Macroscopic optical coherence phenomena

Abstract

Principles of coherent radiation are reviewed as they apply to the coherent interaction between two quantum level atomic oscillators and classical radiation fields. The equivalence between electric dipole and magnetic dipole interactions is outlined for macroscopic systems. The power mechanism for formation of coherent signals is briefly calculated. The self-induced transparency mechanism and area-theorem connected with this mechanism serves as a means of predicting properties of photon echoes. It is stressed that when the classical field is a self-consistent solution to both the equations of the density matrix and Maxwell's equations a reaction field need not be added. THE SEMI-CLASSICAL PICTURE When the Bloch and Purcell groups initiated the science of nmr, it was not anticipated then or for a number of years afterwards that the dynamics of nmr could be applied to electric dipole resonance transitions. The concepts of spin states dominated the interests of investigators because of the tradition of the Rabi atomic beam method and because radio frequency techniques were ripe for application. Although the gas microwave absorption technique was flourishing, it was not until Dicke' (1954) introduced the idea of radiation coherence from an ensemble of phased electric dipole moments that the classical picture was believed to be applicable to dipole radiation from twolevel systems other than magnetic spins. Dicke pointed out that the coherent superpositions of atomic two-level states could be prepared, after which these states would radiate coherently. In 1957 Feynman, Vernon, and Hellwarth2 showed that electric dipole transitions in a two-level system could be formulated by equations which are the analogue of the Bloch torque equations for a spin system. Although the discussion in their paper was restricted to a particular MASER problem, they utilized the viewpoint very well known as the semi-classical method. In this particular discussion the classical electric field is a self-consistent solution of both the 'optical type' Bloch equations, originating from the density matrix, and Maxwell's equations. A number of treatments3 and reviews4 have appeared with the express purpose of clarifying and justifying the assumptions of the semi-classical approach. The approach has been rather successful from an experimental point of view in predicting and accounting for a number of