| The concept of photonic crystal (PC) was first introduced by Yablonovitch and John in 1987, respectively. PC are synthetic micro-structural materials and their refractive index is periodical. The most important characteristic of PC is its photonic band gap, a frequency region for which the propagation of electromagnetic waves is forbidden in certain direction in the structure. So PC has especial ability for inhibiting spontaneous radiation of atoms and controlling light propagation. It will be widely used in the fields of optical communication, microwave communication, integration optical and so on. One-dimensional PC which consists of alternating layers of two dielectric materials is investigated and applied broadly because of its simple theoretical calculation and easy fabrication. When a medium is put into the periodic PC and the structure of PC is destroyed, There will been one or several narrow pass bands appeared in the band gap of PC. These narrow pass bands are called defect modes of PC in academia. The frequency region for which the propagation of electromagnetic waves can transmit in the narrow pass bands. This kind of PC narrow pass band and multi-channel narrow pass band filtering may find applications in super dense wavelength division multiplexing for optical communications and precise optical measurement. In recent years, many people are studying on the changes of defect mode by observing the transmission spectrum (The frequency don't be normalized) of 1-D PC which don't be adulterate impure layer.their conclusions are not thorough and enough, and they don't link the change rules of different defect mode. This paper calculates the transmission spectrum of 1-D PC when the electromagnetic wave frequency is normallized or no-normallized using transfer matrix method,researchs the relations of defect mode and optic thickness of defect layer,refractive index of defect layer,optic thicknesses of PC dielectric,number of periods both side of defect layer when the incidence angle is zero and a medium is put into the periodic PC by analyzing the Accurate data,and compares the rules of defect modes which are obtained under the different adulterated mode. The conclusions are more thorough and enough than other's.This paper also links the different defect mode by studying on the defect mode in the PC transmission spectrum in which the frequency is normalized and the defect mode in the high band gap of PC,gains a lot of new conclusions. It is believed that the results can greatly open up application of PC.In the first chapter of this paper, we introduced the basic concept,the sorts,the theoretical investigate ways,the fabrication,the application of PC and the problems which is appeared in investigating PC, we also introduce the aim and primary content. In the second chapter of this paper, we deduced three theoretical ways which are used to calculating the transmission spectrum and band structure of PC. They are transfer matrix method,planewave expansion method,finite difference time domain. The transfer matrix method is used to calculating the transmission spectrum and band structure of 1-D PC, The planewave expansion method is use to calculating the band structure of 1-D and 2-D PC, The finite difference time domain is use to calculating the transmission spectrum of 1-D,2-D and 3-D PC.the Third chapter is the emphasis of this paper, in this chapter, we analyzed the relations of defect mode and optic thickness of defect layer,refractive index of defect layer,optic thicknesses of PC dielectric,number of periods both side of defect layer when the incidence angle is zero and a medium is put into the periodic PC. We also compared the conclusions which are gained in different adulterate ways. We gained a lot of new results, and the more important results list below:1. The relations of defect mode and optical thickness of impure layer when the optical thicknesses of two PC dielectric materials are equal and the numbers of periods both side of impure layer are equal.(1) When the adulterated mode of impure layer is displaceable mode, only when the optical thickness of impure layer is even times of (where is center wavelength), the position of center wavelength in band gap will appear a defect mode. When the adulterated mode of impure layer is nipped mode, only when the optical thickness of impure layer is odd times of 1/ 4λ0 (whereλ0 is center wavelength), the position of center wavelength in band gap will appear a defect mode.(2) Whether the adulterated mode of impure layer is displaceable mode or nipped mode, the defect mode will move to longer wavelength direction when the optical thickness of impure layer is increased, and the nearer defect mode close to center wavelength, the smaller full width at half maximum (FWHM)of defect mode is. When the adulterated mode of impure layer is displaceable mode, the peak value of defect mode equal approximately to 1 all the time, and when the adulterated mode of impure layer is nipped mode, the nearer defect mode close to center wavelength, the smaller the peak value of defect mode is.(3) Whether the adulterated mode of impure layer is displaceable mode or nipped mode, when the optical thickness of impure layer is integer times of 1/ 4λ0 , the defect modes in the band gap correspond one to one, the distances between two corresponded defect modes and center wavelength position is equal in transmission spectrum in which the frequency is normalized. 2. The relations between defect mode and refractive index of impure layer when the optical thicknesses of two PC dielectric materials are equal and the numbers of periods both side of impure layer are equal.(1) When impure layer displaces the PC dielectric which has bigger refractive index, the defect modes which lie on center wavelength will not move when the refractive index of impure layer varies, and other defect modes will go away from the position of center wavelength when the refractive index of impure layer increases. When the refractive index of impure layer increases, FWHM of defect mode which is close with center wavelength will decrease and FWHM of defect mode which is far away with center wavelength will increase. When impure layer displaces the PC dielectric which has smaller refractive index, the results will be opposite.(2) When impure layer nipped between two mediums of PC by nipped mode, and the numbers of periods both side of impure layer are integers, the peak values of the defect modes which lie on center wavelength only have relation with the refractive index of impure layer, and it don't have relation with the refractive indices of PC mediums. When the refractive index of impure layer increases, the defect modes which lie on center wavelength will not move, and its FWHM will decrease and its peak value will increase. The defect modes in the band gap which is less than the center wavelength will move to shorter wavelength direction at first, and then move to longer wavelength direction when the refractive index of impure layer increases, and The defect modes in the band gap which is bigger than the center wavelength will move to longer wavelength direction at first, and then move to shorter wavelength direction when the refractive index of impure layer increases.3. The relations between defect mode and the optical thicknesses of two PC dielectric materials when the optical thicknesses of two PC dielectric materials are equal and the numbers of periods both side of impure layer are equal.Whether the adulterated mode of impure layer is displaceable mode or nipped mode, when center wavelength varies, but the relation between the optical thickness of impure layer and center wavelength doesn't vary, the position of band gap in transmission spectrum in which the frequency is normalized will not vary, and the position of defect mode will not vary, too. At the same time, FWHM of defect mode and the center wavelength have a linear relationship perfectly.4. The relations between defect mode and number of periods both side of defect layer when the optical thicknesses of two PC dielectric materials are equal and the numbers of periods both side of impure layer are equal.(1) When impure layer displaces the PC dielectric, if increase a PC medium which has bigger refractive index on the both side of PC, the position of defect mode won't vary and FWHM of defect mode will decrease. If increase a PC medium which have smaller refractive index on the both side of PC at the same condition, the position of defect mode also won't vary, but FWHM of defect mode will increase. The decrease times or increase time of defect mode's FWHM don't have relation with the number of periods both side of defect layer. The decrease times or increase time of defect mode's FWHM are equal when the positions of defect modes in transmission spectrum in which the frequency is normalized are the same. The decrease times is bigger than the increase of defect mode's FWHM, so when increase a PC period on the both side of PC, the position of defect mode won't vary, and FWHM of defect mode will increase.(2) Whether the adulterated mode of impure layer is displaceable mode or nipped mode, if the numbers of periods both side of defect layer aren't equal, the position of defect mode won't vary, but the peak value of defect mode will wary. The more the difference between the numbers of periods on both side of defect layer is, the smaller the peak value of defect layer is. In the fourth chapter of this paper, we researched the defect mode in the high band gap of 1-D PC using transfer matrix method when the incidence angle is zero, the optical thicknesses of two PC dielectric materials are equal and the numbers of periods on both side of defect layer are equal. The results list below:1. When the adulterated mode of impure layer is displaceable mode, if the optical thickness of impure layer is even times of it will appear a defect mode at the middle position of the nth band gap in transmission spectrum in which the frequency is normalized. When the adulterated mode of impure layer is nipped mode, if the optical thickness of impure layer is odd times of , it will appear a defect mode at the middle position of the nth band gap in transmission spectrum in which the frequency is normalized.2. if the middle positions of the first, second and third band gap in transmission spectrum in which the frequency is normalized appear defect modes at the same time, the radio of defect mode FWHM in the first and the second band gap will not vary, the radio is about 9.00, and the radio of defect mode FWHM in the second and the third band gap will not vary, too. the radio is about 2.78.These radios don't have relations with the refractive indices of PC mediums,the center wavelength,the adulterated mode of impure layer and so on.3. Whether the adulterated mode of impure layer is displaceable mode or nipped mode, if the optical thickness of impure layer is integer times ofλ0 / 4, the numbers of defect modes in every band gap are the same, they correspond one-to-one, the relative positions of defect modes in every band gap are the same.The conclusions above will play a important role of theoretical guidance when the PC apply to ultra-narrow-band filters and multi-channel narrowband filters in super dense wavelength division multiplexing for optical communications and precise optical measurement.
|
PDF Full Text Request