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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 [beta] of a Si[O.sub.2]/Ti[O.sub.2]/Si[O.sub.2]/Si ARROW with an 8-[micro]m core. The accuracy for the quantity of the imaginary part of [beta] is greater than 98.4% for the T[E.sub.0] mode and 99.3% for T[M.sub.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.