By means of the network equation and generalized dimensionless Floquet-Bloch theorem, this paper investigates the properties of the band number and width for quadrangular multiconnected networks （QMNs） with a differ...By means of the network equation and generalized dimensionless Floquet-Bloch theorem, this paper investigates the properties of the band number and width for quadrangular multiconnected networks （QMNs） with a different number of connected waveguide segments （NCWSs） and various matching ratio of waveguide length （MRWL）. It is found that all photonic bands are wide bands when the MRWL is integer. If the integer attribute of MRWL is broken, narrow bands will be created from the wide band near the centre of band structure. For two-segment-connected networks and three-segment-connected networks, it obtains a series of formulae of the band number and width. On the other hand, it proposes a so-called concept of two-segment-connected quantum subsystem and uses it to discuss the complexity of the band structures of QMNs. Based on these formulae, one can dominate the number, width and position of photonic bands within designed frequencies by adjusting the NCWS and MRWL. There would be potential applications for designing optical switches, optical narrow-band filters, dense wavelength-division-multiplexing devices and other correlative waveguide network devices.展开更多
In this paper, by means of the network equation and generalized dimensionless Floquet-Bloch theorem, we study the influences of the number of connected waveguide segments （NCWS） between adjacent nodes and the matchi...In this paper, by means of the network equation and generalized dimensionless Floquet-Bloch theorem, we study the influences of the number of connected waveguide segments （NCWS） between adjacent nodes and the matching ratio of waveguide length （MRWL） on the photonic bands generated by quadrangular multiconnected networks （QMNs）, and obtain a series of formulae. It is found that multicombining networks （MCNs） and repetitive combining networks （RCNs） are equivalent to each other and they can all be simplified into the simplest fundamental combining systems. It would be useful for adjusting the number, widths, and positions of photonic bands, and would possess potential applications for the designing of all-optical devices and photonic network devices.展开更多
This paper concerns the minimization problem of L2 norm of curl of vector fields prescribed full trace on the boundary of a multiconnected bounded domain.The existence of the minimizers in H1 are shown by orthogonal d...This paper concerns the minimization problem of L2 norm of curl of vector fields prescribed full trace on the boundary of a multiconnected bounded domain.The existence of the minimizers in H1 are shown by orthogonal decompositions of vector function spaces and a constructed auxiliary variational problem.And the H2 estimate of the type II divergence-free part of the minimizers is established by div-curl-gradient type estimates of vector fields.展开更多
基金supported by the National Natural Science Foundation of China (Grant No. 10974061)the Program for Innovative Research Team of the Higher Education in Guangdong of China (Grant No. 06CXTD005)
文摘By means of the network equation and generalized dimensionless Floquet-Bloch theorem, this paper investigates the properties of the band number and width for quadrangular multiconnected networks （QMNs） with a different number of connected waveguide segments （NCWSs） and various matching ratio of waveguide length （MRWL）. It is found that all photonic bands are wide bands when the MRWL is integer. If the integer attribute of MRWL is broken, narrow bands will be created from the wide band near the centre of band structure. For two-segment-connected networks and three-segment-connected networks, it obtains a series of formulae of the band number and width. On the other hand, it proposes a so-called concept of two-segment-connected quantum subsystem and uses it to discuss the complexity of the band structures of QMNs. Based on these formulae, one can dominate the number, width and position of photonic bands within designed frequencies by adjusting the NCWS and MRWL. There would be potential applications for designing optical switches, optical narrow-band filters, dense wavelength-division-multiplexing devices and other correlative waveguide network devices.
基金Project supported by the National Natural Science Foundation of China(Grant No.10974061)
文摘In this paper, by means of the network equation and generalized dimensionless Floquet-Bloch theorem, we study the influences of the number of connected waveguide segments （NCWS） between adjacent nodes and the matching ratio of waveguide length （MRWL） on the photonic bands generated by quadrangular multiconnected networks （QMNs）, and obtain a series of formulae. It is found that multicombining networks （MCNs） and repetitive combining networks （RCNs） are equivalent to each other and they can all be simplified into the simplest fundamental combining systems. It would be useful for adjusting the number, widths, and positions of photonic bands, and would possess potential applications for the designing of all-optical devices and photonic network devices.
基金Supported by the National Natural Science Foundation of China(11501109)Designated Scientific Research Project of Provincial Universities of Fujian Province(JK2015014)。
文摘This paper concerns the minimization problem of L2 norm of curl of vector fields prescribed full trace on the boundary of a multiconnected bounded domain.The existence of the minimizers in H1 are shown by orthogonal decompositions of vector function spaces and a constructed auxiliary variational problem.And the H2 estimate of the type II divergence-free part of the minimizers is established by div-curl-gradient type estimates of vector fields.
