Study On The Theoretical Problems For The Wave Propagation In Multilayered Structures

We study on the theoretical problems for the wave propagation in multilayeredstructures. The thesis concentrates on the transmission of electron in onedimensional finite quantum well and the interaction between light and materials inthe cavity when the light spread in the cavity of photonic crystal. The theoreticalresearch is given in the following.Every quantum well has its only eigen-energy level, and eigen-energy hasrelation with the size of the quantum well. If the width of quantum well isperiodically modulated, which is equivalent to coupling quantum well with differenteigen-energy, it can lead to new transfer phenomenon. The transmittance of the onedimensional multiple quantum well structure with dual-periodically modulatedthickness was calculated by means of transfer matrix method. And the electrical fieldwave function which was modulated by the width of the well is given. When thethickness of the quantum well was modulated periodically, the edge of bands wouldbe moved. The upper band edge would move to higher energy, and the lower bandedge would move to lower energy. Some states of band edges appear in the gap ofthe former single-periodic potential multiple quantum wells, and form some narrowsub-bands. The wave functions in the narrow bands are localized. Because thetransmittance and eigenvalue of electron depend on the matrix product of the welland potential, we need only to change the matrix of the well and potential if thereexist defect in the quantum well, then the transmittance and eigenvalue can beacquired.If the dispersive defect exists in the middle of photonic crystals, this defectcan appear negative refraction index in some frequency range. We calculated thetransmission spectrum and density of states of one dimensional photonic crystalswith dispersive cavity. We use a Lorentz mode as the dispersive medium, therelationship between the real and imaginary part of refraction index and thefrequency of the electromagnetic wave is also calculated, and find out the frequencyrange when the negative refraction appears. Setting the frequency of cavity at the middle of the photonic band gap, when the absorption is negligible, the density ofstates near the cavity mode is very high, and there are a wide transmitted bandappeared in the spectrum of transmission. When the spectrum is widened, plenty oftransmission peak can be seen, it is the result of resonance.We calculated the photonic band gap using transfer matrix method and analyticmethod, and analyst the difference between these two methods. And theoreticallystudy the band gap structure of one-dimensional photonic crystals constituted byalternate layers of left-handed materials (LHM) and right-handed materials (RHM),and find the band gap structure is different from the usual photonic crystals. With anappropriate choice of the parameters, we show that it is possible to realize anabsolute band gap for either TE or TM polarization of the electromagnetic waves,which can not be found in normal photonic crystals. In the end we calculated thetransmittance of one-dimensional photonic crystals constituted by left-handedmaterials (LHM) and right-handed materials (RHM), the LHM is substituted bydispersive medium, we get the zero even gap which is different from Bragg gap.