The Investigation Of Propagation Of Parallel Light In Two-dimensional Nonlinear Materials In The Condensed Phase

The propagation of light in a medium can be explained in essence as the interaction between light and matter.In optics and condensed matter fields,the light-material interaction,has always been studied,with theoretical and practical implications.Objectively speaking,since the laser was discovered,more attention has been paid to the development of optical matter,and few people have focused on the discovery and research of new optical states.However,recent experimental realization of the Bose-Einstein condensation(BEC)of light provides a new way to control the propagation of light in optical media.Inspired by the discovery of the new optical state,in this paper,we aim to analyze and study the propagation of parallel light in the condensed phase in optical materials theoretically.Among the plethora of optical materials,nonlinear media have always attracted the attention of many physicists due to their various physical properties.Especially,second-order nonlinear media the most fundamental and also the first class of nonlinear materials that we know are very important.Therefore,in this paper we first study the propagation properties of parallel light in the second-order nonlinear materials.We aim to investigate two questions:How to describe the propagation of parallel light in the nonlinear medium,when the photon gas is in the condensed phase.And,whether the harmonic conversion rate will be influence by the BEC of photons.In this paper,the propagation and conversion of parallel light are studied both in classical and quantum perspectives.Using the classical field method,by combining the classical propagation equation of electric field and the G-P equation of photons,we derive a coupled wave equation which can be used to describe the conversion law of parallel light in the condensate phase.By resolving the coupling equation,we also find that,quantum phase transition occurs in the system under certain conditions of condensed phase.Over the phase transition point,the fundamental wave can all be converted into the second harmonic.In the quantum framework,we also propose the concept of photon molecule and construct a two-component quantum model(consisting of photon and photon molecule)to describe the interaction between the parallel light and the nonlinear medium.In addition,we study the conversion dynamics of the photon molecules by introducing the notion of harmonic conversion rate.The dependency relation between the harmonic conversion and the effective photon-photon interaction is also discussed.These investigations will be helpful for us to control the conversion of harmonics.It is well known that the atom is an ideal “laboratory” for investigating the quantum properties of radiation fields.Based on the investigation of the quantum phase transition of the system,we furthermore discuss the question how the spontaneous decay of an atom is influenced by both the phase transition and the collective excitation of the system consisting of photons and photon molecules.In the process of solving this problem,by Bogliubov transition we also introduce a correction factor,which can turn the interaction between the atom and the radiation field into the interaction between the atom and the quasiparticle field.Especially,in the pure photon molecule condensate phase,we also find that the spontaneous decay of the atom is influenced by the energy gap of the quasiparticle.We also explain this phenomenon and propose the concept of critical transition frequency of the atom.We also know that photonic crystals the artificial nonlinear materials,have great advantages and operability in controlling the propagation of light.So in this paper,we also propose a two-component BEC model to describe the propagation and localization of parallel light in a two-dimensional optical cavity filled with two types of photonic crystal media.In this model,photons behave themselves as if they are ordinary bosons.We also find that there exists a quantum phase transition for our present system,across the critical point,the system can transform from the Josephson oscillation into the localized phase.The investigation of the quantum phase transition of light offers new possibility for the control and manipulation of light wave.