Numerical Study Of The PT-symmetry Bragg Reflection Waveguide Lasers

The invention of lasers has greatly promoted the development of science and tech-nology in many fields,and different types of lasers play vital roles in their respective applications.Among many types of lasers,semiconductor lasers have been develope-d into the core technology of modern optoelectronics science due to their small sizes,simple structures,long lifetime,low energy consumptions,easy modulations and low costs.Their applications cover almost all optoelectronics fields.The development of semiconductor lasers has experienced such three stages as homojunction.heterojunction and quantum well.After more than half a century of development,quantum well semi-conductor lasers have shown great advantages in many performances,such as threshold current and thermal characteristics,modulation characteristics,polarization characten s-tics,etc.,are known as ideal semiconductor lasers.The concept of parity-time symmetry originates from quantum mechanics.In quan-tum mechanics,the operator of each observable physical quantity must be an Hermitian,or the Hermitian of the Hamiltonian is an sufficient-unnecessary conditions for a sys-tem with real energy eigenvalues.It was later found that the non-Hamiltonian can have real eigenvalues as long as it satisfies the PT symmetry condition.Satisfying the PT-symmetric requires that the real part of the potential energy function becomes an even function and the imaginary part becomes an odd function with respect to the space coor-dinates.The researchers found that the wave function in optics is similar to the stationary Schrodinger equation in quantum mechanics.so the concept of PT symmetry is intro-duced into the field of optics.PT symmetry requires the real part of dielectric constant or refractive index is even function to the spatial position while the imaginary part is odd function.It can be seen that if an optical system satisfies the PT symmetry condition,it is necessary to introduce gain or loss to the system.The application of PT symmetry in optical systems can be divided into two styles:one is that the change of the refractive in-dex of the system is perpendicular to the direction of light propagation,such as a coupled waveguide system;the other is the change of the refractive index of the system parallels to the propagation of light,such as PT symmetric Bragg grating.The concept of PT symmetry applied into semiconductor lasers is a new research direction developed in recent years.At present,there are generally two ways to realize single-mode lasing by using PT symmetry:one is by using PT symmetric coupled res-onator;the other to realize single-mode lasing is by using PT symmetric Bragg grating.Either way,the filter mode mechanism of the PT symmetric structure is utilized.Based on the concept of PT symmetry,two PT symmetric Bragg reflection waveguide(BR-W)lasers are proposed.The numerical results show that PT-BRW lasers exhibit many excellent characteristics.This paper is divided into six chapters,the specific content of which is arranged as follows:The first chapter is a summarize.First the research background,including the de-velopment status of laser and PT symmetry is introduced.Then the development history and progress of semiconductor lasers are introduced in detail,and the definition of PT symmetry in quantum mechanical systems and how to introduce PT symmetry concepts in optical systems are expounded.Finally,the combination of semiconductor laser and PT symmetry concept is introduced,which is the research progress of PT symmetric semiconductor laser.The second chapter is the basic theory.The basic theory of electromagnetic fields is the basis of the work of this thesis.Firstly,the Maxwell s equations and the boundary conditions of electromagnetic fields are described.The Lorentz reciprocity theorem of electromagnetic fields is given.A method of numerical calculation of electromagnetic fields is proposed.Then the basic theory and concept of semiconductor laser are briefly introduced,and a numerical simulation method of laser is proposed.The third chapter analyzes the spectral characteristics of Bragg gratings.Firstly.the structure of the passive Bragg grating is introduced and its reflection spectrum char-acteristics are analyzed.Then,based on passive Bragg grating,the basic structure of PT symmetric Bragg grating is described,and the transmission and reflection spectrum characteristics of PT Bragg grating are analyzed.The results show that the transmission spectrum and the reflection spectrum of the passive Bragg grating are symmetric.The transmission spectrum at both ends of the PT symmetric Bragg grating is the same,but the reflection spectra at either end are different,especially when the real part refractive index modulation of the Bragg grating is equal to the imaginary refractive index modulation.The transmittance at both ends is 1,but one end of the reflection spectrum disappears.In chapter 4,a design scheme of PT-BRW laser is presented.The center of the structure is a low refractive index cavity.The PT symmetric Bragg gratings on both sides of the structure are symmetrically arranged about the central low refractive index cavity.The active layers of the laser are located in the PT symmetric Bragg gratings on both sides of the structure.The feature of this structure is that not only can it make use of PT Bragg grating to filter mode to ensure the transverse single-mode characteristic of the device,but also the distributed active layer can improve the optical field confinement factor and thus improve the mode gain.Because the mode gain of this structure is relative high,the cavity length of the device is much shorter than that of the traditional semicon-ductor laser,and the shorter cavity length not only reduces the threshold current,but also improves the modulation bandwidth of the device.The filtering mode mechanism of PT symmetric Bragg gratings is insensitive to PT phase(i.e,the relation between the real and imaginary part modulation of refractive index).Injection can cause slight change of refractive index of the dielectric.The numerical simulation results show that the device can maintain transverse and longitudinal single-mode characteristics even under higher injection conditions because of the large side mode suppression ratio of the structure.On the lateral,because mode field intensity distribution gradually decreases from the center cavity to both sides of the PT symmetric Bragg grating,so the injection efficiency in re-mote areas is lower than that in central core.So,we put forward the partial PT symmetric Bragg grating structure,that is,uses the PT structure near the central cavity of the grat-ing,and in the outsides using passive Bragg grating.Such desisgn can not only simplify the preparation technology,but also improve the injection efficiency under the condition of guaranteed effective mode filter mechanism.In chapter 5,the PT-BRW structure is improved to realize high power output.The low refractive index central cavity of the structure can be non-conductive materials(such as SiO2.etc.),and PT symmetric Bragg gratings are located on both sides of the low refractiva index central cavity.Due to the mode filtering mechanism of PT-symmetric Bragg gratings on both sides,the device still maintains the transverse single-mode char-acteristic.Mode field distribution also gradually decreases from the center to both sides.namely field mainly confined in the central cavity.The overlap of active layer and the mode field is small within the both sides of the PT symmetric Bragg grating,so it can release the thermal effect.Meanwhile the structure of the injection area locating at both sides of Bragg grating can also reduce the thermal effect caused by injection at the same time.The threshold of optical catastrophic damage(COD)determines the maximum output power of the laser,so the biggest innovation of this structure is that the central cavity can withstand larger COD threshold.Numerical simulation results show that the cavity length of 800?m can achieve watt-scale output power and maintain high energy conversion efficiency.The chapter 6 are conclusions and outlook.