Theoretical Studies On Nonlinear Optical Properties In Quantum Dots And Eigen Equation In Photonic Crystals

In recent years, with the development of the research techniques and the micro-nanoprocessing technology, there are not only many novel physical phenomena such as theinteger quantum hall efect, the fractional quantum hall efect, anomalous quantum hallefect, quantum teleportation, interchangeable quantum entanglement, multi-photon en-tanglement, superluminal neutrinos, dark matter and dark energy, but also many newmaterials for great application prospects such as photonic crystals, carbon nanotubes,graphene, topological insulator, iron-based superconductors, negative refractive index ma-terials. This has greatly enriched and widened the scope of physical research. Thesenew physical phenomena and new materials bring us a lot of challenging research topics.Therefore, it is necessary to not only strengthen basic research and carry out cutting-edgeresearch, but also to broaden the range of research. Based on the above factors, nonlinearoptical properties in quantum dots, eigenvalue equation in photonic crystals were studied.This paper consists of fve chapters.Chapter1. Introduction. We introduce some nonlinear optical common phenomena,applications and common research methods. We also introduce some basic knowledge onquantum dots, applications and preparation methods; At last, we introduce some basicknowledge photonic crystals, theoretical approaches and preparation methods.Chapter2. Linear and nonlinear optical absorption and refractive index changes indisc quantum dots with a parabolic potential plus an inverse squared potential in a staticmagnetic feld are investigated. Linear and nonlinear optical absorption and refractiveindex changes in spherical quantum dots with the three dimensional ring-shaped pseu-doharmonic potential are also studied. The energy levels and the wave functions areobtained by separation of variables. The expression for the optical absorption coefcientsand the refractive index changes are obtained by the density matrix theory and iterativemethod. The infuences of the magnetic feld, the confned frequency and the charac-teristic parameter β of the inverse square potential on the optical absorption coefcientsand the refractive index changes are made concrete analysis of. The infuences of thetwo parameters r0,V0of the pseudo-harmonic oscillator potential and the characteristicparameter γ of the ring-shaped potential on the optical absorption coefcients and therefractive index changes are also discussed in detail.Chapter3. Polaron efect on the optical rectifcation and the second harmonic coef-cients in cylindrical quantum dots under the external magnetic feld are studied. Consid- ering polaron efects, the energy levels and the wave functions in cylindrical quantum dotsare obtained by separation of variables and perturbation theory. A brief introduction ofoptical rectifcation and the second harmonic generation coefcient is given by the densitymatrix theory and the iterative method. The infuences of polaron efects, the magneticfeld, the disc radial confned frequency and the characteristic coefcient V of the linearpotential on the optical rectifcation and the second harmonic coefcient are discussed.Chapter4. A detailed derivation of eigen equation about the magnetic and electricfelds in two-dimensional and three-dimensional photonic crystals. The method used isthe plane wave expansion method. A lot of mathematical skills and fexible mathematicaltransformations are used.Chapter5. Make conclusion.