Study On The Space-time Characteristics Of The Hermite-Gaussian Associated Beanms

There is such a kind of light in nature that its coherence width tends to zero,which we call incoherent light,such as sunlight and lamplight.In contrast to it,when its coherence tends to infinity,we call such light a completely coherent light,like a general laser that belongs to the completely coherent light.But in real life,it is difficult to find completely coherent light and completely incoherent light beam.One of our common beams is a partially coherent beam,which is between the front two.The nature of the beam is related to its corresponding correlation function.If a correlation function of a beam satisfies the classical Gauss distribution,we call this beam a conventional partially coherent beam,which is our familiar Gauss Schell mode correlation beam.In addition to the conventional partially coherent light,the partially coherent beam has another property of light called nonconventional partially coherent light.As its name implies,the nonconventional partially coherent beam has a non-Gaussian distribution of correlation functions.Because of the different beam characteristics,the correlation functions of these special partially coherent lights have a corresponding distribution form.Some common nonconventional partially coherent beams have multi-Gaussian correlated Schell-model(MGCSM)beam?Laguerre-Gaussian correlated Schell-model(LGCSM)beam elliptical Laguerre Gaussian correlated Schell-model(ELGCSM)beam?Cosine Gaussian correlated Schell-model beam and Hermite-Gaussian correlation beam and so on.In this paper,we mainly study a partially coherent beam with a nonconventional correlation function called the Hermite-Gaussian correlated Schell-model beam.Based on the Hermite-Gaussian correlated Schell-model beam in the spatial domain with self-splitting properties,Our main research is some properties of Hermitian Gaussian correlation beam in the space-time domain,which divided into two parts.The first part is complex Gaussian representations of partially coherent beams with nonconventional degrees of coherence,mainly to the self-splitting of the Hermite Gauss Schell model beam propagating in uniaxial crystal as an example.The second part is Hermite-Gaussian correlated Schell-model pulsed beam,We mainly introduce some propagation characteristics of Hermite-Gaussian correlated Schell-model pulsed beam in a special kind of medium,namely dispersion medium.In the first chapter,we mainly introduce the research background and application of partially coherent light.And we also briefly describe the research progress of partially coherent light in the spatial-temporal domain.At the end,we also give a brief summary of the main contents of this article.In the second chapter,some basic theoretical knowledge is discussed,which is mainly about the space time domain and some formulas of spatial frequency domain.We also describe some complex Gaussian representation about nonconventional partially coherent beams,including HGCSM beam,elliptical Laguerre-Gaussian correlated Schell-model(ELGCSM)beam,and multi-Gaussian correlated Schell-model(MGCSM)beam.In the third chapter,we mainly introduce the propagation of a HGCSM beam in a uniaxial crystal,the expression of the spectral intensity and the degree of coherence of a HGCSM beam is also derived.Then the propagation characteristics of Hermite-Gaussian correlated Schell-model beam in uniaxial crystal are introduced,including the spectral intensity of a HGCSM beam in uniaxial crystal at several propagation distances,the normalized spectral intensity of a HGCSM beam in a uniaxial crystal for different values of ne/no and the degree of coherence of a HGCSM beam in a uniaxial crystal for different values of ne/no.Finally,we exchanged and discussed the results,and got a satisfactory conclusion.In chapter 4,we start from the temporal domain,a Hermite-Gaussian correlated Schell-model(HGCSM)pulse is emphasized.First,the correlation function of the spatial-temporal domain is introduced to describe the coherent characteristics of the pulse.Then some numerical results are given,we present the evolution of the average intensity and the temporal degree of coherence of the HGCSM pulse in dispersive media.Compared with the propagation characteristics of the spatial domain,some interesting phenomena are found.In chapter 5,we have summarized and prospected the study of spatial-temporal partially coherent light.Some properties and application of Hermite-Gaussian correlated Schell-model(HGCSM)beam in space and time domain are summarized.Some of the work and ideas that will be carried out are explained and prospected.