Investigation of laser pulse propagation in a three level atomic medium in the presence of eit effect

By increasing the pulse area of the coupling laserpulse weobtain a stable propagation pulse.. When the area of the laser pulseissmallΩc0τ0≤2,5,asshowninFigures2.2aand2.2b,thelaserpulseis

Specialty:Optics Code:62.44.01.09

ASUMMARYOFPHYSICALDOCTORALTHESIS

NGHEAN,2017

Supervisors:Prof.Dr.DinhXuanKhoa

Reviewer1:Prof.Dr.NguyenQuangBau

Reviewer2:Assoc.Prof.DrChuDinhThuy

Reviewer3:Assoc.Prof.DrTranHongNhung

Thethesiswillbepresentedatschool-levelevaluatingCouncilat:

…… ….h…………,date…………month… year2017

Thethesiscanbefoundat:NationallibraryofVietnamorNguyenTh

ucHaoinformationandlibrarycenter,Vinhuniversity

INTRODUCTION

In the past decades, the topic of laser pulses propagationwithoutdistortion (soliton) has been attracted much research attention ofscientistsbecauseoftheirpotentialapplicationsinopticalinformationanddataprocessing.Infact,whenthelightpulsepropagatesint h e r e s o n a n t medium,due to the absorption and dispersion that lead to reduction anddistortion ofthe signal pulse Therefore, to obtain pulse stability, weoftenuseultrashortpulseswithhighintensity.Moreover,mosto f t h e applications in modern photonic devices often require low-intensity lightwith highsensitivity Therefore, reducing the absorption in the resonancedomain is

an excellent solution to reduce the intensity of light pulse andincreasetheoperatingefficiencyof photonicdevices

Currently,aninterestingsolutionisusedtoreduceabsorptioniselectromagnetici n d u c t i o n t r a n s p a r e n c y ( E I T ) e f f e c t T h e b a s i s o f E I T i stheresultofquantuminterferencebetweentheprobabilitya m p l i t u d e s withintheatomicsystemwhichisinducedbylaserfields.UsingEITtechnique, some researchgroups have obtained stable laser pulses (soliton)in EIT medium Most recently, T Nakajimaand coworkers studied thepropagation of two short laser pulse trains in a

lambda-typeatomicmediumunderEITconditions.Theyobtainedlaserpulsespropagatin

g EIT medium without distortion in picosecond domain.Theinitial studies

of pulse propagation inEIT mediumo f t e n i g n o r e t h e

e f f e c t ofDopplerbroadening.Thiscan onlybesuitableforcoldatomicmediumor ultra-short laser pulses Moreover, many applications such as opticalcommunicationsthat require working with long laser pulses in nano ormicro-seconddomain

In addition to quantum interference effects of the shiftprobabilityamplitude,thereisaquantuminterferenceeffectoccursbetweenspontaneous emission channels by the non-orthogonal orientation of theelectricdipole moment is induced by two laser fields This interferencewillcreateacoherentofatomsiscalledthecoherenceisgeneratedbyspontaneousemission(spontaneouslyGeneratedCoherence-SGC).Experimentally, SGC effects wereobserved for the first time by Xia and etal 1996 in molecular sodium The presence of theSGC makes the mediumbecome more transparent and narrower the linewidth; larger and steeperdispersion Furthermore, the results also show thatthe effect of SGC makesan asymmetric medium so that the response of themedium is very sensitivetothephaseoflaserfields

Sofar,theinfluencesofSGCandrelativephaseontheopticalpropertieso f t

h e E I T m e d i u m u n d e r s t e a d y - s t a t e r e g i m e h a v e p u b l i s h e d

 

ikzt



However,theseinfluencesonpulsepropagationeffecthavenotbeeninvestigated

With the urgency of the issue of research and the reasons

mentionedabove,wechooseresearchtopic"investigationoflaserpulsepropagationi

nathree-levelatomicmediuminthepresenceofEITeffect".

TheaimofthethesisistostudytheeffectsoflasercouplingparametersandDopplerbroadeningontheprocessoflaserpulsepropagation in different pulse domains Studying oninfluences of the non-orthogonal orientation of electric dipole moments and therelative phase onthelaserpulsepropagationinthepresence ofincoherentpump

Chapter1 PULSEPROPAGATIONINRESONANTMEDIA

1.1 Interactionbetweentwo-levelatomsandlight

Weassumeasingleopticalfieldpropagatinginthezdirectionhaveform:

→ Ez,t z,te c.c , (1.1)where z,t ist h e e n v e l o p e f u n c t i o n , ωis i s t h e f r e q u en c y o fl ig h t , a n d k =ωis/ccisthewavenumber

In the rotating wave approximation (RWA), to simplify

theHamiltonian, weintroducetheunitary transformmatrix:

H RWUHU †i UU † (1.6)

Intherotationalwavereferencesystem,wederivethewaveequationfor each field:

om ic sy st e m as sh o w n i n Fi gur e 1 4 O ne t e r m ,

whichisduetoexcitationbytheresonantfieldp only,i.e.,adirectpathfromstate 1 tostate 2 ;Anadditionalterm,whichisduetothepresenceofthesecond fiel

d t ec,i e , a n i n d i r e c t p a t h f r o m s t a 1 tostate 2 tostate 3 andb a c k t o t h e s t a t

H e n c e , t h e t o t a l t r a n s i t i o n a m p l

i t u d evanishest h a t l e a d i n g t o t h e t r a n s p a r e n c y f o r t h e p r o b e l a s e r b e a



Fig.1.4.Twoexcitedpathwaysfromthegroundstate1 totheexcitedstate2: directlyviathe 1 2 pathway,orindirectlyvia 1 2 3  2 pathway.

1.3 Physicalofthree-levelatomicsystem

1.3.1 TheRbatomic

Rbatomhastwonaturalisotopes:85Rbisstableisotopeoccupy72%,whileunstableisotope87Rbis28%

1.3.2 Thefinestructure

1.3.3 Thehyperfinestructure

Fig.1.5.Fineandhyperfineenergyleveldiagramofan87 Rbatom.

Chapter2 PROPAGATIONOFPULSEINTHEINHOMOGENEOUSLYBROADENED

EIT MEDIUM

2.1 TheMaxwell-Blochequationsforthepulsepropagation

In this section, we consider three-level atom model as presentedinSection 1.2 Using the electric dipole- and rotating- waveapproximations,the densitymatrixequation(1.25)istransformed as,

In the presence of Doppler broadening the evolution of the laserfieldand couplinglaserfieldinEqs.(2.2) haveform,

K u t t a a n d f i n i t e d i f f e r e n c e m e t h o d s T h e

atomicandlaserparametersarechosenas  21=2π6MHz,  32=2 π M H z ,

N10 15 m 3, d

21

2.53.10 29C.m

795 nm, c762 nm, p0=0 0 2GHzand 

pc0,a s t h e a l l f o r a f i g u r e i n t h i s C h a p t e r W e a s s u me

bothlaserpulseandcouplinglaserpulsehavethesametemporalwidth0

withaGaussiantypeattheentranceofthemedium,

In Fig 2.1, in the left column we represent cases ignore theDopplereffect (D = 0) By increasing the pulse area of the coupling laserpulse weobtain a stable propagation pulse When the area of the laser pulseis

smallΩc0τ0≤2,5,asshowninFigures2.2aand2.2b,thelaserpulseissignificantlyabsorbed and each laser pulse is broken down into severalsub-pulses with apositive-negative amplitude The number ofmodulationsatthetrailingedgeofthepulseincreasesasthepropagationdistanceincreases However, when the peak intensity of the coupling laserpulsebecomes larger Ωc0τ0= 1THz (Fig 2.1d) and accordingly the pulse areasbecome larger

Ωc0τ0= 25, Then propagate of the laser pulse is almost notdistorted, EIT is established Thephysical reason for this case is due to thedepth and width of the EITwindow is increased when the coupling laserintensity increase, so theinfluence of the medium on the pulse form in thiscase, is negligible

Similar consideration for the variation of the laser pulse envelopeinthe right column in the presence of Doppler effect, with D = 3.15GHzwhichc o r r e s p o n d s t o r o o m t e m p e r a t u r e C o m p a r e t h e t w o f

i g u r e s i n t h e left and right columns we see that the dynamic of pulse envelope shape isalmost the same.Thus, the influence of Doppler effect in this pulse domainis negligible andcan be ignored We can understand this because in thedomain ofpicoseconds, the time that the atoms exposed to laser pulses aresmall, sothe change velocity of atoms in each cycle of the laser pulse issignificant

Fig 2.1.Temporal evolution of the probe pulsep (,) at p = 0 (solid), 5

ns1(dashed),a n d 1 0 n s

-1( dotted)w h e n τ0 =2 5 p s T h e p e a k i n t e n s i t y a n d p u l s e areas are givenas infigures.

2.3.2 Pulsepropagationinnanoseconddomain

The next, we consider the propagation of the laser pulse at the

pulseduration ofτ0= 25 ns which are approximate to the life time of theexcitedstate|

2.Theresultsshowthetimevariationofthelaserpulseenvelopeat

differento p t i c a l d e p t h s ,  p0,5 a n d 1 0 n s-1a s s h o w n i n F i g 2 2 T h epulse area and peak intensity of the control laser pulse are given inthefigure,theleftcolumncorrespondsto(D=0)andtherightcolumncorresponds(D= 3.15 GHz)

From Fig 2.2, show that for a small value of the pulse area(Ωc0τ0≤25) the laser pulse is almost collapsed due to resonant absorption inanatomic medium, there is no EIT effect (Figs 2.2a and Fig 2.2b) When

thepulsearea(thus thepulsepeak)of thecouplingbeam in cre ases, although

the leading edge of the probe pulse is still distorted but the endingedgeapproachese a r l i e r t r a n s p a r e n c y , a s s h o w n i n F i g s 2 2

c a n d 2 2 d T h i s phenomenon is due to the energy loss to prepare for the EIT formation ofthe probepulse In particular, when increased peak intensity to Ωc0= 200GHz,respectively the pulse area reaches to the value of Ωc0τ0= 5×103(Fig.2f),the probe pulse is almost unchanged, namely, an ideal EIT or solitonisestablished

SimilarconsiderationforthecaseoftheDopplerbroadeningaspresented

in the right column of Fig 2.1 From this figure we observe thatsimilardynamics occur but in order to reach the EIT form of probe pulse,largerintensity of coupling pulse is required, that is at the same intensityofcoupling pulse (for example, Figs 2f and 2f1), the probe pulseapproachesto later EIT form in presence of the Doppler broadening Thisbehavior isdue to theDopplerbroadening reducesEIT efficiency,hencet h e

p r o b e laserpulseisdecayed faster thanthe caseof Doppler-free

Fig 2.2.Temporal evolution of the probe pulsep (,) at p = 0 (solid), 5

nτ0ontheEITformationoftheprobepulse,weconsiderthet e m p o r a l evolutio

n of the laser pulse p (,)when fixed pulse width τ0= 0.25μ sasshown in Fig.

2.3 By comparing Fig 2.3 with Fig 2.2, we show that theideal EIT effectcan achieve by the increase coupling laser pulse.However,int h e l o n g p u l se r e g i o n m i c r o s e c o n d i s t h e E I T e f f e c t o bt

a in ed a t p u l se area largertentimes (Ωc0τ0=5×104)asshowninFigs.2.3fand2.2f

Similar, when we compare the Figs in the left and right columnsforthecaseignoreandpresentDopplerbroadening.Weshowthatw h e n presentDopplerbroadenislaserpulsedistortedandstrongabsorbed.Influence theDoppler broadening is significant and can’t ignore evenwhenEITpulseformobtainsanideanear

Fig 2.3.Temporal evolution of the probe pulsep (,) at p = 0 (solid), 5

ns-1(dashed), and 10 ns-1(dotted) when τ0= 0.25 µs The peak intensity and

pulseareas are givenasinfigures.

Fig.2.4(a)Temporalevolutionoftheprobepulseatopticaldepthp =5ns-1; (b)variationofprobepeakversusopticaldepthatd i f f e r e n t D o p p l e r w i d t h s when 0 =1nsand c0 = 10 GHz.

Chapter3 INFLUENCESOFELECTRIC- DIPOLEMOMENTORIENTATIONANDRELATIVE PHASE

ONPULSEPROPAGATION 3.1 Theoreticalmodel

We consider the three-level cascade-type atomic system withnearlyequispacedlevelsasshowninFig.3.1.Aweakprobefield1withfrequency

pdrivesthetransition|1|2,whilethetransition|2 |3is

coupled by a strong field2w i t h f r e q u e n c yc We denote21a n d32being the decay rate of the states |2and |3, respectively Anincoherentpumpw i t h a p u m p i n g r a t e 2 R i s a p p l i e d b e t w e e n l e v e l s |

1 a n d | 3 .T h e

Rabi frequencies of the fields are defined as 1 2d12E p /  and

22d23Ec/,withd 12 andd 23 aretheelectricdipolematrixelement,respectively.

createdbytheinterferenceofspontaneousemission

→(–→usuallycalledspontaneousg e n e r a t e d c o h e r e n c e : S

systemdependnotonlyonamplitudesanddetuningbutalsothephaseofthep r o b e a n d c o u p l i n g f i e l d s , t h u s w e h a v e t o t r e a t R a b i f r e q u e n

( ) i 2p    ,(3.1d)

2 p 22 11

ij ij (i j) and the conservation condition

1122331.Inequations(3.1),ijdescribethecoherencedecayratesfromstate|itostate|jandrepresentedwiththepopulationdecayratesijby

h a n a d d i t i o n a l

term2p 213223.If=1,theSGCeffecthastobetakenintoaccountand the strength of SGC will vary versus; otherwise= 0, the effect ofSGC

is absent

wave approximation, and consider in the local frame where= zandtz/cc,

Thesamesection1.2.2,usingtheslowly-varyingenvelopeandtherotating-we also obtained the propagation equations for laser fields,respectively:

 ( ,)2i( ,), (3.4)

 p p1 2

c (,)2ic23 (,) (3.4)Wealsoassumethattheenvelopeoffieldistheslowandattheentrancetothe mediumhaving formedas(2.5)

3.2 InfluenceofSGConthelaserpulsepropagation

Tostartwith,weignoretheeffectofSGC,i.e.,=0andhence=0, thenchoosing the appropriate values of coupling intensity and pulseduration asc0= 25 GHz and0= 25

envelopeisu n d i s t o r t e d d u r i n g t h e p r o p a g a t i o n p r o c e s s t h a t

i s t h e n e a r i d e a l E I T effect isestablished asshown infigure 3.2a

In order to investigate the influence of SGC on the propagationeffectoflaserpulsewefix=1andrelativephase=0,a n d p l o t spatiotemporal



evolution of the pulse probep(,) for different values ofquantum

interference parameterp The results show that, when the SGCpresents,i e , p  0 , t h e p r o b e p u l s e e n v e l o p e i s s i g n i f i c

a n t l y d i s t o r t e d

during the propagation The modulations of the pulse envelope increase

asthe parameterpincreases [see figures (3.2b)-(3.2d)] It is also notable

thatthe modulations of the envelope are mainly concentrated on theleadingedge, and these modulations increase as the propagation distanceincreases.The primary reason for the modulations at leading edge of pulsewith theSGC, arises from the influence of SGC on absorption anddispersion,

theabsorptionpeakonbothsidesofzerodetuningandthelinewidthofabsorptionline become larger and narrower than those in the case ofSGCabsents,thereforethedispersioncurvebecomesmuchsteeper(hencedisper

In order to see the control role of relative phase on the EIT effect

ofprobe pulse we fix the parameterp= 0.7 and plot the temporal evolution

ofthe pulse probep(,) at the optical depthp= 5ns-1for differentvaluesof relative phase, as illustrated in figure 3.3 From figure 3.3a wecan seethat the probe pulse envelope depends sensitively on the relativephase

andthei n f l u e n c e o f r e l a t i v e p h a s e o n t h e t e m p o r a l e v o l u t

i o n o f p u l s e i s a periodo f 2 .F o r 0     /c

2:a t  = 0 , d u e t o S G C m a k i n g t h e l e a d i n g edgeofpulseenvelopeisdistortedasoneconsideredinfigure3.2(c),when