One-dimensional photonic crystals (1D PhCs) have a unique ability to control the propagation of light waves, however certain classes of 1D oxides remain relatively unexplored for use as PhCs. Specifically, there has n...One-dimensional photonic crystals (1D PhCs) have a unique ability to control the propagation of light waves, however certain classes of 1D oxides remain relatively unexplored for use as PhCs. Specifically, there has not been a comparative study of the three different 1D PhC structures to compare the influence of layer thickness, number, and refractive index on the ability of the PhCs to control light transmission. Herein, we use the transfer matrix method (TMM) to theoretically examine the transmission of 1D PhCs composed of layers of TiO<sub>2</sub>/SiO<sub>2</sub>, TiO<sub>2</sub>/SnO<sub>2</sub>, SiO<sub>2</sub>/SnO<sub>2</sub>, and combinations of the three with various top and bottom layer thicknesses to cover a substantial region of the electromagnetic spectrum (UV to NIR). With increasing layer numbers for TiO<sub>2</sub>/SiO<sub>2</sub> and SiO<sub>2</sub>/SnO<sub>2</sub>, the edges became sharper and wider and the photonic bandgap width increased. Moreover, we demonstrated that PhCs with significantly thick TiO<sub>2</sub>/SiO<sub>2</sub> layers had a high transmittance for a wide bandgap, allowing for wide-band optical filter applications. These different PhC architectures could enable a variety of applications, depending on the properties needed.展开更多
Band gaps of elastic waves in 1-D phononic crystals with imperfect interfaces were studied. By using the transfer matrix method （TMM） and the Bloch wave theory in the periodic structure, the dispersion equation was ...Band gaps of elastic waves in 1-D phononic crystals with imperfect interfaces were studied. By using the transfer matrix method （TMM） and the Bloch wave theory in the periodic structure, the dispersion equation was derived for the periodically lami- nated binary system with imperfect interfaces （the traction vector jumps or the displacement vector jumps）. The dispersion equation was solved numerically and wave band gaps were obtained in the Brillouin zone. Band gaps in the case of imperfect interfaces were compared with that in the case of perfect interfaces. The influence of imperfect interfaces on wave band gaps and some interesting phenomena were discussed.展开更多
In this paper, the nonreciprocal properties of a novel kind of 1D magnetized plasma photonic crystals(MPPCs) with the Fibonacci sequence are investigated. The isolation of the proposed 1D MPPCs is also used to analyze...In this paper, the nonreciprocal properties of a novel kind of 1D magnetized plasma photonic crystals(MPPCs) with the Fibonacci sequence are investigated. The isolation of the proposed 1D MPPCs is also used to analyze the nonreciprocal properties. Compared to the conventional 1D MPPCs with periodic structure, the nonreciprocal performance can be significantly improved.The effects of several parameters of the proposed 1D MPPCs on the nonreciprocal properties are studied by the transfer matrix method, which includes the incident angle, order of the Fibonacci sequence, plasma frequency, plasma cyclotron frequency and plasma filling factor. The obtained results show that the nonreciprocal propagation properties can be improved by increasing the values of the plasma cyclotron frequency and incident angle, but they will worsen by blindly increasing the order of the Fibonacci sequence, plasma frequency and filling factor of plasma.The peaks of transmittance also are obviously reduced. In addition, the value of isolation will increase with increasing the incident angle, order of Fibonacci sequence, plasma frequency and plasma filling factor. However, when the plasma cyclotron frequency is increased, the value of isolation will be increased at lower frequencies, but is almost unchanged at higher frequencies.展开更多
We have theoretically studied the modal dispersion equation and effective refractive index of one-dimensional plasma photonic crystals (1-D PPCs) having different materials in one unit cell. The dispersion relations r...We have theoretically studied the modal dispersion equation and effective refractive index of one-dimensional plasma photonic crystals (1-D PPCs) having different materials in one unit cell. The dispersion relations related for such structure is derived by solving Maxwell’s equation using the transfer matrix method. It is found that the presence of plasma in a unit cell enhanced the phase matching ability and provides additional degree of freedom to control phase matching condition compared to the conventional one-dimensional photonic crystals (1-D PCs).展开更多
A method to compute the numerical derivative of eigenvalues of parameterized crystal field Hamiltonian matrix is given, based on the numerical derivatives the general iteration methods such as Levenberg-Marquardt, New...A method to compute the numerical derivative of eigenvalues of parameterized crystal field Hamiltonian matrix is given, based on the numerical derivatives the general iteration methods such as Levenberg-Marquardt, Newton method, and so on, can be used to solve crystal field parameters by fitting to experimental energy levels. With the numerical eigenvalue derivative, a detailed iteration algorithm to compute crystal field parameters by fitting experimental energy levels has also been described. This method is used to compute the crystal parameters of Yb^3＋ in Sc2O3 crystal, which is prepared by a co-precipitation method and whose structure was refined by Rietveld method. By fitting on the parameters of a simple overlap model of crystal field, the results show that the new method can fit the crystal field energy splitting with fast convergence and good stability.展开更多
The band structures of both in-plane and anti-plane elastic waves propagating in two-dimensional ordered and disordered （in one direction） phononic crystals are studied in this paper. The localization of wave propag...The band structures of both in-plane and anti-plane elastic waves propagating in two-dimensional ordered and disordered （in one direction） phononic crystals are studied in this paper. The localization of wave propagation due to random disorder is discussed by introducing the concept of the localization factor that is calculated by the plane-wave-based transfer-matrix method. By treating the quasi-periodicity as the deviation from the periodicity in a special way, two kinds of quasi phononic crystal that has quasi-periodicity （Fibonacci sequence） in one direction and translational symmetry in the other direction are considered and the band structures are characterized by using localization factors. The results show that the localization factor is an effective parameter in characterizing the band gaps of two-dimensional perfect, randomly disordered and quasi-periodic phononic crystals. Band structures of the phononic crystals can be tuned by different random disorder or changing quasi-periodic parameters. The quasi phononic crystals exhibit more band gaps with narrower width than the ordered and randomly disordered systems.展开更多
One of the most basic characteristics of photonic crystal is frequency band gap. When defects are introduced into the periodic photonic crystal, a number of defect modes appear in the stop band.In this paper, we explo...One of the most basic characteristics of photonic crystal is frequency band gap. When defects are introduced into the periodic photonic crystal, a number of defect modes appear in the stop band.In this paper, we exploit transfer matrix method based on photonic crystal theory, and assume the sampled fiber Bragg grating as one-dimensional dual photonic crystal with a large size defect. Characteristics of the sampled fiber Bragg grating are analyzed. Experimental results show that the sampled fiber Bragg grating has many reflective peaks. Its reflectivity, center wavelength, reflective peak intervals and band width all change with the grating parameters, including grating length, duty ratio of the material with high dielectric constant, and index modulation depth and period. Results agree with the conventiona1 couple mode theory which can be used when analyzing other characteristics of the sampled fiber Bragg grating or applying it into practice.展开更多
Using a stiffness matrix method, we in- vestigate the propagation behaviors of elastic waves in one-dimensional （1D） piezoelectric/piezomagnetic （PE/PM） phononic crystals （PCs） with line defects by calculating e...Using a stiffness matrix method, we in- vestigate the propagation behaviors of elastic waves in one-dimensional （1D） piezoelectric/piezomagnetic （PE/PM） phononic crystals （PCs） with line defects by calculating energy reflection/transmittion coefficients of quasi-pressure and quasi-shear waves. Line defects are created by the re- placement of PE or PM constituent layer. The defect modes existing in the first gap are considered and the influences on defect modes of the material properties and volume fraction of the defect layers, the type of incident waves, the location of defect layer and the number of structural layers are discussed in detail. Numerical results indicate that defect modes are the most obvious when the defect layers are inserted in the middle of the perfect PCs; the types of incidence wave and material properties of the defect layers have important effects on the numbers, the location of frequencies and the peaks of defect modes, and the defect modes are strongly de- pendent on volume fraction of the defect layers. We hope this paper will be found useful for the design of PE/PM acoustic filters or acoustic transducer with PCs structures.展开更多
文摘One-dimensional photonic crystals (1D PhCs) have a unique ability to control the propagation of light waves, however certain classes of 1D oxides remain relatively unexplored for use as PhCs. Specifically, there has not been a comparative study of the three different 1D PhC structures to compare the influence of layer thickness, number, and refractive index on the ability of the PhCs to control light transmission. Herein, we use the transfer matrix method (TMM) to theoretically examine the transmission of 1D PhCs composed of layers of TiO<sub>2</sub>/SiO<sub>2</sub>, TiO<sub>2</sub>/SnO<sub>2</sub>, SiO<sub>2</sub>/SnO<sub>2</sub>, and combinations of the three with various top and bottom layer thicknesses to cover a substantial region of the electromagnetic spectrum (UV to NIR). With increasing layer numbers for TiO<sub>2</sub>/SiO<sub>2</sub> and SiO<sub>2</sub>/SnO<sub>2</sub>, the edges became sharper and wider and the photonic bandgap width increased. Moreover, we demonstrated that PhCs with significantly thick TiO<sub>2</sub>/SiO<sub>2</sub> layers had a high transmittance for a wide bandgap, allowing for wide-band optical filter applications. These different PhC architectures could enable a variety of applications, depending on the properties needed.
基金supported by the National Natural Science Foundation of China (No.10672019)
文摘Band gaps of elastic waves in 1-D phononic crystals with imperfect interfaces were studied. By using the transfer matrix method （TMM） and the Bloch wave theory in the periodic structure, the dispersion equation was derived for the periodically lami- nated binary system with imperfect interfaces （the traction vector jumps or the displacement vector jumps）. The dispersion equation was solved numerically and wave band gaps were obtained in the Brillouin zone. Band gaps in the case of imperfect interfaces were compared with that in the case of perfect interfaces. The influence of imperfect interfaces on wave band gaps and some interesting phenomena were discussed.
基金funded by the Postdoctoral Foundation of Jiangsu Province (No. 1501016A)the China Postdoctoral Science Foundation (No. 2015M581790)the special grade China Postdoctoral Science Foundation (No. 2016T90455)
文摘In this paper, the nonreciprocal properties of a novel kind of 1D magnetized plasma photonic crystals(MPPCs) with the Fibonacci sequence are investigated. The isolation of the proposed 1D MPPCs is also used to analyze the nonreciprocal properties. Compared to the conventional 1D MPPCs with periodic structure, the nonreciprocal performance can be significantly improved.The effects of several parameters of the proposed 1D MPPCs on the nonreciprocal properties are studied by the transfer matrix method, which includes the incident angle, order of the Fibonacci sequence, plasma frequency, plasma cyclotron frequency and plasma filling factor. The obtained results show that the nonreciprocal propagation properties can be improved by increasing the values of the plasma cyclotron frequency and incident angle, but they will worsen by blindly increasing the order of the Fibonacci sequence, plasma frequency and filling factor of plasma.The peaks of transmittance also are obviously reduced. In addition, the value of isolation will increase with increasing the incident angle, order of Fibonacci sequence, plasma frequency and plasma filling factor. However, when the plasma cyclotron frequency is increased, the value of isolation will be increased at lower frequencies, but is almost unchanged at higher frequencies.
文摘We have theoretically studied the modal dispersion equation and effective refractive index of one-dimensional plasma photonic crystals (1-D PPCs) having different materials in one unit cell. The dispersion relations related for such structure is derived by solving Maxwell’s equation using the transfer matrix method. It is found that the presence of plasma in a unit cell enhanced the phase matching ability and provides additional degree of freedom to control phase matching condition compared to the conventional one-dimensional photonic crystals (1-D PCs).
基金Project supported by the National Natural Science Foundation of China(Grant Nos.50772112 and 50872135)the Natural Science Foundation of Anhui Province of China(Grant No.08040106820)the Knowledge Innovation Program of the Chinese Academy of Sciences(Grant No.YYYJ-1002)
文摘A method to compute the numerical derivative of eigenvalues of parameterized crystal field Hamiltonian matrix is given, based on the numerical derivatives the general iteration methods such as Levenberg-Marquardt, Newton method, and so on, can be used to solve crystal field parameters by fitting to experimental energy levels. With the numerical eigenvalue derivative, a detailed iteration algorithm to compute crystal field parameters by fitting experimental energy levels has also been described. This method is used to compute the crystal parameters of Yb^3＋ in Sc2O3 crystal, which is prepared by a co-precipitation method and whose structure was refined by Rietveld method. By fitting on the parameters of a simple overlap model of crystal field, the results show that the new method can fit the crystal field energy splitting with fast convergence and good stability.
基金supported by the National Natural Science Foundation of China(No.10632020).
文摘The band structures of both in-plane and anti-plane elastic waves propagating in two-dimensional ordered and disordered （in one direction） phononic crystals are studied in this paper. The localization of wave propagation due to random disorder is discussed by introducing the concept of the localization factor that is calculated by the plane-wave-based transfer-matrix method. By treating the quasi-periodicity as the deviation from the periodicity in a special way, two kinds of quasi phononic crystal that has quasi-periodicity （Fibonacci sequence） in one direction and translational symmetry in the other direction are considered and the band structures are characterized by using localization factors. The results show that the localization factor is an effective parameter in characterizing the band gaps of two-dimensional perfect, randomly disordered and quasi-periodic phononic crystals. Band structures of the phononic crystals can be tuned by different random disorder or changing quasi-periodic parameters. The quasi phononic crystals exhibit more band gaps with narrower width than the ordered and randomly disordered systems.
文摘One of the most basic characteristics of photonic crystal is frequency band gap. When defects are introduced into the periodic photonic crystal, a number of defect modes appear in the stop band.In this paper, we exploit transfer matrix method based on photonic crystal theory, and assume the sampled fiber Bragg grating as one-dimensional dual photonic crystal with a large size defect. Characteristics of the sampled fiber Bragg grating are analyzed. Experimental results show that the sampled fiber Bragg grating has many reflective peaks. Its reflectivity, center wavelength, reflective peak intervals and band width all change with the grating parameters, including grating length, duty ratio of the material with high dielectric constant, and index modulation depth and period. Results agree with the conventiona1 couple mode theory which can be used when analyzing other characteristics of the sampled fiber Bragg grating or applying it into practice.
基金supported by the National Natural Science Foundation of China(11102122)
文摘Using a stiffness matrix method, we in- vestigate the propagation behaviors of elastic waves in one-dimensional （1D） piezoelectric/piezomagnetic （PE/PM） phononic crystals （PCs） with line defects by calculating energy reflection/transmittion coefficients of quasi-pressure and quasi-shear waves. Line defects are created by the re- placement of PE or PM constituent layer. The defect modes existing in the first gap are considered and the influences on defect modes of the material properties and volume fraction of the defect layers, the type of incident waves, the location of defect layer and the number of structural layers are discussed in detail. Numerical results indicate that defect modes are the most obvious when the defect layers are inserted in the middle of the perfect PCs; the types of incidence wave and material properties of the defect layers have important effects on the numbers, the location of frequencies and the peaks of defect modes, and the defect modes are strongly de- pendent on volume fraction of the defect layers. We hope this paper will be found useful for the design of PE/PM acoustic filters or acoustic transducer with PCs structures.
