We present a closed-form approximation for estimating both the field distribution and complex propagating constant of the antiresonant reflecting optical waveguide (ARROW) based on a first-order leaky-mode analysis. The formula was obtained from a novel coupled-electric-coupled-magnetic matrix method and provides six significant figures of the real part of the propagation constant β of a SiO2/TiO2/SiO2/Si ARROW with an 8‐μm core. The accuracy for the quantity of the imaginary part of β is greater than 98.4% for the TE_0 mode and 99.3% for TM_0. The approximate values for field components are 96.1% accurate. In addition, a slight absorption by the substrate will result in modification of the initial improper leaky-mode behavior, which grows exponentially in the substrate, yielding a proper solution.

© 2005 Optical Society of America

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