# What does the field look like inside your laser? A general theory for complex multi-mode open cavities

There is great current interest in novel lasing structures based for example on micro-cavities, random media, quantum dots or photonic bandgap defect states. In these systems the passive cavity resonances are often complex and how they relate to the actual non-linear lasing modes is unclear. In fact there is little theory even of conventional multi-mode lasing above threshold where spatial hole burning and mode-mode interactions are important. Recently we have developed an appropriate "ab initio" theory for treating these non-linear effects to all orders within a self-consistent treatment of the Maxwell-Bloch equations for an open cavity. The theory allows us to predict the emission pattern and output power of the lasing mode(s) far above threshold. The appropriate basis to use is the biorthogonal solutions of the passive cavity with only outgoing waves at infinity, and a general lasing mode is a superposition of these and not described by a single cavity resonance as is usually assumed. Applications of this theory to standard edge-emitting lasers and to random lasers will be discussed. The theory should be useful in designing laser cavities with desirable modal and emission properties.