To the Editor

With 2015 being the United Nation's proclaimed International Year of Light and Light-based Technologies, I thought it would be apt to try to correct an anomaly in the naming of one of the most useful set of equations describing the interaction of light with matter — the so-called Maxwell–Bloch equations.

These coupled equations were not actually derived by Maxwell and Bloch, but instead can be traced back to a little cited (given its significance) publication by Tito Arecchi and Rodolfo Bonifacio1, of Milan, Italy.

The equations describe an electromagnetic pulse interacting self-consistently with an ensemble of two-level atoms. The key advances were in the modelling of non-resonant interactions together with the mutual amplitude and phase evolutions of the electromagnetic wave and induced dipoles of the atomic ensemble. To do this succinctly required the invention of the slowly varying envelope approximation (SVEA) and its application to the wave.

The new information contained in the system of equations is essential in the modelling of now familiar effects, such as self-induced transparency, soliton propagation and photon echo, and the equations continue to be used widely to model and understand light–atom interactions. The term Maxwell–Bloch to describe the equations seems to have developed from a publication by S. L. McCall and E. L. Hahn2 that describes the first experimental demonstration of self-induced transparency. The equations they derived to describe the effect are equivalent to those derived by Arecchi and Bonifacio1.

McCall and Hahn, apparently unaware of the work by Arecchi and Bonifacio1, used a 'reduced Maxwell equation' (in other words, SVEA was applied) to describe the electromagnetic field. They also cited similarities in describing atomic electric dipoles to the work and notation used by F. Bloch3, which describes the interactions between nuclear magnetic moments and radio-frequency fields. Although not used directly in the work by McCall and Hahn2, this Maxwell–Bloch terminology seems to have been adopted subsequently by other researchers.

So, in the interest of factual correctness and to give credit to where it is due, I propose the famous Maxwell–Bloch equations in future be assigned their correct provenance by calling them the Arecchi–Bonifacio (AB) equations.