Normal Modes, and not so Normal Modes

Anthony E. Siegman
McMurtry Professor of Engineering Emeritus
Stanford University

Expanding the fields of any linear physical system, such as an optical waveguide or laser cavity, in a set of orthogonal eigenmodes or "normal modes" of the system is perhaps the most widely used analytical technique in mathematical physics; and many of the most fundamental physical properties of such systems, including their quantum noise properties, stem from this normal mode analysis.

In 1979, however, Klaus Petermann first predicted an excess spontaneous emission or quantum noise emission into the oscillating modes of gain-guided semiconductor lasers. Subsequent research has led to a realization that the propagating or resonant eigenmodes of many common physical systems, including gain-guided optical waveguides and unstable optical resonators as well as more elementary mechanical and acoustic systems, are actually not orthogonal or hermitian in character, and thus are not "normal modes" in the usual sense of the term.

This talk will show how this loss of orthogonality (and its replacement by the concept of biorthogonality) leads to major changes in the fundamental physical, mathematical and quantum properties of these systems, including in particular excess quantum noise properties and greatly increased Schawlow-Townes linewidths for nonnormal laser oscillators. These modified properties have been extensively confirmed by quantum noise experiments carried out on laser oscillators in recent years.

May 3, 2002, Dane Smith Hall, room 125