【正文】 h high transmission efficiency. As a fundamental mode is introduced in the input SMW, at certain frequencies, the SMRW modes are enhanced because of resonance and the lightwaves are coupled to the output SMW. It is demonstrated by the simulation results that the surface mode ring resonator has a low radiation loss with a very small size because of the good waveguiding of surface mode based on PCs, and can be used in the future wavelength division multiplex (WDM) optics munication systems.1. IntroductionOptical waveguide ring resonators can be utilized as channel drop filters, which are very crucial ponents for WDM optic munication systems, photonic integrated circuits, and optical puting [1–7]. In order to make use of the precious bandwidth resource, the free spectral range (FSR) of the resonators is increased regularly and remarkably by reducing the ring radius directly. However, in the stripbased SOI ring resonator, the radiation loss increases exponentially with reduction of the ring radius, so the minimum of the ring radius is about 3 μm in this case [4–7]. To reduce the radius of ring and achieve a larger FSR, a photonic crystal ring resonator is proposed by al. [8]. The ring resonators are posed by the linedefect waveguide in the interior PCs with square lattice, but it is very difficult to build the device based on PCs with hexangular lattice due to the great propagation loss at the corner of the ring resonators [8–12]. Recently, it has been suggested that PCs surface waveguide can realize lightwaves transmission with high efficiency [13,14]. A photonic crystal surface waveguide is created on the surface of a circular photonic crystal (CPC) structure, which is formed by removing a concentric layer from the CPC [14]. The curve waveguide can realize high power transmission because of its smoother bend with smaller discontinuity and the symmetry about the center of the curve waveguide. Compared to linedefect waveguide in the conventional PC with hexangular lattice, it is easier to make use of the curve waveguide to build a photonic crystal ring resonator. In this paper, a surface mode ring resonator based on hexagonal lattice PCs is proposed. The symmetrical resonant filter is formed by sandwiching one SMRW into two parallel SMWs. The SMWs are obtained by increasing the radii of the row of rods between the hexangular lattice dielectric PCs and air. The SMRW is created on the surface of a CPC structure by increasing the radii of the rods at the outmost concentric circumference. The device is calculated by the finite difference time domain (FDTD) method with the perfectly matched layer absorbing boundary conditions at all boundaries. Compared with other surface mode ring resonators [3], the ring resonant structure based on PCs with hexagonal lattice has a very low energy loss, and most of the light in the input waveguide can be transferred to the output waveguide at resonance. The device with simple structure provides a possibility of channel drop filter, and can be used in future WDM optic munication systems or other fields. Fig. 1. (a) Band structures for TM modes PCs with the hexangular lattice posed of rod diameters Db= and permittivity ε= along with the projected surface modes. The diameters of the surface rods are D=, and the distance between two nearestneighbor surface rods is d=. (b) The normalized intensity of the Ez ponents of surfacemode dispersion curves.2. Design of the ring resonanceWe consider a semiinfinite hexangular lattice PCs posed of cylinders with ε= and a diameter of Db= in an air background, where a is the lattice constant. As shown in Fig. 1(a), the surface geometries is researched, supporting the surface states, where the outermost surface rods have increased their diameters D=, and the distance between two nearestneighbor surface rods satisfies d=. For effective localization of electromagnetic lightwaves on the PC surface, two conditions must be met: the surface mode must be in the PBG and only the part of surface mode that lies below the lightline is taken into account [13]. The hexagonal PCs have a fundamental bandgap for TM polarization in the frequency range of (c/a)f(c/a) and supports two surface modes below the lightline for the case of Fig. 1(a), where λ is the wavelength of light in the free space. For the structure of Fig. 1(b), the field intensity has one maximum with each rod and extends into the air, quickly decaying into the crystal with a width of a. For the case of the structure of Fig. 1(b) with enlarged surface rods, the intensity of both surface modes is mainly localized within the surface rods and its extent to the air is small for the whole energy range [14].For conventional linedefect curve waveguide in PCs [13], lightwaves are controlled on both side of the waveguide by the photonic bandgap, which act like a Bragg reflecting curve mirror. However, the SMRW has only a periodic structure on one side of the waveguide. Lightwaves traveling around the SMRW have to change their magnitude and direction vectors. The large concentric distance and small bending radius of the SMRW lead to the abrupt change of magnitude and direction vector of the wavevector. So the lightwaves can radiate to the surrounding air background easily. One way to reduce this radiation loss is to reduce the surface concentric distance dc, and then the waveguide has high overall surface effective index and high confinement factor. Fig. 2(a) shows half the SMRW, which is formed at the outermost concentric layer (., N=8) by increasing the radius of the surface rods to , where the distance dc between the nearestneighbor surface rods at the outermost layer is . Fig. 2(b) shows that high power transmissions for half the SMRWs, and the transmission spectra at dc= and dc= are denoted by the thick and thin solid lines, respectively. The former transmission efficiency is higher than that in the latter for the interest frequency range. It indicates that