We calculate the lateral modes of an ideal broad area laser, including the nonlinear interaction between the carriers and the optical field. The results include periodically modulated near fields and single- and double-lobed far fields similar to those previously measured. The unsaturable losses are higher and quantum efficiencies are lower than those determined from plane-wave approximations. Broad area InGaAs-GaAlAs-GaAs quantum-well lasers are fabricated and measured and found to closely agree with the theory in near, far, and spectrally resolved near fields. An occultation experiment on the far field confirms previously-predicted unstable resonator-like modes with V-shaped phase fronts.