By analyzing the propagating behavior of the supermodes in a coupled-waveguide system, we have derived a universal criterion for designing adiabatic mode transformers. The criterion relates , the fraction of power scattered into the unwanted mode, to waveguide design parameters and gives the shortest possible length of an adiabatic mode transformer, which is approximately 2/ 1/2 times the distance of maximal power transfer between the waveguides. The results from numerical calculations based on a transfer-matrix formalism support this theory very well. [7,8]. Two schemes have been implemented to realize the mode transformationresonant coupling and adiabatic coupling. In a resonant coupler, by designing the coupling region to be of a half beat length, the light transfers from one waveguide to the other [8]. The coupler length can be made very short in this manner; however, it is practically difficult to determine the exact beat length, rendering the efficiency of power transfer uncertain and the resulting devices of dubious value. An adiabatic coupler, on the other hand, does not require a precise definition of power-transfer length [1,9,10], but it has to be sufficiently long to satisfy the adiabatic condition to reduce the coupling of power into other unwanted modes. Clearly a longer coupler not only reduces the component density but also suffers from higher transmission losses and higher probability of material defects and fabrication imperfections. The optimal design procedure of adiabatic mode transformers has been proposed in different ways. Love et al. first studied the fiber tapers, suggesting that for a given taper length the optimal delineating curve should have the local taper angle inversely proportional to the local beat length [1,11]. This design principle was also employed in experiments [10,12]. Another design concept is based on equalization of the "single-step loss" (defined as the overlap integral of the modes in two adjacent segments) along the taper [13,14]. Based on the stationary field distributions rather than the wave propagation behavior, those analyses did not point out the shortest taper length with which a certain coupling efficiency could be achieved. In this Letter we derive a universal criterion for the adiabatic mode transition in a coupledwaveguide system and suggest the shortest length of an adiabatic mode transformer for a given maximal tolerated scattering from the wanted mode into other modes during power transfer.The mode transformer to be analyzed here is based on a coupled-waveguide system shown in Fig. 1. It consists of two waveguides, waveguide 1 and waveguide 2, placed in close proximity to each other. The refractive index or geometry of at least one waveguide is gradually varied along the propagation direction z. Light is coupled into this transformer at input plane z = z i ͑=0͒ and out at output plane z = z f . The normalized local modes (or "supermodes"), denoted as e e for the even mode and e o for the odd mode, of this coupled-waveguide system are expressed as col...

We present a filter design formalism for the synthesis of coupledresonator optical waveguide (CROW) filters. This formalism leads to expressions and a methodology for deriving the coupling coefficients of CROWs for the desired filter responses and is based on coupled-mode theory as well as the recursive properties of the coupling matrix. The coupling coefficients are universal and can be applied to various types of resonators. We describe a method for the conversion of the coupling coefficients to the parameters based on ring resonators and grating defect resonators. The designs of Butterworth and Bessel CROW filters are demonstrated as examples.

Abstract:We propose and describe a new class of optical modes consisting of superposition of three waveguide modes which can be supported by a few-mode waveguide spatially modulated by two co-spatial gratings. These supermodes bear a close, but not exact, formal analogy to the three-level quantum states involved in EIT and its attendant slow light propagation characteristics. Of particular interest is the supermode which we call the dark mode in which, in analogy with the dark state of EIT, one of the three uncoupled waveguide modes is not excited. This mode has unique dispersion characteristics that translate into a slow light propagation which possesses high bandwidth-delay product and can form the basis for a new generation of optical resonators and lasers.

Abstract:We present a systematic design of coupled-resonator optical waveguides (CROWs) based on high-Q tapered grating-defect resonators. The formalism is based on coupled-mode theory where forward and backward waveguide modes are coupled by the grating. Although applied to strong gratings (periodic air holes in single-mode silicon-on-insulator waveguides), coupled-mode theory is shown to be valid, since the spatial Fourier transform of the resonant mode is engineered to minimize the coupling to radiation modes and thus the propagation loss. We demonstrate the numerical characterization of strong gratings, the design of high-Q tapered grating-defect resonators (Q>2 × 10 6 , modal volume = 0.38·(λ/n) 3 ), and the control of inter-resonator coupling for CROWs. Furthermore, we design Butterworth and Bessel filters by tailoring the numbers of holes between adjacent defects. We show with numerical simulation that Butterworth CROWs are more tolerant against fabrication disorder than CROWs with uniform coupling coefficient.

We present a design of "ideal" optical delay lines (i.e., constant amplitude and constant group delay over the desired bandwidth). They are based on reflection from coupled-resonator optical waveguides (CROWs). The inter-resonator coupling coefficients are tailored and decrease monotonically with the distance from the input to realize all-pass Bessel filters. The tailored coupling coefficients result in a frequency-dependent propagating distance which compensates for the group velocity dispersion of CROWs. We present a simple formalism for deriving the time-domain coupling coefficients and convert these coefficients to field coupling coefficients of ring resonators. The reflecting CROWs possess a delay-bandwidth product of 0.5 per resonator, larger than that of any kind of transmitting CROW. In the presence of uniform gain, the gain enhanced by slow light propagation and the constant group delay result in efficient and dispersion-free amplifiers.