Thesis
Reference
Coherent discrimination of biomolecules in the Deep Ultraviolet:
developments and results
RONDI, Ariana
Abstract
Cette thèse s'inscrit dans un effort au sein de notre groupe de développer de nouvelles techniques de détection et d'identification d'organismes biologiques pour des applications biomédicales en imagerie ou en détection d'aérosols pathogènes. Les points-clés du contrôle optimal femtoseconde de chromophores biologiques en phase liquide ont été abordés. Un nouvel algorithme multi--objectif a été employé pour l'optimisation en boucle fermée de la fluorescence multiphotonique, et nous avons décrit ses avantages par rapport à des algorithmes conventionnels à objectif unique. Nous avons également utilisé un dispositif commercial composé de micro-miroirs pour le façonnage temporel direct d'impulsions ultraviolettes large bande femtoseconde. Finalement, nous avons étendu à l'ultraviolet profond la technique de discrimination dynamique optimale, une stratégie de contrôle optimal conçue pour la discrimination de molécules biologiques complexes. La discrimination de deux acides aminés a ainsi été réalisée. Ce résultat permet d'envisager l'application de cette technique à des molécules plus [...]
RONDI, Ariana. Coherent discrimination of biomolecules in the Deep Ultraviolet:
developments and results. Thèse de doctorat : Univ. Genève, 2011, no. Sc. 4398
URN : urn:nbn:ch:unige-231004
DOI : 10.13097/archive-ouverte/unige:23100
Available at:
http://archive-ouverte.unige.ch/unige:23100
Disclaimer: layout of this document may differ from the published version.
1 / 1
Université de Genève Groupe de Physique Appliquée
Faculté des Sciences Professeur Jean-Pierre Wolf
Coherent Discrimination of
Biomolecules in the Deep Ultraviolet:
Developments and Results
THÈSE
présentée à la Faculté des Sciences de l’Université de Genève pour obtenir le grade de Docteur ès Sciences, mention Physique
par
Ariana RONDI
de Bioggio (TI)
Thèse No 4398
Genève
Atelier de reproduction ReproMail 2012
Acknowledgements
Une fois la soutenance de thèse passée, et l’excitation et le stress retombés, c’est avec sérénité et grand plaisir que j’écris ces lignes. Je réalise cependant que cette partie est moins facile à écrire que ce que je pensais. Il est délicat en quelques mots de remercier comme il convient toutes les personnes qui ont si grandement contribué à ce travail. Voici tout de même une tentative.
J’aimerais tout d’abord remercier Jean-Pierre, qui, à ma grande joie (et ma grande surprise à l’époque!) m’a offert la possibilité de faire une thèse au sein de son groupe. Dès le premier jour il m’a accordé son soutien, toute sa confiance et il m’a donné la possibilité de travailler dans les meilleures conditions. Je serai toujours en admiration face à ses qualités pédagogiques, sa créativité, son dynamisme, et son indécrottable optimisme.
I take the opportunity to thank the members of the jury, professors H.
Rabitz, S. Haacke and C. Hauri for agreeing to review my work, for their careful reading of my manuscript, and for coming from far away to attend my defense.
Ma gratitude va également tout particulièrement à Luigi. Je lui suis re- connaissante de m’avoir tout appris, tant dans la théorie que dans la pratique au labo, avec bienveillance et beaucoup, beaucoup de patience. Ses connais- sances, sa pédagogie et sa rigueur sont pour moi un modèle à suivre. Ma reconnaissance enfin pour avoir corrigé toutes les bêtises que j’a écrites au long de ces cinq années, et pour sa relecture particulièrement attentive de ce manuscrit.
Un grand merci ensuite à tous mes collègues Jérôme, Denis, Michel, Pierre, Massimo, Stefano, Christelle, Jérôme, Sébastien, Stefan, Yannick, Pierre, Deeraj et Seïf. Tous ont contribué à ce travail, que ce soit directement au labo, ou simplement en entretenant cet esprit de bonne camaraderie qui a toujours régné dans le groupe. Je remercie tout particulièrement Jérôme E, pour (bien plus que) de grands coups de main, toujours au bon moment, et Michel pour ses vastes compétences techniques et informatiques, indispens- ables au jour le jour au labo. Sans les innombrables pièces dessinées de sa
iii
iv ACKNOWLEDGEMENTS main, mes manipes n’auraient pas été possibles. Merci aussi à Denis pour m’avoir souvent donné à réfléchir, et pour avoir été un si bon camarade de bureau. Merci à Laurent et François, qui m’ont mis le pied à l’étrier tout au début de ma thèse.
Un remerciement tout particulier à Sarah, qui a été ma collègue de labo pendant de longs mois de dures manipes, et avec qui j’ai partagé bien plus que le travail.
Mes remerciements vont aussi à Lorène, qui, venue pour un stage de quelques semaines, a travaillé avec énergie et enthousiasme sur une manipe pour le moins récalcitrante.
Je souhaite beaucoup de réussite aux nouveaux arrivés Thibaud, Andrii, et tout particulièrement à Svetlana, qui a repris courageusement le travail là où je l’ai laissé. Sachant à quel point il peut être difficile de s’insérer dans un projet déjà lancé, elle a fait preuve dès le début de beaucoup d’énergie et d’une grande capacité d’adaptation.
Je voudrais également remercier toutes les personnes qui sont venues as- sister à ma soutenance. Leur présence m’a comblée.
Me gustaría darle las gracias al coche de Angel. Tuvo el buen gusto de averiarse en el mejor lugar, y en el mejor momento, a pesar de lo que su propietario pudiera pensar. Gracias Angel, por un oído atento y una mirada objetiva en un momento clave.
A Christel, JC, Marc, Patrick, Livia, Juan, Maxime, merci pour votre soutien, compréhension, bonne humeur et sens de la dérision.
Mention spéciale pour Jill, Valérie, Marina et Elisabeth, sacrées guer- rières, chacune à votre façon. Merci pour votre soutien, bonne humeur, et grande bienveillance, un baume à mon coeur.
Je remercie aussi GL pour tout le travail.
A Cris, Geo y Cris, las chicas más valientes, que sois mi modelo cada día, gracias por apoyarme siempre con paciencia y afecto, y por ayudarme a sacar lo mejor de mi misma. Comparto con vosotras todo por cuanto paso, mis penas, mis alegrías, mis miedos, y mis ilusiones. Por todo, gracias.
Un tierno y especial agradecimiento a toda mi familia, por su apoyo in- defectible y su admiración, que me llegan de tan lejos.
Il m’est difficile d’exprimer ici toute ma reconnaissance envers mes par- ents, pour leur soutien inébranlable tout au long de mes études, et parti- culièrement pendant ces cinq dernières années. Même si parfois ils ne les comprenaient pas, ils ont toujours respecté mes choix. Pour finir, ma thèse n’aurait pas pu trouver de meilleure conclusion que lors de l’apéritif qui a suivi ma soutenance, qu’ils ont si généreusement organisé. Aux dires de tous,
ACKNOWLEDGEMENTS v il était délicieux, et à mon avis, il était parfait.
Finally, thanks to Jorge, for making me laugh, for always cheering me up in the moments of doubt, and for his support through all these years. Words can’t tell.
Contents
Acknowledgements iii
Abstract xi
Résumé xiii
1 Introduction 1
2 Experimental Techniques 7
2.1 Laser sources . . . 7
2.1.1 Femtosecond oscillator . . . 7
2.1.2 Femtosecond amplified system . . . 8
2.2 Ultrafast laser pulse characterization . . . 8
2.2.1 Temporal characterization . . . 9
2.2.2 Phase characterization . . . 11
2.3 Pulse shaping . . . 13
2.3.1 4f-pulse shapers . . . 14
2.3.2 Acousto-optic programmable dispersive filters . . . 20
2.4 Pulse-shaping experimental implementation . . . 25
2.4.1 Open-loop approach . . . 25
2.4.2 Closed-loop approach . . . 26
2.5 Experimental set-ups . . . 29
2.5.1 Oscillator-based experiments . . . 29
2.5.2 Amplified chain-based experiments . . . 29
2.6 Sample preparation and handling . . . 32
2.7 Flow cells and pump . . . 33
3 Multiobjective Optimal Control 37 3.1 Motivation . . . 37
3.2 Flavin mononucleotide . . . 39
3.3 Multiobjective GA . . . 40 vii
viii ACKNOWLEDGEMENTS
3.4 Experimental set-up . . . 42
3.5 Results . . . 43
3.5.1 Evolution . . . 44
3.5.2 Outcome . . . 47
3.5.3 Physical explanation . . . 48
3.6 Conculsions and outlook . . . 50
4 Development of a Commercial MEMS-based Pulse Shaper in the Deep Ultraviolet 53 4.1 Motivation . . . 53
4.2 Experimental set-up . . . 55
4.3 Synchronization scheme . . . 57
4.3.1 MEMS duty cycle . . . 57
4.3.2 Detection . . . 57
4.4 Optical characterization . . . 59
4.4.1 Compression of a chirped pulse . . . 59
4.4.2 Phase shifts . . . 62
4.5 Discussion . . . 68
4.5.1 Technical remarks. . . 68
4.5.2 Development of a new MEMS device . . . 71
4.6 Conclusions . . . 77
5 Assessing a Control Strategy on Adenine 79 5.1 Motivation . . . 79
5.1.1 Biological relevance of adenine . . . 79
5.1.2 Optical properties of adenine . . . 82
5.1.3 Issues about adenine fluorescence . . . 82
5.1.4 Numerical studies on adenine . . . 84
5.2 Simulations . . . 85
5.2.1 Intrapulse control: strong field regime. . . 86
5.2.2 Pump-probe approach . . . 88
5.3 Experimental set-up . . . 92
5.4 Experimental results . . . 94
5.4.1 Excitation in the strong field regime . . . 94
5.4.2 Pump-probe approach . . . 98
5.5 Discussion . . . 100
5.6 Conclusion . . . 102
6 Optimal Dynamic Discrimination of Amino-Acids 103 6.1 Introduction . . . 103
6.1.1 Approach . . . 103
ACKNOWLEDGEMENTS ix
6.1.2 Target molecules . . . 105
6.2 Experimental . . . 108
6.2.1 Definition of the depletion ratio . . . 111
6.2.2 Objective definition and optimization parameters . . . 111
6.3 Results . . . 112
6.3.1 Preliminary measurements . . . 113
6.3.2 Signal stability and convergence criteria . . . 116
6.3.3 Optimizations leading to non-discriminating solutions . 119 6.3.4 Optimizations leading to discriminating solutions . . . 126
6.3.5 Discrimination mechanism . . . 129
6.4 Discussion . . . 131
6.5 Conclusions and Outlook . . . 133
7 Time-resolved Fluorescence Depletion of Tryptophan and Alanyl- tryptophan 135 7.1 Motivation . . . 135
7.1.1 Photophysics of Trp and Ala-Trp . . . 136
7.1.2 Solvents used in this work . . . 137
7.2 Experimental . . . 138
7.3 Results . . . 140
7.3.1 Steady spectroscopy . . . 140
7.3.2 Time-resolved fluorescence spectroscopy . . . 142
7.4 Discussion . . . 146
7.5 Conclusion . . . 150
8 Conclusions and Outlook 153
A ODD: Successful Two-Objective Optimization 159
Bibliography 163
Abstract
The present work is part of a general effort in our research group for develop- ing new all-optical tools for detection and identification of biomolecules for biomedical applications, selective imaging, or air pollution monitoring.
We first addressed several essential aspects of femtosecond optimal control of biological chromophores in the liquid phase. A new multi-objective genetic algorithm was applied to the closed-loop optimization of multiphoton-excited fluorescence and we demonstrated its advantages with respect to conventional single-objective genetic algorithms. The multi-objective algorithm gives ac- cess to primary information for unraveling the relationship between pulse spectral field features and sample photodynamics.
We implemented a commercial micro-mirror device to direct temporal shaping of broadband femtosecond pulses. We demonstrated phase shaping of deep ultraviolet pulses and described the electronic and optical limitations of this device, setting the basis for the design of a new dedicated device for broadband pulse shaping.
We described the development of an experimental control strategy to enhance the fluorescence of a DNA base by direct shaping in the deep ul- traviolet, based on molecular dynamics simulations. This experiment is a case study for future quantum control experiments, as it puts into light new challenges raised by control of deep ultraviolet pulses in the liquid phase.
Furthermore, we extended to the deep ultraviolet the Optimal Dynamic Discrimination technique, an optimal control strategy designed for discrim- ination of complex biomolecules. We demonstrated discrimination of two amino-acids, opening interesting perspectives for future experiments involv- ing biomolecules of increasing complexity, namely polypeptides and proteins, eventually in a cellular environment.
Finally, a comparative study on the pump-probe fluorescence spectroscopy of an amino-acid and a dipeptide, carried out in different solvents, is pre- sented.
xi
Résumé
Cette thèse s’inscrit dans un effort, au sein de notre groupe, pour le développe- ment de nouvelles techniques de détection et d’identification d’organismes biologiques pour des applications biomédicales, en imagerie, ou en détection d’aérosols pathogènes.
Plusieurs aspects du contrôle optimal femtoseconde de chromophores bi- ologiques en phase liquide ont été abordés. Un nouvel algorithme multi- objectif a été employé pour l’optimisation en boucle fermée de la fluorescence multiphotonique, et nous avons décrit ses avantages par rapport à des algo- rithmes conventionnels à objectif unique. L’algorithme multi-objectif permet de relier les caractéristiques spectrales de l’impulsion à la photodynamique de l’échantillon.
Nous avons utilisé un dispositif commercial composé de micro-miroirs pour le façonnage temporel direct d’impulsions large bande femtoseconde.
Nous avons réalisé un façonnage en phase d’impulsions dans l’ultraviolet profond et décrit les limitations électroniques et optiques de ce dispositif.
Ceci a permis de concevoir un nouveau dispositif exclusivement dédié au façonnage d’impulsions large bande.
Nous avons également décrit le développement d’une stratégie de contrôle pour l’augmentation de la fluorescence d’une base de l’ADN par façonnage direct dans l’ultraviolet profond, basée sur des simulations de dynamique moléculaire. Cette expérience met en lumière de nouveaux défis soulevés par le contrôle dans l’ultraviolet profond en phase liquide et constitue un cas d’étude dans le domaine du contrôle quantique.
De plus, nous avons étendu à l’ultraviolet profond la technique de dis- crimination dynamique optimale, une stratégie de contrôle optimal conçue pour la discrimination de molécules biologiques complexes. La discrimination de deux acides aminés a ainsi été réalisée. Ce résultat permet d’envisager l’application de cette technique à des molécules biologiques plus complexes, comme des polypeptides et des protéines, également en environnement cel- lulaire.
xiii
xiv RÉSUMÉ Finalement, nous avons étudié par spectroscopie pompe-sonde de fluores- cence un acide aminé et un dipeptide, en solution dans différents solvants.
CHAPTER 1
Introduction
One of the first examples of manipulation of chemical reactions by light came with flash photolysis in the late 1940’s. It allowed Eigen, Norrish and Porter to be jointly awarded the Nobel Prize of Chemistry in 1967, "for their studies of extremely fast chemical reactions, effected by disturbing the equilibrium by means of very short pulses of energy" [1]. With the invention of laser in the 1960’s [2], a wealth of new possibilities in photocontrol of chemical reactions became possible.
The initial idea focused on the use of infrared narrowband lasers to excite the vibrational mode of a particular molecular bond, with the aim of selec- tively breaking it [3]. This so-called "mode selective chemistry", however, was unsuccessful, as the molecule experienced rapid internal vibrational re- distribution: the coupling between the different vibrational modes lead to a rapid redistribution of the energy deposited. Selectivity was lost and the result was simply a higher rovibrational temperature in the molecule [4, 5].
With the advent of the mode-locking technique, picosecond laser pulses became available in the 1960’s, while femtosecond pulses were obtained in the 1980’s. With these new lasers, the vibrational and relaxation dynamics of molecules could be accessed with unprecedented time resolution. The fields of femtosecond spectroscopy and femtochemistry developed rapidly, and their achievements were crowned by the Nobel Prize of Chemistry in 1999 awarded to A. Zewail [6]. Particularly, the femtosecond pump-probe technique has become today a standard method for observing the intramolecular motions in real time. It makes use of two ultrashort laser pulses separated by a variable time delay. Numerous results have been obtained using this technique, both in gas phase and liquid phase [7, 8, 9, 10]. Figure 1.1 shows the paradigm
1
2 CHAPTER 1. INTRODUCTION
case of the NaI reaction [11].
!"#$"%&
!"#$%&'"#()$*+ ,-)$. ,*")"/$. -/0 !1$1*"
!"#$%& '($)& *"+& ,-&!"""../. 2345 6 2578 2593
'(:';(:'$ $'" $'"%*"$(&-; 0"<";%=#"/$) )(/&" $'"/> ?'" @AB
*")1;$) 0"#%/)$*-$"0 $'" "C="*(#"/$-; %D)"*<-$(%/ %E F-<"
=-&G"$) (/ #%;"&1;-* )+)$"#). -/0 )(/&" $'"/ $'"+ '-<" D""/
)+/$'")(H"0 (/ -$%#). &%#=;"C #%;"&1;"). -/0 D(%;%:(&-;
)+)$"#). -) F";; -) (/ $'" 0(EE"*"/$ ='-)") %E :-)"). ;(I1(0).
&;1)$"*). -/0 )%;(0)> ?'" D"'-<(%* %D)"*<"0 E%* @AB F-) E%1/0 (/ %$'"* )$10("). $'" #%)$ *"&"/$ () -/ ";":-/$ )"*(") %E
"C="*(#"/$) %E JD1DD;") (/ )%;(0)K D+ L-M"0 A'"*:1(N) :*%1=
(/ O-1)-//">
?'" I1")$(%/ $'"/ F-)P Q%1;0 I1-/$1# &-;&1;-$(%/)
*"=*%01&" $'" "C="*(#"/$-; *")1;$) %D$-(/"0 E%* @ABR S-/
@#*". D"(/: )G"=$(&-; (/ $'" D":(//(/:. 0(0 $'" E(*)$ %E )1&'
&-;&1;-$(%/). -/0 $'" *")1;$) F"*" (#=%*$-/$ (/ )'%F(/: $'"
(/E;1"/&" %E $'" F-<" =-&G"$ #%$(%/ -/0 )=*"-0(/: %/ $'"
%D)"*<"0 !?T $*-/)("/$)> U%*(- L"$(1 -00*"))"0 $'" *%;" %E
*%$-$(%/)> Q" &%#=-*"0 $'" I1-/$1# *")1;$) F($' $'%)"
%D$-(/"0 E*%# $'" &;-))(&-; #%0"; %E V"*)%'/ -/0 W"F-(;
X)"" !(:1*" 8YZ> ?'" #%0"; 0")&*(D"0 $'" "C="*(#"/$-; $*"/0) I1($" F";;. M1)$ -) 0(0 $'" I1-/$1# =(&$1*"> ?'() F-) E%;;%F"0 D+ *"=%*$) %E $*-M"&$%*+ &-;&1;-$(%/) E*%# ["/$ Q(;)%/N) :*%1=
-/0 - 0"/)($+\#-$*(C 0")&*(=$(%/ E*%# T'-1; L1G-#";N) :*%1=> ?'" ;-$$"* "#='-)(H"0 $'" 0(EE"*"/$ ;(#($) %E 0"='-)(/:
-/0 $'" $(#" )&-;" E%* /1&;"-* #%$(%/> ];; $'"%*"$(&-; *")1;$)
"C'(D($"0 $'" :"/"*-; $*"/0) %D)"*<"0 "C="*(#"/$-;;+> @/ %1*
"-*;+ =-="*) %/ @AB. F" )1::")$"0 $'-$ $'"!\E1/&$(%/ ;(#($ %E F-<"\=-&G"$ 0+/-#(&) &%1;0 D" %D$-(/"0 (E =*%="* 0"&%/<%\
;1$(%/ F-) #-0". F'"/ $'" $"#=%*-; *")=%/)" %E $'" =1;)") () G/%F/> ^"*+ *"&"/$;+. ^%;G"* _/:"; -/0 B(";) U"/*(G)"/
*"=%*$"0 - I1-/$1# $'"%*"$(&-; -:*""#"/$ F($' $'() )(#=;"
=(&$1*" -/0 0()&1))"0 ($) :"/"*-;($+>
!"#"!" $%& '() *+,-./&012 3 4(0(5+67 8.0 9%& :+&;5
?'"*" F"*" $F% ())1") $'-$ /""0"0 $% D" ")$-D;()'"0 %/
E(*#"* D-)")P $'" ())1" %E $'" 1/&"*$-(/$+ =*(/&(=;" -/0 $'"
(/E;1"/&" %E #%*" &%#=;"C =%$"/$(-;) %/ $'" -D(;($+ %E $'"
$"&'/(I1" X!?TZ $% =*%D" *"-&$(%/)> ?'" *"-&$(%/) %E -;G-;(
'-;(0") F"*" $'%1:'$ %E -) ="*E"&$ =*%$%$+=")> T(/&" $'"+
(/<%;<" $F% =%$"/$(-;) X&%<-;"/$ -/0 (%/(&Z -;%/: $'" *"-&$(%/
&%%*0(/-$". @ $'%1:'$ F" F%1;0 '-<" E1/ F($' $'")" )+)$"#)>
L%*"%<"*. $'"(* 1/(I1" '()$%*(&-; =%)($(%/ (/ &*%))"0 #%;"&\
1;-* D"-# "C="*(#"/$) XJ$'" -;G-;( -:"KZ #-0" $'"# :%%0
&-/0(0-$") E%* $'" JE"#$% -:"K> ?'" *"-&$(%/ %E B-@. 1/;(G"
@AB. (/<%;<") $F% ";"&$*%/(& &%%*0(/-$") -/0 %/" /1&;"-*
&%%*0(/-$". $'" )"=-*-$(%/ D"$F""/ B- -/0 @> ?'" *")%/-/&"
#%$(%/ D"$F""/ &%<-;"/$ -/0 (%/(& &%/E(:1*-$(%/) () $'" G"+
$% $'" 0+/-#(&) %E D%/0 D*"-G-:"> U%F &%1;0 F" =*%D" )1&'
#%$(%/ (/ *"-; $(#"R Q" 0(0 $'" !?T "C="*(#"/$) %/ B-@ -/0 B-V*. -/0 $'" *")1;$). =1D;()'"0 (/ 8`44. F"*" $'*(;;(/:
X!(:1*" 83Z -/0 #-0" 1) E""; <"*+ &%/E(0"/$ -D%1$ $'" -D(;($+
%E !?T $% =*%D" $*-/)($(%/ )$-$") -/0 E(/-; E*-:#"/$)> ?'"
*")1;$) -;)% (;;1)$*-$"0 $'" (#=%*$-/&" %E &%'"*"/$ F-<"
=-&G"$) (/ I1-)(\D%1/0 )+)$"#)> ?'" B-@ "C="*(#"/$ F-) - F-$"*)'"0 "<"/$ ;"-0(/: $% -/ "/$(*";+ /"F =-*-0(:# (/
$'" E(";0 %E E"#$%&'"#()$*+ -/0 ")$-D;()'(/: )%#" /"F
&%/&"=$) E%* $'" 0+/-#(&) %E $'" &'"#(&-; D%/0. E%* )"<"*-;
*"-)%/)P
8> Q" &%1;0 )'%F "C="*(#"/$-;;+ $'-$ $'" F-<" =-&G"$ F-) '(:';+ ;%&-;(H"0 (/ )=-&" X-D%1$ 9>8 aZ. $'1) ")$-D;()'(/:
$'" &%/&"=$ %E 0+/-#(&) -$ -$%#(&\)&-;" *")%;1$(%/>
2> ?'" )=*"-0(/: %E $'" F-<" =-&G"$ F-) #(/(#-; 1= $% - E"F
=(&%)"&%/0). $'1) ")$-D;()'(/: $'" &%/&"=$ %E )(/:;"\#%;"\
&1;" $*-M"&$%*+. $'-$ (). $'" "/)"#D;" &%'"*"/&" () (/01&"0
"EE"&$(<";+. -) (E $'" #%;"&1;") -*" :;1"0 $%:"$'"*. "<"/
$'%1:' F" )$-*$ F($' - *-/0%# -/0 /%/&%'"*"/$ "/)"#\
D;"b$'() () $'" F%*;0 %E 0+/-#(&)."0+G(/"$(&)>
7> ^(D*-$(%/-; X*%$-$(%/-;Z &%'"*"/&" F-) %D)"*<"0 01*(/:
$'" "/$(*" &%1*)" %E $'" *"-&$(%/ XD+ $'" 0"$"&$(%/ %E
=*%01&$) %* $*-/)($(%/ )$-$")Z. $'1) ")$-D;()'(/: $'" &%/&"=$
%E &%'"*"/$ $*-M"&$%*(") (/ *"-&$(%/). E*%# *"-&$-/$) $%
=*%01&$)>
Y> c/ $'" E"#$%)"&%/0 $(#" )&-;". $'" 0")&*(=$(%/ %E $'"
0+/-#(&) E%;;%F) -/ (/$1($(<" &;-))(&-; =(&$1*" X#-*D;")
!(:1*" 83> !"#$%&'"#()$*+ %E $'" B-@ *"-&$(%/. $'" =-*-0(:# &-)"> ?'" "C="*(#"/$-; *")1;$) )'%F $'" *")%/-/&" #%$(%/ D"$F""/ $'" &%<-;"/$ -/0 (%/(&
)$*1&$1*") %E $'" D%/0. -) F";; -) $'" $(#" )&-;") E%* $'" *"-&$(%/ -/0 E%* $'" )=*"-0(/: %E $'" F-<" =-&G"$> ?F% $*-/)("/$) -*" )'%F/ E%* $'" -&$(<-$"0
&%#=;"C") (/ $'"(* $*-/)($(%/ )$-$") -/0 E%* $'" E(/-; E*-:#"/$)> B%$" $'" JI1-/$(H"0K D"'-<(%* %E $'" )(:/-;. F'(&' () /%$ )(#=;+ -/ "C=%/"/$(-; *()" %* 0"&-+
%E $'" "/)"#D;"> ?'" &;-))(&-; #%$(%/ () )(#1;-$"0 -) $*-M"&$%*(") (/ )=-&" -/0 $(#" X&"/$"*Z>d35. V8. VY. V82. V8Y. V8e. V8`. V24f
Figure 1.1: Femtosecond dynamics of dissociation of NaI reaction. Experi- mental observations of the wavepacket motion, made by the detection of the activated complexes NaI or the free Na atoms. From [11].
Beyond these time-resolved studies of molecular dynamics, quantum con- trol uses the properties of lasers to create a coherent superposition of molec- ular vibrational states on an electronic excited states to drive a quantum system along a specific path and to obtain a target result. Several important steps towards quantum control were made in the 1980’s, when the first theo- retical proposals appeared, soon confirmed by experimental demonstrations.
The most significant ones are the three methodologies described hereafter.
The first approach, proposed by Brumer and Shapiro, relies on two mono- chromatic lasers with tunable frequencies [12, 13]. Consider an initial state and two energetically degenerate final states |Ψi, |Ψ0i, coupled by a one photon or a three photons transition of frequencies 3ω and ω respectively (see Fig. 1.2 (a)). According to this scheme, if the phase difference between the two laser fields is varied, the probability amplitudes of the two reaction pathways (absorption of one or three photons) are also varied, between the limits of constructive and destructive interferences.
The second example is the Tannor-Koslov-Rice pump-dump approach (Fig. 1.2 (b)), in which many vibrational states of a molecule ABC are coherently excited by a first ultrashort laser pulse at t0 to generate a vibra- tional wavepacket [14]. This wavepacket explores, as a function of time, a large fraction of the electronically excited hypersurface. By firing a second
3
laser pulse at a convenient time t1 or t2, the molecule is brought back to its ground state but on different dissociation paths, resulting, respectively, in the species AB+C or A+BC. The system can thus be driven to a specific target by using the quantum control of the dissociation process.
Finally, the third scheme is known as stimulated Raman adiabatic pas- sage (STIRAP) [15,16]. Two time-delayed laser pulses typically of nanosec- ond duration are used to achieve complete population transfer in a three- state Λ-type quantum system (see Fig. 1.2 (c)).The pulse sequence used is counter-intuitive: the pump pulse, that couples the initial |1i state with the intermediate |2i state, is time-delayed with respect to the Stokes pulse, that couples state |2i and final state |3i. The electric fields are strong enough to generate many cycles of Rabi oscillations. It can be shown that the result is a total population transfer from state |1i to state |3i, with no dissipative population losses to state |di.
ψ' ψ ψ'
ω
ω 3ω
ω ABC
ABC‡
AB + C A + BC
t0 t1 t2
,
pump Stokes
1
d 2
ψ 3
) c ( )
b ( )
a (
time pump Stokes
Figure 1.2: Three typical one-parameter quantum control schemes. (a) Brumer-Shapiro two-pathway quantum interference control scheme. (b) Tannor-Kosloff-Rice pump-dump scheme. (c) STIRAP scheme. From [17].
These three methodologies illustrate some of the main ideas of quantum control and all rely on the variation of one parameter: the relative phase of two fields, or the time delay between two pulses. With the advent of fem- tosecond broadband pulses, these ideas have been generalized and refined, and a wealth of new control approaches have appeared. Among them, an- other "one-parameter" control scheme deserves to be mentioned. The control parameter is the linear chirp of the laser pulse, which corresponds to a lin- ear increase or decrease of the instantaneous frequency as a function of time under the pulse envelope. Pioneered by the work of Shank and coworkers,
4 CHAPTER 1. INTRODUCTION
numerous control experiments were achieved with linearly chirped femtosec- ond pulses, including control of vibrational wavepackets [18, 19], control of population transfer via "ladder-climbing" processes [20,21,22,23], or control of electronic excitation in molecules [24, 25,26]. In particular, for molecules with overlapping absorption and emission spectra, positively and negatively chirped pulses can be used to excite vibrational modes preferentially in the excited state or in the ground state, respectively [18, 19] (see Fig. 1.3).
Figure 1.3: Schematic of the time-dependent resonant Raman process lead- ing to ground state wavepacket oscillations, along with the frequency com- ponents as a function of time for a negatively chirped pulse. From [18].
Due to their success and the ease of producing them, linearly chirped laser pulses are widely used in quantum control. However, complex physical and chemical systems may require more sophisticated shapes. Therefore, complex pulse shaping techniques have been developed. Ideally, finding the right pulse shape to drive a specific process would require to solve the time- dependent Schrödinger equation of the system, however, the Hamiltonian of the system usually cannot be calculated (Sect. 2.4.1). Further complications arise from the environment of the system and from technical constraints.
In 1992, H. Rabitz and coworkers introduced the concept of optimal con- trol, in their seminal paper "Teaching laser to control molecules" [27]. They proposed to use a search algorithm to optimize the laser pulse characteristics in a feedback loop configuration to reach most efficiently the desired target.
For this, a large number of parameters (for instance amplitude and phase of
5
each spectral component within the laser pulse) has to be controlled. Ex- cellent results in terms of efficiency have been obtained using genetic-type optimization algorithms (Sect. 2.4.2). Figure 1.4 shows a schematic of the experimental set-up, as well as the evolution of an optimization of one of the first reported closed-loop quantum control experiments [28, 29].
Figure 1.4: Left: Schematic of the pulse shaping feedback apparatus.
Right: Convergence of the genetic algorithm. From [28].
Optimal control can been applied to a wealth of experiments. Excellent reviews have been published on the subject [17, 30, 31, 32]. The targets to optimize can be specific dissociation products, but also the enhancement or reduction of fluorescence of a specific molecule (by driving it preferen- tially into other relaxation pathways). In this regard, a pioneering work was performed by the group of G. Gerber, in which they could demonstrate the capability of distinguishing two dyes using coherent control, although the dyes had very similar absorption and fluorescence characteristics [33].
G. Gerber’s experiment opened new perspectives for distinguishing similar types of molecules. This experiment was followed by other developments of optimal control-based strategies for distinguishing molecules [34], and in particular biological molecules, leading to Optimal Dynamic Discrimination (ODD) [35], a powerful discrimination technique, recently demonstrated ex- perimentally [36].
This work addresses several aspects of femtosecond optimal control of bi- ological chromophores in the liquid phase in the deep UV. Furthermore, it presents the extension to the deep UV of the ODD approach, applied to
6 CHAPTER 1. INTRODUCTION discrimination of two amino-acids. This is the first step of an approach that we aim to generalize in the future to systems of increasing complexity, from polypeptides or proteins, to cells or harmful organisms like bacteria [37, 38, 39].
In Chap. 2 we describe the instruments and techniques used, as well as the experimental schemes specifically developed during this work.
Chapter 3describes the implementation of a multiobjective genetic algo- rithm for closed-loop control. To evaluate its performances, we have applied this algorithm to the closed-loop optimization of multiphoton-excited fluo- rescence of a biological chromophore and compared its performances to a single-objective genetic algorithm, commonly used in the majority of the closed-loop control experiments.
In Chap. 4 we describe the development of a MEMS-based all-reflective pulse shaping device in the deep ultraviolet (266 nm). Reliable pulse shapers are needed in this wavelength region for direct control of biological chro- mophores, since most of these molecules absorb in this wavelength region.
We characterize the device in this wavelength region and demonstrate its phase shaping capabilities. We address a series of technical details related to its operation and synchronization with the experimental set-up and dis- cuss its limitations. We also give an overview of the progresses done in our research group in UV pulse shaping since these experiments were done.
There is a strong interest for understanding the non-radiative deexcitation mechanisms that lead to high photostability of DNA bases. Fluorescence is an interesting observable for understanding the excited-state dynamics of nucleic acids. Chapter 5 describes therefore the development of an experimental strategy, based on numerical simulations, to enhance the fluorescence of the DNA base adenine, as well as its results.
In Chap. 6 we describe the extension to the deep ultraviolet of the ODD approach for discrimination of the two amino-acids tryptophan and tyro- sine. We describe unsuccessful and successful optimizations to understand the criteria needed for good convergence of the optimizations and attempt to identify the mechanism that leads to discrimination.
With the aim of further understanding the mechanisms that allow dis- crimination in Chap. 6, a better understanding of the excited-state dynamics of the molecules is needed. In Chap. 7 we report on preliminary results on the time-resolved fluorescence depletion of the amino-acid tryptophan and the dipeptide alanyltryptophan in different solvents.
Chapter 8 summarizes the main findings of this work and describes pos- sible future developments.
CHAPTER 2
Experimental Techniques
2.1 Laser sources
Two different laser sources were used during this work. The first one is a femtosecond oscillator, and was used for the multiobjective optimal control experiment described in Chap. 3. The second one, a femtosecond amplified system, was used for the rest of the experiments.
2.1.1 Femtosecond oscillator
The femtosecond oscillator we used was a Kapteyn-Murnane (KM) Chi- nook. Lasing was achieved by a Titanium:Sapphire (Ti:Sa) crystal, pumped by a532 nmfrequency-doubledNd : YVO4 1 laser (Millenia,Spectra Phy- sics) operating at5 W. Pulsed regime was allowed by Kerr lens mode-locking in the Ti:Sa crystal rod. Group velocity dispersion was compensated by an intracavity prism compressor that also allowed, in combination with a slit set between the second prism and the 100% reflective end cavity mirror, to tune the spectral bandwidth of the pulses to a certain extent. The main characteristics of this oscillator are summarized in Tab. 2.1.
1Nd : YVO4: Neodymium-doped Yttrium Orthovanadate. Nd:YLF: Neodymium- doped Yttrium Lithium Fluoride.
7
8 CHAPTER 2. EXPERIMENTAL TECHNIQUES Pulse duration 25 fs
Central wavelength 790 nm
Bandwidth (FWHM) 45 nm
Energy per pulse 5 nJ Repetition rate 80 MHz
Beam size (FWHM) 2 mm
Polarization linear, horizontal
Table 2.1: Main characteristics of the KM Chinook oscillator. FWHM: Full width at half-maximum.
2.1.2 Femtosecond amplified system
The major part of the experiments was done with a Coherent amplified laser system. The seed in this case is also provided by a KM Chinook os- cillator, pumped by a 532 nm frequency-doubled Nd : YVO41 diode laser (Verdi, Coherent) usually operating at 5 W. The resulting infrared (IR) pulses have typically an energy of 4 nJ, which is not enough to produce most of the optical nonlinear processes needed. Therefore, the pulses are used as a seeding for a regenerative amplifier (Hidra,Coherent), based on the chirped pulse amplification technique. Before being amplified, the pulses are first temporally stretched to a few hundreds of picoseconds in order to lower the peak power and avoid damaging of the optics during the amplifi- cation process. They are subsequently amplified in a regenerative cavity by passing repeatedly through a Ti:Sa crystal, itself pumped by a Nd : YLF1 Q-switched diode laser (Evolution, Coherent) operating at 20 W. The in- jection and ejection of the pulses into the regenerative cavity are controlled by two Pockels cells, synchronized by the MHz signal from the KM oscillator.
The amplified pulses are finally temporally recompressed by a grating com- pressor, that compensates exactly for the linear chirp of the stretcher and for the second-order dispersion in the amplifier. They exit the system with an energy 106 higher than at the oscillator output, and a repetition rate of 1 kHz, set by the repetition rate of the Evolution. A summary of the main characteristics of the pulses at the amplifier output is presented in Tab. 2.2.
2.2 Ultrafast laser pulse characterization
Together with the advent of pulsed laser sources, the problem of character- izing ultrashort laser pulses appeared. Light pulses are orders of magnitude
2.2. ULTRAFAST LASER PULSE CHARACTERIZATION 9 faster than any electronic device available nowadays. Therefore, no direct characterization is possible, although some experiments toward this goal ex- ist [40]. Numerous indirect characterization methods for extracting the am- plitude E(t), the temporal phase ψ(t) and the spectral phase φ(ω) of the pulses have therefore been developed.
We will briefly describe hereafter the characterization techniques used in this work, beginning with the temporal characterization techniques (Sect.
2.2.1), that allow retrieval of the intensity profile of the pulse I(t), which is proportional to the square of the amplitude of the electric field: I(t) ∝
|E2(t)|. In Sect. 2.2.2, we will describe two approaches that allow retrieval of the phase functions ψ(t) and φ(ω).
2.2.1 Temporal characterization
Autocorrelation
Autocorrelation is one of the most common techniques used for temporal pulse characterization. It is based on the temporal convolution of the test pulse with a reference, orgatepulse, in this case, a replica of the pulse itself.
As the intensity of the field I(t) is too fast to be directly measured, the problem is transposed in the spatial domain by means of an interferomet- ric apparatus. In an interferometric arrangement (for instance a Michelson interferometer) the optical path of one arm can be varied with respect to the other with great precision, giving the temporal resolution needed. As high-precision mechanical positioning devices can attain nanometric preci- sion, steps corresponding to 0.1 fs delay can be produced, and 800 nm pulses can be resolved with sub-cycle resolution.
A non-linear medium, sensitive to the intensity of the field, is then needed to generate a signal proportional to the overlap of the two pulses. Usually,
Pulse duration 35 fs Central wavelength 795 nm
Bandwidth (FWHM) 27 nm
Energy per pulse 2 mJ Repetiton rate 1 kHz Beam size (FWHM) 12 mm
Polarization linear, horizontal
Table 2.2: Principal characteristics of our Hidra regenerative amplifier.
FWHM: Full width at half-maximum.
10 CHAPTER 2. EXPERIMENTAL TECHNIQUES
a nonlinear birefringent crystal like a beta Barium Borate crystal (BBO), is chosen. In fact the second harmonic generated inside the crystal has three contributions, the upconversion of the replicaE(t) and E(t−τ) with them- selves, and the cross-term between both replica:
E2(t, τ)∝E(t)·E(t−τ) (2.1) Experimentally, the two replica can be focused and spatially overlapped into the crystal in a collinear or a non-collinear geometry. If the beams are non- collinear, one can spatially filter the unwanted contributions, so that the only contribution impinging on the photodetector is the cross-termE2(t, τ) (Fig.
2.1). One then obtains a background-free intensimetric autocorrelation.
The photodetector is assumed to be slow with respect to the pulse dura- tion, so that the signal it provides is proportional to the intensity profile of E2(t, τ):
SAC(τ)∝ Z ∞
−∞
|E2(t, τ)|2dt∝ Z ∞
−∞
I(t)·I(t−τ)dt (2.2)
BS
DL
PMT E(t) χ
E(t-τ)
Slit E (t-τ)2
(2)
Figure 2.1: Schematic view of an autocorrelation set-up, in non-collinear configuration. BS: beam splitter. χ(2): the non-linear medium chosen is a BBO crystal. PMT: photomultiplier tube. DL: delay line.
.
This autocorrelation gives therefore access to the autocorrelation function of the intensity envelope of the test pulse. Assuming a Gaussian profile of E(t), we have the following relation between the full width at half-maximum
2.2. ULTRAFAST LASER PULSE CHARACTERIZATION 11 (FWHM) ∆t of I(t) and the FWHM ∆τAC of SAC:
∆τ =√
2∆t (2.3)
Autocorrelation gives therefore a rapid access to the pulse duration, pro- vided that the pulse is "simple" enough (a gaussian profile is assumed). How- ever, autocorrelations are symmetric in time, therefore, there is a time am- biguity. For instance, pre-pulses cannot be distinguished from post-pulses without further measurements.
Cross-correlation
This time ambiguity of autocorrelations can be lifted by using the inten- simetric cross-correlation technique. This approach is similar to the auto- correlation, in the sense that it also involves convolution of two pulses in a non-linear crystal, but here the replica pulse is replaced by an ancillary pulse.
As the signal measured by the photodetector is the convolution of the test pulse with the reference pulse:
SXC(τ) = Z ∞
−∞
I(t)·Iref(t−τ)dt (2.4) the intensity profileI(t)of the test pulse can be retrieved, provided that the reference pulse duration is short enough. This method is thefore well-suited for complex pulse shapes. Another advantage is that gate and test pulses can be of different wavelengths.
Assuming gaussian profiles, the relation between the FWHM ∆t of I(t) and the FWHM ∆τXC of SXC is here:
∆τXC = q
(∆t2+ ∆t2ref) (2.5)
where ∆tref is the FWHM of the reference pulse.
2.2.2 Phase characterization
A widespread and efficient technique for retrieving amplitude as well as spec- tral phase of a pulse is Frequency-Resolved Optical Gating (FROG), devel- oped by R.Trebino [41]. The main idea in FROG is to temporally gate the test pulse (as in autocorrelation and cross-correlation), and to measure the spectrum of the gated pulse, as a function of the time delay τ. This gives a signal:
S(ω, τ)∝
Z ∞
−∞
E(t)Eref(t−τ)eiωtdt
2
(2.6)
12 CHAPTER 2. EXPERIMENTAL TECHNIQUES
A 2D map of the pulse is obtained, whose axes are time and frequency.
Various implementations of FROG exist, depending on the gate used.
SHG FROG
In this case, the gate used is a replica of the test pulse. The signal measured is therefore:
S(ω, τ)∝
Z ∞
−∞
E(t)E(t−τ)eiωtdt
2
(2.7) The optical set-up is identical to the one for autocorrelation, except that the photodetector is replaced by a spectrometer. An alternative to the spec- trometer is to use a thick BBO crystal, mounted on a rotation stage. Given the phase-matching condition, if the crystal is thick enough, each spectral component of the second harmonic signal generated (SHG) will propagate in a specific direction. By rotating the crystal, one can tune the wavelength to be detected. Therefore, rotating the crystal allows to retrieve the whole spec- trum of the SHG signal. Although giving spectral information, SHG FROG, suffers, like autocorrelation, from time ambiguity, given that the traces are symmetric.
X-FROG
In this case, the gate used is an ancillary short pulse. X-FROG is a frequency- resolved cross-correlation and therefore presents the same advantages as cross-correlations measurements. Its signal has the form:
S(ω, τ)∝
Z ∞
−∞
E(t)Eref(t−τ)eiωtdt
2
(2.8) Experimentally, the optical set-up is identical to the one for cross-correlation, but the photodetector is replaced by a spectrometer.
During this work, IR pulses were characterized by autocorrelation and FROG with an commercial device (APE Pulse Check), whereas ultravio- let (UV) pulses (266 nm central wavelength) were characterized by cross- correlation and X-FROG. The optical set-up built for that purpose is shown in Fig. 2.2. The UV pulse, whose shape might be complex due to phase and amplitude shaping, is gated by an IR pulse. They are mixed in a BBO crys- tal cut for difference-frequency mixing (DFM) and the resulting signal (400 nm) is either collected by a photodiode for cross-correlation measurement,
2.3. PULSE SHAPING 13
arrayCCD
Gr
BBO BG40
E (t-τ) E(t)
ref
E (t-τ)2
PD
MM
Figure 2.2: Schematic view of the cross-correlation and XFROG set-up.
BBO: BBO crystal for DFM. MM: movable mirror. BG40: Schott glass for IR filtering. PD: photodiode. Gr: grating.
or spectrally resolved by a diffraction grating on a CCD array for X-FROG measurement.
FROG and X-FROG inversions, for retrieval of the amplitude and spec- tral phase of the tested pulses, were performed with the commercially avail- able FROG3 software.
2.3 Pulse shaping
Pulse shaping consists in modifying the amplitude, phase, polarization, or even transverse spatial profile of laser pulses. Since picosecond lasers became available in the late 60, many efforts have been devoted to generation, shaping and characterization of ultrashort laser pulses, and nowadays a wealth of pulse shaping techniques exist [42,43]. Due to their very short duration, laser pulses are not likely to be shaped easily in the temporal domain, as electronic devices are not fast enough. Thus, the vast majority of the temporal pulse shaping techniques act in the spectral domain.
In this section we will describe the pulse shaping techniques used during this work. For each technique, we will give a brief theoretical overview, followed by a description of the optical device used.
14 CHAPTER 2. EXPERIMENTAL TECHNIQUES
2.3.1 4f -pulse shapers
The first technique presented here is a well-known and characterized tech- nique [42, 43, 44, 45], based on a zero-dispersion compressor, also known as 4f-line.
As shown in Fig. 2.3, the compressor consists of a pair of gratings and cylindrical lenses arranged around a symmetry plane, the so-called Fourier plane. Each element is equally spaced by a distance f, corresponding to the focal length of the lenses. The first grating angularly separates the different spectral components of the pulse. After the first cylindrical lens, the spec- tral components are propagating in parallel and are focused onto the Fourier plane. The lens and grating on the right part of the set-up act inversely, recombining the spectral components of the outgoing pulses. In this configu- ration, the outgoing pulse has the same characteristics as the incoming pulse, hence the namezero-dispersion compressor. In mathematical terms, the first grating operates a temporal Fourier Transform on the pulse (from the time to the frequency domain), and the lens does a spatial Fourier Transform.
The second part of the set-up will carry out the inverse Transforms.
Pulse shaping can then be achieved if a spatial light modulator (SLM) is added at the Fourier plane of this set-up. SLM can be of various types: fixed phase and amplitude masks, liquid crystal masks, acousto-optic deflectors, movable and deformable mirrors, etc.
f f f f
TFT TFTSFT SFTSLM
grating grating
Figure 2.3: Scheme of a 4f-SLM. TFT: Temporal Fourier Transform, SFT:
Spatial Fourier Transform, f: focal length of the lenses. Adapted from [46]
.
2.3. PULSE SHAPING 15
Theoretical description We present hereafter some equations that de- scribe the shaping capabilities of a4f-pulse shaper.
Consider a pulse with a Gaussian distribution in time, frequency and space, with central frequency ω0 (central wavelength λ0). Its spectral band- width is described by the FWHM of the spectral intensity∆ω and its spatial width ∆x by the FWHM of the spatial intensity. It can be derived from Gaussian beam propagation that the FWHM of the spot size at the Fourier plane ∆x0 is:
∆x0 = 2 ln 2cosθi cosθd
f λ0
π∆x (2.9)
where θi is the incident angle, θd is the diffracted angle and f is the focal length of the lenses. If we assume linear dispersion, the spatial coordinate Xk of a frequency ωk at the Fourier plane of the shaper will be:
Xk=αωk = λ20f
2πcdcosθdωk (2.10)
where c is the velocity of light and d is the grating period. The term α depends entirely on the 4f-line geometry.
A crucial quantity is the frequency resolution, which can be written as:
δω = ∆x0/α (2.11)
This corresponds to a shaping time window T: T = 4 ln 2
δω (2.12)
The time window gives the upper temporal bounds for shaping achievable with such a shaper. The shortest feature achievable is in turn given by the inverse of the spectral bandwidth ∆ω.
During this work, we used two kinds of SLM in a 4f configuration: a liquid crystal display (LCD) and an array of movable micromirrors, or Micro- Electro-Mechanical System (MEMS) mirrors. Both are described hereafter.
LCD SLM
A LCD modulator is an array of pixels, each of them being a programmable waveplate controlled by voltage. More precisely, each pixel is made of a thin layer of nematic liquid birefringent crystals placed between two glass plates, to which electrodes are attached. In the absence of applied voltage, the
16 CHAPTER 2. EXPERIMENTAL TECHNIQUES
z y
x
Propagation direction
U = 0 U > 0
1 2 3 N
h
d d d
g g
z y
x
Figure 2.4: Left: Front view of the structure of a LCD. The LCD is an array of N pixels, each of size d×h (d being the width and h the height), separated by a gap g. Right: Side view. The molecules orientation change after application of an electric field. Light propagates in the z direction.
Adapted from [47].
.
molecules of the crystals are aligned parallel to the glass substrates. When a voltage is applied, the orientation of the molecules varies proportionally to the intensity of the electric field (Fig. 2.4). This induces a change in the refraction index, and thus, a change of the optical path for the light traveling through the crystal. To achieve phase and amplitude shaping, two liquid crystal displays are needed. They are placed between two horizontal polarizers, with the orientation of the nematic crystals at +45˚and -45˚with respect to the horizontal axis.
The IR pulse shaper used during this work consisted of two identical 1200 grooves/mm gold gratings, two f = 250 mm cylindrical lenses and a 128 pixels double LCD (CriSLM-256). The main characteristics of this LCD are summarized in Tab. 2.3.
Usually LCD shapers need to be calibrated, in order to determine the absolute phase φ(U, ω) applied to each spectral component ω, as a function of the voltage U. Although this operation assesses a critical importance when working in open-loop configurations, it can be avoided when working in a closed-loop configuration, provided that a shaped beam diagnostics is available (see Sect. 2.4.2 and Chap. 3).
2.3. PULSE SHAPING 17 Masks Pixel number N Pixel size d×h Gap size g
2 128 97µm×2 mm 3µm
Table 2.3: Main characteristics of the LCD used during this work.
MEMS-based SLM
In this case, the SLM is an array of movable micro-mirrors. The geometry of the4f-shaper is slightly modified: the dispersion-free compressor (Fig. 2.3) is folded at the Fourier plane by the MEMS (see Fig. 2.5). A small deflection is introduced by slightly tilting the MEMS in the direction perpendicular to the diffraction plane, in order to extract the output beam after the second passage on the grating. In terms of alignment, this geometry is very convenient because the grating and the lens making the Fourier Transforms also make the inverse Fourier Transforms; therefore the shaper is self-aligned [48].
TFT SFT
SLMgr ating
f f
Figure 2.5: 4f reflective pulse-shaper. The array of micro-mirrors (MEMS SLM) is placed at the Fourier plane of the set-up. Adapted from [46].
.
By the time we started our measurements, the only MEMS device avail- able partially fulfilling the requirements for temporal pulse shaping was the 2D MEMS phase-former kit from Fraunhofer IPMS [49]. Although this de-
18 CHAPTER 2. EXPERIMENTAL TECHNIQUES
vice was originally intended for wavefront correction, it had already been used for shaping of femtosecond pulses previously [50]. The characteristics of this device are reported in Tab. 2.4. As shown in Fig. 2.6 the mirrors are struc- tured on a device layer, and linked to the substrate by thin support posts.
Motion is generated by applying a voltage to an electrode placed under each micro-mirror and separated by a small air gap. Increasing the voltage on the electrode produces a deflection of the mirror into the air gap by the dipolar electrical forces. Modifying the optical path by moving the micro-mirrors of Pixel number N Pixel size d Gap size g Max. mirror displacement
200×240 40 µm×40µm 4.2 µm 450 nm Table 2.4: Main characteristics of the MEMS used during this work.
a quantity δz(ω) in the Fourier plane will result in a spectral phase modu- lation δφ(ω). For each frequency, the relation between mirror displacement and spectral phase modulation is given by:
δφ(ω) = 2ω
c δz(ω) = 4π
λ δz(ω) (2.13)
A more detailed description of the pulse shaper based on the MEMS device from Fraunhofer IPMS will be given in Chap. 4.
Advantages and limitations
4f-pulse shapers present some clear advantages in terms of high spectral resolution and high damage threshold. In addition to that, LCD-based 4f- pulse shapers are able to perform phase, amplitude, and polarization shaping.
They have been carefully used and characterized for the last decades, and nu- merous devices are commercially available. Their transparency range spans from the UV-visible to the IR, although devices capable of shaping in the UV are still rare and in an experimental stage [51]. MEMS-based 4f-pulse shapers, on the contrary, do not suffer from any limitation in terms of wave- length, provided that the appropriate reflective coating is used. On the other side, these4f-pulse shapers suffer from the limitations affecting all pixellated devices. The gaps between pixels diffract the beam, inducing losses and com- promising the beam spatial quality. Moreover, the discrete nature of pixels introduces a discretized transfer function in the frequency domain, that leads to pulse replica in the time domain.
2.3. PULSE SHAPING 19
piston element
support post
address electrode
Us
40 μm
40μm
z x y z
y x
z y
x
Figure 2.6: Fraunhofer MEMS SLM.Left: Scheme of one micromirror (top and side view). Right: Photograph of the array of micromirrors taken by Scanning Electron Microscopy (SEM). Adapted from [50].
.
20 CHAPTER 2. EXPERIMENTAL TECHNIQUES
2.3.2 Acousto-optic programmable dispersive filters
The second technique for temporal pulse shaping we present here is based on acousto-optic programmable dispersive filters (AOPDF). They allow phase and amplitude shaping in different spectral regions, from 200 nm to 2 µm.
Two AOPDFs were used during this work, both purchased from Fastlite (commercial name: Dazzler). The first one (hereafter named IR Dazzler) works in the near IR, from 700 to 900 nm, and the second one (hereafter namedUV Dazzler) works in the UV-visible, between 250 and 400 nm.
Theoretical description
The AOPDF differs from the 4f-pulse shapers described previously (Sect.
2.3.1). It is indeed based on the collinear interaction between an acoustic wave propagating in a highly birefringent crystal and the ultrashort optical
pulse. The interaction is similar to Bragg diffraction.J. Phys. B: At. Mol. Opt. Phys. 43 (2010) 103001 PhD Tutorial
z(ω)
Extraordinary (slow axis) Ordinary
(fast axis)
Figure 18. AOPDF principle: by diffraction on the acoustic grating through an acousto-optic interaction, the different spectral
components can be switched to the extraordinary axis at different positions in the crystal.
!
k
diff(ω
diff) = k !
ac(ω
ac) + k !
in(ω
in) (31)
ω
diff= ω
in+ ω
ac" ω
in(32)
where ‘diff’ denotes the diffracted optical beam, ‘in’ denotes the input optical beam and ‘ac’ denotes the acoustic wave.
This means that the spectral components can be switched to the extraordinary axis at different positions in the crystal, by changing the frequency ω
acalong the crystal. As the group velocities of the ordinary and extraordinary axis are different, one gets a different arrival time at the output of the crystal for each wavelengths. This time depends on the phase matching between the acoustic and the optical frequencies. Moreover the acoustic intensity at the switch location controls the amplitude of the diffracted spectral component.
The shape of the diffracted wave thus depends on both the switch position and the local acoustic intensity. One can write in the spectral domain
E ˜
diff(ω) ∝ E ˜
in(ω) · f (γ ω) (33) or equivalently in the time domain
E
diff(t ) ∝ E
in(t ) ⊗ f (t /γ ) (34) where the scaling factor γ = ω
ac/ω " (v
acδn)/c ( ∼ 10
−7in TeO
2). δn is the crystal optical anisotropy, v
acthe acoustic wave velocity. The factor γ allows the transfer of the acoustic waveform to the shape of the optical wave.
The shaping properties of the AOPDF have different origins from 4f -line shapers and have to be properly defined:
• As for the other pulse shapers, it is possible to define a time window in which it is possible to shape the pulse.
This window has a different physical origin than for a 4f - line and is mainly determined by the crystal thickness and its anisotropy. The shortest programmable delay is fixed by a complete propagation along the ordinary axis while the longest delay corresponds to a propagation along the extraordinary axis. The difference between both gives the maximum time window:
T
max= δn
gcos
2(θ
in) L
c (35)
where L is the length of the crystal and δn
gthe group index difference. For a 25 mm TeO
2crystal [100] this
gives T
max" 3 ps at 800 nm and for a 72 mm KDP crystal
T
max" 7 ps at 300 nm [101]. Usually a part of this
window is used to self-compensate for the dispersion due to the propagation in the acousto-optic crystal itself. This leads, in general, to an available time window of few ps.
• The resolution is given [102] by δλ = 0.8
δn cos
2(θ
in) λ
2L (36)
where θ
inis the angle between the incident wave vector and a reference crystallographic axis. The resolution is typically equal to 0.25 nm at 800 nm and down to 0.1 nm at 266 nm for commercially available devices.
• The number of control parameters, N
cp, is given by the number of resolution points in the programmed diffracted bandwidth. In the case of phase-only shaping, this bandwidth has to be broad enough to diffract all the optical components with a nearly constant amplitude.
Experimentally, it is set to three times the optical bandwidth, which gives
N
cp= &λ
δλ = δnL
0.8 cos
2θ
in3&λ
λ
2. (37)
For a 72 mm KDP crystal (θ
in= 48.5
◦, δn = 0.045 and
&λ = 3 nm at 410 nm) [101], this gives N
cp" 100 and around 400 in the IR [102].
• The efficiency depends on the phase matching, the length of the crystal, the merit factor of the crystal, the wavelength and finally the acoustic power. A detailed theoretical description can be found in [102].
Design and alignment. Taking into account the value of the scaling factor γ , the acoustic wave should have a frequency value around tens of MHz to allow the shaping of visible wavelength (hundreds of THz). The acoustic wave is a travelling wave synchronized with the optical wave. It is generated by a transducer glued on the crystal and monitored by a high frequency synthesizer (cf figure 19).
The crystal angle is chosen to give the best compromise between efficiency and resolution [102].
In practice, two experimental parameters are important:
• The alignment of the beam within the AOPDF has to be performed carefully. The beam has to enter the AOPDF horizontally, in the centre and normally to the inner face (auto-collimation). The best resolution is achieved when the beam is carefully collimated. The fine angular alignment of the device is made by shaping the diffracted optical beam with a thin hole in amplitude and looking at its spectrum. The corresponding spectrogram will present a hole which can be spectrally shifted by rotating the AOPDF. Once the hole is at the same wavelength as the programmed one, the phase matching condition is fulfilled and the AOPDF aligned.
• Due to the difference of speed in the crystal, the acoustic wave is seen frozen by the optical one. However, it is a travelling wave and it has to be precisely synchronized with the optical wave. To avoid any spectral clipping, the acoustic wave should be centred in the crystal when the optical waves enter in it.
14 Figure 2.7: Scheme of the the principle of the Dazzler. Adapted from [45].
.
The acoustic wave travels along the z axis of the crystal (see Fig. 2.7) with a velocity v << c, where c is the velocity of light. It thus reproduces spatially the temporal shape of the acoustic signal, creating a longitudinal transient grating that will be seen as static by the optical pulse.
The optical pulse travels initially along the ordinary (fast) axis of the crystal. The different spectral components will be diffracted on the extraor-
2.3. PULSE SHAPING 21 dinary (slow) axis when the wave vectors and frequencies satisfy two condi- tions, phase-matching:
~kout(ωout) =~kac(ωac) +~kin(ωin) (2.14) and energy conservation:
ωout =ωac+ωin (2.15)
where in denotes the incoming pulse, out the outgoing diffracted pulse, and ac the acoustic wave. As the index of refraction of the extraordinary axis is different from the ordinary axis, the positionz(ω)inside the crystal at which the frequency is diffracted will determine the time delay between the different spectral components. Phase shaping is achieved that way. The amplitude of the diffracted frequency can also be controlled by varying the amplitude of the acoustic wave. It can be shown [52] that, for low values of acoustic power density, the relation between the amplitude of the optical signal E(t) and the acoustic wave S(t)can be written as:
Eout(t)∝Ein(t)⊗S(t/α) (2.16) with
α= ∆nv c
being the scaling factor and ∆n =ne−no the index of refraction difference between extraordinary and ordinary axes. In the frequency domain, this relation becomes:
Eeout(ω)∝Eein(ω)·S(αω) (2.17) As for the other pulse shapers, the time window can be calculated, but in the case of the AOPDF it will depend on the crystal length and its anisotropy. The maximum time window T is given by the difference be- tween the longest programmable delay (propagation along the extraordinary axis) and the shortest programmable delay (propagation along the ordinary axis):
T = ∆ncos2(θin)L
c (2.18)
whereθin s the angle between the incident wave vector and a reference crys- tallographic axis and L is the crystal length. It should however be noted that a part of this window is used to compensate the delay induced by the crystal itself, thus reducing the available temporal window for the optical pulse. Spectral resolution is given by [53]:
δλ= 0.8
∆ncos2(θin) λ2
L (2.19)
