A standard 2 × 2 matrix method used in thin-film optics is applied to planar multilayer optical waveguides. All modes are required to satisfy substrate-to-cover field-transfer equations that reduce to the equation γ<sub>c</sub>m<sub>11</sub> + γ<sub>c</sub>γ<sub>s</sub>m<sub>12</sub> + m<sub>21</sub> + γ<sub>s</sub>m<sub>22</sub> = 0 for bound modes and leaky waves. Expressions are derived for the field profiles and the power in each medium. A first-order perturbation theory is developed and applied to absorbing multilayer guides and to the reflection of plane waves from the prism-loaded lossy multilayer guide. The latter leads to experimental arrangements for measuring losses in which the gap thickness and propagation constant are accessible parameters.
© 1984 Optical Society of America
John Chilwell and Ian Hodgkinson, "Thin-films field-transfer matrix theory of planar multilayer waveguides and reflection from prism-loaded waveguides," J. Opt. Soc. Am. A 1, 742-753 (1984)