title: Comment on "Exact solution of resonant modes in a rectangular resonator".
abstract: We comment on the recent Letter by J. Wu and A. Liu [Opt. Lett. 31, 1720 (2006)] in which an exact scalar solution to the resonant modes and the resonant frequencies in a two-dimensional rectangular microcavity were presented. The analysis is incorrect because (a) the field solutions were imposed to satisfy simultaneously both Dirichlet and Neumann boundary conditions at the four sides of the rectangle, leading to an overdetermined problem, and (b) the modes in the cavity were expanded using an incorrect series ansatz, leading to an expression for the mode fields that does not satisfy the Helmholtz equation.
authors.affiliation: Photonics and Mathematical Optics Group, Tecnológico de Monterrey, Monterrey, Mexico 64849. juliocesar@itesm.mx
authors.forename: Julio C
authors.initials: JC
authors.lastname: Gutiérrez-Vega
authors.forename: Miguel A
authors.initials: MA
authors.lastname: Bandres