The Laser Linewidth – Fairy Tales and Physical Evidence

The laser linewidth manifests the spectral coherence of a lasing resonator mode. It is of fundamental importance, theoretically as much as practically. For more than half a century we have been told that the laser linewidth is a result of quantum fluctuations due to spontaneous emission, which induce amplitude and phase fluctuations, whereas stimulated emission occurs in phase with the incident field. Unfortunately, in such a scenario each emission process would violate the law of energy conservation. We show that a (spontaneous or stimulated) emission process occurs 90 degrees in lead of the incident field, converts one atomic excitation into one photon in the lasing mode and, therefore, conserves the energy, whereas the mentioned fluctuations are the result of vacuum energy and occur at an orders-of-magnitude faster time scale than an emission process.

1. INTRODUCTION

By assuming conservation of energy and momentum, Einstein showed [1] that an incident electromagnetic field at frequency ν triggers a two-level atom in its excited state to emit an additional electromagnetic field with an energy hν that equals the energy gap between the two levels, such that the energy of the incident field increases by this energy during the interaction. The emitted field has the same frequency, the same direction, and the same polarization as the incident field. In his original work, Einstein did not specify the phase difference between the incident and emitted electromagnetic field.