrium vanadate (Nd : Y V O4) laser (Millenia from the company Spectra-Physics). A lithium triborate (LBO) doubling crystal is used to convert the 1064 nm light from the laser crystal to the green 532 nm light that becomes the output of the Millenia with average output power of 4.2 W. Then the cw beam is focused into the Ti:sapphire crystal inside the oscillator. The oscillator generates a pulse train at a repetition rate of 74 MHz with a bandwidth around 40 nm (FWHM) centered at 800 nm. Each laser pulse has an energy that is approximately 5 nJ and a duration of 30 fs.

Stretcher

The pulse train from the oscillator is directed to a pulse stretcher, the rst step of CPA system (Figure 1.2). To protect laser oscillator from back-reected pulse, a Faraday isolator is used in pulse path before stretcher. The Faraday isolator's ability to allow light to pass in one direction, while strongly attenuating light traveling in the opposite direction, eliminates the negative eects of optical feedback.

The stretcher temporally delays the shorter wavelengths more than the longer ones in a pulse; this pulse is said to be positive chirped. The pulses are stretched in time to a duration of ∼ 200 picoseconds, a factor of ∼ 6700 times longer than the original oscillator pulses. Therefore the peak intensity of pulses is strongly reduced. Now the pulses are ready to enter the next step for amplication.

Regenerative amplier

The regenerative amplier is basically a resonator cavity with an amplication crystal. The special characteristics of the Ti:sapphire crystal make it an ideal amplier material. Ti:sapphire inside the amplier is pumped by the second harmonic of a neodymium-doped yttrium-lithium-uoride (Nd:YLF) laser running at a repetition rate of 1 kHz with the central wavelength of 527 nm.

The low-energy stretched laser pulses are injected inside the regenerative cavity using a Pockels cell (PC1) coupled with a quarter wave plate. By activation of PC1 a pulse from the pulse train can be selected and trapped inside the cavity. Indeed a 1 kHz pulse train from the 74-MHz stretched pulses is trapped and amplied in a z shaped Ti:Sapphire cavity (see Figure

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Figure 1.2: The schematic description of 1-kHz laser system using CPA technique. The ab-breviations used in this gure are as follows: PC: Pockels cell, P: polarizer, Ti:sa: Ti:sapphire crystal, λ/2: half-wave plate, λ/4: quarter-wave plate.

1.2). After multiple round-trips the trapped pulse in the cavity reaches its maximum energy; this pulse is extracted out of the cavity by a second Pockels cell (PC2). For the extraction, a voltage is applied on PC2. Then the amplied pulse is reected out of the cavity by the polarizer (P2). The output energy of the amplied pulse is 1.4 mJ per pulse at a repetition rate of 1 kHz and a duration of approximately 200 ps. This pulse train is then directed to a pulse slicer consisting of two polarizers (P3, P4) with a Pockels cell (PC3) between them. A high voltage is applied on this Pockels cell at a repetition rate of 10 Hz. Therefore the pulse slicer picks up laser pulses at a 10-Hz repetition rate and at vertical polarization and sends them to an external 10 Hz amplier systems. The rest of laser pulses in the pulse train have horizontal polarization and a repetition rate of 1 kHz, with holes of 10 Hz and they pass through the polarizer P4.

1 kHz two-pass amplier

The 1.4 mJ amplied pulses with 1 kHz repetition rate are directed towards a two-pass amplier whose gain medium is again a Ti:Sapphire crystal. The gain medium is pumped with the same Nd:YLF laser as used in regenerative amplier. In the two-pass amplier, as its name suggests, the pulse passes through the crystal two times without the use of cavity.

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After the amplication, the laser pulses reach an energy of ∼ 2.8 mJ per pulse. Compressor

In the last step, the amplied pulses are directed the to the optical compressor. This system design minimizes the pulse temporal duration and increases its peak power. In order to compensate the chirp of the laser pulses induced during their propagation inside the ampliers and by the grating of the stretcher, the chirp induced by the compressor is negative. At the end, pulses with maximum energy of 1.9 mJ and minimum duration of 45 fs at 1 kHz are delivered. A polarizer and a half-wave plate is designed before the grating to control the output energy of laser pulses.

10-Hz amplier

The pulses selected by the pulse slicer are directed to the 10 Hz amplier systems to achieve higher pulse energy. Before amplication, a beam splitter is used to divide 10 Hz seed pulses into 2 beams of equal energy. The reected beam is directed to a 2-pass amplier (Figure

1.3) while the transmitted one is directed to another multi-pass amplier; the output of this amplier was not used for the experiments of this thesis.

The Ti:sapphire crystal of two-pass ampliers is pumped by the second harmonic (532 nm) from a neodymium-doped yttrium-aluminum-garnet (Nd:YAG) laser operating at a repetition rate of 10 Hz. The amplier medium is pumped by green pulses with power of 5 W. Laser pulses, emitted at a 10 Hz repetition rate from the two-pass amplier are directed to the last step of optical compression in a portable compressor. The pulses, after this step, were characterized with a maximum output power of 0.2 TW per pulse and a duration of 45 fs. Like the 1-kHz system, here also there is a polarizer and a half-wave plate (Figure 1.3) to adjust the desirable output energy.

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1.1.2 Experimental scheme

The principle of the experiment is depicted in Figure 1.4. In the experiment described in this chapter the output of laser system, mentioned in section 2.2.1, operating at 10 Hz was used to investigate the nonlinear propagation through a tube lled with the air to be studied. The laser pulses are compressed to a transform-limited duration of 45 fs and the beam at the output of the compressor is roughly Gaussian. A telescope further increases the diameter of the beam. The nal laser beam pattern after the telescope has been imaged by a charge-coupled device (CCD) camera (1392 × 1024 pixels with 12 bit dynamic range). Figure 1.5represents this beam pattern, tted by a Gaussian prole whose radius at 1/e2 _{of the maximum is equal} to 5.6 mm.

Figure 1.4: Schematic representation of the experiment used to measure the diameter and length of the lament at dierent pressures. The uorescence signal coming from lament is imaged by a CCD camera equipped with an imaging system.

After the telescope, the laser beam is focused inside a tube by using a converging lens having a one meter focal length. The focusing geometry made it possible to t the lament in the cell and observe the uorescence. Moreover by increasing the size of input beam adequately, the acceptable length of lament (shorter than the opening of side window) would be achieve. The air pressure inside the tube was controlled from 0.30 × 105 _{to 1.01 × 10}5 _Pa.

The CCD camera imaged the uorescence left behind the laser pulses, from the side of the cell, to characterize the spatial distribution of a lament. There is an imaging system (Minolta MD 50 mm 1:2 ϕ = 49 mm) attached to the CCD to adjust the image on CCD.

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Figure 1.5: Beam pattern measured with a CCD camera just before the focusing lens.

Also, a dielectric mirror with high reectivity centered at 800 nm and high transmission for UV light at 0 incidence angle was inserted before the CCD as a lter. This is used to block the scattered laser light and transmit the uorescence signal from air molecules.

1.2 Experimental results and discussions

In order to determine the size (length and diameter) of the lament in these experiments, we recorded the uorescence image of the lament. Note that, uorescence signal in air lament is mainly from nitrogen molecules. The measured nitrogen uorescence zone is smaller than the high intensity zone of the light lament because the nitrogen uorescence is the result of multiphoton/ tunnel ionization. From the experimental point of view, it is equivalent to an eective 11-photon ionization process [43].

A typical image of the lament obtained with the CCD camera integrating the plasma light over 40 successive laser shots is presented in Figure 1.6 (a). In this gure the input energy of laser pulses is 4 mJ and the pressure of air inside the chamber is 0.71 × 105 _Pa.

In the rst part of experiment, the measurements were performed with a constant incident energy of 4 mJ while the pressure of air inside the chamber was increased from 0.30 × 105 to 1.01 × 105 _{Pa. In this interval, the input power is larger than twice the critical power} (Pin > 2Pcr). The critical power for self-focusing is around 10 GW for a 45 fs pulse in air at atmospheric pressure [? ]. The uorescence images for four dierent representative pressures (0.41 × 105_{, 0.61 × 10}5_{, 0.81 × 10}5 _{and 1.01 × 10}5 _{Pa) are shown in Figure} _1.7_{. As can be} seen by increasing the pressure, the location of the beginning of the lament is shifted toward the laser, further from the geometrical focus of the lens. Indeed this gure clearly shows that the collapse distance, Z0

f, is aected by pressure in the constant input power regime, which is predicted by Marburger's equation (see chapter 1, section 1.1.4) for the position of the nonlinear focus that be explained as follows.

As it was mentioned earlier (chapter 1, section 1.1), since the critical power for self-focusing, Pcr = 3.77λ2/8πn0n2, is inversely proportional to the nonlinear refractive index n2,