Numerical techniques have been used to study the intensity pattern of a high‐frequency electromagnetic wave near the critical density for conditions typical of laser fusion plasmas. The investigation considered nonlinear density profiles, collisional absorption, and finite bandwidth effects. Using the results of these calculations as a guide, elementary analytic models were developed to describe the behavior of the intensity pattern. Results of the numerical and analytic methods indicate the following: (i) For a nonlinear but monotonic density profile, the swelling factor can be related to the Airy function pattern by a simple scale factor; (ii) for collisional absorption below 50%, a linear relation holds between the intensity and the absorption; (iii) for laser bandwidth &Dgr;&ohgr;/&ohgr;0<15%, the intensity is reduced in a manner similar to that associated with collisional absorption. Within the ranges given, accuracy of the analytic models is within 10% of the numerical results. These semiquantitative models provide simple, useful tools for estimating the intensity patterns near the critical density.