Study of Photons Orbital Angular Momentum for Optical Communications André Madeira Bastos da Cunha Thesis to obtain the Master of Science Degree in Engineering Physics Supervisors: Professor Paulo Sérgio de Brito André Professor Gonçalo Nuno Marmelo Foito Figueira Examination Committee Chairperson: Professor Luís Paulo da Mota Capitão Lemos Alves Supervisor: Professor Gonçalo Nuno Marmelo Foito Figueira Members of the Committee: Professor João Alberto dos Santos Mendanha Dias Professor Armando Humberto Moreira Nolasco Pinto November 2015 B Ajourneyofathousandmilesbeginswithasinglestep. 老子 Acknowledgments I’dliketostartbythankingmyparentsJuvenalandLídia,whohaveencouragedandsupportedmethrough- outallmylifeandmywifeJoanawhostoodbymysideandprovidedmegreatsupportduringthisjourney. Furthermore, this work would not have been possible without the openness, encouragement and great supportprovidedbybothProfessorsPauloAndréandGonçaloFigueira. Iwouldliketoremarkthatonlythe promptnessandopennessofbothtointer-collaborationandnewideasprovidedthenecessarybasisforthe bridgingbetweenphysicsandopticalcommunicationsbyallowingthiswork,whichfocusonanalbeitexotic, butrathertrendyandinnovativesubject. Andofcourse,ImustalsothankthesupportofInstitutodeTelecomunicações(IT)andFundaçãoparaa Ciência e Tecnologia (FCT) who provided equipment and financial support to enable this work, the Group of Lasers and Plasmas (GOLP), Instituto de Plasmas e Fusão Nuclear (IPFN) who provided the necessary installations at Laboratório de Lasers Intensos (L2I) for our setup and provided multiple optical equipment butalsoascientificenvironmentofhighlycapableandhelpfulpeoplewhoprovidedsupportthroughoutthis work. Finally,Iwanttoacknowledgemycolleaguesandfriends,whowerethereformewhenIneededthem,es- peciallyJoãoRomãofortheprolificdiscussionsandinsightsandPedroMiguelCruzandManuelNascimento for their patience and companionship but also colleagues Alexandra Gouveia and Tiago Guerra Marques giventheworkwedevelopedtogetheryearsago. Fortheonesunmentioned,awordofapologybuttheassurancethatIholdaspecialplaceforyouinmy heart. iii Resumo Acapacidadedetráfegodedadosnainternetestárapidamenteaatingiroslimitesimpostospelosefeitos nãolinearesdafibraóptica,tendoquaseesgotadoosgrausdeliberdadedisponíveisnecessáriosparamul- tiplexar ortogonalmente o tráfego de dados. Desta forma, resultados recentes sugerem que o momento angular orbital (MAO) dos fotões talvez possa ser usado como grau de liberdade adicional para este fim, providenciandoemteoria,umnúmeropotencialmenteilimitadodeestadosortogonais,apresentando-seas- simcomoumpossívelsaltodegiganteparaasredesdetelecomunicaçõesdofuturo. Palavras Chave MomentoAngularOrbital(MAO),TelecomunicaçõesÓpticas,ÓpticaemEspaçoLivre,Laguerre-Gaussiano (LG),Óptica,ModuladorEspacialdeLuz(MEL) v Abstract Theinternet datatraffic capacity israpidly reaching thelimits imposedby optical fibernonlinear effects, havingalmostexhaustedtheavailabledegreesoffreedomneededtoorthogonallymultiplexdata. Therefore the need urges to develop new methods in order to avoid the upcoming capacity crunch using classical communications channels. In this regard, recent results have suggested that the use of the orbital angular momentum (OAM) of photons as an additional degree of freedom is potentially unlimited in the number of achievable orthogonal states, therefore presenting itself as a possible major technological leap for future communicationnetworks. Keywords OrbitalAngularMomentum(OAM),OpticalCommunications,FreeSpaceOptics(FSO),Laguerre-Gaussian (LG),Optics,SpatialLightModulator(SLM) vii