We propose a new type of optical waveguide that consists of a sequence of coupled high-Q resonators. Unlike other types of optical waveguide, waveguiding in the coupled-resonator optical waveguide (CROW) is achieved through weak coupling between otherwise localized high-Q optical cavities. Employing a formalism similar to the tight-binding method in solid-state physics, we obtain the relations for the dispersion and the group velocity of the photonic band of the CROW's and f ind that they are solely characterized by coupling factor k 1 . We also demonstrate the possibility of highly efficient nonlinear optical frequency conversion and perfect transmission through bends in CROW's. © 1999 Optical Society of America OCIS codes: 130.2790, 190.0190, 230.7370. Two mechanisms have been proposed and used in the past for optical waveguiding. 1The most widely used is waveguiding by total internal ref lection, as illustrated in Fig. 1(a). Another mechanism, Bragg waveguiding, in which waveguiding is achieved through Bragg ref lection from a periodic structure, has also been demonstrated. Another possible realization is shown in Fig. 1(d), in which the individual resonators consist of defect cavities 4,5 embedded in a two-dimensional (2D) periodic structure (a 2D photonic crystal). 6,7 These defect resonators are designed such that their resonant frequency falls within the forbidden gap of the surrounding 2D structure, which permits high-Q optical modes. The coupling in this case is due to the evanescent Bloch waves. In both realizations of the CROW we assume sufficiently large separation between the individual resonators that the resonators are weakly coupled. Consequently, we expect that the eigenmode of the electromagnetic field in such a coupled-resonator waveguide will remain essentially the same as the high-Q mode in a single resonator. At the same time one must take into account the coupling between the individual high-Q modes to explain the transmission of the electromagnetic waves. This coupling is exactly the optical analog of the tight-binding limit in condensed-matter physics, 8 in which the overlap of atomic wave functions is large enough that corrections to the picture of isolated atoms are required yet at the same time is not large enough to render the atomic description completely irrelevant. The individual resonators in the CROW are the optical counterpart of the isolated atoms, and the high-Q mode in the resonators corresponds to the atomic wave function.In the spirit of the tight-binding approximation, we take the eigenmode E K ͑r, t͒ of a CROW as a linear combination of the high-Q modes E V ͑r͒ of the individual resonators along a straight line parallel to the e z axis [see Figs. 1(c) and 1(d)]. Denoting the coordinate of the center of the nth resonator as z nR, we haveIt is straightforward to show that the waveguide mode E K ͑r, t͒ satisf ies the Bloch theorem. Consequently we can limit the wave vector K to the first Brillouin zone, i.e., 2p͞R # K # p͞R. By writing E K ͑r, t͒ in this form, we have ...

We combine fiber Bragg grating ͑FBG͒ technology with a wet chemical etch-erosion procedure and demonstrate two types of refractive index sensors using single-mode optical fibers. The first index sensor device is an etch-eroded single FBG with a radius of 3 m, which is used to measure the indices of four different liquids. The second index sensor device is an etch-eroded fiber Fabry-Pérot interferometer ͑FFPI͒ with a radius of ϳ1.5 m and is used to measure the refractive indices of isopropyl alcohol solutions of different concentrations. Due to its narrower resonance spectral feature, the FFPI sensor has a higher sensitivity than the FBG sensor and can detect an index variation of 1.4ϫ 10 −5 . Since we can measure the reflection signal, these two types of sensors can be fabricated at the end of a fiber and used as point sensors. Since the early 1990s, fiber Bragg grating ͑FBG͒ sensors have been intensively developed due to their many desirable advantages such as the small size, absolute measurement capability, immunity to electromagnetic interference, wavelength multiplexing, and distributed sensing possibilities. [1][2][3][4][5] Thus far, the FBG sensors' capability to measure physical quantities such as the temperature, strain, pressure, etc., has been studied extensively. [2][3][4][5][6][7][8] However, the use of FBG sensors for detection of environmental refractive index change has not been fully explored. Refractive index sensing is important for biological and chemical applications since a number of substances can be detected through measurements of the refractive index. [2][3][4][8][9][10][11][12][13] For normal FBGs, removal of the fiber cladding is required to increase the evanescent field interaction with the surrounding environment. This concept has been demonstrated using D-shaped fiber and sidepolished fiber. 9,11,12 In both cases, the strength and durability of the sensor were greatly reduced. Special fiber was also needed, which would raise the costs and limit the possible applications. Long-period fiber gratings have also been demonstrated to have high sensitivity to the refractive index of the ambient media, 2,3,13-15 however, their multiple resonance peaks and broad ͑typically tens of nanometers͒ transmission resonance features limit the measurement accuracy and their multiplexing capabilities. 9 In addition, the relatively long length of the grating limits their application as point sensor devices.In this letter, we first demonstrate a single etch-eroded FBG sensor using standard single-mode telecommunication fiber ͑Corning SMF-28͒. Fiber Fabry-Pérot interferometers ͑FFPIs͒ have also been widely used as sensors. 2,3,16,17 Compared to a single FBG, the FFPI sensors possess narrower resonance peaks and are more desirable for high accuracy wavelength measurement. 2,3,9,18 To that end we propose and demonstrate an etch-eroded FFPI sensor formed by two FBGs. The FFPI sensor is used to measure the refractive index of isopropyl alcohol ͑IPA͒ solutions of different concentrations, exhibiting the capabi...

Using a formalism similar to the quantum scattering theory, we analyze the problem of coupling between optical waveguides and high Q resonators. We give the optical transmission and reflection coefficients as functions of the waveguide-resonator coupling, cavity loss (gain), and cavity resonant frequency. Based on these results, the recently proposed concept of "critical coupling" is discussed. Using a matrix formalism based on the scattering analysis, we find the dispersion relation of indirectly coupled resonator optical waveguides. The coupling between waveguides and multiple cavities is investigated and the reflection and transmission coefficients are derived.

Using both the tight-binding approximation and the finite-difference time domain method, we analyze two types of coupled-resonator optical waveguide (CROW), a coupled-microdisks waveguide and a waveguide composed of coupled defect cavities in a two-dimensional photonic crystal. We find that the dispersion relation of the CROW band can be simply described by a small coupling parameter , and the spatial characteristics of the CROW modes remain the same as those of the single-resonator high Q modes. As applications of these unique properties, we demonstrate that CROW's can be utilized in constructing waveguides without cross talk and enhance the efficiency of second-harmonic generation.

Using an asymptotic analysis, we obtain an eigenvalue equation for the general mode dispersion in Bragg fibers. The asymptotic analysis is applied to calculate the dispersion relation and the field distribution of TE modes in a Bragg fiber. We compare the asymptotic results with exact solutions and find excellent agreement between them. This asymptotic approach greatly simplifies the analysis and design of Bragg fibers.